APPENDIX TO “A COMPUTATIONAL STUDY ON LENS SPACES ISOSPECTRAL ON FORMS” EMILIO A. LAURET Abstract. This appendix supports with computational results the article [La]. For each odd value of n ≤ 17, for low values of q and for each non-empty subset I of {0, 1, . . . , n − 1}, we will indicate all families of (non-isometric) (2n − 1)-dimensional I-isospectral lens spaces (or lens orbifolds) with fundamental group of order q. Here, an I-isospectral family means that I is the largest subset I 0 of {0, 1, . . . , n − 1} satisfying that the members of the family are pairwise p-isospectral for every p ∈ I 0 .
Contents 1. Introduction 2. Computational results for dimension 5 3. Computational results for dimension 7 4. Computational results for dimension 9 5. Computational results for dimension 11 6. Computational results for dimension 13 7. Computational results for dimension 15 8. Computational results for dimension 17 9. Summarizing table for dimension 5 10. Summarizing table for dimension 7 11. Summarizing table for dimension 9 12. Summarizing table for dimension 11 13. Summarizing table for dimension 13 14. Summarizing table for dimension 15 15. Summarizing table for dimension 17 16. Existence and non-existence distribution 17. Algorithms 18. Non-singular matrix References
Date: March 2017. 1
2 3 6 25 51 107 181 247 299 300 301 302 303 304 305 307 308 313 318
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1. Introduction For I ⊂ {0, . . . , n − 1}, we will say that a family (i.e. two or more members) of (2n − 1)dimensional lens orbifolds are I-isospectral if they are mutually p-isospectral for all p ∈ I, and for any p satisfying 0 ≤ p ≤ n − 1 and p 6∈ I there is at least two elements such that they are not p-isospectral. Tables 1–7 show, for a fixed odd dimension 2n − 1 ≤ 17 and for the listed low values of q, all I-isospectral families among (2n − 1)-dimensional lens orbifolds with fundamental group of order q. The third column shows the I-isospectral families described as the indexes of the lens orbifolds, according to the algorithm in Section 17. The parameters of the lens orbifolds appeared in any family are indicated outside the table. An index in bold means that the lens orbifold is actually a lens space (i.e. a manifold). Sections 9–15 include tables summarizing the computational results of Tables 1–7. More precisely, they show in the corresponding dimension, which subsets I satisfy that there exist an I-isospectral family, and also they explain (when is possible) why there is no any I-isospectral family. Furthermore, Section 16 includes a table which shows how the subsets I of {0, . . . , n−1} are distributed into the different options, namely, there is a pair of I-isospectral (2n − 1)dimensional lens spaces or lens orbifolds, or the non-existence of an I-isospectral family is due to the hole obstruction [La, Prop. 2.2 ], or follows by some result proved in [La, Sect. 4 ], or it is not known. The tables in Sections 9–12 as well as in Section 16 are also included in [La]. Section 17 describes the algorithms used. It first gives the one which returns the set of (2n−1)dimensional lens orbifolds with fundamental group of order q, for n and q fixed. It also includes tables which show the cardinalities of these sets for 3 ≤ n ≤ 9 and 0 ≤ q ≤ 40. Furthermore, it is also explained the algorithm which returns the families of I-isospectral (2n − 1)-dimensional lens orbifolds with fundamental group of order q, for every I, for n and q fixed. Finally, Section 18 gives the computational results which show [La, Lem. 4.9 ]. All the computations were made by Sage [Sa].
APPENDIX
3
2. Computational results for dimension 5 q q q q q q q q q q q q q q q q
= 8 : L3 = [0, 1, 3], L12 = [1, 3, 4]. = 11 : L9 = [1, 2, 3], L10 = [1, 2, 4]. = 13 : L11 = [1, 2, 3], L12 = [1, 2, 4], L13 = [1, 2, 5], L14 = [1, 3, 4]. = 15 : L18 = [1, 2, 6], L20 = [1, 3, 4]. = 17 : L16 = [1, 2, 5], L17 = [1, 2, 6], L18 = [1, 2, 7], L19 = [1, 3, 4]. = 19 : L19 = [1, 2, 7], L21 = [1, 3, 4]. = 22 : L33 = [1, 3, 5], L34 = [1, 3, 7]. = 24 : L41 = [1, 3, 5], L43 = [1, 3, 7], L98 = [3, 4, 9], L102 = [3, 8, 9]. = 26 : L39 = [1, 3, 5], L40 = [1, 3, 7], L42 = [1, 3, 9], L44 = [1, 3, 11]. = 28 : L43 = [1, 3, 5], L46 = [1, 3, 9]. = 30 : L55 = [1, 3, 7], L59 = [1, 3, 11]. = 32 : L47 = [1, 3, 7], L49 = [1, 3, 9]. = 33 : L41 = [1, 2, 14], L56 = [1, 4, 5]. = 34 : L51 = [1, 3, 7], L53 = [1, 3, 9], L56 = [1, 3, 13], L74 = [1, 5, 7]. = 38 : L60 = [1, 3, 11], L63 = [1, 3, 15]. = 40 : L63 = [1, 3, 7], L65 = [1, 3, 9], L70 = [1, 3, 15], L94 = [1, 5, 7], L197 = [4, 5, 15], L203 = [5, 8, 15]. q = 44 : L66 = [1, 3, 7], L68 = [1, 3, 9], L72 = [1, 3, 13], L75 = [1, 3, 17], L100 = [1, 5, 7], L102 = [1, 5, 9]. q = 49 : L106 = [1, 6, 15], L108 = [1, 6, 20]. q = 50 : L263 = [2, 5, 18], L267 = [2, 8, 15]. Table 1. n = 3 q 8 11 13 15 17 19 22 24 26 28 30 32 33 34 38 40 44 49 50 52
I {2} {0} {0} {0} {0} {0} {0} {0} {2} {0} {0} {0} {0} {0} {0} {0} {0} {2} {0} {0, 1, 2} {0} {0}
indexes of I-isospectral families {3, 12} {9, 10} {11, 12}, {13, 14} {18, 20} {16, 17}, {18, 19} {19, 21} {33, 34} {41, 43} {98, 102} {39, 42}, {40, 44} {43, 46} {55, 59} {47, 49} {41, 56} {51, 53}, {56, 74} {60, 63} {63, 65}, {70, 94} {197, 203} {66, 68}, {72, 75, 100, 102} {106, 108} {263, 267} {88, 121}, {122, 130}
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Table 1. (continued) n = 3 q 56 64 66 68 72 80 88 98 100 104 108 120 121 128 132 136 147 150
I {0} {2} {0, 1, 2} {0} {0} {0} {2} {0} {2} {0} {0, 1, 2} {0, 1, 2} {2} {0} {2} {0, 1, 2} {0, 1, 2} {0} {2} {0, 1, 2} {0}
indexes of I-isospectral families {91, 93}, {100, 134} {335, 342} {194, 197} {184, 223} {170, 208} {186, 235} {646, 656} {144, 146} {722, 730} {865, 880}, {871, 879}, {888, 902} {490, 497} {406, 412}, {414, 419} {972, 981} {280, 367} {2079, 2171} {458, 461}, {463, 467}, {469, 475}, {636, 644}, {641, 646} {761, 768} {364, 461, 463} {1582, 1594} {1057, 1067} {2586, 2758}
q = 52 : L88 = [1, 3, 19], L121 = [1, 5, 9], L122 = [1, 5, 11], L130 = [1, 5, 23]. q = 56 : L91 = [1, 3, 13], L93 = [1, 3, 15], L100 = [1, 3, 23], L134 = [1, 5, 11], L335 = [4, 7, 21], L342 = [7, 8, 21]. q = 64 : L194 = [1, 7, 17], L197 = [1, 7, 23]. q = 66 : L184 = [1, 5, 29], L223 = [1, 7, 17]. q = 68 : L170 = [1, 5, 25], L208 = [1, 7, 11]. q = 72 : L186 = [1, 5, 17], L235 = [1, 7, 11], L646 = [4, 9, 27], L656 = [8, 9, 27]. q = 80 : L144 = [1, 3, 31], L146 = [1, 3, 33]. q = 88 : L722 = [4, 11, 33], L730 = [8, 11, 33]. q = 98 : L490 = [1, 13, 29], L497 = [1, 13, 41], L865 = [2, 7, 26], L871 = [2, 7, 40], L879 = [2, 12, 21], L880 = [2, 12, 35], L888 = [2, 21, 26], L902 = [2, 35, 40]. q = 100 : L406 = [1, 9, 21], L412 = [1, 9, 29], L414 = [1, 9, 31], L419 = [1, 9, 39]. q = 104 : L972 = [4, 13, 39], L981 = [8, 13, 39]. q = 108 : L280 = [1, 5, 23], L367 = [1, 7, 19]. q = 120 : L2079 = [4, 15, 45], L2171 = [8, 15, 45]. q = 121 : L458 = [1, 10, 23], L461 = [1, 10, 32], L463 = [1, 10, 34], L467 = [1, 10, 43], L469 = [1, 10, 45], L475 = [1, 10, 54], L636 = [1, 21, 34], L641 = [1, 21, 45], L644 = [1, 21, 54], L646 = [1, 21, 56]. q = 128 : L761 = [1, 15, 33], L768 = [1, 15, 47]. q = 132 : L364 = [1, 5, 37], L461 = [1, 7, 17], L463 = [1, 7, 19]. q = 136 : L1582 = [4, 17, 51], L1594 = [8, 17, 51]. q = 147 : L1057 = [1, 20, 43], L1067 = [1, 20, 62]. q = 150 : L2586 = [2, 15, 58], L2758 = [2, 28, 45].
APPENDIX
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Table 1. (continued) n = 3 q I 152 {2} 162 {0} 168 {2} 169 {0, 1, 2} 184 192 196 200
indexes of I-isospectral families {1945, 1956} {2579, 2681}, {2600, 2679}, {2816, 2921} {3727, 3832} {783, 789}, {791, 796}, {798, 805}, {807, 814}, {1093, 1102}, {1096, 1109}, {1104, 1111}, {1264, 1270} {2} {2779, 2792} {0, 1, 2} {1830, 1844} {0, 1, 2} {1144, 1154}, {1156, 1165}, {1167, 1176}, {1178, 1187}, {1917, 1932}, {1925, 1941}, {2449, 2455} {2} {3813, 3879} {0, 1, 2} {1619, 1633}, {1635, 1646}
q = 152 : L1945 = [4, 19, 57], L1956 = [8, 19, 57]. q = 162 : L2579 = [2, 9, 34], L2600 = [2, 9, 70], L2679 = [2, 16, 45], L2681 = [2, 16, 63], L2816 = [2, 34, 45], L2921 = [2, 63, 70]. q = 168 : L3727 = [4, 21, 63], L3832 = [8, 21, 63]. q = 169 : L783 = [1, 12, 27], L789 = [1, 12, 38], L791 = [1, 12, 40], L796 = [1, 12, 51], L798 = [1, 12, 53], L805 = [1, 12, 64], L807 = [1, 12, 66], L814 = [1, 12, 77], L1093 = [1, 25, 40], L1096 = [1, 25, 53], L1102 = [1, 25, 64], L1104 = [1, 25, 66], L1109 = [1, 25, 77], L1111 = [1, 25, 79], L1264 = [1, 38, 53], L1270 = [1, 38, 79]. q = 184 : L2779 = [4, 23, 69], L2792 = [8, 23, 69]. q = 192 : L1830 = [1, 23, 49], L1844 = [1, 23, 71]. q = 196 : L1144 = [1, 13, 29], L1154 = [1, 13, 41], L1156 = [1, 13, 43], L1165 = [1, 13, 55], L1167 = [1, 13, 57], L1176 = [1, 13, 69], L1178 = [1, 13, 71], L1187 = [1, 13, 83], L1917 = [1, 27, 43], L1925 = [1, 27, 57], L1932 = [1, 27, 69], L1941 = [1, 27, 83], L2449 = [1, 41, 71], L2455 = [1, 41, 85]. q = 200 : L1619 = [1, 19, 41], L1633 = [1, 19, 59], L1635 = [1, 19, 61], L1646 = [1, 19, 79], L3813 = [4, 25, 75], L3879 = [8, 25, 75].
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EMILIO A. LAURET
3. Computational results for dimension 7 q = 3 : L1 = [0, 0, 1, 1], L2 = [0, 1, 1, 1]. q = 5 : L2 = [0, 0, 1, 2], L4 = [0, 1, 1, 2]. q = 6 : L7 = [0, 1, 1, 3], L8 = [0, 1, 2, 2], L11 = [0, 2, 2, 3], L15 = [1, 1, 1, 3], L17 = [1, 1, 2, 3], L18 = [1, 1, 3, 3]. q = 9 : L9 = [0, 1, 2, 4], L21 = [1, 2, 3, 4]. q = 10 : L14 = [0, 1, 2, 4], L16 = [0, 1, 3, 5], L21 = [0, 2, 4, 5], L34 = [1, 1, 3, 5], L43 = [1, 2, 3, 5], L47 = [1, 3, 5, 5]. q = 11 : L9 = [0, 1, 2, 3], L10 = [0, 1, 2, 4]. q = 12 : L22 = [0, 1, 3, 5], L24 = [0, 1, 4, 4], L34 = [0, 3, 4, 4], L49 = [1, 1, 3, 5], L61 = [1, 2, 2, 6], L64 = [1, 2, 3, 5], L73 = [1, 3, 3, 5], L76 = [1, 3, 4, 5], L78 = [1, 3, 5, 6], L90 = [2, 2, 3, 6]. q = 13 : L11 = [0, 1, 2, 3], L12 = [0, 1, 2, 4], L13 = [0, 1, 2, 5], L14 = [0, 1, 3, 4], L34 = [1, 2, 3, 4], L35 = [1, 2, 3, 5], L36 = [1, 2, 3, 6]. q = 14 : L66 = [1, 2, 3, 4], L68 = [1, 2, 3, 6]. q = 15 : L18 = [0, 1, 2, 6], L20 = [0, 1, 3, 4], L22 = [0, 1, 3, 6], L24 = [0, 1, 4, 6], L25 = [0, 1, 5, 5], L29 = [0, 3, 5, 5], L30 = [0, 3, 5, 6], L51 = [1, 1, 4, 6], L62 = [1, 2, 3, 7], L66 = [1, 2, 5, 6], L72 = [1, 3, 4, 5], L73 = [1, 3, 4, 6], L78 = [1, 4, 5, 6], L79 = [1, 4, 6, 6]. q = 16 : L78 = [1, 2, 3, 5], L80 = [1, 2, 3, 7]. q = 17 : L16 = [0, 1, 2, 5], L17 = [0, 1, 2, 6], L18 = [0, 1, 2, 7], L19 = [0, 1, 3, 4], L55 = [1, 2, 3, 5], L56 = [1, 2, 3, 6], L57 = [1, 2, 3, 7], L58 = [1, 2, 3, 8], L59 = [1, 2, 4, 5], L62 = [1, 2, 6, 7], L63 = [1, 3, 4, 5]. q = 18 : L40 = [0, 1, 5, 7], L117 = [1, 2, 4, 5], L119 = [1, 2, 4, 7], L146 = [1, 3, 5, 7], L168 = [1, 5, 6, 7], L170 = [1, 5, 7, 9], L198 = [2, 3, 4, 8], L204 = [2, 4, 8, 9]. q = 19 : L19 = [0, 1, 2, 7], L21 = [0, 1, 3, 4], L67 = [1, 2, 3, 5], L68 = [1, 2, 3, 6], L70 = [1, 2, 3, 8], L71 = [1, 2, 3, 9], L72 = [1, 2, 4, 5], L74 = [1, 2, 4, 8], L77 = [1, 2, 6, 8], L79 = [1, 3, 4, 5]. Table 2. n = 4 q 3 5 6 9 10 11 12 13 14 15
16 17 18 19
I {2} {3} {2} {2} {3} {0} {2} {0} {0, 1} {0} {0} {2} {3} {0} {0} {0, 1} {0} {2} {0}
indexes of I-isospectral families {1, 2} {2, 4} {7, 17}, {8, 11}, {15, 18} {9, 21} {14, 21}, {16, 43}, {34, 47} {9, 10} {22, 76}, {24, 34}, {49, 73}, {61, 90}, {64, 78} {11, 12}, {13, 14}, {34, 35, 36} {34, 35} {66, 68} {18, 20}, {66, 72} {24, 78}, {25, 29}, {51, 79}, {62, 73} {22, 30} {78, 80} {16, 17}, {18, 19}, {55, 56, 58}, {62, 63} {57, 59} {117, 119} {40, 168}, {146, 170}, {198, 204} {19, 21}, {67, 68, 71}, {70, 72, 74}, {77, 79}
APPENDIX
7
Table 2. (continued) n = 4 q 20 21
I {3} {0} {2} {0} {0} {0}
indexes of I-isospectral families {39, 64}, {152, 240} {110, 112}, {121, 135} {39, 158}, {41, 48}, {90, 155}, {117, 142}, {120, 160} 22 {33, 34}, {166, 177}, {182, 184}, {242, 243} 23 {102, 104}, {108, 110}, {114, 121} 24 {41, 43}, {213, 217}, {254, 256}, {262, 269}, {264, 275}, {267, 277} {2} {70, 362}, {72, 101}, {163, 364}, {223, 417}, {227, 346}, {266, 276}, {300, 442}, {313, 365} 25 {0} {133, 146}, {141, 142}, {143, 145, 157} 26 {0} {39, 42}, {40, 44}, {218, 244}, {233, 282}, {246, 247}, {249, 251, 252}, {254, 263}, {257, 269}, {360, 361}, {362, 364} {0, 1} {251, 252} 27 {0} {162, 165, 168}, {177, 179} {2} {54, 252}, {222, 246, 254} 28 {0} {43, 46}, {299, 307}, {304, 319} {0, 1} {301, 302} 29 {0} {164, 171}, {215, 216}
q = 20 : L39 = [0, 1, 4, 8], L64 = [0, 4, 5, 8], L152 = [1, 2, 6, 10], L240 = [2, 5, 6, 10]. q = 21 : L39 = [0, 1, 6, 8], L41 = [0, 1, 7, 7], L48 = [0, 3, 7, 7], L90 = [1, 1, 6, 8], L110 = [1, 2, 4, 5], L112 = [1, 2, 4, 8], L117 = [1, 2, 5, 9], L120 = [1, 2, 6, 8], L121 = [1, 2, 6, 9], L135 = [1, 3, 4, 6], L142 = [1, 3, 6, 8], L155 = [1, 6, 6, 8], L158 = [1, 6, 7, 8], L160 = [1, 6, 8, 9]. q = 22 : L33 = [0, 1, 3, 5], L34 = [0, 1, 3, 7], L166 = [1, 2, 8, 9], L177 = [1, 3, 4, 8], L182 = [1, 3, 5, 11], L184 = [1, 3, 7, 11], L242 = [2, 4, 6, 11], L243 = [2, 4, 8, 11]. q = 23 : L102 = [1, 2, 4, 5], L104 = [1, 2, 4, 8], L108 = [1, 2, 5, 7], L110 = [1, 2, 5, 9], L114 = [1, 2, 6, 10], L121 = [1, 3, 4, 9]. q = 24 : L41 = [0, 1, 3, 5], L43 = [0, 1, 3, 7], L70 = [0, 1, 7, 9], L72 = [0, 1, 8, 8], L101 = [0, 3, 8, 8], L163 = [1, 1, 7, 9], L213 = [1, 2, 5, 7], L217 = [1, 2, 5, 11], L223 = [1, 2, 6, 10], L227 = [1, 2, 7, 9], L254 = [1, 3, 4, 5], L256 = [1, 3, 4, 7], L262 = [1, 3, 5, 6], L264 = [1, 3, 5, 8], L266 = [1, 3, 5, 11], L267 = [1, 3, 5, 12], L269 = [1, 3, 6, 7], L275 = [1, 3, 7, 8], L276 = [1, 3, 7, 9], L277 = [1, 3, 7, 12], L300 = [1, 4, 4, 12], L313 = [1, 4, 7, 9], L346 = [1, 6, 7, 9], L362 = [1, 7, 8, 9], L364 = [1, 7, 9, 9], L365 = [1, 7, 9, 12], L417 = [2, 3, 6, 10], L442 = [3, 4, 4, 12]. q = 25 : L133 = [1, 2, 4, 11], L141 = [1, 2, 6, 7], L142 = [1, 2, 6, 8], L143 = [1, 2, 6, 9], L145 = [1, 2, 6, 11], L146 = [1, 2, 7, 8], L157 = [1, 3, 4, 9]. q = 26 : L39 = [0, 1, 3, 5], L40 = [0, 1, 3, 7], L42 = [0, 1, 3, 9], L44 = [0, 1, 3, 11], L218 = [1, 2, 7, 8], L233 = [1, 2, 10, 11], L244 = [1, 3, 4, 8], L246 = [1, 3, 4, 10], L247 = [1, 3, 4, 12], L249 = [1, 3, 5, 7], L251 = [1, 3, 5, 9], L252 = [1, 3, 5, 11], L254 = [1, 3, 5, 13], L257 = [1, 3, 7, 13], L263 = [1, 3, 9, 13], L269 = [1, 3, 11, 13], L282 = [1, 4, 5, 8], L360 = [2, 4, 6, 13], L361 = [2, 4, 8, 13], L362 = [2, 4, 10, 13], L364 = [2, 6, 8, 13]. q = 27 : L54 = [0, 1, 8, 10], L162 = [1, 2, 4, 11], L165 = [1, 2, 5, 7], L168 = [1, 2, 5, 10], L177 = [1, 2, 7, 8], L179 = [1, 2, 7, 10], L222 = [1, 3, 8, 10], L246 = [1, 6, 8, 10], L252 = [1, 8, 9, 10], L254 = [1, 8, 10, 12]. q = 28 : L43 = [0, 1, 3, 5], L46 = [0, 1, 3, 9], L299 = [1, 3, 5, 7], L301 = [1, 3, 5, 9], L302 = [1, 3, 5, 11], L304 = [1, 3, 5, 14], L307 = [1, 3, 7, 9], L319 = [1, 3, 9, 14].
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EMILIO A. LAURET
Table 2. (continued) n = 4 q 30
I {0}
indexes of I-isospectral families {55, 59}, {423, 427}, {444, 463}, {448, 469}, {800, 815}, {805, 837} {2} {107, 670}, {111, 168}, {271, 665}, {367, 847}, {373, 674}, {447, 458}, {507, 781}, {522, 613}, {549, 886}, {572, 675}, {813, 917}, {822, 850} {3} {91, 174}, {461, 893}, {786, 906} 32 {0} {47, 49}, {301, 307}, {357, 359}, {366, 373}, {371, 382}, {480, 483} {0, 1} {362, 367} 33 {0} {41, 56}, {250, 257}, {261, 273}, {301, 387}, {490, 492} {2} {85, 469}, {87, 96}, {206, 471}, {290, 441}, {294, 460}, {360, 472}, {369, 399} 34 {0} {51, 53}, {56, 74}, {413, 416}, {414, 418, 422}, {428, 439}, {456, 540}, {568, 571}, {582, 590}, {682, 683}, {684, 686} {0, 1} {424, 426} 35 {0} {396, 401} {3} {82, 98} 36 {0, 1} {542, 559} {2} {134, 940}, {592, 887, 943}, {798, 944}, {1057, 1097}, {1130, 1155}
q = 29 : L164 = [1, 2, 4, 11], L171 = [1, 2, 5, 10], L215 = [1, 4, 5, 7], L216 = [1, 4, 5, 13]. q = 30 : L55 = [0, 1, 3, 7], L59 = [0, 1, 3, 11], L91 = [0, 1, 6, 12], L107 = [0, 1, 9, 11], L111 = [0, 1, 10, 10], L168 = [0, 3, 10, 10], L174 = [0, 5, 6, 12], L271 = [1, 1, 9, 11], L367 = [1, 2, 8, 12], L373 = [1, 2, 9, 11], L423 = [1, 3, 5, 7], L427 = [1, 3, 5, 11], L444 = [1, 3, 7, 10], L447 = [1, 3, 7, 13], L448 = [1, 3, 7, 15], L458 = [1, 3, 9, 11], L461 = [1, 3, 9, 15], L463 = [1, 3, 10, 11], L469 = [1, 3, 11, 15], L507 = [1, 4, 6, 14], L522 = [1, 4, 9, 11], L549 = [1, 5, 5, 15], L572 = [1, 5, 9, 11], L613 = [1, 6, 9, 11], L665 = [1, 9, 9, 11], L670 = [1, 9, 10, 11], L674 = [1, 9, 11, 12], L675 = [1, 9, 11, 15], L781 = [2, 3, 8, 12], L786 = [2, 3, 9, 15], L800 = [2, 4, 5, 12], L805 = [2, 4, 12, 15], L813 = [2, 5, 5, 15], L815 = [2, 5, 6, 8], L822 = [2, 5, 8, 12], L837 = [2, 6, 8, 15], L847 = [2, 8, 9, 12], L850 = [2, 8, 12, 15], L886 = [3, 5, 5, 15], L893 = [3, 5, 9, 15], L906 = [3, 9, 10, 15], L917 = [5, 5, 6, 15]. q = 32 : L47 = [0, 1, 3, 7], L49 = [0, 1, 3, 9], L301 = [1, 2, 7, 9], L307 = [1, 2, 7, 15], L357 = [1, 3, 5, 7], L359 = [1, 3, 5, 9], L362 = [1, 3, 5, 13], L366 = [1, 3, 7, 8], L367 = [1, 3, 7, 9], L371 = [1, 3, 7, 16], L373 = [1, 3, 8, 9], L382 = [1, 3, 9, 16], L480 = [1, 6, 7, 9], L483 = [1, 6, 7, 15]. q = 33 : L41 = [0, 1, 2, 14], L56 = [0, 1, 4, 5], L85 = [0, 1, 10, 12], L87 = [0, 1, 11, 11], L96 = [0, 3, 11, 11], L206 = [1, 1, 10, 12], L250 = [1, 2, 4, 13], L257 = [1, 2, 5, 10], L261 = [1, 2, 5, 14], L273 = [1, 2, 7, 8], L290 = [1, 2, 9, 13], L294 = [1, 2, 10, 12], L301 = [1, 2, 11, 14], L360 = [1, 3, 8, 14], L369 = [1, 3, 10, 12], L387 = [1, 4, 5, 11], L399 = [1, 4, 7, 15], L441 = [1, 6, 10, 12], L460 = [1, 9, 10, 12], L469 = [1, 10, 11, 12], L471 = [1, 10, 12, 12], L472 = [1, 10, 12, 15], L490 = [3, 6, 9, 11], L492 = [3, 6, 11, 12]. q = 34 : L51 = [0, 1, 3, 7], L53 = [0, 1, 3, 9], L56 = [0, 1, 3, 13], L74 = [0, 1, 5, 7], L413 = [1, 3, 5, 9], L414 = [1, 3, 5, 11], L416 = [1, 3, 5, 13], L418 = [1, 3, 5, 15], L422 = [1, 3, 7, 9], L424 = [1, 3, 7, 11], L426 = [1, 3, 7, 15], L428 = [1, 3, 7, 17], L439 = [1, 3, 9, 17], L456 = [1, 3, 13, 17], L540 = [1, 5, 7, 17], L568 = [1, 6, 9, 10], L571 = [1, 6, 9, 14], L582 = [1, 6, 12, 13], L590 = [1, 6, 14, 15], L682 = [2, 4, 10, 17], L683 = [2, 4, 12, 17], L684 = [2, 4, 14, 17], L686 = [2, 6, 8, 17]. q = 35 : L82 = [0, 1, 7, 14], L98 = [0, 5, 7, 14], L396 = [1, 4, 6, 9], L401 = [1, 4, 6, 16].
APPENDIX
9
Table 2. (continued) n = 4 q I indexes of I-isospectral families 37 {0} {341, 342} 38 {0} {60, 63}, {511, 513}, {515, 523, 539}, {553, 554, 682}, {556, 573}, {767, 769}, {895, 898} 39 {0} {405, 553}, {745, 746}, {748, 749} {2} {109, 710}, {112, 127}, {282, 706}, {410, 652}, {415, 713}, {520, 690}, {530, 578}, {615, 714} 40 {0} {63, 65}, {70, 94}, {524, 532}, {612, 614}, {624, 647}, {625, 649}, {628, 846}, {633, 652}, {657, 847}, {689, 851}, {943, 948} {3} {133, 204}, {793, 1297} 42 {0} {844, 874}, {922, 925}, {1081, 1084} {2} {191, 1514}, {194, 282}, {479, 1517}, {675, 1883}, {682, 1489}, {846, 1401}, {861, 1078}, {986, 1718}, {1007, 1518}, {1153, 1861}, {1191, 1347}, {1232, 1949}, {1278, 1519}, {1810, 1988}, {1826, 1886} 43 {0} {502, 508}
q = 36 : L134 = [0, 1, 11, 13], L542 = [1, 3, 5, 17], L559 = [1, 3, 7, 11], L592 = [1, 3, 11, 13], L798 = [1, 6, 11, 13], L887 = [1, 9, 11, 13], L940 = [1, 11, 12, 13], L943 = [1, 11, 13, 15], L944 = [1, 11, 13, 18], L1057 = [2, 3, 10, 14], L1097 = [2, 9, 10, 14], L1130 = [3, 4, 8, 16], L1155 = [4, 8, 9, 16]. q = 37 : L341 = [1, 3, 4, 11], L342 = [1, 3, 4, 12]. q = 38 : L60 = [0, 1, 3, 11], L63 = [0, 1, 3, 15], L511 = [1, 3, 5, 13], L513 = [1, 3, 5, 15], L515 = [1, 3, 5, 17], L523 = [1, 3, 7, 13], L539 = [1, 3, 9, 11], L553 = [1, 3, 11, 15], L554 = [1, 3, 11, 17], L556 = [1, 3, 11, 19], L573 = [1, 3, 15, 19], L682 = [1, 5, 7, 9], L767 = [1, 7, 8, 12], L769 = [1, 7, 8, 18], L895 = [2, 4, 14, 19], L898 = [2, 6, 8, 19]. q = 39 : L109 = [0, 1, 12, 14], L112 = [0, 1, 13, 13], L127 = [0, 3, 13, 13], L282 = [1, 1, 12, 14], L405 = [1, 2, 10, 17], L410 = [1, 2, 11, 15], L415 = [1, 2, 12, 14], L520 = [1, 3, 10, 16], L530 = [1, 3, 12, 14], L553 = [1, 4, 5, 11], L578 = [1, 4, 9, 17], L615 = [1, 5, 8, 18], L652 = [1, 6, 12, 14], L690 = [1, 9, 12, 14], L706 = [1, 12, 12, 14], L710 = [1, 12, 13, 14], L713 = [1, 12, 14, 15], L714 = [1, 12, 14, 18], L745 = [3, 6, 9, 13], L746 = [3, 6, 12, 13], L748 = [3, 6, 13, 15], L749 = [3, 9, 12, 13]. q = 40 : L63 = [0, 1, 3, 7], L65 = [0, 1, 3, 9], L70 = [0, 1, 3, 15], L94 = [0, 1, 5, 7], L133 = [0, 1, 8, 16], L204 = [0, 5, 8, 16], L524 = [1, 2, 9, 11], L532 = [1, 2, 9, 19], L612 = [1, 3, 5, 11], L614 = [1, 3, 5, 13], L624 = [1, 3, 7, 10], L625 = [1, 3, 7, 11], L628 = [1, 3, 7, 15], L633 = [1, 3, 7, 20], L647 = [1, 3, 9, 10], L649 = [1, 3, 9, 13], L652 = [1, 3, 9, 20], L657 = [1, 3, 10, 15], L689 = [1, 3, 15, 20], L793 = [1, 4, 12, 20], L846 = [1, 5, 7, 9], L847 = [1, 5, 7, 10], L851 = [1, 5, 7, 20], L943 = [1, 6, 9, 11], L948 = [1, 6, 9, 19], L1297 = [4, 5, 12, 20]. q = 42 : L191 = [0, 1, 13, 15], L194 = [0, 1, 14, 14], L282 = [0, 3, 14, 14], L479 = [1, 1, 13, 15], L675 = [1, 2, 12, 16], L682 = [1, 2, 13, 15], L844 = [1, 3, 11, 15], L846 = [1, 3, 11, 17], L861 = [1, 3, 13, 15], L874 = [1, 3, 15, 17], L922 = [1, 4, 5, 16], L925 = [1, 4, 5, 20], L986 = [1, 4, 10, 18], L1007 = [1, 4, 13, 15], L1078 = [1, 5, 9, 19], L1081 = [1, 5, 11, 13], L1084 = [1, 5, 11, 17], L1153 = [1, 6, 8, 20], L1191 = [1, 6, 13, 15], L1232 = [1, 7, 7, 21], L1278 = [1, 7, 13, 15], L1347 = [1, 8, 13, 15], L1401 = [1, 9, 13, 15], L1489 = [1, 12, 13, 15], L1514 = [1, 13, 14, 15], L1517 = [1, 13, 15, 15], L1518 = [1, 13, 15, 18], L1519 = [1, 13, 15, 21], L1718 = [2, 3, 12, 16], L1810 = [2, 7, 7, 21], L1826 = [2, 7, 12, 16], L1861 = [2, 9, 12, 16], L1883 = [2, 12, 15, 16], L1886 = [2, 12, 16, 21], L1949 = [3, 7, 7, 21], L1988 = [6, 7, 7, 21]. q = 43 : L502 = [1, 3, 8, 14], L508 = [1, 3, 9, 14].
10
EMILIO A. LAURET
Table 2. (continued) n = 4 q 44
45
46 48
49 50
I {0}
indexes of I-isospectral families {66, 68}, {72, 75, 100, 102}, {694, 696}, {707, 733}, {709, 970}, {716, 738}, {752, 755, 971, 985}, {776, 796, 974, 989}, {1401, 1403}, {1441, 1442} {0, 1} {713, 734}, {715, 737} {0} {585, 797}, {1221, 1224} {2} {158, 1166}, {746, 1152, 1169}, {1006, 1099, 1170}, {1230, 1248} {3} {139, 186} {0} {733, 737}, {800, 1045}, {819, 1043} {0} {788, 798}, {967, 1002}, {1145, 1149}, {1177, 1182}, {1310, 1377}, {1315, 1318}, {1483, 1489}, {1812, 1817}, {2205, 2209} {2} {229, 2012}, {235, 317}, {567, 2005}, {826, 2305}, {835, 2018}, {1051, 2019}, {1068, 1362}, {1242, 2388}, {1259, 1925}, {1479, 2231}, {1520, 1846}, {1572, 1760}, {1611, 2427}, {1668, 2020} {0, 1, 2, 3} {106, 108}, {887, 889}, {894, 896}, {902, 904}, {908, 912} {0} {263, 267}, {932, 935, 962}, {937, 963}, {1058, 1574}, {1227, 1480}, {2130, 2154}, {2143, 2159}
q = 44 : L66 = [0, 1, 3, 7], L68 = [0, 1, 3, 9], L72 = [0, 1, 3, 13], L75 = [0, 1, 3, 17], L100 = [0, 1, 5, 7], L102 = [0, 1, 5, 9], L694 = [1, 3, 5, 13], L696 = [1, 3, 5, 15], L707 = [1, 3, 7, 11], L709 = [1, 3, 7, 13], L713 = [1, 3, 7, 19], L715 = [1, 3, 7, 21], L716 = [1, 3, 7, 22], L733 = [1, 3, 9, 11], L734 = [1, 3, 9, 13], L737 = [1, 3, 9, 19], L738 = [1, 3, 9, 22], L752 = [1, 3, 11, 13], L755 = [1, 3, 11, 17], L776 = [1, 3, 13, 22], L796 = [1, 3, 17, 22], L970 = [1, 5, 7, 9], L971 = [1, 5, 7, 11], L974 = [1, 5, 7, 22], L985 = [1, 5, 9, 11], L989 = [1, 5, 9, 22], L1401 = [2, 6, 10, 11], L1403 = [2, 6, 11, 14], L1441 = [4, 8, 11, 12], L1442 = [4, 8, 11, 16]. q = 45 : L139 = [0, 1, 9, 18], L158 = [0, 1, 14, 16], L186 = [0, 5, 9, 18], L585 = [1, 2, 14, 19], L746 = [1, 3, 14, 16], L797 = [1, 4, 7, 11], L1006 = [1, 6, 14, 16], L1099 = [1, 9, 14, 16], L1152 = [1, 12, 14, 16], L1166 = [1, 14, 15, 16], L1169 = [1, 14, 16, 18], L1170 = [1, 14, 16, 21], L1221 = [3, 5, 6, 18], L1224 = [3, 5, 9, 12], L1230 = [3, 5, 10, 20], L1248 = [5, 9, 10, 20]. q = 46 : L733 = [1, 3, 5, 11], L737 = [1, 3, 5, 15], L800 = [1, 3, 11, 17], L819 = [1, 3, 13, 19], L1043 = [1, 5, 9, 11], L1045 = [1, 5, 9, 13]. q = 48 : L229 = [0, 1, 15, 17], L235 = [0, 1, 16, 16], L317 = [0, 3, 16, 16], L567 = [1, 1, 15, 17], L788 = [1, 2, 11, 13], L798 = [1, 2, 11, 23], L826 = [1, 2, 14, 18], L835 = [1, 2, 15, 17], L967 = [1, 3, 7, 15], L1002 = [1, 3, 9, 17], L1051 = [1, 3, 13, 19], L1068 = [1, 3, 15, 17], L1145 = [1, 4, 5, 19], L1149 = [1, 4, 5, 23], L1177 = [1, 4, 7, 17], L1182 = [1, 4, 7, 23], L1242 = [1, 4, 12, 20], L1259 = [1, 4, 15, 17], L1310 = [1, 5, 6, 13], L1315 = [1, 5, 6, 19], L1318 = [1, 5, 6, 23], L1362 = [1, 5, 11, 21], L1377 = [1, 5, 13, 18], L1479 = [1, 6, 10, 22], L1483 = [1, 6, 11, 13], L1489 = [1, 6, 11, 23], L1520 = [1, 6, 15, 17], L1572 = [1, 7, 9, 23], L1611 = [1, 8, 8, 24], L1668 = [1, 8, 15, 17], L1760 = [1, 9, 15, 17], L1812 = [1, 10, 11, 13], L1817 = [1, 10, 11, 23], L1846 = [1, 10, 15, 17], L1925 = [1, 12, 15, 17], L2005 = [1, 15, 15, 17], L2012 = [1, 15, 16, 17], L2018 = [1, 15, 17, 18], L2019 = [1, 15, 17, 21], L2020 = [1, 15, 17, 24], L2205 = [2, 3, 9, 15], L2209 = [2, 3, 9, 21], L2231 = [2, 3, 14, 18], L2305 = [2, 9, 14, 18], L2388 = [3, 4, 12, 20], L2427 = [3, 8, 8, 24]. q = 49 : L106 = [0, 1, 6, 15], L108 = [0, 1, 6, 20], L887 = [1, 6, 7, 15], L889 = [1, 6, 7, 20], L894 = [1, 6, 8, 20], L896 = [1, 6, 8, 22], L902 = [1, 6, 14, 15], L904 = [1, 6, 14, 20], L908 = [1, 6, 15, 21], L912 = [1, 6, 20, 21]. q = 50 : L263 = [0, 2, 5, 18], L267 = [0, 2, 8, 15], L932 = [1, 3, 7, 13], L935 = [1, 3, 7, 17], L937 = [1, 3, 7, 19], L962 = [1, 3, 9, 11], L963 = [1, 3, 9, 13], L1058 = [1, 3, 19, 21], L1227 = [1, 4, 14, 21],
APPENDIX
11
Table 2. (continued) n = 4 q 51
52
54
55 56
I {0} {2}
indexes of I-isospectral families {660, 983}, {1488, 1490}, {1491, 1492} {182, 1445}, {185, 202}, {472, 1448}, {710, 1355}, {717, 1431}, {925, 1246}, {939, 1218}, {1048, 1449}, {1142, 1450}, {1145, 1407} {0} {88, 121}, {122, 130}, {955, 957}, {959, 970, 973}, {1059, 1400}, {1082, 1376}, {1107, 1382, 1398}, {1112, 1405}, {1407, 1428}, {1413, 1460}, {2141, 2145}, {2143, 2147}, {2196, 2198}, {2199, 2202} {0, 1} {1036, 1083} {0} {1437, 1439}, {1645, 1650, 1682}, {1706, 1748}, {2082, 2084} {2} {277, 2658}, {1320, 2584, 2662}, {1916, 2449, 2663}, {2263, 2664}, {2940, 3131, 3147}, {3085, 3148} {0} {1592, 1593} {3} {170, 206} {0} {91, 93}, {100, 134}, {983, 995}, {1196, 1200}, {1251, 1264}, {1254, 1671}, {1262, 1287}, {1271, 1681}, {1283, 1678}, {1347, 1686}, {1859, 1866}, {2279, 2283}, {2337, 2342}, {2786, 2789}
L1480 = [1, 6, 9, 24], L1574 = [1, 7, 9, 11], L2130 = [2, 5, 10, 18], L2143 = [2, 5, 18, 20], L2154 = [2, 8, 10, 15], L2159 = [2, 8, 15, 20]. q = 51 : L182 = [0, 1, 16, 18], L185 = [0, 1, 17, 17], L202 = [0, 3, 17, 17], L472 = [1, 1, 16, 18], L660 = [1, 2, 10, 23], L710 = [1, 2, 15, 19], L717 = [1, 2, 16, 18], L925 = [1, 3, 14, 20], L939 = [1, 3, 16, 18], L983 = [1, 4, 5, 20], L1048 = [1, 4, 13, 21], L1142 = [1, 5, 12, 22], L1145 = [1, 5, 16, 18], L1218 = [1, 6, 11, 23], L1246 = [1, 6, 16, 18], L1355 = [1, 9, 16, 18], L1407 = [1, 12, 16, 18], L1431 = [1, 15, 16, 18], L1445 = [1, 16, 17, 18], L1448 = [1, 16, 18, 18], L1449 = [1, 16, 18, 21], L1450 = [1, 16, 18, 24], L1488 = [3, 6, 15, 17], L1490 = [3, 6, 17, 18], L1491 = [3, 6, 17, 21], L1492 = [3, 9, 12, 17]. q = 52 : L88 = [0, 1, 3, 19], L121 = [0, 1, 5, 9], L122 = [0, 1, 5, 11], L130 = [0, 1, 5, 23], L955 = [1, 3, 5, 15], L957 = [1, 3, 5, 17], L959 = [1, 3, 5, 19], L970 = [1, 3, 7, 11], L973 = [1, 3, 7, 15], L1036 = [1, 3, 11, 23], L1059 = [1, 3, 13, 19], L1082 = [1, 3, 15, 21], L1083 = [1, 3, 15, 23], L1107 = [1, 3, 19, 21], L1112 = [1, 3, 19, 26], L1376 = [1, 5, 7, 11], L1382 = [1, 5, 7, 23], L1398 = [1, 5, 9, 11], L1400 = [1, 5, 9, 13], L1405 = [1, 5, 9, 26], L1407 = [1, 5, 11, 13], L1413 = [1, 5, 11, 26], L1428 = [1, 5, 13, 23], L1460 = [1, 5, 23, 26], L2141 = [2, 6, 10, 13], L2143 = [2, 6, 13, 14], L2145 = [2, 6, 13, 18], L2147 = [2, 6, 13, 22], L2196 = [4, 8, 12, 13], L2198 = [4, 8, 13, 16], L2199 = [4, 8, 13, 20], L2202 = [4, 12, 13, 16]. q = 54 : L277 = [0, 1, 17, 19], L1320 = [1, 3, 17, 19], L1437 = [1, 4, 7, 17], L1439 = [1, 4, 7, 19], L1645 = [1, 5, 7, 17], L1650 = [1, 5, 7, 25], L1682 = [1, 5, 11, 13], L1706 = [1, 5, 13, 17], L1748 = [1, 5, 19, 23], L1916 = [1, 6, 17, 19], L2082 = [1, 8, 10, 17], L2084 = [1, 8, 10, 19], L2263 = [1, 9, 17, 19], L2449 = [1, 12, 17, 19], L2584 = [1, 15, 17, 19], L2658 = [1, 17, 18, 19], L2662 = [1, 17, 19, 21], L2663 = [1, 17, 19, 24], L2664 = [1, 17, 19, 27], L2940 = [2, 3, 16, 20], L3085 = [2, 9, 16, 20], L3131 = [2, 15, 16, 20], L3147 = [2, 16, 20, 21], L3148 = [2, 16, 20, 27]. q = 55 : L170 = [0, 1, 11, 22], L206 = [0, 5, 11, 22], L1592 = [5, 10, 11, 15], L1593 = [5, 10, 11, 20]. q = 56 : L91 = [0, 1, 3, 13], L93 = [0, 1, 3, 15], L100 = [0, 1, 3, 23], L134 = [0, 1, 5, 11], L983 = [1, 2, 13, 15], L995 = [1, 2, 13, 27], L1196 = [1, 3, 9, 17], L1200 = [1, 3, 9, 23], L1251 = [1, 3, 13, 14], L1254 = [1, 3, 13, 17], L1262 = [1, 3, 13, 28], L1264 = [1, 3, 14, 15], L1271 = [1, 3, 14, 23], L1283 = [1, 3, 15, 23], L1287 = [1, 3, 15, 28], L1347 = [1, 3, 23, 28], L1671 = [1, 5, 9, 13], L1678 = [1, 5, 9, 25], L1681 = [1, 5, 11, 14], L1686 = [1, 5, 11, 28], L1859 = [1, 6, 13, 15], L1866 = [1, 6, 13, 27], L2279 = [1, 9, 15, 17], L2283 = [1, 9, 15, 25], L2337 = [1, 10, 13, 15], L2342 = [1, 10, 13, 27], L2786 = [2, 6, 7, 10], L2789 = [2, 6, 7, 18].
12
EMILIO A. LAURET
Table 2. (continued) n = 4 q I indexes of I-isospectral families 57 {0} {2001, 2003} {2} {223, 1943}, {227, 245}, {586, 1938}, {893, 1760}, {901, 1947}, {1175, 1618}, {1190, 1597}, {1346, 1948}, {1361, 1915}, {1673, 1949}, {1687, 1867} 58 {0} {1280, 1309}, {1693, 1717} 60 {0} {2289, 2363}, {4658, 4664}, {4797, 4802}, {5493, 5507}, {5555, 5567} {2} {373, 4092}, {377, 562}, {1000, 4096}, {1416, 4884}, {1426, 4036}, {1790, 4098}, {1811, 2886}, {2132, 5335}, {2164, 4097}, {2426, 5250}, {2468, 3894}, {2689, 4544}, {2746, 3799}, {3035, 5146}, {3094, 3648}, {3209, 3291}, {3365, 5383}, {3456, 4099}, {4737, 5638}, {4751, 4949}, {5518, 5668}, {5522, 5580} {3} {304, 605}, {2744, 5642} 62 {0} {1929, 1933} 63 {0} {2315, 2318} {2} {291, 2781}, {1501, 2761, 2785}, {2102, 2722, 2786}, {2469, 2618, 2787}, {2875, 2898} q = 57 : L223 = [0, 1, 18, 20], L227 = [0, 1, 19, 19], L245 = [0, 3, 19, 19], L586 = [1, 1, 18, 20], L893 = [1, 2, 17, 21], L901 = [1, 2, 18, 20], L1175 = [1, 3, 16, 22], L1190 = [1, 3, 18, 20], L1346 = [1, 4, 15, 23], L1361 = [1, 4, 18, 20], L1597 = [1, 6, 13, 25], L1618 = [1, 6, 18, 20], L1673 = [1, 7, 12, 26], L1687 = [1, 7, 18, 20], L1760 = [1, 9, 18, 20], L1867 = [1, 12, 18, 20], L1915 = [1, 15, 18, 20], L1938 = [1, 18, 18, 20], L1943 = [1, 18, 19, 20], L1947 = [1, 18, 20, 21], L1948 = [1, 18, 20, 24], L1949 = [1, 18, 20, 27], L2001 = [3, 6, 19, 21], L2003 = [3, 9, 12, 19]. q = 58 : L1280 = [1, 3, 13, 21], L1309 = [1, 3, 15, 23], L1693 = [1, 5, 7, 25], L1717 = [1, 5, 9, 23]. q = 60 : L304 = [0, 1, 12, 24], L373 = [0, 1, 19, 21], L377 = [0, 1, 20, 20], L562 = [0, 3, 20, 20], L605 = [0, 5, 12, 24], L1000 = [1, 1, 19, 21], L1416 = [1, 2, 18, 22], L1426 = [1, 2, 19, 21], L1790 = [1, 3, 17, 23], L1811 = [1, 3, 19, 21], L2132 = [1, 4, 16, 24], L2164 = [1, 4, 19, 21], L2289 = [1, 5, 7, 17], L2363 = [1, 5, 11, 13], L2426 = [1, 5, 15, 25], L2468 = [1, 5, 19, 21], L2689 = [1, 6, 14, 26], L2744 = [1, 6, 18, 30], L2746 = [1, 6, 19, 21], L2886 = [1, 7, 13, 27], L3035 = [1, 8, 12, 28], L3094 = [1, 8, 19, 21], L3209 = [1, 9, 11, 29], L3291 = [1, 9, 19, 21], L3365 = [1, 10, 10, 30], L3456 = [1, 10, 19, 21], L3648 = [1, 12, 19, 21], L3799 = [1, 14, 19, 21], L3894 = [1, 15, 19, 21], L4036 = [1, 18, 19, 21], L4092 = [1, 19, 20, 21], L4096 = [1, 19, 21, 21], L4097 = [1, 19, 21, 24], L4098 = [1, 19, 21, 27], L4099 = [1, 19, 21, 30], L4544 = [2, 3, 18, 22], L4658 = [2, 5, 6, 14], L4664 = [2, 5, 6, 22], L4737 = [2, 5, 15, 25], L4751 = [2, 5, 18, 22], L4797 = [2, 6, 14, 15], L4802 = [2, 6, 15, 22], L4884 = [2, 9, 18, 22], L4949 = [2, 15, 18, 22], L5146 = [3, 4, 16, 24], L5250 = [3, 5, 15, 25], L5335 = [3, 8, 12, 28], L5383 = [3, 10, 10, 30], L5493 = [4, 5, 8, 24], L5507 = [4, 5, 12, 16], L5518 = [4, 5, 15, 25], L5522 = [4, 5, 16, 24], L5555 = [4, 8, 15, 24], L5567 = [4, 12, 15, 16], L5580 = [4, 15, 16, 24], L5638 = [5, 6, 15, 25], L5642 = [5, 6, 18, 30], L5668 = [5, 12, 15, 25]. q = 62 : L1929 = [1, 5, 6, 26], L1933 = [1, 5, 6, 30]. q = 63 : L291 = [0, 1, 20, 22], L1501 = [1, 3, 20, 22], L2102 = [1, 6, 20, 22], L2315 = [1, 8, 10, 19], L2318 = [1, 8, 10, 26], L2469 = [1, 9, 20, 22], L2618 = [1, 12, 20, 22], L2722 = [1, 15, 20, 22], L2761 = [1, 18, 20, 22], L2781 = [1, 20, 21, 22], L2785 = [1, 20, 22, 24], L2786 = [1, 20, 22, 27], L2787 = [1, 20, 22, 30], L2875 = [3, 7, 14, 28], L2898 = [7, 9, 14, 28]. q = 64 : L194 = [0, 1, 7, 17], L197 = [0, 1, 7, 23], L1195 = [1, 2, 15, 17], L1209 = [1, 2, 15, 31], L1388 = [1, 3, 5, 23], L1410 = [1, 3, 7, 21], L1412 = [1, 3, 7, 23], L1457 = [1, 3, 9, 25], L1490 = [1, 3, 11, 17], L1492 = [1, 3, 11, 19], L1494 = [1, 3, 11, 23], L1531 = [1, 3, 13, 23], L1592 = [1, 3, 17, 25],
APPENDIX
13
Table 2. (continued) n = 4 q 64
I {0}
indexes of I-isospectral families {1195, 1209}, {1388, 1410}, {1412, 1457}, {1490, 1531}, {1492, 2093}, {1494, 2098}, {1592, 2096}, {2375, 2385}, {2841, 2849}, {3112, 3117} {0, 1, 2, 3} {194, 197}, {2492, 2495}, {2548, 2551}, {2561, 2581}, {2564, 2585} 65 {0} {2490, 2491}, {2492, 2498} {3} {238, 278} 66 {0} {184, 223}, {2659, 3227}, {2686, 2760}, {2689, 2727}, {2780, 3278}, {2824, 3281}, {5469, 5613}, {5504, 5615}, {6079, 6080}, {6086, 6087}, {6166, 6168} {2} {418, 4871}, {426, 600}, {1081, 4862}, {1586, 5970}, {1598, 4879}, {2049, 4545}, {2072, 3262}, {2454, 5976}, {2487, 4751}, {2733, 3738}, {2765, 4880}, {3039, 5922}, {3098, 4649}, {3446, 5387}, {3513, 4881}, {3862, 5730}, {3951, 4297}, {4043, 6099}, {4143, 4882}, {5789, 6165}, {5826, 5977} 68 {0} {170, 208}, {1627, 1668}, {1629, 1675}, {1794, 2947}, {1859, 2410}, {2493, 2977}, {2538, 2973}, {2590, 2979}, {4315, 4318}, {4321, 4340}, {4407, 4408}, {4409, 4411}
L2093 = [1, 5, 9, 17], L2096 = [1, 5, 9, 25], L2098 = [1, 5, 9, 29], L2375 = [1, 6, 15, 17], L2385 = [1, 6, 15, 31], L2492 = [1, 7, 8, 17], L2495 = [1, 7, 8, 23], L2548 = [1, 7, 16, 17], L2551 = [1, 7, 16, 23], L2561 = [1, 7, 17, 24], L2564 = [1, 7, 17, 32], L2581 = [1, 7, 23, 24], L2585 = [1, 7, 23, 32], L2841 = [1, 10, 15, 17], L2849 = [1, 10, 15, 31], L3112 = [1, 14, 15, 17], L3117 = [1, 14, 15, 31]. q = 65 : L238 = [0, 1, 13, 26], L278 = [0, 5, 13, 26], L2490 = [5, 10, 13, 15], L2491 = [5, 10, 13, 20], L2492 = [5, 10, 13, 25], L2498 = [5, 13, 15, 20]. q = 66 : L184 = [0, 1, 5, 29], L223 = [0, 1, 7, 17], L418 = [0, 1, 21, 23], L426 = [0, 1, 22, 22], L600 = [0, 3, 22, 22], L1081 = [1, 1, 21, 23], L1586 = [1, 2, 20, 24], L1598 = [1, 2, 21, 23], L2049 = [1, 3, 19, 25], L2072 = [1, 3, 21, 23], L2454 = [1, 4, 18, 26], L2487 = [1, 4, 21, 23], L2659 = [1, 5, 11, 29], L2686 = [1, 5, 13, 19], L2689 = [1, 5, 13, 23], L2727 = [1, 5, 17, 19], L2733 = [1, 5, 17, 27], L2760 = [1, 5, 19, 31], L2765 = [1, 5, 21, 23], L2780 = [1, 5, 22, 29], L2824 = [1, 5, 29, 33], L3039 = [1, 6, 16, 28], L3098 = [1, 6, 21, 23], L3227 = [1, 7, 11, 17], L3262 = [1, 7, 15, 29], L3278 = [1, 7, 17, 22], L3281 = [1, 7, 17, 33], L3446 = [1, 8, 14, 30], L3513 = [1, 8, 21, 23], L3738 = [1, 9, 21, 23], L3862 = [1, 10, 12, 32], L3951 = [1, 10, 21, 23], L4043 = [1, 11, 11, 33], L4143 = [1, 11, 21, 23], L4297 = [1, 12, 21, 23], L4545 = [1, 15, 21, 23], L4649 = [1, 16, 21, 23], L4751 = [1, 18, 21, 23], L4862 = [1, 21, 21, 23], L4871 = [1, 21, 22, 23], L4879 = [1, 21, 23, 24], L4880 = [1, 21, 23, 27], L4881 = [1, 21, 23, 30], L4882 = [1, 21, 23, 33], L5387 = [2, 3, 20, 24], L5469 = [2, 4, 11, 28], L5504 = [2, 4, 28, 33], L5613 = [2, 8, 10, 11], L5615 = [2, 8, 10, 33], L5730 = [2, 9, 20, 24], L5789 = [2, 11, 11, 33], L5826 = [2, 11, 20, 24], L5922 = [2, 15, 20, 24], L5970 = [2, 20, 21, 24], L5976 = [2, 20, 24, 27], L5977 = [2, 20, 24, 33], L6079 = [3, 9, 11, 15], L6080 = [3, 9, 11, 21], L6086 = [3, 9, 15, 22], L6087 = [3, 9, 21, 22], L6099 = [3, 11, 11, 33], L6165 = [6, 11, 11, 33], L6166 = [6, 11, 12, 18], L6168 = [6, 11, 12, 24]. q = 68 : L170 = [0, 1, 5, 25], L208 = [0, 1, 7, 11], L1627 = [1, 3, 7, 23], L1629 = [1, 3, 7, 25], L1668 = [1, 3, 9, 13], L1675 = [1, 3, 9, 23], L1794 = [1, 3, 15, 25], L1859 = [1, 3, 19, 27], L2410 = [1, 5, 7, 19], L2493 = [1, 5, 13, 19], L2538 = [1, 5, 17, 25], L2590 = [1, 5, 25, 34], L2947 = [1, 7, 9, 13], L2973 = [1, 7, 11, 17], L2977 = [1, 7, 11, 31], L2979 = [1, 7, 11, 34], L4315 = [2, 6, 14, 17], L4318 = [2, 6, 17, 18], L4321 = [2, 6, 17, 26], L4340 = [2, 10, 14, 17], L4407 = [4, 8, 17, 20], L4408 = [4, 8, 17, 24], L4409 = [4, 8, 17, 28], L4411 = [4, 12, 16, 17].
14
EMILIO A. LAURET
Table 2. (continued) n = 4 q 69
70 72
74 75
I {2}
indexes of I-isospectral families {319, 3277}, {323, 346}, {849, 3281}, {1321, 3061}, {1331, 3255}, {1760, 3160}, {1781, 2749}, {2047, 2548}, {2079, 3282}, {2267, 2900}, {2291, 3207}, {2678, 3284}, {2689, 3283} {0} {4081, 4085}, {4490, 4494} {3} {373, 610}, {3723, 6416}, {6106, 6473} {0} {186, 235}, {1734, 1750}, {2179, 2216}, {3007, 3009}, {3016, 3077}, {3076, 3083}, {3093, 3756}, {3121, 3725}, {3168, 3759}, {3172, 3763}, {3181, 3769}, {3547, 3559}, {4668, 4677}, {5168, 5176}, {6440, 6447}, {6914, 6918}, {7021, 7024} {0, 1} {6406, 6427} {2} {490, 6011}, {2387, 5891, 6016}, {3630, 5693, 6017}, {4474, 5397, 6018}, {5055, 6019}, {6496, 6730, 6816}, {6966, 7144}, {7050, 7190} {0} {1893, 1943}, {4103, 4110} {2} {411, 4750}, {417, 476}, {1075, 4743}, {1650, 4327}, {1661, 4756}, {2192, 4758}, {2213, 3705}, {2567, 3356}, {2599, 4705}, {2962, 5026}, {3002, 4757}, {3548, 4606}, {3868, 4759}, {3924, 4169}, {4052, 4971}, {4106, 4521}
q = 69 : L319 = [0, 1, 22, 24], L323 = [0, 1, 23, 23], L346 = [0, 3, 23, 23], L849 = [1, 1, 22, 24], L1321 = [1, 2, 21, 25], L1331 = [1, 2, 22, 24], L1760 = [1, 3, 20, 26], L1781 = [1, 3, 22, 24], L2047 = [1, 4, 19, 27], L2079 = [1, 4, 22, 24], L2267 = [1, 5, 18, 28], L2291 = [1, 5, 22, 24], L2548 = [1, 6, 22, 24], L2678 = [1, 7, 16, 30], L2689 = [1, 7, 22, 24], L2749 = [1, 8, 15, 31], L2900 = [1, 9, 22, 24], L3061 = [1, 12, 22, 24], L3160 = [1, 15, 22, 24], L3207 = [1, 18, 22, 24], L3255 = [1, 21, 22, 24], L3277 = [1, 22, 23, 24], L3281 = [1, 22, 24, 24], L3282 = [1, 22, 24, 27], L3283 = [1, 22, 24, 30], L3284 = [1, 22, 24, 33]. q = 70 : L373 = [0, 1, 14, 28], L610 = [0, 5, 14, 28], L3723 = [1, 7, 21, 35], L4081 = [1, 9, 11, 19], L4085 = [1, 9, 11, 29], L4490 = [1, 11, 16, 24], L4494 = [1, 11, 16, 34], L6106 = [2, 7, 21, 35], L6416 = [5, 7, 21, 35], L6473 = [7, 10, 21, 35]. q = 72 : L186 = [0, 1, 5, 17], L235 = [0, 1, 7, 11], L490 = [0, 1, 23, 25], L1734 = [1, 2, 17, 19], L1750 = [1, 2, 17, 35], L2179 = [1, 3, 11, 29], L2216 = [1, 3, 13, 19], L2387 = [1, 3, 23, 25], L3007 = [1, 5, 7, 23], L3009 = [1, 5, 7, 25], L3016 = [1, 5, 7, 33], L3076 = [1, 5, 11, 19], L3077 = [1, 5, 11, 21], L3083 = [1, 5, 11, 29], L3093 = [1, 5, 12, 17], L3121 = [1, 5, 13, 27], L3168 = [1, 5, 17, 18], L3172 = [1, 5, 17, 24], L3181 = [1, 5, 17, 36], L3547 = [1, 6, 17, 19], L3559 = [1, 6, 17, 35], L3630 = [1, 6, 23, 25], L3725 = [1, 7, 9, 19], L3756 = [1, 7, 11, 12], L3759 = [1, 7, 11, 18], L3763 = [1, 7, 11, 24], L3769 = [1, 7, 11, 36], L4474 = [1, 9, 23, 25], L4668 = [1, 10, 17, 19], L4677 = [1, 10, 17, 35], L5055 = [1, 12, 23, 25], L5168 = [1, 14, 17, 19], L5176 = [1, 14, 17, 35], L5397 = [1, 15, 23, 25], L5693 = [1, 18, 23, 25], L5891 = [1, 21, 23, 25], L6011 = [1, 23, 24, 25], L6016 = [1, 23, 25, 27], L6017 = [1, 23, 25, 30], L6018 = [1, 23, 25, 33], L6019 = [1, 23, 25, 36], L6406 = [2, 3, 10, 34], L6427 = [2, 3, 14, 22], L6440 = [2, 3, 15, 21], L6447 = [2, 3, 15, 33], L6496 = [2, 3, 22, 26], L6730 = [2, 9, 22, 26], L6816 = [2, 15, 22, 26], L6914 = [3, 4, 9, 15], L6918 = [3, 4, 9, 21], L6966 = [3, 4, 20, 28], L7021 = [3, 8, 9, 15], L7024 = [3, 8, 9, 21], L7050 = [3, 8, 16, 32], L7144 = [4, 9, 20, 28], L7190 = [8, 9, 16, 32]. q = 74 : L1893 = [1, 3, 7, 27], L1943 = [1, 3, 9, 25], L4103 = [1, 10, 11, 26], L4110 = [1, 10, 11, 36]. q = 75 : L411 = [0, 1, 24, 26], L417 = [0, 1, 25, 25], L476 = [0, 3, 25, 25], L1075 = [1, 1, 24, 26], L1650 = [1, 2, 23, 27], L1661 = [1, 2, 24, 26], L2192 = [1, 3, 22, 28], L2213 = [1, 3, 24, 26], L2567 = [1, 4, 21, 29], L2599 = [1, 4, 24, 26], L2962 = [1, 5, 20, 30], L3002 = [1, 5, 24, 26], L3356 = [1, 6, 24, 26], L3548 = [1, 7, 18, 32], L3705 = [1, 8, 17, 33], L3868 = [1, 9, 16, 34], L3924 = [1, 9, 24, 26], L4052 =
APPENDIX
15
Table 2. (continued) n = 4 q I indexes of I-isospectral families 76 {0} {2064, 2069}, {2169, 3090}, {2214, 3077}, {5819, 5822}, {5929, 5932} 77 {0} {3350, 3353}, {3763, 3765} 78 {0} {3698, 3709}, {6905, 6912}, {9473, 9477}, {9474, 9479}, {9482, 9486}, {9483, 9488}, {9588, 9589}, {9591, 9599} {2} {573, 7675}, {578, 807}, {1479, 7680}, {2192, 9335}, {2205, 7614}, {2854, 5448}, {2881, 5353}, {3447, 9340}, {3486, 7681}, {3869, 7458}, {4362, 8899}, {4432, 7351}, {4700, 6803}, {4751, 7682}, {5021, 8393}, {5108, 7192}, {5665, 9293}, {5776, 7683}, {5937, 9203}, {6097, 6572}, {6194, 9518}, {6355, 7684}, {9066, 9598}, {9111, 9341} 80 {0} {144, 146}, {2023, 2041}, {2346, 2407}, {2604, 3681}, {2666, 2668}, {2812, 2828}, {3037, 3045}, {3090, 3099}, {4302, 4315}, {5190, 5194}, {5321, 5329}, {5470, 5482}, {5633, 5639}, {6211, 6220}, {6774, 6781}, {7687, 7691} {3} {462, 686}, {5058, 8065} [1, 10, 15, 35], L4106 = [1, 10, 24, 26], L4169 = [1, 11, 14, 36], L4327 = [1, 12, 24, 26], L4521 = [1, 15, 24, 26], L4606 = [1, 18, 24, 26], L4705 = [1, 21, 24, 26], L4743 = [1, 24, 24, 26], L4750 = [1, 24, 25, 26], L4756 = [1, 24, 26, 27], L4757 = [1, 24, 26, 30], L4758 = [1, 24, 26, 33], L4759 = [1, 24, 26, 36], L4971 = [3, 5, 20, 30], L5026 = [3, 10, 15, 35]. q = 76 : L2064 = [1, 3, 9, 17], L2069 = [1, 3, 9, 25], L2169 = [1, 3, 13, 27], L2214 = [1, 3, 15, 27], L3077 = [1, 5, 9, 17], L3090 = [1, 5, 9, 35], L5819 = [2, 6, 19, 22], L5822 = [2, 6, 19, 30], L5929 = [4, 8, 19, 28], L5932 = [4, 12, 16, 19]. q = 77 : L3350 = [1, 10, 12, 23], L3353 = [1, 10, 12, 32], L3763 = [7, 11, 14, 21], L3765 = [7, 11, 14, 28]. q = 78 : L573 = [0, 1, 25, 27], L578 = [0, 1, 26, 26], L807 = [0, 3, 26, 26], L1479 = [1, 1, 25, 27], L2192 = [1, 2, 24, 28], L2205 = [1, 2, 25, 27], L2854 = [1, 3, 23, 29], L2881 = [1, 3, 25, 27], L3447 = [1, 4, 22, 30], L3486 = [1, 4, 25, 27], L3698 = [1, 5, 11, 19], L3709 = [1, 5, 11, 35], L3869 = [1, 5, 21, 31], L4362 = [1, 6, 20, 32], L4432 = [1, 6, 25, 27], L4700 = [1, 7, 19, 33], L4751 = [1, 7, 25, 27], L5021 = [1, 8, 18, 34], L5108 = [1, 8, 25, 27], L5353 = [1, 9, 17, 35], L5448 = [1, 9, 25, 27], L5665 = [1, 10, 16, 36], L5776 = [1, 10, 25, 27], L5937 = [1, 12, 14, 38], L6097 = [1, 12, 25, 27], L6194 = [1, 13, 13, 39], L6355 = [1, 13, 25, 27], L6572 = [1, 14, 25, 27], L6803 = [1, 15, 25, 27], L6905 = [1, 16, 17, 22], L6912 = [1, 16, 17, 38], L7192 = [1, 18, 25, 27], L7351 = [1, 20, 25, 27], L7458 = [1, 21, 25, 27], L7614 = [1, 24, 25, 27], L7675 = [1, 25, 26, 27], L7680 = [1, 25, 27, 27], L7681 = [1, 25, 27, 30], L7682 = [1, 25, 27, 33], L7683 = [1, 25, 27, 36], L7684 = [1, 25, 27, 39], L8393 = [2, 3, 24, 28], L8899 = [2, 9, 24, 28], L9066 = [2, 13, 13, 39], L9111 = [2, 13, 24, 28], L9203 = [2, 15, 24, 28], L9293 = [2, 21, 24, 28], L9335 = [2, 24, 27, 28], L9340 = [2, 24, 28, 33], L9341 = [2, 24, 28, 39], L9473 = [3, 9, 13, 15], L9474 = [3, 9, 13, 21], L9477 = [3, 9, 13, 27], L9479 = [3, 9, 13, 33], L9482 = [3, 9, 15, 26], L9483 = [3, 9, 21, 26], L9486 = [3, 9, 26, 27], L9488 = [3, 9, 26, 33], L9518 = [3, 13, 13, 39], L9588 = [6, 12, 13, 18], L9589 = [6, 12, 13, 24], L9591 = [6, 12, 13, 30], L9598 = [6, 13, 13, 39], L9599 = [6, 13, 18, 24]. q = 80 : L144 = [0, 1, 3, 31], L146 = [0, 1, 3, 33], L462 = [0, 1, 16, 32], L686 = [0, 5, 16, 32], L2023 = [1, 2, 19, 21], L2041 = [1, 2, 19, 39], L2346 = [1, 3, 7, 31], L2407 = [1, 3, 9, 33], L2604 = [1, 3, 17, 25], L2666 = [1, 3, 20, 31], L2668 = [1, 3, 20, 33], L2812 = [1, 3, 31, 40], L2828 = [1, 3, 33, 40], L3037 = [1, 4, 9, 31], L3045 = [1, 4, 9, 39], L3090 = [1, 4, 11, 29], L3099 = [1, 4, 11, 39], L3681 = [1, 5, 13, 21], L4302 = [1, 6, 19, 21], L4315 = [1, 6, 19, 39], L5058 = [1, 8, 24, 40], L5190 = [1, 9, 12, 31], L5194 = [1, 9, 12, 39], L5321 = [1, 10, 11, 29], L5329 = [1, 10, 11, 39], L5470 = [1, 10, 19, 21], L5482 = [1, 10, 19, 39], L5633 = [1, 11, 12, 29], L5639 = [1, 11, 12, 39], L6211 = [1, 14, 19, 21], L6220 =
16
EMILIO A. LAURET
Table 2. (continued) n = 4 q 81
84
85 86 87
I {2}
indexes of I-isospectral families {408, 4881}, {2450, 4855, 4886}, {3628, 4820, 4887}, {4233, 4771, 4888}, {4484, 4680, 4889} {0, 1, 2, 3} {3897, 3899}, {3901, 3903}, {3991, 4008} {0} {4448, 5565}, {7352, 7361}, {12289, 12293}, {12537, 12540}, {12547, 12550} {2} {679, 9891}, {690, 988}, {1813, 9879}, {2644, 11683}, {2659, 9902}, {3416, 6787}, {3445, 6677}, {4138, 12581}, {4182, 9662}, {4661, 9905}, {4706, 9903}, {5244, 11494}, {5319, 9524}, {5772, 12373}, {5841, 9373}, {6225, 12118}, {6323, 9904}, {7082, 10776}, {7223, 8966}, {7649, 12490}, {7798, 8735}, {7933, 8493}, {8029, 12602}, {8209, 9906}, {11222, 13037}, {11243, 11771}, {12883, 13094}, {12889, 12969} {0} {5142, 5143}, {5145, 5147} {3} {381, 448} {0} {2586, 2592}, {4345, 4351} {2} {494, 6235}, {499, 529}, {1338, 6240}, {2125, 5842}, {2138, 6203}, {2870, 6243}, {2896, 5282}, {3412, 6242}, {3451, 6241}, {3839, 4381}, {3877, 6166}, {4857, 6002}, {4872, 6097}, {5068, 6244}, {5125, 5621}, {5446, 5533}
[1, 14, 19, 39], L6774 = [1, 18, 19, 21], L6781 = [1, 18, 19, 39], L7687 = [2, 5, 15, 25], L7691 = [2, 5, 15, 35], L8065 = [5, 8, 24, 40]. q = 81 : L408 = [0, 1, 26, 28], L2450 = [1, 3, 26, 28], L3628 = [1, 6, 26, 28], L3897 = [1, 8, 10, 26], L3899 = [1, 8, 10, 28], L3901 = [1, 8, 10, 35], L3903 = [1, 8, 10, 37], L3991 = [1, 8, 19, 37], L4008 = [1, 8, 26, 37], L4233 = [1, 9, 26, 28], L4484 = [1, 12, 26, 28], L4680 = [1, 15, 26, 28], L4771 = [1, 18, 26, 28], L4820 = [1, 21, 26, 28], L4855 = [1, 24, 26, 28], L4881 = [1, 26, 27, 28], L4886 = [1, 26, 28, 30], L4887 = [1, 26, 28, 33], L4888 = [1, 26, 28, 36], L4889 = [1, 26, 28, 39]. q = 84 : L679 = [0, 1, 27, 29], L690 = [0, 1, 28, 28], L988 = [0, 3, 28, 28], L1813 = [1, 1, 27, 29], L2644 = [1, 2, 26, 30], L2659 = [1, 2, 27, 29], L3416 = [1, 3, 25, 31], L3445 = [1, 3, 27, 29], L4138 = [1, 4, 24, 32], L4182 = [1, 4, 27, 29], L4448 = [1, 5, 11, 35], L4661 = [1, 5, 23, 33], L4706 = [1, 5, 27, 29], L5244 = [1, 6, 22, 34], L5319 = [1, 6, 27, 29], L5565 = [1, 7, 11, 23], L5772 = [1, 7, 21, 35], L5841 = [1, 7, 27, 29], L6225 = [1, 8, 20, 36], L6323 = [1, 8, 27, 29], L6677 = [1, 9, 19, 37], L6787 = [1, 9, 27, 29], L7082 = [1, 10, 18, 38], L7223 = [1, 10, 27, 29], L7352 = [1, 11, 13, 23], L7361 = [1, 11, 13, 37], L7649 = [1, 12, 16, 40], L7798 = [1, 12, 27, 29], L7933 = [1, 13, 15, 41], L8029 = [1, 14, 14, 42], L8209 = [1, 14, 27, 29], L8493 = [1, 15, 27, 29], L8735 = [1, 16, 27, 29], L8966 = [1, 18, 27, 29], L9373 = [1, 21, 27, 29], L9524 = [1, 22, 27, 29], L9662 = [1, 24, 27, 29], L9879 = [1, 27, 27, 29], L9891 = [1, 27, 28, 29], L9902 = [1, 27, 29, 30], L9903 = [1, 27, 29, 33], L9904 = [1, 27, 29, 36], L9905 = [1, 27, 29, 39], L9906 = [1, 27, 29, 42], L10776 = [2, 3, 26, 30], L11222 = [2, 7, 21, 35], L11243 = [2, 7, 26, 30], L11494 = [2, 9, 26, 30], L11683 = [2, 15, 26, 30], L11771 = [2, 21, 26, 30], L12118 = [3, 4, 24, 32], L12289 = [3, 7, 9, 15], L12293 = [3, 7, 9, 27], L12373 = [3, 7, 21, 35], L12490 = [3, 8, 20, 36], L12537 = [3, 9, 14, 15], L12540 = [3, 9, 14, 27], L12547 = [3, 9, 15, 28], L12550 = [3, 9, 27, 28], L12581 = [3, 12, 16, 40], L12602 = [3, 14, 14, 42], L12883 = [4, 7, 21, 35], L12889 = [4, 7, 24, 32], L12969 = [4, 21, 24, 32], L13037 = [6, 7, 21, 35], L13094 = [7, 12, 21, 35]. q = 85 : L381 = [0, 1, 17, 34], L448 = [0, 5, 17, 34], L5142 = [5, 10, 17, 25], L5143 = [5, 10, 17, 30], L5145 = [5, 10, 17, 35], L5147 = [5, 15, 17, 20]. q = 86 : L2586 = [1, 3, 9, 19], L2592 = [1, 3, 9, 27], L4345 = [1, 6, 7, 36], L4351 = [1, 6, 7, 42]. q = 87 : L494 = [0, 1, 28, 30], L499 = [0, 1, 29, 29], L529 = [0, 3, 29, 29], L1338 = [1, 1, 28, 30], L2125 = [1, 2, 27, 31], L2138 = [1, 2, 28, 30], L2870 = [1, 3, 26, 32], L2896 = [1, 3, 28, 30], L3412 =
APPENDIX
17
Table 2. (continued) n = 4 q I indexes of I-isospectral families 88 {0} {2349, 2369}, {2718, 2785}, {2918, 2965}, {5011, 5025}, {6551, 6563}, {7576, 7585}, {8107, 8114}, {9055, 9057}, {9061, 9065, 9093, 9095}, {9253, 9255}, {9309, 9310} 90 {0} {6540, 6576}, {9346, 9348}, {15728, 15733}, {15875, 15879}, {16058, 16073} {2} {787, 12188}, {3972, 12005, 12194}, {6306, 11616, 12195}, {7941, 11206, 12196}, {9181, 10682, 12197}, {9949, 12198}, {13301, 15474, 15524}, {14489, 15288, 15525}, {14973, 15526}, {15823, 16162}, {15938, 16298}, {16096, 16210} {3} {615, 1191}, {7923, 16167}, {14487, 16301} 91 {0} {5303, 5307}, {5928, 5930}, {5931, 5933} 92 {0} {4563, 4574}, {4661, 5773} 93 {2} {556, 7498}, {562, 598}, {1525, 7491}, {2436, 7024}, {2450, 7504}, {3302, 7309}, {3329, 6265}, {3944, 7506}, {3986, 7456}, {4454, 5090}, {4503, 7505}, {5405, 6078}, {5442, 7398}, {6419, 7508}, {6444, 7507}, {6600, 7190}, {6677, 6759} [1, 4, 25, 33], L3451 = [1, 4, 28, 30], L3839 = [1, 5, 24, 34], L3877 = [1, 5, 28, 30], L4381 = [1, 6, 28, 30], L4857 = [1, 8, 21, 37], L4872 = [1, 8, 28, 30], L5068 = [1, 9, 20, 38], L5125 = [1, 9, 28, 30], L5282 = [1, 10, 19, 39], L5446 = [1, 12, 17, 41], L5533 = [1, 12, 28, 30], L5621 = [1, 13, 16, 42], L5842 = [1, 15, 28, 30], L6002 = [1, 18, 28, 30], L6097 = [1, 21, 28, 30], L6166 = [1, 24, 28, 30], L6203 = [1, 27, 28, 30], L6235 = [1, 28, 29, 30], L6240 = [1, 28, 30, 30], L6241 = [1, 28, 30, 33], L6242 = [1, 28, 30, 36], L6243 = [1, 28, 30, 39], L6244 = [1, 28, 30, 42]. q = 88 : L2349 = [1, 2, 21, 23], L2369 = [1, 2, 21, 43], L2718 = [1, 3, 7, 27], L2785 = [1, 3, 9, 27], L2918 = [1, 3, 13, 35], L2965 = [1, 3, 15, 25], L5011 = [1, 6, 21, 23], L5025 = [1, 6, 21, 43], L6551 = [1, 10, 21, 23], L6563 = [1, 10, 21, 43], L7576 = [1, 14, 21, 23], L7585 = [1, 14, 21, 43], L8107 = [1, 18, 21, 23], L8114 = [1, 18, 21, 43], L9055 = [2, 6, 11, 14], L9057 = [2, 6, 11, 18], L9061 = [2, 6, 11, 26], L9065 = [2, 6, 11, 34], L9093 = [2, 10, 11, 14], L9095 = [2, 10, 11, 18], L9253 = [4, 11, 12, 20], L9255 = [4, 11, 12, 28], L9309 = [8, 11, 16, 24], L9310 = [8, 11, 16, 32]. q = 90 : L615 = [0, 1, 18, 36], L787 = [0, 1, 29, 31], L1191 = [0, 5, 18, 36], L3972 = [1, 3, 29, 31], L6306 = [1, 6, 29, 31], L6540 = [1, 7, 11, 41], L6576 = [1, 7, 13, 23], L7923 = [1, 9, 27, 45], L7941 = [1, 9, 29, 31], L9181 = [1, 12, 29, 31], L9346 = [1, 14, 16, 29], L9348 = [1, 14, 16, 31], L9949 = [1, 15, 29, 31], L10682 = [1, 18, 29, 31], L11206 = [1, 21, 29, 31], L11616 = [1, 24, 29, 31], L12005 = [1, 27, 29, 31], L12188 = [1, 29, 30, 31], L12194 = [1, 29, 31, 33], L12195 = [1, 29, 31, 36], L12196 = [1, 29, 31, 39], L12197 = [1, 29, 31, 42], L12198 = [1, 29, 31, 45], L13301 = [2, 3, 28, 32], L14487 = [2, 9, 27, 45], L14489 = [2, 9, 28, 32], L14973 = [2, 15, 28, 32], L15288 = [2, 21, 28, 32], L15474 = [2, 27, 28, 32], L15524 = [2, 28, 32, 33], L15525 = [2, 28, 32, 39], L15526 = [2, 28, 32, 45], L15728 = [3, 5, 9, 21], L15733 = [3, 5, 9, 33], L15823 = [3, 5, 25, 35], L15875 = [3, 9, 10, 21], L15879 = [3, 9, 10, 33], L15938 = [3, 10, 20, 40], L16058 = [5, 6, 12, 36], L16073 = [5, 6, 18, 24], L16096 = [5, 6, 25, 35], L16162 = [5, 9, 25, 35], L16167 = [5, 9, 27, 45], L16210 = [5, 18, 25, 35], L16298 = [9, 10, 20, 40], L16301 = [9, 10, 27, 45]. q = 91 : L5303 = [1, 12, 25, 27], L5307 = [1, 12, 25, 38], L5928 = [7, 13, 14, 21], L5930 = [7, 13, 14, 28], L5931 = [7, 13, 14, 35], L5933 = [7, 13, 21, 28]. q = 92 : L4563 = [1, 5, 9, 21], L4574 = [1, 5, 9, 35], L4661 = [1, 5, 13, 43], L5773 = [1, 7, 11, 25]. q = 93 : L556 = [0, 1, 30, 32], L562 = [0, 1, 31, 31], L598 = [0, 3, 31, 31], L1525 = [1, 1, 30, 32], L2436 = [1, 2, 29, 33], L2450 = [1, 2, 30, 32], L3302 = [1, 3, 28, 34], L3329 = [1, 3, 30, 32], L3944 = [1, 4, 27, 35], L3986 = [1, 4, 30, 32], L4454 = [1, 5, 26, 36], L4503 = [1, 5, 30, 32], L5090 = [1, 6, 30, 32], L5405 = [1, 7, 24, 38], L5442 = [1, 7, 30, 32], L6078 = [1, 9, 30, 32], L6265 = [1, 10, 21, 41], L6419 =
18
EMILIO A. LAURET
Table 2. (continued) n = 4 q 95
I {0} {3} {0}
indexes of I-isospectral families {6974, 6978} {472, 548} 96 {3058, 3080}, {5576, 5578}, {6156, 6162}, {6593, 6612}, {6923, 6928}, {7075, 7135}, {7160, 7165}, {7703, 7714}, {8982, 8998}, {9271, 9273}, {10460, 10473}, {11576, 11586}, {12321, 12330}, {14169, 14181}, {14635, 14638}, {15567, 15569}, {15693, 15695}, {15703, 15705} {2} {836, 13311}, {842, 1114}, {2124, 13317}, {3213, 14986}, {3229, 13217}, {4232, 12198}, {4265, 9396}, {5153, 15739}, {5202, 13318}, {5861, 13321}, {5928, 12973}, {6668, 15108}, {6753, 12834}, {7257, 8529}, {7325, 13319}, {7837, 15650}, {7930, 12668}, {8975, 14259}, {9122, 13320}, {9781, 15425}, {9952, 11947}, {10385, 14762}, {10589, 11686}, {10764, 10973}, {11101, 15774}, {11312, 13322} 98 {0} {865, 880}, {871, 879}, {888, 902}, {10476, 10484}, {12656, 12811}, {12662, 12810}, {12718, 12826}, {12721, 12834}, {12728, 12819}, {12752, 12823}, {12847, 12865}, {12893, 12931}, {12896, 12945} {0, 1, 2, 3} {490, 497}, {6840, 6847}, {9336, 9343}, {9359, 9361}, {9408, 9414}, {9477, 9484}, {9494, 9534}, {9497, 9555}, {9500, 9558}, {12642, 12645}, {12820, 12822}, {12828, 12833}, {12829, 12837} [1, 11, 20, 42], L6444 = [1, 11, 30, 32], L6600 = [1, 12, 19, 43], L6677 = [1, 12, 30, 32], L6759 = [1, 13, 18, 44], L7024 = [1, 15, 30, 32], L7190 = [1, 18, 30, 32], L7309 = [1, 21, 30, 32], L7398 = [1, 24, 30, 32], L7456 = [1, 27, 30, 32], L7491 = [1, 30, 30, 32], L7498 = [1, 30, 31, 32], L7504 = [1, 30, 32, 33], L7505 = [1, 30, 32, 36], L7506 = [1, 30, 32, 39], L7507 = [1, 30, 32, 42], L7508 = [1, 30, 32, 45]. q = 95 : L472 = [0, 1, 19, 38], L548 = [0, 5, 19, 38], L6974 = [5, 10, 19, 35], L6978 = [5, 15, 19, 20]. q = 96 : L836 = [0, 1, 31, 33], L842 = [0, 1, 32, 32], L1114 = [0, 3, 32, 32], L2124 = [1, 1, 31, 33], L3058 = [1, 2, 23, 25], L3080 = [1, 2, 23, 47], L3213 = [1, 2, 30, 34], L3229 = [1, 2, 31, 33], L4232 = [1, 3, 29, 35], L4265 = [1, 3, 31, 33], L5153 = [1, 4, 28, 36], L5202 = [1, 4, 31, 33], L5576 = [1, 5, 13, 23], L5578 = [1, 5, 13, 25], L5861 = [1, 5, 27, 37], L5928 = [1, 5, 31, 33], L6156 = [1, 6, 7, 41], L6162 = [1, 6, 7, 47], L6593 = [1, 6, 23, 25], L6612 = [1, 6, 23, 47], L6668 = [1, 6, 26, 38], L6753 = [1, 6, 31, 33], L6923 = [1, 7, 8, 41], L6928 = [1, 7, 8, 47], L7075 = [1, 7, 15, 25], L7135 = [1, 7, 17, 39], L7160 = [1, 7, 18, 41], L7165 = [1, 7, 18, 47], L7257 = [1, 7, 25, 39], L7325 = [1, 7, 31, 33], L7703 = [1, 8, 17, 31], L7714 = [1, 8, 17, 47], L7837 = [1, 8, 24, 40], L7930 = [1, 8, 31, 33], L8529 = [1, 9, 31, 33], L8975 = [1, 10, 22, 42], L8982 = [1, 10, 23, 25], L8998 = [1, 10, 23, 47], L9122 = [1, 10, 31, 33], L9271 = [1, 11, 13, 23], L9273 = [1, 11, 13, 25], L9396 = [1, 11, 21, 43], L9781 = [1, 12, 20, 44], L9952 = [1, 12, 31, 33], L10385 = [1, 14, 18, 46], L10460 = [1, 14, 23, 25], L10473 = [1, 14, 23, 47], L10589 = [1, 14, 31, 33], L10764 = [1, 15, 17, 47], L10973 = [1, 15, 31, 33], L11101 = [1, 16, 16, 48], L11312 = [1, 16, 31, 33], L11576 = [1, 18, 23, 25], L11586 = [1, 18, 23, 47], L11686 = [1, 18, 31, 33], L11947 = [1, 20, 31, 33], L12198 = [1, 21, 31, 33], L12321 = [1, 22, 23, 25], L12330 = [1, 22, 23, 47], L12668 = [1, 24, 31, 33], L12834 = [1, 26, 31, 33], L12973 = [1, 27, 31, 33], L13217 = [1, 30, 31, 33], L13311 = [1, 31, 32, 33], L13317 = [1, 31, 33, 33], L13318 = [1, 31, 33, 36], L13319 = [1, 31, 33, 39], L13320 = [1, 31, 33, 42], L13321 = [1, 31, 33, 45], L13322 = [1, 31, 33, 48], L14169 = [2, 3, 21, 27], L14181 = [2, 3, 21, 45], L14259 = [2, 3, 30, 34], L14635 = [2, 9, 15, 33], L14638 = [2, 9, 15, 39], L14762 = [2, 9, 30, 34], L14986 = [2, 15, 30, 34], L15108 = [2, 21, 30, 34], L15425 = [3, 4, 28, 36], L15567 = [3, 8, 9, 21], L15569 = [3, 8, 9, 27], L15650 = [3, 8, 24, 40], L15693 = [3, 9, 16, 21], L15695 = [3, 9, 16, 27], L15703 = [3, 9, 21, 32], L15705 = [3, 9, 27, 32], L15739 = [3, 12, 20, 44], L15774 = [3, 16, 16, 48].
APPENDIX
19
Table 2. (continued) n = 4 q 99
I {0} {2}
indexes of I-isospectral families {9564, 9593}, {9655, 9657} {656, 9417}, {3824, 9382, 9423}, {5903, 9312, 9424}, {7180, 9244, 9425}, {8088, 9034, 9426}, {8462, 8850, 9427}, {9624, 9660} 100 {0, 1, 2, 3} {406, 412}, {414, 419}, {8507, 8513}, {8515, 8520}, {8538, 8540}, {8669, 8675}, {8677, 8682}, {8694, 8761}, {8696, 8793}, {8701, 8794}, {8702, 8798}, {8707, 8803}, {8763, 8768}, {8805, 8810}, {8823, 8874}, {8829, 8879} 102 {0} {6398, 6401}, {19632, 19634}, {19638, 19683}, {19643, 19645}, {19649, 19690}, {19818, 19820}, {19821, 19830} {2} {949, 16099}, {961, 1306}, {2457, 16086}, {3693, 19424}, {3711, 16111}, {4862, 16114}, {4897, 10923}, {5937, 18286}, {5987, 15882}, {6773, 15606}, {6839, 16112}, {7721, 19434}, {7805, 15752}, {9110, 19203}, {9208, 16113}, {9811, 12856}, {9915, 12623}, {10447, 19346}, {10587, 15216}, {11388, 17356}, {11556, 14938}, {11821, 14687}, {12149, 19433}, {12361, 16115}, {13055, 18810}, {13273, 13996}, {13400, 19706}, {13644, 16116}, {18928, 19829}, {19007, 19435} q = 98 : L490 = [0, 1, 13, 29], L497 = [0, 1, 13, 41], L865 = [0, 2, 7, 26], L871 = [0, 2, 7, 40], L879 = [0, 2, 12, 21], L880 = [0, 2, 12, 35], L888 = [0, 2, 21, 26], L902 = [0, 2, 35, 40], L6840 = [1, 7, 13, 29], L6847 = [1, 7, 13, 41], L9336 = [1, 13, 14, 29], L9343 = [1, 13, 14, 41], L9359 = [1, 13, 15, 41], L9361 = [1, 13, 15, 43], L9408 = [1, 13, 21, 29], L9414 = [1, 13, 21, 41], L9477 = [1, 13, 28, 29], L9484 = [1, 13, 28, 41], L9494 = [1, 13, 29, 35], L9497 = [1, 13, 29, 42], L9500 = [1, 13, 29, 49], L9534 = [1, 13, 35, 41], L9555 = [1, 13, 41, 42], L9558 = [1, 13, 41, 49], L10476 = [1, 18, 19, 30], L10484 = [1, 18, 19, 48], L12642 = [2, 7, 12, 30], L12645 = [2, 7, 12, 40], L12656 = [2, 7, 14, 26], L12662 = [2, 7, 14, 40], L12718 = [2, 7, 26, 28], L12721 = [2, 7, 26, 42], L12728 = [2, 7, 28, 40], L12752 = [2, 7, 40, 42], L12810 = [2, 12, 14, 21], L12811 = [2, 12, 14, 35], L12819 = [2, 12, 21, 28], L12820 = [2, 12, 21, 30], L12822 = [2, 12, 21, 40], L12823 = [2, 12, 21, 42], L12826 = [2, 12, 28, 35], L12828 = [2, 12, 30, 35], L12829 = [2, 12, 30, 49], L12833 = [2, 12, 35, 40], L12834 = [2, 12, 35, 42], L12837 = [2, 12, 40, 49], L12847 = [2, 14, 21, 26], L12865 = [2, 14, 35, 40], L12893 = [2, 21, 26, 28], L12896 = [2, 21, 26, 42], L12931 = [2, 28, 35, 40], L12945 = [2, 35, 40, 42]. q = 99 : L656 = [0, 1, 32, 34], L3824 = [1, 3, 32, 34], L5903 = [1, 6, 32, 34], L7180 = [1, 9, 32, 34], L8088 = [1, 12, 32, 34], L8462 = [1, 15, 32, 34], L8850 = [1, 18, 32, 34], L9034 = [1, 21, 32, 34], L9244 = [1, 24, 32, 34], L9312 = [1, 27, 32, 34], L9382 = [1, 30, 32, 34], L9417 = [1, 32, 33, 34], L9423 = [1, 32, 34, 36], L9424 = [1, 32, 34, 39], L9425 = [1, 32, 34, 42], L9426 = [1, 32, 34, 45], L9427 = [1, 32, 34, 48], L9564 = [3, 6, 11, 42], L9593 = [3, 11, 12, 15], L9624 = [3, 11, 22, 44], L9655 = [9, 11, 18, 27], L9657 = [9, 11, 18, 36], L9660 = [9, 11, 22, 44]. q = 100 : L406 = [0, 1, 9, 21], L412 = [0, 1, 9, 29], L414 = [0, 1, 9, 31], L419 = [0, 1, 9, 39], L8507 = [1, 9, 10, 21], L8513 = [1, 9, 10, 29], L8515 = [1, 9, 10, 31], L8520 = [1, 9, 10, 39], L8538 = [1, 9, 11, 29], L8540 = [1, 9, 11, 31], L8669 = [1, 9, 20, 21], L8675 = [1, 9, 20, 29], L8677 = [1, 9, 20, 31], L8682 = [1, 9, 20, 39], L8694 = [1, 9, 21, 25], L8696 = [1, 9, 21, 30], L8701 = [1, 9, 21, 39], L8702 = [1, 9, 21, 40], L8707 = [1, 9, 21, 50], L8761 = [1, 9, 25, 29], L8763 = [1, 9, 25, 31], L8768 = [1, 9, 25, 39], L8793 = [1, 9, 29, 30], L8794 = [1, 9, 29, 31], L8798 = [1, 9, 29, 40], L8803 = [1, 9, 29, 50], L8805 = [1, 9, 30, 31], L8810 = [1, 9, 30, 39], L8823 = [1, 9, 31, 40], L8829 = [1, 9, 31, 50], L8874 = [1, 9, 39, 40], L8879 = [1, 9, 39, 50]. q = 102 : L949 = [0, 1, 33, 35], L961 = [0, 1, 34, 34], L1306 = [0, 3, 34, 34], L2457 = [1, 1, 33, 35], L3693 = [1, 2, 32, 36], L3711 = [1, 2, 33, 35], L4862 = [1, 3, 31, 37], L4897 = [1, 3, 33, 35], L5937 =
20
EMILIO A. LAURET
Table 2. (continued) n = 4 q I indexes of I-isospectral families 104 {0} {3258, 3282}, {7170, 7189}, {7735, 7850}, {9606, 9621}, {11323, 11336}, {12203, 12214}, {12723, 12733}, {14269, 14306}, {14307, 14316}, {14511, 14515}, {14513, 14518}, {14596, 14598}, {14600, 14603} 105 {0} {11890, 11896}, {15269, 15288}, {15369, 15378} {2} {867, 13883}, {873, 1042}, {2263, 13889}, {3463, 12318}, {3479, 13821}, {4619, 10808}, {4651, 10657}, {5530, 9404}, {5579, 13890}, {6494, 15129}, {6553, 13723}, {7366, 7446}, {8181, 15092}, {8254, 13891}, {8752, 13893}, {8831, 13492}, {9867, 14562}, {9990, 13892}, {10280, 13894}, {10353, 13193}, {11079, 14846}, {11234, 12858}, {11455, 15000}, {11669, 12594}, {15297, 15384}, {15301, 15344} {3} {720, 1066} [1, 4, 30, 38], L5987 = [1, 4, 33, 35], L6398 = [1, 5, 13, 37], L6401 = [1, 5, 13, 41], L6773 = [1, 5, 29, 39], L6839 = [1, 5, 33, 35], L7721 = [1, 6, 28, 40], L7805 = [1, 6, 33, 35], L9110 = [1, 8, 26, 42], L9208 = [1, 8, 33, 35], L9811 = [1, 9, 25, 43], L9915 = [1, 9, 33, 35], L10447 = [1, 10, 24, 44], L10587 = [1, 10, 33, 35], L10923 = [1, 11, 23, 45], L11388 = [1, 12, 22, 46], L11556 = [1, 12, 33, 35], L11821 = [1, 13, 21, 47], L12149 = [1, 14, 20, 48], L12361 = [1, 14, 33, 35], L12623 = [1, 15, 19, 49], L12856 = [1, 15, 33, 35], L13055 = [1, 16, 18, 50], L13273 = [1, 16, 33, 35], L13400 = [1, 17, 17, 51], L13644 = [1, 17, 33, 35], L13996 = [1, 18, 33, 35], L14687 = [1, 21, 33, 35], L14938 = [1, 22, 33, 35], L15216 = [1, 24, 33, 35], L15606 = [1, 27, 33, 35], L15752 = [1, 28, 33, 35], L15882 = [1, 30, 33, 35], L16086 = [1, 33, 33, 35], L16099 = [1, 33, 34, 35], L16111 = [1, 33, 35, 36], L16112 = [1, 33, 35, 39], L16113 = [1, 33, 35, 42], L16114 = [1, 33, 35, 45], L16115 = [1, 33, 35, 48], L16116 = [1, 33, 35, 51], L17356 = [2, 3, 32, 36], L18286 = [2, 9, 32, 36], L18810 = [2, 15, 32, 36], L18928 = [2, 17, 17, 51], L19007 = [2, 17, 32, 36], L19203 = [2, 21, 32, 36], L19346 = [2, 27, 32, 36], L19424 = [2, 32, 33, 36], L19433 = [2, 32, 36, 39], L19434 = [2, 32, 36, 45], L19435 = [2, 32, 36, 51], L19632 = [3, 9, 17, 21], L19634 = [3, 9, 17, 27], L19638 = [3, 9, 17, 39], L19643 = [3, 9, 21, 34], L19645 = [3, 9, 27, 34], L19649 = [3, 9, 34, 39], L19683 = [3, 15, 17, 21], L19690 = [3, 15, 21, 34], L19706 = [3, 17, 17, 51], L19818 = [6, 12, 17, 30], L19820 = [6, 12, 17, 36], L19821 = [6, 12, 17, 42], L19829 = [6, 17, 17, 51], L19830 = [6, 17, 18, 24]. q = 104 : L3258 = [1, 2, 25, 27], L3282 = [1, 2, 25, 51], L7170 = [1, 6, 25, 27], L7189 = [1, 6, 25, 51], L7735 = [1, 7, 17, 41], L7850 = [1, 7, 23, 41], L9606 = [1, 10, 25, 27], L9621 = [1, 10, 25, 51], L11323 = [1, 14, 25, 27], L11336 = [1, 14, 25, 51], L12203 = [1, 18, 25, 27], L12214 = [1, 18, 25, 51], L12723 = [1, 22, 25, 27], L12733 = [1, 22, 25, 51], L14269 = [2, 6, 13, 38], L14306 = [2, 10, 13, 18], L14307 = [2, 10, 13, 22], L14316 = [2, 10, 13, 46], L14511 = [4, 12, 13, 20], L14513 = [4, 12, 13, 28], L14515 = [4, 12, 13, 36], L14518 = [4, 12, 13, 44], L14596 = [8, 13, 16, 24], L14598 = [8, 13, 16, 32], L14600 = [8, 13, 16, 40], L14603 = [8, 13, 24, 32]. q = 105 : L720 = [0, 1, 21, 42], L867 = [0, 1, 34, 36], L873 = [0, 1, 35, 35], L1042 = [0, 3, 35, 35], L1066 = [0, 5, 21, 42], L2263 = [1, 1, 34, 36], L3463 = [1, 2, 33, 37], L3479 = [1, 2, 34, 36], L4619 = [1, 3, 32, 38], L4651 = [1, 3, 34, 36], L5530 = [1, 4, 31, 39], L5579 = [1, 4, 34, 36], L6494 = [1, 5, 30, 40], L6553 = [1, 5, 34, 36], L7366 = [1, 6, 29, 41], L7446 = [1, 6, 34, 36], L8181 = [1, 7, 28, 42], L8254 = [1, 7, 34, 36], L8752 = [1, 8, 27, 43], L8831 = [1, 8, 34, 36], L9404 = [1, 9, 34, 36], L9867 = [1, 10, 25, 45], L9990 = [1, 10, 34, 36], L10280 = [1, 11, 24, 46], L10353 = [1, 11, 34, 36], L10657 = [1, 12, 23, 47], L10808 = [1, 12, 34, 36], L11079 = [1, 14, 21, 49], L11234 = [1, 14, 34, 36], L11455 = [1, 15, 20, 50], L11669 = [1, 15, 34, 36], L11890 = [1, 16, 29, 31], L11896 = [1, 16, 29, 46], L12318 = [1, 18, 34, 36], L12594 = [1, 20, 34, 36], L12858 = [1, 21, 34, 36], L13193 = [1, 24, 34, 36], L13492 = [1, 27, 34, 36], L13723 = [1, 30, 34, 36], L13821 = [1, 33, 34, 36], L13883 = [1, 34, 35, 36], L13889 = [1, 34, 36, 36], L13890 = [1, 34, 36, 39], L13891 = [1, 34, 36, 42], L13892 = [1, 34, 36, 45], L13893 = [1, 34, 36, 48],
APPENDIX
21
Table 2. (continued) n = 4 q I indexes of I-isospectral families 108 {0} {280, 367}, {7193, 9085}, {7240, 8927}, {7245, 8921}, {7319, 9118}, {7328, 9124}, {7343, 9136} {2} {1035, 18429}, {5366, 18206, 18436}, {8638, 17908, 18437}, {11037, 17478, 18438}, {12987, 17000, 18439}, {14456, 16301, 18440}, {15571, 18441}, {19633, 20672, 20905}, {20318, 21001}, {21361, 21585, 21688}, {21920, 21999} 110 {0} {21235, 21237}, {21285, 21286}, {21343, 21345} {3} {846, 1341}, {12628, 21272}, {20469, 21356} 111 {2} {776, 12354}, {783, 835}, {2161, 12346}, {3496, 11131}, {3513, 12361}, {4776, 10196}, {4809, 10072}, {5780, 9350}, {5831, 12288}, {6589, 10808}, {6654, 12362}, {7518, 7584}, {8160, 11621}, {8230, 12184}, {8699, 12365}, {8784, 12363}, {9682, 12364}, {9735, 12093}, {10414, 12366}, {10482, 11871} L13894 = [1, 34, 36, 51], L14562 = [3, 5, 30, 40], L14846 = [3, 7, 28, 42], L15000 = [3, 10, 25, 45], L15092 = [3, 14, 21, 49], L15129 = [3, 15, 20, 50], L15269 = [5, 7, 14, 42], L15288 = [5, 7, 21, 28], L15297 = [5, 7, 28, 42], L15301 = [5, 7, 30, 40], L15344 = [5, 21, 30, 40], L15369 = [7, 14, 15, 42], L15378 = [7, 15, 21, 28], L15384 = [7, 15, 28, 42]. q = 108 : L280 = [0, 1, 5, 23], L367 = [0, 1, 7, 19], L1035 = [0, 1, 35, 37], L5366 = [1, 3, 35, 37], L7193 = [1, 5, 18, 23], L7240 = [1, 5, 19, 39], L7245 = [1, 5, 19, 45], L7319 = [1, 5, 23, 27], L7328 = [1, 5, 23, 36], L7343 = [1, 5, 23, 54], L8638 = [1, 6, 35, 37], L8921 = [1, 7, 11, 45], L8927 = [1, 7, 11, 51], L9085 = [1, 7, 18, 19], L9118 = [1, 7, 19, 27], L9124 = [1, 7, 19, 36], L9136 = [1, 7, 19, 54], L11037 = [1, 9, 35, 37], L12987 = [1, 12, 35, 37], L14456 = [1, 15, 35, 37], L15571 = [1, 18, 35, 37], L16301 = [1, 21, 35, 37], L17000 = [1, 24, 35, 37], L17478 = [1, 27, 35, 37], L17908 = [1, 30, 35, 37], L18206 = [1, 33, 35, 37], L18429 = [1, 35, 36, 37], L18436 = [1, 35, 37, 39], L18437 = [1, 35, 37, 42], L18438 = [1, 35, 37, 45], L18439 = [1, 35, 37, 48], L18440 = [1, 35, 37, 51], L18441 = [1, 35, 37, 54], L19633 = [2, 3, 34, 38], L20318 = [2, 9, 34, 38], L20672 = [2, 15, 34, 38], L20905 = [2, 21, 34, 38], L21001 = [2, 27, 34, 38], L21361 = [3, 4, 32, 40], L21585 = [3, 8, 28, 44], L21688 = [3, 16, 20, 52], L21920 = [4, 9, 32, 40], L21999 = [4, 27, 32, 40]. q = 110 : L846 = [0, 1, 22, 44], L1341 = [0, 5, 22, 44], L12628 = [1, 11, 33, 55], L20469 = [2, 11, 33, 55], L21235 = [5, 11, 15, 25], L21237 = [5, 11, 15, 35], L21272 = [5, 11, 33, 55], L21285 = [5, 15, 22, 25], L21286 = [5, 15, 22, 35], L21343 = [10, 11, 20, 30], L21345 = [10, 11, 20, 40], L21356 = [10, 11, 33, 55]. q = 111 : L776 = [0, 1, 36, 38], L783 = [0, 1, 37, 37], L835 = [0, 3, 37, 37], L2161 = [1, 1, 36, 38], L3496 = [1, 2, 35, 39], L3513 = [1, 2, 36, 38], L4776 = [1, 3, 34, 40], L4809 = [1, 3, 36, 38], L5780 = [1, 4, 33, 41], L5831 = [1, 4, 36, 38], L6589 = [1, 5, 32, 42], L6654 = [1, 5, 36, 38], L7518 = [1, 6, 31, 43], L7584 = [1, 6, 36, 38], L8160 = [1, 7, 30, 44], L8230 = [1, 7, 36, 38], L8699 = [1, 8, 29, 45], L8784 = [1, 8, 36, 38], L9350 = [1, 9, 36, 38], L9682 = [1, 10, 27, 47], L9735 = [1, 10, 36, 38], L10072 = [1, 12, 25, 49], L10196 = [1, 12, 36, 38], L10414 = [1, 13, 24, 50], L10482 = [1, 13, 36, 38], L10808 = [1, 15, 36, 38], L11131 = [1, 18, 36, 38], L11621 = [1, 21, 36, 38], L11871 = [1, 24, 36, 38], L12093 = [1, 27, 36, 38], L12184 = [1, 30, 36, 38], L12288 = [1, 33, 36, 38], L12346 = [1, 36, 36, 38], L12354 = [1, 36, 37, 38], L12361 = [1, 36, 38, 39], L12362 = [1, 36, 38, 42], L12363 = [1, 36, 38, 45], L12364 = [1, 36, 38, 48], L12365 = [1, 36, 38, 51], L12366 = [1, 36, 38, 54]. q = 112 : L3852 = [1, 2, 27, 29], L3878 = [1, 2, 27, 55], L6003 = [1, 4, 13, 43], L6015 = [1, 4, 13, 55], L6081 = [1, 4, 15, 41], L6094 = [1, 4, 15, 55], L7441 = [1, 5, 27, 35], L8531 = [1, 6, 27, 29], L8552 = [1, 6, 27, 55], L9066 = [1, 7, 11, 39], L11820 = [1, 10, 27, 29], L11838 = [1, 10, 27, 55], L12615 = [1, 12, 13, 43], L12622 = [1, 12, 13, 55], L12676 = [1, 12, 15, 41], L12686 = [1, 12, 15, 55], L13223 =
22
EMILIO A. LAURET
Table 2. (continued) n = 4 q I indexes of I-isospectral families 112 {0} {3852, 3878}, {6003, 6015}, {6081, 6094}, {7441, 9066}, {8531, 8552}, {11820, 11838}, {12615, 12622}, {12676, 12686}, {13223, 13230}, {13325, 13332}, {13856, 13870}, {14109, 14115}, {14152, 14159}, {15176, 15187}, {16304, 16314}, {16856, 16865}, {18655, 18661}, {19052, 19056} 114 {0} {10078, 10082}, {26712, 26716}, {26725, 26729}, {26939, 26944} {2} {1171, 21998}, {1178, 1603}, {3038, 22005}, {4591, 26472}, {4610, 21879}, {6067, 22009}, {6106, 15321}, {7437, 24794}, {7494, 22006}, {8513, 16670}, {8593, 21599}, {9737, 26480}, {9840, 21432}, {10652, 20736}, {10743, 22007}, {11626, 26412}, {11754, 21243}, {12563, 19377}, {12696, 17504}, {13420, 25505}, {13582, 22008}, {14720, 23592}, {14919, 20479}, {15820, 26283}, {16018, 20094}, {17039, 26479}, {17276, 22010}, {17758, 26050}, {18049, 18967}, {18223, 26821}, {18530, 22011}, {25733, 26954}, {25847, 26481} 115 {3} {685, 780} 117 {0} {15323, 15324}, {15326, 15331} {2} {895, 14992}, {5398, 14944, 14999}, {8560, 14889, 15000}, {10672, 14800, 15001}, {12083, 14682, 15002}, {13181, 14438, 15003}, {13805, 14214, 15004}, {15280, 15330} [1, 13, 14, 43], L13230 = [1, 13, 14, 55], L13325 = [1, 13, 20, 43], L13332 = [1, 13, 20, 55], L13856 = [1, 14, 27, 29], L13870 = [1, 14, 27, 55], L14109 = [1, 15, 17, 33], L14115 = [1, 15, 17, 47], L14152 = [1, 15, 20, 41], L14159 = [1, 15, 20, 55], L15176 = [1, 18, 27, 29], L15187 = [1, 18, 27, 55], L16304 = [1, 22, 27, 29], L16314 = [1, 22, 27, 55], L16856 = [1, 26, 27, 29], L16865 = [1, 26, 27, 55], L18655 = [2, 7, 21, 35], L18661 = [2, 7, 21, 49], L19052 = [4, 7, 12, 20], L19056 = [4, 7, 12, 36]. q = 114 : L1171 = [0, 1, 37, 39], L1178 = [0, 1, 38, 38], L1603 = [0, 3, 38, 38], L3038 = [1, 1, 37, 39], L4591 = [1, 2, 36, 40], L4610 = [1, 2, 37, 39], L6067 = [1, 3, 35, 41], L6106 = [1, 3, 37, 39], L7437 = [1, 4, 34, 42], L7494 = [1, 4, 37, 39], L8513 = [1, 5, 33, 43], L8593 = [1, 5, 37, 39], L9737 = [1, 6, 32, 44], L9840 = [1, 6, 37, 39], L10078 = [1, 7, 8, 50], L10082 = [1, 7, 8, 56], L10652 = [1, 7, 31, 45], L10743 = [1, 7, 37, 39], L11626 = [1, 8, 30, 46], L11754 = [1, 8, 37, 39], L12563 = [1, 9, 29, 47], L12696 = [1, 9, 37, 39], L13420 = [1, 10, 28, 48], L13582 = [1, 10, 37, 39], L14720 = [1, 12, 26, 50], L14919 = [1, 12, 37, 39], L15321 = [1, 13, 25, 51], L15820 = [1, 14, 24, 52], L16018 = [1, 14, 37, 39], L16670 = [1, 15, 37, 39], L17039 = [1, 16, 22, 54], L17276 = [1, 16, 37, 39], L17504 = [1, 17, 21, 55], L17758 = [1, 18, 20, 56], L18049 = [1, 18, 37, 39], L18223 = [1, 19, 19, 57], L18530 = [1, 19, 37, 39], L18967 = [1, 20, 37, 39], L19377 = [1, 21, 37, 39], L20094 = [1, 24, 37, 39], L20479 = [1, 26, 37, 39], L20736 = [1, 27, 37, 39], L21243 = [1, 30, 37, 39], L21432 = [1, 32, 37, 39], L21599 = [1, 33, 37, 39], L21879 = [1, 36, 37, 39], L21998 = [1, 37, 38, 39], L22005 = [1, 37, 39, 39], L22006 = [1, 37, 39, 42], L22007 = [1, 37, 39, 45], L22008 = [1, 37, 39, 48], L22009 = [1, 37, 39, 51], L22010 = [1, 37, 39, 54], L22011 = [1, 37, 39, 57], L23592 = [2, 3, 36, 40], L24794 = [2, 9, 36, 40], L25505 = [2, 15, 36, 40], L25733 = [2, 19, 19, 57], L25847 = [2, 19, 36, 40], L26050 = [2, 21, 36, 40], L26283 = [2, 27, 36, 40], L26412 = [2, 33, 36, 40], L26472 = [2, 36, 39, 40], L26479 = [2, 36, 40, 45], L26480 = [2, 36, 40, 51], L26481 = [2, 36, 40, 57], L26712 = [3, 9, 19, 33], L26716 = [3, 9, 19, 45], L26725 = [3, 9, 33, 38], L26729 = [3, 9, 38, 45], L26821 = [3, 19, 19, 57], L26939 = [6, 12, 19, 42], L26944 = [6, 18, 19, 24], L26954 = [6, 19, 19, 57]. q = 115 : L685 = [0, 1, 23, 46], L780 = [0, 5, 23, 46]. q = 117 : L895 = [0, 1, 38, 40], L5398 = [1, 3, 38, 40], L8560 = [1, 6, 38, 40], L10672 = [1, 9, 38, 40], L12083 = [1, 12, 38, 40], L13181 = [1, 15, 38, 40], L13805 = [1, 18, 38, 40], L14214 = [1, 21, 38, 40], L14438 = [1, 24, 38, 40], L14682 = [1, 27, 38, 40], L14800 = [1, 30, 38, 40], L14889 = [1, 33, 38, 40], L14944 = [1, 36, 38, 40], L14992 = [1, 38, 39, 40], L14999 = [1, 38, 40, 42], L15000 = [1, 38, 40, 45],
APPENDIX
23
Table 2. (continued) n = 4 q I indexes of I-isospectral families 119 {0} {11325, 11329}, {12455, 12456}, {12457, 12464} 120 {0} {5241, 5269}, {10722, 10731}, {11378, 11403}, {15663, 15678}, {15974, 15996}, {16563, 16569}, {18872, 18893}, {21212, 21231}, {23308, 23325}, {24988, 25002}, {29857, 29875}, {30813, 30826}, {31667, 31674}, {35314, 35316}, {35322, 35416}, {35334, 35336}, {35342, 35781}, {35348, 35350}, {35356, 35797}, {36644, 36651}, {36665, 36669}, {36936, 36941}, {37222, 37225}, {37426, 37429}, {37445, 37465}, {37575, 37577}, {37655, 37657}, {37855, 37868} {2} {1390, 28018}, {1405, 2029}, {3757, 28002}, {5487, 32982}, {5508, 28033}, {7131, 25582}, {7172, 18058}, {8667, 35736}, {8729, 27659}, {10142, 35812}, {10223, 28034}, {11528, 33337}, {11636, 27244}, {12627, 28038}, {12727, 27003}, {13798, 35909}, {13956, 28035}, {14966, 15121}, {16016, 35573}, {16190, 26387}, {16713, 28036}, {17356, 34127}, {17586, 25958}, {18804, 30021}, {19083, 28037}, {19634, 34638}, {19934, 24735}, {20392, 35206}, {20703, 24262}, {21050, 31882}, {21419, 23503}, {21654, 22905}, {21866, 36106}, {22305, 28039}, {30968, 37324}, {30995, 32543}, {36805, 37625}, {36812, 37037}, {37495, 37884}, {37501, 37699} {3} {1069, 2151}, {17544, 37632} L15001 = [1, 38, 40, 48], L15002 = [1, 38, 40, 51], L15003 = [1, 38, 40, 54], L15004 = [1, 38, 40, 57], L15280 = [3, 13, 26, 52], L15323 = [9, 13, 18, 27], L15324 = [9, 13, 18, 36], L15326 = [9, 13, 18, 45], L15330 = [9, 13, 26, 52], L15331 = [9, 13, 27, 36]. q = 119 : L11325 = [1, 16, 18, 33], L11329 = [1, 16, 18, 50], L12455 = [7, 14, 17, 35], L12456 = [7, 14, 17, 42], L12457 = [7, 14, 17, 49], L12464 = [7, 17, 21, 28]. q = 120 : L1069 = [0, 1, 24, 48], L1390 = [0, 1, 39, 41], L1405 = [0, 1, 40, 40], L2029 = [0, 3, 40, 40], L2151 = [0, 5, 24, 48], L3757 = [1, 1, 39, 41], L5241 = [1, 2, 29, 31], L5269 = [1, 2, 29, 59], L5487 = [1, 2, 38, 42], L5508 = [1, 2, 39, 41], L7131 = [1, 3, 37, 43], L7172 = [1, 3, 39, 41], L8667 = [1, 4, 36, 44], L8729 = [1, 4, 39, 41], L10142 = [1, 5, 35, 45], L10223 = [1, 5, 39, 41], L10722 = [1, 6, 11, 49], L10731 = [1, 6, 11, 59], L11378 = [1, 6, 29, 31], L11403 = [1, 6, 29, 59], L11528 = [1, 6, 34, 46], L11636 = [1, 6, 39, 41], L12627 = [1, 7, 33, 47], L12727 = [1, 7, 39, 41], L13798 = [1, 8, 32, 48], L13956 = [1, 8, 39, 41], L14966 = [1, 9, 31, 49], L15121 = [1, 9, 39, 41], L15663 = [1, 10, 19, 41], L15678 = [1, 10, 19, 59], L15974 = [1, 10, 29, 31], L15996 = [1, 10, 29, 59], L16016 = [1, 10, 30, 50], L16190 = [1, 10, 39, 41], L16563 = [1, 11, 18, 49], L16569 = [1, 11, 18, 59], L16713 = [1, 11, 29, 51], L17356 = [1, 12, 28, 52], L17544 = [1, 12, 36, 60], L17586 = [1, 12, 39, 41], L18058 = [1, 13, 27, 53], L18804 = [1, 14, 26, 54], L18872 = [1, 14, 29, 31], L18893 = [1, 14, 29, 59], L19083 = [1, 14, 39, 41], L19634 = [1, 15, 25, 55], L19934 = [1, 15, 39, 41], L20392 = [1, 16, 24, 56], L20703 = [1, 16, 39, 41], L21050 = [1, 18, 22, 58], L21212 = [1, 18, 29, 31], L21231 = [1, 18, 29, 59], L21419 = [1, 18, 39, 41], L21654 = [1, 19, 21, 59], L21866 = [1, 20, 20, 60], L22305 = [1, 20, 39, 41], L22905 = [1, 21, 39, 41], L23308 = [1, 22, 29, 31], L23325 = [1, 22, 29, 59], L23503 = [1, 22, 39, 41], L24262 = [1, 24, 39, 41], L24735 = [1, 25, 39, 41], L24988 = [1, 26, 29, 31], L25002 = [1, 26, 29, 59], L25582 = [1, 27, 39, 41], L25958 = [1, 28, 39, 41], L26387 = [1, 30, 39, 41], L27003 = [1, 33, 39, 41], L27244 = [1, 34, 39, 41], L27659 = [1, 36, 39, 41], L28002 = [1, 39, 39, 41], L28018 = [1, 39, 40, 41], L28033 = [1, 39, 41, 42], L28034 = [1, 39, 41, 45], L28035 = [1, 39, 41, 48], L28036 = [1, 39, 41, 51], L28037 = [1, 39, 41, 54], L28038 = [1, 39, 41, 57], L28039 = [1, 39, 41, 60], L29857 = [2, 3, 27, 33], L29875 = [2, 3, 27, 57], L30021 = [2, 3, 38, 42], L30813 = [2, 5, 25, 35], L30826 = [2, 5, 25, 55], L30968 = [2, 5, 35, 45], L30995 = [2, 5, 38, 42], L31667 = [2, 9, 21, 39], L31674 = [2, 9, 21, 51], L31882 = [2, 9, 38, 42], L32543 = [2, 15, 38, 42], L32982 = [2, 21, 38, 42], L33337 = [2, 27, 38, 42], L34127 = [3, 4, 36, 44], L34638 = [3, 5, 35, 45], L35206 = [3, 8, 32, 48], L35314 = [3, 9, 10, 21], L35316 = [3, 9, 10, 27], L35322 = [3, 9, 10, 45], L35334 = [3, 9, 20, 21], L35336 =
24
EMILIO A. LAURET
[3, 9, 20, 27], L35342 = [3, 9, 20, 45], L35348 = [3, 9, 21, 40], L35350 = [3, 9, 27, 40], L35356 = [3, 9, 40, 45], L35416 = [3, 10, 15, 21], L35573 = [3, 10, 30, 50], L35736 = [3, 12, 28, 52], L35781 = [3, 15, 20, 21], L35797 = [3, 15, 21, 40], L35812 = [3, 15, 25, 55], L35909 = [3, 16, 24, 56], L36106 = [3, 20, 20, 60], L36644 = [4, 5, 12, 28], L36651 = [4, 5, 12, 44], L36665 = [4, 5, 15, 25], L36669 = [4, 5, 15, 35], L36805 = [4, 5, 35, 45], L36812 = [4, 5, 36, 44], L36936 = [4, 12, 15, 28], L36941 = [4, 12, 15, 44], L37037 = [4, 15, 36, 44], L37222 = [5, 6, 15, 25], L37225 = [5, 6, 15, 35], L37324 = [5, 6, 35, 45], L37426 = [5, 8, 15, 25], L37429 = [5, 8, 15, 35], L37445 = [5, 8, 16, 48], L37465 = [5, 8, 24, 32], L37495 = [5, 8, 32, 48], L37501 = [5, 8, 35, 45], L37575 = [5, 12, 15, 25], L37577 = [5, 12, 15, 35], L37625 = [5, 12, 35, 45], L37632 = [5, 12, 36, 60], L37655 = [5, 15, 24, 25], L37657 = [5, 15, 24, 35], L37699 = [5, 24, 35, 45], L37855 = [8, 15, 16, 48], L37868 = [8, 15, 24, 32], L37884 = [8, 15, 32, 48].
APPENDIX
25
4. Computational results for dimension 9 q = 4 : L4 = [0, 0, 1, 1, 2], L8 = [0, 1, 1, 2, 2]. q = 7 : L6 = [0, 0, 1, 2, 3], L11 = [0, 1, 1, 2, 3]. q = 8 : L21 = [0, 1, 1, 3, 3], L47 = [1, 1, 3, 3, 4]. q = 11 : L9 = [0, 0, 1, 2, 3], L10 = [0, 0, 1, 2, 4]. q = 12 : L64 = [0, 1, 2, 3, 5], L67 = [0, 1, 2, 4, 5], L93 = [0, 2, 3, 3, 6], L99 = [0, 3, 3, 4, 6], L116 = [1, 1, 1, 3, 5], L146 = [1, 1, 3, 5, 5], L168 = [1, 2, 2, 4, 5], L182 = [1, 2, 4, 4, 5], L184 = [1, 2, 4, 5, 6], L200 = [1, 3, 4, 5, 6]. q = 13 : L11 = [0, 0, 1, 2, 3], L12 = [0, 0, 1, 2, 4], L13 = [0, 0, 1, 2, 5], L14 = [0, 0, 1, 3, 4], L34 = [0, 1, 2, 3, 4], L35 = [0, 1, 2, 3, 5], L36 = [0, 1, 2, 3, 6]. q = 14 : L66 = [0, 1, 2, 3, 4], L68 = [0, 1, 2, 3, 6], L71 = [0, 1, 2, 4, 6], L80 = [0, 1, 3, 5, 7], L96 = [0, 2, 4, 6, 7], L156 = [1, 1, 3, 5, 7], L198 = [1, 2, 3, 4, 7], L199 = [1, 2, 3, 5, 7], L200 = [1, 2, 3, 6, 7], L218 = [1, 3, 5, 7, 7]. q = 15 : L18 = [0, 0, 1, 2, 6], L20 = [0, 0, 1, 3, 4], L66 = [0, 1, 2, 5, 6], L72 = [0, 1, 3, 4, 5], L175 = [1, 2, 3, 6, 6], L179 = [1, 2, 5, 5, 6], L187 = [1, 3, 3, 4, 6], L191 = [1, 3, 4, 5, 5]. q = 16 : L78 = [0, 1, 2, 3, 5], L80 = [0, 1, 2, 3, 7], L96 = [0, 1, 3, 5, 7], L180 = [1, 1, 3, 3, 5], L181 = [1, 1, 3, 3, 7], L233 = [1, 2, 2, 3, 5], L235 = [1, 2, 2, 3, 7], L250 = [1, 2, 3, 4, 5], L252 = [1, 2, 3, 4, 7], L256 = [1, 2, 3, 5, 8], L258 = [1, 2, 3, 7, 8], L282 = [1, 3, 4, 5, 7], L285 = [1, 3, 5, 7, 8]. q = 17 : L16 = [0, 0, 1, 2, 5], L17 = [0, 0, 1, 2, 6], L18 = [0, 0, 1, 2, 7], L19 = [0, 0, 1, 3, 4], L55 = [0, 1, 2, 3, 5], L56 = [0, 1, 2, 3, 6], L57 = [0, 1, 2, 3, 7], L58 = [0, 1, 2, 3, 8], L59 = [0, 1, 2, 4, 5], L62 = [0, 1, 2, 6, 7], L63 = [0, 1, 3, 4, 5], L156 = [1, 2, 3, 4, 5], L157 = [1, 2, 3, 4, 6], L158 = [1, 2, 3, 4, 7], L159 = [1, 2, 3, 4, 8], L160 = [1, 2, 3, 5, 6], L161 = [1, 2, 3, 5, 8], L162 = [1, 2, 3, 6, 7]. q = 18 : L117 = [0, 1, 2, 4, 5], L119 = [0, 1, 2, 4, 7], L407 = [1, 2, 3, 4, 5], L409 = [1, 2, 3, 4, 7], L429 = [1, 2, 4, 5, 6], L432 = [1, 2, 4, 5, 9], L434 = [1, 2, 4, 6, 7], L437 = [1, 2, 4, 7, 9]. q = 19 : L19 = [0, 0, 1, 2, 7], L21 = [0, 0, 1, 3, 4], L67 = [0, 1, 2, 3, 5], L68 = [0, 1, 2, 3, 6], L70 = [0, 1, 2, 3, 8], L71 = [0, 1, 2, 3, 9], L72 = [0, 1, 2, 4, 5], L74 = [0, 1, 2, 4, 8], L77 = [0, 1, 2, 6, 8], Table 3. n = 5 q 4 7 8 11 12
17
I {2, 3} {3, 4} {2, 3} {0} {2, 3} {4} {0} {0, 1} {0} {3, 4} {0} {0} {2, 3} {2, 3, 4} {0}
18
{0, 1} {0}
13 14 15 16
indexes of I-isospectral families {4, 8} {6, 11} {21, 47} {9, 10} {67, 184}, {93, 99}, {168, 182} {64, 200}, {116, 146} {11, 12}, {13, 14}, {34, 35, 36} {34, 35} {66, 68}, {198, 200} {71, 96}, {80, 199}, {156, 218} {18, 20}, {66, 72}, {175, 187}, {179, 191} {78, 80}, {180, 181}, {233, 235}, {250, 252}, {256, 258} {96, 282, 285} {96, 285} {16, 17}, {18, 19}, {55, 56, 58}, {62, 63}, {156, 157, 158, 159, 160}, {161, 162} {57, 59}, {157, 158} {117, 119}, {407, 409}, {429, 434}, {432, 437}
26
EMILIO A. LAURET
Table 3. (continued) n = 5 q 19
I {0}
indexes of I-isospectral families {19, 21}, {67, 68, 71}, {70, 72, 74}, {77, 79}, {209, 210}, {211, 213, 215, 217}, {214, 216, 218, 220}, {219, 222} {0, 1} {216, 218} 20 {0} {355, 357}, {505, 507} {2, 3} {188, 660}, {239, 250}, {541, 658}, {632, 655} 21 {0} {110, 112}, {121, 135}, {384, 389}, {385, 387}, {390, 394}, {391, 402}, {401, 459}, {404, 408}, {426, 462} {3, 4} {143, 174} 22 {0} {33, 34}, {166, 177}, {182, 184}, {242, 243}, {567, 570}, {577, 600}, {582, 623}, {624, 641}, {662, 686}, {694, 697}, {818, 819} 23 {0} {102, 104}, {108, 110}, {114, 121}, {357, 358}, {361, 362}, {365, 369}, {368, 371, 373}, {376, 378, 386, 392}, {383, 385}, {388, 390}, {391, 396} L79 = [0, 1, 3, 4, 5], L209 = [1, 2, 3, 4, 5], L210 = [1, 2, 3, 4, 6], L211 = [1, 2, 3, 4, 7], L213 = [1, 2, 3, 4, 9], L214 = [1, 2, 3, 5, 6], L215 = [1, 2, 3, 5, 7], L216 = [1, 2, 3, 5, 9], L217 = [1, 2, 3, 6, 7], L218 = [1, 2, 3, 6, 8], L219 = [1, 2, 3, 7, 8], L220 = [1, 2, 3, 7, 9], L222 = [1, 2, 5, 6, 8]. q = 20 : L188 = [0, 1, 4, 6, 9], L239 = [0, 2, 5, 5, 10], L250 = [0, 4, 5, 5, 10], L355 = [1, 1, 3, 3, 7], L357 = [1, 1, 3, 3, 9], L505 = [1, 2, 3, 4, 7], L507 = [1, 2, 3, 4, 9], L541 = [1, 2, 4, 6, 9], L632 = [1, 4, 4, 6, 9], L655 = [1, 4, 6, 6, 9], L658 = [1, 4, 6, 8, 9], L660 = [1, 4, 6, 9, 10]. q = 21 : L110 = [0, 1, 2, 4, 5], L112 = [0, 1, 2, 4, 8], L121 = [0, 1, 2, 6, 9], L135 = [0, 1, 3, 4, 6], L143 = [0, 1, 3, 6, 9], L174 = [0, 3, 6, 7, 9], L384 = [1, 2, 3, 4, 8], L385 = [1, 2, 3, 4, 9], L387 = [1, 2, 3, 5, 6], L389 = [1, 2, 3, 5, 8], L390 = [1, 2, 3, 5, 9], L391 = [1, 2, 3, 5, 10], L394 = [1, 2, 3, 6, 8], L401 = [1, 2, 3, 8, 9], L402 = [1, 2, 3, 8, 10], L404 = [1, 2, 4, 5, 7], L408 = [1, 2, 4, 7, 8], L426 = [1, 2, 6, 7, 9], L459 = [1, 3, 4, 5, 6], L462 = [1, 3, 4, 6, 7]. q = 22 : L33 = [0, 0, 1, 3, 5], L34 = [0, 0, 1, 3, 7], L166 = [0, 1, 2, 8, 9], L177 = [0, 1, 3, 4, 8], L182 = [0, 1, 3, 5, 11], L184 = [0, 1, 3, 7, 11], L242 = [0, 2, 4, 6, 11], L243 = [0, 2, 4, 8, 11], L567 = [1, 2, 3, 4, 9], L570 = [1, 2, 3, 5, 6], L577 = [1, 2, 3, 6, 8], L582 = [1, 2, 3, 7, 10], L600 = [1, 2, 4, 5, 6], L623 = [1, 2, 5, 6, 7], L624 = [1, 2, 5, 6, 8], L641 = [1, 2, 6, 7, 10], L662 = [1, 2, 8, 9, 11], L686 = [1, 3, 4, 8, 11], L694 = [1, 3, 5, 11, 11], L697 = [1, 3, 7, 11, 11], L818 = [2, 4, 6, 11, 11], L819 = [2, 4, 8, 11, 11]. q = 23 : L102 = [0, 1, 2, 4, 5], L104 = [0, 1, 2, 4, 8], L108 = [0, 1, 2, 5, 7], L110 = [0, 1, 2, 5, 9], L114 = [0, 1, 2, 6, 10], L121 = [0, 1, 3, 4, 9], L357 = [1, 2, 3, 4, 7], L358 = [1, 2, 3, 4, 8], L361 = [1, 2, 3, 4, 11], L362 = [1, 2, 3, 5, 6], L365 = [1, 2, 3, 5, 9], L368 = [1, 2, 3, 6, 7], L369 = [1, 2, 3, 6, 8], L371 = [1, 2, 3, 6, 10], L373 = [1, 2, 3, 7, 9], L376 = [1, 2, 3, 8, 10], L378 = [1, 2, 3, 9, 10], L383 = [1, 2, 4, 5, 11], L385 = [1, 2, 4, 7, 11], L386 = [1, 2, 4, 9, 10], L388 = [1, 2, 5, 6, 8], L390 = [1, 2, 5, 6, 10], L391 = [1, 2, 6, 7, 10], L392 = [1, 2, 6, 8, 9], L396 = [1, 3, 4, 5, 7]. q = 24 : L41 = [0, 0, 1, 3, 5], L43 = [0, 0, 1, 3, 7], L213 = [0, 1, 2, 5, 7], L217 = [0, 1, 2, 5, 11], L254 = [0, 1, 3, 4, 5], L256 = [0, 1, 3, 4, 7], L262 = [0, 1, 3, 5, 6], L264 = [0, 1, 3, 5, 8], L267 = [0, 1, 3, 5, 12], L269 = [0, 1, 3, 6, 7], L275 = [0, 1, 3, 7, 8], L277 = [0, 1, 3, 7, 12], L333 = [0, 1, 5, 7, 11], L846 = [1, 2, 2, 5, 7], L850 = [1, 2, 2, 5, 11], L856 = [1, 2, 2, 6, 10], L899 = [1, 2, 3, 5, 10], L911 = [1, 2, 3, 7, 10], L938 = [1, 2, 4, 5, 7], L942 = [1, 2, 4, 5, 11], L969 = [1, 2, 5, 6, 7], L973 = [1, 2, 5, 6, 11], L975 = [1, 2, 5, 7, 8], L979 = [1, 2, 5, 7, 12], L983 = [1, 2, 5, 8, 11], L988 = [1, 2, 5, 11, 12], L1009 = [1, 2, 6, 10, 10], L1071 = [1, 3, 3, 5, 9], L1082 = [1, 3, 3, 7, 9], L1099 = [1, 3, 4, 4, 5], L1101 = [1, 3, 4, 4, 7], L1107 = [1, 3, 4, 5, 6], L1109 = [1, 3, 4, 5, 8], L1112 = [1, 3, 4, 5, 12], L1114 = [1, 3, 4, 6, 7], L1120 = [1, 3, 4, 7, 8], L1122 = [1, 3, 4, 7, 12], L1137 = [1, 3, 5, 6, 6], L1139 = [1, 3, 5, 6, 8], L1142 = [1, 3, 5, 6, 12],
APPENDIX
27
Table 3. (continued) n = 5 q 24
I {0}
indexes of I-isospectral families {41, 43}, {213, 217}, {254, 256}, {262, 269}, {264, 275}, {267, 277}, {846, 850}, {899, 911}, {938, 942}, {969, 973}, {975, 983}, {979, 988}, {1071, 1082}, {1099, 1101}, {1107, 1114}, {1109, 1120}, {1112, 1122}, {1137, 1155}, {1139, 1161}, {1142, 1163}, {1147, 1178}, {1150, 1180}, {1153, 1183} {2, 3} {333, 1327}, {1254, 1325}, {1572, 1582} {4} {856, 1009} 25 {0} {133, 146}, {141, 142}, {143, 145, 157}, {499, 514}, {504, 508}, {509, 511}, {510, 513, 516, 524}, {515, 519, 521}, {518, 535}, {523, 563}, {529, 534}, {538, 554}, {565, 567} {0, 1} {518, 535}, {519, 521} 26 {0} {39, 42}, {40, 44}, {218, 244}, {233, 282}, {246, 247}, {249, 251, 252}, {254, 263}, {257, 269}, {360, 361}, {362, 364}, {902, 961}, {952, 965}, {994, 1045}, {1020, 1088}, {1044, 1077}, {1057, 1181}, {1093, 1095}, {1099, 1104, 1105}, {1108, 1129}, {1114, 1141}, {1352, 1353, 1354}, {1355, 1356}, {1357, 1359} {0, 1} {251, 252}, {1104, 1105}, {1352, 1353}
L1147 = [1, 3, 5, 8, 8], L1150 = [1, 3, 5, 8, 12], L1153 = [1, 3, 5, 12, 12], L1155 = [1, 3, 6, 6, 7], L1161 = [1, 3, 6, 7, 8], L1163 = [1, 3, 6, 7, 12], L1178 = [1, 3, 7, 8, 8], L1180 = [1, 3, 7, 8, 12], L1183 = [1, 3, 7, 12, 12], L1254 = [1, 4, 5, 7, 11], L1325 = [1, 5, 7, 8, 11], L1327 = [1, 5, 7, 11, 12], L1572 = [3, 3, 4, 9, 9], L1582 = [3, 3, 8, 9, 9]. q = 25 : L133 = [0, 1, 2, 4, 11], L141 = [0, 1, 2, 6, 7], L142 = [0, 1, 2, 6, 8], L143 = [0, 1, 2, 6, 9], L145 = [0, 1, 2, 6, 11], L146 = [0, 1, 2, 7, 8], L157 = [0, 1, 3, 4, 9], L499 = [1, 2, 3, 4, 11], L504 = [1, 2, 3, 5, 8], L508 = [1, 2, 3, 5, 12], L509 = [1, 2, 3, 6, 7], L510 = [1, 2, 3, 6, 8], L511 = [1, 2, 3, 6, 9], L513 = [1, 2, 3, 6, 11], L514 = [1, 2, 3, 6, 12], L515 = [1, 2, 3, 7, 8], L516 = [1, 2, 3, 7, 9], L518 = [1, 2, 3, 7, 11], L519 = [1, 2, 3, 7, 12], L521 = [1, 2, 3, 8, 12], L523 = [1, 2, 3, 9, 11], L524 = [1, 2, 3, 9, 12], L529 = [1, 2, 4, 5, 7], L534 = [1, 2, 4, 5, 12], L535 = [1, 2, 4, 7, 8], L538 = [1, 2, 4, 9, 10], L554 = [1, 2, 5, 7, 8], L563 = [1, 2, 6, 7, 8], L565 = [1, 2, 6, 7, 11], L567 = [1, 2, 6, 8, 11]. q = 26 : L39 = [0, 0, 1, 3, 5], L40 = [0, 0, 1, 3, 7], L42 = [0, 0, 1, 3, 9], L44 = [0, 0, 1, 3, 11], L218 = [0, 1, 2, 7, 8], L233 = [0, 1, 2, 10, 11], L244 = [0, 1, 3, 4, 8], L246 = [0, 1, 3, 4, 10], L247 = [0, 1, 3, 4, 12], L249 = [0, 1, 3, 5, 7], L251 = [0, 1, 3, 5, 9], L252 = [0, 1, 3, 5, 11], L254 = [0, 1, 3, 5, 13], L257 = [0, 1, 3, 7, 13], L263 = [0, 1, 3, 9, 13], L269 = [0, 1, 3, 11, 13], L282 = [0, 1, 4, 5, 8], L360 = [0, 2, 4, 6, 13], L361 = [0, 2, 4, 8, 13], L362 = [0, 2, 4, 10, 13], L364 = [0, 2, 6, 8, 13], L902 = [1, 2, 3, 9, 12], L952 = [1, 2, 4, 10, 11], L961 = [1, 2, 5, 6, 7], L965 = [1, 2, 5, 6, 12], L994 = [1, 2, 6, 7, 8], L1020 = [1, 2, 7, 8, 13], L1044 = [1, 2, 9, 10, 11], L1045 = [1, 2, 9, 10, 12], L1057 = [1, 2, 10, 11, 13], L1077 = [1, 3, 4, 5, 8], L1088 = [1, 3, 4, 8, 13], L1093 = [1, 3, 4, 10, 13], L1095 = [1, 3, 4, 12, 13], L1099 = [1, 3, 5, 7, 13], L1104 = [1, 3, 5, 9, 13], L1105 = [1, 3, 5, 11, 13], L1108 = [1, 3, 5, 13, 13], L1114 = [1, 3, 7, 13, 13], L1129 = [1, 3, 9, 13, 13], L1141 = [1, 3, 11, 13, 13], L1181 = [1, 4, 5, 8, 13], L1352 = [2, 4, 6, 8, 13], L1353 = [2, 4, 6, 10, 13], L1354 = [2, 4, 6, 12, 13], L1355 = [2, 4, 6, 13, 13], L1356 = [2, 4, 8, 13, 13], L1357 = [2, 4, 10, 13, 13], L1359 = [2, 6, 8, 13, 13]. q = 27 : L162 = [0, 1, 2, 4, 11], L165 = [0, 1, 2, 5, 7], L168 = [0, 1, 2, 5, 10], L177 = [0, 1, 2, 7, 8], L179 = [0, 1, 2, 7, 10], L687 = [1, 2, 3, 5, 10], L690 = [1, 2, 3, 5, 13], L704 = [1, 2, 3, 7, 13], L716 = [1, 2, 3, 10, 13], L720 = [1, 2, 4, 5, 7], L721 = [1, 2, 4, 5, 8], L723 = [1, 2, 4, 5, 10], L724 = [1, 2, 4, 5, 11], L727 = [1, 2, 4, 7, 8], L730 = [1, 2, 4, 7, 11], L732 = [1, 2, 4, 7, 13], L736 = [1, 2, 4, 9, 11], L738 =
28
EMILIO A. LAURET
Table 3. (continued) n = 5 q 27
28
29 30
31
I {0}
indexes of I-isospectral families {162, 165, 168}, {177, 179}, {687, 690}, {704, 716}, {720, 721}, {723, 724, 727, 732}, {736, 749, 755}, {738, 748}, {739, 751}, {781, 786} {0, 1} {723, 724}, {0, 1, 2} {730, 750} {0} {43, 46}, {299, 307}, {304, 319}, {1134, 1141}, {1399, 1411}, {1433, 1451}, {1438, 1463}, {1448, 1496}, {1915, 1917} {0, 1} {301, 302}, {1435, 1436}, {1444, 1445} {2, 3} {405, 1749}, {488, 502}, {1293, 1747}, {1599, 1744}, {1706, 1740} {3, 4} {365, 503}, {1300, 1938} {0} {164, 171}, {215, 216}, {728, 750, 755}, {799, 815} {0} {55, 59}, {423, 427}, {444, 463}, {448, 469}, {800, 815}, {805, 837}, {1814, 1820}, {1817, 1819}, {2140, 2155}, {2241, 2245}, {2262, 2281}, {2266, 2287}, {2311, 2334}, {2354, 2413}, {2358, 2419}, {2366, 2431}, {3413, 3463}, {3520, 3560}, {3532, 3586}, {3535, 3588}, {3547, 3644}, {3550, 3646} {0} {874, 910}, {969, 983, 992}, {1014, 1017}
[1, 2, 4, 10, 11], L739 = [1, 2, 4, 10, 12], L748 = [1, 2, 5, 7, 8], L749 = [1, 2, 5, 7, 9], L750 = [1, 2, 5, 7, 11], L751 = [1, 2, 5, 7, 12], L755 = [1, 2, 5, 9, 10], L781 = [1, 2, 7, 8, 9], L786 = [1, 2, 7, 9, 10]. q = 28 : L43 = [0, 0, 1, 3, 5], L46 = [0, 0, 1, 3, 9], L299 = [0, 1, 3, 5, 7], L301 = [0, 1, 3, 5, 9], L302 = [0, 1, 3, 5, 11], L304 = [0, 1, 3, 5, 14], L307 = [0, 1, 3, 7, 9], L319 = [0, 1, 3, 9, 14], L365 = [0, 1, 4, 8, 12], L405 = [0, 1, 6, 8, 13], L488 = [0, 2, 7, 7, 14], L502 = [0, 4, 7, 7, 14], L503 = [0, 4, 7, 8, 12], L1134 = [1, 2, 3, 5, 10], L1141 = [1, 2, 3, 6, 9], L1293 = [1, 2, 6, 8, 13], L1300 = [1, 2, 6, 10, 14], L1399 = [1, 3, 4, 5, 12], L1411 = [1, 3, 4, 8, 9], L1433 = [1, 3, 5, 7, 7], L1435 = [1, 3, 5, 7, 9], L1436 = [1, 3, 5, 7, 11], L1438 = [1, 3, 5, 7, 14], L1444 = [1, 3, 5, 9, 14], L1445 = [1, 3, 5, 11, 14], L1448 = [1, 3, 5, 14, 14], L1451 = [1, 3, 7, 7, 9], L1463 = [1, 3, 7, 9, 14], L1496 = [1, 3, 9, 14, 14], L1599 = [1, 4, 6, 8, 13], L1706 = [1, 6, 6, 8, 13], L1740 = [1, 6, 8, 8, 13], L1744 = [1, 6, 8, 10, 13], L1747 = [1, 6, 8, 12, 13], L1749 = [1, 6, 8, 13, 14], L1915 = [2, 4, 6, 7, 8], L1917 = [2, 4, 6, 7, 12], L1938 = [2, 6, 7, 10, 14]. q = 29 : L164 = [0, 1, 2, 4, 11], L171 = [0, 1, 2, 5, 10], L215 = [0, 1, 4, 5, 7], L216 = [0, 1, 4, 5, 13], L728 = [1, 2, 3, 8, 13], L750 = [1, 2, 4, 7, 8], L755 = [1, 2, 4, 7, 14], L799 = [1, 2, 7, 8, 9], L815 = [1, 2, 10, 11, 12]. q = 30 : L55 = [0, 0, 1, 3, 7], L59 = [0, 0, 1, 3, 11], L423 = [0, 1, 3, 5, 7], L427 = [0, 1, 3, 5, 11], L444 = [0, 1, 3, 7, 10], L448 = [0, 1, 3, 7, 15], L463 = [0, 1, 3, 10, 11], L469 = [0, 1, 3, 11, 15], L800 = [0, 2, 4, 5, 12], L805 = [0, 2, 4, 12, 15], L815 = [0, 2, 5, 6, 8], L837 = [0, 2, 6, 8, 15], L1814 = [1, 2, 4, 7, 8], L1817 = [1, 2, 4, 7, 11], L1819 = [1, 2, 4, 7, 13], L1820 = [1, 2, 4, 7, 14], L2140 = [1, 3, 3, 7, 9], L2155 = [1, 3, 3, 9, 11], L2241 = [1, 3, 5, 5, 7], L2245 = [1, 3, 5, 5, 11], L2262 = [1, 3, 5, 7, 10], L2266 = [1, 3, 5, 7, 15], L2281 = [1, 3, 5, 10, 11], L2287 = [1, 3, 5, 11, 15], L2311 = [1, 3, 6, 7, 12], L2334 = [1, 3, 6, 11, 12], L2354 = [1, 3, 7, 10, 10], L2358 = [1, 3, 7, 10, 15], L2366 = [1, 3, 7, 15, 15], L2413 = [1, 3, 10, 10, 11], L2419 = [1, 3, 10, 11, 15], L2431 = [1, 3, 11, 15, 15], L3413 = [2, 3, 4, 9, 12], L3463 = [2, 3, 6, 8, 9], L3520 = [2, 4, 5, 5, 12], L3532 = [2, 4, 5, 10, 12], L3535 = [2, 4, 5, 12, 15], L3547 = [2, 4, 10, 12, 15], L3550 = [2, 4, 12, 15, 15], L3560 = [2, 5, 5, 6, 8], L3586 = [2, 5, 6, 8, 10], L3588 = [2, 5, 6, 8, 15], L3644 = [2, 6, 8, 10, 15], L3646 = [2, 6, 8, 15, 15]. q = 31 : L874 = [1, 2, 3, 8, 11], L910 = [1, 2, 4, 7, 12], L969 = [1, 2, 6, 8, 14], L983 = [1, 2, 7, 9, 10], L992 = [1, 2, 8, 10, 13], L1014 = [1, 3, 4, 7, 9], L1017 = [1, 3, 4, 9, 10].
APPENDIX
29
Table 3. (continued) n = 5 q 32
I {0}
indexes of I-isospectral families {47, 49}, {301, 307}, {357, 359}, {366, 373}, {371, 382}, {480, 483}, {1151, 1154}, {1396, 1402}, {1459, 1468}, {1503, 1614}, {1505, 1610}, {1561, 1567}, {1652, 1811}, {1670, 1675}, {1672, 1686}, {1708, 1714}, {1716, 1726}, {1718, 1734}, {1722, 1739}, {1862, 1877}, {1904, 1911}, {1905, 1906, 1908, 1918}, {1909, 1919}, {1922, 1929}, {1936, 1954}, {1941, 1963}, {1952, 1987}, {2119, 2122}, {2253, 2256}, {2283, 2286}, {2289, 2295}, {2291, 2297} {0, 1} {362, 367}, {1855, 1860}, {1887, 1925}, {1906, 1908}, {1914, 1937}, {1930, 1943} {2, 3} {513, 2368}, {2152, 2366} 33 {0} {41, 56}, {250, 257}, {261, 273}, {301, 387}, {490, 492}, {1354, 1402}, {1376, 1416}, {1421, 1481}, {1460, 1752}, {1563, 1855}, {2077, 2080} q = 32 : L47 = [0, 0, 1, 3, 7], L49 = [0, 0, 1, 3, 9], L301 = [0, 1, 2, 7, 9], L307 = [0, 1, 2, 7, 15], L357 = [0, 1, 3, 5, 7], L359 = [0, 1, 3, 5, 9], L362 = [0, 1, 3, 5, 13], L366 = [0, 1, 3, 7, 8], L367 = [0, 1, 3, 7, 9], L371 = [0, 1, 3, 7, 16], L373 = [0, 1, 3, 8, 9], L382 = [0, 1, 3, 9, 16], L480 = [0, 1, 6, 7, 9], L483 = [0, 1, 6, 7, 15], L513 = [0, 1, 7, 9, 15], L1151 = [1, 1, 7, 7, 9], L1154 = [1, 1, 7, 7, 15], L1396 = [1, 2, 2, 7, 9], L1402 = [1, 2, 2, 7, 15], L1459 = [1, 2, 3, 5, 10], L1468 = [1, 2, 3, 6, 9], L1503 = [1, 2, 3, 10, 13], L1505 = [1, 2, 3, 10, 15], L1561 = [1, 2, 4, 7, 9], L1567 = [1, 2, 4, 7, 15], L1610 = [1, 2, 5, 6, 11], L1614 = [1, 2, 5, 6, 15], L1652 = [1, 2, 5, 13, 14], L1670 = [1, 2, 6, 7, 9], L1672 = [1, 2, 6, 7, 11], L1675 = [1, 2, 6, 7, 15], L1686 = [1, 2, 6, 9, 11], L1708 = [1, 2, 7, 8, 9], L1714 = [1, 2, 7, 8, 15], L1716 = [1, 2, 7, 9, 10], L1718 = [1, 2, 7, 9, 12], L1722 = [1, 2, 7, 9, 16], L1726 = [1, 2, 7, 10, 15], L1734 = [1, 2, 7, 12, 15], L1739 = [1, 2, 7, 15, 16], L1811 = [1, 2, 11, 13, 14], L1855 = [1, 3, 4, 5, 13], L1860 = [1, 3, 4, 7, 9], L1862 = [1, 3, 4, 7, 12], L1877 = [1, 3, 4, 9, 12], L1887 = [1, 3, 4, 11, 13], L1904 = [1, 3, 5, 7, 8], L1905 = [1, 3, 5, 7, 9], L1906 = [1, 3, 5, 7, 11], L1908 = [1, 3, 5, 7, 13], L1909 = [1, 3, 5, 7, 16], L1911 = [1, 3, 5, 8, 9], L1914 = [1, 3, 5, 8, 13], L1918 = [1, 3, 5, 9, 11], L1919 = [1, 3, 5, 9, 16], L1922 = [1, 3, 5, 11, 15], L1925 = [1, 3, 5, 12, 13], L1929 = [1, 3, 5, 13, 15], L1930 = [1, 3, 5, 13, 16], L1936 = [1, 3, 7, 8, 8], L1937 = [1, 3, 7, 8, 9], L1941 = [1, 3, 7, 8, 16], L1943 = [1, 3, 7, 9, 16], L1952 = [1, 3, 7, 16, 16], L1954 = [1, 3, 8, 8, 9], L1963 = [1, 3, 8, 9, 16], L1987 = [1, 3, 9, 16, 16], L2119 = [1, 4, 6, 7, 9], L2122 = [1, 4, 6, 7, 15], L2152 = [1, 4, 7, 9, 15], L2253 = [1, 6, 6, 7, 9], L2256 = [1, 6, 6, 7, 15], L2283 = [1, 6, 7, 8, 9], L2286 = [1, 6, 7, 8, 15], L2289 = [1, 6, 7, 9, 12], L2291 = [1, 6, 7, 9, 16], L2295 = [1, 6, 7, 12, 15], L2297 = [1, 6, 7, 15, 16], L2366 = [1, 7, 9, 12, 15], L2368 = [1, 7, 9, 15, 16]. q = 33 : L41 = [0, 0, 1, 2, 14], L56 = [0, 0, 1, 4, 5], L250 = [0, 1, 2, 4, 13], L257 = [0, 1, 2, 5, 10], L261 = [0, 1, 2, 5, 14], L273 = [0, 1, 2, 7, 8], L301 = [0, 1, 2, 11, 14], L387 = [0, 1, 4, 5, 11], L490 = [0, 3, 6, 9, 11], L492 = [0, 3, 6, 11, 12], L1354 = [1, 2, 4, 7, 14], L1376 = [1, 2, 4, 11, 13], L1402 = [1, 2, 5, 7, 13], L1416 = [1, 2, 5, 10, 11], L1421 = [1, 2, 5, 11, 14], L1460 = [1, 2, 6, 9, 15], L1481 = [1, 2, 7, 8, 11], L1563 = [1, 2, 11, 11, 14], L1752 = [1, 3, 6, 9, 10], L1855 = [1, 4, 5, 11, 11], L2077 = [3, 6, 9, 11, 11], L2080 = [3, 6, 11, 11, 12]. q = 34 : L51 = [0, 0, 1, 3, 7], L53 = [0, 0, 1, 3, 9], L56 = [0, 0, 1, 3, 13], L74 = [0, 0, 1, 5, 7], L413 = [0, 1, 3, 5, 9], L414 = [0, 1, 3, 5, 11], L416 = [0, 1, 3, 5, 13], L418 = [0, 1, 3, 5, 15], L422 = [0, 1, 3, 7, 9], L424 = [0, 1, 3, 7, 11], L426 = [0, 1, 3, 7, 15], L428 = [0, 1, 3, 7, 17], L439 = [0, 1, 3, 9, 17], L456 = [0, 1, 3, 13, 17], L540 = [0, 1, 5, 7, 17], L568 = [0, 1, 6, 9, 10], L571 = [0, 1, 6, 9, 14], L582 = [0, 1, 6, 12, 13], L590 = [0, 1, 6, 14, 15], L682 = [0, 2, 4, 10, 17], L683 = [0, 2, 4, 12, 17], L684 = [0, 2, 4, 14, 17], L686 = [0, 2, 6, 8, 17], L1876 = [1, 2, 4, 8, 9], L1882 = [1, 2, 4, 8, 15], L1888 = [1, 2, 4, 9, 13], L1890 = [1, 2, 4, 9, 15], L2322 = [1, 3, 5, 7, 9], L2323 = [1, 3, 5, 7, 11], L2325 = [1, 3, 5, 7, 13], L2326 = [1, 3, 5, 7, 15], L2337 = [1, 3, 5, 9, 11], L2338 = [1, 3, 5, 9, 13], L2340 = [1, 3, 5, 9, 17], L2342 = [1, 3, 5, 11, 15],
30
EMILIO A. LAURET
Table 3. (continued) n = 5 q 34
I {0}
35
{0, 1} {0}
{3, 4} 36 {0} {0, 1} {2, 3}
37
{4} {0}
indexes of I-isospectral families {51, 53}, {56, 74}, {413, 416}, {414, 418, 422}, {428, 439}, {456, 540}, {568, 571}, {582, 590}, {682, 683}, {684, 686}, {1876, 1882}, {1888, 1890}, {2322, 2325}, {2323, 2326, 2337, 2338, 2342}, {2340, 2351}, {2344, 2356, 2369}, {2385, 2422}, {2476, 2756}, {2852, 2875}, {2855, 2858}, {2856, 2865}, {2895, 2912}, {3122, 3123, 3125}, {3131, 3133}, {3132, 3136}, {3134, 3137} {424, 426}, {2326, 2337}, {2376, 2382}, {3124, 3127} {396, 401}, {1451, 1512, 1516}, {1622, 1708}, {1623, 1626}, {1633, 1707}, {1977, 1982}, {1984, 1994} {446, 517} {2665, 2669}, {3318, 3320}, {3323, 3344}, {3775, 3780}, {5169, 5171}, {5320, 5322} {542, 559}, {3120, 3137}, {3314, 3385}, {3341, 3450}, {3352, 3461}, {3368, 3463} {844, 4595}, {1095, 1159}, {2891, 4593}, {3951, 4587}, {4334, 4582}, {4507, 4576}, {5225, 5505} {3158, 3555}, {5179, 5243} {341, 342}, {1508, 1522, 1526}
L2344 = [1, 3, 5, 11, 17], L2351 = [1, 3, 5, 13, 17], L2356 = [1, 3, 5, 15, 17], L2369 = [1, 3, 7, 9, 17], L2376 = [1, 3, 7, 11, 17], L2382 = [1, 3, 7, 15, 17], L2385 = [1, 3, 7, 17, 17], L2422 = [1, 3, 9, 17, 17], L2476 = [1, 3, 13, 17, 17], L2756 = [1, 5, 7, 17, 17], L2852 = [1, 6, 9, 10, 12], L2855 = [1, 6, 9, 10, 15], L2856 = [1, 6, 9, 10, 17], L2858 = [1, 6, 9, 12, 13], L2865 = [1, 6, 9, 14, 17], L2875 = [1, 6, 10, 12, 13], L2895 = [1, 6, 12, 13, 17], L2912 = [1, 6, 14, 15, 17], L3122 = [2, 4, 6, 10, 17], L3123 = [2, 4, 6, 12, 17], L3124 = [2, 4, 6, 14, 17], L3125 = [2, 4, 6, 16, 17], L3127 = [2, 4, 8, 10, 17], L3131 = [2, 4, 10, 17, 17], L3132 = [2, 4, 12, 14, 17], L3133 = [2, 4, 12, 17, 17], L3134 = [2, 4, 14, 17, 17], L3136 = [2, 6, 8, 10, 17], L3137 = [2, 6, 8, 17, 17]. q = 35 : L396 = [0, 1, 4, 6, 9], L401 = [0, 1, 4, 6, 16], L446 = [0, 1, 5, 10, 15], L517 = [0, 5, 7, 10, 15], L1451 = [1, 2, 3, 8, 16], L1512 = [1, 2, 4, 8, 9], L1516 = [1, 2, 4, 8, 16], L1622 = [1, 2, 6, 7, 16], L1623 = [1, 2, 6, 8, 9], L1626 = [1, 2, 6, 8, 12], L1633 = [1, 2, 6, 9, 12], L1707 = [1, 2, 8, 9, 12], L1708 = [1, 2, 8, 9, 14], L1977 = [1, 4, 6, 7, 9], L1982 = [1, 4, 6, 7, 16], L1984 = [1, 4, 6, 9, 14], L1994 = [1, 4, 6, 14, 16]. q = 36 : L542 = [0, 1, 3, 5, 17], L559 = [0, 1, 3, 7, 11], L844 = [0, 1, 8, 10, 17], L1095 = [0, 2, 9, 9, 18], L1159 = [0, 4, 9, 9, 18], L2665 = [1, 2, 5, 7, 10], L2669 = [1, 2, 5, 7, 14], L2891 = [1, 2, 8, 10, 17], L3120 = [1, 3, 3, 5, 17], L3137 = [1, 3, 3, 7, 11], L3158 = [1, 3, 3, 9, 15], L3314 = [1, 3, 5, 6, 17], L3318 = [1, 3, 5, 7, 11], L3320 = [1, 3, 5, 7, 13], L3323 = [1, 3, 5, 7, 17], L3341 = [1, 3, 5, 9, 17], L3344 = [1, 3, 5, 11, 13], L3352 = [1, 3, 5, 12, 17], L3368 = [1, 3, 5, 17, 18], L3385 = [1, 3, 6, 7, 11], L3450 = [1, 3, 7, 9, 11], L3461 = [1, 3, 7, 11, 12], L3463 = [1, 3, 7, 11, 18], L3555 = [1, 3, 9, 15, 15], L3775 = [1, 4, 5, 7, 16], L3780 = [1, 4, 5, 8, 11], L3951 = [1, 4, 8, 10, 17], L4334 = [1, 6, 8, 10, 17], L4507 = [1, 8, 8, 10, 17], L4576 = [1, 8, 10, 10, 17], L4582 = [1, 8, 10, 12, 17], L4587 = [1, 8, 10, 14, 17], L4593 = [1, 8, 10, 16, 17], L4595 = [1, 8, 10, 17, 18], L5169 = [2, 3, 4, 8, 10], L5171 = [2, 3, 4, 8, 14], L5179 = [2, 3, 4, 9, 15], L5225 = [2, 3, 6, 12, 15], L5243 = [2, 3, 8, 9, 15], L5320 = [2, 4, 8, 9, 10], L5322 = [2, 4, 8, 9, 14], L5505 = [3, 4, 6, 12, 15]. q = 37 : L341 = [0, 1, 3, 4, 11], L342 = [0, 1, 3, 4, 12], L1508 = [1, 2, 4, 5, 16], L1522 = [1, 2, 4, 8, 9], L1526 = [1, 2, 4, 8, 16]. q = 38 : L60 = [0, 0, 1, 3, 11], L63 = [0, 0, 1, 3, 15], L511 = [0, 1, 3, 5, 13], L513 = [0, 1, 3, 5, 15], L515 = [0, 1, 3, 5, 17], L523 = [0, 1, 3, 7, 13], L539 = [0, 1, 3, 9, 11], L553 = [0, 1, 3, 11, 15], L554 =
APPENDIX
31
Table 3. (continued) n = 5 q 38
I {0}
indexes of I-isospectral families {60, 63}, {511, 513}, {515, 523, 539}, {553, 554, 682}, {556, 573}, {767, 769}, {895, 898}, {3182, 3185}, {3184, 3187, 3200, 3203}, {3201, 3205, 3209, 3220}, {3222, 3231}, {3230, 3251}, {3237, 3270, 3334}, {3392, 3394, 3882}, {3397, 3451}, {4150, 4155}, {4475, 4476, 4479}, {4478, 4481, 4483}, {4488, 4494}, {4491, 4495} {0, 1} {3201, 3205} 39 {0} {405, 553}, {745, 746}, {748, 749}, {2273, 2424}, {2517, 3119}, {2766, 2782}, {2771, 2794}, {3600, 3602, 3603}, {3601, 3604}, {3606, 3607} {0, 1} {3600, 3602} [0, 1, 3, 11, 17], L556 = [0, 1, 3, 11, 19], L573 = [0, 1, 3, 15, 19], L682 = [0, 1, 5, 7, 9], L767 = [0, 1, 7, 8, 12], L769 = [0, 1, 7, 8, 18], L895 = [0, 2, 4, 14, 19], L898 = [0, 2, 6, 8, 19], L3182 = [1, 3, 5, 7, 11], L3184 = [1, 3, 5, 7, 13], L3185 = [1, 3, 5, 7, 15], L3187 = [1, 3, 5, 7, 17], L3200 = [1, 3, 5, 9, 11], L3201 = [1, 3, 5, 9, 13], L3203 = [1, 3, 5, 9, 15], L3205 = [1, 3, 5, 9, 17], L3209 = [1, 3, 5, 11, 15], L3220 = [1, 3, 5, 13, 17], L3222 = [1, 3, 5, 13, 19], L3230 = [1, 3, 5, 15, 17], L3231 = [1, 3, 5, 15, 19], L3237 = [1, 3, 5, 17, 19], L3251 = [1, 3, 7, 9, 13], L3270 = [1, 3, 7, 13, 19], L3334 = [1, 3, 9, 11, 19], L3392 = [1, 3, 11, 15, 19], L3394 = [1, 3, 11, 17, 19], L3397 = [1, 3, 11, 19, 19], L3451 = [1, 3, 15, 19, 19], L3882 = [1, 5, 7, 9, 19], L4150 = [1, 7, 8, 12, 19], L4155 = [1, 7, 8, 18, 19], L4475 = [2, 4, 6, 10, 19], L4476 = [2, 4, 6, 12, 19], L4478 = [2, 4, 6, 16, 19], L4479 = [2, 4, 6, 18, 19], L4481 = [2, 4, 8, 10, 19], L4483 = [2, 4, 8, 16, 19], L4488 = [2, 4, 12, 16, 19], L4491 = [2, 4, 14, 19, 19], L4494 = [2, 6, 8, 10, 19], L4495 = [2, 6, 8, 19, 19]. q = 39 : L405 = [0, 1, 2, 10, 17], L553 = [0, 1, 4, 5, 11], L745 = [0, 3, 6, 9, 13], L746 = [0, 3, 6, 12, 13], L748 = [0, 3, 6, 13, 15], L749 = [0, 3, 9, 12, 13], L2273 = [1, 2, 5, 14, 16], L2424 = [1, 2, 8, 10, 14], L2517 = [1, 2, 10, 13, 17], L2766 = [1, 3, 4, 9, 17], L2771 = [1, 3, 4, 10, 14], L2782 = [1, 3, 4, 12, 14], L2794 = [1, 3, 4, 14, 17], L3119 = [1, 4, 5, 11, 13], L3600 = [3, 6, 9, 12, 13], L3601 = [3, 6, 9, 13, 13], L3602 = [3, 6, 9, 13, 15], L3603 = [3, 6, 9, 13, 18], L3604 = [3, 6, 12, 13, 13], L3606 = [3, 6, 13, 13, 15], L3607 = [3, 9, 12, 13, 13]. q = 40 : L63 = [0, 0, 1, 3, 7], L65 = [0, 0, 1, 3, 9], L70 = [0, 0, 1, 3, 15], L94 = [0, 0, 1, 5, 7], L524 = [0, 1, 2, 9, 11], L532 = [0, 1, 2, 9, 19], L612 = [0, 1, 3, 5, 11], L614 = [0, 1, 3, 5, 13], L624 = [0, 1, 3, 7, 10], L625 = [0, 1, 3, 7, 11], L628 = [0, 1, 3, 7, 15], L633 = [0, 1, 3, 7, 20], L647 = [0, 1, 3, 9, 10], L649 = [0, 1, 3, 9, 13], L652 = [0, 1, 3, 9, 20], L657 = [0, 1, 3, 10, 15], L689 = [0, 1, 3, 15, 20], L846 = [0, 1, 5, 7, 9], L847 = [0, 1, 5, 7, 10], L851 = [0, 1, 5, 7, 20], L943 = [0, 1, 6, 9, 11], L948 = [0, 1, 6, 9, 19], L1079 = [0, 1, 9, 11, 19], L2915 = [1, 2, 2, 9, 11], L2923 = [1, 2, 2, 9, 19], L3105 = [1, 2, 3, 14, 17], L3107 = [1, 2, 3, 14, 19], L3203 = [1, 2, 4, 9, 11], L3211 = [1, 2, 4, 9, 19], L3416 = [1, 2, 6, 7, 13], L3422 = [1, 2, 6, 7, 19], L3438 = [1, 2, 6, 9, 11], L3446 = [1, 2, 6, 9, 19], L3586 = [1, 2, 8, 9, 11], L3594 = [1, 2, 8, 9, 19], L3654 = [1, 2, 9, 10, 11], L3662 = [1, 2, 9, 10, 19], L3664 = [1, 2, 9, 11, 12], L3666 = [1, 2, 9, 11, 14], L3668 = [1, 2, 9, 11, 16], L3672 = [1, 2, 9, 11, 20], L3680 = [1, 2, 9, 12, 19], L3690 = [1, 2, 9, 14, 19], L3700 = [1, 2, 9, 16, 19], L3704 = [1, 2, 9, 19, 20], L3939 = [1, 3, 4, 7, 12], L3962 = [1, 3, 4, 9, 12], L3991 = [1, 3, 4, 12, 15], L4047 = [1, 3, 5, 7, 11], L4050 = [1, 3, 5, 7, 15], L4052 = [1, 3, 5, 7, 17], L4070 = [1, 3, 5, 9, 11], L4071 = [1, 3, 5, 9, 13], L4073 = [1, 3, 5, 9, 15], L4079 = [1, 3, 5, 10, 11], L4081 = [1, 3, 5, 10, 13], L4095 = [1, 3, 5, 11, 20], L4108 = [1, 3, 5, 13, 20], L4116 = [1, 3, 5, 15, 15], L4142 = [1, 3, 7, 8, 16], L4148 = [1, 3, 7, 9, 11], L4149 = [1, 3, 7, 9, 13], L4152 = [1, 3, 7, 9, 19], L4154 = [1, 3, 7, 10, 10], L4155 = [1, 3, 7, 10, 11], L4158 = [1, 3, 7, 10, 15], L4163 = [1, 3, 7, 10, 20], L4166 = [1, 3, 7, 11, 20], L4176 = [1, 3, 7, 13, 19], L4183 = [1, 3, 7, 15, 20], L4190 = [1, 3, 7, 17, 19], L4196 = [1, 3, 7, 20, 20], L4214 = [1, 3, 8, 9, 16], L4254 = [1, 3, 8, 15, 16],
32
EMILIO A. LAURET
Table 3. (continued) n = 5 q 40
I {0}
indexes of I-isospectral families {63, 65}, {70, 94}, {524, 532}, {612, 614}, {624, 647}, {625, 649}, {628, 846}, {633, 652}, {657, 847}, {689, 851}, {943, 948}, {2915, 2923}, {3105, 3422}, {3107, 3416}, {3203, 3211}, {3438, 3446}, {3586, 3594}, {3654, 3662}, {3664, 3680}, {3666, 3690}, {3668, 3700}, {3672, 3704}, {3939, 3962}, {3991, 4606}, {4047, 4071}, {4050, 4073}, {4052, 4070}, {4079, 4081}, {4095, 4108}, {4116, 5045}, {4142, 4214}, {4148, 4149, 4152}, {4154, 4272}, {4155, 4274}, {4158, 5197}, {4163, 4277}, {4166, 4280}, {4176, 4190}, {4183, 5200}, {4196, 4285}, {4254, 5193}, {4290, 5201}, {4322, 5205}, {4433, 5215}, {4711, 4716}, {5463, 5468}, {5547, 5552}, {5594, 5599}, {5601, 5610}, {5603, 5619}, {5605, 5621} {0, 1} {4149, 4152} {2, 3} {1079, 6034}, {4867, 6032}, {5880, 6029}, {6665, 6726} 41 {0} {1958, 1959}, {2061, 2141}, {2070, 2139} 42 {0} {844, 874}, {922, 925}, {1081, 1084}, {5483, 5487}, {5489, 5512}, {5493, 5515}, {5495, 5528}, {5499, 5513}, {5727, 5757}, {6005, 6096}, {6015, 6132}, {6345, 6348}, {6389, 6392}, {6398, 6404}, {7070, 7073}, {7183, 7188}, {7185, 7194}, {9688, 9935}, {9957, 9959}, {9977, 10085}, {9988, 9990}, {10027, 10123}, {10605, 10608}, {10623, 10626} {3, 4} {1187, 1990}, {5914, 10667}, {9835, 10695}
L4272 = [1, 3, 9, 10, 10], L4274 = [1, 3, 9, 10, 13], L4277 = [1, 3, 9, 10, 20], L4280 = [1, 3, 9, 13, 20], L4285 = [1, 3, 9, 20, 20], L4290 = [1, 3, 10, 10, 15], L4322 = [1, 3, 10, 15, 20], L4433 = [1, 3, 15, 20, 20], L4606 = [1, 4, 5, 7, 12], L4711 = [1, 4, 6, 9, 11], L4716 = [1, 4, 6, 9, 19], L4867 = [1, 4, 9, 11, 19], L5045 = [1, 5, 5, 7, 15], L5193 = [1, 5, 7, 8, 16], L5197 = [1, 5, 7, 9, 10], L5200 = [1, 5, 7, 9, 20], L5201 = [1, 5, 7, 10, 10], L5205 = [1, 5, 7, 10, 20], L5215 = [1, 5, 7, 20, 20], L5463 = [1, 6, 6, 9, 11], L5468 = [1, 6, 6, 9, 19], L5547 = [1, 6, 8, 9, 11], L5552 = [1, 6, 8, 9, 19], L5594 = [1, 6, 9, 10, 11], L5599 = [1, 6, 9, 10, 19], L5601 = [1, 6, 9, 11, 12], L5603 = [1, 6, 9, 11, 16], L5605 = [1, 6, 9, 11, 20], L5610 = [1, 6, 9, 12, 19], L5619 = [1, 6, 9, 16, 19], L5621 = [1, 6, 9, 19, 20], L5880 = [1, 8, 9, 11, 19], L6029 = [1, 9, 11, 12, 19], L6032 = [1, 9, 11, 16, 19], L6034 = [1, 9, 11, 19, 20], L6665 = [4, 5, 5, 15, 15], L6726 = [5, 5, 8, 15, 15]. q = 41 : L1958 = [1, 2, 3, 9, 13], L1959 = [1, 2, 3, 9, 14], L2061 = [1, 2, 4, 9, 18], L2070 = [1, 2, 4, 10, 18], L2139 = [1, 2, 5, 8, 18], L2141 = [1, 2, 5, 9, 10]. q = 42 : L844 = [0, 1, 3, 11, 15], L874 = [0, 1, 3, 15, 17], L922 = [0, 1, 4, 5, 16], L925 = [0, 1, 4, 5, 20], L1081 = [0, 1, 5, 11, 13], L1084 = [0, 1, 5, 11, 17], L1187 = [0, 1, 6, 12, 18], L1990 = [0, 6, 7, 12, 18], L5483 = [1, 3, 5, 9, 13], L5487 = [1, 3, 5, 9, 17], L5489 = [1, 3, 5, 9, 19], L5493 = [1, 3, 5, 11, 13], L5495 = [1, 3, 5, 11, 15], L5499 = [1, 3, 5, 11, 19], L5512 = [1, 3, 5, 13, 15], L5513 = [1, 3, 5, 13, 17], L5515 = [1, 3, 5, 13, 19], L5528 = [1, 3, 5, 15, 19], L5727 = [1, 3, 7, 11, 15], L5757 = [1, 3, 7, 15, 17], L5914 = [1, 3, 9, 15, 21], L6005 = [1, 3, 11, 14, 15], L6015 = [1, 3, 11, 15, 21], L6096 = [1, 3, 14, 15, 17], L6132 = [1, 3, 15, 17, 21], L6345 = [1, 4, 5, 7, 16], L6348 = [1, 4, 5, 7, 20], L6389 = [1, 4, 5, 14, 16], L6392 = [1, 4, 5, 14, 20], L6398 = [1, 4, 5, 16, 21], L6404 = [1, 4, 5, 20, 21], L7070 = [1, 5, 7, 11, 13], L7073 = [1, 5, 7, 11, 17], L7183 = [1, 5, 11, 13, 14], L7185 = [1, 5, 11, 13, 21], L7188 = [1, 5, 11, 14, 17], L7194 = [1, 5, 11, 17, 21], L9688 = [2, 3, 6, 10, 20], L9835 = [2, 3, 9, 15, 21], L9935 = [2, 4, 6, 9, 10], L9957 = [2, 4, 7, 8, 10], L9959 = [2, 4, 7, 8, 16], L9977 = [2, 4, 7, 12, 18], L9988 = [2, 4, 8, 10, 21], L9990 = [2, 4, 8, 16, 21], L10027 = [2, 4, 12, 18, 21], L10085 = [2, 6, 7, 8, 12], L10123 = [2, 6, 8, 12, 21],
APPENDIX
33
Table 3. (continued) n = 5 q 43 44
I {0} {0}
indexes of I-isospectral families {502, 508} {66, 68}, {72, 75, 100, 102}, {694, 696}, {707, 733}, {709, 970}, {716, 738}, {752, 755, 971, 985}, {776, 796, 974, 989}, {1401, 1403}, {1441, 1442}, {4986, 5011}, {4991, 5013}, {4993, 5009}, {5014, 5044}, {5016, 5055}, {5020, 5022}, {5043, 5099}, {5046, 5058}, {5057, 5101}, {5115, 5269}, {5117, 6415}, {5124, 5274}, {5137, 6417}, {5160, 5286}, {5350, 5353, 6418, 6477}, {5374, 5394, 6421, 6481}, {5475, 5545, 6427, 6490}, {7919, 7931}, {7934, 7939}, {7937, 7944}, {8049, 8050}, {8053, 8054} {0, 1} {713, 734}, {715, 737}, {5121, 5270}, {5123, 5273}, {5155, 5277}, {5159, 5285} {2, 3} {1228, 7410}, {1422, 1446}, {4533, 7408}, {6126, 7405}, {6804, 7401}, {7157, 7396}, {7328, 7390}
L10605 = [3, 6, 7, 9, 12], L10608 = [3, 6, 7, 9, 18], L10623 = [3, 6, 9, 12, 14], L10626 = [3, 6, 9, 14, 18], L10667 = [3, 7, 9, 15, 21], L10695 = [3, 9, 14, 15, 21]. q = 43 : L502 = [0, 1, 3, 8, 14], L508 = [0, 1, 3, 9, 14]. q = 44 : L66 = [0, 0, 1, 3, 7], L68 = [0, 0, 1, 3, 9], L72 = [0, 0, 1, 3, 13], L75 = [0, 0, 1, 3, 17], L100 = [0, 0, 1, 5, 7], L102 = [0, 0, 1, 5, 9], L694 = [0, 1, 3, 5, 13], L696 = [0, 1, 3, 5, 15], L707 = [0, 1, 3, 7, 11], L709 = [0, 1, 3, 7, 13], L713 = [0, 1, 3, 7, 19], L715 = [0, 1, 3, 7, 21], L716 = [0, 1, 3, 7, 22], L733 = [0, 1, 3, 9, 11], L734 = [0, 1, 3, 9, 13], L737 = [0, 1, 3, 9, 19], L738 = [0, 1, 3, 9, 22], L752 = [0, 1, 3, 11, 13], L755 = [0, 1, 3, 11, 17], L776 = [0, 1, 3, 13, 22], L796 = [0, 1, 3, 17, 22], L970 = [0, 1, 5, 7, 9], L971 = [0, 1, 5, 7, 11], L974 = [0, 1, 5, 7, 22], L985 = [0, 1, 5, 9, 11], L989 = [0, 1, 5, 9, 22], L1228 = [0, 1, 10, 12, 21], L1401 = [0, 2, 6, 10, 11], L1403 = [0, 2, 6, 11, 14], L1422 = [0, 2, 11, 11, 22], L1441 = [0, 4, 8, 11, 12], L1442 = [0, 4, 8, 11, 16], L1446 = [0, 4, 11, 11, 22], L4533 = [1, 2, 10, 12, 21], L4986 = [1, 3, 5, 7, 13], L4991 = [1, 3, 5, 7, 19], L4993 = [1, 3, 5, 7, 21], L5009 = [1, 3, 5, 9, 13], L5011 = [1, 3, 5, 9, 15], L5013 = [1, 3, 5, 9, 17], L5014 = [1, 3, 5, 9, 19], L5016 = [1, 3, 5, 9, 21], L5020 = [1, 3, 5, 11, 13], L5022 = [1, 3, 5, 11, 15], L5043 = [1, 3, 5, 13, 17], L5044 = [1, 3, 5, 13, 19], L5046 = [1, 3, 5, 13, 22], L5055 = [1, 3, 5, 15, 17], L5057 = [1, 3, 5, 15, 21], L5058 = [1, 3, 5, 15, 22], L5099 = [1, 3, 7, 9, 13], L5101 = [1, 3, 7, 9, 19], L5115 = [1, 3, 7, 11, 11], L5117 = [1, 3, 7, 11, 13], L5121 = [1, 3, 7, 11, 19], L5123 = [1, 3, 7, 11, 21], L5124 = [1, 3, 7, 11, 22], L5137 = [1, 3, 7, 13, 22], L5155 = [1, 3, 7, 19, 22], L5159 = [1, 3, 7, 21, 22], L5160 = [1, 3, 7, 22, 22], L5269 = [1, 3, 9, 11, 11], L5270 = [1, 3, 9, 11, 13], L5273 = [1, 3, 9, 11, 19], L5274 = [1, 3, 9, 11, 22], L5277 = [1, 3, 9, 13, 22], L5285 = [1, 3, 9, 19, 22], L5286 = [1, 3, 9, 22, 22], L5350 = [1, 3, 11, 11, 13], L5353 = [1, 3, 11, 11, 17], L5374 = [1, 3, 11, 13, 22], L5394 = [1, 3, 11, 17, 22], L5475 = [1, 3, 13, 22, 22], L5545 = [1, 3, 17, 22, 22], L6126 = [1, 4, 10, 12, 21], L6415 = [1, 5, 7, 9, 11], L6417 = [1, 5, 7, 9, 22], L6418 = [1, 5, 7, 11, 11], L6421 = [1, 5, 7, 11, 22], L6427 = [1, 5, 7, 22, 22], L6477 = [1, 5, 9, 11, 11], L6481 = [1, 5, 9, 11, 22], L6490 = [1, 5, 9, 22, 22], L6804 = [1, 6, 10, 12, 21], L7157 = [1, 8, 10, 12, 21], L7328 = [1, 10, 10, 12, 21], L7390 = [1, 10, 12, 12, 21], L7396 = [1, 10, 12, 14, 21], L7401 = [1, 10, 12, 16, 21], L7405 = [1, 10, 12, 18, 21], L7408 = [1, 10, 12, 20, 21], L7410 = [1, 10, 12, 21, 22], L7919 = [2, 4, 11, 16, 18], L7931 = [2, 6, 8, 11, 16], L7934 = [2, 6, 10, 11, 11], L7937 = [2, 6, 10, 11, 22], L7939 = [2, 6, 11, 11, 14], L7944 = [2, 6, 11, 14, 22], L8049 = [4, 8, 11, 11, 12], L8050 = [4, 8, 11, 11, 16], L8053 = [4, 8, 11, 12, 22], L8054 = [4, 8, 11, 16, 22]. q = 45 : L585 = [0, 1, 2, 14, 19], L797 = [0, 1, 4, 7, 11], L1221 = [0, 3, 5, 6, 18], L1224 = [0, 3, 5, 9, 12], L3378 = [1, 2, 4, 7, 14], L3389 = [1, 2, 4, 8, 13], L3454 = [1, 2, 4, 14, 19], L3464 = [1, 2, 4, 16, 17], L3755 = [1, 2, 7, 8, 13], L3756 = [1, 2, 7, 8, 14], L4184 = [1, 2, 14, 15, 19], L4494 = [1, 3, 4, 11, 19], L4512 = [1, 3, 4, 14, 16], L4743 = [1, 3, 6, 12, 19], L4764 = [1, 3, 6, 17, 21], L5271 = [1, 4, 6, 11, 19],
34
EMILIO A. LAURET
Table 3. (continued) n = 5 q I indexes of I-isospectral families 45 {0} {585, 797}, {1221, 1224}, {3378, 3389}, {3454, 3755}, {3464, 3756}, {4184, 5312}, {4494, 4512}, {4743, 4764}, {5271, 5275}, {6688, 6692}, {6717, 6729}, {6722, 6733} 46 {0} {733, 737}, {800, 1045}, {819, 1043}, {5518, 5551}, {5537, 5540}, {5542, 5545}, {5549, 5639, 5643}, {5553, 5602}, {5557, 5590}, {5572, 5662}, {5574, 5600, 5641, 5660}, {5676, 5821}, {5952, 7118}, {6039, 7108}, {8495, 8497}, {8502, 8504}, {8509, 8522} L5275 = [1, 4, 6, 14, 16], L5312 = [1, 4, 7, 11, 15], L6688 = [3, 5, 5, 6, 18], L6692 = [3, 5, 5, 9, 12], L6717 = [3, 5, 6, 10, 18], L6722 = [3, 5, 6, 15, 18], L6729 = [3, 5, 9, 10, 12], L6733 = [3, 5, 9, 12, 15]. q = 46 : L733 = [0, 1, 3, 5, 11], L737 = [0, 1, 3, 5, 15], L800 = [0, 1, 3, 11, 17], L819 = [0, 1, 3, 13, 19], L1043 = [0, 1, 5, 9, 11], L1045 = [0, 1, 5, 9, 13], L5518 = [1, 3, 5, 7, 19], L5537 = [1, 3, 5, 9, 11], L5540 = [1, 3, 5, 9, 15], L5542 = [1, 3, 5, 9, 17], L5545 = [1, 3, 5, 9, 21], L5549 = [1, 3, 5, 11, 13], L5551 = [1, 3, 5, 11, 15], L5553 = [1, 3, 5, 11, 17], L5557 = [1, 3, 5, 11, 23], L5572 = [1, 3, 5, 13, 17], L5574 = [1, 3, 5, 13, 19], L5590 = [1, 3, 5, 15, 23], L5600 = [1, 3, 5, 17, 19], L5602 = [1, 3, 5, 17, 21], L5639 = [1, 3, 7, 9, 13], L5641 = [1, 3, 7, 9, 17], L5643 = [1, 3, 7, 9, 21], L5660 = [1, 3, 7, 11, 15], L5662 = [1, 3, 7, 11, 17], L5676 = [1, 3, 7, 13, 17], L5821 = [1, 3, 9, 11, 17], L5952 = [1, 3, 11, 17, 23], L6039 = [1, 3, 13, 19, 23], L7108 = [1, 5, 9, 11, 23], L7118 = [1, 5, 9, 13, 23], L8495 = [2, 4, 8, 10, 23], L8497 = [2, 4, 8, 16, 23], L8502 = [2, 4, 10, 14, 23], L8504 = [2, 4, 10, 18, 23], L8509 = [2, 4, 12, 20, 23], L8522 = [2, 6, 8, 18, 23]. q = 48 : L788 = [0, 1, 2, 11, 13], L798 = [0, 1, 2, 11, 23], L967 = [0, 1, 3, 7, 15], L1002 = [0, 1, 3, 9, 17], L1145 = [0, 1, 4, 5, 19], L1149 = [0, 1, 4, 5, 23], L1177 = [0, 1, 4, 7, 17], L1182 = [0, 1, 4, 7, 23], L1310 = [0, 1, 5, 6, 13], L1315 = [0, 1, 5, 6, 19], L1318 = [0, 1, 5, 6, 23], L1377 = [0, 1, 5, 13, 18], L1483 = [0, 1, 6, 11, 13], L1489 = [0, 1, 6, 11, 23], L1812 = [0, 1, 10, 11, 13], L1817 = [0, 1, 10, 11, 23], L1891 = [0, 1, 11, 13, 23], L2205 = [0, 2, 3, 9, 15], L2209 = [0, 2, 3, 9, 21], L3534 = [1, 1, 5, 5, 19], L3537 = [1, 1, 5, 5, 23], L4482 = [1, 1, 11, 11, 13], L4487 = [1, 1, 11, 11, 23], L5164 = [1, 2, 2, 11, 13], L5174 = [1, 2, 2, 11, 23], L5629 = [1, 2, 4, 11, 13], L5639 = [1, 2, 4, 11, 23], L5828 = [1, 2, 5, 13, 14], L5837 = [1, 2, 5, 13, 23], L5844 = [1, 2, 5, 14, 19], L5848 = [1, 2, 5, 14, 23], L5985 = [1, 2, 6, 11, 13], L5995 = [1, 2, 6, 11, 23], L6119 = [1, 2, 7, 10, 17], L6124 = [1, 2, 7, 10, 23], L6127 = [1, 2, 7, 11, 13], L6128 = [1, 2, 7, 11, 14], L6263 = [1, 2, 8, 11, 13], L6273 = [1, 2, 8, 11, 23], L6497 = [1, 2, 10, 11, 13], L6506 = [1, 2, 10, 11, 23], L6580 = [1, 2, 11, 12, 13], L6590 = [1, 2, 11, 12, 23], L6592 = [1, 2, 11, 13, 14], L6594 = [1, 2, 11, 13, 16], L6596 = [1, 2, 11, 13, 18], L6598 = [1, 2, 11, 13, 20], L6602 = [1, 2, 11, 13, 24], L6610 = [1, 2, 11, 14, 23], L6627 = [1, 2, 11, 16, 23], L6639 = [1, 2, 11, 18, 23], L6647 = [1, 2, 11, 20, 23], L6653 = [1, 2, 11, 23, 24], L7371 = [1, 3, 4, 12, 20], L7498 = [1, 3, 5, 9, 11], L7500 = [1, 3, 5, 9, 13], L7515 = [1, 3, 5, 11, 15], L7522 = [1, 3, 5, 11, 23], L7538 = [1, 3, 5, 13, 15], L7545 = [1, 3, 5, 13, 23], L7630 = [1, 3, 6, 7, 15], L7665 = [1, 3, 6, 9, 17], L7784 = [1, 3, 7, 8, 15], L7832 = [1, 3, 7, 12, 15], L7848 = [1, 3, 7, 13, 23], L7851 = [1, 3, 7, 15, 16], L7853 = [1, 3, 7, 15, 18], L7858 = [1, 3, 7, 15, 24], L7869 = [1, 3, 7, 17, 19], L7920 = [1, 3, 8, 9, 17], L8075 = [1, 3, 9, 12, 17], L8107 = [1, 3, 9, 16, 17], L8114 = [1, 3, 9, 17, 18], L8116 = [1, 3, 9, 17, 24], L8655 = [1, 4, 4, 5, 19], L8659 = [1, 4, 4, 5, 23], L8687 = [1, 4, 4, 7, 17], L8692 = [1, 4, 4, 7, 23], L8752 = [1, 4, 4, 12, 20], L8826 = [1, 4, 5, 6, 19], L8830 = [1, 4, 5, 6, 23], L8854 = [1, 4, 5, 8, 19], L8858 = [1, 4, 5, 8, 23], L8889 = [1, 4, 5, 12, 19], L8893 = [1, 4, 5, 12, 23], L8915 = [1, 4, 5, 16, 19], L8919 = [1, 4, 5, 16, 23], L8929 = [1, 4, 5, 18, 19], L8933 = [1, 4, 5, 18, 23], L8939 = [1, 4, 5, 19, 24], L8949 = [1, 4, 5, 23, 24], L8977 = [1, 4, 6, 7, 17], L8982 = [1, 4, 6, 7, 23], L9030 = [1, 4, 6, 11, 13], L9038 = [1, 4, 6, 11, 23], L9124 = [1, 4, 7, 8, 17], L9129 = [1, 4, 7, 8, 23], L9157 = [1, 4, 7, 12, 17], L9162 = [1, 4, 7, 12, 23], L9178 = [1, 4, 7, 16, 17], L9183 = [1, 4, 7, 16, 23], L9185 = [1, 4, 7, 17, 18], L9190 = [1, 4, 7, 17, 24], L9195 = [1, 4, 7, 18, 23], L9203 =
APPENDIX
35
Table 3. (continued) n = 5 q 48
I {0}
indexes of I-isospectral families {788, 798}, {967, 1002}, {1145, 1149}, {1177, 1182}, {1310, 1377}, {1315, 1318}, {1483, 1489}, {1812, 1817}, {2205, 2209}, {3534, 3537}, {4482, 4487}, {5164, 5174}, {5629, 5639}, {5828, 6128}, {5837, 6127}, {5844, 5848}, {5985, 5995}, {6119, 6124}, {6263, 6273}, {6497, 6506}, {6580, 6590}, {6592, 6610}, {6594, 6627}, {6596, 6639}, {6598, 6647}, {6602, 6653}, {7498, 7500}, {7515, 7538}, {7522, 7545}, {7630, 7665}, {7784, 7920}, {7832, 8075}, {7848, 7869}, {7851, 8107}, {7853, 8114}, {7858, 8116}, {8655, 8659}, {8687, 8692}, {8826, 8830}, {8854, 8858}, {8889, 8893}, {8915, 8919}, {8929, 8933}, {8939, 8949}, {8977, 8982}, {9030, 9038}, {9124, 9129}, {9157, 9162}, {9178, 9183}, {9185, 9195}, {9190, 9203}, {9436, 9442}, {9809, 10220}, {9814, 9817}, {9835, 10032}, {9840, 9843}, {9867, 10174}, {9872, 9875}, {9878, 10216}, {9884, 10222}, {9896, 9899}, {9915, 9922}, {9946, 9949}, {9948, 9950}, {10382, 10388}, {10542, 10548}, {10724, 10730}, {10800, 10806}, {10808, 10819}, {10809, 10825}, {10811, 10832}, {10814, 10836}, {11452, 11457}, {12192, 12197}, {12265, 12270}, {12273, 12284}, {12274, 12288}, {12276, 12292}, {13301, 13305}, {13607, 13611}, {13692, 13696}, {13763, 13767}, {13833, 13837}, {13840, 13843}, {13846, 13855}, {13847, 13860}, {13848, 13863}, {13851, 13866}, {14514, 14518}, {14659, 14662}, {14682, 14685} {2, 3} {1891, 12556}, {9518, 12554}, {11531, 12551}, {14582, 14734, 14774} {4} {7371, 9590}, {8752, 9589}, {2, 3, 4} {14734, 14774}
[1, 4, 7, 23, 24], L9436 = [1, 4, 10, 11, 13], L9442 = [1, 4, 10, 11, 23], L9518 = [1, 4, 11, 13, 23], L9589 = [1, 4, 12, 20, 20], L9590 = [1, 4, 12, 20, 21], L9809 = [1, 5, 6, 6, 13], L9814 = [1, 5, 6, 6, 19], L9817 = [1, 5, 6, 6, 23], L9835 = [1, 5, 6, 8, 13], L9840 = [1, 5, 6, 8, 19], L9843 = [1, 5, 6, 8, 23], L9867 = [1, 5, 6, 12, 13], L9872 = [1, 5, 6, 12, 19], L9875 = [1, 5, 6, 12, 23], L9878 = [1, 5, 6, 13, 16], L9884 = [1, 5, 6, 13, 24], L9896 = [1, 5, 6, 16, 19], L9899 = [1, 5, 6, 16, 23], L9915 = [1, 5, 6, 19, 24], L9922 = [1, 5, 6, 23, 24], L9946 = [1, 5, 7, 11, 13], L9948 = [1, 5, 7, 11, 17], L9949 = [1, 5, 7, 11, 19], L9950 = [1, 5, 7, 11, 23], L10032 = [1, 5, 8, 13, 18], L10174 = [1, 5, 12, 13, 18], L10216 = [1, 5, 13, 16, 18], L10220 = [1, 5, 13, 18, 18], L10222 = [1, 5, 13, 18, 24], L10382 = [1, 6, 6, 11, 13], L10388 = [1, 6, 6, 11, 23], L10542 = [1, 6, 8, 11, 13], L10548 = [1, 6, 8, 11, 23], L10724 = [1, 6, 10, 11, 13], L10730 = [1, 6, 10, 11, 23], L10800 = [1, 6, 11, 12, 13], L10806 = [1, 6, 11, 12, 23], L10808 = [1, 6, 11, 13, 14], L10809 = [1, 6, 11, 13, 16], L10811 = [1, 6, 11, 13, 20], L10814 = [1, 6, 11, 13, 24], L10819 = [1, 6, 11, 14, 23], L10825 = [1, 6, 11, 16, 23], L10832 = [1, 6, 11, 20, 23], L10836 = [1, 6, 11, 23, 24], L11452 = [1, 8, 10, 11, 13], L11457 = [1, 8, 10, 11, 23], L11531 = [1, 8, 11, 13, 23], L12192 = [1, 10, 10, 11, 13], L12197 = [1, 10, 10, 11, 23], L12265 = [1, 10, 11, 12, 13], L12270 = [1, 10, 11, 12, 23], L12273 = [1, 10, 11, 13, 16], L12274 = [1, 10, 11, 13, 20], L12276 = [1, 10, 11, 13, 24], L12284 = [1, 10, 11, 16, 23], L12288 = [1, 10, 11, 20, 23], L12292 = [1, 10, 11, 23, 24], L12551 = [1, 11, 13, 16, 23], L12554 = [1, 11, 13, 20, 23], L12556 = [1, 11, 13, 23, 24], L13301 = [2, 2, 3, 9, 15], L13305 = [2, 2, 3, 9, 21], L13607 = [2, 3, 4, 9, 15], L13611 = [2, 3, 4, 9, 21], L13692 = [2, 3, 6, 9, 15], L13696 = [2, 3, 6, 9, 21], L13763 = [2, 3, 8, 9, 15], L13767 = [2, 3, 8, 9, 21], L13833 = [2, 3, 9, 12, 15], L13837 = [2, 3, 9, 12, 21], L13840 = [2, 3, 9, 14, 15], L13843 = [2, 3, 9, 14, 21], L13846 = [2, 3, 9, 15, 16], L13847 = [2, 3, 9, 15, 18], L13848 = [2, 3, 9, 15, 20], L13851 = [2, 3, 9, 15, 24], L13855 = [2, 3, 9, 16, 21], L13860 = [2, 3, 9, 18, 21], L13863 = [2, 3, 9, 20, 21], L13866 = [2, 3, 9, 21, 24], L14514 = [3, 4, 6, 9, 15], L14518 = [3, 4, 6, 9, 21],
36
EMILIO A. LAURET
Table 3. (continued) n = 5 q I indexes of I-isospectral families 49 {0, 1, 2, 3, 4} {106, 108}, {887, 889}, {894, 896}, {902, 904}, {908, 912}, {5481, 5483}, {5488, 5490}, {5496, 5498}, {5502, 5506}, {5514, 5516}, {5517, 5520}, {5529, 5531}, {5535, 5539}, {5543, 5547} 50 {0} {263, 267}, {932, 935, 962}, {937, 963}, {1058, 1574}, {1227, 1480}, {2130, 2154}, {2143, 2159}, {7593, 7714}, {7596, 7633}, {7687, 7692}, {7690, 7694, 7713, 7716}, {7743, 7765, 7944}, {7744, 7767, 7947}, {7763, 7946}, {7778, 7943}, {7779, 7953}, {8101, 8147}, {8117, 8360}, {8463, 11344}, {8834, 9928}, {9338, 10898}, {9547, 10919}, {9571, 10934}, {9577, 10943}, {13280, 13321}, {13300, 13432}, {13315, 13351}, {13335, 13342}, {13343, 13345, 13529}, {13349, 13488}, {13484, 13544}, {13497, 13549}, {13520, 13566} {0, 1} {7718, 7721}, {7743, 7944}
L14582 = [3, 4, 9, 15, 21], L14659 = [3, 6, 8, 9, 15], L14662 = [3, 6, 8, 9, 21], L14682 = [3, 6, 9, 15, 16], L14685 = [3, 6, 9, 16, 21], L14734 = [3, 8, 9, 15, 21], L14774 = [3, 9, 15, 16, 21]. q = 49 : L106 = [0, 0, 1, 6, 15], L108 = [0, 0, 1, 6, 20], L887 = [0, 1, 6, 7, 15], L889 = [0, 1, 6, 7, 20], L894 = [0, 1, 6, 8, 20], L896 = [0, 1, 6, 8, 22], L902 = [0, 1, 6, 14, 15], L904 = [0, 1, 6, 14, 20], L908 = [0, 1, 6, 15, 21], L912 = [0, 1, 6, 20, 21], L5481 = [1, 6, 7, 7, 15], L5483 = [1, 6, 7, 7, 20], L5488 = [1, 6, 7, 8, 20], L5490 = [1, 6, 7, 8, 22], L5496 = [1, 6, 7, 14, 15], L5498 = [1, 6, 7, 14, 20], L5502 = [1, 6, 7, 15, 21], L5506 = [1, 6, 7, 20, 21], L5514 = [1, 6, 8, 14, 20], L5516 = [1, 6, 8, 14, 22], L5517 = [1, 6, 8, 20, 21], L5520 = [1, 6, 8, 21, 22], L5529 = [1, 6, 14, 14, 15], L5531 = [1, 6, 14, 14, 20], L5535 = [1, 6, 14, 15, 21], L5539 = [1, 6, 14, 20, 21], L5543 = [1, 6, 15, 21, 21], L5547 = [1, 6, 20, 21, 21]. q = 50 : L263 = [0, 0, 2, 5, 18], L267 = [0, 0, 2, 8, 15], L932 = [0, 1, 3, 7, 13], L935 = [0, 1, 3, 7, 17], L937 = [0, 1, 3, 7, 19], L962 = [0, 1, 3, 9, 11], L963 = [0, 1, 3, 9, 13], L1058 = [0, 1, 3, 19, 21], L1227 = [0, 1, 4, 14, 21], L1480 = [0, 1, 6, 9, 24], L1574 = [0, 1, 7, 9, 11], L2130 = [0, 2, 5, 10, 18], L2143 = [0, 2, 5, 18, 20], L2154 = [0, 2, 8, 10, 15], L2159 = [0, 2, 8, 15, 20], L7593 = [1, 3, 5, 13, 19], L7596 = [1, 3, 5, 13, 23], L7633 = [1, 3, 5, 17, 23], L7687 = [1, 3, 7, 9, 13], L7690 = [1, 3, 7, 9, 19], L7692 = [1, 3, 7, 9, 21], L7694 = [1, 3, 7, 9, 23], L7713 = [1, 3, 7, 11, 13], L7714 = [1, 3, 7, 11, 15], L7716 = [1, 3, 7, 11, 17], L7718 = [1, 3, 7, 11, 19], L7721 = [1, 3, 7, 11, 23], L7743 = [1, 3, 7, 13, 23], L7744 = [1, 3, 7, 13, 25], L7763 = [1, 3, 7, 17, 21], L7765 = [1, 3, 7, 17, 23], L7767 = [1, 3, 7, 17, 25], L7778 = [1, 3, 7, 19, 23], L7779 = [1, 3, 7, 19, 25], L7943 = [1, 3, 9, 11, 17], L7944 = [1, 3, 9, 11, 19], L7946 = [1, 3, 9, 11, 23], L7947 = [1, 3, 9, 11, 25], L7953 = [1, 3, 9, 13, 25], L8101 = [1, 3, 11, 13, 19], L8117 = [1, 3, 11, 15, 19], L8147 = [1, 3, 11, 21, 23], L8360 = [1, 3, 15, 19, 21], L8463 = [1, 3, 19, 21, 25], L8834 = [1, 4, 5, 14, 21], L9338 = [1, 4, 10, 14, 21], L9547 = [1, 4, 14, 15, 21], L9571 = [1, 4, 14, 20, 21], L9577 = [1, 4, 14, 21, 25], L9928 = [1, 5, 6, 9, 24], L10898 = [1, 6, 9, 10, 24], L10919 = [1, 6, 9, 15, 24], L10934 = [1, 6, 9, 20, 24], L10943 = [1, 6, 9, 24, 25], L11344 = [1, 7, 9, 11, 25], L13280 = [2, 4, 5, 18, 20], L13300 = [2, 4, 6, 15, 18], L13315 = [2, 4, 8, 22, 25], L13321 = [2, 4, 10, 14, 15], L13335 = [2, 4, 12, 14, 25], L13342 = [2, 4, 12, 16, 25], L13343 = [2, 4, 12, 18, 25], L13345 = [2, 4, 12, 22, 25], L13349 = [2, 4, 14, 15, 20], L13351 = [2, 4, 14, 16, 25], L13432 = [2, 5, 6, 8, 14], L13484 = [2, 5, 10, 10, 18], L13488 = [2, 5, 10, 14, 16], L13497 = [2, 5, 10, 18, 20], L13520 = [2, 5, 18, 20, 20], L13529 = [2, 6, 8, 18, 25], L13544 = [2, 8, 10, 10, 15], L13549 = [2, 8, 10, 15, 20], L13566 = [2, 8, 15, 20, 20]. q = 51 : L660 = [0, 1, 2, 10, 23], L983 = [0, 1, 4, 5, 20], L1488 = [0, 3, 6, 15, 17], L1490 = [0, 3, 6, 17, 18], L1491 = [0, 3, 6, 17, 21], L1492 = [0, 3, 9, 12, 17], L5452 = [1, 2, 10, 17, 23], L7278 = [1, 4, 5, 17, 20], L7453 = [1, 4, 7, 19, 23], L7557 = [1, 4, 10, 19, 22], L8986 = [3, 6, 9, 15, 17], L8988 = [3, 6, 9, 17, 18], L8989 = [3, 6, 9, 17, 21], L8990 = [3, 6, 9, 17, 24], L8991 = [3, 6, 12, 15, 17], L8995 =
APPENDIX
37
Table 3. (continued) n = 5 q 51
I {0}
indexes of I-isospectral families {660, 983}, {1488, 1490}, {1491, 1492}, {5452, 7278}, {7453, 7557}, {8986, 8988, 8990}, {8995, 8997}, {8998, 9001}, {8999, 9000} {0, 1} {8989, 8991} 52 {0} {88, 121}, {122, 130}, {955, 957}, {959, 970, 973}, {1059, 1400}, {1082, 1376}, {1107, 1382, 1398}, {1112, 1405}, {1407, 1428}, {1413, 1460}, {2141, 2145}, {2143, 2147}, {2196, 2198}, {2199, 2202}, {3469, 3473}, {6343, 6347}, {8066, 8069}, {8073, 8152}, {8082, 8220}, {8107, 8109}, {8111, 8241, 8266}, {8134, 8244}, {8138, 8155}, {8150, 8218}, {8166, 8247}, {8170, 8250, 8281}, {8222, 8293}, {8249, 8280}, {8295, 8512}, {8830, 10848}, {8853, 10723}, {8878, 10739, 10838}, {8883, 10853}, {9002, 10727}, {9113, 10756, 10841}, {9125, 10867}, {9424, 9427}, {10801, 10805}, {10875, 10944}, {10881, 10976}, {10901, 11070}, {13842, 13869}, {13857, 13918}, {13871, 13872}, {13874, 13884}, {13875, 13877, 13878}, {13880, 13897}, {13882, 13886}, {13891, 13903}, {14059, 14065}, {14060, 14061, 14062}, {14063, 14068}, {14066, 14072}, {14069, 14074} {0, 1} {1036, 1083}, {8681, 8854}, {8721, 9004}, {13877, 13878}, {14060, 14061} {2, 3} {1928, 13149}, {2175, 2206}, {7337, 13147}, {10245, 13144}, {11601, 13140}, {12336, 13135}, {12777, 13129}, {13043, 13122} [3, 6, 15, 17, 17], L8997 = [3, 6, 17, 17, 18], L8998 = [3, 6, 17, 17, 21], L8999 = [3, 6, 17, 18, 21], L9000 = [3, 9, 12, 15, 17], L9001 = [3, 9, 12, 17, 17]. q = 52 : L88 = [0, 0, 1, 3, 19], L121 = [0, 0, 1, 5, 9], L122 = [0, 0, 1, 5, 11], L130 = [0, 0, 1, 5, 23], L955 = [0, 1, 3, 5, 15], L957 = [0, 1, 3, 5, 17], L959 = [0, 1, 3, 5, 19], L970 = [0, 1, 3, 7, 11], L973 = [0, 1, 3, 7, 15], L1036 = [0, 1, 3, 11, 23], L1059 = [0, 1, 3, 13, 19], L1082 = [0, 1, 3, 15, 21], L1083 = [0, 1, 3, 15, 23], L1107 = [0, 1, 3, 19, 21], L1112 = [0, 1, 3, 19, 26], L1376 = [0, 1, 5, 7, 11], L1382 = [0, 1, 5, 7, 23], L1398 = [0, 1, 5, 9, 11], L1400 = [0, 1, 5, 9, 13], L1405 = [0, 1, 5, 9, 26], L1407 = [0, 1, 5, 11, 13], L1413 = [0, 1, 5, 11, 26], L1428 = [0, 1, 5, 13, 23], L1460 = [0, 1, 5, 23, 26], L1928 = [0, 1, 12, 14, 25], L2141 = [0, 2, 6, 10, 13], L2143 = [0, 2, 6, 13, 14], L2145 = [0, 2, 6, 13, 18], L2147 = [0, 2, 6, 13, 22], L2175 = [0, 2, 13, 13, 26], L2196 = [0, 4, 8, 12, 13], L2198 = [0, 4, 8, 13, 16], L2199 = [0, 4, 8, 13, 20], L2202 = [0, 4, 12, 13, 16], L2206 = [0, 4, 13, 13, 26], L3469 = [1, 1, 5, 5, 21], L3473 = [1, 1, 5, 5, 25], L6343 = [1, 2, 5, 16, 21], L6347 = [1, 2, 5, 16, 25], L7337 = [1, 2, 12, 14, 25], L8066 = [1, 3, 5, 9, 15], L8069 = [1, 3, 5, 9, 19], L8073 = [1, 3, 5, 9, 23], L8082 = [1, 3, 5, 11, 17], L8107 = [1, 3, 5, 13, 15], L8109 = [1, 3, 5, 13, 17], L8111 = [1, 3, 5, 13, 19], L8134 = [1, 3, 5, 15, 19], L8138 = [1, 3, 5, 15, 26], L8150 = [1, 3, 5, 17, 21], L8152 = [1, 3, 5, 17, 23], L8155 = [1, 3, 5, 17, 26], L8166 = [1, 3, 5, 19, 21], L8170 = [1, 3, 5, 19, 26], L8218 = [1, 3, 7, 9, 19], L8220 = [1, 3, 7, 9, 21], L8222 = [1, 3, 7, 9, 23], L8241 = [1, 3, 7, 11, 13], L8244 = [1, 3, 7, 11, 17], L8247 = [1, 3, 7, 11, 23], L8249 = [1, 3, 7, 11, 25], L8250 = [1, 3, 7, 11, 26], L8266 = [1, 3, 7, 13, 15], L8280 = [1, 3, 7, 15, 25], L8281 = [1, 3, 7, 15, 26], L8293 = [1, 3, 7, 17, 23], L8295 = [1, 3, 7, 17, 25], L8512 = [1, 3, 9, 11, 17], L8681 = [1, 3, 11, 13, 23], L8721 = [1, 3, 11, 23, 26], L8830 = [1, 3, 13, 13, 19], L8853 = [1, 3, 13, 15, 21], L8854 = [1, 3, 13, 15, 23], L8878 = [1, 3, 13, 19, 21], L8883 = [1, 3, 13, 19, 26], L9002 = [1, 3, 15, 21, 26], L9004 = [1, 3, 15, 23, 26], L9113 = [1, 3, 19, 21, 26], L9125 = [1, 3, 19, 26, 26], L9424 = [1, 4, 5, 6, 21], L9427 = [1, 4, 5, 6, 25], L10245 = [1, 4, 12, 14, 25], L10723 = [1, 5, 7, 11, 13], L10727 = [1, 5, 7, 11, 26], L10739 = [1, 5, 7, 13, 23], L10756 = [1, 5, 7, 23, 26], L10801 = [1, 5, 8, 14, 21], L10805 = [1, 5, 8, 14, 25], L10838 = [1, 5, 9, 11, 13], L10841 = [1, 5, 9, 11, 26], L10848 = [1, 5, 9, 13, 13], L10853 = [1, 5, 9, 13, 26], L10867 = [1, 5, 9, 26, 26], L10875 = [1, 5, 11, 13, 13], L10881 = [1, 5, 11, 13, 26], L10901 = [1, 5, 11, 26, 26],
38
EMILIO A. LAURET
Table 3. (continued) n = 5 q 54
I {0}
indexes of I-isospectral families {1437, 1439}, {1645, 1650, 1682}, {1706, 1748}, {2082, 2084}, {9152, 12600}, {10317, 10716}, {10349, 10390}, {10751, 11358}, {10875, 10877}, {12647, 12655}, {13801, 13804}, {13830, 13940}, {13916, 13921, 14102}, {13925, 13945}, {13927, 13928}, {13943, 13949, 13961, 14195}, {13958, 13967, 14194}, {13962, 13976, 14196}, {14126, 14168}, {14326, 14477}, {14332, 14508}, {14892, 14894}, {16249, 16251}, {16369, 16371}, {16398, 16400}, {16416, 16424}, {16418, 16432}, {16420, 16433}, {16422, 16434}, {19970, 19990}, {20337, 20406}, {20533, 20556, 20559}, {20541, 20603, 20606}, {20572, 20574}, {20633, 20635} {0, 1} {13961, 14195} {0, 1, 2} {13930, 13947}
L10944 = [1, 5, 13, 13, 23], L10976 = [1, 5, 13, 23, 26], L11070 = [1, 5, 23, 26, 26], L11601 = [1, 6, 12, 14, 25], L12336 = [1, 8, 12, 14, 25], L12777 = [1, 10, 12, 14, 25], L13043 = [1, 12, 12, 14, 25], L13122 = [1, 12, 14, 14, 25], L13129 = [1, 12, 14, 16, 25], L13135 = [1, 12, 14, 18, 25], L13140 = [1, 12, 14, 20, 25], L13144 = [1, 12, 14, 22, 25], L13147 = [1, 12, 14, 24, 25], L13149 = [1, 12, 14, 25, 26], L13842 = [2, 4, 13, 14, 16], L13857 = [2, 4, 13, 20, 22], L13869 = [2, 6, 8, 13, 16], L13871 = [2, 6, 8, 13, 20], L13872 = [2, 6, 8, 13, 24], L13874 = [2, 6, 10, 13, 13], L13875 = [2, 6, 10, 13, 14], L13877 = [2, 6, 10, 13, 18], L13878 = [2, 6, 10, 13, 22], L13880 = [2, 6, 10, 13, 26], L13882 = [2, 6, 13, 13, 14], L13884 = [2, 6, 13, 13, 18], L13886 = [2, 6, 13, 13, 22], L13891 = [2, 6, 13, 14, 26], L13897 = [2, 6, 13, 18, 26], L13903 = [2, 6, 13, 22, 26], L13918 = [2, 8, 10, 13, 16], L14059 = [4, 8, 12, 13, 13], L14060 = [4, 8, 12, 13, 16], L14061 = [4, 8, 12, 13, 20], L14062 = [4, 8, 12, 13, 24], L14063 = [4, 8, 12, 13, 26], L14065 = [4, 8, 13, 13, 16], L14066 = [4, 8, 13, 13, 20], L14068 = [4, 8, 13, 16, 26], L14069 = [4, 8, 13, 20, 26], L14072 = [4, 12, 13, 13, 16], L14074 = [4, 12, 13, 16, 26]. q = 54 : L1437 = [0, 1, 4, 7, 17], L1439 = [0, 1, 4, 7, 19], L1645 = [0, 1, 5, 7, 17], L1650 = [0, 1, 5, 7, 25], L1682 = [0, 1, 5, 11, 13], L1706 = [0, 1, 5, 13, 17], L1748 = [0, 1, 5, 19, 23], L2082 = [0, 1, 8, 10, 17], L2084 = [0, 1, 8, 10, 19], L9152 = [1, 2, 13, 17, 23], L10317 = [1, 3, 5, 11, 23], L10349 = [1, 3, 5, 13, 25], L10390 = [1, 3, 5, 17, 25], L10716 = [1, 3, 7, 11, 13], L10751 = [1, 3, 7, 13, 25], L10875 = [1, 3, 8, 10, 17], L10877 = [1, 3, 8, 10, 19], L11358 = [1, 3, 11, 19, 23], L12600 = [1, 4, 7, 11, 17], L12647 = [1, 4, 7, 17, 18], L12655 = [1, 4, 7, 18, 19], L13801 = [1, 5, 6, 11, 19], L13804 = [1, 5, 6, 11, 25], L13830 = [1, 5, 6, 13, 25], L13916 = [1, 5, 7, 9, 17], L13921 = [1, 5, 7, 9, 25], L13925 = [1, 5, 7, 11, 17], L13927 = [1, 5, 7, 11, 19], L13928 = [1, 5, 7, 11, 23], L13930 = [1, 5, 7, 11, 25], L13940 = [1, 5, 7, 12, 25], L13943 = [1, 5, 7, 13, 17], L13945 = [1, 5, 7, 13, 19], L13947 = [1, 5, 7, 13, 23], L13949 = [1, 5, 7, 13, 25], L13958 = [1, 5, 7, 17, 18], L13961 = [1, 5, 7, 17, 25], L13962 = [1, 5, 7, 17, 27], L13967 = [1, 5, 7, 18, 25], L13976 = [1, 5, 7, 25, 27], L14102 = [1, 5, 9, 11, 13], L14126 = [1, 5, 9, 13, 17], L14168 = [1, 5, 9, 19, 23], L14194 = [1, 5, 11, 13, 18], L14195 = [1, 5, 11, 13, 19], L14196 = [1, 5, 11, 13, 27], L14326 = [1, 5, 13, 17, 18], L14332 = [1, 5, 13, 17, 27], L14477 = [1, 5, 18, 19, 23], L14508 = [1, 5, 19, 23, 27], L14892 = [1, 6, 8, 10, 17], L14894 = [1, 6, 8, 10, 19], L16249 = [1, 8, 9, 10, 17], L16251 = [1, 8, 9, 10, 19], L16369 = [1, 8, 10, 12, 17], L16371 = [1, 8, 10, 12, 19], L16398 = [1, 8, 10, 15, 17], L16400 = [1, 8, 10, 15, 19], L16416 = [1, 8, 10, 17, 18], L16418 = [1, 8, 10, 17, 21], L16420 = [1, 8, 10, 17, 24], L16422 = [1, 8, 10, 17, 27], L16424 = [1, 8, 10, 18, 19], L16432 = [1, 8, 10, 19, 21], L16433 = [1, 8, 10, 19, 24], L16434 = [1, 8, 10, 19, 27], L19970 = [2, 3, 4, 8, 20], L19990 = [2, 3, 4, 10, 14], L20337 = [2, 3, 10, 22, 26], L20406 = [2, 3, 14, 22, 26], L20533 = [2, 4, 8, 9, 22], L20541 = [2, 4, 8, 22, 27], L20556 = [2, 4, 9, 10, 14], L20559 = [2, 4, 9, 10, 20], L20572 = [2, 4, 9, 14, 16], L20574 = [2, 4, 9, 14, 20], L20603 = [2, 4, 10, 14, 27], L20606 = [2, 4, 10, 20, 27], L20633 = [2, 4, 14, 16, 27], L20635 = [2, 4, 14, 20, 27].
APPENDIX
39
Table 3. (continued) n = 5 q 55 56
I {0} {0}
indexes of I-isospectral families {1592, 1593}, {7532, 7551}, {10162, 10163}, {10166, 10167} {91, 93}, {100, 134}, {983, 995}, {1196, 1200}, {1251, 1264}, {1254, 1671}, {1262, 1287}, {1271, 1681}, {1283, 1678}, {1347, 1686}, {1859, 1866}, {2279, 2283}, {2337, 2342}, {2786, 2789}, {7084, 7096}, {7706, 7718}, {8223, 8234}, {8671, 8683}, {9002, 9013}, {9258, 9270}, {9379, 9391}, {9393, 9417}, {9395, 9434}, {9397, 9451}, {9399, 9463}, {9401, 9471}, {9405, 9475}, {10294, 10296}, {10298, 10312}, {10344, 10373}, {10395, 10575}, {10510, 10518}, {10573, 13845}, {10577, 10603}, {10581, 11543}, {10659, 13859}, {10915, 10924}, {10928, 10932}, {10948, 10965}, {11131, 11136, 11152}, {11335, 11405}, {11338, 14076}, {11346, 11428}, {11348, 11519}, {11369, 14079}, {11403, 11561}, {11412, 14120}, {11424, 14086}, {11488, 14125}, {11554, 14116}, {11838, 14139}, {12416, 12423}, {13027, 13033}, {13855, 13861}, {14546, 14553}, {14864, 14871}, {15052, 15059}, {15144, 15151}, {15223, 15230}, {15232, 15246}, {15233, 15252}, {15234, 15258}, {15237, 15266}, {15239, 15268}, {15925, 15929}, {16691, 16696}, {17298, 17302}, {17328, 17334}, {17330, 17340}, {17424, 17429}, {17505, 17510}, {17573, 17578}, {17580, 17590}, {17582, 17597}, {17583, 17600}, {17585, 17602}, {19208, 19211}, {19229, 19238}, {19232, 19252}, {19235, 19253}, {19606, 19609} {0, 1} {19231, 19233} {2, 3} {2498, 18214}, {13287, 18212}, {16861, 18209}, {17926, 18205}, {19591, 19690} {3, 4} {2193, 2919}, {13253, 19638}
q = 55 : L1592 = [0, 5, 10, 11, 15], L1593 = [0, 5, 10, 11, 20], L7532 = [1, 3, 8, 12, 19], L7551 = [1, 3, 8, 14, 21], L10162 = [5, 10, 11, 11, 15], L10163 = [5, 10, 11, 11, 20], L10166 = [5, 10, 11, 15, 22], L10167 = [5, 10, 11, 20, 22]. q = 56 : L91 = [0, 0, 1, 3, 13], L93 = [0, 0, 1, 3, 15], L100 = [0, 0, 1, 3, 23], L134 = [0, 0, 1, 5, 11], L983 = [0, 1, 2, 13, 15], L995 = [0, 1, 2, 13, 27], L1196 = [0, 1, 3, 9, 17], L1200 = [0, 1, 3, 9, 23], L1251 = [0, 1, 3, 13, 14], L1254 = [0, 1, 3, 13, 17], L1262 = [0, 1, 3, 13, 28], L1264 = [0, 1, 3, 14, 15], L1271 = [0, 1, 3, 14, 23], L1283 = [0, 1, 3, 15, 23], L1287 = [0, 1, 3, 15, 28], L1347 = [0, 1, 3, 23, 28], L1671 = [0, 1, 5, 9, 13], L1678 = [0, 1, 5, 9, 25], L1681 = [0, 1, 5, 11, 14], L1686 = [0, 1, 5, 11, 28], L1859 = [0, 1, 6, 13, 15], L1866 = [0, 1, 6, 13, 27], L2193 = [0, 1, 8, 16, 24], L2279 = [0, 1, 9, 15, 17], L2283 = [0, 1, 9, 15, 25], L2337 = [0, 1, 10, 13, 15], L2342 = [0, 1, 10, 13, 27], L2498 = [0, 1, 13, 15, 27], L2786 = [0, 2, 6, 7, 10], L2789 = [0, 2, 6, 7, 18], L2919 = [0, 7, 8, 16, 24], L7084 = [1, 2, 2, 13, 15], L7096 = [1, 2, 2, 13, 27], L7706 = [1, 2, 4, 13, 15], L7718 = [1, 2, 4, 13, 27], L8223 = [1, 2, 6, 13, 15], L8234 = [1, 2, 6, 13, 27], L8671 = [1, 2, 8, 13, 15], L8683 = [1, 2, 8, 13, 27], L9002 = [1, 2, 10, 13, 15], L9013 = [1, 2, 10, 13, 27], L9258 = [1, 2, 12, 13, 15], L9270 = [1, 2, 12, 13, 27], L9379 = [1, 2, 13, 14, 15], L9391 = [1, 2, 13, 14, 27], L9393 = [1, 2, 13, 15, 16], L9395 = [1, 2, 13, 15, 18], L9397 = [1, 2, 13, 15, 20], L9399 = [1, 2, 13, 15, 22], L9401 = [1, 2, 13, 15, 24], L9405 = [1, 2, 13, 15, 28], L9417 = [1, 2, 13, 16, 27], L9434 = [1, 2, 13, 18, 27], L9451 = [1, 2, 13, 20, 27], L9463 = [1, 2, 13, 22, 27], L9471 = [1, 2, 13, 24, 27], L9475 = [1, 2, 13, 27, 28], L10294 = [1, 3, 5, 9, 13], L10296 = [1, 3, 5, 9, 15], L10298 = [1, 3, 5, 9, 17], L10312 = [1, 3, 5, 11, 15], L10344 = [1, 3, 5, 13, 17], L10373 = [1, 3, 5, 15, 19], L10395 = [1, 3, 5, 17, 21], L10510 = [1, 3, 7, 9, 19], L10518 = [1, 3, 7, 9, 27], L10573 = [1, 3, 7, 13, 17], L10575 = [1, 3, 7, 13, 19], L10577 =
40
EMILIO A. LAURET
Table 3. (continued) n = 5 q I indexes of I-isospectral families 57 {0} {2001, 2003}, {6211, 6228}, {12332, 12373}, {13275, 13276, 13280}, {13279, 13281, 13284}, {13289, 13294}, {13291, 13295} 58 {0} {1280, 1309}, {1693, 1717}, {11197, 11210}, {11987, 11988, 16408}, {11990, 12179}, {14647, 14792}, {18971, 18979}, {19041, 19042} 59 {0} {8276, 8406}
[1, 3, 7, 13, 21], L10581 = [1, 3, 7, 13, 27], L10603 = [1, 3, 7, 15, 21], L10659 = [1, 3, 7, 21, 23], L10915 = [1, 3, 9, 11, 25], L10924 = [1, 3, 9, 13, 27], L10928 = [1, 3, 9, 14, 17], L10932 = [1, 3, 9, 14, 23], L10948 = [1, 3, 9, 17, 28], L10965 = [1, 3, 9, 23, 28], L11131 = [1, 3, 11, 13, 17], L11136 = [1, 3, 11, 13, 25], L11152 = [1, 3, 11, 15, 17], L11335 = [1, 3, 13, 14, 14], L11338 = [1, 3, 13, 14, 17], L11346 = [1, 3, 13, 14, 28], L11348 = [1, 3, 13, 15, 17], L11369 = [1, 3, 13, 17, 28], L11403 = [1, 3, 13, 28, 28], L11405 = [1, 3, 14, 14, 15], L11412 = [1, 3, 14, 14, 23], L11424 = [1, 3, 14, 15, 23], L11428 = [1, 3, 14, 15, 28], L11488 = [1, 3, 14, 23, 28], L11519 = [1, 3, 15, 17, 27], L11543 = [1, 3, 15, 21, 27], L11554 = [1, 3, 15, 23, 28], L11561 = [1, 3, 15, 28, 28], L11838 = [1, 3, 23, 28, 28], L12416 = [1, 4, 6, 13, 15], L12423 = [1, 4, 6, 13, 27], L13027 = [1, 4, 10, 13, 15], L13033 = [1, 4, 10, 13, 27], L13253 = [1, 4, 12, 20, 28], L13287 = [1, 4, 13, 15, 27], L13845 = [1, 5, 7, 9, 13], L13855 = [1, 5, 7, 11, 13], L13859 = [1, 5, 7, 11, 21], L13861 = [1, 5, 7, 11, 25], L14076 = [1, 5, 9, 13, 14], L14079 = [1, 5, 9, 13, 28], L14086 = [1, 5, 9, 14, 25], L14116 = [1, 5, 9, 25, 28], L14120 = [1, 5, 11, 14, 14], L14125 = [1, 5, 11, 14, 28], L14139 = [1, 5, 11, 28, 28], L14546 = [1, 6, 6, 13, 15], L14553 = [1, 6, 6, 13, 27], L14864 = [1, 6, 8, 13, 15], L14871 = [1, 6, 8, 13, 27], L15052 = [1, 6, 10, 13, 15], L15059 = [1, 6, 10, 13, 27], L15144 = [1, 6, 12, 13, 15], L15151 = [1, 6, 12, 13, 27], L15223 = [1, 6, 13, 14, 15], L15230 = [1, 6, 13, 14, 27], L15232 = [1, 6, 13, 15, 16], L15233 = [1, 6, 13, 15, 18], L15234 = [1, 6, 13, 15, 20], L15237 = [1, 6, 13, 15, 24], L15239 = [1, 6, 13, 15, 28], L15246 = [1, 6, 13, 16, 27], L15252 = [1, 6, 13, 18, 27], L15258 = [1, 6, 13, 20, 27], L15266 = [1, 6, 13, 24, 27], L15268 = [1, 6, 13, 27, 28], L15925 = [1, 7, 9, 15, 17], L15929 = [1, 7, 9, 15, 25], L16691 = [1, 8, 10, 13, 15], L16696 = [1, 8, 10, 13, 27], L16861 = [1, 8, 13, 15, 27], L17298 = [1, 9, 14, 15, 17], L17302 = [1, 9, 14, 15, 25], L17328 = [1, 9, 15, 17, 21], L17330 = [1, 9, 15, 17, 28], L17334 = [1, 9, 15, 21, 25], L17340 = [1, 9, 15, 25, 28], L17424 = [1, 10, 10, 13, 15], L17429 = [1, 10, 10, 13, 27], L17505 = [1, 10, 12, 13, 15], L17510 = [1, 10, 12, 13, 27], L17573 = [1, 10, 13, 14, 15], L17578 = [1, 10, 13, 14, 27], L17580 = [1, 10, 13, 15, 16], L17582 = [1, 10, 13, 15, 20], L17583 = [1, 10, 13, 15, 24], L17585 = [1, 10, 13, 15, 28], L17590 = [1, 10, 13, 16, 27], L17597 = [1, 10, 13, 20, 27], L17600 = [1, 10, 13, 24, 27], L17602 = [1, 10, 13, 27, 28], L17926 = [1, 12, 13, 15, 27], L18205 = [1, 13, 15, 16, 27], L18209 = [1, 13, 15, 20, 27], L18212 = [1, 13, 15, 24, 27], L18214 = [1, 13, 15, 27, 28], L19208 = [2, 6, 7, 7, 10], L19211 = [2, 6, 7, 7, 18], L19229 = [2, 6, 7, 10, 14], L19231 = [2, 6, 7, 10, 18], L19232 = [2, 6, 7, 10, 21], L19233 = [2, 6, 7, 10, 22], L19235 = [2, 6, 7, 10, 28], L19238 = [2, 6, 7, 14, 18], L19252 = [2, 6, 7, 18, 21], L19253 = [2, 6, 7, 18, 28], L19591 = [4, 7, 7, 21, 21], L19606 = [4, 7, 8, 12, 16], L19609 = [4, 7, 8, 12, 24], L19638 = [4, 7, 12, 20, 28], L19690 = [7, 7, 8, 21, 21]. q = 57 : L2001 = [0, 3, 6, 19, 21], L2003 = [0, 3, 9, 12, 19], L6211 = [1, 2, 4, 7, 25], L6228 = [1, 2, 4, 8, 25], L12332 = [1, 7, 12, 26, 27], L12373 = [1, 7, 18, 20, 27], L13275 = [3, 6, 9, 15, 19], L13276 = [3, 6, 9, 18, 19], L13279 = [3, 6, 9, 19, 24], L13280 = [3, 6, 9, 19, 27], L13281 = [3, 6, 12, 15, 19], L13284 = [3, 6, 12, 19, 24], L13289 = [3, 6, 18, 19, 24], L13291 = [3, 6, 19, 19, 21], L13294 = [3, 9, 12, 15, 19], L13295 = [3, 9, 12, 19, 19]. q = 58 : L1280 = [0, 1, 3, 13, 21], L1309 = [0, 1, 3, 15, 23], L1693 = [0, 1, 5, 7, 25], L1717 = [0, 1, 5, 9, 23], L11197 = [1, 3, 7, 21, 25], L11210 = [1, 3, 7, 23, 25], L11987 = [1, 3, 13, 21, 25], L11988 = [1, 3, 13, 21, 27], L11990 = [1, 3, 13, 21, 29], L12179 = [1, 3, 15, 23, 29], L14647 = [1, 5, 7, 25, 29], L14792 = [1, 5, 9, 23, 29], L16408 = [1, 7, 9, 11, 15], L18971 = [2, 4, 8, 22, 29], L18979 = [2, 4, 10, 20, 29], L19041 = [2, 8, 10, 14, 29], L19042 = [2, 8, 10, 26, 29]. q = 59 : L8276 = [1, 3, 7, 22, 27], L8406 = [1, 3, 9, 13, 20].
APPENDIX
41
Table 3. (continued) n = 5 q 60
I {0}
indexes of I-isospectral families {2289, 2363}, {4658, 4664}, {4797, 4802}, {5493, 5507}, {5555, 5567}, {12753, 12763}, {15526, 15532}, {16089, 16092}, {16166, 16208}, {16612, 16639}, {20060, 20067}, {21831, 22407}, {21854, 21874}, {21886, 22584}, {21912, 22586}, {21918, 22590}, {25926, 25930}, {35852, 35858}, {36022, 36028}, {36047, 36061}, {36050, 36086}, {36053, 36097}, {36055, 36098}, {36782, 36787}, {36803, 36815}, {36806, 36834}, {36810, 36840}, {40224, 40238}, {40348, 40389}, {40362, 40430}, {40370, 40437}, {40374, 40439}, {40375, 40440}, {40591, 40624}, {40603, 40657}, {40609, 40663}, {40612, 40665} {2, 3} {3784, 31209}, {4940, 5577}, {13927, 31207}, {20482, 31201}, {24940, 31191}, {27140, 31184}, {29328, 31168}, {30268, 31158}, {30971, 31147}, {35056, 39691}, {36372, 40414}, {36769, 38749}, {39877, 39954}, {40884, 40976} {4} {15639, 23070}, {21393, 23068}, {21893, 22812}, {35572, 36500}, {36419, 40317}, {36526, 40470}
q = 60 : L2289 = [0, 1, 5, 7, 17], L2363 = [0, 1, 5, 11, 13], L3784 = [0, 1, 14, 16, 29], L4658 = [0, 2, 5, 6, 14], L4664 = [0, 2, 5, 6, 22], L4797 = [0, 2, 6, 14, 15], L4802 = [0, 2, 6, 15, 22], L4940 = [0, 2, 15, 15, 30], L5493 = [0, 4, 5, 8, 24], L5507 = [0, 4, 5, 12, 16], L5555 = [0, 4, 8, 15, 24], L5567 = [0, 4, 12, 15, 16], L5577 = [0, 4, 15, 15, 30], L12753 = [1, 2, 8, 11, 19], L12763 = [1, 2, 8, 11, 29], L13927 = [1, 2, 14, 16, 29], L15526 = [1, 3, 5, 9, 17], L15532 = [1, 3, 5, 9, 23], L15639 = [1, 3, 5, 15, 25], L16089 = [1, 3, 7, 9, 13], L16092 = [1, 3, 7, 9, 17], L16166 = [1, 3, 7, 13, 21], L16208 = [1, 3, 7, 17, 21], L16612 = [1, 3, 9, 11, 27], L16639 = [1, 3, 9, 13, 21], L20060 = [1, 4, 11, 14, 19], L20067 = [1, 4, 11, 14, 29], L20482 = [1, 4, 14, 16, 29], L21393 = [1, 5, 5, 15, 25], L21831 = [1, 5, 7, 10, 17], L21854 = [1, 5, 7, 11, 29], L21874 = [1, 5, 7, 13, 17], L21886 = [1, 5, 7, 15, 17], L21893 = [1, 5, 7, 15, 25], L21912 = [1, 5, 7, 17, 20], L21918 = [1, 5, 7, 17, 30], L22407 = [1, 5, 10, 11, 13], L22584 = [1, 5, 11, 13, 15], L22586 = [1, 5, 11, 13, 20], L22590 = [1, 5, 11, 13, 30], L22812 = [1, 5, 13, 15, 25], L23068 = [1, 5, 15, 25, 25], L23070 = [1, 5, 15, 25, 27], L24940 = [1, 6, 14, 16, 29], L25926 = [1, 7, 11, 13, 19], L25930 = [1, 7, 11, 13, 29], L27140 = [1, 8, 14, 16, 29], L29328 = [1, 10, 14, 16, 29], L30268 = [1, 12, 14, 16, 29], L30971 = [1, 14, 14, 16, 29], L31147 = [1, 14, 16, 16, 29], L31158 = [1, 14, 16, 18, 29], L31168 = [1, 14, 16, 20, 29], L31184 = [1, 14, 16, 22, 29], L31191 = [1, 14, 16, 24, 29], L31201 = [1, 14, 16, 26, 29], L31207 = [1, 14, 16, 28, 29], L31209 = [1, 14, 16, 29, 30], L35056 = [2, 3, 12, 18, 27], L35572 = [2, 4, 5, 15, 25], L35852 = [2, 5, 5, 6, 14], L35858 = [2, 5, 5, 6, 22], L36022 = [2, 5, 6, 10, 14], L36028 = [2, 5, 6, 10, 22], L36047 = [2, 5, 6, 14, 15], L36050 = [2, 5, 6, 14, 20], L36053 = [2, 5, 6, 14, 25], L36055 = [2, 5, 6, 14, 30], L36061 = [2, 5, 6, 15, 22], L36086 = [2, 5, 6, 20, 22], L36097 = [2, 5, 6, 22, 25], L36098 = [2, 5, 6, 22, 30], L36372 = [2, 5, 10, 20, 25], L36419 = [2, 5, 12, 15, 25], L36500 = [2, 5, 15, 16, 25], L36526 = [2, 5, 15, 24, 25], L36769 = [2, 6, 9, 21, 24], L36782 = [2, 6, 10, 14, 15], L36787 = [2, 6, 10, 15, 22], L36803 = [2, 6, 14, 15, 15], L36806 = [2, 6, 14, 15, 20], L36810 = [2, 6, 14, 15, 30], L36815 = [2, 6, 15, 15, 22], L36834 = [2, 6, 15, 20, 22], L36840 = [2, 6, 15, 22, 30], L38749 = [3, 4, 12, 18, 27], L39691 = [3, 8, 12, 18, 27], L39877 = [3, 10, 12, 18, 27], L39954 = [3, 12, 18, 20, 27], L40224 = [4, 5, 5, 8, 24], L40238 = [4, 5, 5, 12, 16], L40317 = [4, 5, 6, 15, 25], L40348 = [4, 5, 8, 10, 24], L40362 = [4, 5, 8, 15, 24], L40370 = [4, 5, 8, 20, 24], L40374 = [4, 5, 8, 24, 25], L40375 = [4, 5, 8, 24, 30], L40389 = [4, 5, 10, 12, 16], L40414 = [4, 5, 10, 20, 25], L40430 = [4, 5, 12, 15, 16], L40437 = [4, 5, 12, 16, 20], L40439 = [4, 5, 12, 16, 25], L40440 = [4, 5, 12, 16, 30], L40470 = [4, 5, 15, 18, 25], L40591 = [4, 8, 10, 15, 24], L40603 = [4, 8, 15, 15, 24], L40609 = [4, 8, 15, 20, 24], L40612 = [4, 8, 15, 24, 30], L40624 = [4, 10, 12, 15, 16], L40657 = [4, 12, 15, 15, 16], L40663 = [4, 12, 15, 16, 20], L40665 = [4, 12, 15, 16, 30], L40884 = [5, 6, 10, 20, 25], L40976 = [5, 10, 12, 20, 25].
42
EMILIO A. LAURET
Table 3. (continued) n = 5 q 62
I {0}
indexes of I-isospectral families {1929, 1933}, {13435, 13440}, {13525, 13576, 13926}, {14296, 14816}, {17952, 17964} 63 {0} {2315, 2318}, {13094, 13157}, {17291, 17325}, {18149, 18152}, {18944, 18947}, {18961, 18966}, {18963, 18971}, {18993, 19013}, {20805, 20807}, {20822, 20880} {3, 4} {2458, 2900} q = 62 : L1929 = [0, 1, 5, 6, 26], L1933 = [0, 1, 5, 6, 30], L13435 = [1, 3, 7, 9, 21], L13440 = [1, 3, 7, 9, 27], L13525 = [1, 3, 7, 15, 27], L13576 = [1, 3, 7, 19, 27], L13926 = [1, 3, 9, 13, 19], L14296 = [1, 3, 11, 17, 19], L14816 = [1, 3, 15, 23, 25], L17952 = [1, 5, 6, 26, 31], L17964 = [1, 5, 6, 30, 31]. q = 63 : L2315 = [0, 1, 8, 10, 19], L2318 = [0, 1, 8, 10, 26], L2458 = [0, 1, 9, 18, 27], L2900 = [0, 7, 9, 18, 27], L13094 = [1, 3, 8, 13, 29], L13157 = [1, 3, 8, 20, 22], L17291 = [1, 6, 8, 13, 29], L17325 = [1, 6, 8, 20, 22], L18149 = [1, 7, 8, 10, 19], L18152 = [1, 7, 8, 10, 26], L18944 = [1, 8, 10, 14, 19], L18947 = [1, 8, 10, 14, 26], L18961 = [1, 8, 10, 19, 21], L18963 = [1, 8, 10, 19, 28], L18966 = [1, 8, 10, 21, 26], L18971 = [1, 8, 10, 26, 28], L18993 = [1, 8, 12, 13, 29], L19013 = [1, 8, 12, 20, 22], L20805 = [3, 6, 7, 12, 15], L20807 = [3, 6, 7, 12, 24], L20822 = [3, 6, 7, 18, 27], L20880 = [3, 7, 9, 12, 18]. q = 64 : L194 = [0, 0, 1, 7, 17], L197 = [0, 0, 1, 7, 23], L1195 = [0, 1, 2, 15, 17], L1209 = [0, 1, 2, 15, 31], L1388 = [0, 1, 3, 5, 23], L1410 = [0, 1, 3, 7, 21], L1412 = [0, 1, 3, 7, 23], L1457 = [0, 1, 3, 9, 25], L1490 = [0, 1, 3, 11, 17], L1492 = [0, 1, 3, 11, 19], L1494 = [0, 1, 3, 11, 23], L1531 = [0, 1, 3, 13, 23], L1592 = [0, 1, 3, 17, 25], L2093 = [0, 1, 5, 9, 17], L2096 = [0, 1, 5, 9, 25], L2098 = [0, 1, 5, 9, 29], L2375 = [0, 1, 6, 15, 17], L2385 = [0, 1, 6, 15, 31], L2492 = [0, 1, 7, 8, 17], L2495 = [0, 1, 7, 8, 23], L2548 = [0, 1, 7, 16, 17], L2551 = [0, 1, 7, 16, 23], L2561 = [0, 1, 7, 17, 24], L2564 = [0, 1, 7, 17, 32], L2581 = [0, 1, 7, 23, 24], L2585 = [0, 1, 7, 23, 32], L2841 = [0, 1, 10, 15, 17], L2849 = [0, 1, 10, 15, 31], L3112 = [0, 1, 14, 15, 17], L3117 = [0, 1, 14, 15, 31], L3194 = [0, 1, 15, 17, 31], L8192 = [1, 1, 15, 15, 17], L8199 = [1, 1, 15, 15, 31], L9530 = [1, 2, 2, 15, 17], L9544 = [1, 2, 2, 15, 31], L10363 = [1, 2, 4, 15, 17], L10377 = [1, 2, 4, 15, 31], L11074 = [1, 2, 6, 15, 17], L11088 = [1, 2, 6, 15, 31], L11422 = [1, 2, 7, 18, 25], L11428 = [1, 2, 7, 18, 31], L11673 = [1, 2, 8, 15, 17], L11687 = [1, 2, 8, 15, 31], L11910 = [1, 2, 9, 14, 23], L11918 = [1, 2, 9, 14, 31], L12159 = [1, 2, 10, 15, 17], L12173 = [1, 2, 10, 15, 31], L12557 = [1, 2, 12, 15, 17], L12571 = [1, 2, 12, 15, 31], L12881 = [1, 2, 14, 15, 17], L12895 = [1, 2, 14, 15, 31], L13028 = [1, 2, 15, 16, 17], L13042 = [1, 2, 15, 16, 31], L13044 = [1, 2, 15, 17, 18], L13046 = [1, 2, 15, 17, 20], L13048 = [1, 2, 15, 17, 22], L13050 = [1, 2, 15, 17, 24], L13052 = [1, 2, 15, 17, 26], L13054 = [1, 2, 15, 17, 28], L13058 = [1, 2, 15, 17, 32], L13070 = [1, 2, 15, 18, 31], L13093 = [1, 2, 15, 20, 31], L13112 = [1, 2, 15, 22, 31], L13128 = [1, 2, 15, 24, 31], L13140 = [1, 2, 15, 26, 31], L13148 = [1, 2, 15, 28, 31], L13153 = [1, 2, 15, 31, 32], L14275 = [1, 3, 5, 9, 19], L14277 = [1, 3, 5, 9, 21], L14369 = [1, 3, 5, 15, 21], L14371 = [1, 3, 5, 15, 23], L14374 = [1, 3, 5, 15, 27], L14386 = [1, 3, 5, 16, 23], L14399 = [1, 3, 5, 17, 21], L14401 = [1, 3, 5, 17, 23], L14405 = [1, 3, 5, 17, 27], L14449 = [1, 3, 5, 21, 25], L14471 = [1, 3, 5, 23, 27], L14475 = [1, 3, 5, 23, 32], L14587 = [1, 3, 7, 11, 19], L14618 = [1, 3, 7, 13, 15], L14637 = [1, 3, 7, 15, 19], L14654 = [1, 3, 7, 16, 21], L14656 = [1, 3, 7, 16, 23], L14698 = [1, 3, 7, 19, 27], L14718 = [1, 3, 7, 21, 27], L14720 = [1, 3, 7, 21, 31], L14721 = [1, 3, 7, 21, 32], L14741 = [1, 3, 7, 23, 32], L14752 = [1, 3, 7, 25, 27], L15094 = [1, 3, 9, 11, 17], L15097 = [1, 3, 9, 11, 23], L15100 = [1, 3, 9, 11, 29], L15112 = [1, 3, 9, 13, 31], L15133 = [1, 3, 9, 16, 25], L15153 = [1, 3, 9, 19, 25], L15157 = [1, 3, 9, 19, 31], L15190 = [1, 3, 9, 25, 32], L15271 = [1, 3, 10, 13, 18], L15444 = [1, 3, 11, 13, 17], L15484 = [1, 3, 11, 16, 17], L15486 = [1, 3, 11, 16, 19], L15488 = [1, 3, 11, 16, 23], L15506 = [1, 3, 11, 17, 32], L15520 = [1, 3, 11, 19, 27], L15525 = [1, 3, 11, 19, 32], L15541 = [1, 3, 11, 23, 32], L15771 = [1, 3, 13, 14, 22], L15790 = [1, 3, 13, 15, 29], L15791 = [1, 3, 13, 15, 31], L15799 = [1, 3, 13, 16, 23], L15808 = [1, 3, 13, 17, 19], L15813 = [1, 3, 13, 17, 31], L15856 = [1, 3, 13, 23, 27], L15860 = [1, 3, 13, 23, 32], L16083 = [1, 3, 15, 23, 25], L16085 = [1, 3, 15, 23, 27], L16143 = [1, 3, 16, 17, 25], L16301 = [1, 3, 17, 25, 32], L17511 = [1, 4, 6, 15, 17], L17521 = [1, 4, 6, 15, 31], L17762 = [1, 4, 7, 17, 28], L17803 = [1, 4, 7, 23, 28], L18316 = [1, 4, 10, 15, 17],
APPENDIX
43
Table 3. (continued) n = 5 q 64
L18324 L19659 L19942 L19973 L20898 L21397 L21611 L21825 L21839 L21854 L21891 L22373 L22406 L22469 L22684
I {0}
indexes of I-isospectral families {1195, 1209}, {1388, 1410}, {1412, 1457}, {1490, 1531}, {1492, 2093}, {1494, 2098}, {1592, 2096}, {2375, 2385}, {2841, 2849}, {3112, 3117}, {8192, 8199}, {9530, 9544}, {10363, 10377}, {11074, 11088}, {11422, 11918}, {11428, 11910}, {11673, 11687}, {12159, 12173}, {12557, 12571}, {12881, 12895}, {13028, 13042}, {13044, 13070}, {13046, 13093}, {13048, 13112}, {13050, 13128}, {13052, 13140}, {13054, 13148}, {13058, 13153}, {14275, 14277}, {14369, 14399}, {14371, 14449}, {14374, 14405}, {14386, 14654}, {14401, 15094}, {14471, 15097}, {14475, 14721}, {14587, 14718}, {14618, 14637}, {14656, 15133}, {14698, 19660}, {14720, 15100}, {14741, 15190}, {14752, 19659}, {15112, 15157}, {15153, 15444}, {15271, 15771}, {15484, 15799}, {15486, 19942}, {15488, 19947}, {15506, 15860}, {15520, 16083}, {15525, 19956}, {15541, 19980}, {15790, 15808}, {15791, 15813}, {15856, 19681}, {16085, 19927}, {16143, 19945}, {16301, 19973}, {17511, 17521}, {18316, 18324}, {18792, 18798}, {20760, 20770}, {20898, 20909}, {21128, 21138}, {21397, 21405}, {21402, 21425}, {21611, 21621}, {21727, 21736}, {21825, 21835}, {21837, 21854}, {21838, 21863}, {21839, 21870}, {21841, 21881}, {21844, 21891}, {21846, 21893}, {22469, 22479}, {23125, 23133}, {23428, 23434}, {23938, 23946}, {24110, 24117}, {24201, 24208}, {24278, 24286}, {24288, 24300}, {24289, 24308}, {24291, 24317}, {24292, 24323}, {24294, 24326}, {24936, 24941}, {25329, 25334}, {25403, 25408}, {25411, 25423}, {25412, 25427}, {25413, 25430}, {25415, 25432} {2, 3} {3194, 25713}, {18910, 25711}, {23527, 25708}, {25019, 25704} {0, 1, 2, 3, 4} {194, 197}, {2492, 2495}, {2548, 2551}, {2561, 2581}, {2564, 2585}, {17762, 17803}, {22317, 22320}, {22373, 22376}, {22386, 22406}, {22389, 22410}, {22445, 22446}, {22636, 22651}, {22684, 22687}, {22697, 22717}, {22700, 22721}, {22755, 22828}, {22758, 22832}, {22761, 22841} = [1, 4, 10, 15, 31], L18792 = [1, 4, 14, 15, 17], L18798 = [1, 4, 14, 15, 31], L18910 = [1, 4, 15, 17, 31], = [1, 5, 7, 13, 27], L19660 = [1, 5, 7, 13, 29], L19681 = [1, 5, 7, 17, 29], L19927 = [1, 5, 9, 13, 29], = [1, 5, 9, 16, 17], L19945 = [1, 5, 9, 16, 25], L19947 = [1, 5, 9, 16, 29], L19956 = [1, 5, 9, 17, 32], = [1, 5, 9, 25, 32], L19980 = [1, 5, 9, 29, 32], L20760 = [1, 6, 6, 15, 17], L20770 = [1, 6, 6, 15, 31], = [1, 6, 7, 9, 22], L20909 = [1, 6, 7, 10, 15], L21128 = [1, 6, 8, 15, 17], L21138 = [1, 6, 8, 15, 31], = [1, 6, 10, 15, 17], L21402 = [1, 6, 10, 15, 25], L21405 = [1, 6, 10, 15, 31], L21425 = [1, 6, 10, 17, 23], = [1, 6, 12, 15, 17], L21621 = [1, 6, 12, 15, 31], L21727 = [1, 6, 14, 15, 17], L21736 = [1, 6, 14, 15, 31], = [1, 6, 15, 16, 17], L21835 = [1, 6, 15, 16, 31], L21837 = [1, 6, 15, 17, 18], L21838 = [1, 6, 15, 17, 20], = [1, 6, 15, 17, 22], L21841 = [1, 6, 15, 17, 24], L21844 = [1, 6, 15, 17, 28], L21846 = [1, 6, 15, 17, 32], = [1, 6, 15, 18, 31], L21863 = [1, 6, 15, 20, 31], L21870 = [1, 6, 15, 22, 31], L21881 = [1, 6, 15, 24, 31], = [1, 6, 15, 28, 31], L21893 = [1, 6, 15, 31, 32], L22317 = [1, 7, 8, 8, 17], L22320 = [1, 7, 8, 8, 23], = [1, 7, 8, 16, 17], L22376 = [1, 7, 8, 16, 23], L22386 = [1, 7, 8, 17, 24], L22389 = [1, 7, 8, 17, 32], = [1, 7, 8, 23, 24], L22410 = [1, 7, 8, 23, 32], L22445 = [1, 7, 9, 15, 25], L22446 = [1, 7, 9, 15, 31], = [1, 7, 9, 23, 31], L22479 = [1, 7, 9, 25, 31], L22636 = [1, 7, 12, 17, 20], L22651 = [1, 7, 12, 20, 23], = [1, 7, 16, 16, 17], L22687 = [1, 7, 16, 16, 23], L22697 = [1, 7, 16, 17, 24], L22700 = [1, 7, 16, 17, 32],
44
EMILIO A. LAURET
Table 3. (continued) n = 5 q 65
I {0}
indexes of I-isospectral families {2490, 2491}, {2492, 2498}, {13130, 13344}, {17307, 17325}, {18302, 18303}, {18304, 18316}, {18306, 18307, 18309}, {18308, 18310}, {18311, 18320} {1} {18306, 18307} {0, 1} {18306, 18307} 66 {0} {184, 223}, {2659, 3227}, {2686, 2760}, {2689, 2727}, {2780, 3278}, {2824, 3281}, {5469, 5613}, {5504, 5615}, {6079, 6080}, {6086, 6087}, {6166, 6168}, {20547, 20611}, {26928, 26945}, {27454, 31799}, {27481, 27555}, {27484, 27522}, {27575, 31850}, {27619, 31853}, {27827, 28296}, {27832, 28326}, {27841, 28123}, {27849, 28127}, {28397, 32150}, {28441, 32153}, {28600, 32158}, {45216, 45344}, {45236, 45359}, {45349, 45401}, {45370, 45513}, {45384, 46430}, {45454, 46434}, {45466, 46437}, {45658, 46445}, {45670, 46449}, {48364, 48424}, {48404, 48448}, {48414, 48415}, {48428, 48431}, {48430, 48433}, {48452, 48455}, {48454, 48457}, {48690, 48692}, {48699, 48703}, {48701, 48705}, {48714, 48716} L22717 = [1, 7, 16, 23, 24], L22721 = [1, 7, 16, 23, 32], L22755 = [1, 7, 17, 24, 24], L22758 = [1, 7, 17, 24, 32], L22761 = [1, 7, 17, 32, 32], L22828 = [1, 7, 23, 24, 24], L22832 = [1, 7, 23, 24, 32], L22841 = [1, 7, 23, 32, 32], L23125 = [1, 8, 10, 15, 17], L23133 = [1, 8, 10, 15, 31], L23428 = [1, 8, 14, 15, 17], L23434 = [1, 8, 14, 15, 31], L23527 = [1, 8, 15, 17, 31], L23938 = [1, 10, 10, 15, 17], L23946 = [1, 10, 10, 15, 31], L24110 = [1, 10, 12, 15, 17], L24117 = [1, 10, 12, 15, 31], L24201 = [1, 10, 14, 15, 17], L24208 = [1, 10, 14, 15, 31], L24278 = [1, 10, 15, 16, 17], L24286 = [1, 10, 15, 16, 31], L24288 = [1, 10, 15, 17, 18], L24289 = [1, 10, 15, 17, 20], L24291 = [1, 10, 15, 17, 24], L24292 = [1, 10, 15, 17, 28], L24294 = [1, 10, 15, 17, 32], L24300 = [1, 10, 15, 18, 31], L24308 = [1, 10, 15, 20, 31], L24317 = [1, 10, 15, 24, 31], L24323 = [1, 10, 15, 28, 31], L24326 = [1, 10, 15, 31, 32], L24936 = [1, 12, 14, 15, 17], L24941 = [1, 12, 14, 15, 31], L25019 = [1, 12, 15, 17, 31], L25329 = [1, 14, 14, 15, 17], L25334 = [1, 14, 14, 15, 31], L25403 = [1, 14, 15, 16, 17], L25408 = [1, 14, 15, 16, 31], L25411 = [1, 14, 15, 17, 20], L25412 = [1, 14, 15, 17, 24], L25413 = [1, 14, 15, 17, 28], L25415 = [1, 14, 15, 17, 32], L25423 = [1, 14, 15, 20, 31], L25427 = [1, 14, 15, 24, 31], L25430 = [1, 14, 15, 28, 31], L25432 = [1, 14, 15, 31, 32], L25704 = [1, 15, 17, 20, 31], L25708 = [1, 15, 17, 24, 31], L25711 = [1, 15, 17, 28, 31], L25713 = [1, 15, 17, 31, 32]. q = 65 : L2490 = [0, 5, 10, 13, 15], L2491 = [0, 5, 10, 13, 20], L2492 = [0, 5, 10, 13, 25], L2498 = [0, 5, 13, 15, 20], L13130 = [1, 3, 12, 16, 29], L13344 = [1, 3, 14, 16, 23], L17307 = [1, 8, 12, 14, 21], L17325 = [1, 8, 12, 21, 31], L18302 = [5, 10, 13, 13, 15], L18303 = [5, 10, 13, 13, 20], L18304 = [5, 10, 13, 13, 25], L18306 = [5, 10, 13, 15, 20], L18307 = [5, 10, 13, 15, 25], L18308 = [5, 10, 13, 15, 26], L18309 = [5, 10, 13, 15, 30], L18310 = [5, 10, 13, 20, 26], L18311 = [5, 10, 13, 25, 26], L18316 = [5, 13, 13, 15, 20], L18320 = [5, 13, 15, 20, 26]. q = 66 : L184 = [0, 0, 1, 5, 29], L223 = [0, 0, 1, 7, 17], L2659 = [0, 1, 5, 11, 29], L2686 = [0, 1, 5, 13, 19], L2689 = [0, 1, 5, 13, 23], L2727 = [0, 1, 5, 17, 19], L2760 = [0, 1, 5, 19, 31], L2780 = [0, 1, 5, 22, 29], L2824 = [0, 1, 5, 29, 33], L3227 = [0, 1, 7, 11, 17], L3278 = [0, 1, 7, 17, 22], L3281 = [0, 1, 7, 17, 33], L5469 = [0, 2, 4, 11, 28], L5504 = [0, 2, 4, 28, 33], L5613 = [0, 2, 8, 10, 11], L5615 = [0, 2, 8, 10, 33], L6079 = [0, 3, 9, 11, 15], L6080 = [0, 3, 9, 11, 21], L6086 = [0, 3, 9, 15, 22], L6087 = [0, 3, 9, 21, 22], L6166 = [0, 6, 11, 12, 18], L6168 = [0, 6, 11, 12, 24], L20547 = [1, 3, 9, 17, 21], L20611 = [1, 3, 9, 23, 27], L26928 = [1, 5, 7, 13, 31], L26945 = [1, 5, 7, 17, 19], L27454 = [1, 5, 11, 11, 29], L27481 = [1, 5, 11, 13, 19], L27484 = [1, 5, 11, 13, 23], L27522 = [1, 5, 11, 17, 19], L27555 = [1, 5, 11, 19, 31], L27575 = [1, 5, 11, 22, 29], L27619 = [1, 5, 11, 29, 33], L27827 = [1, 5, 13, 19, 22], L27832 = [1, 5, 13, 19, 33], L27841 = [1, 5, 13, 22, 23], L27849 = [1, 5, 13, 23, 33], L28123 = [1, 5, 17, 19, 22], L28127 = [1, 5, 17, 19, 33], L28296 = [1, 5, 19, 22, 31], L28326 = [1, 5, 19, 31, 33], L28397 = [1, 5, 22, 22, 29], L28441 = [1, 5, 22, 29, 33], L28600 = [1, 5, 29, 33, 33],
APPENDIX
45
Table 3. (continued) n = 5 q 68
I {0}
indexes of I-isospectral families {170, 208}, {1627, 1668}, {1629, 1675}, {1794, 2947}, {1859, 2410}, {2493, 2977}, {2538, 2973}, {2590, 2979}, {4315, 4318}, {4321, 4340}, {4407, 4408}, {4409, 4411}, {9474, 9482}, {14113, 14125}, {17480, 17499}, {17506, 17802}, {17889, 18454}, {17938, 18463}, {17940, 18511}, {17967, 18464}, {18022, 18471}, {18023, 18474}, {18041, 18556}, {18068, 20594}, {18559, 18887}, {19301, 24629}, {19304, 20342}, {19352, 24988}, {19355, 24963}, {19623, 28383}, {19674, 24614}, {19708, 28389}, {19938, 24676}, {20209, 24705}, {23170, 23177}, {25318, 28543}, {25342, 28561}, {25607, 28539}, {25659, 28545}, {25898, 28564}, {27379, 27399}, {30521, 30522}, {32161, 32166}, {35086, 35089}, {35087, 35091, 35096}, {35095, 35114}, {35102, 35123}, {35117, 35236}, {35140, 35239}, {35283, 35286}, {35297, 35305}, {35477, 35478, 35480}, {35488, 35489}, {35490, 35497}, {35492, 35494}, {35493, 35498}, {35495, 35499} {0, 1} {35098, 35100}, {35479, 35483} {2, 3} {3931, 33595}, {4372, 4419}, {16010, 33593}, {23594, 33590}, {27692, 33586}, {29831, 33581}, {31414, 33575}, {32356, 33568}, {33067, 33560}, {33421, 33551}
L31799 = [1, 7, 11, 11, 17], L31850 = [1, 7, 11, 17, 22], L31853 = [1, 7, 11, 17, 33], L32150 = [1, 7, 17, 22, 22], L32153 = [1, 7, 17, 22, 33], L32158 = [1, 7, 17, 33, 33], L45216 = [2, 4, 8, 11, 26], L45236 = [2, 4, 8, 26, 33], L45344 = [2, 4, 10, 11, 20], L45349 = [2, 4, 10, 11, 28], L45359 = [2, 4, 10, 20, 33], L45370 = [2, 4, 10, 28, 33], L45384 = [2, 4, 11, 11, 28], L45401 = [2, 4, 11, 14, 16], L45454 = [2, 4, 11, 22, 28], L45466 = [2, 4, 11, 28, 33], L45513 = [2, 4, 14, 16, 33], L45658 = [2, 4, 22, 28, 33], L45670 = [2, 4, 28, 33, 33], L46430 = [2, 8, 10, 11, 11], L46434 = [2, 8, 10, 11, 22], L46437 = [2, 8, 10, 11, 33], L46445 = [2, 8, 10, 22, 33], L46449 = [2, 8, 10, 33, 33], L48364 = [3, 6, 11, 24, 27], L48404 = [3, 6, 22, 24, 27], L48414 = [3, 9, 11, 11, 15], L48415 = [3, 9, 11, 11, 21], L48424 = [3, 9, 11, 12, 24], L48428 = [3, 9, 11, 15, 22], L48430 = [3, 9, 11, 15, 33], L48431 = [3, 9, 11, 21, 22], L48433 = [3, 9, 11, 21, 33], L48448 = [3, 9, 12, 22, 24], L48452 = [3, 9, 15, 22, 22], L48454 = [3, 9, 15, 22, 33], L48455 = [3, 9, 21, 22, 22], L48457 = [3, 9, 21, 22, 33], L48690 = [6, 11, 11, 12, 18], L48692 = [6, 11, 11, 12, 24], L48699 = [6, 11, 12, 18, 22], L48701 = [6, 11, 12, 18, 33], L48703 = [6, 11, 12, 22, 24], L48705 = [6, 11, 12, 24, 33], L48714 = [6, 12, 18, 22, 33], L48716 = [6, 12, 22, 24, 33]. q = 68 : L170 = [0, 0, 1, 5, 25], L208 = [0, 0, 1, 7, 11], L1627 = [0, 1, 3, 7, 23], L1629 = [0, 1, 3, 7, 25], L1668 = [0, 1, 3, 9, 13], L1675 = [0, 1, 3, 9, 23], L1794 = [0, 1, 3, 15, 25], L1859 = [0, 1, 3, 19, 27], L2410 = [0, 1, 5, 7, 19], L2493 = [0, 1, 5, 13, 19], L2538 = [0, 1, 5, 17, 25], L2590 = [0, 1, 5, 25, 34], L2947 = [0, 1, 7, 9, 13], L2973 = [0, 1, 7, 11, 17], L2977 = [0, 1, 7, 11, 31], L2979 = [0, 1, 7, 11, 34], L3931 = [0, 1, 16, 18, 33], L4315 = [0, 2, 6, 14, 17], L4318 = [0, 2, 6, 17, 18], L4321 = [0, 2, 6, 17, 26], L4340 = [0, 2, 10, 14, 17], L4372 = [0, 2, 17, 17, 34], L4407 = [0, 4, 8, 17, 20], L4408 = [0, 4, 8, 17, 24], L4409 = [0, 4, 8, 17, 28], L4411 = [0, 4, 12, 16, 17], L4419 = [0, 4, 17, 17, 34], L9474 = [1, 1, 13, 13, 21], L9482 = [1, 1, 13, 13, 33], L14113 = [1, 2, 8, 13, 21], L14125 = [1, 2, 8, 13, 33], L16010 = [1, 2, 16, 18, 33], L17480 = [1, 3, 5, 9, 23], L17499 = [1, 3, 5, 11, 19], L17506 = [1, 3, 5, 11, 27], L17802 = [1, 3, 7, 9, 23], L17889 = [1, 3, 7, 13, 25], L17938 = [1, 3, 7, 17, 23], L17940 = [1, 3, 7, 17, 25], L17967 = [1, 3, 7, 19, 21], L18022 = [1, 3, 7, 23, 33], L18023 = [1, 3, 7, 23, 34], L18041 = [1, 3, 7, 25, 34], L18068 = [1, 3, 7, 29, 33], L18454 = [1, 3, 9, 11, 27], L18463 = [1, 3, 9, 13, 17], L18464 = [1, 3, 9, 13, 19], L18471 = [1, 3, 9, 13, 31], L18474 = [1, 3, 9, 13, 34], L18511 = [1, 3, 9, 17, 23], L18556 = [1, 3, 9, 23, 34], L18559 = [1, 3, 9, 25, 29], L18887 = [1, 3, 11, 13, 31], L19301 = [1, 3, 13, 15, 21], L19304 = [1, 3, 13, 15, 25], L19352 = [1, 3, 13, 19, 21], L19355 = [1, 3, 13, 19, 25], L19623 = [1, 3, 15, 17, 25], L19674 = [1, 3, 15, 21, 27], L19708 = [1, 3, 15, 25, 34],
46
EMILIO A. LAURET
Table 3. (continued) n = 5 q 69 70
I {0} {0}
indexes of I-isospectral families {26279, 26282}, {26286, 26289}, {26294, 26307} {4081, 4085}, {4490, 4494}, {22913, 23007}, {23005, 23340}, {24074, 24573}, {24367, 24368, 40508}, {33651, 33659}, {33654, 33656}, {36587, 36591}, {37028, 37032}, {40517, 40521}, {40529, 40538}, {40531, 40548}, {40534, 40552}, {42869, 42873}, {42948, 42952}, {42956, 42967}, {42959, 42973}, {51578, 51585}, {52010, 52020}, {52011, 52030}, {53049, 53053}, {53150, 53153} {3, 4} {4380, 6471}, {31950, 53105}, {50988, 53191}
L19938 = [1, 3, 17, 19, 27], L20209 = [1, 3, 19, 27, 34], L20342 = [1, 3, 21, 25, 29], L20594 = [1, 3, 27, 29, 33], L23170 = [1, 4, 13, 18, 21], L23177 = [1, 4, 13, 18, 33], L23594 = [1, 4, 16, 18, 33], L24614 = [1, 5, 7, 9, 19], L24629 = [1, 5, 7, 11, 27], L24676 = [1, 5, 7, 17, 19], L24705 = [1, 5, 7, 19, 34], L24963 = [1, 5, 9, 11, 31], L24988 = [1, 5, 9, 13, 33], L25318 = [1, 5, 13, 17, 19], L25342 = [1, 5, 13, 19, 34], L25607 = [1, 5, 17, 17, 25], L25659 = [1, 5, 17, 25, 34], L25898 = [1, 5, 25, 34, 34], L27379 = [1, 6, 13, 21, 24], L27399 = [1, 6, 13, 24, 33], L27692 = [1, 6, 16, 18, 33], L28383 = [1, 7, 9, 13, 17], L28389 = [1, 7, 9, 13, 34], L28539 = [1, 7, 11, 17, 17], L28543 = [1, 7, 11, 17, 31], L28545 = [1, 7, 11, 17, 34], L28561 = [1, 7, 11, 31, 34], L28564 = [1, 7, 11, 34, 34], L29831 = [1, 8, 16, 18, 33], L30521 = [1, 9, 13, 15, 25], L30522 = [1, 9, 13, 15, 33], L31414 = [1, 10, 16, 18, 33], L32161 = [1, 12, 13, 14, 21], L32166 = [1, 12, 13, 14, 33], L32356 = [1, 12, 16, 18, 33], L33067 = [1, 14, 16, 18, 33], L33421 = [1, 16, 16, 18, 33], L33551 = [1, 16, 18, 18, 33], L33560 = [1, 16, 18, 20, 33], L33568 = [1, 16, 18, 22, 33], L33575 = [1, 16, 18, 24, 33], L33581 = [1, 16, 18, 26, 33], L33586 = [1, 16, 18, 28, 33], L33590 = [1, 16, 18, 30, 33], L33593 = [1, 16, 18, 32, 33], L33595 = [1, 16, 18, 33, 34], L35086 = [2, 6, 10, 17, 18], L35087 = [2, 6, 10, 17, 22], L35089 = [2, 6, 10, 17, 26], L35091 = [2, 6, 10, 17, 30], L35095 = [2, 6, 14, 17, 17], L35096 = [2, 6, 14, 17, 18], L35098 = [2, 6, 14, 17, 22], L35100 = [2, 6, 14, 17, 30], L35102 = [2, 6, 14, 17, 34], L35114 = [2, 6, 17, 17, 18], L35117 = [2, 6, 17, 17, 26], L35123 = [2, 6, 17, 18, 34], L35140 = [2, 6, 17, 26, 34], L35236 = [2, 10, 14, 17, 17], L35239 = [2, 10, 14, 17, 34], L35283 = [2, 12, 17, 18, 20], L35286 = [2, 12, 17, 18, 28], L35297 = [2, 12, 17, 24, 26], L35305 = [2, 12, 17, 28, 30], L35477 = [4, 8, 12, 17, 20], L35478 = [4, 8, 12, 17, 24], L35479 = [4, 8, 12, 17, 28], L35480 = [4, 8, 12, 17, 32], L35483 = [4, 8, 16, 17, 20], L35488 = [4, 8, 17, 17, 20], L35489 = [4, 8, 17, 17, 24], L35490 = [4, 8, 17, 17, 28], L35492 = [4, 8, 17, 20, 34], L35493 = [4, 8, 17, 24, 28], L35494 = [4, 8, 17, 24, 34], L35495 = [4, 8, 17, 28, 34], L35497 = [4, 12, 16, 17, 17], L35498 = [4, 12, 16, 17, 20], L35499 = [4, 12, 16, 17, 34]. q = 69 : L26279 = [3, 6, 12, 15, 23], L26282 = [3, 6, 12, 23, 24], L26286 = [3, 6, 15, 21, 23], L26289 = [3, 6, 15, 23, 27], L26294 = [3, 6, 18, 23, 30], L26307 = [3, 9, 12, 23, 27]. q = 70 : L4081 = [0, 1, 9, 11, 19], L4085 = [0, 1, 9, 11, 29], L4380 = [0, 1, 10, 20, 30], L4490 = [0, 1, 11, 16, 24], L4494 = [0, 1, 11, 16, 34], L6471 = [0, 7, 10, 20, 30], L22913 = [1, 3, 11, 17, 29], L23005 = [1, 3, 11, 27, 29], L23007 = [1, 3, 11, 27, 31], L23340 = [1, 3, 13, 17, 29], L24074 = [1, 3, 17, 21, 27], L24367 = [1, 3, 19, 27, 31], L24368 = [1, 3, 19, 27, 33], L24573 = [1, 3, 21, 27, 31], L31950 = [1, 5, 15, 25, 35], L33651 = [1, 6, 8, 13, 22], L33654 = [1, 6, 8, 13, 27], L33656 = [1, 6, 8, 13, 29], L33659 = [1, 6, 8, 13, 34], L36587 = [1, 7, 9, 11, 19], L36591 = [1, 7, 9, 11, 29], L37028 = [1, 7, 11, 16, 24], L37032 = [1, 7, 11, 16, 34], L40508 = [1, 9, 11, 13, 17], L40517 = [1, 9, 11, 14, 19], L40521 = [1, 9, 11, 14, 29], L40529 = [1, 9, 11, 19, 21], L40531 = [1, 9, 11, 19, 28], L40534 = [1, 9, 11, 19, 35], L40538 = [1, 9, 11, 21, 29], L40548 = [1, 9, 11, 28, 29], L40552 = [1, 9, 11, 29, 35], L42869 = [1, 11, 14, 16, 24], L42873 = [1, 11, 14, 16, 34], L42948 = [1, 11, 16, 21, 24], L42952 = [1, 11, 16, 21, 34], L42956 = [1, 11, 16, 24, 28], L42959 = [1, 11, 16, 24, 35], L42967 = [1, 11, 16, 28, 34], L42973 = [1, 11, 16, 34, 35], L50988 = [2, 5, 15, 25, 35], L51578 = [2, 7, 8, 12, 18], L51585 = [2, 7, 8, 12, 32], L52010 = [2, 8, 12, 18, 21], L52011 = [2, 8, 12, 18, 35], L52020 = [2, 8, 12, 21, 32], L52030 = [2, 8, 12, 32, 35], L53049 = [5, 7, 10, 15, 20], L53053 = [5, 7, 10, 15, 30], L53105 = [5, 7, 15, 25, 35], L53150 = [5, 10, 14, 15, 20], L53153 = [5, 10, 14, 15, 30], L53191 = [5, 14, 15, 25, 35].
APPENDIX
47
Table 3. (continued) n = 5 q I indexes of I-isospectral families 72 {0} {186, 235}, {1734, 1750}, {2179, 2216}, {3007, 3009}, {3016, 3077}, {3076, 3083}, {3093, 3756}, {3121, 3725}, {3168, 3759}, {3172, 3763}, {3181, 3769}, {3547, 3559}, {4668, 4677}, {5168, 5176}, {6440, 6447}, {6914, 6918}, {7021, 7024}, {15876, 15892}, {17001, 17017}, {17958, 17974}, {18789, 18805}, {19533, 19548}, {19742, 19746}, {20125, 20141}, {20620, 20635}, {21055, 21071}, {21249, 21265}, {21267, 21299}, {21269, 21327}, {21271, 21351}, {21273, 21370}, {21275, 21388}, {21277, 21399}, {21279, 21407}, {21283, 21412}, {24657, 24738}, {25943, 26222}, {25959, 25961}, {26054, 26541}, {26118, 26560}, {26168, 26568}, {26922, 26953}, {29507, 29521}, {30938, 30949}, {31836, 31846}, {33527, 36727}, {33559, 33596}, {33739, 33773}, {33740, 33778}, {33745, 33776}, {33750, 33780}, {33759, 33761}, {33768, 34558}, {33808, 34573}, {33823, 33825}, {33832, 34615}, {33839, 34652}, {33844, 34577}, {33862, 33873}, {33871, 33891}, {33880, 34639}, {33935, 34648}, {34391, 39832}, {34557, 34564}, {34614, 34621}, {34628, 34662}, {34636, 34689}, {34708, 40149}, {34736, 39841}, {34783, 40152}, {34787, 40156}, {34796, 40162}, {34972, 35000}, {34985, 39898}, {35039, 39912}, {35057, 39917}, {35445, 40186}, {35449, 40190}, {35458, 40196}, {35492, 40215}, {35501, 40221}, {35543, 40241}, {36502, 36514}, {36794, 36846}, {37106, 37118}, {37721, 37732}, {38058, 38070}, {38265, 38277}, {38606, 38617}, {38754, 38766}, {38768, 38790}, {38769, 38800}, {38770, 38811}, {38771, 38823}, {38773, 38837}, {38776, 38846}, {38779, 38850}, {40420, 40457}, {41801, 41810}, {42511, 42519}, {44282, 44284}, {46034, 46043}, {46202, 46210}, {46397, 46406}, {46681, 46690}, {47013, 47022}, {47146, 47155}, {47157, 47174}, {47158, 47182}, {47159, 47190}, {47161, 47204}, {47162, 47208}, {47165, 47212}, {47994, 47996}, {48623, 48631}, {49734, 49742}, {50038, 50046}, {50159, 50167}, {50169, 50184}, {50171, 50196}, {50172, 50206}, {50173, 50210}, {50176, 50214}, {55153, 55161}, {56062, 56070}, {56280, 56287}, {56466, 56474}, {56649, 56695}, {56759, 56761}, {56767, 56821}, {56771, 56775}, {56899, 56906}, {57080, 57087}, {57092, 57099}, {57103, 57110}, {57114, 57127}, {57115, 57134}, {57117, 57145}, {57118, 57150}, {57119, 57153}, {57122, 57156}, {59670, 59674}, {59821, 59826}, {59895, 59899}, {59930, 59934}, {60000, 60004}, {60011, 60023}, {60012, 60032}, {60013, 60039}, {60015, 60046}, {60017, 60048}, {60019, 60049}, {60378, 60382}, {60431, 60434}, {60509, 60512}, {60518, 60526}, {60519, 60534}, {60521, 60540}, {60524, 60542}, {60901, 60904} q = 72 : L186 = [0, 0, 1, 5, 17], L235 = [0, 0, 1, 7, 11], L1734 = [0, 1, 2, 17, 19], L1750 = [0, 1, 2, 17, 35], L2179 = [0, 1, 3, 11, 29], L2216 = [0, 1, 3, 13, 19], L3007 = [0, 1, 5, 7, 23], L3009 = [0, 1, 5, 7, 25], L3016 = [0, 1, 5, 7, 33], L3076 = [0, 1, 5, 11, 19], L3077 = [0, 1, 5, 11, 21], L3083 = [0, 1, 5, 11, 29], L3093 = [0, 1, 5, 12, 17], L3121 = [0, 1, 5, 13, 27], L3168 = [0, 1, 5, 17, 18], L3172 = [0, 1, 5, 17, 24], L3181 = [0, 1, 5, 17, 36], L3547 = [0, 1, 6, 17, 19], L3559 = [0, 1, 6, 17, 35], L3725 = [0, 1, 7, 9, 19],
48
EMILIO A. LAURET
Table 3. (continued) n = 5 q 72 (cont.)
I {0, 1}
indexes of I-isospectral families {6406, 6427}, {55794, 55817}, {56244, 56267}, {56606, 56628}, {56752, 56886}, {56802, 57006}, {56834, 57025}, {56846, 57026}, {56857, 57027}, {56863, 57029}, {56865, 57030}, {57964, 57984} {2, 3} {5609, 52545}, {32389, 52543}, {42990, 52540}, {49064, 52536}, {51885, 52531}, {60157, 60613}, {60969, 61199} {4} {36526, 38963}, {56310, 58112} {0, 1, 2, 3, 4} {33818, 33847}
L3756 = [0, 1, 7, 11, 12], L3759 = [0, 1, 7, 11, 18], L3763 = [0, 1, 7, 11, 24], L3769 = [0, 1, 7, 11, 36], L4668 = [0, 1, 10, 17, 19], L4677 = [0, 1, 10, 17, 35], L5168 = [0, 1, 14, 17, 19], L5176 = [0, 1, 14, 17, 35], L5609 = [0, 1, 17, 19, 35], L6406 = [0, 2, 3, 10, 34], L6427 = [0, 2, 3, 14, 22], L6440 = [0, 2, 3, 15, 21], L6447 = [0, 2, 3, 15, 33], L6914 = [0, 3, 4, 9, 15], L6918 = [0, 3, 4, 9, 21], L7021 = [0, 3, 8, 9, 15], L7024 = [0, 3, 8, 9, 21], L15876 = [1, 2, 2, 17, 19], L15892 = [1, 2, 2, 17, 35], L17001 = [1, 2, 4, 17, 19], L17017 = [1, 2, 4, 17, 35], L17958 = [1, 2, 6, 17, 19], L17974 = [1, 2, 6, 17, 35], L18789 = [1, 2, 8, 17, 19], L18805 = [1, 2, 8, 17, 35], L19533 = [1, 2, 10, 17, 19], L19548 = [1, 2, 10, 17, 35], L19742 = [1, 2, 11, 13, 22], L19746 = [1, 2, 11, 13, 26], L20125 = [1, 2, 12, 17, 19], L20141 = [1, 2, 12, 17, 35], L20620 = [1, 2, 14, 17, 19], L20635 = [1, 2, 14, 17, 35], L21055 = [1, 2, 16, 17, 19], L21071 = [1, 2, 16, 17, 35], L21249 = [1, 2, 17, 18, 19], L21265 = [1, 2, 17, 18, 35], L21267 = [1, 2, 17, 19, 20], L21269 = [1, 2, 17, 19, 22], L21271 = [1, 2, 17, 19, 24], L21273 = [1, 2, 17, 19, 26], L21275 = [1, 2, 17, 19, 28], L21277 = [1, 2, 17, 19, 30], L21279 = [1, 2, 17, 19, 32], L21283 = [1, 2, 17, 19, 36], L21299 = [1, 2, 17, 20, 35], L21327 = [1, 2, 17, 22, 35], L21351 = [1, 2, 17, 24, 35], L21370 = [1, 2, 17, 26, 35], L21388 = [1, 2, 17, 28, 35], L21399 = [1, 2, 17, 30, 35], L21407 = [1, 2, 17, 32, 35], L21412 = [1, 2, 17, 35, 36], L24657 = [1, 3, 7, 17, 31], L24738 = [1, 3, 7, 23, 25], L25943 = [1, 3, 11, 12, 29], L25959 = [1, 3, 11, 13, 23], L25961 = [1, 3, 11, 13, 25], L26054 = [1, 3, 11, 18, 29], L26118 = [1, 3, 11, 24, 29], L26168 = [1, 3, 11, 29, 36], L26222 = [1, 3, 12, 13, 19], L26541 = [1, 3, 13, 18, 19], L26560 = [1, 3, 13, 19, 24], L26568 = [1, 3, 13, 19, 36], L26922 = [1, 3, 15, 17, 21], L26953 = [1, 3, 15, 19, 21], L29507 = [1, 4, 6, 17, 19], L29521 = [1, 4, 6, 17, 35], L30938 = [1, 4, 10, 17, 19], L30949 = [1, 4, 10, 17, 35], L31836 = [1, 4, 14, 17, 19], L31846 = [1, 4, 14, 17, 35], L32389 = [1, 4, 17, 19, 35], L33527 = [1, 5, 6, 17, 30], L33559 = [1, 5, 6, 19, 29], L33596 = [1, 5, 6, 23, 25], L33739 = [1, 5, 7, 11, 19], L33740 = [1, 5, 7, 11, 23], L33745 = [1, 5, 7, 11, 29], L33750 = [1, 5, 7, 11, 35], L33759 = [1, 5, 7, 12, 23], L33761 = [1, 5, 7, 12, 25], L33768 = [1, 5, 7, 12, 33], L33773 = [1, 5, 7, 13, 17], L33776 = [1, 5, 7, 13, 23], L33778 = [1, 5, 7, 13, 25], L33780 = [1, 5, 7, 13, 29], L33808 = [1, 5, 7, 17, 23], L33818 = [1, 5, 7, 17, 35], L33823 = [1, 5, 7, 18, 23], L33825 = [1, 5, 7, 18, 25], L33832 = [1, 5, 7, 18, 33], L33839 = [1, 5, 7, 19, 25], L33844 = [1, 5, 7, 19, 31], L33847 = [1, 5, 7, 19, 35], L33862 = [1, 5, 7, 23, 24], L33871 = [1, 5, 7, 23, 36], L33873 = [1, 5, 7, 24, 25], L33880 = [1, 5, 7, 24, 33], L33891 = [1, 5, 7, 25, 36], L33935 = [1, 5, 7, 33, 36], L34391 = [1, 5, 9, 17, 27], L34557 = [1, 5, 11, 12, 19], L34558 = [1, 5, 11, 12, 21], L34564 = [1, 5, 11, 12, 29], L34573 = [1, 5, 11, 13, 19], L34577 = [1, 5, 11, 13, 25], L34614 = [1, 5, 11, 18, 19], L34615 = [1, 5, 11, 18, 21], L34621 = [1, 5, 11, 18, 29], L34628 = [1, 5, 11, 19, 24], L34636 = [1, 5, 11, 19, 36], L34639 = [1, 5, 11, 21, 24], L34648 = [1, 5, 11, 21, 36], L34652 = [1, 5, 11, 23, 29], L34662 = [1, 5, 11, 24, 29], L34689 = [1, 5, 11, 29, 36], L34708 = [1, 5, 12, 12, 17], L34736 = [1, 5, 12, 13, 27], L34783 = [1, 5, 12, 17, 18], L34787 = [1, 5, 12, 17, 24], L34796 = [1, 5, 12, 17, 36], L34972 = [1, 5, 13, 17, 23], L34985 = [1, 5, 13, 18, 27], L35000 = [1, 5, 13, 19, 31], L35039 = [1, 5, 13, 24, 27], L35057 = [1, 5, 13, 27, 36], L35445 = [1, 5, 17, 18, 18], L35449 = [1, 5, 17, 18, 24], L35458 = [1, 5, 17, 18, 36], L35492 = [1, 5, 17, 24, 24], L35501 = [1, 5, 17, 24, 36], L35543 = [1, 5, 17, 36, 36], L36502 = [1, 6, 6, 17, 19], L36514 = [1, 6, 6, 17, 35], L36526 = [1, 6, 6, 18, 30], L36727 = [1, 6, 7, 11, 30], L36794 = [1, 6, 7, 17, 31], L36846 = [1, 6, 7, 23, 25], L37106 = [1, 6, 8, 17, 19], L37118 = [1, 6, 8, 17, 35], L37721 = [1, 6, 10, 17, 19], L37732 = [1, 6, 10, 17, 35], L38058 = [1, 6, 12, 17, 19], L38070 = [1, 6, 12, 17, 35], L38265 = [1, 6, 14, 17, 19], L38277 = [1, 6, 14, 17, 35], L38606 = [1, 6, 16, 17, 19], L38617 = [1, 6, 16, 17, 35], L38754 = [1, 6, 17, 18, 19], L38766 = [1, 6, 17, 18, 35],
APPENDIX
49
Table 3. (continued) n = 5 q I indexes of I-isospectral families 74 {0} {1893, 1943}, {4103, 4110}, {22851, 23469}, {33105, 33117, 36792}, {40351, 40377}, {45304, 45305} 75 {0} {42403, 42451}, {42546, 42561}, {42555, 42556}, {42558, 42560, 42579} L38768 L38773 L38800 L38846 L39841 L40149 L40186 L40221 L41801 L42990 L46043 L46406 L47022 L47158 L47165 L47204 L47996 L49734 L50159 L50172 L50196 L51885 L52543 L55794 L56244 L56310 L56628 L56759 L56775 L56846 L56886 L57025 L57030 L57099 L57115 L57122 L57150 L57984 L59821 L59930 L60011 L60017
= [1, 6, 17, 19, 20], L38769 = [1, 6, 17, 19, 22], L38770 = [1, 6, 17, 19, 24], L38771 = [1, 6, 17, 19, 26], = [1, 6, 17, 19, 28], L38776 = [1, 6, 17, 19, 32], L38779 = [1, 6, 17, 19, 36], L38790 = [1, 6, 17, 20, 35], = [1, 6, 17, 22, 35], L38811 = [1, 6, 17, 24, 35], L38823 = [1, 6, 17, 26, 35], L38837 = [1, 6, 17, 28, 35], = [1, 6, 17, 32, 35], L38850 = [1, 6, 17, 35, 36], L38963 = [1, 6, 18, 30, 30], L39832 = [1, 7, 9, 11, 27], = [1, 7, 9, 12, 19], L39898 = [1, 7, 9, 18, 19], L39912 = [1, 7, 9, 19, 24], L39917 = [1, 7, 9, 19, 36], = [1, 7, 11, 12, 12], L40152 = [1, 7, 11, 12, 18], L40156 = [1, 7, 11, 12, 24], L40162 = [1, 7, 11, 12, 36], = [1, 7, 11, 18, 18], L40190 = [1, 7, 11, 18, 24], L40196 = [1, 7, 11, 18, 36], L40215 = [1, 7, 11, 24, 24], = [1, 7, 11, 24, 36], L40241 = [1, 7, 11, 36, 36], L40420 = [1, 7, 15, 17, 31], L40457 = [1, 7, 15, 23, 25], = [1, 8, 10, 17, 19], L41810 = [1, 8, 10, 17, 35], L42511 = [1, 8, 14, 17, 19], L42519 = [1, 8, 14, 17, 35], = [1, 8, 17, 19, 35], L44282 = [1, 9, 11, 13, 23], L44284 = [1, 9, 11, 13, 25], L46034 = [1, 10, 10, 17, 19], = [1, 10, 10, 17, 35], L46202 = [1, 10, 11, 13, 34], L46210 = [1, 10, 11, 14, 23], L46397 = [1, 10, 12, 17, 19], = [1, 10, 12, 17, 35], L46681 = [1, 10, 14, 17, 19], L46690 = [1, 10, 14, 17, 35], L47013 = [1, 10, 16, 17, 19], = [1, 10, 16, 17, 35], L47146 = [1, 10, 17, 18, 19], L47155 = [1, 10, 17, 18, 35], L47157 = [1, 10, 17, 19, 20], = [1, 10, 17, 19, 22], L47159 = [1, 10, 17, 19, 24], L47161 = [1, 10, 17, 19, 28], L47162 = [1, 10, 17, 19, 32], = [1, 10, 17, 19, 36], L47174 = [1, 10, 17, 20, 35], L47182 = [1, 10, 17, 22, 35], L47190 = [1, 10, 17, 24, 35], = [1, 10, 17, 28, 35], L47208 = [1, 10, 17, 32, 35], L47212 = [1, 10, 17, 35, 36], L47994 = [1, 11, 13, 15, 23], = [1, 11, 13, 15, 25], L48623 = [1, 12, 14, 17, 19], L48631 = [1, 12, 14, 17, 35], L49064 = [1, 12, 17, 19, 35], = [1, 14, 14, 17, 19], L49742 = [1, 14, 14, 17, 35], L50038 = [1, 14, 16, 17, 19], L50046 = [1, 14, 16, 17, 35], = [1, 14, 17, 18, 19], L50167 = [1, 14, 17, 18, 35], L50169 = [1, 14, 17, 19, 20], L50171 = [1, 14, 17, 19, 24], = [1, 14, 17, 19, 28], L50173 = [1, 14, 17, 19, 32], L50176 = [1, 14, 17, 19, 36], L50184 = [1, 14, 17, 20, 35], = [1, 14, 17, 24, 35], L50206 = [1, 14, 17, 28, 35], L50210 = [1, 14, 17, 32, 35], L50214 = [1, 14, 17, 35, 36], = [1, 16, 17, 19, 35], L52531 = [1, 17, 19, 20, 35], L52536 = [1, 17, 19, 24, 35], L52540 = [1, 17, 19, 28, 35], = [1, 17, 19, 32, 35], L52545 = [1, 17, 19, 35, 36], L55153 = [2, 2, 3, 15, 21], L55161 = [2, 2, 3, 15, 33], = [2, 3, 3, 10, 34], L55817 = [2, 3, 3, 14, 22], L56062 = [2, 3, 4, 15, 21], L56070 = [2, 3, 4, 15, 33], = [2, 3, 6, 10, 34], L56267 = [2, 3, 6, 14, 22], L56280 = [2, 3, 6, 15, 21], L56287 = [2, 3, 6, 15, 33], = [2, 3, 6, 18, 30], L56466 = [2, 3, 8, 15, 21], L56474 = [2, 3, 8, 15, 33], L56606 = [2, 3, 9, 10, 34], = [2, 3, 9, 14, 22], L56649 = [2, 3, 9, 15, 34], L56695 = [2, 3, 9, 21, 34], L56752 = [2, 3, 10, 12, 34], = [2, 3, 10, 14, 22], L56761 = [2, 3, 10, 14, 26], L56767 = [2, 3, 10, 14, 34], L56771 = [2, 3, 10, 15, 21], = [2, 3, 10, 15, 33], L56802 = [2, 3, 10, 18, 34], L56821 = [2, 3, 10, 22, 26], L56834 = [2, 3, 10, 24, 34], = [2, 3, 10, 27, 34], L56857 = [2, 3, 10, 30, 34], L56863 = [2, 3, 10, 33, 34], L56865 = [2, 3, 10, 34, 36], = [2, 3, 12, 14, 22], L56899 = [2, 3, 12, 15, 21], L56906 = [2, 3, 12, 15, 33], L57006 = [2, 3, 14, 18, 22], = [2, 3, 14, 22, 24], L57026 = [2, 3, 14, 22, 27], L57027 = [2, 3, 14, 22, 30], L57029 = [2, 3, 14, 22, 33], = [2, 3, 14, 22, 36], L57080 = [2, 3, 15, 16, 21], L57087 = [2, 3, 15, 16, 33], L57092 = [2, 3, 15, 18, 21], = [2, 3, 15, 18, 33], L57103 = [2, 3, 15, 20, 21], L57110 = [2, 3, 15, 20, 33], L57114 = [2, 3, 15, 21, 22], = [2, 3, 15, 21, 24], L57117 = [2, 3, 15, 21, 28], L57118 = [2, 3, 15, 21, 30], L57119 = [2, 3, 15, 21, 32], = [2, 3, 15, 21, 36], L57127 = [2, 3, 15, 22, 33], L57134 = [2, 3, 15, 24, 33], L57145 = [2, 3, 15, 28, 33], = [2, 3, 15, 30, 33], L57153 = [2, 3, 15, 32, 33], L57156 = [2, 3, 15, 33, 36], L57964 = [2, 6, 9, 10, 34], = [2, 6, 9, 14, 22], L58112 = [2, 6, 15, 18, 30], L59670 = [3, 4, 4, 9, 15], L59674 = [3, 4, 4, 9, 21], = [3, 4, 6, 15, 21], L59826 = [3, 4, 6, 15, 33], L59895 = [3, 4, 8, 9, 15], L59899 = [3, 4, 8, 9, 21], = [3, 4, 8, 16, 20], L59934 = [3, 4, 8, 16, 28], L60000 = [3, 4, 9, 12, 15], L60004 = [3, 4, 9, 12, 21], = [3, 4, 9, 15, 16], L60012 = [3, 4, 9, 15, 18], L60013 = [3, 4, 9, 15, 20], L60015 = [3, 4, 9, 15, 24], = [3, 4, 9, 15, 32], L60019 = [3, 4, 9, 15, 36], L60023 = [3, 4, 9, 16, 21], L60032 = [3, 4, 9, 18, 21],
50
EMILIO A. LAURET
L60039 = [3, 4, 9, 20, 21], L60046 = [3, 4, 9, 21, 24], L60048 = [3, 4, 9, 21, 32], L60049 = [3, 4, 9, 21, 36], L60157 = [3, 4, 15, 21, 33], L60378 = [3, 6, 8, 15, 21], L60382 = [3, 6, 8, 15, 33], L60431 = [3, 8, 8, 9, 15], L60434 = [3, 8, 8, 9, 21], L60509 = [3, 8, 9, 12, 15], L60512 = [3, 8, 9, 12, 21], L60518 = [3, 8, 9, 15, 16], L60519 = [3, 8, 9, 15, 18], L60521 = [3, 8, 9, 15, 24], L60524 = [3, 8, 9, 15, 36], L60526 = [3, 8, 9, 16, 21], L60534 = [3, 8, 9, 18, 21], L60540 = [3, 8, 9, 21, 24], L60542 = [3, 8, 9, 21, 36], L60613 = [3, 8, 15, 21, 33], L60901 = [4, 8, 9, 16, 20], L60904 = [4, 8, 9, 16, 28], L60969 = [4, 9, 9, 27, 27], L61199 = [8, 9, 9, 27, 27]. q = 74 : L1893 = [0, 1, 3, 7, 27], L1943 = [0, 1, 3, 9, 25], L4103 = [0, 1, 10, 11, 26], L4110 = [0, 1, 10, 11, 36], L22851 = [1, 3, 7, 27, 37], L23469 = [1, 3, 9, 25, 37], L33105 = [1, 5, 21, 29, 33], L33117 = [1, 5, 21, 33, 35], L36792 = [1, 7, 9, 19, 23], L40351 = [1, 10, 11, 26, 37], L40377 = [1, 10, 11, 36, 37], L45304 = [2, 6, 8, 22, 37], L45305 = [2, 6, 8, 24, 37]. q = 75 : L42403 = [3, 5, 10, 21, 30], L42451 = [3, 5, 15, 20, 21], L42546 = [3, 6, 12, 25, 33], L42555 = [3, 6, 18, 21, 25], L42556 = [3, 6, 18, 24, 25], L42558 = [3, 6, 18, 25, 27], L42560 = [3, 6, 18, 25, 33], L42561 = [3, 6, 21, 24, 25], L42579 = [3, 9, 12, 25, 27].
APPENDIX
51
5. Computational results for dimension 11 q q q q q
= 5 : L7 = [0, 0, 1, 1, 2, 2], L10 = [0, 1, 1, 1, 2, 2]. = 7 : L6 = [0, 0, 0, 1, 2, 3], L11 = [0, 0, 1, 1, 2, 3], L16 = [0, 1, 1, 1, 2, 3], L18 = [0, 1, 1, 2, 2, 3]. = 8 : L27 = [0, 0, 1, 2, 3, 4], L55 = [0, 1, 2, 3, 4, 4]. = 9 : L21 = [0, 0, 1, 2, 3, 4], L40 = [0, 1, 2, 3, 3, 4]. = 10 : L43 = [0, 0, 1, 2, 3, 5], L82 = [0, 1, 1, 3, 3, 5], L96 = [0, 1, 2, 2, 4, 4], L103 = [0, 1, 2, 4, 5, 5], L114 = [0, 2, 2, 4, 4, 5], L146 = [1, 1, 1, 3, 3, 5], L165 = [1, 1, 2, 3, 3, 5], L173 = [1, 1, 3, 3, 5, 5]. q = 11 : L9 = [0, 0, 0, 1, 2, 3], L10 = [0, 0, 0, 1, 2, 4]. q = 13 : L11 = [0, 0, 0, 1, 2, 3], L12 = [0, 0, 0, 1, 2, 4], L13 = [0, 0, 0, 1, 2, 5], L14 = [0, 0, 0, 1, 3, 4], L34 = [0, 0, 1, 2, 3, 4], L35 = [0, 0, 1, 2, 3, 5], L36 = [0, 0, 1, 2, 3, 6]. q = 14 : L66 = [0, 0, 1, 2, 3, 4], L68 = [0, 0, 1, 2, 3, 6], L71 = [0, 0, 1, 2, 4, 6], L80 = [0, 0, 1, 3, 5, 7], L96 = [0, 0, 2, 4, 6, 7], L140 = [0, 1, 1, 2, 4, 6], L156 = [0, 1, 1, 3, 5, 7], L188 = [0, 1, 2, 2, 4, 6], L197 = [0, 1, 2, 3, 4, 6], L198 = [0, 1, 2, 3, 4, 7], L199 = [0, 1, 2, 3, 5, 7], L200 = [0, 1, 2, 3, 6, 7], L203 = [0, 1, 2, 4, 4, 6], L205 = [0, 1, 2, 4, 6, 6], L206 = [0, 1, 2, 4, 6, 7], L218 = [0, 1, 3, 5, 7, 7], L240 = [0, 2, 2, 4, 6, 7], L244 = [0, 2, 4, 6, 7, 7], L307 = [1, 1, 1, 3, 5, 7], L361 = [1, 1, 2, 3, 5, 7], L387 = [1, 1, 3, 3, 5, 7], L394 = [1, 1, 3, 4, 5, 7], L399 = [1, 1, 3, 5, 6, 7], L400 = [1, 1, 3, 5, 7, 7], L454 = [1, 2, 2, 3, 5, 7], L477 = [1, 2, 3, 4, 5, 7], L479 = [1, 2, 3, 4, 7, 7], L480 = [1, 2, 3, 5, 7, 7], L481 = [1, 2, 3, 6, 7, 7], L506 = [1, 3, 5, 7, 7, 7]. q = 15 : L18 = [0, 0, 0, 1, 2, 6], L20 = [0, 0, 0, 1, 3, 4], L66 = [0, 0, 1, 2, 5, 6], L72 = [0, 0, 1, 3, 4, 5], L175 = [0, 1, 2, 3, 6, 6], L177 = [0, 1, 2, 4, 5, 7], L179 = [0, 1, 2, 5, 5, 6], L187 = [0, 1, 3, 3, 4, 6], L190 = [0, 1, 3, 3, 6, 6], L191 = [0, 1, 3, 4, 5, 5], L212 = [0, 3, 3, 5, 6, 6], L331 = [1, 1, 2, 4, 5, 7], L403 = [1, 2, 3, 4, 5, 7], L408 = [1, 2, 3, 5, 6, 6], L411 = [1, 2, 4, 5, 5, 7], L413 = [1, 2, 5, 5, 5, 6], L427 = [1, 3, 3, 4, 5, 6], L433 = [1, 3, 4, 5, 5, 5]. q = 16 : L78 = [0, 0, 1, 2, 3, 5], L80 = [0, 0, 1, 2, 3, 7], L96 = [0, 0, 1, 3, 5, 7], L97 = [0, 0, 1, 3, 5, 8], L180 = [0, 1, 1, 3, 3, 5], L181 = [0, 1, 1, 3, 3, 7], L189 = [0, 1, 1, 3, 5, 7], L233 = [0, 1, 2, 2, 3, 5], L235 = [0, 1, 2, 2, 3, 7], L250 = [0, 1, 2, 3, 4, 5], L252 = [0, 1, 2, 3, 4, 7], L255 = [0, 1, 2, 3, 5, 7], L256 = [0, 1, 2, 3, 5, 8], L258 = [0, 1, 2, 3, 7, 8], L282 = [0, 1, 3, 4, 5, 7], L285 = [0, 1, 3, 5, 7, 8], L286 = [0, 1, 3, 5, 8, 8], L390 = [1, 1, 1, 3, 5, 7], L472 = [1, 1, 2, 3, 5, 7], L512 = [1, 1, 3, 3, 4, 5], Table 4. n = 6 q I 5 {2, 3, 4} 7 {5} 8 {4, 5} 9 {3, 4, 5} 10 {3} {2, 3, 4} 11 {0} 13 {0} {0, 1} 14 {0} {5}
indexes of I-isospectral families {7, 10} {6, 11, 16, 18} {27, 55} {21, 40} {43, 103}, {82, 165}, {96, 114}, {146, 173} {9, 10} {11, 12}, {13, 14}, {34, 35, 36} {34, 35} {66, 68}, {198, 200}, {479, 481} {71, 96, 188, 203, 205, 240}, {80, 199, 454, 477}, {140, 197, 206, 244}, {156, 218, 361, 394, 399, 480}, {307, 387, 400, 506} 15 {0} {18, 20}, {66, 72}, {175, 187}, {179, 191}, {408, 427}, {413, 433} {2, 3, 4} {177, 403}, {190, 212}, {331, 411}
52
EMILIO A. LAURET
Table 4. (continued) n = 6 q 16
I {0}
indexes of I-isospectral families {78, 80}, {180, 181}, {233, 235}, {250, 252}, {256, 258}, {512, 513}, {517, 518}, {604, 606}, {621, 623}, {625, 629}, {627, 631}, {655, 657}, {661, 663}, {668, 670} {5} {97, 286}, {4, 5} {96, 285, 710}, {189, 538}, {255, 667}, {282, 707}, {390, 537}, {472, 535}, {626, 665} 17 {0} {16, 17}, {18, 19}, {55, 56, 58}, {62, 63}, {156, 157, 158, 159, 160}, {161, 162}, {376, 377, 378, 379} {0, 1} {57, 59}, {157, 158}, {376, 377, 378} {0, 1, 2} {377, 378} 18 {0} {117, 119}, {407, 409}, {429, 434}, {432, 437}, {1182, 1184}, {1204, 1209}, {1207, 1212}, {1251, 1260}, {1254, 1263}, {1258, 1267} {3, 4, 5} {498, 1381}, {603, 612}, {1340, 1383} 19 {0} {19, 21}, {67, 68, 71}, {70, 72, 74}, {77, 79}, {209, 210}, {211, 213, 215, 217}, {214, 216, 218, 220}, {219, 222}, {548, 549, 550, 551, 552, 553, 554}, {555, 556, 557} {0, 1} {216, 218}, {550, 551}, {552, 554}, {555, 557} L513 = [1, 1, 3, 3, 4, 7], L517 = [1, 1, 3, 3, 5, 8], L518 = [1, 1, 3, 3, 7, 8], L535 = [1, 1, 3, 5, 6, 7], L537 = [1, 1, 3, 5, 7, 7], L538 = [1, 1, 3, 5, 7, 8], L604 = [1, 2, 2, 2, 3, 5], L606 = [1, 2, 2, 2, 3, 7], L621 = [1, 2, 2, 3, 4, 5], L623 = [1, 2, 2, 3, 4, 7], L625 = [1, 2, 2, 3, 5, 6], L626 = [1, 2, 2, 3, 5, 7], L627 = [1, 2, 2, 3, 5, 8], L629 = [1, 2, 2, 3, 6, 7], L631 = [1, 2, 2, 3, 7, 8], L655 = [1, 2, 3, 4, 4, 5], L657 = [1, 2, 3, 4, 4, 7], L661 = [1, 2, 3, 4, 5, 8], L663 = [1, 2, 3, 4, 7, 8], L665 = [1, 2, 3, 5, 6, 7], L667 = [1, 2, 3, 5, 7, 8], L668 = [1, 2, 3, 5, 8, 8], L670 = [1, 2, 3, 7, 8, 8], L707 = [1, 3, 4, 5, 7, 8], L710 = [1, 3, 5, 7, 8, 8]. q = 17 : L16 = [0, 0, 0, 1, 2, 5], L17 = [0, 0, 0, 1, 2, 6], L18 = [0, 0, 0, 1, 2, 7], L19 = [0, 0, 0, 1, 3, 4], L55 = [0, 0, 1, 2, 3, 5], L56 = [0, 0, 1, 2, 3, 6], L57 = [0, 0, 1, 2, 3, 7], L58 = [0, 0, 1, 2, 3, 8], L59 = [0, 0, 1, 2, 4, 5], L62 = [0, 0, 1, 2, 6, 7], L63 = [0, 0, 1, 3, 4, 5], L156 = [0, 1, 2, 3, 4, 5], L157 = [0, 1, 2, 3, 4, 6], L158 = [0, 1, 2, 3, 4, 7], L159 = [0, 1, 2, 3, 4, 8], L160 = [0, 1, 2, 3, 5, 6], L161 = [0, 1, 2, 3, 5, 8], L162 = [0, 1, 2, 3, 6, 7], L376 = [1, 2, 3, 4, 5, 6], L377 = [1, 2, 3, 4, 5, 7], L378 = [1, 2, 3, 4, 5, 8], L379 = [1, 2, 3, 4, 6, 8]. q = 18 : L117 = [0, 0, 1, 2, 4, 5], L119 = [0, 0, 1, 2, 4, 7], L407 = [0, 1, 2, 3, 4, 5], L409 = [0, 1, 2, 3, 4, 7], L429 = [0, 1, 2, 4, 5, 6], L432 = [0, 1, 2, 4, 5, 9], L434 = [0, 1, 2, 4, 6, 7], L437 = [0, 1, 2, 4, 7, 9], L498 = [0, 1, 3, 5, 7, 9], L603 = [0, 2, 3, 4, 6, 8], L612 = [0, 2, 4, 6, 8, 9], L1182 = [1, 2, 3, 3, 4, 5], L1184 = [1, 2, 3, 3, 4, 7], L1204 = [1, 2, 3, 4, 5, 6], L1207 = [1, 2, 3, 4, 5, 9], L1209 = [1, 2, 3, 4, 6, 7], L1212 = [1, 2, 3, 4, 7, 9], L1251 = [1, 2, 4, 5, 6, 6], L1254 = [1, 2, 4, 5, 6, 9], L1258 = [1, 2, 4, 5, 9, 9], L1260 = [1, 2, 4, 6, 6, 7], L1263 = [1, 2, 4, 6, 7, 9], L1267 = [1, 2, 4, 7, 9, 9], L1340 = [1, 3, 3, 5, 7, 9], L1381 = [1, 3, 5, 6, 7, 9], L1383 = [1, 3, 5, 7, 9, 9]. q = 19 : L19 = [0, 0, 0, 1, 2, 7], L21 = [0, 0, 0, 1, 3, 4], L67 = [0, 0, 1, 2, 3, 5], L68 = [0, 0, 1, 2, 3, 6], L70 = [0, 0, 1, 2, 3, 8], L71 = [0, 0, 1, 2, 3, 9], L72 = [0, 0, 1, 2, 4, 5], L74 = [0, 0, 1, 2, 4, 8], L77 = [0, 0, 1, 2, 6, 8], L79 = [0, 0, 1, 3, 4, 5], L209 = [0, 1, 2, 3, 4, 5], L210 = [0, 1, 2, 3, 4, 6], L211 = [0, 1, 2, 3, 4, 7], L213 = [0, 1, 2, 3, 4, 9], L214 = [0, 1, 2, 3, 5, 6], L215 = [0, 1, 2, 3, 5, 7], L216 = [0, 1, 2, 3, 5, 9], L217 = [0, 1, 2, 3, 6, 7], L218 = [0, 1, 2, 3, 6, 8], L219 = [0, 1, 2, 3, 7, 8], L220 = [0, 1, 2, 3, 7, 9], L222 = [0, 1, 2, 5, 6, 8], L548 = [1, 2, 3, 4, 5, 6], L549 = [1, 2, 3, 4, 5, 7], L550 = [1, 2, 3, 4, 5, 8], L551 = [1, 2, 3, 4, 5, 9], L552 = [1, 2, 3, 4, 6, 7], L553 = [1, 2, 3, 4, 6, 8], L554 = [1, 2, 3, 4, 6, 9], L555 = [1, 2, 3, 4, 7, 9], L556 = [1, 2, 3, 5, 6, 9], L557 = [1, 2, 3, 5, 7, 8].
APPENDIX
53
Table 4. (continued) n = 6 q 20
I {0}
indexes of I-isospectral families {355, 357}, {505, 507}, {1175, 1177}, {1182, 1186}, {1574, 1576}, {1584, 1588} {2, 3, 4} {608, 1774}, {634, 779}, {1227, 1793}, {1547, 2053}, {1600, 1798} 21 {0} {110, 112}, {121, 135}, {384, 389}, {385, 387}, {390, 394}, {391, 402}, {401, 459}, {404, 408}, {426, 462}, {1150, 1155, 1165}, {1157, 1168}, {1158, 1164}, {1169, 1179}, {1170, 1190}, {1189, 1298}, {1194, 1200}, {1231, 1304} {0, 1} {1171, 1183} {5} {143, 174, 453, 472, 477, 521}, {298, 395, 463, 475, 476, 525} 22 {0} {33, 34}, {166, 177}, {182, 184}, {242, 243}, {567, 570}, {577, 600}, {582, 623}, {624, 641}, {662, 686}, {694, 697}, {818, 819}, {1880, 1882}, {1881, 1883, 1885, 1887}, {1886, 1888}, {1892, 1913}, {1898, 1904}, {1899, 1907}, {1903, 1908}, {1922, 1976}, {1924, 1979}, {1932, 2027}, {1977, 1982}, {2030, 2063}, {2099, 2142}, {2152, 2156}, {2379, 2380} q = 20 : L355 = [0, 1, 1, 3, 3, 7], L357 = [0, 1, 1, 3, 3, 9], L505 = [0, 1, 2, 3, 4, 7], L507 = [0, 1, 2, 3, 4, 9], L608 = [0, 1, 3, 5, 7, 9], L634 = [0, 1, 4, 4, 8, 8], L779 = [0, 4, 4, 5, 8, 8], L1175 = [1, 1, 3, 3, 5, 7], L1177 = [1, 1, 3, 3, 5, 9], L1182 = [1, 1, 3, 3, 7, 10], L1186 = [1, 1, 3, 3, 9, 10], L1227 = [1, 1, 3, 5, 7, 9], L1547 = [1, 2, 2, 6, 6, 10], L1574 = [1, 2, 3, 4, 5, 7], L1576 = [1, 2, 3, 4, 5, 9], L1584 = [1, 2, 3, 4, 7, 10], L1588 = [1, 2, 3, 4, 9, 10], L1600 = [1, 2, 3, 5, 7, 9], L1774 = [1, 3, 4, 5, 7, 9], L1793 = [1, 3, 5, 5, 7, 9], L1798 = [1, 3, 5, 7, 9, 10], L2053 = [2, 2, 5, 6, 6, 10]. q = 21 : L110 = [0, 0, 1, 2, 4, 5], L112 = [0, 0, 1, 2, 4, 8], L121 = [0, 0, 1, 2, 6, 9], L135 = [0, 0, 1, 3, 4, 6], L143 = [0, 0, 1, 3, 6, 9], L174 = [0, 0, 3, 6, 7, 9], L298 = [0, 1, 1, 3, 6, 9], L384 = [0, 1, 2, 3, 4, 8], L385 = [0, 1, 2, 3, 4, 9], L387 = [0, 1, 2, 3, 5, 6], L389 = [0, 1, 2, 3, 5, 8], L390 = [0, 1, 2, 3, 5, 9], L391 = [0, 1, 2, 3, 5, 10], L394 = [0, 1, 2, 3, 6, 8], L395 = [0, 1, 2, 3, 6, 9], L401 = [0, 1, 2, 3, 8, 9], L402 = [0, 1, 2, 3, 8, 10], L404 = [0, 1, 2, 4, 5, 7], L408 = [0, 1, 2, 4, 7, 8], L426 = [0, 1, 2, 6, 7, 9], L453 = [0, 1, 3, 3, 6, 9], L459 = [0, 1, 3, 4, 5, 6], L462 = [0, 1, 3, 4, 6, 7], L463 = [0, 1, 3, 4, 6, 9], L472 = [0, 1, 3, 6, 6, 9], L475 = [0, 1, 3, 6, 7, 9], L476 = [0, 1, 3, 6, 8, 9], L477 = [0, 1, 3, 6, 9, 9], L521 = [0, 3, 3, 6, 7, 9], L525 = [0, 3, 6, 7, 7, 9], L1150 = [1, 2, 3, 4, 5, 9], L1155 = [1, 2, 3, 4, 6, 10], L1157 = [1, 2, 3, 4, 7, 8], L1158 = [1, 2, 3, 4, 7, 9], L1164 = [1, 2, 3, 5, 6, 7], L1165 = [1, 2, 3, 5, 6, 8], L1168 = [1, 2, 3, 5, 7, 8], L1169 = [1, 2, 3, 5, 7, 9], L1170 = [1, 2, 3, 5, 7, 10], L1171 = [1, 2, 3, 5, 8, 9], L1179 = [1, 2, 3, 6, 7, 8], L1183 = [1, 2, 3, 6, 8, 10], L1189 = [1, 2, 3, 7, 8, 9], L1190 = [1, 2, 3, 7, 8, 10], L1194 = [1, 2, 4, 5, 7, 7], L1200 = [1, 2, 4, 7, 7, 8], L1231 = [1, 2, 6, 7, 7, 9], L1298 = [1, 3, 4, 5, 6, 7], L1304 = [1, 3, 4, 6, 7, 7]. q = 22 : L33 = [0, 0, 0, 1, 3, 5], L34 = [0, 0, 0, 1, 3, 7], L166 = [0, 0, 1, 2, 8, 9], L177 = [0, 0, 1, 3, 4, 8], L182 = [0, 0, 1, 3, 5, 11], L184 = [0, 0, 1, 3, 7, 11], L242 = [0, 0, 2, 4, 6, 11], L243 = [0, 0, 2, 4, 8, 11], L567 = [0, 1, 2, 3, 4, 9], L570 = [0, 1, 2, 3, 5, 6], L577 = [0, 1, 2, 3, 6, 8], L582 = [0, 1, 2, 3, 7, 10], L600 = [0, 1, 2, 4, 5, 6], L623 = [0, 1, 2, 5, 6, 7], L624 = [0, 1, 2, 5, 6, 8], L641 = [0, 1, 2, 6, 7, 10], L662 = [0, 1, 2, 8, 9, 11], L686 = [0, 1, 3, 4, 8, 11], L694 = [0, 1, 3, 5, 11, 11], L697 = [0, 1, 3, 7, 11, 11], L818 = [0, 2, 4, 6, 11, 11], L819 = [0, 2, 4, 8, 11, 11], L1880 = [1, 2, 3, 4, 5, 7], L1881 = [1, 2, 3, 4, 5, 8], L1882 = [1, 2, 3, 4, 5, 9], L1883 = [1, 2, 3, 4, 5, 10], L1885 = [1, 2, 3, 4, 6, 7], L1886 = [1, 2, 3, 4, 6, 8], L1887 = [1, 2, 3, 4, 6, 9], L1888 = [1, 2, 3, 4, 6, 10], L1892 = [1, 2, 3, 4, 7, 10], L1898 = [1, 2, 3, 4, 9, 10], L1899 = [1, 2, 3, 4, 9, 11], L1903 = [1, 2, 3, 5, 6, 7], L1904 = [1, 2, 3, 5, 6, 8], L1907 = [1, 2, 3, 5, 6, 11], L1908 = [1, 2, 3, 5, 7, 8], L1913 = [1, 2, 3, 5, 8, 10], L1922 = [1, 2, 3, 6, 8, 9], L1924 = [1, 2, 3, 6, 8, 11], L1932 = [1, 2, 3, 7, 10, 11], L1976 = [1, 2, 4, 5, 6, 7], L1977 = [1, 2, 4, 5, 6, 8], L1979 = [1, 2, 4, 5, 6, 11],
54
EMILIO A. LAURET
Table 4. (continued) n = 6 q 23
I {0}
indexes of I-isospectral families {102, 104}, {108, 110}, {114, 121}, {357, 358}, {361, 362}, {365, 369}, {368, 371, 373}, {376, 378, 386, 392}, {383, 385}, {388, 390}, {391, 396}, {1085, 1086, 1090}, {1087, 1089, 1092, 1093, 1094, 1100}, {1088, 1091}, {1095, 1105}, {1097, 1102, 1103, 1104, 1106, 1107, 1108}, {1099, 1117}, {1101, 1112, 1113, 1114, 1120}, {1109, 1110, 1111, 1118}, {1119, 1124} {0, 1} {1092, 1094}, {1102, 1108}
L1982 = [1, 2, 4, 5, 8, 10], L2027 = [1, 2, 5, 6, 7, 11], L2030 = [1, 2, 5, 6, 8, 11], L2063 = [1, 2, 6, 7, 10, 11], L2099 = [1, 2, 8, 9, 11, 11], L2142 = [1, 3, 4, 8, 11, 11], L2152 = [1, 3, 5, 11, 11, 11], L2156 = [1, 3, 7, 11, 11, 11], L2379 = [2, 4, 6, 11, 11, 11], L2380 = [2, 4, 8, 11, 11, 11]. q = 23 : L102 = [0, 0, 1, 2, 4, 5], L104 = [0, 0, 1, 2, 4, 8], L108 = [0, 0, 1, 2, 5, 7], L110 = [0, 0, 1, 2, 5, 9], L114 = [0, 0, 1, 2, 6, 10], L121 = [0, 0, 1, 3, 4, 9], L357 = [0, 1, 2, 3, 4, 7], L358 = [0, 1, 2, 3, 4, 8], L361 = [0, 1, 2, 3, 4, 11], L362 = [0, 1, 2, 3, 5, 6], L365 = [0, 1, 2, 3, 5, 9], L368 = [0, 1, 2, 3, 6, 7], L369 = [0, 1, 2, 3, 6, 8], L371 = [0, 1, 2, 3, 6, 10], L373 = [0, 1, 2, 3, 7, 9], L376 = [0, 1, 2, 3, 8, 10], L378 = [0, 1, 2, 3, 9, 10], L383 = [0, 1, 2, 4, 5, 11], L385 = [0, 1, 2, 4, 7, 11], L386 = [0, 1, 2, 4, 9, 10], L388 = [0, 1, 2, 5, 6, 8], L390 = [0, 1, 2, 5, 6, 10], L391 = [0, 1, 2, 6, 7, 10], L392 = [0, 1, 2, 6, 8, 9], L396 = [0, 1, 3, 4, 5, 7], L1085 = [1, 2, 3, 4, 5, 8], L1086 = [1, 2, 3, 4, 5, 9], L1087 = [1, 2, 3, 4, 5, 10], L1088 = [1, 2, 3, 4, 5, 11], L1089 = [1, 2, 3, 4, 6, 7], L1090 = [1, 2, 3, 4, 6, 8], L1091 = [1, 2, 3, 4, 6, 9], L1092 = [1, 2, 3, 4, 6, 10], L1093 = [1, 2, 3, 4, 6, 11], L1094 = [1, 2, 3, 4, 7, 8], L1095 = [1, 2, 3, 4, 7, 9], L1097 = [1, 2, 3, 4, 7, 11], L1099 = [1, 2, 3, 4, 8, 10], L1100 = [1, 2, 3, 4, 8, 11], L1101 = [1, 2, 3, 4, 9, 10], L1102 = [1, 2, 3, 4, 9, 11], L1103 = [1, 2, 3, 5, 6, 7], L1104 = [1, 2, 3, 5, 6, 8], L1105 = [1, 2, 3, 5, 6, 9], L1106 = [1, 2, 3, 5, 6, 10], L1107 = [1, 2, 3, 5, 7, 8], L1108 = [1, 2, 3, 5, 7, 10], L1109 = [1, 2, 3, 5, 7, 11], L1110 = [1, 2, 3, 5, 8, 9], L1111 = [1, 2, 3, 5, 8, 11], L1112 = [1, 2, 3, 5, 9, 10], L1113 = [1, 2, 3, 5, 9, 11], L1114 = [1, 2, 3, 6, 7, 9], L1117 = [1, 2, 3, 6, 8, 11], L1118 = [1, 2, 3, 6, 9, 10], L1119 = [1, 2, 3, 8, 9, 10], L1120 = [1, 2, 3, 8, 9, 11], L1124 = [1, 2, 6, 8, 9, 10]. q = 24 : L41 = [0, 0, 0, 1, 3, 5], L43 = [0, 0, 0, 1, 3, 7], L213 = [0, 0, 1, 2, 5, 7], L217 = [0, 0, 1, 2, 5, 11], L254 = [0, 0, 1, 3, 4, 5], L256 = [0, 0, 1, 3, 4, 7], L262 = [0, 0, 1, 3, 5, 6], L264 = [0, 0, 1, 3, 5, 8], L267 = [0, 0, 1, 3, 5, 12], L269 = [0, 0, 1, 3, 6, 7], L275 = [0, 0, 1, 3, 7, 8], L277 = [0, 0, 1, 3, 7, 12], L846 = [0, 1, 2, 2, 5, 7], L850 = [0, 1, 2, 2, 5, 11], L899 = [0, 1, 2, 3, 5, 10], L911 = [0, 1, 2, 3, 7, 10], L938 = [0, 1, 2, 4, 5, 7], L942 = [0, 1, 2, 4, 5, 11], L969 = [0, 1, 2, 5, 6, 7], L973 = [0, 1, 2, 5, 6, 11], L975 = [0, 1, 2, 5, 7, 8], L979 = [0, 1, 2, 5, 7, 12], L983 = [0, 1, 2, 5, 8, 11], L988 = [0, 1, 2, 5, 11, 12], L1071 = [0, 1, 3, 3, 5, 9], L1082 = [0, 1, 3, 3, 7, 9], L1099 = [0, 1, 3, 4, 4, 5], L1101 = [0, 1, 3, 4, 4, 7], L1107 = [0, 1, 3, 4, 5, 6], L1109 = [0, 1, 3, 4, 5, 8], L1112 = [0, 1, 3, 4, 5, 12], L1114 = [0, 1, 3, 4, 6, 7], L1120 = [0, 1, 3, 4, 7, 8], L1122 = [0, 1, 3, 4, 7, 12], L1137 = [0, 1, 3, 5, 6, 6], L1139 = [0, 1, 3, 5, 6, 8], L1142 = [0, 1, 3, 5, 6, 12], L1147 = [0, 1, 3, 5, 8, 8], L1150 = [0, 1, 3, 5, 8, 12], L1153 = [0, 1, 3, 5, 12, 12], L1155 = [0, 1, 3, 6, 6, 7], L1161 = [0, 1, 3, 6, 7, 8], L1163 = [0, 1, 3, 6, 7, 12], L1178 = [0, 1, 3, 7, 8, 8], L1180 = [0, 1, 3, 7, 8, 12], L1183 = [0, 1, 3, 7, 12, 12], L1606 = [0, 3, 4, 6, 9, 12], L1622 = [0, 3, 6, 8, 9, 12], L2380 = [1, 1, 3, 5, 5, 11], L2389 = [1, 1, 3, 5, 7, 7], L2942 = [1, 2, 2, 2, 5, 7], L2946 = [1, 2, 2, 2, 5, 11], L3034 = [1, 2, 2, 4, 5, 7], L3038 = [1, 2, 2, 4, 5, 11], L3065 = [1, 2, 2, 5, 6, 7], L3069 = [1, 2, 2, 5, 6, 11], L3071 = [1, 2, 2, 5, 7, 8], L3073 = [1, 2, 2, 5, 7, 10], L3075 = [1, 2, 2, 5, 7, 12], L3079 = [1, 2, 2, 5, 8, 11], L3085 = [1, 2, 2, 5, 10, 11], L3087 = [1, 2, 2, 5, 11, 12], L3214 = [1, 2, 3, 4, 5, 10], L3226 = [1, 2, 3, 4, 7, 10], L3247 = [1, 2, 3, 5, 6, 10], L3251 = [1, 2, 3, 5, 7, 9], L3257 = [1, 2, 3, 5, 8, 10], L3262 = [1, 2, 3, 5, 9, 11], L3265 = [1, 2, 3, 5, 10, 12], L3277 = [1, 2, 3, 6, 7, 10], L3296 = [1, 2, 3, 7, 8, 10], L3302 = [1, 2, 3, 7, 10, 12], L3344 = [1, 2, 4, 4, 5, 7], L3348 = [1, 2, 4, 4, 5, 11], L3375 = [1, 2, 4, 5, 6, 7], L3379 = [1, 2, 4, 5, 6, 11], L3381 = [1, 2, 4, 5, 7, 8], L3385 = [1, 2, 4, 5, 7, 12], L3389 = [1, 2, 4, 5, 8, 11], L3394 = [1, 2, 4, 5, 11, 12],
APPENDIX
55
Table 4. (continued) n = 6 q 24
I {0}
indexes of I-isospectral families {41, 43}, {213, 217}, {254, 256}, {262, 269}, {264, 275}, {267, 277}, {846, 850}, {899, 911}, {938, 942}, {969, 973}, {975, 983}, {979, 988}, {1071, 1082}, {1099, 1101}, {1107, 1114}, {1109, 1120}, {1112, 1122}, {1137, 1155}, {1139, 1161}, {1142, 1163}, {1147, 1178}, {1150, 1180}, {1153, 1183}, {2380, 2389}, {2942, 2946}, {3034, 3038}, {3065, 3069}, {3071, 3079}, {3073, 3085}, {3075, 3087}, {3214, 3226}, {3247, 3277}, {3251, 3262}, {3257, 3296}, {3265, 3302}, {3344, 3348}, {3375, 3379}, {3381, 3389}, {3385, 3394}, {3456, 3460}, {3462, 3470}, {3466, 3475}, {3477, 3491}, {3481, 3496}, {3487, 3502}, {3685, 3696}, {3715, 3739}, {3723, 3756}, {3728, 3759}, {3792, 3794}, {3800, 3807}, {3802, 3813}, {3805, 3815}, {3830, 3848}, {3832, 3854}, {3835, 3856}, {3840, 3871}, {3843, 3873}, {3846, 3876}, {3906, 3942}, {3908, 3948}, {3911, 3950}, {3916, 3965}, {3919, 3967}, {3922, 3970}, {3931, 4000}, {3934, 4002}, {3937, 4005}, {3940, 4009} {0, 1} {2380, 2389} {0, 5} {3073, 3085}, {3247, 3277} {4, 5} {1606, 1622}
L3456 = [1, 2, 5, 6, 6, 7], L3460 = [1, 2, 5, 6, 6, 11], L3462 = [1, 2, 5, 6, 7, 8], L3466 = [1, 2, 5, 6, 7, 12], L3470 = [1, 2, 5, 6, 8, 11], L3475 = [1, 2, 5, 6, 11, 12], L3477 = [1, 2, 5, 7, 8, 8], L3481 = [1, 2, 5, 7, 8, 12], L3487 = [1, 2, 5, 7, 12, 12], L3491 = [1, 2, 5, 8, 8, 11], L3496 = [1, 2, 5, 8, 11, 12], L3502 = [1, 2, 5, 11, 12, 12], L3685 = [1, 3, 3, 4, 5, 9], L3696 = [1, 3, 3, 4, 7, 9], L3715 = [1, 3, 3, 5, 6, 9], L3723 = [1, 3, 3, 5, 8, 9], L3728 = [1, 3, 3, 5, 9, 12], L3739 = [1, 3, 3, 6, 7, 9], L3756 = [1, 3, 3, 7, 8, 9], L3759 = [1, 3, 3, 7, 9, 12], L3792 = [1, 3, 4, 4, 4, 5], L3794 = [1, 3, 4, 4, 4, 7], L3800 = [1, 3, 4, 4, 5, 6], L3802 = [1, 3, 4, 4, 5, 8], L3805 = [1, 3, 4, 4, 5, 12], L3807 = [1, 3, 4, 4, 6, 7], L3813 = [1, 3, 4, 4, 7, 8], L3815 = [1, 3, 4, 4, 7, 12], L3830 = [1, 3, 4, 5, 6, 6], L3832 = [1, 3, 4, 5, 6, 8], L3835 = [1, 3, 4, 5, 6, 12], L3840 = [1, 3, 4, 5, 8, 8], L3843 = [1, 3, 4, 5, 8, 12], L3846 = [1, 3, 4, 5, 12, 12], L3848 = [1, 3, 4, 6, 6, 7], L3854 = [1, 3, 4, 6, 7, 8], L3856 = [1, 3, 4, 6, 7, 12], L3871 = [1, 3, 4, 7, 8, 8], L3873 = [1, 3, 4, 7, 8, 12], L3876 = [1, 3, 4, 7, 12, 12], L3906 = [1, 3, 5, 6, 6, 6], L3908 = [1, 3, 5, 6, 6, 8], L3911 = [1, 3, 5, 6, 6, 12], L3916 = [1, 3, 5, 6, 8, 8], L3919 = [1, 3, 5, 6, 8, 12], L3922 = [1, 3, 5, 6, 12, 12], L3931 = [1, 3, 5, 8, 8, 8], L3934 = [1, 3, 5, 8, 8, 12], L3937 = [1, 3, 5, 8, 12, 12], L3940 = [1, 3, 5, 12, 12, 12], L3942 = [1, 3, 6, 6, 6, 7], L3948 = [1, 3, 6, 6, 7, 8], L3950 = [1, 3, 6, 6, 7, 12], L3965 = [1, 3, 6, 7, 8, 8], L3967 = [1, 3, 6, 7, 8, 12], L3970 = [1, 3, 6, 7, 12, 12], L4000 = [1, 3, 7, 8, 8, 8], L4002 = [1, 3, 7, 8, 8, 12], L4005 = [1, 3, 7, 8, 12, 12], L4009 = [1, 3, 7, 12, 12, 12]. q = 25 : L133 = [0, 0, 1, 2, 4, 11], L141 = [0, 0, 1, 2, 6, 7], L142 = [0, 0, 1, 2, 6, 8], L143 = [0, 0, 1, 2, 6, 9], L145 = [0, 0, 1, 2, 6, 11], L146 = [0, 0, 1, 2, 7, 8], L157 = [0, 0, 1, 3, 4, 9], L499 = [0, 1, 2, 3, 4, 11], L504 = [0, 1, 2, 3, 5, 8], L508 = [0, 1, 2, 3, 5, 12], L509 = [0, 1, 2, 3, 6, 7], L510 = [0, 1, 2, 3, 6, 8], L511 = [0, 1, 2, 3, 6, 9], L513 = [0, 1, 2, 3, 6, 11], L514 = [0, 1, 2, 3, 6, 12], L515 = [0, 1, 2, 3, 7, 8], L516 = [0, 1, 2, 3, 7, 9], L518 = [0, 1, 2, 3, 7, 11], L519 = [0, 1, 2, 3, 7, 12], L521 = [0, 1, 2, 3, 8, 12], L523 = [0, 1, 2, 3, 9, 11], L524 = [0, 1, 2, 3, 9, 12], L529 = [0, 1, 2, 4, 5, 7], L534 = [0, 1, 2, 4, 5, 12], L535 = [0, 1, 2, 4, 7, 8], L538 = [0, 1, 2, 4, 9, 10], L554 = [0, 1, 2, 5, 7, 8], L563 = [0, 1, 2, 6, 7, 8], L565 = [0, 1, 2, 6, 7, 11], L567 = [0, 1, 2, 6, 8, 11], L605 = [0, 1, 4, 6, 9, 11], L1406 = [1, 1, 4, 4, 6, 11], L1411 = [1, 1, 4, 4, 9, 11], L1456 = [1, 1, 4, 6, 9, 9], L1463 = [1, 1, 4, 6, 11, 11], L1655 = [1, 2, 3, 4, 5, 11], L1657 = [1, 2, 3, 4, 6, 7], L1658 = [1, 2, 3, 4, 6, 8], L1660 = [1, 2, 3, 4, 6, 10], L1661 = [1, 2, 3, 4, 6, 11], L1662 = [1, 2, 3, 4, 6, 12], L1663 = [1, 2, 3, 4, 7, 8], L1664 = [1, 2, 3, 4, 7, 9], L1665 = [1, 2, 3, 4, 7, 10], L1666 = [1, 2, 3, 4, 7, 11], L1668 = [1, 2, 3, 4, 8, 9], L1670 = [1, 2, 3, 4, 8, 11], L1671 = [1, 2, 3, 4, 8, 12], L1673 = [1, 2, 3, 4, 9, 11], L1674 = [1, 2, 3, 4, 9, 12], L1677 = [1, 2, 3, 4, 10, 12],
56
EMILIO A. LAURET
Table 4. (continued) n = 6 q 25
I {0}
indexes of I-isospectral families {133, 146}, {141, 142}, {143, 145, 157}, {499, 514}, {504, 508}, {509, 511}, {510, 513, 516, 524}, {515, 519, 521}, {523, 563}, {529, 534}, {538, 554}, {565, 567}, {1406, 1411}, {1456, 1463}, {1655, 1660}, {1657, 1658}, {1661, 1663, 1671}, {1662, 1666}, {1664, 1668}, {1665, 1688}, {1670, 1674, 1707}, {1673, 1706, 1711, 1712, 1717}, {1677, 1691}, {1687, 1715}, {1696, 1724}, {1699, 1722}, {1719, 1740, 1774}, {1747, 1783}, {1775, 1777}, {1779, 1782, 1815} {0, 1} {518, 535}, {519, 521}, {1674, 1707}, {1712, 1717} {2, 3, 4} {605, 1841, 1846}
L1687 = [1, 2, 3, 5, 6, 8], L1688 = [1, 2, 3, 5, 6, 9], L1691 = [1, 2, 3, 5, 6, 12], L1696 = [1, 2, 3, 5, 7, 12], L1699 = [1, 2, 3, 5, 8, 12], L1706 = [1, 2, 3, 6, 7, 8], L1707 = [1, 2, 3, 6, 7, 9], L1711 = [1, 2, 3, 6, 8, 12], L1712 = [1, 2, 3, 6, 9, 11], L1715 = [1, 2, 3, 6, 10, 12], L1717 = [1, 2, 3, 7, 8, 11], L1719 = [1, 2, 3, 7, 9, 10], L1722 = [1, 2, 3, 7, 10, 12], L1724 = [1, 2, 3, 8, 10, 12], L1740 = [1, 2, 4, 5, 7, 12], L1747 = [1, 2, 4, 5, 10, 11], L1774 = [1, 2, 5, 6, 7, 8], L1775 = [1, 2, 5, 6, 7, 10], L1777 = [1, 2, 5, 6, 8, 10], L1779 = [1, 2, 5, 6, 9, 10], L1782 = [1, 2, 5, 6, 10, 11], L1783 = [1, 2, 5, 7, 8, 10], L1815 = [1, 3, 4, 5, 9, 10], L1841 = [1, 4, 5, 6, 9, 11], L1846 = [1, 4, 6, 9, 10, 11]. q = 26 : L39 = [0, 0, 0, 1, 3, 5], L40 = [0, 0, 0, 1, 3, 7], L42 = [0, 0, 0, 1, 3, 9], L44 = [0, 0, 0, 1, 3, 11], L218 = [0, 0, 1, 2, 7, 8], L233 = [0, 0, 1, 2, 10, 11], L244 = [0, 0, 1, 3, 4, 8], L246 = [0, 0, 1, 3, 4, 10], L247 = [0, 0, 1, 3, 4, 12], L249 = [0, 0, 1, 3, 5, 7], L251 = [0, 0, 1, 3, 5, 9], L252 = [0, 0, 1, 3, 5, 11], L254 = [0, 0, 1, 3, 5, 13], L257 = [0, 0, 1, 3, 7, 13], L263 = [0, 0, 1, 3, 9, 13], L269 = [0, 0, 1, 3, 11, 13], L282 = [0, 0, 1, 4, 5, 8], L360 = [0, 0, 2, 4, 6, 13], L361 = [0, 0, 2, 4, 8, 13], L362 = [0, 0, 2, 4, 10, 13], L364 = [0, 0, 2, 6, 8, 13], L902 = [0, 1, 2, 3, 9, 12], L952 = [0, 1, 2, 4, 10, 11], L961 = [0, 1, 2, 5, 6, 7], L965 = [0, 1, 2, 5, 6, 12], L994 = [0, 1, 2, 6, 7, 8], L1020 = [0, 1, 2, 7, 8, 13], L1044 = [0, 1, 2, 9, 10, 11], L1045 = [0, 1, 2, 9, 10, 12], L1057 = [0, 1, 2, 10, 11, 13], L1077 = [0, 1, 3, 4, 5, 8], L1088 = [0, 1, 3, 4, 8, 13], L1093 = [0, 1, 3, 4, 10, 13], L1095 = [0, 1, 3, 4, 12, 13], L1099 = [0, 1, 3, 5, 7, 13], L1104 = [0, 1, 3, 5, 9, 13], L1105 = [0, 1, 3, 5, 11, 13], L1108 = [0, 1, 3, 5, 13, 13], L1114 = [0, 1, 3, 7, 13, 13], L1129 = [0, 1, 3, 9, 13, 13], L1141 = [0, 1, 3, 11, 13, 13], L1181 = [0, 1, 4, 5, 8, 13], L1352 = [0, 2, 4, 6, 8, 13], L1353 = [0, 2, 4, 6, 10, 13], L1354 = [0, 2, 4, 6, 12, 13], L1355 = [0, 2, 4, 6, 13, 13], L1356 = [0, 2, 4, 8, 13, 13], L1357 = [0, 2, 4, 10, 13, 13], L1359 = [0, 2, 6, 8, 13, 13], L3289 = [1, 2, 3, 4, 7, 8], L3298 = [1, 2, 3, 4, 8, 11], L3317 = [1, 2, 3, 5, 6, 10], L3323 = [1, 2, 3, 5, 7, 10], L3334 = [1, 2, 3, 5, 9, 12], L3345 = [1, 2, 3, 6, 7, 9], L3351 = [1, 2, 3, 6, 8, 9], L3352 = [1, 2, 3, 6, 8, 10], L3359 = [1, 2, 3, 6, 10, 11], L3368 = [1, 2, 3, 7, 8, 10], L3372 = [1, 2, 3, 7, 9, 10], L3400 = [1, 2, 3, 9, 10, 12], L3405 = [1, 2, 3, 9, 12, 13], L3470 = [1, 2, 4, 5, 6, 12], L3485 = [1, 2, 4, 5, 10, 12], L3500 = [1, 2, 4, 6, 7, 8], L3501 = [1, 2, 4, 6, 7, 9], L3544 = [1, 2, 4, 9, 10, 11], L3557 = [1, 2, 4, 10, 11, 13], L3575 = [1, 2, 5, 6, 7, 8], L3578 = [1, 2, 5, 6, 7, 13], L3586 = [1, 2, 5, 6, 11, 12], L3589 = [1, 2, 5, 6, 12, 13], L3660 = [1, 2, 6, 7, 8, 13], L3661 = [1, 2, 6, 7, 9, 10], L3716 = [1, 2, 7, 8, 13, 13], L3764 = [1, 2, 9, 10, 11, 13], L3766 = [1, 2, 9, 10, 12, 13], L3786 = [1, 2, 10, 11, 13, 13], L3835 = [1, 3, 4, 5, 8, 13], L3857 = [1, 3, 4, 8, 13, 13], L3866 = [1, 3, 4, 10, 13, 13], L3869 = [1, 3, 4, 12, 13, 13], L3875 = [1, 3, 5, 7, 13, 13], L3885 = [1, 3, 5, 9, 13, 13], L3886 = [1, 3, 5, 11, 13, 13], L3890 = [1, 3, 5, 13, 13, 13], L3900 = [1, 3, 7, 13, 13, 13], L3931 = [1, 3, 9, 13, 13, 13], L3951 = [1, 3, 11, 13, 13, 13], L4052 = [1, 4, 5, 8, 13, 13], L4385 = [2, 4, 6, 8, 13, 13], L4386 = [2, 4, 6, 10, 13, 13], L4387 = [2, 4, 6, 12, 13, 13], L4388 = [2, 4, 6, 13, 13, 13], L4389 = [2, 4, 8, 13, 13, 13], L4390 = [2, 4, 10, 13, 13, 13], L4392 = [2, 6, 8, 13, 13, 13]. q = 27 : L162 = [0, 0, 1, 2, 4, 11], L165 = [0, 0, 1, 2, 5, 7], L168 = [0, 0, 1, 2, 5, 10], L177 = [0, 0, 1, 2, 7, 8], L179 = [0, 0, 1, 2, 7, 10], L687 = [0, 1, 2, 3, 5, 10], L690 = [0, 1, 2, 3, 5, 13], L704 = [0, 1, 2, 3, 7, 13], L716 = [0, 1, 2, 3, 10, 13], L720 = [0, 1, 2, 4, 5, 7], L721 = [0, 1, 2, 4, 5, 8], L723 = [0, 1, 2, 4, 5, 10], L724 = [0, 1, 2, 4, 5, 11], L727 = [0, 1, 2, 4, 7, 8], L730 = [0, 1, 2, 4, 7, 11], L732 =
APPENDIX
57
Table 4. (continued) n = 6 q 26
I {0}
indexes of I-isospectral families {39, 42}, {40, 44}, {218, 244}, {233, 282}, {246, 247}, {249, 251, 252}, {254, 263}, {257, 269}, {360, 361}, {362, 364}, {902, 961}, {952, 965}, {994, 1045}, {1020, 1088}, {1044, 1077}, {1057, 1181}, {1093, 1095}, {1099, 1104, 1105}, {1108, 1129}, {1114, 1141}, {1352, 1353, 1354}, {1355, 1356}, {1357, 1359}, {3289, 3351}, {3298, 3317}, {3323, 3345}, {3334, 3372}, {3352, 3470}, {3359, 3501}, {3368, 3661}, {3400, 3575}, {3405, 3578}, {3485, 3500}, {3544, 3586}, {3557, 3589}, {3660, 3766}, {3716, 3857}, {3764, 3835}, {3786, 4052}, {3866, 3869}, {3875, 3885, 3886}, {3890, 3931}, {3900, 3951}, {4385, 4386, 4387}, {4388, 4389}, {4390, 4392} {0, 1} {251, 252}, {1104, 1105}, {1352, 1353}, {3885, 3886}, {4385, 4386} 27 {0} {162, 165, 168}, {177, 179}, {687, 690}, {704, 716}, {720, 721}, {723, 724, 727, 732}, {736, 749, 755}, {738, 748}, {739, 751}, {781, 786}, {2478, 2483}, {2480, 2481}, {2487, 2489}, {2492, 2507}, {2496, 2511}, {2504, 2563}, {2525, 2561}, {2528, 2531}, {2574, 2593}, {2575, 2699}, {2576, 2705}, {2583, 2710}, {2602, 2604, 2610}, {2603, 2608}, {2605, 2611, 2617}, {2613, 2614, 2620, 2625}, {2618, 2649}, {2633, 2661, 2669}, {2635, 2659}, {2636, 2663}, {2724, 2733} {0, 1} {723, 724}, {2613, 2614}, {0, 1, 2} {730, 750}, {2607, 2609}, {2611, 2617}, {2623, 2662} [0, 1, 2, 4, 7, 13], L736 = [0, 1, 2, 4, 9, 11], L738 = [0, 1, 2, 4, 10, 11], L739 = [0, 1, 2, 4, 10, 12], L748 = [0, 1, 2, 5, 7, 8], L749 = [0, 1, 2, 5, 7, 9], L750 = [0, 1, 2, 5, 7, 11], L751 = [0, 1, 2, 5, 7, 12], L755 = [0, 1, 2, 5, 9, 10], L781 = [0, 1, 2, 7, 8, 9], L786 = [0, 1, 2, 7, 9, 10], L2478 = [1, 2, 3, 4, 5, 12], L2480 = [1, 2, 3, 4, 6, 7], L2481 = [1, 2, 3, 4, 6, 8], L2483 = [1, 2, 3, 4, 6, 10], L2487 = [1, 2, 3, 4, 7, 8], L2489 = [1, 2, 3, 4, 7, 10], L2492 = [1, 2, 3, 4, 7, 13], L2496 = [1, 2, 3, 4, 8, 12], L2504 = [1, 2, 3, 4, 10, 12], L2507 = [1, 2, 3, 4, 11, 13], L2511 = [1, 2, 3, 5, 6, 8], L2525 = [1, 2, 3, 5, 8, 12], L2528 = [1, 2, 3, 5, 9, 10], L2531 = [1, 2, 3, 5, 9, 13], L2561 = [1, 2, 3, 6, 10, 13], L2563 = [1, 2, 3, 6, 11, 13], L2574 = [1, 2, 3, 7, 9, 13], L2575 = [1, 2, 3, 7, 10, 12], L2576 = [1, 2, 3, 7, 11, 12], L2583 = [1, 2, 3, 8, 10, 12], L2593 = [1, 2, 3, 9, 10, 13], L2602 = [1, 2, 4, 5, 7, 8], L2603 = [1, 2, 4, 5, 7, 9], L2604 = [1, 2, 4, 5, 7, 10], L2605 = [1, 2, 4, 5, 7, 11], L2607 = [1, 2, 4, 5, 7, 13], L2608 = [1, 2, 4, 5, 8, 9], L2609 = [1, 2, 4, 5, 8, 10], L2610 = [1, 2, 4, 5, 8, 11], L2611 = [1, 2, 4, 5, 8, 13], L2613 = [1, 2, 4, 5, 9, 10], L2614 = [1, 2, 4, 5, 9, 11], L2617 = [1, 2, 4, 5, 10, 13], L2618 = [1, 2, 4, 5, 11, 12], L2620 = [1, 2, 4, 7, 8, 9], L2623 = [1, 2, 4, 7, 9, 11], L2625 = [1, 2, 4, 7, 9, 13], L2633 = [1, 2, 4, 9, 9, 11], L2635 = [1, 2, 4, 9, 10, 11], L2636 = [1, 2, 4, 9, 10, 12], L2649 = [1, 2, 5, 6, 7, 8], L2659 = [1, 2, 5, 7, 8, 9], L2661 = [1, 2, 5, 7, 9, 9], L2662 = [1, 2, 5, 7, 9, 11], L2663 = [1, 2, 5, 7, 9, 12], L2669 = [1, 2, 5, 9, 9, 10], L2699 = [1, 2, 6, 7, 8, 12], L2705 = [1, 2, 6, 7, 11, 12], L2710 = [1, 2, 6, 8, 10, 12], L2724 = [1, 2, 7, 8, 9, 9], L2733 = [1, 2, 7, 9, 9, 10]. q = 28 : L43 = [0, 0, 0, 1, 3, 5], L46 = [0, 0, 0, 1, 3, 9], L299 = [0, 0, 1, 3, 5, 7], L301 = [0, 0, 1, 3, 5, 9], L302 = [0, 0, 1, 3, 5, 11], L304 = [0, 0, 1, 3, 5, 14], L307 = [0, 0, 1, 3, 7, 9], L319 = [0, 0, 1, 3, 9, 14], L365 = [0, 0, 1, 4, 8, 12], L503 = [0, 0, 4, 7, 8, 12], L819 = [0, 1, 1, 4, 8, 12], L1134 = [0, 1, 2, 3, 5, 10], L1141 = [0, 1, 2, 3, 6, 9], L1220 = [0, 1, 2, 4, 8, 12], L1300 = [0, 1, 2, 6, 10, 14], L1399 = [0, 1, 3, 4, 5, 12], L1411 = [0, 1, 3, 4, 8, 9], L1414 = [0, 1, 3, 4, 8, 12], L1433 = [0, 1, 3, 5, 7, 7], L1435 = [0, 1, 3, 5, 7, 9], L1436 = [0, 1, 3, 5, 7, 11], L1438 = [0, 1, 3, 5, 7, 14], L1444 = [0, 1, 3, 5, 9, 14], L1445 = [0, 1, 3, 5, 11, 14], L1448 = [0, 1, 3, 5, 14, 14], L1451 = [0, 1, 3, 7, 7, 9], L1463 = [0, 1, 3, 7, 9, 14], L1496 = [0, 1, 3, 9, 14, 14], L1554 = [0, 1, 4, 4, 8, 12], L1578 = [0, 1, 4, 5, 8, 12], L1598 = [0, 1, 4, 6, 8, 12], L1620 = [0, 1, 4, 7, 8, 12], L1637 = [0, 1, 4, 8, 8, 12], L1642 = [0, 1, 4, 8, 10, 12], L1646 = [0, 1, 4, 8, 12, 12], L1647 = [0, 1, 4, 8, 12, 13], L1648 = [0, 1, 4, 8, 12, 14], L1915 = [0, 2, 4, 6, 7, 8], L1917 = [0, 2, 4, 6, 7, 12], L1925 = [0, 2, 4, 7, 8, 12],
58
EMILIO A. LAURET
Table 4. (continued) n = 6 q 28
I {0}
indexes of I-isospectral families {43, 46}, {299, 307}, {304, 319}, {1134, 1141}, {1399, 1411}, {1433, 1451}, {1438, 1463}, {1448, 1496}, {1915, 1917}, {3023, 3113}, {4538, 4572}, {4558, 4609}, {4561, 4578}, {4566, 4596}, {4585, 4611}, {5337, 5366}, {5342, 5347}, {5343, 5394}, {5354, 5396}, {5438, 5472}, {5443, 5484}, {5453, 5517}, {5469, 5587}, {6566, 6568}, {6573, 6575} {0, 1} {301, 302}, {1435, 1436}, {1444, 1445}, {4942, 5084}, {5440, 5441}, {5449, 5450}, {5464, 5465} {5} {365, 503, 1554, 1637, 1646, 1970}, {819, 1414, 1578, 1620, 1647, 1977}, {1220, 1598, 1642, 1648, 1925, 1980}, {1300, 1938, 4839, 5089, 5104, 6574}, {2863, 4616, 4949, 5072, 5105, 6609}, {4402, 5048, 5101, 5106, 6505, 6614}, {5441, 5448} 29 {0} {164, 171}, {215, 216}, {728, 750, 755}, {799, 815}, {2582, 2589}, {2591, 2608, 2611}, {2593, 2630}, {2597, 2644}, {2601, 2637}, {2610, 2638}, {2617, 2628}, {2622, 2635}, {2632, 2639, 2645}, {2650, 2698}, {2672, 2712}, {2677, 2692}, {2678, 2735}, {2713, 2745}, {2723, 2726}, {2725, 2755}, {2727, 2740}, {2728, 2772}, {2767, 2769} L1938 = [0, 2, 6, 7, 10, 14], L1970 = [0, 4, 4, 7, 8, 12], L1977 = [0, 4, 7, 7, 8, 12], L1980 = [0, 4, 7, 8, 12, 14], L2863 = [1, 1, 2, 6, 10, 14], L3023 = [1, 1, 3, 3, 9, 11], L3113 = [1, 1, 3, 5, 5, 13], L4402 = [1, 2, 2, 6, 10, 14], L4538 = [1, 2, 3, 4, 9, 11], L4558 = [1, 2, 3, 5, 6, 10], L4561 = [1, 2, 3, 5, 6, 13], L4566 = [1, 2, 3, 5, 7, 10], L4572 = [1, 2, 3, 5, 8, 9], L4578 = [1, 2, 3, 5, 9, 10], L4585 = [1, 2, 3, 5, 10, 14], L4596 = [1, 2, 3, 6, 7, 9], L4609 = [1, 2, 3, 6, 9, 10], L4611 = [1, 2, 3, 6, 9, 14], L4616 = [1, 2, 3, 6, 10, 14], L4839 = [1, 2, 4, 6, 10, 14], L4942 = [1, 2, 5, 6, 8, 12], L4949 = [1, 2, 5, 6, 10, 14], L5048 = [1, 2, 6, 6, 10, 14], L5072 = [1, 2, 6, 7, 10, 14], L5084 = [1, 2, 6, 8, 9, 12], L5089 = [1, 2, 6, 8, 10, 14], L5101 = [1, 2, 6, 10, 10, 14], L5104 = [1, 2, 6, 10, 12, 14], L5105 = [1, 2, 6, 10, 13, 14], L5106 = [1, 2, 6, 10, 14, 14], L5337 = [1, 3, 4, 5, 7, 12], L5342 = [1, 3, 4, 5, 8, 11], L5343 = [1, 3, 4, 5, 8, 12], L5347 = [1, 3, 4, 5, 9, 12], L5354 = [1, 3, 4, 5, 12, 14], L5366 = [1, 3, 4, 7, 8, 9], L5394 = [1, 3, 4, 8, 9, 12], L5396 = [1, 3, 4, 8, 9, 14], L5438 = [1, 3, 5, 7, 7, 7], L5440 = [1, 3, 5, 7, 7, 9], L5441 = [1, 3, 5, 7, 7, 11], L5443 = [1, 3, 5, 7, 7, 14], L5448 = [1, 3, 5, 7, 9, 11], L5449 = [1, 3, 5, 7, 9, 14], L5450 = [1, 3, 5, 7, 11, 14], L5453 = [1, 3, 5, 7, 14, 14], L5464 = [1, 3, 5, 9, 14, 14], L5465 = [1, 3, 5, 11, 14, 14], L5469 = [1, 3, 5, 14, 14, 14], L5472 = [1, 3, 7, 7, 7, 9], L5484 = [1, 3, 7, 7, 9, 14], L5517 = [1, 3, 7, 9, 14, 14], L5587 = [1, 3, 9, 14, 14, 14], L6505 = [2, 2, 6, 7, 10, 14], L6566 = [2, 4, 6, 7, 7, 8], L6568 = [2, 4, 6, 7, 7, 12], L6573 = [2, 4, 6, 7, 8, 14], L6574 = [2, 4, 6, 7, 10, 14], L6575 = [2, 4, 6, 7, 12, 14], L6609 = [2, 6, 7, 7, 10, 14], L6614 = [2, 6, 7, 10, 14, 14]. q = 29 : L164 = [0, 0, 1, 2, 4, 11], L171 = [0, 0, 1, 2, 5, 10], L215 = [0, 0, 1, 4, 5, 7], L216 = [0, 0, 1, 4, 5, 13], L728 = [0, 1, 2, 3, 8, 13], L750 = [0, 1, 2, 4, 7, 8], L755 = [0, 1, 2, 4, 7, 14], L799 = [0, 1, 2, 7, 8, 9], L815 = [0, 1, 2, 10, 11, 12], L2582 = [1, 2, 3, 4, 7, 13], L2589 = [1, 2, 3, 4, 8, 14], L2591 = [1, 2, 3, 4, 9, 11], L2593 = [1, 2, 3, 4, 9, 13], L2597 = [1, 2, 3, 4, 10, 13], L2601 = [1, 2, 3, 4, 11, 14], L2608 = [1, 2, 3, 5, 6, 11], L2610 = [1, 2, 3, 5, 6, 13], L2611 = [1, 2, 3, 5, 6, 14], L2617 = [1, 2, 3, 5, 7, 13], L2622 = [1, 2, 3, 5, 8, 12], L2628 = [1, 2, 3, 5, 9, 14], L2630 = [1, 2, 3, 5, 10, 12], L2632 = [1, 2, 3, 5, 10, 14], L2635 = [1, 2, 3, 5, 11, 14], L2637 = [1, 2, 3, 5, 12, 14], L2638 = [1, 2, 3, 6, 7, 8], L2639 = [1, 2, 3, 6, 7, 9], L2644 = [1, 2, 3, 6, 7, 14], L2645 = [1, 2, 3, 6, 8, 9], L2650 = [1, 2, 3, 6, 8, 14], L2672 = [1, 2, 3, 7, 11, 13], L2677 = [1, 2, 3, 8, 9, 12], L2678 = [1, 2, 3, 8, 9, 13], L2692 = [1, 2, 3, 10, 11, 12], L2698 = [1, 2, 4, 5, 7, 9], L2712 = [1, 2, 4, 5, 11, 12], L2713 = [1, 2, 4, 5, 11, 13], L2723 = [1, 2, 4, 7, 12, 13], L2725 = [1, 2, 4, 10, 11, 12], L2726 = [1, 2, 4, 10, 11, 13], L2727 = [1, 2, 4, 10, 12, 13], L2728 = [1, 2, 4, 11, 12, 13], L2735 = [1, 2, 5, 6, 8, 10], L2740 = [1, 2, 5, 6, 11, 13], L2745 = [1, 2, 5, 7, 10, 11], L2755 = [1, 2, 6, 7, 8, 11], L2767 = [1, 2, 7, 8, 12, 13], L2769 = [1, 2, 7, 10, 12, 13], L2772 = [1, 2, 10, 11, 12, 13].
APPENDIX
59
Table 4. (continued) n = 6 q 30
I {0}
indexes of I-isospectral families {55, 59}, {423, 427}, {444, 463}, {448, 469}, {800, 815}, {805, 837}, {1814, 1820}, {1817, 1819}, {2140, 2155}, {2241, 2245}, {2262, 2281}, {2266, 2287}, {2311, 2334}, {2354, 2413}, {2358, 2419}, {2366, 2431}, {3413, 3463}, {3520, 3560}, {3532, 3586}, {3535, 3588}, {3547, 3644}, {3550, 3646}, {7672, 8282}, {7780, 7786}, {7783, 7785}, {7873, 7888}, {7874, 7896}, {7878, 7898}, {7885, 7887}, {7892, 7897}, {8886, 8901}, {8978, 9030}, {8982, 9036}, {9326, 9330}, {9347, 9366}, {9351, 9372}, {9396, 9419}, {9439, 9498}, {9443, 9504}, {9451, 9516}, {9594, 9659}, {9602, 9671}, {9712, 9854}, {9716, 9860}, {9724, 9872}, {9736, 9892}, {12669, 12778}, {12718, 12856}, {12721, 12858}, {12960, 13051}, {12972, 13077}, {12975, 13079}, {12991, 13128}, {13001, 13144}, {13004, 13146}, {13008, 13149}, {13024, 13241}, {13034, 13269}, {13037, 13271}, {13041, 13274} {0, 1} {7411, 7416}, {7890, 8284} {2, 3, 4} {2781, 10854}, {2886, 3852}, {6047, 10730}, {7915, 12996}, {8122, 10940}, {9028, 13471}, {9445, 10943}, {12622, 13504}, {12710, 13029}
q = 30 : L55 = [0, 0, 0, 1, 3, 7], L59 = [0, 0, 0, 1, 3, 11], L423 = [0, 0, 1, 3, 5, 7], L427 = [0, 0, 1, 3, 5, 11], L444 = [0, 0, 1, 3, 7, 10], L448 = [0, 0, 1, 3, 7, 15], L463 = [0, 0, 1, 3, 10, 11], L469 = [0, 0, 1, 3, 11, 15], L800 = [0, 0, 2, 4, 5, 12], L805 = [0, 0, 2, 4, 12, 15], L815 = [0, 0, 2, 5, 6, 8], L837 = [0, 0, 2, 6, 8, 15], L1814 = [0, 1, 2, 4, 7, 8], L1817 = [0, 1, 2, 4, 7, 11], L1819 = [0, 1, 2, 4, 7, 13], L1820 = [0, 1, 2, 4, 7, 14], L2140 = [0, 1, 3, 3, 7, 9], L2155 = [0, 1, 3, 3, 9, 11], L2241 = [0, 1, 3, 5, 5, 7], L2245 = [0, 1, 3, 5, 5, 11], L2262 = [0, 1, 3, 5, 7, 10], L2266 = [0, 1, 3, 5, 7, 15], L2281 = [0, 1, 3, 5, 10, 11], L2287 = [0, 1, 3, 5, 11, 15], L2311 = [0, 1, 3, 6, 7, 12], L2334 = [0, 1, 3, 6, 11, 12], L2354 = [0, 1, 3, 7, 10, 10], L2358 = [0, 1, 3, 7, 10, 15], L2366 = [0, 1, 3, 7, 15, 15], L2413 = [0, 1, 3, 10, 10, 11], L2419 = [0, 1, 3, 10, 11, 15], L2431 = [0, 1, 3, 11, 15, 15], L2781 = [0, 1, 5, 7, 11, 13], L2886 = [0, 1, 6, 6, 12, 12], L3413 = [0, 2, 3, 4, 9, 12], L3463 = [0, 2, 3, 6, 8, 9], L3520 = [0, 2, 4, 5, 5, 12], L3532 = [0, 2, 4, 5, 10, 12], L3535 = [0, 2, 4, 5, 12, 15], L3547 = [0, 2, 4, 10, 12, 15], L3550 = [0, 2, 4, 12, 15, 15], L3560 = [0, 2, 5, 5, 6, 8], L3586 = [0, 2, 5, 6, 8, 10], L3588 = [0, 2, 5, 6, 8, 15], L3644 = [0, 2, 6, 8, 10, 15], L3646 = [0, 2, 6, 8, 15, 15], L3852 = [0, 5, 6, 6, 12, 12], L6047 = [1, 1, 5, 7, 11, 13], L7411 = [1, 2, 3, 4, 7, 14], L7416 = [1, 2, 3, 4, 8, 11], L7672 = [1, 2, 3, 11, 12, 14], L7780 = [1, 2, 4, 5, 7, 8], L7783 = [1, 2, 4, 5, 7, 11], L7785 = [1, 2, 4, 5, 7, 13], L7786 = [1, 2, 4, 5, 7, 14], L7873 = [1, 2, 4, 7, 8, 10], L7874 = [1, 2, 4, 7, 8, 11], L7878 = [1, 2, 4, 7, 8, 15], L7885 = [1, 2, 4, 7, 10, 11], L7887 = [1, 2, 4, 7, 10, 13], L7888 = [1, 2, 4, 7, 10, 14], L7890 = [1, 2, 4, 7, 11, 12], L7892 = [1, 2, 4, 7, 11, 15], L7896 = [1, 2, 4, 7, 13, 14], L7897 = [1, 2, 4, 7, 13, 15], L7898 = [1, 2, 4, 7, 14, 15], L7915 = [1, 2, 4, 8, 10, 14], L8122 = [1, 2, 5, 7, 11, 13], L8282 = [1, 2, 6, 7, 8, 9], L8284 = [1, 2, 6, 7, 8, 11], L8886 = [1, 3, 3, 5, 7, 9], L8901 = [1, 3, 3, 5, 9, 11], L8978 = [1, 3, 3, 7, 9, 10], L8982 = [1, 3, 3, 7, 9, 15], L9028 = [1, 3, 3, 9, 9, 15], L9030 = [1, 3, 3, 9, 10, 11], L9036 = [1, 3, 3, 9, 11, 15], L9326 = [1, 3, 5, 5, 5, 7], L9330 = [1, 3, 5, 5, 5, 11], L9347 = [1, 3, 5, 5, 7, 10], L9351 = [1, 3, 5, 5, 7, 15], L9366 = [1, 3, 5, 5, 10, 11], L9372 = [1, 3, 5, 5, 11, 15], L9396 = [1, 3, 5, 6, 7, 12], L9419 = [1, 3, 5, 6, 11, 12], L9439 = [1, 3, 5, 7, 10, 10], L9443 = [1, 3, 5, 7, 10, 15], L9445 = [1, 3, 5, 7, 11, 13], L9451 = [1, 3, 5, 7, 15, 15], L9498 = [1, 3, 5, 10, 10, 11], L9504 = [1, 3, 5, 10, 11, 15], L9516 = [1, 3, 5, 11, 15, 15], L9594 = [1, 3, 6, 7, 10, 12], L9602 = [1, 3, 6, 7, 12, 15], L9659 = [1, 3, 6, 10, 11, 12], L9671 = [1, 3, 6, 11, 12, 15], L9712 = [1, 3, 7, 10, 10, 10], L9716 = [1, 3, 7, 10, 10, 15], L9724 = [1, 3, 7, 10, 15, 15], L9736 = [1, 3, 7, 15, 15, 15], L9854 = [1, 3, 10, 10, 10, 11], L9860 = [1, 3, 10, 10, 11, 15], L9872 = [1, 3, 10, 11, 15, 15], L9892 = [1, 3, 11, 15, 15, 15], L10730 = [1, 5, 5, 7, 11, 13], L10854 = [1, 5, 6, 7, 11, 13], L10940 = [1, 5, 7, 10, 11, 13], L10943 = [1, 5, 7, 11, 13, 15], L12622 = [2, 3, 3, 9, 9, 15], L12669 = [2, 3, 4, 5, 9, 12], L12710 = [2, 3, 4, 8, 10, 14], L12718 = [2, 3, 4, 9, 10, 12], L12721 = [2, 3, 4, 9, 12, 15], L12778 = [2, 3, 5, 6, 8, 9], L12856 = [2, 3, 6, 8, 9, 10],
60
EMILIO A. LAURET
Table 4. (continued) n = 6 q I indexes of I-isospectral families 31 {0} {874, 910}, {969, 983, 992}, {1014, 1017}, {3311, 3319}, {3323, 3384}, {3344, 3348}, {3364, 3380}, {3396, 3468}, {3409, 3496}, {3437, 3575}, {3460, 3550}, {3498, 3546}, {3544, 3596} L12858 = [2, 3, 6, 8, 9, 15], L12960 = [2, 4, 5, 5, 5, 12], L12972 = [2, 4, 5, 5, 10, 12], L12975 = [2, 4, 5, 5, 12, 15], L12991 = [2, 4, 5, 6, 12, 12], L12996 = [2, 4, 5, 8, 10, 14], L13001 = [2, 4, 5, 10, 10, 12], L13004 = [2, 4, 5, 10, 12, 15], L13008 = [2, 4, 5, 12, 15, 15], L13024 = [2, 4, 6, 12, 12, 15], L13029 = [2, 4, 8, 10, 14, 15], L13034 = [2, 4, 10, 10, 12, 15], L13037 = [2, 4, 10, 12, 15, 15], L13041 = [2, 4, 12, 15, 15, 15], L13051 = [2, 5, 5, 5, 6, 8], L13077 = [2, 5, 5, 6, 8, 10], L13079 = [2, 5, 5, 6, 8, 15], L13128 = [2, 5, 6, 6, 8, 12], L13144 = [2, 5, 6, 8, 10, 10], L13146 = [2, 5, 6, 8, 10, 15], L13149 = [2, 5, 6, 8, 15, 15], L13241 = [2, 6, 6, 8, 12, 15], L13269 = [2, 6, 8, 10, 10, 15], L13271 = [2, 6, 8, 10, 15, 15], L13274 = [2, 6, 8, 15, 15, 15], L13471 = [3, 3, 5, 9, 9, 15], L13504 = [3, 3, 9, 9, 10, 15]. q = 31 : L874 = [0, 1, 2, 3, 8, 11], L910 = [0, 1, 2, 4, 7, 12], L969 = [0, 1, 2, 6, 8, 14], L983 = [0, 1, 2, 7, 9, 10], L992 = [0, 1, 2, 8, 10, 13], L1014 = [0, 1, 3, 4, 7, 9], L1017 = [0, 1, 3, 4, 9, 10], L3311 = [1, 2, 3, 4, 7, 14], L3319 = [1, 2, 3, 4, 8, 15], L3323 = [1, 2, 3, 4, 9, 13], L3344 = [1, 2, 3, 5, 6, 11], L3348 = [1, 2, 3, 5, 6, 15], L3364 = [1, 2, 3, 5, 9, 11], L3380 = [1, 2, 3, 5, 12, 15], L3384 = [1, 2, 3, 6, 7, 9], L3396 = [1, 2, 3, 6, 8, 14], L3409 = [1, 2, 3, 6, 12, 14], L3437 = [1, 2, 3, 8, 9, 11], L3460 = [1, 2, 3, 9, 12, 14], L3468 = [1, 2, 3, 10, 13, 15], L3496 = [1, 2, 4, 5, 11, 15], L3498 = [1, 2, 4, 5, 12, 14], L3544 = [1, 2, 5, 6, 11, 14], L3546 = [1, 2, 5, 7, 8, 9], L3550 = [1, 2, 5, 7, 9, 10], L3575 = [1, 2, 6, 7, 8, 14], L3596 = [1, 2, 7, 8, 10, 13]. q = 32 : L47 = [0, 0, 0, 1, 3, 7], L49 = [0, 0, 0, 1, 3, 9], L301 = [0, 0, 1, 2, 7, 9], L307 = [0, 0, 1, 2, 7, 15], L357 = [0, 0, 1, 3, 5, 7], L359 = [0, 0, 1, 3, 5, 9], L362 = [0, 0, 1, 3, 5, 13], L366 = [0, 0, 1, 3, 7, 8], L367 = [0, 0, 1, 3, 7, 9], L371 = [0, 0, 1, 3, 7, 16], L373 = [0, 0, 1, 3, 8, 9], L382 = [0, 0, 1, 3, 9, 16], L480 = [0, 0, 1, 6, 7, 9], L483 = [0, 0, 1, 6, 7, 15], L1151 = [0, 1, 1, 7, 7, 9], L1154 = [0, 1, 1, 7, 7, 15], L1396 = [0, 1, 2, 2, 7, 9], L1402 = [0, 1, 2, 2, 7, 15], L1459 = [0, 1, 2, 3, 5, 10], L1468 = [0, 1, 2, 3, 6, 9], L1503 = [0, 1, 2, 3, 10, 13], L1505 = [0, 1, 2, 3, 10, 15], L1561 = [0, 1, 2, 4, 7, 9], L1567 = [0, 1, 2, 4, 7, 15], L1610 = [0, 1, 2, 5, 6, 11], L1614 = [0, 1, 2, 5, 6, 15], L1652 = [0, 1, 2, 5, 13, 14], L1670 = [0, 1, 2, 6, 7, 9], L1672 = [0, 1, 2, 6, 7, 11], L1675 = [0, 1, 2, 6, 7, 15], L1686 = [0, 1, 2, 6, 9, 11], L1692 = [0, 1, 2, 6, 10, 14], L1708 = [0, 1, 2, 7, 8, 9], L1714 = [0, 1, 2, 7, 8, 15], L1716 = [0, 1, 2, 7, 9, 10], L1718 = [0, 1, 2, 7, 9, 12], L1722 = [0, 1, 2, 7, 9, 16], L1726 = [0, 1, 2, 7, 10, 15], L1734 = [0, 1, 2, 7, 12, 15], L1739 = [0, 1, 2, 7, 15, 16], L1811 = [0, 1, 2, 11, 13, 14], L1855 = [0, 1, 3, 4, 5, 13], L1860 = [0, 1, 3, 4, 7, 9], L1862 = [0, 1, 3, 4, 7, 12], L1877 = [0, 1, 3, 4, 9, 12], L1887 = [0, 1, 3, 4, 11, 13], L1904 = [0, 1, 3, 5, 7, 8], L1905 = [0, 1, 3, 5, 7, 9], L1906 = [0, 1, 3, 5, 7, 11], L1908 = [0, 1, 3, 5, 7, 13], L1909 = [0, 1, 3, 5, 7, 16], L1911 = [0, 1, 3, 5, 8, 9], L1914 = [0, 1, 3, 5, 8, 13], L1918 = [0, 1, 3, 5, 9, 11], L1919 = [0, 1, 3, 5, 9, 16], L1920 = [0, 1, 3, 5, 11, 13], L1922 = [0, 1, 3, 5, 11, 15], L1925 = [0, 1, 3, 5, 12, 13], L1929 = [0, 1, 3, 5, 13, 15], L1930 = [0, 1, 3, 5, 13, 16], L1936 = [0, 1, 3, 7, 8, 8], L1937 = [0, 1, 3, 7, 8, 9], L1941 = [0, 1, 3, 7, 8, 16], L1943 = [0, 1, 3, 7, 9, 16], L1952 = [0, 1, 3, 7, 16, 16], L1954 = [0, 1, 3, 8, 8, 9], L1963 = [0, 1, 3, 8, 9, 16], L1987 = [0, 1, 3, 9, 16, 16], L2119 = [0, 1, 4, 6, 7, 9], L2122 = [0, 1, 4, 6, 7, 15], L2253 = [0, 1, 6, 6, 7, 9], L2256 = [0, 1, 6, 6, 7, 15], L2283 = [0, 1, 6, 7, 8, 9], L2286 = [0, 1, 6, 7, 8, 15], L2289 = [0, 1, 6, 7, 9, 12], L2291 = [0, 1, 6, 7, 9, 16], L2295 = [0, 1, 6, 7, 12, 15], L2297 = [0, 1, 6, 7, 15, 16], L3726 = [1, 1, 2, 6, 10, 14], L4694 = [1, 1, 4, 7, 7, 9], L4697 = [1, 1, 4, 7, 7, 15], L5417 = [1, 1, 7, 7, 8, 9], L5420 = [1, 1, 7, 7, 8, 15], L5423 = [1, 1, 7, 7, 9, 12], L5426 = [1, 1, 7, 7, 9, 16], L5429 = [1, 1, 7, 7, 12, 15], L5433 = [1, 1, 7, 7, 15, 16], L5970 = [1, 2, 2, 2, 7, 9], L5976 = [1, 2, 2, 2, 7, 15], L6137 = [1, 2, 2, 4, 7, 9], L6143 = [1, 2, 2, 4, 7, 15], L6254 = [1, 2, 2, 6, 7, 9], L6260 = [1, 2, 2, 6, 7, 15], L6281 = [1, 2, 2, 6, 10, 14], L6301 = [1, 2, 2, 7, 8, 9], L6307 = [1, 2, 2, 7, 8, 15], L6309 = [1, 2, 2, 7, 9, 10], L6311 = [1, 2, 2, 7, 9, 12], L6313 = [1, 2, 2, 7, 9, 14], L6315 = [1, 2, 2, 7, 9, 16], L6321 = [1, 2, 2, 7, 10, 15], L6330 = [1, 2, 2, 7, 12, 15], L6335 = [1, 2, 2, 7, 14, 15], L6337 = [1, 2, 2, 7, 15, 16], L6553 = [1, 2, 3, 5, 8, 10], L6560 = [1, 2, 3, 5, 9, 10], L6572 = [1, 2, 3, 5, 10, 16], L6593 = [1, 2, 3, 6, 7, 10],
APPENDIX
61
Table 4. (continued) n = 6 q 32
L6596 L6611 L6621 L6693 L6749 L6835 L6984 L6994 L7015 L7148 L7163 L7295
I {0}
indexes of I-isospectral families {47, 49}, {301, 307}, {357, 359}, {366, 373}, {371, 382}, {480, 483}, {1151, 1154}, {1396, 1402}, {1459, 1468}, {1503, 1614}, {1505, 1610}, {1561, 1567}, {1652, 1811}, {1670, 1675}, {1672, 1686}, {1708, 1714}, {1716, 1726}, {1718, 1734}, {1722, 1739}, {1862, 1877}, {1904, 1911}, {1905, 1906, 1908, 1918}, {1909, 1919}, {1922, 1929}, {1936, 1954}, {1941, 1963}, {1952, 1987}, {2119, 2122}, {2253, 2256}, {2283, 2286}, {2289, 2295}, {2291, 2297}, {4694, 4697}, {5417, 5420}, {5423, 5429}, {5426, 5433}, {5970, 5976}, {6137, 6143}, {6254, 6260}, {6301, 6307}, {6309, 6321}, {6311, 6330}, {6313, 6335}, {6315, 6337}, {6553, 6600}, {6560, 6609}, {6572, 6612}, {6593, 6611}, {6596, 6608}, {6620, 6646}, {6621, 6656}, {6657, 7151}, {6693, 7139}, {6695, 7135}, {6718, 7141}, {6729, 6993}, {6749, 7153}, {6750, 7163}, {6754, 7154}, {6829, 6835}, {6940, 6945}, {6984, 6990}, {6992, 7002}, {6994, 7010}, {6998, 7015}, {7221, 7587}, {7270, 7685}, {7290, 7295}, {7328, 7333}, {7330, 7365}, {7335, 7344}, {7337, 7350}, {7338, 7352}, {7340, 7354}, {7347, 7391}, {7434, 7440}, {7442, 7452}, {7444, 7460}, {7448, 7465}, {7467, 7488}, {7468, 7492}, {7471, 7495}, {7475, 7505}, {7479, 7510}, {7484, 7515}, {7794, 7795}, {7796, 7809}, {7797, 7798, 7808, 7810}, {7815, 7823, 7839, 7850}, {7833, 7865}, {7849, 7901}, {7897, 7898}, {7956, 7972}, {7957, 7958, 7960, 7979}, {7961, 7980}, {7965, 7966, 7969, 7997}, {7970, 7998}, {7983, 7990}, {8005, 8019}, {8028, 8065}, {8033, 8074}, {8044, 8098}, {8063, 8149}, {8324, 8327}, {8481, 8484}, {8511, 8514}, {8517, 8523}, {8519, 8525}, {8782, 8785}, {8812, 8815}, {8817, 8823}, {8818, 8826}, {8820, 8828}, {8890, 8893}, {8896, 8902}, {8898, 8904}, {8909, 8918}, {8911, 8920}, {8913, 8922} {0, 1} {362, 367}, {1855, 1860}, {1887, 1925}, {1906, 1908}, {1914, 1937}, {1930, 1943}, {7743, 7748}, {7776, 8008}, {7804, 7831}, {7818, 7838}, {7824, 7841}, {7875, 7986}, {7925, 8012}, {7958, 7960}, {7962, 7963}, {7966, 7969}, {7975, 8029}, {7991, 8035}, {8020, 8047} {0, 3} {7813, 7840} {4} {1920, 8001} {4, 5} {1692, 7408}, {3726, 7407}, {6281, 7406}, {6616, 7148}, {6965, 7403}, {7312, 7399}
= [1, 2, 3, 6, 7, 14], L6600 = [1, 2, 3, 6, 8, 9], L6608 = [1, 2, 3, 6, 9, 10], L6609 = [1, 2, 3, 6, 9, 11], = [1, 2, 3, 6, 9, 14], L6612 = [1, 2, 3, 6, 9, 16], L6616 = [1, 2, 3, 6, 10, 14], L6620 = [1, 2, 3, 6, 11, 13], = [1, 2, 3, 6, 11, 14], L6646 = [1, 2, 3, 7, 9, 10], L6656 = [1, 2, 3, 7, 10, 14], L6657 = [1, 2, 3, 7, 10, 15], = [1, 2, 3, 8, 10, 13], L6695 = [1, 2, 3, 8, 10, 15], L6718 = [1, 2, 3, 9, 10, 14], L6729 = [1, 2, 3, 9, 12, 15], = [1, 2, 3, 10, 13, 15], L6750 = [1, 2, 3, 10, 13, 16], L6754 = [1, 2, 3, 10, 15, 16], L6829 = [1, 2, 4, 4, 7, 9], = [1, 2, 4, 4, 7, 15], L6940 = [1, 2, 4, 6, 7, 9], L6945 = [1, 2, 4, 6, 7, 15], L6965 = [1, 2, 4, 6, 10, 14], = [1, 2, 4, 7, 8, 9], L6990 = [1, 2, 4, 7, 8, 15], L6992 = [1, 2, 4, 7, 9, 10], L6993 = [1, 2, 4, 7, 9, 11], = [1, 2, 4, 7, 9, 12], L6998 = [1, 2, 4, 7, 9, 16], L7002 = [1, 2, 4, 7, 10, 15], L7010 = [1, 2, 4, 7, 12, 15], = [1, 2, 4, 7, 15, 16], L7135 = [1, 2, 5, 6, 8, 11], L7139 = [1, 2, 5, 6, 8, 15], L7141 = [1, 2, 5, 6, 9, 10], = [1, 2, 5, 6, 10, 14], L7151 = [1, 2, 5, 6, 11, 13], L7153 = [1, 2, 5, 6, 11, 15], L7154 = [1, 2, 5, 6, 11, 16], = [1, 2, 5, 6, 15, 16], L7221 = [1, 2, 5, 8, 13, 14], L7270 = [1, 2, 5, 13, 14, 16], L7290 = [1, 2, 6, 6, 7, 9], = [1, 2, 6, 6, 7, 15], L7312 = [1, 2, 6, 6, 10, 14], L7328 = [1, 2, 6, 7, 8, 9], L7330 = [1, 2, 6, 7, 8, 11],
62
EMILIO A. LAURET
Table 4. (continued) n = 6 q 33
I {0}
indexes of I-isospectral families {41, 56}, {250, 257}, {261, 273}, {301, 387}, {490, 492}, {1354, 1402}, {1376, 1416}, {1421, 1481}, {1460, 1752}, {1563, 1855}, {2077, 2080}, {5519, 5617}, {5762, 6785}, {5807, 5811, 5816}, {5813, 5814}, {5839, 5994}, {5866, 6008}, {5926, 6049}, {6055, 6239}, {6185, 6996}, {6425, 7189}, {7606, 7610} {0, 1} {5826, 5846}
L7333 = [1, 2, 6, 7, 8, 15], L7335 = [1, 2, 6, 7, 9, 10], L7337 = [1, 2, 6, 7, 9, 12], L7338 = [1, 2, 6, 7, 9, 14], L7340 = [1, 2, 6, 7, 9, 16], L7344 = [1, 2, 6, 7, 10, 15], L7347 = [1, 2, 6, 7, 11, 16], L7350 = [1, 2, 6, 7, 12, 15], L7352 = [1, 2, 6, 7, 14, 15], L7354 = [1, 2, 6, 7, 15, 16], L7365 = [1, 2, 6, 8, 9, 11], L7391 = [1, 2, 6, 9, 11, 16], L7399 = [1, 2, 6, 10, 10, 14], L7403 = [1, 2, 6, 10, 12, 14], L7406 = [1, 2, 6, 10, 14, 14], L7407 = [1, 2, 6, 10, 14, 15], L7408 = [1, 2, 6, 10, 14, 16], L7434 = [1, 2, 7, 8, 8, 9], L7440 = [1, 2, 7, 8, 8, 15], L7442 = [1, 2, 7, 8, 9, 10], L7444 = [1, 2, 7, 8, 9, 12], L7448 = [1, 2, 7, 8, 9, 16], L7452 = [1, 2, 7, 8, 10, 15], L7460 = [1, 2, 7, 8, 12, 15], L7465 = [1, 2, 7, 8, 15, 16], L7467 = [1, 2, 7, 9, 10, 10], L7468 = [1, 2, 7, 9, 10, 12], L7471 = [1, 2, 7, 9, 10, 16], L7475 = [1, 2, 7, 9, 12, 12], L7479 = [1, 2, 7, 9, 12, 16], L7484 = [1, 2, 7, 9, 16, 16], L7488 = [1, 2, 7, 10, 10, 15], L7492 = [1, 2, 7, 10, 12, 15], L7495 = [1, 2, 7, 10, 15, 16], L7505 = [1, 2, 7, 12, 12, 15], L7510 = [1, 2, 7, 12, 15, 16], L7515 = [1, 2, 7, 15, 16, 16], L7587 = [1, 2, 8, 11, 13, 14], L7685 = [1, 2, 11, 13, 14, 16], L7743 = [1, 3, 4, 4, 5, 13], L7748 = [1, 3, 4, 4, 7, 9], L7776 = [1, 3, 4, 4, 11, 13], L7794 = [1, 3, 4, 5, 7, 9], L7795 = [1, 3, 4, 5, 7, 11], L7796 = [1, 3, 4, 5, 7, 12], L7797 = [1, 3, 4, 5, 7, 13], L7798 = [1, 3, 4, 5, 7, 15], L7804 = [1, 3, 4, 5, 8, 13], L7808 = [1, 3, 4, 5, 9, 11], L7809 = [1, 3, 4, 5, 9, 12], L7810 = [1, 3, 4, 5, 9, 15], L7813 = [1, 3, 4, 5, 11, 13], L7815 = [1, 3, 4, 5, 11, 15], L7818 = [1, 3, 4, 5, 12, 13], L7823 = [1, 3, 4, 5, 13, 15], L7824 = [1, 3, 4, 5, 13, 16], L7831 = [1, 3, 4, 7, 8, 9], L7833 = [1, 3, 4, 7, 8, 12], L7838 = [1, 3, 4, 7, 9, 12], L7839 = [1, 3, 4, 7, 9, 13], L7840 = [1, 3, 4, 7, 9, 15], L7841 = [1, 3, 4, 7, 9, 16], L7849 = [1, 3, 4, 7, 12, 16], L7850 = [1, 3, 4, 7, 13, 15], L7865 = [1, 3, 4, 8, 9, 12], L7875 = [1, 3, 4, 8, 11, 13], L7897 = [1, 3, 4, 9, 11, 13], L7898 = [1, 3, 4, 9, 11, 15], L7901 = [1, 3, 4, 9, 12, 16], L7925 = [1, 3, 4, 11, 13, 16], L7956 = [1, 3, 5, 7, 8, 8], L7957 = [1, 3, 5, 7, 8, 9], L7958 = [1, 3, 5, 7, 8, 11], L7960 = [1, 3, 5, 7, 8, 13], L7961 = [1, 3, 5, 7, 8, 16], L7962 = [1, 3, 5, 7, 9, 11], L7963 = [1, 3, 5, 7, 9, 13], L7965 = [1, 3, 5, 7, 9, 16], L7966 = [1, 3, 5, 7, 11, 16], L7969 = [1, 3, 5, 7, 13, 16], L7970 = [1, 3, 5, 7, 16, 16], L7972 = [1, 3, 5, 8, 8, 9], L7975 = [1, 3, 5, 8, 8, 13], L7979 = [1, 3, 5, 8, 9, 11], L7980 = [1, 3, 5, 8, 9, 16], L7983 = [1, 3, 5, 8, 11, 15], L7986 = [1, 3, 5, 8, 12, 13], L7990 = [1, 3, 5, 8, 13, 15], L7991 = [1, 3, 5, 8, 13, 16], L7997 = [1, 3, 5, 9, 11, 16], L7998 = [1, 3, 5, 9, 16, 16], L8001 = [1, 3, 5, 11, 13, 16], L8005 = [1, 3, 5, 11, 15, 16], L8008 = [1, 3, 5, 12, 12, 13], L8012 = [1, 3, 5, 12, 13, 16], L8019 = [1, 3, 5, 13, 15, 16], L8020 = [1, 3, 5, 13, 16, 16], L8028 = [1, 3, 7, 8, 8, 8], L8029 = [1, 3, 7, 8, 8, 9], L8033 = [1, 3, 7, 8, 8, 16], L8035 = [1, 3, 7, 8, 9, 16], L8044 = [1, 3, 7, 8, 16, 16], L8047 = [1, 3, 7, 9, 16, 16], L8063 = [1, 3, 7, 16, 16, 16], L8065 = [1, 3, 8, 8, 8, 9], L8074 = [1, 3, 8, 8, 9, 16], L8098 = [1, 3, 8, 9, 16, 16], L8149 = [1, 3, 9, 16, 16, 16], L8324 = [1, 4, 4, 6, 7, 9], L8327 = [1, 4, 4, 6, 7, 15], L8481 = [1, 4, 6, 6, 7, 9], L8484 = [1, 4, 6, 6, 7, 15], L8511 = [1, 4, 6, 7, 8, 9], L8514 = [1, 4, 6, 7, 8, 15], L8517 = [1, 4, 6, 7, 9, 12], L8519 = [1, 4, 6, 7, 9, 16], L8523 = [1, 4, 6, 7, 12, 15], L8525 = [1, 4, 6, 7, 15, 16], L8782 = [1, 6, 6, 6, 7, 9], L8785 = [1, 6, 6, 6, 7, 15], L8812 = [1, 6, 6, 7, 8, 9], L8815 = [1, 6, 6, 7, 8, 15], L8817 = [1, 6, 6, 7, 9, 10], L8818 = [1, 6, 6, 7, 9, 12], L8820 = [1, 6, 6, 7, 9, 16], L8823 = [1, 6, 6, 7, 10, 15], L8826 = [1, 6, 6, 7, 12, 15], L8828 = [1, 6, 6, 7, 15, 16], L8890 = [1, 6, 7, 8, 8, 9], L8893 = [1, 6, 7, 8, 8, 15], L8896 = [1, 6, 7, 8, 9, 12], L8898 = [1, 6, 7, 8, 9, 16], L8902 = [1, 6, 7, 8, 12, 15], L8904 = [1, 6, 7, 8, 15, 16], L8909 = [1, 6, 7, 9, 12, 12], L8911 = [1, 6, 7, 9, 12, 16], L8913 = [1, 6, 7, 9, 16, 16], L8918 = [1, 6, 7, 12, 12, 15], L8920 = [1, 6, 7, 12, 15, 16], L8922 = [1, 6, 7, 15, 16, 16]. q = 33 : L41 = [0, 0, 0, 1, 2, 14], L56 = [0, 0, 0, 1, 4, 5], L250 = [0, 0, 1, 2, 4, 13], L257 = [0, 0, 1, 2, 5, 10], L261 = [0, 0, 1, 2, 5, 14], L273 = [0, 0, 1, 2, 7, 8], L301 = [0, 0, 1, 2, 11, 14], L387 = [0, 0, 1, 4, 5, 11], L490 = [0, 0, 3, 6, 9, 11], L492 = [0, 0, 3, 6, 11, 12], L1354 = [0, 1, 2, 4, 7, 14], L1376 =
APPENDIX
63
Table 4. (continued) n = 6 q 34
I {0}
indexes of I-isospectral families {51, 53}, {56, 74}, {413, 416}, {414, 418, 422}, {428, 439}, {456, 540}, {568, 571}, {582, 590}, {682, 683}, {684, 686}, {1876, 1882}, {1888, 1890}, {2322, 2325}, {2323, 2326, 2337, 2338, 2342}, {2340, 2351}, {2344, 2356, 2369}, {2385, 2422}, {2476, 2756}, {2852, 2875}, {2855, 2858}, {2856, 2865}, {2895, 2912}, {3122, 3123, 3125}, {3131, 3133}, {3132, 3136}, {3134, 3137}, {8482, 8818}, {8556, 9072}, {8584, 9533}, {8886, 8909}, {8890, 8916}, {8937, 8941}, {8990, 9726}, {9003, 9556}, {10268, 10269, 10270, 10272}, {10271, 10280}, {10274, 10282, 10314, 10316, 10324}, {10319, 10344}, {10327, 10353, 10386}, {10419, 10516}, {10646, 11409}, {11680, 11728}, {11686, 11693}, {11687, 11700}, {11767, 11796}, {12245, 12246, 12247, 12248, 12250}, {12251, 12253}, {12252, 12254, 12256}, {12262, 12264}, {12263, 12267}, {12265, 12268} {0, 1} {424, 426}, {2326, 2337}, {2376, 2382}, {3124, 3127}, {10269, 10270, 10272}, {10282, 10314}, {10403, 10415}, {11677, 11679}, {12246, 12247}, {12255, 12258} {0, 1, 2} {10270, 10272}
[0, 1, 2, 4, 11, 13], L1402 = [0, 1, 2, 5, 7, 13], L1416 = [0, 1, 2, 5, 10, 11], L1421 = [0, 1, 2, 5, 11, 14], L1460 = [0, 1, 2, 6, 9, 15], L1481 = [0, 1, 2, 7, 8, 11], L1563 = [0, 1, 2, 11, 11, 14], L1752 = [0, 1, 3, 6, 9, 10], L1855 = [0, 1, 4, 5, 11, 11], L2077 = [0, 3, 6, 9, 11, 11], L2080 = [0, 3, 6, 11, 11, 12], L5519 = [1, 2, 3, 4, 10, 15], L5617 = [1, 2, 3, 6, 8, 10], L5762 = [1, 2, 3, 10, 12, 15], L5807 = [1, 2, 4, 5, 7, 14], L5811 = [1, 2, 4, 5, 8, 10], L5813 = [1, 2, 4, 5, 8, 13], L5814 = [1, 2, 4, 5, 8, 14], L5816 = [1, 2, 4, 5, 8, 16], L5826 = [1, 2, 4, 5, 10, 13], L5839 = [1, 2, 4, 5, 13, 14], L5846 = [1, 2, 4, 7, 8, 13], L5866 = [1, 2, 4, 7, 11, 14], L5926 = [1, 2, 4, 11, 11, 13], L5994 = [1, 2, 5, 7, 8, 10], L6008 = [1, 2, 5, 7, 11, 13], L6049 = [1, 2, 5, 10, 11, 11], L6055 = [1, 2, 5, 11, 11, 14], L6185 = [1, 2, 6, 9, 11, 15], L6239 = [1, 2, 7, 8, 11, 11], L6425 = [1, 2, 11, 11, 11, 14], L6785 = [1, 3, 4, 6, 7, 15], L6996 = [1, 3, 6, 9, 10, 11], L7189 = [1, 4, 5, 11, 11, 11], L7606 = [3, 6, 9, 11, 11, 11], L7610 = [3, 6, 11, 11, 11, 12]. q = 34 : L51 = [0, 0, 0, 1, 3, 7], L53 = [0, 0, 0, 1, 3, 9], L56 = [0, 0, 0, 1, 3, 13], L74 = [0, 0, 0, 1, 5, 7], L413 = [0, 0, 1, 3, 5, 9], L414 = [0, 0, 1, 3, 5, 11], L416 = [0, 0, 1, 3, 5, 13], L418 = [0, 0, 1, 3, 5, 15], L422 = [0, 0, 1, 3, 7, 9], L424 = [0, 0, 1, 3, 7, 11], L426 = [0, 0, 1, 3, 7, 15], L428 = [0, 0, 1, 3, 7, 17], L439 = [0, 0, 1, 3, 9, 17], L456 = [0, 0, 1, 3, 13, 17], L540 = [0, 0, 1, 5, 7, 17], L568 = [0, 0, 1, 6, 9, 10], L571 = [0, 0, 1, 6, 9, 14], L582 = [0, 0, 1, 6, 12, 13], L590 = [0, 0, 1, 6, 14, 15], L682 = [0, 0, 2, 4, 10, 17], L683 = [0, 0, 2, 4, 12, 17], L684 = [0, 0, 2, 4, 14, 17], L686 = [0, 0, 2, 6, 8, 17], L1876 = [0, 1, 2, 4, 8, 9], L1882 = [0, 1, 2, 4, 8, 15], L1888 = [0, 1, 2, 4, 9, 13], L1890 = [0, 1, 2, 4, 9, 15], L2322 = [0, 1, 3, 5, 7, 9], L2323 = [0, 1, 3, 5, 7, 11], L2325 = [0, 1, 3, 5, 7, 13], L2326 = [0, 1, 3, 5, 7, 15], L2337 = [0, 1, 3, 5, 9, 11], L2338 = [0, 1, 3, 5, 9, 13], L2340 = [0, 1, 3, 5, 9, 17], L2342 = [0, 1, 3, 5, 11, 15], L2344 = [0, 1, 3, 5, 11, 17], L2351 = [0, 1, 3, 5, 13, 17], L2356 = [0, 1, 3, 5, 15, 17], L2369 = [0, 1, 3, 7, 9, 17], L2376 = [0, 1, 3, 7, 11, 17], L2382 = [0, 1, 3, 7, 15, 17], L2385 = [0, 1, 3, 7, 17, 17], L2422 = [0, 1, 3, 9, 17, 17], L2476 = [0, 1, 3, 13, 17, 17], L2756 = [0, 1, 5, 7, 17, 17], L2852 = [0, 1, 6, 9, 10, 12], L2855 = [0, 1, 6, 9, 10, 15], L2856 = [0, 1, 6, 9, 10, 17], L2858 = [0, 1, 6, 9, 12, 13], L2865 = [0, 1, 6, 9, 14, 17], L2875 = [0, 1, 6, 10, 12, 13], L2895 = [0, 1, 6, 12, 13, 17], L2912 = [0, 1, 6, 14, 15, 17], L3122 = [0, 2, 4, 6, 10, 17], L3123 = [0, 2, 4, 6, 12, 17], L3124 = [0, 2, 4, 6, 14, 17], L3125 = [0, 2, 4, 6, 16, 17], L3127 = [0, 2, 4, 8, 10, 17], L3131 = [0, 2, 4, 10, 17, 17], L3132 = [0, 2, 4, 12, 14, 17], L3133 = [0, 2, 4, 12, 17, 17], L3134 = [0, 2, 4, 14, 17, 17], L3136 = [0, 2, 6, 8, 10, 17], L3137 = [0, 2, 6, 8, 17, 17], L8482 = [1, 2, 3, 8, 15, 16], L8556 = [1, 2, 3, 11, 14, 16], L8584 = [1, 2, 3, 13, 14, 16], L8818 = [1, 2, 4, 6, 13, 15], L8886 = [1, 2, 4, 8, 9, 13], L8890 = [1, 2, 4, 8, 9, 17], L8909 = [1, 2, 4, 8, 13, 15], L8916 = [1, 2, 4, 8, 15, 17],
64
EMILIO A. LAURET
Table 4. (continued) n = 6 q 35
I {0}
indexes of I-isospectral families {396, 401}, {1451, 1512, 1516}, {1622, 1708}, {1623, 1626}, {1633, 1707}, {1977, 1982}, {1984, 1994}, {6350, 6469, 6474}, {6352, 6471}, {6472, 6488}, {6484, 6606}, {6489, 6586, 6611}, {6568, 6601}, {6575, 6607}, {6605, 7165}, {6637, 6964}, {6948, 6951}, {7164, 7173}, {7166, 7183}, {7169, 7182}, {7956, 7969}, {8025, 8030}, {8032, 8042}, {8046, 8063} {2, 3, 4} {2151, 8376}, {2184, 2251}, {5543, 8398}, {7066, 8394}, {7185, 8255} {5} {446, 517, 2059, 2115, 2122, 2244}, {1077, 1967, 2080, 2117, 2120, 2250}, {1596, 1863, 2099, 2110, 2252}
L8937 = [1, 2, 4, 9, 13, 17], L8941 = [1, 2, 4, 9, 15, 17], L8990 = [1, 2, 4, 12, 13, 15], L9003 = [1, 2, 4, 13, 14, 15], L9072 = [1, 2, 5, 6, 11, 16], L9533 = [1, 2, 7, 8, 9, 10], L9556 = [1, 2, 7, 8, 15, 16], L9726 = [1, 2, 8, 11, 15, 16], L10268 = [1, 3, 5, 7, 9, 11], L10269 = [1, 3, 5, 7, 9, 13], L10270 = [1, 3, 5, 7, 9, 15], L10271 = [1, 3, 5, 7, 9, 17], L10272 = [1, 3, 5, 7, 11, 13], L10274 = [1, 3, 5, 7, 11, 17], L10280 = [1, 3, 5, 7, 13, 17], L10282 = [1, 3, 5, 7, 15, 17], L10314 = [1, 3, 5, 9, 11, 17], L10316 = [1, 3, 5, 9, 13, 17], L10319 = [1, 3, 5, 9, 17, 17], L10324 = [1, 3, 5, 11, 15, 17], L10327 = [1, 3, 5, 11, 17, 17], L10344 = [1, 3, 5, 13, 17, 17], L10353 = [1, 3, 5, 15, 17, 17], L10386 = [1, 3, 7, 9, 17, 17], L10403 = [1, 3, 7, 11, 17, 17], L10415 = [1, 3, 7, 15, 17, 17], L10419 = [1, 3, 7, 17, 17, 17], L10516 = [1, 3, 9, 17, 17, 17], L10646 = [1, 3, 13, 17, 17, 17], L11409 = [1, 5, 7, 17, 17, 17], L11677 = [1, 6, 9, 10, 12, 13], L11679 = [1, 6, 9, 10, 12, 15], L11680 = [1, 6, 9, 10, 12, 17], L11686 = [1, 6, 9, 10, 15, 17], L11687 = [1, 6, 9, 10, 17, 17], L11693 = [1, 6, 9, 12, 13, 17], L11700 = [1, 6, 9, 14, 17, 17], L11728 = [1, 6, 10, 12, 13, 17], L11767 = [1, 6, 12, 13, 17, 17], L11796 = [1, 6, 14, 15, 17, 17], L12245 = [2, 4, 6, 8, 10, 17], L12246 = [2, 4, 6, 8, 12, 17], L12247 = [2, 4, 6, 8, 14, 17], L12248 = [2, 4, 6, 8, 16, 17], L12250 = [2, 4, 6, 10, 12, 17], L12251 = [2, 4, 6, 10, 16, 17], L12252 = [2, 4, 6, 10, 17, 17], L12253 = [2, 4, 6, 12, 14, 17], L12254 = [2, 4, 6, 12, 17, 17], L12255 = [2, 4, 6, 14, 17, 17], L12256 = [2, 4, 6, 16, 17, 17], L12258 = [2, 4, 8, 10, 17, 17], L12262 = [2, 4, 10, 17, 17, 17], L12263 = [2, 4, 12, 14, 17, 17], L12264 = [2, 4, 12, 17, 17, 17], L12265 = [2, 4, 14, 17, 17, 17], L12267 = [2, 6, 8, 10, 17, 17], L12268 = [2, 6, 8, 17, 17, 17]. q = 35 : L396 = [0, 0, 1, 4, 6, 9], L401 = [0, 0, 1, 4, 6, 16], L446 = [0, 0, 1, 5, 10, 15], L517 = [0, 0, 5, 7, 10, 15], L1077 = [0, 1, 1, 5, 10, 15], L1451 = [0, 1, 2, 3, 8, 16], L1512 = [0, 1, 2, 4, 8, 9], L1516 = [0, 1, 2, 4, 8, 16], L1596 = [0, 1, 2, 5, 10, 15], L1622 = [0, 1, 2, 6, 7, 16], L1623 = [0, 1, 2, 6, 8, 9], L1626 = [0, 1, 2, 6, 8, 12], L1633 = [0, 1, 2, 6, 9, 12], L1707 = [0, 1, 2, 8, 9, 12], L1708 = [0, 1, 2, 8, 9, 14], L1863 = [0, 1, 3, 5, 10, 15], L1967 = [0, 1, 4, 5, 10, 15], L1977 = [0, 1, 4, 6, 7, 9], L1982 = [0, 1, 4, 6, 7, 16], L1984 = [0, 1, 4, 6, 9, 14], L1994 = [0, 1, 4, 6, 14, 16], L2059 = [0, 1, 5, 5, 10, 15], L2080 = [0, 1, 5, 6, 10, 15], L2099 = [0, 1, 5, 7, 10, 15], L2110 = [0, 1, 5, 8, 10, 15], L2115 = [0, 1, 5, 10, 10, 15], L2117 = [0, 1, 5, 10, 11, 15], L2120 = [0, 1, 5, 10, 14, 15], L2122 = [0, 1, 5, 10, 15, 15], L2151 = [0, 1, 6, 8, 13, 15], L2184 = [0, 1, 7, 7, 14, 14], L2244 = [0, 5, 5, 7, 10, 15], L2250 = [0, 5, 7, 7, 10, 15], L2251 = [0, 5, 7, 7, 14, 14], L2252 = [0, 5, 7, 10, 14, 15], L5543 = [1, 1, 6, 8, 13, 15], L6350 = [1, 2, 3, 4, 11, 16], L6352 = [1, 2, 3, 4, 12, 13], L6469 = [1, 2, 3, 6, 8, 17], L6471 = [1, 2, 3, 6, 9, 11], L6472 = [1, 2, 3, 6, 9, 13], L6474 = [1, 2, 3, 6, 9, 16], L6484 = [1, 2, 3, 6, 11, 13], L6488 = [1, 2, 3, 6, 11, 17], L6489 = [1, 2, 3, 6, 12, 13], L6568 = [1, 2, 3, 8, 10, 11], L6575 = [1, 2, 3, 8, 11, 13], L6586 = [1, 2, 3, 8, 13, 16], L6601 = [1, 2, 3, 9, 10, 16], L6605 = [1, 2, 3, 9, 11, 16], L6606 = [1, 2, 3, 9, 11, 17], L6607 = [1, 2, 3, 9, 12, 13], L6611 = [1, 2, 3, 9, 12, 17], L6637 = [1, 2, 3, 10, 12, 15], L6948 = [1, 2, 5, 6, 8, 9], L6951 = [1, 2, 5, 6, 8, 12], L6964 = [1, 2, 5, 6, 10, 11], L7066 = [1, 2, 5, 9, 12, 16], L7164 = [1, 2, 6, 8, 9, 10], L7165 = [1, 2, 6, 8, 9, 11], L7166 = [1, 2, 6, 8, 9, 12], L7169 = [1, 2, 6, 8, 9, 15], L7173 = [1, 2, 6, 8, 10, 12], L7182 = [1, 2, 6, 8, 12, 15], L7183 = [1, 2, 6, 8, 12, 16], L7185 = [1, 2, 6, 8, 13, 15], L7956 = [1, 4, 5, 6, 9, 15], L7969 = [1, 4, 5, 6, 15, 16], L8025 = [1, 4, 6, 7, 7, 9], L8030 = [1, 4, 6, 7, 7, 16], L8032 = [1, 4, 6, 7, 9, 14], L8042 = [1, 4, 6, 7, 14, 16], L8046 = [1, 4, 6, 9, 14, 14], L8063 = [1, 4, 6, 14, 14, 16], L8255 = [1, 5, 6, 8, 13, 15], L8376 = [1, 6, 7, 8, 13, 15], L8394 = [1, 6, 8, 10, 13, 15], L8398 = [1, 6, 8, 13, 15, 15].
APPENDIX
65
Table 4. (continued) n = 6 q 36
I {0}
indexes of I-isospectral families {2665, 2669}, {3318, 3320}, {3323, 3344}, {3775, 3780}, {5169, 5171}, {5320, 5322}, {12325, 12335}, {13059, 13402}, {13327, 13331}, {13405, 13409}, {13415, 13429}, {13419, 13440}, {15034, 15036}, {15039, 15060}, {15536, 15652}, {15928, 15930}, {15933, 15954}, {15988, 15990}, {15993, 16065}, {15995, 16002}, {16000, 16007}, {16005, 16092}, {16013, 16095}, {17544, 17549}, {17597, 17625}, {17606, 17632}, {17613, 17634}, {21471, 21473}, {21674, 21676}, {21712, 21714}, {21718, 21724}, {21722, 21729}, {22091, 22093}, {22121, 22123}, {22126, 22131}, {22129, 22134} {0, 1} {542, 559}, {3120, 3137}, {3314, 3385}, {3341, 3450}, {3352, 3461}, {3368, 3463}, {14836, 14853}, {15030, 15104}, {15057, 15171}, {15069, 15184}, {15082, 15185}, {15087, 15187}, {15924, 16166}, {15951, 16231}, {15962, 16242}, {15978, 16244}, {15996, 15999}, {16062, 16463}, {16073, 16474}, {16089, 16476}, {16104, 16504}, {16120, 16506}, {16149, 16509} {0, 5} {21720, 21728} {3, 4, 5} {5516, 5585}, {21875, 22240}
q = 36 : L542 = [0, 0, 1, 3, 5, 17], L559 = [0, 0, 1, 3, 7, 11], L2665 = [0, 1, 2, 5, 7, 10], L2669 = [0, 1, 2, 5, 7, 14], L3120 = [0, 1, 3, 3, 5, 17], L3137 = [0, 1, 3, 3, 7, 11], L3314 = [0, 1, 3, 5, 6, 17], L3318 = [0, 1, 3, 5, 7, 11], L3320 = [0, 1, 3, 5, 7, 13], L3323 = [0, 1, 3, 5, 7, 17], L3341 = [0, 1, 3, 5, 9, 17], L3344 = [0, 1, 3, 5, 11, 13], L3352 = [0, 1, 3, 5, 12, 17], L3368 = [0, 1, 3, 5, 17, 18], L3385 = [0, 1, 3, 6, 7, 11], L3450 = [0, 1, 3, 7, 9, 11], L3461 = [0, 1, 3, 7, 11, 12], L3463 = [0, 1, 3, 7, 11, 18], L3775 = [0, 1, 4, 5, 7, 16], L3780 = [0, 1, 4, 5, 8, 11], L5169 = [0, 2, 3, 4, 8, 10], L5171 = [0, 2, 3, 4, 8, 14], L5320 = [0, 2, 4, 8, 9, 10], L5322 = [0, 2, 4, 8, 9, 14], L5516 = [0, 3, 4, 8, 12, 16], L5585 = [0, 4, 8, 9, 12, 16], L12325 = [1, 2, 3, 5, 10, 11], L12335 = [1, 2, 3, 5, 11, 14], L13059 = [1, 2, 4, 7, 11, 13], L13327 = [1, 2, 5, 6, 7, 10], L13331 = [1, 2, 5, 6, 7, 14], L13402 = [1, 2, 5, 7, 8, 17], L13405 = [1, 2, 5, 7, 9, 10], L13409 = [1, 2, 5, 7, 9, 14], L13415 = [1, 2, 5, 7, 10, 12], L13419 = [1, 2, 5, 7, 10, 18], L13429 = [1, 2, 5, 7, 12, 14], L13440 = [1, 2, 5, 7, 14, 18], L14836 = [1, 3, 3, 3, 5, 17], L14853 = [1, 3, 3, 3, 7, 11], L15030 = [1, 3, 3, 5, 6, 17], L15034 = [1, 3, 3, 5, 7, 11], L15036 = [1, 3, 3, 5, 7, 13], L15039 = [1, 3, 3, 5, 7, 17], L15057 = [1, 3, 3, 5, 9, 17], L15060 = [1, 3, 3, 5, 11, 13], L15069 = [1, 3, 3, 5, 12, 17], L15082 = [1, 3, 3, 5, 15, 17], L15087 = [1, 3, 3, 5, 17, 18], L15104 = [1, 3, 3, 6, 7, 11], L15171 = [1, 3, 3, 7, 9, 11], L15184 = [1, 3, 3, 7, 11, 12], L15185 = [1, 3, 3, 7, 11, 15], L15187 = [1, 3, 3, 7, 11, 18], L15536 = [1, 3, 4, 5, 11, 16], L15652 = [1, 3, 4, 7, 8, 13], L15924 = [1, 3, 5, 6, 6, 17], L15928 = [1, 3, 5, 6, 7, 11], L15930 = [1, 3, 5, 6, 7, 13], L15933 = [1, 3, 5, 6, 7, 17], L15951 = [1, 3, 5, 6, 9, 17], L15954 = [1, 3, 5, 6, 11, 13], L15962 = [1, 3, 5, 6, 12, 17], L15978 = [1, 3, 5, 6, 17, 18], L15988 = [1, 3, 5, 7, 9, 11], L15990 = [1, 3, 5, 7, 9, 13], L15993 = [1, 3, 5, 7, 9, 17], L15995 = [1, 3, 5, 7, 11, 12], L15996 = [1, 3, 5, 7, 11, 13], L15999 = [1, 3, 5, 7, 11, 17], L16000 = [1, 3, 5, 7, 11, 18], L16002 = [1, 3, 5, 7, 12, 13], L16005 = [1, 3, 5, 7, 12, 17], L16007 = [1, 3, 5, 7, 13, 18], L16013 = [1, 3, 5, 7, 17, 18], L16062 = [1, 3, 5, 9, 9, 17], L16065 = [1, 3, 5, 9, 11, 13], L16073 = [1, 3, 5, 9, 12, 17], L16089 = [1, 3, 5, 9, 17, 18], L16092 = [1, 3, 5, 11, 12, 13], L16095 = [1, 3, 5, 11, 13, 18], L16104 = [1, 3, 5, 12, 12, 17], L16120 = [1, 3, 5, 12, 17, 18], L16149 = [1, 3, 5, 17, 18, 18], L16166 = [1, 3, 6, 6, 7, 11], L16231 = [1, 3, 6, 7, 9, 11], L16242 = [1, 3, 6, 7, 11, 12], L16244 = [1, 3, 6, 7, 11, 18], L16463 = [1, 3, 7, 9, 9, 11], L16474 = [1, 3, 7, 9, 11, 12], L16476 = [1, 3, 7, 9, 11, 18], L16504 = [1, 3, 7, 11, 12, 12], L16506 = [1, 3, 7, 11, 12, 18], L16509 = [1, 3, 7, 11, 18, 18], L17544 = [1, 4, 5, 6, 7, 16], L17549 = [1, 4, 5, 6, 8, 11], L17597 = [1, 4, 5, 7, 9, 16], L17606 = [1, 4, 5, 7, 12, 16], L17613 = [1, 4, 5, 7, 16, 18], L17625 = [1, 4, 5, 8, 9, 11], L17632 = [1, 4, 5, 8, 11, 12], L17634 = [1, 4, 5, 8, 11, 18], L21471 = [2, 3, 3, 4, 8, 10], L21473 = [2, 3, 3, 4, 8, 14], L21674 = [2, 3, 4, 6, 8, 10], L21676 = [2, 3, 4, 6, 8, 14], L21712 = [2, 3, 4, 8, 9, 10], L21714 = [2, 3, 4, 8, 9, 14], L21718 = [2, 3, 4, 8, 10, 12],
66
EMILIO A. LAURET
Table 4. (continued) n = 6 q 37
I {0} {0, 1} 38 {0}
indexes of I-isospectral families {341, 342}, {1508, 1522, 1526}, {7100, 7119}, {7434, 7437} {7432, 7435} {60, 63}, {511, 513}, {515, 523, 539}, {553, 554, 682}, {556, 573}, {767, 769}, {895, 898}, {3182, 3185}, {3184, 3187, 3200, 3203}, {3201, 3205, 3209, 3220}, {3222, 3231}, {3230, 3251}, {3237, 3270, 3334}, {3392, 3394, 3882}, {3397, 3451}, {4150, 4155}, {4475, 4476, 4479}, {4478, 4481, 4483}, {4488, 4494}, {4491, 4495}, {13213, 13265}, {13710, 14226}, {15534, 15536, 15543}, {15535, 15538, 15541 {15555, 15563, 15613, 15621}, {15615, 15625, 15636, 15670}, {15673, 15696}, {15695, 15754}, {15708, 15802, 15992}, {16163, 16166, 17634}, {16170, 16300}, {18327, 18336}, {19086, 19087}, {19088, 19090, 19093, 19096}, {19092, 19094, 19097, 19100}, {19095, 19098, 19103}, {19099, 19110}, {19102, 19106, 19108}, {19114, 19120}, {19117, 19121} {0, 1} {3201, 3205}, {15536, 15543}, {15538, 15541}, {15553, 15611}, {15615, 15625}, {19094, 19097}
L21720 = [2, 3, 4, 8, 10, 15], L21722 = [2, 3, 4, 8, 10, 18], L21724 = [2, 3, 4, 8, 12, 14], L21728 = [2, 3, 4, 8, 14, 15], L21729 = [2, 3, 4, 8, 14, 18], L21875 = [2, 3, 6, 10, 14, 18], L22091 = [2, 4, 6, 8, 9, 10], L22093 = [2, 4, 6, 8, 9, 14], L22121 = [2, 4, 8, 9, 9, 10], L22123 = [2, 4, 8, 9, 9, 14], L22126 = [2, 4, 8, 9, 10, 12], L22129 = [2, 4, 8, 9, 10, 18], L22131 = [2, 4, 8, 9, 12, 14], L22134 = [2, 4, 8, 9, 14, 18], L22240 = [2, 6, 9, 10, 14, 18]. q = 37 : L341 = [0, 0, 1, 3, 4, 11], L342 = [0, 0, 1, 3, 4, 12], L1508 = [0, 1, 2, 4, 5, 16], L1522 = [0, 1, 2, 4, 8, 9], L1526 = [0, 1, 2, 4, 8, 16], L7100 = [1, 2, 5, 7, 10, 11], L7119 = [1, 2, 5, 8, 10, 13], L7432 = [1, 3, 4, 7, 9, 16], L7434 = [1, 3, 4, 7, 10, 12], L7435 = [1, 3, 4, 7, 12, 16], L7437 = [1, 3, 4, 9, 10, 12]. q = 38 : L60 = [0, 0, 0, 1, 3, 11], L63 = [0, 0, 0, 1, 3, 15], L511 = [0, 0, 1, 3, 5, 13], L513 = [0, 0, 1, 3, 5, 15], L515 = [0, 0, 1, 3, 5, 17], L523 = [0, 0, 1, 3, 7, 13], L539 = [0, 0, 1, 3, 9, 11], L553 = [0, 0, 1, 3, 11, 15], L554 = [0, 0, 1, 3, 11, 17], L556 = [0, 0, 1, 3, 11, 19], L573 = [0, 0, 1, 3, 15, 19], L682 = [0, 0, 1, 5, 7, 9], L767 = [0, 0, 1, 7, 8, 12], L769 = [0, 0, 1, 7, 8, 18], L895 = [0, 0, 2, 4, 14, 19], L898 = [0, 0, 2, 6, 8, 19], L3182 = [0, 1, 3, 5, 7, 11], L3184 = [0, 1, 3, 5, 7, 13], L3185 = [0, 1, 3, 5, 7, 15], L3187 = [0, 1, 3, 5, 7, 17], L3200 = [0, 1, 3, 5, 9, 11], L3201 = [0, 1, 3, 5, 9, 13], L3203 = [0, 1, 3, 5, 9, 15], L3205 = [0, 1, 3, 5, 9, 17], L3209 = [0, 1, 3, 5, 11, 15], L3220 = [0, 1, 3, 5, 13, 17], L3222 = [0, 1, 3, 5, 13, 19], L3230 = [0, 1, 3, 5, 15, 17], L3231 = [0, 1, 3, 5, 15, 19], L3237 = [0, 1, 3, 5, 17, 19], L3251 = [0, 1, 3, 7, 9, 13], L3270 = [0, 1, 3, 7, 13, 19], L3334 = [0, 1, 3, 9, 11, 19], L3392 = [0, 1, 3, 11, 15, 19], L3394 = [0, 1, 3, 11, 17, 19], L3397 = [0, 1, 3, 11, 19, 19], L3451 = [0, 1, 3, 15, 19, 19], L3882 = [0, 1, 5, 7, 9, 19], L4150 = [0, 1, 7, 8, 12, 19], L4155 = [0, 1, 7, 8, 18, 19], L4475 = [0, 2, 4, 6, 10, 19], L4476 = [0, 2, 4, 6, 12, 19], L4478 = [0, 2, 4, 6, 16, 19], L4479 = [0, 2, 4, 6, 18, 19], L4481 = [0, 2, 4, 8, 10, 19], L4483 = [0, 2, 4, 8, 16, 19], L4488 = [0, 2, 4, 12, 16, 19], L4491 = [0, 2, 4, 14, 19, 19], L4494 = [0, 2, 6, 8, 10, 19], L4495 = [0, 2, 6, 8, 19, 19], L13213 = [1, 2, 4, 10, 11, 17], L13265 = [1, 2, 4, 11, 15, 16], L13710 = [1, 2, 5, 14, 15, 18], L14226 = [1, 2, 7, 9, 10, 12], L15534 = [1, 3, 5, 7, 9, 11], L15535 = [1, 3, 5, 7, 9, 13], L15536 = [1, 3, 5, 7, 9, 15], L15538 = [1, 3, 5, 7, 9, 17], L15541 = [1, 3, 5, 7, 11, 13], L15542 = [1, 3, 5, 7, 11, 15], L15543 = [1, 3, 5, 7, 11, 17], L15545 = [1, 3, 5, 7, 11, 19], L15553 = [1, 3, 5, 7, 13, 17], L15555 = [1, 3, 5, 7, 13, 19], L15556 = [1, 3, 5, 7, 15, 17], L15557 = [1, 3, 5, 7, 15, 19], L15563 = [1, 3, 5, 7, 17, 19], L15611 = [1, 3, 5, 9, 11, 13], L15613 = [1, 3, 5, 9, 11, 19], L15615 = [1, 3, 5, 9, 13, 19], L15621 = [1, 3, 5, 9, 15, 19], L15625 = [1, 3, 5, 9, 17, 19], L15636 = [1, 3, 5, 11, 15, 19], L15670 = [1, 3, 5, 13, 17, 19], L15673 = [1, 3, 5, 13, 19, 19], L15695 = [1, 3, 5, 15, 17, 19], L15696 = [1, 3, 5, 15, 19, 19], L15708 = [1, 3, 5, 17, 19, 19], L15754 = [1, 3, 7, 9, 13, 19], L15802 = [1, 3, 7, 13, 19, 19], L15992 = [1, 3, 9, 11, 19, 19], L16163 = [1, 3, 11, 15, 19, 19], L16166 = [1, 3, 11, 17, 19, 19], L16170 = [1, 3, 11, 19, 19, 19], L16300 = [1, 3, 15, 19, 19, 19], L17634 = [1, 5, 7, 9, 19, 19], L18327 = [1, 7, 8, 12, 19, 19], L18336 = [1, 7, 8, 18, 19, 19], L19086 = [2, 4, 6, 8, 10, 19], L19087 = [2, 4, 6, 8, 12, 19], L19088 = [2, 4, 6, 8, 14, 19],
APPENDIX
67
Table 4. (continued) n = 6 q 39
I {0}
indexes of I-isospectral families {405, 553}, {745, 746}, {748, 749}, {2273, 2424}, {2517, 3119}, {2766, 2782}, {2771, 2794}, {3600, 3602, 3603}, {3601, 3604}, {3606, 3607}, {10701, 10710}, {10730, 10771}, {10757, 10803}, {10759, 10773}, {10775, 10788}, {10827, 11661}, {11293, 11849}, {12124, 13964}, {13034, 13088}, {13058, 13108}, {13385, 13412}, {14982, 14985, 14986}, {14984, 14987}, {14989, 14990} {0, 1} {3600, 3602}, {14982, 14985}
L19090 = [2, 4, 6, 8, 18, 19], L19092 = [2, 4, 6, 10, 12, 19], L19093 = [2, 4, 6, 10, 14, 19], L19094 = [2, 4, 6, 10, 18, 19], L19095 = [2, 4, 6, 10, 19, 19], L19096 = [2, 4, 6, 12, 14, 19], L19097 = [2, 4, 6, 12, 16, 19], L19098 = [2, 4, 6, 12, 19, 19], L19099 = [2, 4, 6, 14, 16, 19], L19100 = [2, 4, 6, 14, 18, 19], L19102 = [2, 4, 6, 16, 19, 19], L19103 = [2, 4, 6, 18, 19, 19], L19106 = [2, 4, 8, 10, 19, 19], L19108 = [2, 4, 8, 16, 19, 19], L19110 = [2, 4, 10, 12, 16, 19], L19114 = [2, 4, 12, 16, 19, 19], L19117 = [2, 4, 14, 19, 19, 19], L19120 = [2, 6, 8, 10, 19, 19], L19121 = [2, 6, 8, 19, 19, 19]. q = 39 : L405 = [0, 0, 1, 2, 10, 17], L553 = [0, 0, 1, 4, 5, 11], L745 = [0, 0, 3, 6, 9, 13], L746 = [0, 0, 3, 6, 12, 13], L748 = [0, 0, 3, 6, 13, 15], L749 = [0, 0, 3, 9, 12, 13], L2273 = [0, 1, 2, 5, 14, 16], L2424 = [0, 1, 2, 8, 10, 14], L2517 = [0, 1, 2, 10, 13, 17], L2766 = [0, 1, 3, 4, 9, 17], L2771 = [0, 1, 3, 4, 10, 14], L2782 = [0, 1, 3, 4, 12, 14], L2794 = [0, 1, 3, 4, 14, 17], L3119 = [0, 1, 4, 5, 11, 13], L3600 = [0, 3, 6, 9, 12, 13], L3601 = [0, 3, 6, 9, 13, 13], L3602 = [0, 3, 6, 9, 13, 15], L3603 = [0, 3, 6, 9, 13, 18], L3604 = [0, 3, 6, 12, 13, 13], L3606 = [0, 3, 6, 13, 13, 15], L3607 = [0, 3, 9, 12, 13, 13], L10701 = [1, 2, 4, 5, 7, 17], L10710 = [1, 2, 4, 5, 8, 16], L10730 = [1, 2, 4, 5, 10, 17], L10757 = [1, 2, 4, 5, 14, 17], L10759 = [1, 2, 4, 5, 14, 19], L10771 = [1, 2, 4, 7, 8, 11], L10773 = [1, 2, 4, 7, 8, 14], L10775 = [1, 2, 4, 7, 8, 17], L10788 = [1, 2, 4, 7, 10, 11], L10803 = [1, 2, 4, 7, 11, 19], L10827 = [1, 2, 4, 7, 16, 17], L11293 = [1, 2, 5, 13, 14, 16], L11661 = [1, 2, 7, 8, 10, 11], L11849 = [1, 2, 8, 10, 13, 14], L12124 = [1, 2, 10, 13, 13, 17], L13034 = [1, 3, 4, 9, 13, 17], L13058 = [1, 3, 4, 10, 13, 14], L13088 = [1, 3, 4, 12, 13, 14], L13108 = [1, 3, 4, 13, 14, 17], L13385 = [1, 3, 6, 7, 10, 15], L13412 = [1, 3, 6, 8, 10, 18], L13964 = [1, 4, 5, 11, 13, 13], L14982 = [3, 6, 9, 12, 13, 13], L14984 = [3, 6, 9, 13, 13, 13], L14985 = [3, 6, 9, 13, 13, 15], L14986 = [3, 6, 9, 13, 13, 18], L14987 = [3, 6, 12, 13, 13, 13], L14989 = [3, 6, 13, 13, 13, 15], L14990 = [3, 9, 12, 13, 13, 13]. q = 40 : L63 = [0, 0, 0, 1, 3, 7], L65 = [0, 0, 0, 1, 3, 9], L70 = [0, 0, 0, 1, 3, 15], L94 = [0, 0, 0, 1, 5, 7], L524 = [0, 0, 1, 2, 9, 11], L532 = [0, 0, 1, 2, 9, 19], L612 = [0, 0, 1, 3, 5, 11], L614 = [0, 0, 1, 3, 5, 13], L624 = [0, 0, 1, 3, 7, 10], L625 = [0, 0, 1, 3, 7, 11], L628 = [0, 0, 1, 3, 7, 15], L633 = [0, 0, 1, 3, 7, 20], L647 = [0, 0, 1, 3, 9, 10], L649 = [0, 0, 1, 3, 9, 13], L652 = [0, 0, 1, 3, 9, 20], L657 = [0, 0, 1, 3, 10, 15], L689 = [0, 0, 1, 3, 15, 20], L846 = [0, 0, 1, 5, 7, 9], L847 = [0, 0, 1, 5, 7, 10], L851 = [0, 0, 1, 5, 7, 20], L943 = [0, 0, 1, 6, 9, 11], L948 = [0, 0, 1, 6, 9, 19], L2915 = [0, 1, 2, 2, 9, 11], L2923 = [0, 1, 2, 2, 9, 19], L3105 = [0, 1, 2, 3, 14, 17], L3107 = [0, 1, 2, 3, 14, 19], L3203 = [0, 1, 2, 4, 9, 11], L3211 = [0, 1, 2, 4, 9, 19], L3416 = [0, 1, 2, 6, 7, 13], L3422 = [0, 1, 2, 6, 7, 19], L3438 = [0, 1, 2, 6, 9, 11], L3446 = [0, 1, 2, 6, 9, 19], L3586 = [0, 1, 2, 8, 9, 11], L3594 = [0, 1, 2, 8, 9, 19], L3654 = [0, 1, 2, 9, 10, 11], L3662 = [0, 1, 2, 9, 10, 19], L3664 = [0, 1, 2, 9, 11, 12], L3666 = [0, 1, 2, 9, 11, 14], L3668 = [0, 1, 2, 9, 11, 16], L3672 = [0, 1, 2, 9, 11, 20], L3680 = [0, 1, 2, 9, 12, 19], L3690 = [0, 1, 2, 9, 14, 19], L3700 = [0, 1, 2, 9, 16, 19], L3704 = [0, 1, 2, 9, 19, 20], L3939 = [0, 1, 3, 4, 7, 12], L3962 = [0, 1, 3, 4, 9, 12], L3991 = [0, 1, 3, 4, 12, 15], L4047 = [0, 1, 3, 5, 7, 11], L4050 = [0, 1, 3, 5, 7, 15], L4052 = [0, 1, 3, 5, 7, 17], L4070 = [0, 1, 3, 5, 9, 11], L4071 = [0, 1, 3, 5, 9, 13], L4073 = [0, 1, 3, 5, 9, 15], L4079 = [0, 1, 3, 5, 10, 11], L4081 = [0, 1, 3, 5, 10, 13], L4095 = [0, 1, 3, 5, 11, 20], L4108 = [0, 1, 3, 5, 13, 20], L4116 = [0, 1, 3, 5, 15, 15], L4142 = [0, 1, 3, 7, 8, 16], L4148 = [0, 1, 3, 7, 9, 11], L4149 = [0, 1, 3, 7, 9, 13], L4152 = [0, 1, 3, 7, 9, 19], L4154 = [0, 1, 3, 7, 10, 10], L4155 = [0, 1, 3, 7, 10, 11], L4158 = [0, 1, 3, 7, 10, 15], L4163 = [0, 1, 3, 7, 10, 20], L4166 = [0, 1, 3, 7, 11, 20], L4176 = [0, 1, 3, 7, 13, 19], L4183 = [0, 1, 3, 7, 15, 20], L4190 = [0, 1, 3, 7, 17, 19], L4196 = [0, 1, 3, 7, 20, 20], L4214 = [0, 1, 3, 8, 9, 16],
68
EMILIO A. LAURET
Table 4. (continued) n = 6 q I indexes of I-isospectral families 40 {0} {63, 65}, {70, 94}, {524, 532}, {612, 614}, {624, 647}, {625, 649}, {628, 846}, {633, 652}, {657, 847}, {689, 851}, {943, 948}, {2915, 2923}, {3105, 3422}, {3107, 3416}, {3203, 3211}, {3438, 3446}, {3586, 3594}, {3654, 3662}, {3664, 3680}, {3666, 3690}, {3668, 3700}, {3672, 3704}, {3939, 3962}, {3991, 4606}, {4047, 4071}, {4050, 4073}, {4052, 4070}, {4079, 4081}, {4095, 4108}, {4116, 5045}, {4142, 4214}, {4148, 4149, 4152}, {4154, 4272}, {4155, 4274}, {4158, 5197}, {4163, 4277}, {4166, 4280}, {4176, 4190}, {4183, 5200}, {4196, 4285}, {4254, 5193}, {4290, 5201}, {4322, 5205}, {4433, 5215}, {4711, 4716}, {5463, 5468}, {5547, 5552}, {5594, 5599}, {5601, 5610}, {5603, 5619}, {5605, 5621}, {15060, 15068}, {15350, 15358}, {15589, 15597}, {15754, 15762}, {15823, 15831}, {15833, 15849}, {15835, 15862}, {15837, 15872}, {15839, 15877}, {15841, 15879}, {16522, 16582}, {16675, 17960}, {16728, 18499}, {16730, 18493}, {16771, 18517}, {16868, 18519}, {16869, 18540}, {16873, 18520}, {16993, 17001}, {17229, 17237}, {17268, 18728}, {17388, 17396}, {17456, 17464}, {17466, 17482}, {17468, 17492}, {17470, 17502}, {17474, 17506}, {18110, 18140}, {18409, 18416}, {18487, 18523}, {18556, 18564}, {18621, 18629}, {18631, 18645}, {18633, 18656}, {18635, 18666}, {18636, 18669}, {18638, 18671}, {19134, 19142}, {19202, 19210}, {19212, 19228}, {19214, 19238}, {19216, 19248}, {19220, 19252}, {19453, 19461}, {19463, 19479}, {19465, 19489}, {19467, 19499}, {19471, 19503}, {19505, 19545}, {19507, 19555}, {19509, 19565}, {19513, 19569}, {19518, 19584}, {19520, 19592}, {19523, 19595}, {19528, 19612}, {19532, 19616}, {19537, 19620}, {20348, 20357}, {20412, 20429}, {20416, 20559}, {20420, 20550}, {20428, 20566}, {20434, 23038}, {20439, 20569}, {20447, 21008}, {20613, 23044},
L4254 = [0, 1, 3, 8, 15, 16], L4272 = [0, 1, 3, 9, 10, 10], L4274 = [0, 1, 3, 9, 10, 13], L4277 = [0, 1, 3, 9, 10, 20], L4280 = [0, 1, 3, 9, 13, 20], L4285 = [0, 1, 3, 9, 20, 20], L4290 = [0, 1, 3, 10, 10, 15], L4322 = [0, 1, 3, 10, 15, 20], L4433 = [0, 1, 3, 15, 20, 20], L4606 = [0, 1, 4, 5, 7, 12], L4711 = [0, 1, 4, 6, 9, 11], L4716 = [0, 1, 4, 6, 9, 19], L5045 = [0, 1, 5, 5, 7, 15], L5193 = [0, 1, 5, 7, 8, 16], L5197 = [0, 1, 5, 7, 9, 10], L5200 = [0, 1, 5, 7, 9, 20], L5201 = [0, 1, 5, 7, 10, 10], L5205 = [0, 1, 5, 7, 10, 20], L5215 = [0, 1, 5, 7, 20, 20], L5463 = [0, 1, 6, 6, 9, 11], L5468 = [0, 1, 6, 6, 9, 19], L5547 = [0, 1, 6, 8, 9, 11], L5552 = [0, 1, 6, 8, 9, 19], L5594 = [0, 1, 6, 9, 10, 11], L5599 = [0, 1, 6, 9, 10, 19], L5601 = [0, 1, 6, 9, 11, 12], L5603 = [0, 1, 6, 9, 11, 16], L5605 = [0, 1, 6, 9, 11, 20], L5610 = [0, 1, 6, 9, 12, 19], L5619 = [0, 1, 6, 9, 16, 19], L5621 = [0, 1, 6, 9, 19, 20], L5778 = [0, 1, 7, 9, 15, 17], L5863 = [0, 1, 8, 8, 16, 16], L6698 = [0, 4, 5, 10, 15, 20], L6742 = [0, 5, 8, 8, 16, 16], L6750 = [0, 5, 8, 10, 15, 20], L13212 = [1, 1, 7, 9, 15, 17], L15060 = [1, 2, 2, 2, 9, 11], L15068 = [1, 2, 2, 2, 9, 19], L15350 = [1, 2, 2, 4, 9, 11], L15358 = [1, 2, 2, 4, 9, 19], L15589 = [1, 2, 2, 6, 9, 11], L15597 = [1, 2, 2, 6, 9, 19], L15754 = [1, 2, 2, 8, 9, 11], L15762 = [1, 2, 2, 8, 9, 19], L15823 = [1, 2, 2, 9, 10, 11], L15831 = [1, 2, 2, 9, 10, 19], L15833 = [1, 2, 2, 9, 11, 12], L15835 = [1, 2, 2, 9, 11, 14], L15837 = [1, 2, 2, 9, 11, 16], L15839 = [1, 2, 2, 9, 11, 18], L15841 = [1, 2, 2, 9, 11, 20], L15849 = [1, 2, 2, 9, 12, 19], L15862 = [1, 2, 2, 9, 14, 19], L15872 = [1, 2, 2, 9, 16, 19], L15877 = [1, 2, 2, 9, 18, 19], L15879 = [1, 2, 2, 9, 19, 20], L16413 = [1, 2, 3, 6, 11, 13], L16479 = [1, 2, 3, 7, 9, 14], L16522 = [1, 2, 3, 7, 14, 16], L16582 = [1, 2, 3, 8, 11, 14], L16675 = [1, 2, 3, 9, 15, 18], L16728 = [1, 2, 3, 10, 14, 17], L16730 = [1, 2, 3, 10, 14, 19], L16771 = [1, 2, 3, 11, 14, 19], L16868 = [1, 2, 3, 14, 17, 19], L16869 = [1, 2, 3, 14, 17, 20],
APPENDIX
69
Table 4. (continued) n = 6 q I indexes of I-isospectral families 40 (cont.) {0} {20700, 23053}, {20819, 20843}, {20864, 20876}, {20921, 20922, 20926}, {20925, 20939, 20942, 21064}, {20929, 21057}, {20932, 21059}, {20934, 21056}, {20940, 21070}, {20943, 21072}, {20956, 24546}, {20961, 21080}, {20969, 21069}, {21012, 21024}, {21090, 21092}, {21106, 21119}, {21127, 24550}, {21168, 21215}, {21247, 24557}, {21300, 21316}, {21303, 21361}, {21310, 21575}, {21317, 21581}, {21331, 25129}, {21340, 21588}, {21350, 21351, 21354}, {21360, 21363, 21368}, {21370, 21776}, {21371, 21778}, {21374, 25150}, {21379, 21781}, {21382, 21784}, {21392, 21406}, {21399, 25153}, {21412, 21789}, {21418, 21793}, {21450, 21486}, {21469, 25158}, {21494, 21800}, {21628, 25134}, {21743, 25145}, {21805, 25159}, {21837, 25163}, {21948, 25173}, {22235, 25193}, {22530, 22535}, {23344, 23349}, {23435, 23440}, {23482, 23487}, {23489, 23498}, {23491, 23507}, {23493, 23509}, {24961, 24976}, {25842, 25847}, {25926, 25931}, {25973, 25978}, {25980, 25989}, {25981, 25994}, {25982, 26000}, {25984, 26002}, {26207, 26212}, {26254, 26259}, {26261, 26270}, {26263, 26279}, {26265, 26281}, {26403, 26408}, {26410, 26419}, {26412, 26428}, {26414, 26430}, {26432, 26449}, {26434, 26458}, {26436, 26460}, {26440, 26475}, {26442, 26477}, {26444, 26479}, {28395, 28398}, {28650, 28653} L16873 = [1, 2, 3, 14, 19, 20], L16993 = [1, 2, 4, 4, 9, 11], L17001 = [1, 2, 4, 4, 9, 19], L17229 = [1, 2, 4, 6, 9, 11], L17237 = [1, 2, 4, 6, 9, 19], L17268 = [1, 2, 4, 6, 13, 17], L17388 = [1, 2, 4, 8, 9, 11], L17396 = [1, 2, 4, 8, 9, 19], L17456 = [1, 2, 4, 9, 10, 11], L17464 = [1, 2, 4, 9, 10, 19], L17466 = [1, 2, 4, 9, 11, 12], L17468 = [1, 2, 4, 9, 11, 14], L17470 = [1, 2, 4, 9, 11, 16], L17474 = [1, 2, 4, 9, 11, 20], L17482 = [1, 2, 4, 9, 12, 19], L17492 = [1, 2, 4, 9, 14, 19], L17502 = [1, 2, 4, 9, 16, 19], L17506 = [1, 2, 4, 9, 19, 20], L17960 = [1, 2, 5, 7, 9, 18], L18110 = [1, 2, 5, 9, 11, 15], L18140 = [1, 2, 5, 9, 15, 19], L18409 = [1, 2, 6, 6, 9, 11], L18416 = [1, 2, 6, 6, 9, 19], L18487 = [1, 2, 6, 7, 9, 18], L18493 = [1, 2, 6, 7, 10, 13], L18499 = [1, 2, 6, 7, 10, 19], L18517 = [1, 2, 6, 7, 13, 17], L18519 = [1, 2, 6, 7, 13, 19], L18520 = [1, 2, 6, 7, 13, 20], L18523 = [1, 2, 6, 7, 14, 17], L18540 = [1, 2, 6, 7, 19, 20], L18556 = [1, 2, 6, 8, 9, 11], L18564 = [1, 2, 6, 8, 9, 19], L18621 = [1, 2, 6, 9, 10, 11], L18629 = [1, 2, 6, 9, 10, 19], L18631 = [1, 2, 6, 9, 11, 12], L18633 = [1, 2, 6, 9, 11, 14], L18635 = [1, 2, 6, 9, 11, 16], L18636 = [1, 2, 6, 9, 11, 18], L18638 = [1, 2, 6, 9, 11, 20], L18645 = [1, 2, 6, 9, 12, 19], L18656 = [1, 2, 6, 9, 14, 19], L18666 = [1, 2, 6, 9, 16, 19], L18669 = [1, 2, 6, 9, 18, 19], L18671 = [1, 2, 6, 9, 19, 20], L18708 = [1, 2, 6, 10, 14, 18], L18728 = [1, 2, 6, 11, 12, 13], L18952 = [1, 2, 7, 9, 15, 17], L19134 = [1, 2, 8, 8, 9, 11], L19142 = [1, 2, 8, 8, 9, 19], L19202 = [1, 2, 8, 9, 10, 11], L19210 = [1, 2, 8, 9, 10, 19], L19212 = [1, 2, 8, 9, 11, 12], L19214 = [1, 2, 8, 9, 11, 14], L19216 = [1, 2, 8, 9, 11, 16], L19220 = [1, 2, 8, 9, 11, 20], L19228 = [1, 2, 8, 9, 12, 19], L19238 = [1, 2, 8, 9, 14, 19], L19248 = [1, 2, 8, 9, 16, 19], L19252 = [1, 2, 8, 9, 19, 20], L19453 = [1, 2, 9, 10, 10, 11], L19461 = [1, 2, 9, 10, 10, 19], L19463 = [1, 2, 9, 10, 11, 12], L19465 = [1, 2, 9, 10, 11, 14], L19467 = [1, 2, 9, 10, 11, 16], L19471 = [1, 2, 9, 10, 11, 20], L19479 = [1, 2, 9, 10, 12, 19], L19489 = [1, 2, 9, 10, 14, 19], L19499 = [1, 2, 9, 10, 16, 19], L19503 = [1, 2, 9, 10, 19, 20], L19505 = [1, 2, 9, 11, 12, 12], L19507 = [1, 2, 9, 11, 12, 14], L19509 = [1, 2, 9, 11, 12, 16], L19513 = [1, 2, 9, 11, 12, 20], L19518 = [1, 2, 9, 11, 14, 14], L19520 = [1, 2, 9, 11, 14, 16], L19523 = [1, 2, 9, 11, 14, 20], L19528 = [1, 2, 9, 11, 16, 16], L19532 = [1, 2, 9, 11, 16, 20], L19537 = [1, 2, 9, 11, 20, 20], L19545 = [1, 2, 9, 12, 12, 19], L19555 = [1, 2, 9, 12, 14, 19], L19565 = [1, 2, 9, 12, 16, 19], L19569 = [1, 2, 9, 12, 19, 20], L19584 = [1, 2, 9, 14, 14, 19], L19592 = [1, 2, 9, 14, 16, 19], L19595 = [1, 2, 9, 14, 19, 20], L19612 = [1, 2, 9, 16, 16, 19], L19616 = [1, 2, 9, 16, 19, 20], L19620 = [1, 2, 9, 19, 20, 20], L20348 = [1, 3, 4, 5, 11, 12], L20357 = [1, 3, 4, 5, 12, 13], L20412 = [1, 3, 4, 7, 9, 13], L20416 = [1, 3, 4, 7, 9, 19],
70
EMILIO A. LAURET
Table 4. (continued) n = 6 q 40 (cont.)
I {0, 1}
indexes of I-isospectral families {4149, 4152}, {20925, 20939}, {20942, 21064}, {21351, 21354}, {21363, 21368} {0, 1, 2} {16413, 16479} {2, 3, 4} {5778, 26816}, {5863, 6742}, {13212, 26873}, {18708, 28931}, {18952, 26868}, {21153, 25155}, {22758, 29202}, {23682, 26875} {4, 5} {6698, 6750}
L20420 = [1, 3, 4, 7, 10, 12], L20428 = [1, 3, 4, 7, 11, 12], L20429 = [1, 3, 4, 7, 11, 13], L20434 = [1, 3, 4, 7, 12, 15], L20439 = [1, 3, 4, 7, 12, 20], L20447 = [1, 3, 4, 7, 15, 16], L20550 = [1, 3, 4, 9, 10, 12], L20559 = [1, 3, 4, 9, 11, 13], L20566 = [1, 3, 4, 9, 12, 13], L20569 = [1, 3, 4, 9, 12, 20], L20613 = [1, 3, 4, 10, 12, 15], L20700 = [1, 3, 4, 12, 15, 20], L20819 = [1, 3, 5, 5, 7, 11], L20843 = [1, 3, 5, 5, 9, 13], L20864 = [1, 3, 5, 5, 11, 15], L20876 = [1, 3, 5, 5, 13, 15], L20921 = [1, 3, 5, 7, 9, 11], L20922 = [1, 3, 5, 7, 9, 13], L20925 = [1, 3, 5, 7, 9, 17], L20926 = [1, 3, 5, 7, 9, 19], L20929 = [1, 3, 5, 7, 10, 11], L20932 = [1, 3, 5, 7, 10, 15], L20934 = [1, 3, 5, 7, 10, 17], L20939 = [1, 3, 5, 7, 11, 13], L20940 = [1, 3, 5, 7, 11, 15], L20942 = [1, 3, 5, 7, 11, 19], L20943 = [1, 3, 5, 7, 11, 20], L20956 = [1, 3, 5, 7, 15, 15], L20961 = [1, 3, 5, 7, 15, 20], L20969 = [1, 3, 5, 7, 17, 20], L21008 = [1, 3, 5, 8, 11, 12], L21012 = [1, 3, 5, 8, 11, 16], L21024 = [1, 3, 5, 8, 13, 16], L21056 = [1, 3, 5, 9, 10, 11], L21057 = [1, 3, 5, 9, 10, 13], L21059 = [1, 3, 5, 9, 10, 15], L21064 = [1, 3, 5, 9, 11, 13], L21069 = [1, 3, 5, 9, 11, 20], L21070 = [1, 3, 5, 9, 13, 15], L21072 = [1, 3, 5, 9, 13, 20], L21080 = [1, 3, 5, 9, 15, 20], L21090 = [1, 3, 5, 10, 10, 11], L21092 = [1, 3, 5, 10, 10, 13], L21106 = [1, 3, 5, 10, 11, 20], L21119 = [1, 3, 5, 10, 13, 20], L21127 = [1, 3, 5, 10, 15, 15], L21153 = [1, 3, 5, 11, 13, 19], L21168 = [1, 3, 5, 11, 20, 20], L21215 = [1, 3, 5, 13, 20, 20], L21247 = [1, 3, 5, 15, 15, 20], L21300 = [1, 3, 7, 8, 9, 13], L21303 = [1, 3, 7, 8, 9, 19], L21310 = [1, 3, 7, 8, 10, 16], L21316 = [1, 3, 7, 8, 11, 13], L21317 = [1, 3, 7, 8, 11, 16], L21331 = [1, 3, 7, 8, 15, 16], L21340 = [1, 3, 7, 8, 16, 20], L21350 = [1, 3, 7, 9, 10, 11], L21351 = [1, 3, 7, 9, 10, 13], L21354 = [1, 3, 7, 9, 10, 19], L21360 = [1, 3, 7, 9, 11, 20], L21361 = [1, 3, 7, 9, 13, 16], L21363 = [1, 3, 7, 9, 13, 20], L21368 = [1, 3, 7, 9, 19, 20], L21370 = [1, 3, 7, 10, 10, 10], L21371 = [1, 3, 7, 10, 10, 11], L21374 = [1, 3, 7, 10, 10, 15], L21379 = [1, 3, 7, 10, 10, 20], L21382 = [1, 3, 7, 10, 11, 20], L21392 = [1, 3, 7, 10, 13, 19], L21399 = [1, 3, 7, 10, 15, 20], L21406 = [1, 3, 7, 10, 17, 19], L21412 = [1, 3, 7, 10, 20, 20], L21418 = [1, 3, 7, 11, 20, 20], L21450 = [1, 3, 7, 13, 19, 20], L21469 = [1, 3, 7, 15, 20, 20], L21486 = [1, 3, 7, 17, 19, 20], L21494 = [1, 3, 7, 20, 20, 20], L21575 = [1, 3, 8, 9, 10, 16], L21581 = [1, 3, 8, 9, 13, 16], L21588 = [1, 3, 8, 9, 16, 20], L21628 = [1, 3, 8, 10, 15, 16], L21743 = [1, 3, 8, 15, 16, 20], L21776 = [1, 3, 9, 10, 10, 10], L21778 = [1, 3, 9, 10, 10, 13], L21781 = [1, 3, 9, 10, 10, 20], L21784 = [1, 3, 9, 10, 13, 20], L21789 = [1, 3, 9, 10, 20, 20], L21793 = [1, 3, 9, 13, 20, 20], L21800 = [1, 3, 9, 20, 20, 20], L21805 = [1, 3, 10, 10, 10, 15], L21837 = [1, 3, 10, 10, 15, 20], L21948 = [1, 3, 10, 15, 20, 20], L22235 = [1, 3, 15, 20, 20, 20], L22530 = [1, 4, 4, 6, 9, 11], L22535 = [1, 4, 4, 6, 9, 19], L22758 = [1, 4, 4, 12, 12, 20], L23038 = [1, 4, 5, 7, 9, 12], L23044 = [1, 4, 5, 7, 10, 12], L23053 = [1, 4, 5, 7, 12, 20], L23344 = [1, 4, 6, 6, 9, 11], L23349 = [1, 4, 6, 6, 9, 19], L23435 = [1, 4, 6, 8, 9, 11], L23440 = [1, 4, 6, 8, 9, 19], L23482 = [1, 4, 6, 9, 10, 11], L23487 = [1, 4, 6, 9, 10, 19], L23489 = [1, 4, 6, 9, 11, 12], L23491 = [1, 4, 6, 9, 11, 16], L23493 = [1, 4, 6, 9, 11, 20], L23498 = [1, 4, 6, 9, 12, 19], L23507 = [1, 4, 6, 9, 16, 19], L23509 = [1, 4, 6, 9, 19, 20], L23682 = [1, 4, 7, 9, 15, 17], L24546 = [1, 5, 5, 7, 9, 15], L24550 = [1, 5, 5, 7, 10, 15], L24557 = [1, 5, 5, 7, 15, 20], L24961 = [1, 5, 6, 9, 11, 15], L24976 = [1, 5, 6, 9, 15, 19], L25129 = [1, 5, 7, 8, 9, 16], L25134 = [1, 5, 7, 8, 10, 16], L25145 = [1, 5, 7, 8, 16, 20], L25150 = [1, 5, 7, 9, 10, 10], L25153 = [1, 5, 7, 9, 10, 20], L25155 = [1, 5, 7, 9, 15, 17], L25158 = [1, 5, 7, 9, 20, 20], L25159 = [1, 5, 7, 10, 10, 10], L25163 = [1, 5, 7, 10, 10, 20], L25173 = [1, 5, 7, 10, 20, 20], L25193 = [1, 5, 7, 20, 20, 20], L25842 = [1, 6, 6, 6, 9, 11], L25847 = [1, 6, 6, 6, 9, 19], L25926 = [1, 6, 6, 8, 9, 11], L25931 = [1, 6, 6, 8, 9, 19], L25973 = [1, 6, 6, 9, 10, 11], L25978 = [1, 6, 6, 9, 10, 19], L25980 = [1, 6, 6, 9, 11, 12], L25981 = [1, 6, 6, 9, 11, 14], L25982 = [1, 6, 6, 9, 11, 16], L25984 = [1, 6, 6, 9, 11, 20], L25989 = [1, 6, 6, 9, 12, 19], L25994 = [1, 6, 6, 9, 14, 19], L26000 = [1, 6, 6, 9, 16, 19], L26002 = [1, 6, 6, 9, 19, 20], L26207 = [1, 6, 8, 8, 9, 11], L26212 = [1, 6, 8, 8, 9, 19], L26254 = [1, 6, 8, 9, 10, 11], L26259 = [1, 6, 8, 9, 10, 19], L26261 = [1, 6, 8, 9, 11, 12],
APPENDIX
71
Table 4. (continued) n = 6 q I indexes of I-isospectral families 41 {0} {1958, 1959}, {2061, 2141}, {2070, 2139}, {9870, 9876}, {10243, 10247}, {11329, 11333}, {11508, 11517} L26263 = [1, 6, 8, 9, 11, 16], L26265 = [1, 6, 8, 9, 11, 20], L26270 = [1, 6, 8, 9, 12, 19], L26279 = [1, 6, 8, 9, 16, 19], L26281 = [1, 6, 8, 9, 19, 20], L26403 = [1, 6, 9, 10, 10, 11], L26408 = [1, 6, 9, 10, 10, 19], L26410 = [1, 6, 9, 10, 11, 12], L26412 = [1, 6, 9, 10, 11, 16], L26414 = [1, 6, 9, 10, 11, 20], L26419 = [1, 6, 9, 10, 12, 19], L26428 = [1, 6, 9, 10, 16, 19], L26430 = [1, 6, 9, 10, 19, 20], L26432 = [1, 6, 9, 11, 12, 12], L26434 = [1, 6, 9, 11, 12, 16], L26436 = [1, 6, 9, 11, 12, 20], L26440 = [1, 6, 9, 11, 16, 16], L26442 = [1, 6, 9, 11, 16, 20], L26444 = [1, 6, 9, 11, 20, 20], L26449 = [1, 6, 9, 12, 12, 19], L26458 = [1, 6, 9, 12, 16, 19], L26460 = [1, 6, 9, 12, 19, 20], L26475 = [1, 6, 9, 16, 16, 19], L26477 = [1, 6, 9, 16, 19, 20], L26479 = [1, 6, 9, 19, 20, 20], L26816 = [1, 7, 8, 9, 15, 17], L26868 = [1, 7, 9, 10, 15, 17], L26873 = [1, 7, 9, 15, 15, 17], L26875 = [1, 7, 9, 15, 17, 20], L28395 = [2, 2, 5, 6, 6, 14], L28398 = [2, 2, 5, 6, 6, 18], L28650 = [2, 4, 5, 6, 8, 14], L28653 = [2, 4, 5, 6, 8, 18], L28931 = [2, 5, 6, 10, 14, 18], L29202 = [4, 4, 5, 12, 12, 20]. q = 41 : L1958 = [0, 1, 2, 3, 9, 13], L1959 = [0, 1, 2, 3, 9, 14], L2061 = [0, 1, 2, 4, 9, 18], L2070 = [0, 1, 2, 4, 10, 18], L2139 = [0, 1, 2, 5, 8, 18], L2141 = [0, 1, 2, 5, 9, 10], L9870 = [1, 2, 3, 6, 13, 18], L9876 = [1, 2, 3, 6, 14, 18], L10243 = [1, 2, 4, 5, 9, 16], L10247 = [1, 2, 4, 5, 9, 20], L11329 = [1, 3, 4, 5, 12, 15], L11333 = [1, 3, 4, 5, 14, 15], L11508 = [1, 4, 5, 6, 13, 19], L11517 = [1, 4, 5, 11, 16, 17]. q = 42 : L844 = [0, 0, 1, 3, 11, 15], L874 = [0, 0, 1, 3, 15, 17], L922 = [0, 0, 1, 4, 5, 16], L925 = [0, 0, 1, 4, 5, 20], L1081 = [0, 0, 1, 5, 11, 13], L1084 = [0, 0, 1, 5, 11, 17], L1187 = [0, 0, 1, 6, 12, 18], L1990 = [0, 0, 6, 7, 12, 18], L3034 = [0, 1, 1, 6, 12, 18], L4485 = [0, 1, 2, 6, 12, 18], L5483 = [0, 1, 3, 5, 9, 13], L5487 = [0, 1, 3, 5, 9, 17], L5489 = [0, 1, 3, 5, 9, 19], L5493 = [0, 1, 3, 5, 11, 13], L5495 = [0, 1, 3, 5, 11, 15], L5499 = [0, 1, 3, 5, 11, 19], L5512 = [0, 1, 3, 5, 13, 15], L5513 = [0, 1, 3, 5, 13, 17], L5515 = [0, 1, 3, 5, 13, 19], L5528 = [0, 1, 3, 5, 15, 19], L5631 = [0, 1, 3, 6, 12, 18], L5727 = [0, 1, 3, 7, 11, 15], L5757 = [0, 1, 3, 7, 15, 17], L5914 = [0, 1, 3, 9, 15, 21], L6005 = [0, 1, 3, 11, 14, 15], L6015 = [0, 1, 3, 11, 15, 21], L6096 = [0, 1, 3, 14, 15, 17], L6132 = [0, 1, 3, 15, 17, 21], L6345 = [0, 1, 4, 5, 7, 16], L6348 = [0, 1, 4, 5, 7, 20], L6389 = [0, 1, 4, 5, 14, 16], L6392 = [0, 1, 4, 5, 14, 20], L6398 = [0, 1, 4, 5, 16, 21], L6404 = [0, 1, 4, 5, 20, 21], L6482 = [0, 1, 4, 6, 12, 18], L7015 = [0, 1, 5, 6, 12, 18], L7070 = [0, 1, 5, 7, 11, 13], L7073 = [0, 1, 5, 7, 11, 17], L7183 = [0, 1, 5, 11, 13, 14], L7185 = [0, 1, 5, 11, 13, 21], L7188 = [0, 1, 5, 11, 14, 17], L7194 = [0, 1, 5, 11, 17, 21], L7338 = [0, 1, 6, 6, 12, 18], L7430 = [0, 1, 6, 7, 12, 18], L7505 = [0, 1, 6, 8, 12, 18], L7559 = [0, 1, 6, 9, 12, 18], L7613 = [0, 1, 6, 10, 12, 18], L7647 = [0, 1, 6, 11, 12, 18], L7666 = [0, 1, 6, 12, 12, 18], L7671 = [0, 1, 6, 12, 13, 18], L7676 = [0, 1, 6, 12, 14, 18], L7681 = [0, 1, 6, 12, 15, 18], L7685 = [0, 1, 6, 12, 16, 18], L7688 = [0, 1, 6, 12, 18, 18], L7689 = [0, 1, 6, 12, 18, 20], L7690 = [0, 1, 6, 12, 18, 21], L9688 = [0, 2, 3, 6, 10, 20], L9694 = [0, 2, 3, 6, 12, 18], L9835 = [0, 2, 3, 9, 15, 21], L9935 = [0, 2, 4, 6, 9, 10], L9957 = [0, 2, 4, 7, 8, 10], L9959 = [0, 2, 4, 7, 8, 16], L9977 = [0, 2, 4, 7, 12, 18], L9988 = [0, 2, 4, 8, 10, 21], L9990 = [0, 2, 4, 8, 16, 21], L10027 = [0, 2, 4, 12, 18, 21], L10085 = [0, 2, 6, 7, 8, 12], L10105 = [0, 2, 6, 7, 12, 18], L10123 = [0, 2, 6, 8, 12, 21], L10146 = [0, 2, 6, 9, 12, 18], L10171 = [0, 2, 6, 12, 15, 18], L10174 = [0, 2, 6, 12, 18, 21], L10605 = [0, 3, 6, 7, 9, 12], L10608 = [0, 3, 6, 7, 9, 18], L10612 = [0, 3, 6, 7, 12, 18], L10623 = [0, 3, 6, 9, 12, 14], L10626 = [0, 3, 6, 9, 14, 18], L10630 = [0, 3, 6, 12, 14, 18], L10667 = [0, 3, 7, 9, 15, 21], L10695 = [0, 3, 9, 14, 15, 21], L10731 = [0, 6, 6, 7, 12, 18], L10747 = [0, 6, 7, 7, 12, 18], L10753 = [0, 6, 7, 12, 14, 18], L10755 = [0, 6, 7, 12, 18, 21], L10762 = [0, 6, 12, 14, 18, 21], L15009 = [1, 1, 3, 9, 15, 21], L23177 = [1, 2, 3, 9, 15, 21], L24294 = [1, 2, 4, 11, 13, 19], L24916 = [1, 2, 5, 10, 11, 13], L26658 = [1, 2, 8, 10, 11, 16], L27527 = [1, 2, 10, 16, 17, 20], L29036 = [1, 3, 3, 9, 15, 21], L29905 = [1, 3, 4, 9, 15, 21], L30289 = [1, 3, 5, 7, 9, 13], L30293 = [1, 3, 5, 7, 9, 17], L30295 = [1, 3, 5, 7, 9, 19], L30299 = [1, 3, 5, 7, 11, 13], L30301 = [1, 3, 5, 7, 11, 15], L30305 = [1, 3, 5, 7, 11, 19], L30318 = [1, 3, 5, 7, 13, 15], L30319 = [1, 3, 5, 7, 13, 17], L30321 = [1, 3, 5, 7, 13, 19], L30334 = [1, 3, 5, 7, 15, 19], L30440 = [1, 3, 5, 9, 11, 17], L30442 = [1, 3, 5, 9, 11, 19], L30454 = [1, 3, 5, 9, 13, 14], L30458 = [1, 3, 5, 9, 13, 19], L30460 = [1, 3, 5, 9, 13, 21], L30464 = [1, 3, 5, 9, 14, 17], L30466 = [1, 3, 5, 9, 14, 19], L30473 = [1, 3, 5, 9, 15, 21], L30479 = [1, 3, 5, 9, 17, 19],
72
EMILIO A. LAURET
Table 4. (continued) n = 6 q 42
I {0}
indexes of I-isospectral families {844, 874}, {922, 925}, {1081, 1084}, {5483, 5487}, {5489, 5512}, {5493, 5515}, {5495, 5528}, {5499, 5513}, {5727, 5757}, {6005, 6096}, {6015, 6132}, {6345, 6348}, {6389, 6392}, {6398, 6404}, {7070, 7073}, {7183, 7188}, {7185, 7194}, {9688, 9935}, {9957, 9959}, {9977, 10085}, {9988, 9990}, {10027, 10123}, {10605, 10608}, {10623, 10626}, {24294, 24916}, {26658, 27527}, {30289, 30293}, {30295, 30318}, {30299, 30321}, {30301, 30334}, {30305, 30319}, {30442, 30479, 30585}, {30454, 30464}, {30460, 30481}, {30466, 30578}, {30487, 30586}, {30500, 30581}, {30505, 30594}, {30507, 30608}, {30511, 30579}, {30515, 30636}, {30527, 30589}, {31380, 31410}, {31658, 31749}, {31668, 31785}, {32728, 32975}, {32738, 33011}, {32765, 33101}, {34078, 34081}, {34122, 34125}, {34131, 34137}, {34290, 34293}, {34299, 34305}, {34317, 34326}, {36691, 36712}, {36825, 36828}, {36938, 36943}, {36940, 36949}, {37265, 37273}, {37267, 37279}, {37270, 37289}, {45862, 45868}, {46224, 46954}, {46904, 46917}, {46905, 46915}, {46918, 46923}, {46919, 46933}, {46932, 47455}, {46942, 46974}, {46943, 46972}, {46975, 46980}, {46976, 46990}, {46989, 47559}, {47005, 47007}, {47025, 47419}, {47036, 47041}, {47039, 47044}, {47095, 47459}, {47100, 47462}, {47118, 47123}, {47121, 47126}, {47221, 47565}, {47226, 47570}, {48803, 48806}, {48822, 48828}, {48825, 48831}, {48860, 48866}, {48863, 48869} {0, 1} {30440, 30458} {5} {1187, 1990, 7338, 7666, 7688, 10731}, {3034, 7015, 7430, 7647, 7671, 10747}, {4485, 6482, 7505, 7613, 7676, 7685, 7689, 10105, 10753}, {5631, 7559, 7681, 7690, 10612, 10755}, {5914, 10667, 31050, 32345, 32407, 48830}, {9694, 10146, 10171, 10174, 10630, 10762}, {9835, 10695, 46210, 46657, 46684, 48868}, {15009, 30473, 31567, 32315, 32366, 48923}, {23177, 29905, 31971, 32289, 32381, 32404, 32409, 46418, 48954}, {29036, 32238, 32400, 32410, 48654, 48956}, {43944, 45923, 46515, 46671, 46682, 49002}, {45633, 46627, 46680, 46685, 48702, 49004}
L30481 = [1, 3, 5, 9, 17, 21], L30487 = [1, 3, 5, 9, 19, 21], L30500 = [1, 3, 5, 11, 13, 14], L30505 = [1, 3, 5, 11, 13, 21], L30507 = [1, 3, 5, 11, 14, 15], L30511 = [1, 3, 5, 11, 14, 19], L30515 = [1, 3, 5, 11, 15, 21], L30527 = [1, 3, 5, 11, 19, 21], L30578 = [1, 3, 5, 13, 14, 15], L30579 = [1, 3, 5, 13, 14, 17], L30581 = [1, 3, 5, 13, 14, 19], L30585 = [1, 3, 5, 13, 15, 19], L30586 = [1, 3, 5, 13, 15, 21], L30589 = [1, 3, 5, 13, 17, 21], L30594 = [1, 3, 5, 13, 19, 21], L30608 = [1, 3, 5, 14, 15, 19], L30636 = [1, 3, 5, 15, 19, 21], L31050 = [1, 3, 6, 9, 15, 21], L31380 = [1, 3, 7, 7, 11, 15], L31410 = [1, 3, 7, 7, 15, 17], L31567 = [1, 3, 7, 9, 15, 21], L31658 = [1, 3, 7, 11, 14, 15], L31668 = [1, 3, 7, 11, 15, 21], L31749 = [1, 3, 7, 14, 15, 17], L31785 = [1, 3, 7, 15, 17, 21], L31971 = [1, 3, 8, 9, 15, 21], L32238 = [1, 3, 9, 9, 15, 21], L32289 = [1, 3, 9, 10, 15, 21], L32315 = [1, 3, 9, 11, 15, 21], L32345 = [1, 3, 9, 12, 15, 21], L32366 = [1, 3, 9, 13, 15, 21], L32381 = [1, 3, 9, 14, 15, 21], L32400 = [1, 3, 9, 15, 15, 21], L32404 = [1, 3, 9, 15, 16, 21], L32407 = [1, 3, 9, 15, 18, 21], L32409 = [1, 3, 9, 15, 20, 21], L32410 = [1, 3, 9, 15, 21, 21], L32728 = [1, 3, 11, 14, 14, 15], L32738 = [1, 3, 11, 14, 15, 21], L32765 = [1, 3, 11, 15, 21, 21], L32975 = [1, 3, 14, 14, 15, 17], L33011 = [1, 3, 14, 15, 17, 21], L33101 = [1, 3, 15, 17, 21, 21], L34078 = [1, 4, 5, 7, 7, 16], L34081 = [1, 4, 5, 7, 7, 20], L34122 = [1, 4, 5, 7, 14, 16], L34125 = [1, 4, 5, 7, 14, 20], L34131 = [1, 4, 5, 7, 16, 21], L34137 = [1, 4, 5, 7, 20, 21], L34290 = [1, 4, 5, 14, 14, 16], L34293 = [1, 4, 5, 14, 14, 20], L34299 = [1, 4, 5, 14, 16, 21], L34305 = [1, 4, 5, 14, 20, 21], L34317 =
APPENDIX
73
Table 4. (continued) n = 6 q I indexes of I-isospectral families 43 {0} {502, 508} [1, 4, 5, 16, 21, 21], L34326 = [1, 4, 5, 20, 21, 21], L36691 = [1, 5, 6, 11, 12, 13], L36712 = [1, 5, 6, 11, 17, 18], L36825 = [1, 5, 7, 7, 11, 13], L36828 = [1, 5, 7, 7, 11, 17], L36938 = [1, 5, 7, 11, 13, 14], L36940 = [1, 5, 7, 11, 13, 21], L36943 = [1, 5, 7, 11, 14, 17], L36949 = [1, 5, 7, 11, 17, 21], L37265 = [1, 5, 11, 13, 14, 14], L37267 = [1, 5, 11, 13, 14, 21], L37270 = [1, 5, 11, 13, 21, 21], L37273 = [1, 5, 11, 14, 14, 17], L37279 = [1, 5, 11, 14, 17, 21], L37289 = [1, 5, 11, 17, 21, 21], L43944 = [2, 2, 3, 9, 15, 21], L45633 = [2, 3, 3, 9, 15, 21], L45862 = [2, 3, 4, 8, 9, 16], L45868 = [2, 3, 4, 8, 10, 15], L45923 = [2, 3, 4, 9, 15, 21], L46210 = [2, 3, 6, 9, 15, 21], L46224 = [2, 3, 6, 10, 14, 20], L46418 = [2, 3, 7, 9, 15, 21], L46515 = [2, 3, 8, 9, 15, 21], L46627 = [2, 3, 9, 9, 15, 21], L46657 = [2, 3, 9, 12, 15, 21], L46671 = [2, 3, 9, 14, 15, 21], L46680 = [2, 3, 9, 15, 15, 21], L46682 = [2, 3, 9, 15, 16, 21], L46684 = [2, 3, 9, 15, 18, 21], L46685 = [2, 3, 9, 15, 21, 21], L46904 = [2, 4, 6, 7, 8, 16], L46905 = [2, 4, 6, 7, 8, 18], L46915 = [2, 4, 6, 7, 10, 12], L46917 = [2, 4, 6, 7, 10, 16], L46918 = [2, 4, 6, 7, 10, 18], L46919 = [2, 4, 6, 7, 10, 20], L46923 = [2, 4, 6, 7, 12, 16], L46932 = [2, 4, 6, 7, 16, 18], L46933 = [2, 4, 6, 7, 16, 20], L46942 = [2, 4, 6, 8, 16, 21], L46943 = [2, 4, 6, 8, 18, 21], L46954 = [2, 4, 6, 9, 10, 14], L46972 = [2, 4, 6, 10, 12, 21], L46974 = [2, 4, 6, 10, 16, 21], L46975 = [2, 4, 6, 10, 18, 21], L46976 = [2, 4, 6, 10, 20, 21], L46980 = [2, 4, 6, 12, 16, 21], L46989 = [2, 4, 6, 16, 18, 21], L46990 = [2, 4, 6, 16, 20, 21], L47005 = [2, 4, 7, 7, 8, 10], L47007 = [2, 4, 7, 7, 8, 16], L47025 = [2, 4, 7, 7, 12, 18], L47036 = [2, 4, 7, 8, 10, 14], L47039 = [2, 4, 7, 8, 10, 21], L47041 = [2, 4, 7, 8, 14, 16], L47044 = [2, 4, 7, 8, 16, 21], L47095 = [2, 4, 7, 12, 14, 18], L47100 = [2, 4, 7, 12, 18, 21], L47118 = [2, 4, 8, 10, 14, 21], L47121 = [2, 4, 8, 10, 21, 21], L47123 = [2, 4, 8, 14, 16, 21], L47126 = [2, 4, 8, 16, 21, 21], L47221 = [2, 4, 12, 14, 18, 21], L47226 = [2, 4, 12, 18, 21, 21], L47419 = [2, 6, 7, 7, 8, 12], L47455 = [2, 6, 7, 8, 10, 12], L47459 = [2, 6, 7, 8, 12, 14], L47462 = [2, 6, 7, 8, 12, 21], L47559 = [2, 6, 8, 10, 12, 21], L47565 = [2, 6, 8, 12, 14, 21], L47570 = [2, 6, 8, 12, 21, 21], L48654 = [3, 3, 7, 9, 15, 21], L48702 = [3, 3, 9, 14, 15, 21], L48803 = [3, 6, 7, 7, 9, 12], L48806 = [3, 6, 7, 7, 9, 18], L48822 = [3, 6, 7, 9, 12, 14], L48825 = [3, 6, 7, 9, 12, 21], L48828 = [3, 6, 7, 9, 14, 18], L48830 = [3, 6, 7, 9, 15, 21], L48831 = [3, 6, 7, 9, 18, 21], L48860 = [3, 6, 9, 12, 14, 14], L48863 = [3, 6, 9, 12, 14, 21], L48866 = [3, 6, 9, 14, 14, 18], L48868 = [3, 6, 9, 14, 15, 21], L48869 = [3, 6, 9, 14, 18, 21], L48923 = [3, 7, 7, 9, 15, 21], L48954 = [3, 7, 9, 14, 15, 21], L48956 = [3, 7, 9, 15, 21, 21], L49002 = [3, 9, 14, 14, 15, 21], L49004 = [3, 9, 14, 15, 21, 21]. q = 43 : L502 = [0, 0, 1, 3, 8, 14], L508 = [0, 0, 1, 3, 9, 14]. q = 44 : L66 = [0, 0, 0, 1, 3, 7], L68 = [0, 0, 0, 1, 3, 9], L72 = [0, 0, 0, 1, 3, 13], L75 = [0, 0, 0, 1, 3, 17], L100 = [0, 0, 0, 1, 5, 7], L102 = [0, 0, 0, 1, 5, 9], L694 = [0, 0, 1, 3, 5, 13], L696 = [0, 0, 1, 3, 5, 15], L707 = [0, 0, 1, 3, 7, 11], L709 = [0, 0, 1, 3, 7, 13], L713 = [0, 0, 1, 3, 7, 19], L715 = [0, 0, 1, 3, 7, 21], L716 = [0, 0, 1, 3, 7, 22], L733 = [0, 0, 1, 3, 9, 11], L734 = [0, 0, 1, 3, 9, 13], L737 = [0, 0, 1, 3, 9, 19], L738 = [0, 0, 1, 3, 9, 22], L752 = [0, 0, 1, 3, 11, 13], L755 = [0, 0, 1, 3, 11, 17], L776 = [0, 0, 1, 3, 13, 22], L796 = [0, 0, 1, 3, 17, 22], L970 = [0, 0, 1, 5, 7, 9], L971 = [0, 0, 1, 5, 7, 11], L974 = [0, 0, 1, 5, 7, 22], L985 = [0, 0, 1, 5, 9, 11], L989 = [0, 0, 1, 5, 9, 22], L1401 = [0, 0, 2, 6, 10, 11], L1403 = [0, 0, 2, 6, 11, 14], L1441 = [0, 0, 4, 8, 11, 12], L1442 = [0, 0, 4, 8, 11, 16], L4986 = [0, 1, 3, 5, 7, 13], L4991 = [0, 1, 3, 5, 7, 19], L4993 = [0, 1, 3, 5, 7, 21], L5009 = [0, 1, 3, 5, 9, 13], L5011 = [0, 1, 3, 5, 9, 15], L5013 = [0, 1, 3, 5, 9, 17], L5014 = [0, 1, 3, 5, 9, 19], L5016 = [0, 1, 3, 5, 9, 21], L5020 = [0, 1, 3, 5, 11, 13], L5022 = [0, 1, 3, 5, 11, 15], L5043 = [0, 1, 3, 5, 13, 17], L5044 = [0, 1, 3, 5, 13, 19], L5046 = [0, 1, 3, 5, 13, 22], L5055 = [0, 1, 3, 5, 15, 17], L5057 = [0, 1, 3, 5, 15, 21], L5058 = [0, 1, 3, 5, 15, 22], L5099 = [0, 1, 3, 7, 9, 13], L5101 = [0, 1, 3, 7, 9, 19], L5115 = [0, 1, 3, 7, 11, 11], L5117 = [0, 1, 3, 7, 11, 13], L5121 = [0, 1, 3, 7, 11, 19], L5123 = [0, 1, 3, 7, 11, 21], L5124 = [0, 1, 3, 7, 11, 22], L5137 = [0, 1, 3, 7, 13, 22], L5155 = [0, 1, 3, 7, 19, 22], L5159 = [0, 1, 3, 7, 21, 22], L5160 = [0, 1, 3, 7, 22, 22], L5269 = [0, 1, 3, 9, 11, 11], L5270 = [0, 1, 3, 9, 11, 13], L5273 = [0, 1, 3, 9, 11, 19], L5274 = [0, 1, 3, 9, 11, 22], L5277 = [0, 1, 3, 9, 13, 22], L5285 = [0, 1, 3, 9, 19, 22], L5286 = [0, 1, 3, 9, 22, 22], L5350 = [0, 1, 3, 11, 11, 13], L5353 = [0, 1, 3, 11, 11, 17], L5374 = [0, 1, 3, 11, 13, 22], L5394 = [0, 1, 3, 11, 17, 22],
74
EMILIO A. LAURET
Table 4. (continued) n = 6 q 44
I {0}
indexes of I-isospectral families {66, 68}, {72, 75, 100, 102}, {694, 696}, {707, 733}, {709, 970}, {716, 738}, {752, 755, 971, 985}, {776, 796, 974, 989}, {1401, 1403}, {1441, 1442}, {4986, 5011}, {4991, 5013}, {4993, 5009}, {5014, 5044}, {5016, 5055}, {5020, 5022}, {5043, 5099}, {5046, 5058}, {5057, 5101}, {5115, 5269}, {5117, 6415}, {5124, 5274}, {5137, 6417}, {5160, 5286}, {5350, 5353, 6418, 6477}, {5374, 5394, 6421, 6481}, {5475, 5545, 6427, 6490}, {7919, 7931}, {7934, 7939}, {7937, 7944}, {8049, 8050}, {8053, 8054}, {24282, 24466}, {24303, 24733}, {24689, 26220}, {27315, 27339}, {27317, 27413}, {27889, 27890, 27892, 27895}, {27893, 27918, 27920, 28042}, {27899, 28034}, {27904, 28036}, {27906, 28032}, {27922, 28055}, {27945, 28063}, {27949, 28047}, {28037, 28098}, {28039, 28109}, {28066, 28206}, {28070, 28245}, {28074, 28076}, {28097, 28399}, {28100, 28112}, {28111, 28401}, {28204, 28406}, {28209, 28250}, {28249, 28412}, {28473, 29083}, {28475, 33317}, {28482, 29088}, {28495, 33319}, {28518, 29100}, {28562, 33321}, {28614, 29122}, {28894, 31707}, {29360, 29363, 33322, 33509}, {29384, 29404, 33325, 33513}, {29485, 29555, 33331, 33522}, {29787, 29966, 33341, 33538}, {37639, 37643}, {37657, 37682}, {37662, 37718}, {37719, 37761}, {37746, 37806}, {37782, 37813}, {37817, 37827}, {37820, 37832}, {37825, 37841}, {38084, 38085}, {38088, 38089}, {38093, 38094} {0, 1} {713, 734}, {715, 737}, {5121, 5270}, {5123, 5273}, {5155, 5277}, {5159, 5285}, {27892, 27895}, {27918, 27920}, {27926, 28045}, {27935, 28062}, {27944, 28044}, {28479, 29084}, {28481, 29087}, {28513, 29091}, {28517, 29099}, {28607, 29106}, {28613, 29121}
L5475 = [0, 1, 3, 13, 22, 22], L5545 = [0, 1, 3, 17, 22, 22], L6415 = [0, 1, 5, 7, 9, 11], L6417 = [0, 1, 5, 7, 9, 22], L6418 = [0, 1, 5, 7, 11, 11], L6421 = [0, 1, 5, 7, 11, 22], L6427 = [0, 1, 5, 7, 22, 22], L6477 = [0, 1, 5, 9, 11, 11], L6481 = [0, 1, 5, 9, 11, 22], L6490 = [0, 1, 5, 9, 22, 22], L7919 = [0, 2, 4, 11, 16, 18], L7931 = [0, 2, 6, 8, 11, 16], L7934 = [0, 2, 6, 10, 11, 11], L7937 = [0, 2, 6, 10, 11, 22], L7939 = [0, 2, 6, 11, 11, 14], L7944 = [0, 2, 6, 11, 14, 22], L8049 = [0, 4, 8, 11, 11, 12], L8050 = [0, 4, 8, 11, 11, 16], L8053 = [0, 4, 8, 11, 12, 22], L8054 = [0, 4, 8, 11, 16, 22], L24282 = [1, 2, 6, 7, 13, 17], L24303 = [1, 2, 6, 7, 17, 18], L24466 = [1, 2, 6, 9, 15, 17], L24689 = [1, 2, 6, 13, 17, 18], L24733 = [1, 2, 6, 15, 17, 18], L26220 = [1, 2, 10, 15, 18, 19], L27315 = [1, 3, 4, 7, 12, 13], L27317 = [1, 3, 4, 7, 12, 16], L27339 = [1, 3, 4, 7, 16, 17], L27413 = [1, 3, 4, 8, 12, 13], L27889 = [1, 3, 5, 7, 9, 13], L27890 = [1, 3, 5, 7, 9, 15], L27892 = [1, 3, 5, 7, 9, 17], L27893 = [1, 3, 5, 7, 9, 19], L27895 = [1, 3, 5, 7, 9, 21], L27899 = [1, 3, 5, 7, 11, 13], L27904 = [1, 3, 5, 7, 11, 19], L27906 = [1, 3, 5, 7, 11, 21], L27918 = [1, 3, 5, 7, 13, 15], L27920 = [1, 3, 5, 7, 13, 17], L27922 = [1, 3, 5, 7, 13, 22], L27926 = [1, 3, 5, 7, 15, 21], L27935 = [1, 3, 5, 7, 17, 19], L27944 = [1, 3, 5, 7, 19, 21], L27945 = [1, 3, 5, 7, 19, 22], L27949 = [1, 3, 5, 7, 21, 22], L28032 = [1, 3, 5, 9, 11, 13], L28034 = [1, 3, 5, 9, 11, 15], L28036 = [1, 3, 5, 9, 11, 17], L28037 = [1, 3, 5, 9, 11, 19], L28039 = [1, 3, 5, 9, 11, 21], L28042 = [1, 3, 5, 9, 13, 15], L28044 = [1, 3, 5, 9, 13, 17], L28045 = [1, 3, 5, 9, 13, 19], L28047 = [1, 3, 5, 9, 13, 22], L28055 = [1, 3, 5, 9, 15, 22], L28062 = [1, 3, 5, 9, 17, 21], L28063 = [1, 3, 5, 9, 17, 22], L28066 = [1, 3, 5, 9, 19, 22], L28070 = [1, 3, 5, 9, 21, 22], L28074 = [1, 3, 5, 11, 11, 13], L28076 = [1, 3, 5, 11, 11, 15], L28097 = [1, 3, 5, 11, 13, 17], L28098 = [1, 3, 5, 11, 13, 19], L28100 = [1, 3, 5, 11, 13, 22], L28109 = [1, 3, 5, 11, 15, 17], L28111 = [1, 3, 5, 11, 15, 21], L28112 = [1, 3, 5, 11, 15, 22], L28204 = [1, 3, 5, 13, 17, 22], L28206 = [1, 3, 5, 13, 19, 22], L28209 = [1, 3, 5, 13, 22, 22], L28245 = [1, 3, 5, 15, 17, 22], L28249 = [1, 3, 5, 15, 21, 22], L28250 = [1, 3, 5, 15, 22, 22], L28399 = [1, 3, 7, 9, 11, 13], L28401 = [1, 3, 7, 9, 11, 19], L28406 =
APPENDIX
75
Table 4. (continued) n = 6 q 45
I {0}
indexes of I-isospectral families {585, 797}, {1221, 1224}, {3378, 3389}, {3454, 3755}, {3464, 3756}, {4184, 5312}, {4494, 4512}, {4743, 4764}, {5271, 5275}, {6688, 6692}, {6717, 6729}, {6722, 6733}, {19482, 19490}, {19529, 19570}, {19567, 19646}, {19590, 19645}, {19591, 19641}, {19839, 19861}, {19841, 19933}, {19964, 21536}, {19992, 21541}, {21523, 21554}, {22450, 27598}, {23113, 27629}, {23514, 23534}, {24370, 24389}, {24506, 24524}, {24635, 24699}, {24642, 24704}, {24646, 24706}, {24983, 25011}, {25598, 25613}, {25707, 25728}, {25770, 25812}, {25777, 25829}, {27384, 27388}, {27456, 27460}, {27520, 27532}, {27525, 27537}, {31407, 31411}, {31439, 31456}, {31445, 31460}, {31448, 31462}, {31509, 31534}, {31514, 31538}, {31517, 31540}, {31521, 31546} {0, 1} {19565, 19581}, {20364, 20430}, {24628, 24630}, {27513, 27515} {4} {31540, 31545} {2, 3, 4} {6285, 30417}, {6347, 6781}, {16028, 30468}, {21727, 29000}, {21995, 30492}, {25772, 31519}, {26114, 30487} {3, 4, 5} {6743, 6784}
[1, 3, 7, 9, 13, 22], L28412 = [1, 3, 7, 9, 19, 22], L28473 = [1, 3, 7, 11, 11, 11], L28475 = [1, 3, 7, 11, 11, 13], L28479 = [1, 3, 7, 11, 11, 19], L28481 = [1, 3, 7, 11, 11, 21], L28482 = [1, 3, 7, 11, 11, 22], L28495 = [1, 3, 7, 11, 13, 22], L28513 = [1, 3, 7, 11, 19, 22], L28517 = [1, 3, 7, 11, 21, 22], L28518 = [1, 3, 7, 11, 22, 22], L28562 = [1, 3, 7, 13, 22, 22], L28607 = [1, 3, 7, 19, 22, 22], L28613 = [1, 3, 7, 21, 22, 22], L28614 = [1, 3, 7, 22, 22, 22], L28894 = [1, 3, 8, 12, 13, 16], L29083 = [1, 3, 9, 11, 11, 11], L29084 = [1, 3, 9, 11, 11, 13], L29087 = [1, 3, 9, 11, 11, 19], L29088 = [1, 3, 9, 11, 11, 22], L29091 = [1, 3, 9, 11, 13, 22], L29099 = [1, 3, 9, 11, 19, 22], L29100 = [1, 3, 9, 11, 22, 22], L29106 = [1, 3, 9, 13, 22, 22], L29121 = [1, 3, 9, 19, 22, 22], L29122 = [1, 3, 9, 22, 22, 22], L29360 = [1, 3, 11, 11, 11, 13], L29363 = [1, 3, 11, 11, 11, 17], L29384 = [1, 3, 11, 11, 13, 22], L29404 = [1, 3, 11, 11, 17, 22], L29485 = [1, 3, 11, 13, 22, 22], L29555 = [1, 3, 11, 17, 22, 22], L29787 = [1, 3, 13, 22, 22, 22], L29966 = [1, 3, 17, 22, 22, 22], L31707 = [1, 4, 7, 8, 12, 13], L33317 = [1, 5, 7, 9, 11, 11], L33319 = [1, 5, 7, 9, 11, 22], L33321 = [1, 5, 7, 9, 22, 22], L33322 = [1, 5, 7, 11, 11, 11], L33325 = [1, 5, 7, 11, 11, 22], L33331 = [1, 5, 7, 11, 22, 22], L33341 = [1, 5, 7, 22, 22, 22], L33509 = [1, 5, 9, 11, 11, 11], L33513 = [1, 5, 9, 11, 11, 22], L33522 = [1, 5, 9, 11, 22, 22], L33538 = [1, 5, 9, 22, 22, 22], L37639 = [2, 4, 6, 8, 11, 18], L37643 = [2, 4, 6, 10, 11, 12], L37657 = [2, 4, 6, 11, 12, 16], L37662 = [2, 4, 6, 11, 14, 20], L37682 = [2, 4, 8, 10, 11, 12], L37718 = [2, 4, 10, 11, 12, 14], L37719 = [2, 4, 10, 11, 12, 16], L37746 = [2, 4, 11, 11, 16, 18], L37761 = [2, 4, 11, 12, 14, 20], L37782 = [2, 4, 11, 16, 18, 22], L37806 = [2, 6, 8, 11, 11, 16], L37813 = [2, 6, 8, 11, 16, 22], L37817 = [2, 6, 10, 11, 11, 11], L37820 = [2, 6, 10, 11, 11, 22], L37825 = [2, 6, 10, 11, 22, 22], L37827 = [2, 6, 11, 11, 11, 14], L37832 = [2, 6, 11, 11, 14, 22], L37841 = [2, 6, 11, 14, 22, 22], L38084 = [4, 8, 11, 11, 11, 12], L38085 = [4, 8, 11, 11, 11, 16], L38088 = [4, 8, 11, 11, 12, 22], L38089 = [4, 8, 11, 11, 16, 22], L38093 = [4, 8, 11, 12, 22, 22], L38094 = [4, 8, 11, 16, 22, 22]. q = 45 : L585 = [0, 0, 1, 2, 14, 19], L797 = [0, 0, 1, 4, 7, 11], L1221 = [0, 0, 3, 5, 6, 18], L1224 = [0, 0, 3, 5, 9, 12], L3378 = [0, 1, 2, 4, 7, 14], L3389 = [0, 1, 2, 4, 8, 13], L3454 = [0, 1, 2, 4, 14, 19], L3464 = [0, 1, 2, 4, 16, 17], L3755 = [0, 1, 2, 7, 8, 13], L3756 = [0, 1, 2, 7, 8, 14], L4184 = [0, 1, 2, 14, 15, 19], L4494 = [0, 1, 3, 4, 11, 19], L4512 = [0, 1, 3, 4, 14, 16], L4743 = [0, 1, 3, 6, 12, 19], L4764 = [0, 1, 3, 6, 17, 21], L5271 = [0, 1, 4, 6, 11, 19], L5275 = [0, 1, 4, 6, 14, 16], L5312 = [0, 1, 4, 7, 11, 15], L6285 = [0, 1, 8, 10, 17, 19], L6347 = [0, 1, 9, 9, 18, 18], L6688 = [0, 3, 5, 5, 6, 18], L6692 = [0, 3, 5, 5, 9, 12], L6717 = [0, 3, 5, 6, 10, 18], L6722 = [0, 3, 5, 6, 15, 18], L6729 = [0, 3, 5, 9, 10, 12], L6733 = [0, 3, 5, 9, 12, 15], L6743 = [0, 3, 5, 10, 15, 20], L6781 = [0, 5, 9, 9, 18, 18], L6784 = [0, 5, 9, 10, 15, 20], L16028 = [1, 1, 8, 10, 17, 19], L19482 = [1, 2, 4, 5, 13, 22],
76
EMILIO A. LAURET
Table 4. (continued) n = 6 q 46
I {0}
indexes of I-isospectral families {733, 737}, {800, 1045}, {819, 1043}, {5518, 5551}, {5537, 5540}, {5542, 5545}, {5549, 5639, 5643}, {5553, 5602}, {5557, 5590}, {5572, 5662}, {5574, 5600, 5641, 5660}, {5676, 5821}, {5952, 7118}, {6039, 7108}, {8495, 8497}, {8502, 8504}, {8509, 8522}, {26146, 27008}, {30713, 38021}, {31937, 33001}, {32053, 32059, 32066, 32085}, {32060, 32064}, {32062, 32078}, {32080, 32082, 32088, 32101, 32210, 32219, 32234}, {32087, 32216, 32223, 32368, 32634}, {32111, 32282}, {32214, 32222, 32246}, {32217, 32235}, {32221, 32629}, {32244, 32268}, {32245, 32254}, {32270, 32272, 32291, 32386, 32633, 32725}, {32273, 32636, 32650}, {32292, 32487}, {32301, 32443}, {32380, 32738}, {32388, 32483, 32645, 32730}, {32788, 33356}, {33832, 38055}, {34112, 38025}, {41967, 41968}, {41971, 41973}, {41976, 41981}, {41980, 41983, 41986}, {41990, 41993, 42008, 42023}, {42002, 42005}, {42003, 42007}, {42013, 42015}, {42017, 42019}, {42021, 42040}, {42028, 42043} {0, 1} {32082, 32219}, {32272, 32725}
L19490 = [1, 2, 4, 5, 14, 22], L19529 = [1, 2, 4, 7, 8, 19], L19565 = [1, 2, 4, 7, 11, 17], L19567 = [1, 2, 4, 7, 11, 19], L19570 = [1, 2, 4, 7, 11, 22], L19581 = [1, 2, 4, 7, 13, 14], L19590 = [1, 2, 4, 7, 14, 15], L19591 = [1, 2, 4, 7, 14, 16], L19641 = [1, 2, 4, 8, 11, 19], L19645 = [1, 2, 4, 8, 13, 15], L19646 = [1, 2, 4, 8, 13, 17], L19839 = [1, 2, 4, 11, 13, 14], L19841 = [1, 2, 4, 11, 13, 16], L19861 = [1, 2, 4, 11, 16, 17], L19933 = [1, 2, 4, 13, 14, 19], L19964 = [1, 2, 4, 14, 15, 19], L19992 = [1, 2, 4, 15, 16, 17], L20364 = [1, 2, 5, 7, 11, 20], L20430 = [1, 2, 5, 8, 10, 19], L21523 = [1, 2, 7, 8, 11, 19], L21536 = [1, 2, 7, 8, 13, 15], L21541 = [1, 2, 7, 8, 14, 15], L21554 = [1, 2, 7, 8, 16, 19], L21727 = [1, 2, 7, 11, 16, 20], L21995 = [1, 2, 8, 10, 17, 19], L22450 = [1, 2, 9, 14, 18, 19], L23113 = [1, 2, 14, 15, 15, 19], L23514 = [1, 3, 3, 4, 11, 19], L23534 = [1, 3, 3, 4, 14, 16], L24370 = [1, 3, 4, 6, 11, 19], L24389 = [1, 3, 4, 6, 14, 16], L24506 = [1, 3, 4, 9, 11, 19], L24524 = [1, 3, 4, 9, 14, 16], L24628 = [1, 3, 4, 11, 14, 16], L24630 = [1, 3, 4, 11, 14, 19], L24635 = [1, 3, 4, 11, 15, 19], L24642 = [1, 3, 4, 11, 18, 19], L24646 = [1, 3, 4, 11, 19, 21], L24699 = [1, 3, 4, 14, 15, 16], L24704 = [1, 3, 4, 14, 16, 18], L24706 = [1, 3, 4, 14, 16, 21], L24983 = [1, 3, 5, 6, 12, 19], L25011 = [1, 3, 5, 6, 17, 21], L25598 = [1, 3, 6, 8, 12, 19], L25613 = [1, 3, 6, 8, 17, 21], L25707 = [1, 3, 6, 10, 12, 19], L25728 = [1, 3, 6, 10, 17, 21], L25770 = [1, 3, 6, 12, 15, 19], L25772 = [1, 3, 6, 12, 15, 21], L25777 = [1, 3, 6, 12, 19, 20], L25812 = [1, 3, 6, 15, 17, 21], L25829 = [1, 3, 6, 17, 20, 21], L26114 = [1, 3, 8, 10, 17, 19], L27384 = [1, 4, 6, 6, 11, 19], L27388 = [1, 4, 6, 6, 14, 16], L27456 = [1, 4, 6, 9, 11, 19], L27460 = [1, 4, 6, 9, 14, 16], L27513 = [1, 4, 6, 11, 14, 16], L27515 = [1, 4, 6, 11, 14, 19], L27520 = [1, 4, 6, 11, 15, 19], L27525 = [1, 4, 6, 11, 18, 19], L27532 = [1, 4, 6, 14, 15, 16], L27537 = [1, 4, 6, 14, 16, 18], L27598 = [1, 4, 7, 9, 11, 18], L27629 = [1, 4, 7, 11, 15, 15], L29000 = [1, 5, 8, 10, 17, 19], L30417 = [1, 8, 9, 10, 17, 19], L30468 = [1, 8, 10, 10, 17, 19], L30487 = [1, 8, 10, 15, 17, 19], L30492 = [1, 8, 10, 17, 19, 20], L31407 = [3, 5, 5, 5, 6, 18], L31411 = [3, 5, 5, 5, 9, 12], L31439 = [3, 5, 5, 6, 10, 18], L31445 = [3, 5, 5, 6, 15, 18], L31448 = [3, 5, 5, 6, 18, 20], L31456 = [3, 5, 5, 9, 10, 12], L31460 = [3, 5, 5, 9, 12, 15], L31462 = [3, 5, 5, 9, 12, 20], L31509 = [3, 5, 6, 9, 18, 18], L31514 = [3, 5, 6, 10, 15, 18], L31517 = [3, 5, 6, 10, 18, 20], L31519 = [3, 5, 6, 12, 15, 21], L31521 = [3, 5, 6, 15, 15, 18], L31534 = [3, 5, 9, 9, 12, 18], L31538 = [3, 5, 9, 10, 12, 15], L31540 = [3, 5, 9, 10, 12, 20], L31545 = [3, 5, 9, 10, 18, 20], L31546 = [3, 5, 9, 12, 15, 15]. q = 46 : L733 = [0, 0, 1, 3, 5, 11], L737 = [0, 0, 1, 3, 5, 15], L800 = [0, 0, 1, 3, 11, 17], L819 = [0, 0, 1, 3, 13, 19], L1043 = [0, 0, 1, 5, 9, 11], L1045 = [0, 0, 1, 5, 9, 13], L5518 = [0, 1, 3, 5, 7, 19], L5537 = [0, 1, 3, 5, 9, 11], L5540 = [0, 1, 3, 5, 9, 15], L5542 = [0, 1, 3, 5, 9, 17], L5545 = [0, 1, 3, 5, 9, 21],
APPENDIX
77
Table 4. (continued) n = 6 48 {0} {788, 798}, {967, 1002}, {1145, 1149}, {1177, 1182}, {1310, 1377}, {1315, 1318}, {1483, 1489}, {1812, 1817}, {2205, 2209}, {3534, 3537}, {4482, 4487}, {5164, 5174}, {5629, 5639}, {5828, 6128}, {5837, 6127}, {5844, 5848}, {5985, 5995}, {6119, 6124}, {6263, 6273}, {6497, 6506}, {6580, 6590}, {6592, 6610}, {6594, 6627}, {6596, 6639}, {6598, 6647}, {6602, 6653}, {7498, 7500}, {7515, 7538}, {7522, 7545}, {7630, 7665}, {7784, 7920}, {7832, 8075}, {7848, 7869}, {7851, 8107}, {7853, 8114}, {7858, 8116}, {8655, 8659}, {8687, 8692}, {8826, 8830}, {8854, 8858}, {8889, 8893}, {8915, 8919}, {8929, 8933}, {8939, 8949}, {8977, 8982}, {9030, 9038}, {9124, 9129}, {9157, 9162}, {9178, 9183}, {9185, 9195}, {9190, 9203}, {9436, 9442}, {9809, 10220}, {9814, 9817}, {9835, 10032}, {9840, 9843}, {9867, 10174}, {9872, 9875}, {9878, 10216}, {9884, 10222}, {9896, 9899}, {9915, 9922}, {9946, 9949}, {9948, 9950}, {10382, 10388}, L5549 = [0, 1, 3, 5, 11, 13], L5551 = [0, 1, 3, 5, 11, 15], L5553 = [0, 1, 3, 5, 11, 17], L5557 = [0, 1, 3, 5, 11, 23], L5572 = [0, 1, 3, 5, 13, 17], L5574 = [0, 1, 3, 5, 13, 19], L5590 = [0, 1, 3, 5, 15, 23], L5600 = [0, 1, 3, 5, 17, 19], L5602 = [0, 1, 3, 5, 17, 21], L5639 = [0, 1, 3, 7, 9, 13], L5641 = [0, 1, 3, 7, 9, 17], L5643 = [0, 1, 3, 7, 9, 21], L5660 = [0, 1, 3, 7, 11, 15], L5662 = [0, 1, 3, 7, 11, 17], L5676 = [0, 1, 3, 7, 13, 17], L5821 = [0, 1, 3, 9, 11, 17], L5952 = [0, 1, 3, 11, 17, 23], L6039 = [0, 1, 3, 13, 19, 23], L7108 = [0, 1, 5, 9, 11, 23], L7118 = [0, 1, 5, 9, 13, 23], L8495 = [0, 2, 4, 8, 10, 23], L8497 = [0, 2, 4, 8, 16, 23], L8502 = [0, 2, 4, 10, 14, 23], L8504 = [0, 2, 4, 10, 18, 23], L8509 = [0, 2, 4, 12, 20, 23], L8522 = [0, 2, 6, 8, 18, 23], L26146 = [1, 2, 4, 10, 18, 21], L27008 = [1, 2, 5, 10, 14, 18], L30713 = [1, 2, 13, 18, 19, 21], L31937 = [1, 3, 4, 14, 19, 20], L32053 = [1, 3, 5, 7, 9, 19], L32059 = [1, 3, 5, 7, 11, 13], L32060 = [1, 3, 5, 7, 11, 15], L32062 = [1, 3, 5, 7, 11, 17], L32064 = [1, 3, 5, 7, 11, 19], L32066 = [1, 3, 5, 7, 11, 21], L32078 = [1, 3, 5, 7, 13, 15], L32080 = [1, 3, 5, 7, 13, 17], L32082 = [1, 3, 5, 7, 13, 21], L32085 = [1, 3, 5, 7, 15, 17], L32087 = [1, 3, 5, 7, 15, 19], L32088 = [1, 3, 5, 7, 15, 21], L32101 = [1, 3, 5, 7, 17, 21], L32111 = [1, 3, 5, 7, 19, 23], L32210 = [1, 3, 5, 9, 11, 13], L32214 = [1, 3, 5, 9, 11, 17], L32216 = [1, 3, 5, 9, 11, 21], L32217 = [1, 3, 5, 9, 11, 23], L32219 = [1, 3, 5, 9, 13, 15], L32221 = [1, 3, 5, 9, 13, 17], L32222 = [1, 3, 5, 9, 13, 19], L32223 = [1, 3, 5, 9, 13, 21], L32234 = [1, 3, 5, 9, 15, 17], L32235 = [1, 3, 5, 9, 15, 23], L32244 = [1, 3, 5, 9, 17, 21], L32245 = [1, 3, 5, 9, 17, 23], L32246 = [1, 3, 5, 9, 19, 21], L32254 = [1, 3, 5, 9, 21, 23], L32268 = [1, 3, 5, 11, 13, 15], L32270 = [1, 3, 5, 11, 13, 17], L32272 = [1, 3, 5, 11, 13, 21], L32273 = [1, 3, 5, 11, 13, 23], L32282 = [1, 3, 5, 11, 15, 23], L32291 = [1, 3, 5, 11, 17, 21], L32292 = [1, 3, 5, 11, 17, 23], L32301 = [1, 3, 5, 11, 23, 23], L32368 = [1, 3, 5, 13, 15, 19], L32380 = [1, 3, 5, 13, 17, 23], L32386 = [1, 3, 5, 13, 19, 21], L32388 = [1, 3, 5, 13, 19, 23], L32443 = [1, 3, 5, 15, 23, 23], L32483 = [1, 3, 5, 17, 19, 23], L32487 = [1, 3, 5, 17, 21, 23], L32629 = [1, 3, 7, 9, 11, 17], L32633 = [1, 3, 7, 9, 13, 17], L32634 = [1, 3, 7, 9, 13, 21], L32636 = [1, 3, 7, 9, 13, 23], L32645 = [1, 3, 7, 9, 17, 23], L32650 = [1, 3, 7, 9, 21, 23], L32725 = [1, 3, 7, 11, 13, 17], L32730 = [1, 3, 7, 11, 15, 23], L32738 = [1, 3, 7, 11, 17, 23], L32788 = [1, 3, 7, 13, 17, 23], L33001 = [1, 3, 8, 9, 14, 22], L33356 = [1, 3, 9, 11, 17, 23], L33832 = [1, 3, 11, 17, 23, 23], L34112 = [1, 3, 13, 19, 23, 23], L38021 = [1, 5, 9, 11, 14, 16], L38025 = [1, 5, 9, 11, 23, 23], L38055 = [1, 5, 9, 13, 23, 23], L41967 = [2, 4, 6, 8, 14, 23], L41968 = [2, 4, 6, 8, 16, 23], L41971 = [2, 4, 6, 8, 22, 23], L41973 = [2, 4, 6, 10, 12, 23], L41976 = [2, 4, 6, 10, 18, 23], L41980 = [2, 4, 6, 12, 14, 23], L41981 = [2, 4, 6, 12, 16, 23], L41983 = [2, 4, 6, 12, 20, 23], L41986 = [2, 4, 6, 14, 18, 23], L41990 = [2, 4, 6, 16, 20, 23], L41993 = [2, 4, 6, 18, 20, 23], L42002 = [2, 4, 8, 10, 22, 23], L42003 = [2, 4, 8, 10, 23, 23], L42005 = [2, 4, 8, 14, 22, 23], L42007 = [2, 4, 8, 16, 23, 23], L42008 = [2, 4, 8, 18, 20, 23], L42013 = [2, 4, 10, 12, 16, 23], L42015 = [2, 4, 10, 12, 20, 23], L42017 = [2, 4, 10, 14, 23, 23], L42019 = [2, 4, 10, 18, 23, 23], L42021 = [2, 4, 12, 14, 20, 23], L42023 = [2, 4, 12, 16, 18, 23], L42028 = [2, 4, 12, 20, 23, 23], L42040 = [2, 6, 8, 10, 14, 23], L42043 = [2, 6, 8, 18, 23, 23]. q = 48 : L788 = [0, 0, 1, 2, 11, 13], L798 = [0, 0, 1, 2, 11, 23], L967 = [0, 0, 1, 3, 7, 15], L1002 = [0, 0, 1, 3, 9, 17], L1145 = [0, 0, 1, 4, 5, 19], L1149 = [0, 0, 1, 4, 5, 23], L1177 = [0, 0, 1, 4, 7, 17], L1182 =
78
EMILIO A. LAURET
Table 4. (continued) n = 6 48 {0} {10542, 10548}, {10724, 10730}, {10800, 10806}, {10808, 10819}, {10809, 10825}, (cont.) {10811, 10832}, {10814, 10836}, {11452, 11457}, {12192, 12197}, {12265, 12270}, {12273, 12284}, {12274, 12288}, {12276, 12292}, {13301, 13305}, {13607, 13611}, {13692, 13696}, {13763, 13767}, {13833, 13837}, {13840, 13843}, {13846, 13855}, {13847, 13860}, {13848, 13863}, {13851, 13866}, {14514, 14518}, {14659, 14662}, {14682, 14685}, {22897, 22902}, {23466, 23469}, {23502, 23505}, {23529, 23532}, {23551, 23559}, {27518, 27523}, {29442, 29447}, {29450, 29460}, {29452, 29468}, {29455, 29473}, {31574, 31584}, {32039, 32049}, {32401, 32411}, {32690, 32700}, {32927, 32937}, {33022, 33032}, {33034, 33054}, {33036, 33072}, {33038, 33085}, {33040, 33094}, {33042, 33100}, {33044, 33102}, {34381, 34661}, {35436, 35446}, {35605, 35609}, {35653, 35657}, {35795, 35805}, {35929, 35935}, {35939, 35962}, {35975, 35980}, {36081, 36091}, {36315, 36325}, {36409, 36419}, {36421, 36440}, {36423, 36457}, {36425, 36469}, {36427, 36477}, {36431, 36483}, {36757, 42926}, [0, 0, 1, 4, 7, 23], L1310 = [0, 0, 1, 5, 6, 13], L1315 = [0, 0, 1, 5, 6, 19], L1318 = [0, 0, 1, 5, 6, 23], L1377 = [0, 0, 1, 5, 13, 18], L1483 = [0, 0, 1, 6, 11, 13], L1489 = [0, 0, 1, 6, 11, 23], L1812 = [0, 0, 1, 10, 11, 13], L1817 = [0, 0, 1, 10, 11, 23], L2205 = [0, 0, 2, 3, 9, 15], L2209 = [0, 0, 2, 3, 9, 21], L3534 = [0, 1, 1, 5, 5, 19], L3537 = [0, 1, 1, 5, 5, 23], L4482 = [0, 1, 1, 11, 11, 13], L4487 = [0, 1, 1, 11, 11, 23], L5164 = [0, 1, 2, 2, 11, 13], L5174 = [0, 1, 2, 2, 11, 23], L5629 = [0, 1, 2, 4, 11, 13], L5639 = [0, 1, 2, 4, 11, 23], L5828 = [0, 1, 2, 5, 13, 14], L5837 = [0, 1, 2, 5, 13, 23], L5844 = [0, 1, 2, 5, 14, 19], L5848 = [0, 1, 2, 5, 14, 23], L5985 = [0, 1, 2, 6, 11, 13], L5995 = [0, 1, 2, 6, 11, 23], L6119 = [0, 1, 2, 7, 10, 17], L6124 = [0, 1, 2, 7, 10, 23], L6127 = [0, 1, 2, 7, 11, 13], L6128 = [0, 1, 2, 7, 11, 14], L6263 = [0, 1, 2, 8, 11, 13], L6273 = [0, 1, 2, 8, 11, 23], L6497 = [0, 1, 2, 10, 11, 13], L6506 = [0, 1, 2, 10, 11, 23], L6580 = [0, 1, 2, 11, 12, 13], L6590 = [0, 1, 2, 11, 12, 23], L6592 = [0, 1, 2, 11, 13, 14], L6594 = [0, 1, 2, 11, 13, 16], L6596 = [0, 1, 2, 11, 13, 18], L6598 = [0, 1, 2, 11, 13, 20], L6602 = [0, 1, 2, 11, 13, 24], L6610 = [0, 1, 2, 11, 14, 23], L6627 = [0, 1, 2, 11, 16, 23], L6639 = [0, 1, 2, 11, 18, 23], L6647 = [0, 1, 2, 11, 20, 23], L6653 = [0, 1, 2, 11, 23, 24], L7498 = [0, 1, 3, 5, 9, 11], L7500 = [0, 1, 3, 5, 9, 13], L7515 = [0, 1, 3, 5, 11, 15], L7522 = [0, 1, 3, 5, 11, 23], L7538 = [0, 1, 3, 5, 13, 15], L7545 = [0, 1, 3, 5, 13, 23], L7630 = [0, 1, 3, 6, 7, 15], L7665 = [0, 1, 3, 6, 9, 17], L7784 = [0, 1, 3, 7, 8, 15], L7832 = [0, 1, 3, 7, 12, 15], L7848 = [0, 1, 3, 7, 13, 23], L7851 = [0, 1, 3, 7, 15, 16], L7853 = [0, 1, 3, 7, 15, 18], L7858 = [0, 1, 3, 7, 15, 24], L7869 = [0, 1, 3, 7, 17, 19], L7920 = [0, 1, 3, 8, 9, 17], L8075 = [0, 1, 3, 9, 12, 17], L8102 = [0, 1, 3, 9, 15, 21], L8107 = [0, 1, 3, 9, 16, 17], L8114 = [0, 1, 3, 9, 17, 18], L8116 = [0, 1, 3, 9, 17, 24], L8655 = [0, 1, 4, 4, 5, 19], L8659 = [0, 1, 4, 4, 5, 23], L8687 = [0, 1, 4, 4, 7, 17], L8692 = [0, 1, 4, 4, 7, 23], L8826 = [0, 1, 4, 5, 6, 19], L8830 = [0, 1, 4, 5, 6, 23], L8854 = [0, 1, 4, 5, 8, 19], L8858 = [0, 1, 4, 5, 8, 23], L8889 = [0, 1, 4, 5, 12, 19], L8893 = [0, 1, 4, 5, 12, 23], L8915 = [0, 1, 4, 5, 16, 19], L8919 = [0, 1, 4, 5, 16, 23], L8929 = [0, 1, 4, 5, 18, 19], L8933 = [0, 1, 4, 5, 18, 23], L8939 = [0, 1, 4, 5, 19, 24], L8949 = [0, 1, 4, 5, 23, 24], L8977 = [0, 1, 4, 6, 7, 17], L8982 = [0, 1, 4, 6, 7, 23], L9030 = [0, 1, 4, 6, 11, 13], L9038 = [0, 1, 4, 6, 11, 23], L9124 = [0, 1, 4, 7, 8, 17], L9129 = [0, 1, 4, 7, 8, 23], L9157 = [0, 1, 4, 7, 12, 17], L9162 = [0, 1, 4, 7, 12, 23], L9178 = [0, 1, 4, 7, 16, 17], L9183 = [0, 1, 4, 7, 16, 23], L9185 = [0, 1, 4, 7, 17, 18], L9190 = [0, 1, 4, 7, 17, 24], L9195 = [0, 1, 4, 7, 18, 23], L9203 = [0, 1, 4, 7, 23, 24], L9436 = [0, 1, 4, 10, 11, 13], L9442 = [0, 1, 4, 10, 11, 23], L9809 = [0, 1, 5, 6, 6, 13], L9814 = [0, 1, 5, 6, 6, 19], L9817 = [0, 1, 5, 6, 6, 23], L9835 = [0, 1, 5, 6, 8, 13], L9840 = [0, 1, 5, 6, 8, 19], L9843 = [0, 1, 5, 6, 8, 23], L9867 = [0, 1, 5, 6, 12, 13], L9872 = [0, 1, 5, 6, 12, 19], L9875 = [0, 1, 5, 6, 12, 23], L9878 = [0, 1, 5, 6, 13, 16], L9884 = [0, 1, 5, 6, 13, 24], L9896 = [0, 1, 5, 6, 16, 19], L9899 = [0, 1, 5, 6, 16, 23], L9915 = [0, 1, 5, 6, 19, 24], L9922 = [0, 1, 5, 6, 23, 24], L9946 = [0, 1, 5, 7, 11, 13], L9948 = [0, 1, 5, 7, 11, 17], L9949 = [0, 1, 5, 7, 11, 19], L9950 = [0, 1, 5, 7, 11, 23], L9972 = [0, 1, 5, 7, 17, 19], L10032 = [0, 1, 5, 8, 13, 18], L10174 = [0, 1, 5, 12, 13, 18], L10216 = [0, 1, 5, 13, 16, 18], L10220 = [0, 1, 5, 13, 18, 18], L10222 = [0, 1, 5, 13, 18, 24], L10382 = [0, 1, 6, 6, 11, 13], L10388 = [0, 1, 6, 6, 11, 23], L10542 = [0, 1, 6, 8, 11, 13], L10548 = [0, 1, 6, 8, 11, 23], L10724 = [0, 1, 6, 10, 11, 13], L10730 = [0, 1, 6, 10, 11, 23], L10800 = [0, 1, 6, 11, 12, 13], L10806 =
APPENDIX
79
Table 4. (continued) n = 6 48 {0} {36905, 36908}, {36936, 38173}, {36952, 36956}, {37220, 39103}, {37229, 39102}, (cont.) {37236, 37240}, {37438, 37444}, {37575, 39408}, {37584, 39407}, {37591, 37595}, {37650, 39427}, {37652, 39428}, {37654, 41821}, {37656, 39328}, {37658, 39431}, {37676, 39419}, {37705, 39426}, {37730, 37734}, {37743, 37747}, {37749, 37757}, {37753, 37765}, {38030, 38040}, {38164, 38169}, {38308, 38318}, {38543, 38552}, {38626, 38636}, {38638, 38657}, {38640, 38674}, {38642, 38687}, {38644, 38696}, {38646, 38701}, {38648, 38703}, {39094, 39099}, {39342, 39347}, {39374, 39379}, {39381, 39391}, {39382, 39396}, {39386, 39404}, {39826, 39836}, {40060, 40069}, {40143, 40153}, {40155, 40173}, {40157, 40190}, {40159, 40202}, {40161, 40210}, {40165, 40216}, {41230, 41239}, {41313, 41322}, {41324, 41341}, {41326, 41356}, {41328, 41366}, {41329, 41371}, {41331, 41376}, {41333, 41378}, {41666, 41676}, {41678, 41696}, {41680, 41713}, {41682, 41725}, {41684, 41733}, {41688, 41739}, {41741, 41799}, {41743, 41813}, {41744, 41819}, {41746, 41826}, {41749, 41830}, {41758, 41873}, {41760, 41885}, {41762, 41893}, {41766, 41899}, {41772, 41922}, {41774, 41929}, {41777, 41933}, {41781, 41944}, {41785, 41950}, {41791, 41958}, {43947, 44224}, {45407, 45429}, {46079, 51355}, {46449, 46661, 46691}, {46450, 46633, 46655}, [0, 1, 6, 11, 12, 23], L10808 = [0, 1, 6, 11, 13, 14], L10809 = [0, 1, 6, 11, 13, 16], L10811 = [0, 1, 6, 11, 13, 20], L10814 = [0, 1, 6, 11, 13, 24], L10819 = [0, 1, 6, 11, 14, 23], L10825 = [0, 1, 6, 11, 16, 23], L10832 = [0, 1, 6, 11, 20, 23], L10836 = [0, 1, 6, 11, 23, 24], L11452 = [0, 1, 8, 10, 11, 13], L11457 = [0, 1, 8, 10, 11, 23], L12192 = [0, 1, 10, 10, 11, 13], L12197 = [0, 1, 10, 10, 11, 23], L12265 = [0, 1, 10, 11, 12, 13], L12270 = [0, 1, 10, 11, 12, 23], L12273 = [0, 1, 10, 11, 13, 16], L12274 = [0, 1, 10, 11, 13, 20], L12276 = [0, 1, 10, 11, 13, 24], L12284 = [0, 1, 10, 11, 16, 23], L12288 = [0, 1, 10, 11, 20, 23], L12292 = [0, 1, 10, 11, 23, 24], L13301 = [0, 2, 2, 3, 9, 15], L13305 = [0, 2, 2, 3, 9, 21], L13607 = [0, 2, 3, 4, 9, 15], L13611 = [0, 2, 3, 4, 9, 21], L13692 = [0, 2, 3, 6, 9, 15], L13696 = [0, 2, 3, 6, 9, 21], L13763 = [0, 2, 3, 8, 9, 15], L13767 = [0, 2, 3, 8, 9, 21], L13833 = [0, 2, 3, 9, 12, 15], L13837 = [0, 2, 3, 9, 12, 21], L13840 = [0, 2, 3, 9, 14, 15], L13843 = [0, 2, 3, 9, 14, 21], L13846 = [0, 2, 3, 9, 15, 16], L13847 = [0, 2, 3, 9, 15, 18], L13848 = [0, 2, 3, 9, 15, 20], L13849 = [0, 2, 3, 9, 15, 21], L13851 = [0, 2, 3, 9, 15, 24], L13855 = [0, 2, 3, 9, 16, 21], L13860 = [0, 2, 3, 9, 18, 21], L13863 = [0, 2, 3, 9, 20, 21], L13866 = [0, 2, 3, 9, 21, 24], L14514 = [0, 3, 4, 6, 9, 15], L14518 = [0, 3, 4, 6, 9, 21], L14582 = [0, 3, 4, 9, 15, 21], L14659 = [0, 3, 6, 8, 9, 15], L14662 = [0, 3, 6, 8, 9, 21], L14682 = [0, 3, 6, 9, 15, 16], L14685 = [0, 3, 6, 9, 16, 21], L14734 = [0, 3, 8, 9, 15, 21], L14735 = [0, 3, 8, 9, 15, 24], L14774 = [0, 3, 9, 15, 16, 21], L14775 = [0, 3, 9, 15, 16, 24], L20984 = [1, 1, 3, 9, 15, 21], L22897 = [1, 1, 4, 11, 11, 13], L22902 = [1, 1, 4, 11, 11, 23], L23466 = [1, 1, 5, 5, 8, 19], L23469 = [1, 1, 5, 5, 8, 23], L23502 = [1, 1, 5, 5, 12, 19], L23505 = [1, 1, 5, 5, 12, 23], L23529 = [1, 1, 5, 5, 16, 19], L23532 = [1, 1, 5, 5, 16, 23], L23551 = [1, 1, 5, 5, 19, 24], L23559 = [1, 1, 5, 5, 23, 24], L27518 = [1, 1, 8, 11, 11, 13], L27523 = [1, 1, 8, 11, 11, 23], L29442 = [1, 1, 11, 11, 12, 13], L29447 = [1, 1, 11, 11, 12, 23], L29450 = [1, 1, 11, 11, 13, 16], L29452 = [1, 1, 11, 11, 13, 20], L29455 = [1, 1, 11, 11, 13, 24], L29460 = [1, 1, 11, 11, 16, 23], L29468 = [1, 1, 11, 11, 20, 23], L29473 = [1, 1, 11, 11, 23, 24], L31574 = [1, 2, 2, 2, 11, 13], L31584 = [1, 2, 2, 2, 11, 23], L32039 = [1, 2, 2, 4, 11, 13], L32049 = [1, 2, 2, 4, 11, 23], L32401 = [1, 2, 2, 6, 11, 13], L32411 = [1, 2, 2, 6, 11, 23], L32690 = [1, 2, 2, 8, 11, 13], L32700 = [1, 2, 2, 8, 11, 23], L32927 = [1, 2, 2, 10, 11, 13], L32937 = [1, 2, 2, 10, 11, 23], L33022 = [1, 2, 2, 11, 12, 13], L33032 = [1, 2, 2, 11, 12, 23], L33034 = [1, 2, 2, 11, 13, 14], L33036 = [1, 2, 2, 11, 13, 16], L33038 = [1, 2, 2, 11, 13, 18], L33040 = [1, 2, 2, 11, 13, 20], L33042 = [1, 2, 2, 11, 13, 22], L33044 = [1, 2, 2, 11, 13, 24], L33054 = [1, 2, 2, 11, 14, 23], L33072 = [1, 2, 2, 11, 16, 23], L33085 = [1, 2, 2, 11, 18, 23], L33094 = [1, 2, 2, 11, 20, 23], L33100 = [1, 2, 2, 11, 22, 23], L33102 = [1, 2, 2, 11, 23, 24], L34381 = [1, 2, 3, 7, 14, 15], L34661 = [1, 2, 3, 9, 14, 17], L34675 = [1, 2, 3, 9, 15, 21], L35436 = [1, 2, 4, 4, 11, 13], L35446 = [1, 2, 4, 4, 11, 23], L35605 = [1, 2, 4, 5, 10, 19], L35609 = [1, 2, 4, 5, 10, 23], L35653 = [1, 2, 4, 5, 14, 19], L35657 = [1, 2, 4, 5, 14, 23],
80
EMILIO A. LAURET
Table 4. (continued) n = 6 48 {0} {46510, 46512}, {46527, 46550}, {46534, 46557}, {46630, 46642}, {46634, 46656}, (cont.) {46638, 46674}, {46639, 48295}, {46640, 46662}, {46692, 48299}, {46722, 46800}, {46729, 46807}, {46750, 46876}, {46755, 46881}, {46762, 46888}, {46784, 46912}, {46880, 48313}, {47144, 47179}, {47298, 47434}, {47346, 47590}, {47365, 47624}, {47367, 47631}, {47372, 47633}, {48157, 48735}, {48205, 48890}, {48221, 48242}, {48224, 48922}, {48226, 48929}, {48231, 48931}, {48318, 49497}, {48402, 49606}, {48477, 49681}, {48493, 48514}, {48496, 49713}, {48498, 49720}, {48503, 49722}, {48553, 48623}, {48570, 48656}, {48581, 49848}, {48583, 49855}, {48588, 49857}, {48594, 49878}, {48599, 49880}, {48612, 49883}, {51691, 51695}, {51723, 51728}, {51862, 51866}, {51890, 51894}, {51925, 51929}, {51951, 51955}, {51965, 51969}, {51975, 51987}, {52015, 52020}, {52068, 52076}, {52163, 52168}, {52196, 52201}, {52219, 52224}, {52226, 52236}, {52231, 52248}, {52482, 52488}, {52872, 52876}, {52900, 52904}, {52935, 52939}, {52946, 53397}, {52962, 52966}, {52976, 52980}, {52982, 52989}, {52986, 52997}, {53023, 53026}, {53025, 53028}, {53042, 53044}, {53087, 53091}, {53122, 53126}, {53148, 53152}, {53162, 53166}, {53172, 53182}, {53291, 53294}, {53318, 53322}, {53344, 53348}, {53358, 53362}, {53368, 53378}, {53436, 53447}, {53454, 53458}, {53468, 53472}, {53478, 53488}, {53512, 53516}, {53521, 53531}, {53542, 53560}, {53588, 53593}, {53641, 53649}, {53736, 53741}, {53769, 53774}, {53791, 53796}, {53798, 53808}, {53803, 53816}, {53864, 53872}, {54063, 54070}, {54141, 54149}, {54151, 54164}, {54152, 54172}, {54155, 54185}, {54158, 54189}, {54502, 54507}, {54535, 54540}, {54556, 54561}, {54563, 54573}, L35795 = [1, 2, 4, 6, 11, 13], L35805 = [1, 2, 4, 6, 11, 23], L35929 = [1, 2, 4, 7, 10, 17], L35935 = [1, 2, 4, 7, 10, 23], L35939 = [1, 2, 4, 7, 11, 14], L35962 = [1, 2, 4, 7, 13, 14], L35975 = [1, 2, 4, 7, 14, 17], L35980 = [1, 2, 4, 7, 14, 23], L36081 = [1, 2, 4, 8, 11, 13], L36091 = [1, 2, 4, 8, 11, 23], L36315 = [1, 2, 4, 10, 11, 13], L36325 = [1, 2, 4, 10, 11, 23], L36409 = [1, 2, 4, 11, 12, 13], L36419 = [1, 2, 4, 11, 12, 23], L36421 = [1, 2, 4, 11, 13, 14], L36423 = [1, 2, 4, 11, 13, 16], L36425 = [1, 2, 4, 11, 13, 18], L36427 = [1, 2, 4, 11, 13, 20], L36431 = [1, 2, 4, 11, 13, 24], L36440 = [1, 2, 4, 11, 14, 23], L36457 = [1, 2, 4, 11, 16, 23], L36469 = [1, 2, 4, 11, 18, 23], L36477 = [1, 2, 4, 11, 20, 23], L36483 = [1, 2, 4, 11, 23, 24], L36757 = [1, 2, 4, 17, 19, 22], L36905 = [1, 2, 5, 6, 10, 19], L36908 = [1, 2, 5, 6, 10, 23], L36936 = [1, 2, 5, 6, 13, 14], L36952 = [1, 2, 5, 6, 14, 19], L36956 = [1, 2, 5, 6, 14, 23], L37220 = [1, 2, 5, 8, 13, 14], L37229 = [1, 2, 5, 8, 13, 23], L37236 = [1, 2, 5, 8, 14, 19], L37240 = [1, 2, 5, 8, 14, 23], L37438 = [1, 2, 5, 10, 13, 14], L37444 = [1, 2, 5, 10, 13, 22], L37575 = [1, 2, 5, 12, 13, 14], L37584 = [1, 2, 5, 12, 13, 23], L37591 = [1, 2, 5, 12, 14, 19], L37595 = [1, 2, 5, 12, 14, 23], L37650 = [1, 2, 5, 13, 14, 16], L37652 = [1, 2, 5, 13, 14, 18], L37654 = [1, 2, 5, 13, 14, 20], L37656 = [1, 2, 5, 13, 14, 22], L37658 = [1, 2, 5, 13, 14, 24], L37676 = [1, 2, 5, 13, 16, 23], L37705 = [1, 2, 5, 13, 23, 24], L37730 = [1, 2, 5, 14, 16, 19], L37734 = [1, 2, 5, 14, 16, 23], L37743 = [1, 2, 5, 14, 18, 19], L37747 = [1, 2, 5, 14, 18, 23], L37749 = [1, 2, 5, 14, 19, 20], L37753 = [1, 2, 5, 14, 19, 24], L37757 = [1, 2, 5, 14, 20, 23], L37765 = [1, 2, 5, 14, 23, 24], L38030 = [1, 2, 6, 6, 11, 13], L38040 = [1, 2, 6, 6, 11, 23], L38164 = [1, 2, 6, 7, 10, 17], L38169 = [1, 2, 6, 7, 10, 23], L38173 = [1, 2, 6, 7, 11, 14], L38308 = [1, 2, 6, 8, 11, 13], L38318 = [1, 2, 6, 8, 11, 23], L38543 = [1, 2, 6, 10, 11, 13], L38552 = [1, 2, 6, 10, 11, 23], L38626 = [1, 2, 6, 11, 12, 13], L38636 = [1, 2, 6, 11, 12, 23], L38638 = [1, 2, 6, 11, 13, 14], L38640 = [1, 2, 6, 11, 13, 16], L38642 = [1, 2, 6, 11, 13, 18], L38644 = [1, 2, 6, 11, 13, 20], L38646 = [1, 2, 6, 11, 13, 22], L38648 = [1, 2, 6, 11, 13, 24], L38657 = [1, 2, 6, 11, 14, 23], L38674 = [1, 2, 6, 11, 16, 23], L38687 = [1, 2, 6, 11, 18, 23], L38696 = [1, 2, 6, 11, 20, 23], L38701 = [1, 2, 6, 11, 22, 23], L38703 = [1, 2, 6, 11, 23, 24], L39094 = [1, 2, 7, 8, 10, 17], L39099 = [1, 2, 7, 8, 10, 23], L39102 = [1, 2, 7, 8, 11, 13], L39103 = [1, 2, 7, 8, 11, 14], L39328 = [1, 2, 7, 10, 11, 14], L39342 = [1, 2, 7, 10, 12, 17], L39347 = [1, 2, 7, 10, 12, 23], L39374 = [1, 2, 7, 10, 16, 17], L39379 = [1, 2, 7, 10, 16, 23], L39381 = [1, 2, 7, 10, 17, 18], L39382 = [1, 2, 7, 10, 17, 20],
APPENDIX
81
Table 4. (continued) n = 6 48 {0} {54568, 54581}, {54615, 54619}, {54687, 54699}, {54707, 54712}, {54728, 54733}, (cont.) {54735, 54745}, {54740, 54753}, {54799, 54804}, {54806, 54816}, {54811, 54824}, {54826, 54845}, {54831, 54853}, {54840, 54864}, {55097, 55103}, {55921, 55927}, {55996, 56002}, {56005, 56017}, {56006, 56023}, {56008, 56027}, {57169, 58784}, {57174, 57177}, {57195, 58199}, {57200, 57203}, {57227, 58663}, {57232, 57235}, {57238, 58777}, {57240, 57627}, {57244, 58786}, {57256, 57259}, {57268, 57271}, {57276, 57283}, {57356, 58011}, {57361, 57364}, {57388, 58153}, {57393, 57396}, {57399, 58195}, {57405, 58201}, {57417, 57420}, {57436, 57443}, {57552, 58617}, {57557, 57560}, {57563, 58659}, {57569, 58665}, {57581, 57584}, {57600, 57607}, {57616, 58773}, {57622, 58779}, {57636, 58789}, {57659, 57666}, {57673, 57676}, {57692, 57699}, {57735, 57747}, {57771, 57774}, {57773, 57775}, {57852, 57855}, {57854, 57856}, {57858, 57865}, {57862, 57870}, {57864, 57866}, {57869, 57871}, {59054, 59060}, {59214, 59220}, {59397, 59403}, {59473, 59479}, {59481, 59493}, L39386 = [1, 2, 7, 10, 17, 24], L39391 = [1, 2, 7, 10, 18, 23], L39396 = [1, 2, 7, 10, 20, 23], L39404 = [1, 2, 7, 10, 23, 24], L39407 = [1, 2, 7, 11, 12, 13], L39408 = [1, 2, 7, 11, 12, 14], L39419 = [1, 2, 7, 11, 13, 16], L39426 = [1, 2, 7, 11, 13, 24], L39427 = [1, 2, 7, 11, 14, 16], L39428 = [1, 2, 7, 11, 14, 18], L39431 = [1, 2, 7, 11, 14, 24], L39826 = [1, 2, 8, 8, 11, 13], L39836 = [1, 2, 8, 8, 11, 23], L40060 = [1, 2, 8, 10, 11, 13], L40069 = [1, 2, 8, 10, 11, 23], L40143 = [1, 2, 8, 11, 12, 13], L40153 = [1, 2, 8, 11, 12, 23], L40155 = [1, 2, 8, 11, 13, 14], L40157 = [1, 2, 8, 11, 13, 16], L40159 = [1, 2, 8, 11, 13, 18], L40161 = [1, 2, 8, 11, 13, 20], L40165 = [1, 2, 8, 11, 13, 24], L40173 = [1, 2, 8, 11, 14, 23], L40190 = [1, 2, 8, 11, 16, 23], L40202 = [1, 2, 8, 11, 18, 23], L40210 = [1, 2, 8, 11, 20, 23], L40216 = [1, 2, 8, 11, 23, 24], L41230 = [1, 2, 10, 10, 11, 13], L41239 = [1, 2, 10, 10, 11, 23], L41313 = [1, 2, 10, 11, 12, 13], L41322 = [1, 2, 10, 11, 12, 23], L41324 = [1, 2, 10, 11, 13, 14], L41326 = [1, 2, 10, 11, 13, 16], L41328 = [1, 2, 10, 11, 13, 18], L41329 = [1, 2, 10, 11, 13, 20], L41331 = [1, 2, 10, 11, 13, 22], L41333 = [1, 2, 10, 11, 13, 24], L41341 = [1, 2, 10, 11, 14, 23], L41356 = [1, 2, 10, 11, 16, 23], L41366 = [1, 2, 10, 11, 18, 23], L41371 = [1, 2, 10, 11, 20, 23], L41376 = [1, 2, 10, 11, 22, 23], L41378 = [1, 2, 10, 11, 23, 24], L41666 = [1, 2, 11, 12, 12, 13], L41676 = [1, 2, 11, 12, 12, 23], L41678 = [1, 2, 11, 12, 13, 14], L41680 = [1, 2, 11, 12, 13, 16], L41682 = [1, 2, 11, 12, 13, 18], L41684 = [1, 2, 11, 12, 13, 20], L41688 = [1, 2, 11, 12, 13, 24], L41696 = [1, 2, 11, 12, 14, 23], L41713 = [1, 2, 11, 12, 16, 23], L41725 = [1, 2, 11, 12, 18, 23], L41733 = [1, 2, 11, 12, 20, 23], L41739 = [1, 2, 11, 12, 23, 24], L41741 = [1, 2, 11, 13, 14, 14], L41743 = [1, 2, 11, 13, 14, 16], L41744 = [1, 2, 11, 13, 14, 18], L41746 = [1, 2, 11, 13, 14, 20], L41749 = [1, 2, 11, 13, 14, 24], L41758 = [1, 2, 11, 13, 16, 16], L41760 = [1, 2, 11, 13, 16, 18], L41762 = [1, 2, 11, 13, 16, 20], L41766 = [1, 2, 11, 13, 16, 24], L41772 = [1, 2, 11, 13, 18, 18], L41774 = [1, 2, 11, 13, 18, 20], L41777 = [1, 2, 11, 13, 18, 24], L41781 = [1, 2, 11, 13, 20, 20], L41785 = [1, 2, 11, 13, 20, 24], L41791 = [1, 2, 11, 13, 24, 24], L41799 = [1, 2, 11, 14, 14, 23], L41813 = [1, 2, 11, 14, 16, 23], L41819 = [1, 2, 11, 14, 18, 23], L41821 = [1, 2, 11, 14, 19, 20], L41826 = [1, 2, 11, 14, 20, 23], L41830 = [1, 2, 11, 14, 23, 24], L41873 = [1, 2, 11, 16, 16, 23], L41885 = [1, 2, 11, 16, 18, 23], L41893 = [1, 2, 11, 16, 20, 23], L41899 = [1, 2, 11, 16, 23, 24], L41922 = [1, 2, 11, 18, 18, 23], L41929 = [1, 2, 11, 18, 20, 23], L41933 = [1, 2, 11, 18, 23, 24], L41944 = [1, 2, 11, 20, 20, 23], L41950 = [1, 2, 11, 20, 23, 24], L41958 = [1, 2, 11, 23, 24, 24], L42926 = [1, 2, 17, 19, 20, 22], L43947 = [1, 3, 3, 7, 15, 21], L44210 = [1, 3, 3, 9, 15, 21], L44224 = [1, 3, 3, 9, 17, 21], L45390 = [1, 3, 4, 7, 15, 20], L45407 = [1, 3, 4, 7, 17, 21], L45429 = [1, 3, 4, 7, 21, 23], L45655 = [1, 3, 4, 9, 15, 21], L45670 = [1, 3, 4, 9, 17, 20], L46079 = [1, 3, 4, 15, 19, 21], L46423 = [1, 3, 5, 7, 11, 23], L46437 = [1, 3, 5, 7, 13, 15], L46439 = [1, 3, 5, 7, 13, 17], L46449 = [1, 3, 5, 7, 15, 19], L46450 = [1, 3, 5, 7, 15, 21], L46510 = [1, 3, 5, 8, 9, 11], L46512 = [1, 3, 5, 8, 9, 13], L46527 = [1, 3, 5, 8, 11, 15], L46534 = [1, 3, 5, 8, 11, 23], L46550 = [1, 3, 5, 8, 13, 15], L46557 = [1, 3, 5, 8, 13, 23], L46630 = [1, 3, 5, 9, 11, 12], L46633 = [1, 3, 5, 9, 11, 15], L46634 = [1, 3, 5, 9, 11, 16], L46635 = [1, 3, 5, 9, 11, 17], L46638 = [1, 3, 5, 9, 11, 21], L46639 = [1, 3, 5, 9, 11, 23], L46640 = [1, 3, 5, 9, 11, 24], L46642 = [1, 3, 5, 9, 12, 13], L46655 = [1, 3, 5, 9, 13, 15], L46656 = [1, 3, 5, 9, 13, 16], L46661 = [1, 3, 5, 9, 13, 23],
82
EMILIO A. LAURET
Table 4. (continued) n = 6 48 {0} {59482, 59499}, {59483, 59504}, {59484, 59508}, {59487, 59512}, {59965, 59971}, (cont.) {60147, 60153}, {60223, 60229}, {60231, 60242}, {60232, 60248}, {60234, 60255}, {60237, 60259}, {60947, 60953}, {61023, 61029}, {61031, 61043}, {61032, 61049}, {61033, 61053}, {61034, 61057}, {61037, 61061}, {61317, 61323}, {61325, 61336}, {61326, 61342}, {61328, 61349}, {61331, 61353}, {61355, 61382}, {61356, 61387}, {61357, 61391}, {61360, 61395}, {61361, 61401}, {61363, 61408}, {61366, 61412}, {61370, 61422}, {61373, 61426}, {61377, 61431}, {62861, 62866}, {63601, 63606}, {63674, 63679}, {63682, 63693}, {63683, 63697}, {63685, 63701}, {66125, 66130}, {66198, 66203}, {66205, 66214}, {66206, 66219}, {66207, 66223}, {66209, 66227}, {66471, 66476}, {66479, 66490}, {66480, 66494}, {66482, 66498}, {66504, 66526}, {66505, 66530}, {66507, 66534}, {66508, 66538}, {66510, 66542}, {66512, 66547}, {69051, 69055}, {69364, 69368}, {69453, 69457}, {69529, 69533}, {69603, 69607}, {69612, 69616}, {69620, 69624}, {69628, 69637}, {69629, 69642}, {69630, 69646}, {69632, 69649}, {69633, 69650}, {70913, 70917}, {70998, 71002}, {71071, 71075}, {71138, 71142}, {71147, 71151}, {71154, 71158}, {71162, 71171}, {71163, 71176}, {71164, 71179}, {71167, 71182}, {71373, 71377}, {71444, 71448}, {71510, 71513, 71525, 71528}, {71518, 71522}, {71531, 71540}, {71532, 71545}, L46662 = [1, 3, 5, 9, 13, 24], L46674 = [1, 3, 5, 9, 15, 17], L46691 = [1, 3, 5, 9, 17, 19], L46692 = [1, 3, 5, 9, 17, 21], L46722 = [1, 3, 5, 11, 12, 15], L46729 = [1, 3, 5, 11, 12, 23], L46750 = [1, 3, 5, 11, 15, 16], L46755 = [1, 3, 5, 11, 15, 24], L46762 = [1, 3, 5, 11, 16, 23], L46784 = [1, 3, 5, 11, 23, 24], L46800 = [1, 3, 5, 12, 13, 15], L46807 = [1, 3, 5, 12, 13, 23], L46876 = [1, 3, 5, 13, 15, 16], L46880 = [1, 3, 5, 13, 15, 21], L46881 = [1, 3, 5, 13, 15, 24], L46888 = [1, 3, 5, 13, 16, 23], L46912 = [1, 3, 5, 13, 23, 24], L47144 = [1, 3, 6, 6, 7, 15], L47179 = [1, 3, 6, 6, 9, 17], L47298 = [1, 3, 6, 7, 8, 15], L47346 = [1, 3, 6, 7, 12, 15], L47365 = [1, 3, 6, 7, 15, 16], L47367 = [1, 3, 6, 7, 15, 18], L47372 = [1, 3, 6, 7, 15, 24], L47434 = [1, 3, 6, 8, 9, 17], L47590 = [1, 3, 6, 9, 12, 17], L47619 = [1, 3, 6, 9, 15, 21], L47624 = [1, 3, 6, 9, 16, 17], L47631 = [1, 3, 6, 9, 17, 18], L47633 = [1, 3, 6, 9, 17, 24], L48157 = [1, 3, 7, 8, 8, 15], L48205 = [1, 3, 7, 8, 12, 15], L48221 = [1, 3, 7, 8, 13, 23], L48224 = [1, 3, 7, 8, 15, 16], L48226 = [1, 3, 7, 8, 15, 18], L48231 = [1, 3, 7, 8, 15, 24], L48242 = [1, 3, 7, 8, 17, 19], L48295 = [1, 3, 7, 9, 11, 13], L48299 = [1, 3, 7, 9, 11, 21], L48313 = [1, 3, 7, 9, 13, 15], L48318 = [1, 3, 7, 9, 15, 15], L48323 = [1, 3, 7, 9, 15, 21], L48402 = [1, 3, 7, 10, 15, 22], L48477 = [1, 3, 7, 12, 12, 15], L48493 = [1, 3, 7, 12, 13, 23], L48496 = [1, 3, 7, 12, 15, 16], L48498 = [1, 3, 7, 12, 15, 18], L48503 = [1, 3, 7, 12, 15, 24], L48514 = [1, 3, 7, 12, 17, 19], L48553 = [1, 3, 7, 13, 16, 23], L48570 = [1, 3, 7, 13, 23, 24], L48581 = [1, 3, 7, 15, 16, 16], L48583 = [1, 3, 7, 15, 16, 18], L48588 = [1, 3, 7, 15, 16, 24], L48594 = [1, 3, 7, 15, 18, 18], L48599 = [1, 3, 7, 15, 18, 24], L48612 = [1, 3, 7, 15, 24, 24], L48623 = [1, 3, 7, 16, 17, 19], L48656 = [1, 3, 7, 17, 19, 24], L48735 = [1, 3, 8, 8, 9, 17], L48890 = [1, 3, 8, 9, 12, 17], L48917 = [1, 3, 8, 9, 15, 21], L48922 = [1, 3, 8, 9, 16, 17], L48929 = [1, 3, 8, 9, 17, 18], L48931 = [1, 3, 8, 9, 17, 24], L49497 = [1, 3, 9, 9, 15, 17], L49500 = [1, 3, 9, 9, 15, 21], L49592 = [1, 3, 9, 10, 15, 21], L49606 = [1, 3, 9, 10, 17, 22], L49681 = [1, 3, 9, 12, 12, 17], L49713 = [1, 3, 9, 12, 16, 17], L49720 = [1, 3, 9, 12, 17, 18], L49722 = [1, 3, 9, 12, 17, 24], L49776 = [1, 3, 9, 14, 15, 21], L49812 = [1, 3, 9, 15, 15, 21], L49820 = [1, 3, 9, 15, 16, 21], L49825 = [1, 3, 9, 15, 17, 21], L49829 = [1, 3, 9, 15, 18, 21], L49834 = [1, 3, 9, 15, 20, 21], L49838 = [1, 3, 9, 15, 21, 21], L49839 = [1, 3, 9, 15, 21, 22], L49840 = [1, 3, 9, 15, 21, 23], L49841 = [1, 3, 9, 15, 21, 24], L49848 = [1, 3, 9, 16, 16, 17], L49855 = [1, 3, 9, 16, 17, 18], L49857 = [1, 3, 9, 16, 17, 24], L49878 = [1, 3, 9, 17, 18, 18], L49880 = [1, 3, 9, 17, 18, 24], L49883 = [1, 3, 9, 17, 24, 24], L51355 = [1, 3, 15, 19, 20, 21], L51691 = [1, 4, 4, 4, 5, 19], L51695 = [1, 4, 4, 4, 5, 23], L51723 = [1, 4, 4, 4, 7, 17], L51728 = [1, 4, 4, 4, 7, 23], L51862 = [1, 4, 4, 5, 6, 19], L51866 = [1, 4, 4, 5, 6, 23], L51890 = [1, 4, 4, 5, 8, 19], L51894 = [1, 4, 4, 5, 8, 23], L51925 = [1, 4, 4, 5, 12, 19], L51929 = [1, 4, 4, 5, 12, 23], L51951 = [1, 4, 4, 5, 16, 19], L51955 = [1, 4, 4, 5, 16, 23], L51965 = [1, 4, 4, 5, 18, 19], L51969 = [1, 4, 4, 5, 18, 23], L51971 = [1, 4, 4, 5, 19, 20], L51975 = [1, 4, 4, 5, 19, 24], L51979 = [1, 4, 4, 5, 20, 23],
APPENDIX
83
Table 4. (continued) n = 6 48 {0} {71533, 71549}, {71535, 71552}, {71536, 71553}, {71723, 71727}, {71793, 71797}, (cont.) {71800, 71803}, {71806, 71815}, {71807, 71820}, {71808, 71823}, {71811, 71826}, {72019, 72021}, {72034, 72038}, {72041, 72044}, {72047, 72056}, {72048, 72061}, {72049, 72064}, {72052, 72067}, {72071, 72077}, {72072, 72080}, {72074, 72082}, {72089, 72110}, {72090, 72115}, {72091, 72118}, {72094, 72121}, {72095, 72126}, {72096, 72129}, {72098, 72131}, {72099, 72134}, {72102, 72137}, {72106, 72140}, {73663, 73666}, {73879, 73881}, {73952, 73954}, {74097, 74101}, {74244, 74248}, {74284, 74288}, {74314, 74318}, {74320, 74328}, {74322, 74332}, {74324, 74334}, {74619, 74622}, {74643, 74646}, {74675, 74678}, {74698, 74701}, {74703, 74709}, {74706, 74712}, {74751, 74754}, {74756, 74762}, {74759, 74765} L51987 = [1, 4, 4, 5, 23, 24], L52015 = [1, 4, 4, 6, 7, 17], L52020 = [1, 4, 4, 6, 7, 23], L52068 = [1, 4, 4, 6, 11, 13], L52076 = [1, 4, 4, 6, 11, 23], L52163 = [1, 4, 4, 7, 8, 17], L52168 = [1, 4, 4, 7, 8, 23], L52196 = [1, 4, 4, 7, 12, 17], L52201 = [1, 4, 4, 7, 12, 23], L52219 = [1, 4, 4, 7, 16, 17], L52224 = [1, 4, 4, 7, 16, 23], L52226 = [1, 4, 4, 7, 17, 18], L52228 = [1, 4, 4, 7, 17, 20], L52231 = [1, 4, 4, 7, 17, 24], L52236 = [1, 4, 4, 7, 18, 23], L52243 = [1, 4, 4, 7, 20, 23], L52248 = [1, 4, 4, 7, 23, 24], L52482 = [1, 4, 4, 10, 11, 13], L52488 = [1, 4, 4, 10, 11, 23], L52872 = [1, 4, 5, 6, 6, 19], L52876 = [1, 4, 5, 6, 6, 23], L52900 = [1, 4, 5, 6, 8, 19], L52904 = [1, 4, 5, 6, 8, 23], L52935 = [1, 4, 5, 6, 12, 19], L52939 = [1, 4, 5, 6, 12, 23], L52946 = [1, 4, 5, 6, 13, 20], L52962 = [1, 4, 5, 6, 16, 19], L52966 = [1, 4, 5, 6, 16, 23], L52976 = [1, 4, 5, 6, 18, 19], L52980 = [1, 4, 5, 6, 18, 23], L52982 = [1, 4, 5, 6, 19, 20], L52986 = [1, 4, 5, 6, 19, 24], L52989 = [1, 4, 5, 6, 20, 23], L52997 = [1, 4, 5, 6, 23, 24], L53023 = [1, 4, 5, 7, 11, 13], L53025 = [1, 4, 5, 7, 11, 17], L53026 = [1, 4, 5, 7, 11, 19], L53028 = [1, 4, 5, 7, 11, 23], L53042 = [1, 4, 5, 7, 13, 19], L53044 = [1, 4, 5, 7, 13, 23], L53055 = [1, 4, 5, 7, 17, 19], L53058 = [1, 4, 5, 7, 17, 23], L53068 = [1, 4, 5, 7, 19, 23], L53087 = [1, 4, 5, 8, 8, 19], L53091 = [1, 4, 5, 8, 8, 23], L53122 = [1, 4, 5, 8, 12, 19], L53126 = [1, 4, 5, 8, 12, 23], L53148 = [1, 4, 5, 8, 16, 19], L53152 = [1, 4, 5, 8, 16, 23], L53162 = [1, 4, 5, 8, 18, 19], L53166 = [1, 4, 5, 8, 18, 23], L53172 = [1, 4, 5, 8, 19, 24], L53182 = [1, 4, 5, 8, 23, 24], L53269 = [1, 4, 5, 11, 13, 19], L53272 = [1, 4, 5, 11, 13, 23], L53291 = [1, 4, 5, 11, 17, 19], L53294 = [1, 4, 5, 11, 17, 23], L53303 = [1, 4, 5, 11, 19, 23], L53318 = [1, 4, 5, 12, 12, 19], L53322 = [1, 4, 5, 12, 12, 23], L53344 = [1, 4, 5, 12, 16, 19], L53348 = [1, 4, 5, 12, 16, 23], L53358 = [1, 4, 5, 12, 18, 19], L53362 = [1, 4, 5, 12, 18, 23], L53368 = [1, 4, 5, 12, 19, 24], L53378 = [1, 4, 5, 12, 23, 24], L53397 = [1, 4, 5, 13, 18, 20], L53436 = [1, 4, 5, 14, 19, 22], L53447 = [1, 4, 5, 14, 22, 23], L53454 = [1, 4, 5, 16, 16, 19], L53458 = [1, 4, 5, 16, 16, 23], L53468 = [1, 4, 5, 16, 18, 19], L53472 = [1, 4, 5, 16, 18, 23], L53478 = [1, 4, 5, 16, 19, 24], L53488 = [1, 4, 5, 16, 23, 24], L53512 = [1, 4, 5, 18, 18, 19], L53516 = [1, 4, 5, 18, 18, 23], L53521 = [1, 4, 5, 18, 19, 24], L53531 = [1, 4, 5, 18, 23, 24], L53542 = [1, 4, 5, 19, 24, 24], L53560 = [1, 4, 5, 23, 24, 24], L53588 = [1, 4, 6, 6, 7, 17], L53593 = [1, 4, 6, 6, 7, 23], L53641 = [1, 4, 6, 6, 11, 13], L53649 = [1, 4, 6, 6, 11, 23], L53736 = [1, 4, 6, 7, 8, 17], L53741 = [1, 4, 6, 7, 8, 23], L53769 = [1, 4, 6, 7, 12, 17], L53774 = [1, 4, 6, 7, 12, 23], L53791 = [1, 4, 6, 7, 16, 17], L53796 = [1, 4, 6, 7, 16, 23], L53798 = [1, 4, 6, 7, 17, 18], L53803 = [1, 4, 6, 7, 17, 24], L53808 = [1, 4, 6, 7, 18, 23], L53816 = [1, 4, 6, 7, 23, 24], L53864 = [1, 4, 6, 8, 11, 13], L53872 = [1, 4, 6, 8, 11, 23], L54063 = [1, 4, 6, 10, 11, 13], L54070 = [1, 4, 6, 10, 11, 23], L54141 = [1, 4, 6, 11, 12, 13], L54149 = [1, 4, 6, 11, 12, 23], L54151 = [1, 4, 6, 11, 13, 14], L54152 = [1, 4, 6, 11, 13, 16], L54155 = [1, 4, 6, 11, 13, 20], L54158 = [1, 4, 6, 11, 13, 24], L54164 = [1, 4, 6, 11, 14, 23], L54172 = [1, 4, 6, 11, 16, 23], L54185 = [1, 4, 6, 11, 20, 23], L54189 = [1, 4, 6, 11, 23, 24], L54502 = [1, 4, 7, 8, 8, 17], L54507 = [1, 4, 7, 8, 8, 23], L54535 = [1, 4, 7, 8, 12, 17], L54540 = [1, 4, 7, 8, 12, 23], L54556 = [1, 4, 7, 8, 16, 17], L54561 = [1, 4, 7, 8, 16, 23], L54563 = [1, 4, 7, 8, 17, 18], L54568 = [1, 4, 7, 8, 17, 24], L54573 = [1, 4, 7, 8, 18, 23], L54581 = [1, 4, 7, 8, 23, 24], L54615 = [1, 4, 7, 9, 15, 17], L54619 = [1, 4, 7, 9, 15, 23], L54687 = [1, 4, 7, 10, 17, 22], L54699 = [1, 4, 7, 10, 22, 23], L54707 = [1, 4, 7, 12, 12, 17], L54712 = [1, 4, 7, 12, 12, 23], L54728 = [1, 4, 7, 12, 16, 17], L54733 = [1, 4, 7, 12, 16, 23], L54735 = [1, 4, 7, 12, 17, 18], L54740 = [1, 4, 7, 12, 17, 24], L54745 = [1, 4, 7, 12, 18, 23], L54753 = [1, 4, 7, 12, 23, 24], L54799 = [1, 4, 7, 16, 16, 17], L54804 = [1, 4, 7, 16, 16, 23], L54806 = [1, 4, 7, 16, 17, 18],
84
EMILIO A. LAURET
Table 4. (continued) n = 6 48 {0, 1} (cont.) {0, 3} {4} {5} {0, 5} {4, 5}
{46423, 46439}, {46437, 46635}, {46449, 46661}, {53058, 53269}, {53068, 53303} {53055, 53272} {9972, 57942}, {57797, 57922} {14735, 14775} {45390, 45670}, {51971, 51979}, {52228, 52243} {8102, 49841}, {13849, 72104}, {14582, 74499}, {14734, 14774, 74881, 74955}, {20984, 49840}, {34675, 49839}, {44210, 49838}, {45655, 49834}, {47619, 49829}, {48323, 49825}, {48917, 49820}, {49500, 49812}, {49592, 49776}, {69631, 72103}, {70676, 71997}, {71165, 72100}, {71534, 72097}, {71809, 72092}, {72025, 72073}, {73891, 73964}, {74167, 74497}, {74428, 74495}, {74705, 74758}, {74833, 74879, 74953}, {74873, 74947}
L54811 = [1, 4, 7, 16, 17, 24], L54816 = [1, 4, 7, 16, 18, 23], L54824 = [1, 4, 7, 16, 23, 24], L54826 = [1, 4, 7, 17, 18, 18], L54831 = [1, 4, 7, 17, 18, 24], L54840 = [1, 4, 7, 17, 24, 24], L54845 = [1, 4, 7, 18, 18, 23], L54853 = [1, 4, 7, 18, 23, 24], L54864 = [1, 4, 7, 23, 24, 24], L55097 = [1, 4, 8, 10, 11, 13], L55103 = [1, 4, 8, 10, 11, 23], L55921 = [1, 4, 10, 10, 11, 13], L55927 = [1, 4, 10, 10, 11, 23], L55996 = [1, 4, 10, 11, 12, 13], L56002 = [1, 4, 10, 11, 12, 23], L56005 = [1, 4, 10, 11, 13, 16], L56006 = [1, 4, 10, 11, 13, 20], L56008 = [1, 4, 10, 11, 13, 24], L56017 = [1, 4, 10, 11, 16, 23], L56023 = [1, 4, 10, 11, 20, 23], L56027 = [1, 4, 10, 11, 23, 24], L57169 = [1, 5, 6, 6, 6, 13], L57174 = [1, 5, 6, 6, 6, 19], L57177 = [1, 5, 6, 6, 6, 23], L57195 = [1, 5, 6, 6, 8, 13], L57200 = [1, 5, 6, 6, 8, 19], L57203 = [1, 5, 6, 6, 8, 23], L57227 = [1, 5, 6, 6, 12, 13], L57232 = [1, 5, 6, 6, 12, 19], L57235 = [1, 5, 6, 6, 12, 23], L57238 = [1, 5, 6, 6, 13, 16], L57240 = [1, 5, 6, 6, 13, 18], L57244 = [1, 5, 6, 6, 13, 24], L57256 = [1, 5, 6, 6, 16, 19], L57259 = [1, 5, 6, 6, 16, 23], L57268 = [1, 5, 6, 6, 18, 19], L57271 = [1, 5, 6, 6, 18, 23], L57276 = [1, 5, 6, 6, 19, 24], L57283 = [1, 5, 6, 6, 23, 24], L57356 = [1, 5, 6, 8, 8, 13], L57361 = [1, 5, 6, 8, 8, 19], L57364 = [1, 5, 6, 8, 8, 23], L57388 = [1, 5, 6, 8, 12, 13], L57393 = [1, 5, 6, 8, 12, 19], L57396 = [1, 5, 6, 8, 12, 23], L57399 = [1, 5, 6, 8, 13, 16], L57405 = [1, 5, 6, 8, 13, 24], L57417 = [1, 5, 6, 8, 16, 19], L57420 = [1, 5, 6, 8, 16, 23], L57436 = [1, 5, 6, 8, 19, 24], L57443 = [1, 5, 6, 8, 23, 24], L57552 = [1, 5, 6, 12, 12, 13], L57557 = [1, 5, 6, 12, 12, 19], L57560 = [1, 5, 6, 12, 12, 23], L57563 = [1, 5, 6, 12, 13, 16], L57569 = [1, 5, 6, 12, 13, 24], L57581 = [1, 5, 6, 12, 16, 19], L57584 = [1, 5, 6, 12, 16, 23], L57600 = [1, 5, 6, 12, 19, 24], L57607 = [1, 5, 6, 12, 23, 24], L57616 = [1, 5, 6, 13, 16, 16], L57622 = [1, 5, 6, 13, 16, 24], L57627 = [1, 5, 6, 13, 18, 18], L57636 = [1, 5, 6, 13, 24, 24], L57659 = [1, 5, 6, 14, 19, 22], L57666 = [1, 5, 6, 14, 22, 23], L57673 = [1, 5, 6, 16, 16, 19], L57676 = [1, 5, 6, 16, 16, 23], L57692 = [1, 5, 6, 16, 19, 24], L57699 = [1, 5, 6, 16, 23, 24], L57735 = [1, 5, 6, 19, 24, 24], L57747 = [1, 5, 6, 23, 24, 24], L57771 = [1, 5, 7, 8, 11, 13], L57773 = [1, 5, 7, 8, 11, 17], L57774 = [1, 5, 7, 8, 11, 19], L57775 = [1, 5, 7, 8, 11, 23], L57797 = [1, 5, 7, 8, 17, 19], L57852 = [1, 5, 7, 11, 12, 13], L57854 = [1, 5, 7, 11, 12, 17], L57855 = [1, 5, 7, 11, 12, 19], L57856 = [1, 5, 7, 11, 12, 23], L57858 = [1, 5, 7, 11, 13, 16], L57862 = [1, 5, 7, 11, 13, 24], L57864 = [1, 5, 7, 11, 16, 17], L57865 = [1, 5, 7, 11, 16, 19], L57866 = [1, 5, 7, 11, 16, 23], L57869 = [1, 5, 7, 11, 17, 24], L57870 = [1, 5, 7, 11, 19, 24], L57871 = [1, 5, 7, 11, 23, 24], L57922 = [1, 5, 7, 16, 17, 19], L57942 = [1, 5, 7, 17, 19, 24], L58011 = [1, 5, 8, 8, 13, 18], L58153 = [1, 5, 8, 12, 13, 18], L58195 = [1, 5, 8, 13, 16, 18], L58199 = [1, 5, 8, 13, 18, 18], L58201 = [1, 5, 8, 13, 18, 24], L58617 = [1, 5, 12, 12, 13, 18], L58659 = [1, 5, 12, 13, 16, 18], L58663 = [1, 5, 12, 13, 18, 18], L58665 = [1, 5, 12, 13, 18, 24], L58773 = [1, 5, 13, 16, 16, 18], L58777 = [1, 5, 13, 16, 18, 18], L58779 = [1, 5, 13, 16, 18, 24], L58784 = [1, 5, 13, 18, 18, 18], L58786 = [1, 5, 13, 18, 18, 24], L58789 = [1, 5, 13, 18, 24, 24], L59054 = [1, 6, 6, 6, 11, 13], L59060 = [1, 6, 6, 6, 11, 23], L59214 = [1, 6, 6, 8, 11, 13], L59220 = [1, 6, 6, 8, 11, 23], L59397 = [1, 6, 6, 10, 11, 13], L59403 = [1, 6, 6, 10, 11, 23], L59473 = [1, 6, 6, 11, 12, 13], L59479 = [1, 6, 6, 11, 12, 23], L59481 = [1, 6, 6, 11, 13, 14], L59482 = [1, 6, 6, 11, 13, 16], L59483 = [1, 6, 6, 11, 13, 18], L59484 = [1, 6, 6, 11, 13, 20], L59487 = [1, 6, 6, 11, 13, 24],
APPENDIX
85
L59493 = [1, 6, 6, 11, 14, 23], L59499 = [1, 6, 6, 11, 16, 23], L59504 = [1, 6, 6, 11, 18, 23], L59508 = [1, 6, 6, 11, 20, 23], L59512 = [1, 6, 6, 11, 23, 24], L59965 = [1, 6, 8, 8, 11, 13], L59971 = [1, 6, 8, 8, 11, 23], L60147 = [1, 6, 8, 10, 11, 13], L60153 = [1, 6, 8, 10, 11, 23], L60223 = [1, 6, 8, 11, 12, 13], L60229 = [1, 6, 8, 11, 12, 23], L60231 = [1, 6, 8, 11, 13, 14], L60232 = [1, 6, 8, 11, 13, 16], L60234 = [1, 6, 8, 11, 13, 20], L60237 = [1, 6, 8, 11, 13, 24], L60242 = [1, 6, 8, 11, 14, 23], L60248 = [1, 6, 8, 11, 16, 23], L60255 = [1, 6, 8, 11, 20, 23], L60259 = [1, 6, 8, 11, 23, 24], L60947 = [1, 6, 10, 10, 11, 13], L60953 = [1, 6, 10, 10, 11, 23], L61023 = [1, 6, 10, 11, 12, 13], L61029 = [1, 6, 10, 11, 12, 23], L61031 = [1, 6, 10, 11, 13, 14], L61032 = [1, 6, 10, 11, 13, 16], L61033 = [1, 6, 10, 11, 13, 18], L61034 = [1, 6, 10, 11, 13, 20], L61037 = [1, 6, 10, 11, 13, 24], L61043 = [1, 6, 10, 11, 14, 23], L61049 = [1, 6, 10, 11, 16, 23], L61053 = [1, 6, 10, 11, 18, 23], L61057 = [1, 6, 10, 11, 20, 23], L61061 = [1, 6, 10, 11, 23, 24], L61317 = [1, 6, 11, 12, 12, 13], L61323 = [1, 6, 11, 12, 12, 23], L61325 = [1, 6, 11, 12, 13, 14], L61326 = [1, 6, 11, 12, 13, 16], L61328 = [1, 6, 11, 12, 13, 20], L61331 = [1, 6, 11, 12, 13, 24], L61336 = [1, 6, 11, 12, 14, 23], L61342 = [1, 6, 11, 12, 16, 23], L61349 = [1, 6, 11, 12, 20, 23], L61353 = [1, 6, 11, 12, 23, 24], L61355 = [1, 6, 11, 13, 14, 14], L61356 = [1, 6, 11, 13, 14, 16], L61357 = [1, 6, 11, 13, 14, 20], L61360 = [1, 6, 11, 13, 14, 24], L61361 = [1, 6, 11, 13, 16, 16], L61363 = [1, 6, 11, 13, 16, 20], L61366 = [1, 6, 11, 13, 16, 24], L61370 = [1, 6, 11, 13, 20, 20], L61373 = [1, 6, 11, 13, 20, 24], L61377 = [1, 6, 11, 13, 24, 24], L61382 = [1, 6, 11, 14, 14, 23], L61387 = [1, 6, 11, 14, 16, 23], L61391 = [1, 6, 11, 14, 20, 23], L61395 = [1, 6, 11, 14, 23, 24], L61401 = [1, 6, 11, 16, 16, 23], L61408 = [1, 6, 11, 16, 20, 23], L61412 = [1, 6, 11, 16, 23, 24], L61422 = [1, 6, 11, 20, 20, 23], L61426 = [1, 6, 11, 20, 23, 24], L61431 = [1, 6, 11, 23, 24, 24], L62861 = [1, 8, 8, 10, 11, 13], L62866 = [1, 8, 8, 10, 11, 23], L63601 = [1, 8, 10, 10, 11, 13], L63606 = [1, 8, 10, 10, 11, 23], L63674 = [1, 8, 10, 11, 12, 13], L63679 = [1, 8, 10, 11, 12, 23], L63682 = [1, 8, 10, 11, 13, 16], L63683 = [1, 8, 10, 11, 13, 20], L63685 = [1, 8, 10, 11, 13, 24], L63693 = [1, 8, 10, 11, 16, 23], L63697 = [1, 8, 10, 11, 20, 23], L63701 = [1, 8, 10, 11, 23, 24], L66125 = [1, 10, 10, 10, 11, 13], L66130 = [1, 10, 10, 10, 11, 23], L66198 = [1, 10, 10, 11, 12, 13], L66203 = [1, 10, 10, 11, 12, 23], L66205 = [1, 10, 10, 11, 13, 14], L66206 = [1, 10, 10, 11, 13, 16], L66207 = [1, 10, 10, 11, 13, 20], L66209 = [1, 10, 10, 11, 13, 24], L66214 = [1, 10, 10, 11, 14, 23 L66219 = [1, 10, 10, 11, 16, 23], L66223 = [1, 10, 10, 11, 20, 23], L66227 = [1, 10, 10, 11, 23, 24], L66471 = [1, 10, 11, 12, 12, 13], L66476 = [1, 10, 11, 12, 12, 23], L66479 = [1, 10, 11, 12, 13, 16], L66480 = [1, 10, 11, 12, 13, 20 L66482 = [1, 10, 11, 12, 13, 24], L66490 = [1, 10, 11, 12, 16, 23], L66494 = [1, 10, 11, 12, 20, 23], L66498 = [1, 10, 11, 12, 23, 24], L66504 = [1, 10, 11, 13, 16, 16], L66505 = [1, 10, 11, 13, 16, 20], L66507 = [1, 10, 11, 13, 16, 24 L66508 = [1, 10, 11, 13, 20, 20], L66510 = [1, 10, 11, 13, 20, 24], L66512 = [1, 10, 11, 13, 24, 24], L66526 = [1, 10, 11, 16, 16, 23], L66530 = [1, 10, 11, 16, 20, 23], L66534 = [1, 10, 11, 16, 23, 24], L66538 = [1, 10, 11, 20, 20, 23 L66542 = [1, 10, 11, 20, 23, 24], L66547 = [1, 10, 11, 23, 24, 24], L69051 = [2, 2, 2, 3, 9, 15], L69055 = [2, 2, 2, 3, 9, 21], L69364 = [2, 2, 3, 4, 9, 15], L69368 = [2, 2, 3, 4, 9, 21], L69453 = [2, 2, 3, 6, 9, 15], L69457 = [2, 2, 3, 6, 9, 21], L69529 = [2, 2, 3, 8, 9, 15], L69533 = [2, 2, 3, 8, 9, 21], L69603 = [2, 2, 3, 9, 10, 15], L69607 = [2, 2, 3, 9, 10, 21], L69612 = [2, 2, 3, 9, 12, 15], L69616 = [2, 2, 3, 9, 12, 21], L69620 = [2, 2, 3, 9, 14, 15], L69624 = [2, 2, 3, 9, 14, 21], L69628 = [2, 2, 3, 9, 15, 16], L69629 = [2, 2, 3, 9, 15, 18], L69630 = [2, 2, 3, 9, 15, 20], L69631 = [2, 2, 3, 9, 15, 21], L69632 = [2, 2, 3, 9, 15, 22], L69633 = [2, 2, 3, 9, 15, 24], L69637 = [2, 2, 3, 9, 16, 21], L69642 = [2, 2, 3, 9, 18, 21], L69646 = [2, 2, 3, 9, 20, 21], L69649 = [2, 2, 3, 9, 21, 22], L69650 = [2, 2, 3, 9, 21, 24], L70676 = [2, 3, 3, 9, 15, 21], L70913 = [2, 3, 4, 4, 9, 15], L70917 = [2, 3, 4, 4, 9, 21], L70998 = [2, 3, 4, 6, 9, 15], L71002 = [2, 3, 4, 6, 9, 21], L71071 = [2, 3, 4, 8, 9, 15], L71075 = [2, 3, 4, 8, 9, 21], L71138 = [2, 3, 4, 9, 10, 15], L71142 = [2, 3, 4, 9, 10, 21], L71147 = [2, 3, 4, 9, 12, 15], L71151 = [2, 3, 4, 9, 12, 21], L71154 = [2, 3, 4, 9, 14, 15], L71158 = [2, 3, 4, 9, 14, 21], L71162 = [2, 3, 4, 9, 15, 16], L71163 = [2, 3, 4, 9, 15, 18], L71164 = [2, 3, 4, 9, 15, 20], L71165 = [2, 3, 4, 9, 15, 21], L71167 = [2, 3, 4, 9, 15, 24], L71171 = [2, 3, 4, 9, 16, 21], L71176 = [2, 3, 4, 9, 18, 21], L71179 = [2, 3, 4, 9, 20, 21], L71182 = [2, 3, 4, 9, 21, 24], L71373 = [2, 3, 6, 6, 9, 15], L71377 = [2, 3, 6, 6, 9, 21], L71444 = [2, 3, 6, 8, 9, 15], L71448 = [2, 3, 6, 8, 9, 21], L71510 = [2, 3, 6, 9, 10, 15], L71513 = [2, 3, 6, 9, 10, 21], L71518 = [2, 3, 6, 9, 12, 15], L71522 = [2, 3, 6, 9, 12, 21], L71525 = [2, 3, 6, 9, 14, 15], L71528 = [2, 3, 6, 9, 14, 21], L71531 = [2, 3, 6, 9, 15, 16], L71532 = [2, 3, 6, 9, 15, 18], L71533 = [2, 3, 6, 9, 15, 20], L71534 = [2, 3, 6, 9, 15, 21], L71535 = [2, 3, 6, 9, 15, 22], L71536 = [2, 3, 6, 9, 15, 24], L71540 = [2, 3, 6, 9, 16, 21], L71545 = [2, 3, 6, 9, 18, 21], L71549 = [2, 3, 6, 9, 20, 21], L71552 = [2, 3, 6, 9, 21, 22], L71553 = [2, 3, 6, 9, 21, 24], L71723 = [2, 3, 8, 8, 9, 15], L71727 = [2, 3, 8, 8, 9, 21], L71793 = [2, 3, 8, 9, 12, 15], L71797 = [2, 3, 8, 9, 12, 21], L71800 = [2, 3, 8, 9, 14, 15],
86
EMILIO A. LAURET
Table 4. (continued) n = 6 q 49
I {0} {5}
indexes of I-isospectral families {23573, 23597}, {24564, 24578}, {24566, 24624}, {26814, 26850} {944, 5580, 5614, 5623}, {2506, 5499, 5607, 5622}, {4070, 4849, 5251, 5431, 5597, 5617, 5619} {0, 1, 2, 3, 4, 5} {106, 108}, {887, 889}, {894, 896}, {902, 904}, {908, 912}, {5481, 5483}, {5488, 5490}, {5496, 5498}, {5502, 5506}, {5514, 5516}, {5517, 5520}, {5529, 5531}, {5535, 5539}, {5543, 5547}, {27986, 27988}, {27993, 27995}, {28001, 28003}, {28007, 28011}, {28019, 28021}, {28022, 28025}, {28034, 28036}, {28040, 28044}, {28048, 28052}, {28064, 28066}, {28067, 28070}, {28071, 28074}, {28086, 28088}, {28092, 28096}, {28100, 28104}, {28108, 28112}
L71803 = [2, 3, 8, 9, 14, 21], L71806 = [2, 3, 8, 9, 15, 16], L71807 = [2, 3, 8, 9, 15, 18], L71808 = [2, 3, 8, 9, 15, 20], L71809 = [2, 3, 8, 9, 15, 21], L71811 = [2, 3, 8, 9, 15, 24], L71815 = [2, 3, 8, 9, 16, 21], L71820 = [2, 3, 8, 9, 18, 21], L71823 = [2, 3, 8, 9, 20, 21], L71826 = [2, 3, 8, 9, 21, 24], L71997 = [2, 3, 9, 9, 15, 21], L72019 = [2, 3, 9, 10, 14, 15], L72021 = [2, 3, 9, 10, 14, 21], L72025 = [2, 3, 9, 10, 15, 21], L72034 = [2, 3, 9, 12, 12, 15], L72038 = [2, 3, 9, 12, 12, 21], L72041 = [2, 3, 9, 12, 14, 15], L72044 = [2, 3, 9, 12, 14, 21], L72047 = [2, 3, 9, 12, 15, 16], L72048 = [2, 3, 9, 12, 15, 18], L72049 = [2, 3, 9, 12, 15, 20], L72052 = [2, 3, 9, 12, 15, 24], L72056 = [2, 3, 9, 12, 16, 21], L72061 = [2, 3, 9, 12, 18, 21], L72064 = [2, 3, 9, 12, 20, 21], L72067 = [2, 3, 9, 12, 21, 24], L72071 = [2, 3, 9, 14, 15, 16], L72072 = [2, 3, 9, 14, 15, 18], L72073 = [2, 3, 9, 14, 15, 21], L72074 = [2, 3, 9, 14, 15, 24], L72077 = [2, 3, 9, 14, 16, 21], L72080 = [2, 3, 9, 14, 18, 21], L72082 = [2, 3, 9, 14, 21, 24], L72089 = [2, 3, 9, 15, 16, 16], L72090 = [2, 3, 9, 15, 16, 18], L72091 = [2, 3, 9, 15, 16, 20], L72092 = [2, 3, 9, 15, 16, 21], L72094 = [2, 3, 9, 15, 16, 24], L72095 = [2, 3, 9, 15, 18, 18], L72096 = [2, 3, 9, 15, 18, 20], L72097 = [2, 3, 9, 15, 18, 21], L72098 = [2, 3, 9, 15, 18, 24], L72099 = [2, 3, 9, 15, 20, 20], L72100 = [2, 3, 9, 15, 20, 21], L72102 = [2, 3, 9, 15, 20, 24], L72103 = [2, 3, 9, 15, 21, 22], L72104 = [2, 3, 9, 15, 21, 24], L72106 = [2, 3, 9, 15, 24, 24], L72110 = [2, 3, 9, 16, 16, 21], L72115 = [2, 3, 9, 16, 18, 21], L72118 = [2, 3, 9, 16, 20, 21], L72121 = [2, 3, 9, 16, 21, 24], L72126 = [2, 3, 9, 18, 18, 21], L72129 = [2, 3, 9, 18, 20, 21], L72131 = [2, 3, 9, 18, 21, 24], L72134 = [2, 3, 9, 20, 20, 21], L72137 = [2, 3, 9, 20, 21, 24], L72140 = [2, 3, 9, 21, 24, 24], L73663 = [3, 3, 4, 9, 9, 15], L73666 = [3, 3, 4, 9, 9, 21], L73879 = [3, 3, 8, 9, 9, 15], L73881 = [3, 3, 8, 9, 9, 21], L73891 = [3, 3, 8, 9, 15, 21], L73952 = [3, 3, 9, 9, 15, 16], L73954 = [3, 3, 9, 9, 16, 21], L73964 = [3, 3, 9, 15, 16, 21], L74097 = [3, 4, 4, 6, 9, 15], L74101 = [3, 4, 4, 6, 9, 21], L74167 = [3, 4, 4, 9, 15, 21], L74244 = [3, 4, 6, 6, 9, 15], L74248 = [3, 4, 6, 6, 9, 21], L74284 = [3, 4, 6, 8, 9, 15], L74288 = [3, 4, 6, 8, 9, 21], L74314 = [3, 4, 6, 9, 12, 15], L74318 = [3, 4, 6, 9, 12, 21], L74320 = [3, 4, 6, 9, 15, 16], L74322 = [3, 4, 6, 9, 15, 20], L74324 = [3, 4, 6, 9, 15, 24], L74328 = [3, 4, 6, 9, 16, 21], L74332 = [3, 4, 6, 9, 20, 21], L74334 = [3, 4, 6, 9, 21, 24], L74428 = [3, 4, 8, 9, 15, 21], L74495 = [3, 4, 9, 15, 16, 21], L74497 = [3, 4, 9, 15, 20, 21], L74499 = [3, 4, 9, 15, 21, 24], L74619 = [3, 6, 6, 8, 9, 15], L74622 = [3, 6, 6, 8, 9, 21], L74643 = [3, 6, 6, 9, 15, 16], L74646 = [3, 6, 6, 9, 16, 21], L74675 = [3, 6, 8, 8, 9, 15], L74678 = [3, 6, 8, 8, 9, 21], L74698 = [3, 6, 8, 9, 12, 15], L74701 = [3, 6, 8, 9, 12, 21], L74703 = [3, 6, 8, 9, 15, 16], L74705 = [3, 6, 8, 9, 15, 21], L74706 = [3, 6, 8, 9, 15, 24], L74709 = [3, 6, 8, 9, 16, 21], L74712 = [3, 6, 8, 9, 21, 24], L74751 = [3, 6, 9, 12, 15, 16], L74754 = [3, 6, 9, 12, 16, 21], L74756 = [3, 6, 9, 15, 16, 16], L74758 = [3, 6, 9, 15, 16, 21], L74759 = [3, 6, 9, 15, 16, 24], L74762 = [3, 6, 9, 16, 16, 21], L74765 = [3, 6, 9, 16, 21, 24], L74833 = [3, 8, 8, 9, 15, 21], L74873 = [3, 8, 9, 12, 15, 21], L74879 = [3, 8, 9, 15, 16, 21], L74881 = [3, 8, 9, 15, 21, 24], L74947 = [3, 9, 12, 15, 16, 21], L74953 = [3, 9, 15, 16, 16, 21], L74955 = [3, 9, 15, 16, 21, 24]. q = 49 : L106 = [0, 0, 0, 1, 6, 15], L108 = [0, 0, 0, 1, 6, 20], L887 = [0, 0, 1, 6, 7, 15], L889 = [0, 0, 1, 6, 7, 20], L894 = [0, 0, 1, 6, 8, 20], L896 = [0, 0, 1, 6, 8, 22], L902 = [0, 0, 1, 6, 14, 15], L904 = [0, 0, 1, 6, 14, 20], L908 = [0, 0, 1, 6, 15, 21], L912 = [0, 0, 1, 6, 20, 21], L944 = [0, 0, 1, 7, 14, 21], L2506 = [0, 1, 1, 7, 14, 21], L4070 = [0, 1, 2, 7, 14, 21], L4849 = [0, 1, 3, 7, 14, 21], L5251 = [0, 1, 4, 7, 14, 21],
APPENDIX
87
Table 4. (continued) n = 6 q I indexes of I-isospectral families 50 {0} {263, 267}, {932, 935, 962}, {937, 963}, {1058, 1574}, {1227, 1480}, {2130, 2154}, {2143, 2159}, {7593, 7714}, {7596, 7633}, {7687, 7692}, {7690, 7694, 7713, 7716}, {7743, 7765, 7944}, {7744, 7767, 7947}, {7763, 7946}, {7778, 7943}, {7779, 7953}, {8101, 8147}, {8117, 8360}, {8463, 11344}, {8834, 9928}, {9338, 10898}, {9547, 10919}, {9571, 10934}, {9577, 10943}, {13280, 13321}, {13300, 13432}, {13315, 13351}, {13335, 13342}, {13343, 13345, 13529}, {13349, 13488}, {13484, 13544}, {13497, 13549}, {13520, 13566}, {28680, 28713}, {28934, 28947}, {42429, 42483}, {42642, 42714}, {43414, 44449}, {43625, 49547}, {47847, 48087}, {47863, 47875, 48085}, {47871, 48088}, {47877, 48095}, {47894, 48126, 48456}, {48293, 48647}, {48295, 48341}, {48459, 49183}, {48469, 49180}, {48470, 49077}, {48478, 48665}, {48579, 59695}, {48898, 48921}, {48899, 48906, 48911, 48929, 49064}, {48902, 48923, 48931}, {48907, 49087}, {48912, 48939}, {48932, 48945, 49069, 49089}, {48993, 49015, 50078}, {48995, 50077}, {49029, 50085}, {49066, 49104}, {49068, 49098, 49204}, {49208, 50125},
L5431 = [0, 1, 5, 7, 14, 21], L5481 = [0, 1, 6, 7, 7, 15], L5483 = [0, 1, 6, 7, 7, 20], L5488 = [0, 1, 6, 7, 8, 20], L5490 = [0, 1, 6, 7, 8, 22], L5496 = [0, 1, 6, 7, 14, 15], L5498 = [0, 1, 6, 7, 14, 20], L5499 = [0, 1, 6, 7, 14, 21], L5502 = [0, 1, 6, 7, 15, 21], L5506 = [0, 1, 6, 7, 20, 21], L5514 = [0, 1, 6, 8, 14, 20], L5516 = [0, 1, 6, 8, 14, 22], L5517 = [0, 1, 6, 8, 20, 21], L5520 = [0, 1, 6, 8, 21, 22], L5529 = [0, 1, 6, 14, 14, 15], L5531 = [0, 1, 6, 14, 14, 20], L5535 = [0, 1, 6, 14, 15, 21], L5539 = [0, 1, 6, 14, 20, 21], L5543 = [0, 1, 6, 15, 21, 21], L5547 = [0, 1, 6, 20, 21, 21], L5580 = [0, 1, 7, 7, 14, 21], L5597 = [0, 1, 7, 9, 14, 21], L5607 = [0, 1, 7, 13, 14, 21], L5614 = [0, 1, 7, 14, 14, 21], L5617 = [0, 1, 7, 14, 17, 21], L5619 = [0, 1, 7, 14, 18, 21], L5622 = [0, 1, 7, 14, 20, 21], L5623 = [0, 1, 7, 14, 21, 21], L23573 = [1, 2, 6, 13, 15, 20], L23597 = [1, 2, 6, 13, 20, 22], L24564 = [1, 2, 8, 13, 15, 20], L24566 = [1, 2, 8, 13, 15, 22], L24578 = [1, 2, 8, 13, 20, 22], L24624 = [1, 2, 8, 15, 20, 22], L26814 = [1, 3, 8, 13, 15, 20], L26850 = [1, 3, 8, 15, 20, 22], L27986 = [1, 6, 7, 7, 7, 15], L27988 = [1, 6, 7, 7, 7, 20], L27993 = [1, 6, 7, 7, 8, 20], L27995 = [1, 6, 7, 7, 8, 22], L28001 = [1, 6, 7, 7, 14, 15], L28003 = [1, 6, 7, 7, 14, 20], L28007 = [1, 6, 7, 7, 15, 21], L28011 = [1, 6, 7, 7, 20, 21], L28019 = [1, 6, 7, 8, 14, 20], L28021 = [1, 6, 7, 8, 14, 22], L28022 = [1, 6, 7, 8, 20, 21], L28025 = [1, 6, 7, 8, 21, 22], L28034 = [1, 6, 7, 14, 14, 15], L28036 = [1, 6, 7, 14, 14, 20], L28040 = [1, 6, 7, 14, 15, 21], L28044 = [1, 6, 7, 14, 20, 21], L28048 = [1, 6, 7, 15, 21, 21], L28052 = [1, 6, 7, 20, 21, 21], L28064 = [1, 6, 8, 14, 14, 20], L28066 = [1, 6, 8, 14, 14, 22], L28067 = [1, 6, 8, 14, 20, 21], L28070 = [1, 6, 8, 14, 21, 22], L28071 = [1, 6, 8, 20, 21, 21], L28074 = [1, 6, 8, 21, 21, 22], L28086 = [1, 6, 14, 14, 14, 15], L28088 = [1, 6, 14, 14, 14, 20], L28092 = [1, 6, 14, 14, 15, 21], L28096 = [1, 6, 14, 14, 20, 21], L28100 = [1, 6, 14, 15, 21, 21], L28104 = [1, 6, 14, 20, 21, 21], L28108 = [1, 6, 15, 21, 21, 21], L28112 = [1, 6, 20, 21, 21, 21]. q = 50 : L263 = [0, 0, 0, 2, 5, 18], L267 = [0, 0, 0, 2, 8, 15], L932 = [0, 0, 1, 3, 7, 13], L935 = [0, 0, 1, 3, 7, 17], L937 = [0, 0, 1, 3, 7, 19], L962 = [0, 0, 1, 3, 9, 11], L963 = [0, 0, 1, 3, 9, 13], L1058 = [0, 0, 1, 3, 19, 21], L1227 = [0, 0, 1, 4, 14, 21], L1480 = [0, 0, 1, 6, 9, 24], L1574 = [0, 0, 1, 7, 9, 11], L2130 = [0, 0, 2, 5, 10, 18], L2143 = [0, 0, 2, 5, 18, 20], L2154 = [0, 0, 2, 8, 10, 15], L2159 = [0, 0, 2, 8, 15, 20], L7593 = [0, 1, 3, 5, 13, 19], L7596 = [0, 1, 3, 5, 13, 23], L7633 = [0, 1, 3, 5, 17, 23], L7687 = [0, 1, 3, 7, 9, 13], L7690 = [0, 1, 3, 7, 9, 19], L7692 = [0, 1, 3, 7, 9, 21], L7694 = [0, 1, 3, 7, 9, 23], L7713 = [0, 1, 3, 7, 11, 13], L7714 = [0, 1, 3, 7, 11, 15], L7716 = [0, 1, 3, 7, 11, 17], L7718 = [0, 1, 3, 7, 11, 19], L7721 = [0, 1, 3, 7, 11, 23], L7743 = [0, 1, 3, 7, 13, 23], L7744 = [0, 1, 3, 7, 13, 25], L7763 = [0, 1, 3, 7, 17, 21], L7765 = [0, 1, 3, 7, 17, 23], L7767 = [0, 1, 3, 7, 17, 25], L7778 = [0, 1, 3, 7, 19, 23], L7779 = [0, 1, 3, 7, 19, 25], L7943 = [0, 1, 3, 9, 11, 17], L7944 = [0, 1, 3, 9, 11, 19], L7946 = [0, 1, 3, 9, 11, 23], L7947 = [0, 1, 3, 9, 11, 25], L7953 = [0, 1, 3, 9, 13, 25],
88
EMILIO A. LAURET
Table 4. (continued) n = 6 50 {0} {49213, 49301, 50126}, {49214, 49304, 50130}, {49295, 50129}, (cont.) {49340, 50124}, {49341, 50150}, {50689, 64555}, {50824, 50998}, {50905, 51832}, {52123, 64586}, {53588, 58149}, {54098, 59158}, {54307, 59181}, {54331, 59196}, {54337, 59205}, {54826, 54828}, {54829, 54831}, {54832, 54853}, {54851, 54854}, {54865, 54998}, {54867, 54874, 54996, 55022}, {54869, 54999}, {54872, 55015}, {54882, 55016}, {55145, 55147}, {55159, 55235, 56266, 56385}, {55169, 55237}, {56263, 56270}, {56276, 56383}, {56491, 63089}, {56700, 63110}, {56724, 63125}, {56730, 63134}, {56934, 57001}, {57463, 63189}, {57487, 63204}, {57493, 63213}, {57564, 63246}, {57570, 63255}, {57582, 63270}, {70786, 70823}, {70797, 70825}, {70800, 70801}, {70837, 70924}, {70900, 70906}, {70907, 70909, 71414}, {70959, 71151}, {70962, 71152}, {70995, 71020}, {71007, 71164, 71406}, {71009, 71013}, {71015, 71017}, {71016, 71019, 71028, 71054}, {71027, 71031, 71050}, {71053, 71154}, {71064, 71069}, {71076, 71118}, {71082, 71196}, {71156, 71176}, {71157, 71177}, {71180, 71184, 71608}, {71520, 71634}, {71533, 71639}, {71557, 71656}, {71592, 71691} L8101 = [0, 1, 3, 11, 13, 19], L8117 = [0, 1, 3, 11, 15, 19], L8147 = [0, 1, 3, 11, 21, 23], L8360 = [0, 1, 3, 15, 19, 21], L8463 = [0, 1, 3, 19, 21, 25], L8834 = [0, 1, 4, 5, 14, 21], L9338 = [0, 1, 4, 10, 14, 21], L9547 = [0, 1, 4, 14, 15, 21], L9571 = [0, 1, 4, 14, 20, 21], L9577 = [0, 1, 4, 14, 21, 25], L9928 = [0, 1, 5, 6, 9, 24], L10898 = [0, 1, 6, 9, 10, 24], L10919 = [0, 1, 6, 9, 15, 24], L10934 = [0, 1, 6, 9, 20, 24], L10943 = [0, 1, 6, 9, 24, 25], L11344 = [0, 1, 7, 9, 11, 25], L11937 = [0, 1, 9, 11, 19, 21], L13280 = [0, 2, 4, 5, 18, 20], L13300 = [0, 2, 4, 6, 15, 18], L13315 = [0, 2, 4, 8, 22, 25], L13321 = [0, 2, 4, 10, 14, 15], L13335 = [0, 2, 4, 12, 14, 25], L13342 = [0, 2, 4, 12, 16, 25], L13343 = [0, 2, 4, 12, 18, 25], L13345 = [0, 2, 4, 12, 22, 25], L13349 = [0, 2, 4, 14, 15, 20], L13351 = [0, 2, 4, 14, 16, 25], L13432 = [0, 2, 5, 6, 8, 14], L13484 = [0, 2, 5, 10, 10, 18], L13488 = [0, 2, 5, 10, 14, 16], L13497 = [0, 2, 5, 10, 18, 20], L13520 = [0, 2, 5, 18, 20, 20], L13529 = [0, 2, 6, 8, 18, 25], L13544 = [0, 2, 8, 10, 10, 15], L13549 = [0, 2, 8, 10, 15, 20], L13566 = [0, 2, 8, 15, 20, 20], L28680 = [1, 1, 9, 9, 11, 21], L28713 = [1, 1, 9, 9, 19, 21], L28934 = [1, 1, 9, 11, 19, 19], L28947 = [1, 1, 9, 11, 21, 21], L42429 = [1, 2, 8, 9, 12, 21], L42483 = [1, 2, 8, 9, 18, 21], L42642 = [1, 2, 8, 11, 12, 19], L42714 = [1, 2, 8, 11, 21, 22], L43414 = [1, 2, 9, 12, 21, 22], L43625 = [1, 2, 9, 16, 22, 23], L44449 = [1, 2, 11, 12, 18, 21], L47847 = [1, 3, 5, 7, 11, 21], L47863 = [1, 3, 5, 7, 13, 15], L47871 = [1, 3, 5, 7, 13, 23], L47875 = [1, 3, 5, 7, 15, 17], L47877 = [1, 3, 5, 7, 15, 19], L47894 = [1, 3, 5, 7, 17, 21], L48085 = [1, 3, 5, 9, 11, 15], L48087 = [1, 3, 5, 9, 11, 17], L48088 = [1, 3, 5, 9, 11, 19], L48095 = [1, 3, 5, 9, 13, 15], L48126 = [1, 3, 5, 9, 17, 19], L48293 = [1, 3, 5, 11, 13, 19], L48295 = [1, 3, 5, 11, 13, 23], L48341 = [1, 3, 5, 11, 21, 23], L48456 = [1, 3, 5, 13, 17, 19], L48459 = [1, 3, 5, 13, 17, 23], L48469 = [1, 3, 5, 13, 19, 23], L48470 = [1, 3, 5, 13, 19, 25], L48478 = [1, 3, 5, 13, 23, 25], L48579 = [1, 3, 5, 15, 19, 21], L48647 = [1, 3, 5, 17, 19, 23], L48665 = [1, 3, 5, 17, 23, 25], L48898 = [1, 3, 7, 9, 11, 17], L48899 = [1, 3, 7, 9, 11, 19], L48902 = [1, 3, 7, 9, 11, 23], L48906 = [1, 3, 7, 9, 13, 17], L48907 = [1, 3, 7, 9, 13, 19], L48911 = [1, 3, 7, 9, 13, 23], L48912 = [1, 3, 7, 9, 13, 25], L48921 = [1, 3, 7, 9, 17, 19], L48923 = [1, 3, 7, 9, 17, 21], L48929 = [1, 3, 7, 9, 19, 21], L48931 = [1, 3, 7, 9, 19, 23], L48932 = [1, 3, 7, 9, 19, 25], L48939 = [1, 3, 7, 9, 21, 25], L48945 = [1, 3, 7, 9, 23, 25], L48993 = [1, 3, 7, 10, 13, 20], L48995 = [1, 3, 7, 10, 13, 23], L49015 = [1, 3, 7, 10, 17, 20], L49029 = [1, 3, 7, 10, 19, 20], L49064 = [1, 3, 7, 11, 13, 17], L49066 = [1, 3, 7, 11, 13, 19], L49068 = [1, 3, 7, 11, 13, 23], L49069 = [1, 3, 7, 11, 13, 25], L49077 = [1, 3, 7, 11, 15, 25], L49087 = [1, 3, 7, 11, 17, 21], L49089 = [1, 3, 7, 11, 17, 25], L49098 = [1, 3, 7, 11, 19, 21], L49099 = [1, 3, 7, 11, 19, 25], L49104 = [1, 3, 7, 11, 21, 23], L49108 = [1, 3, 7, 11, 23, 25], L49180 = [1, 3, 7, 13, 15, 19], L49183 = [1, 3, 7, 13, 15, 23], L49204 = [1, 3, 7, 13, 19, 23], L49208 = [1, 3, 7, 13, 20, 23], L49213 = [1, 3, 7, 13, 23, 25], L49214 = [1, 3, 7, 13, 25, 25], L49295 = [1, 3, 7, 17, 21, 25], L49301 =
APPENDIX
89
Table 4. (continued) n = 6 50 (cont.)
{0, 1}
{7718, 7721}, {7743, 7944}, {48911, 49064}, {48923, 48931}, {49099, 49108}, {49213, 50126}, {55159, 56385}, {71030, 71071}, {71031, 71050} {2, 3, 4} {11937, 66459, 66548}, {60435, 66539, 66550}, {71492, 71671, 71677}
[1, 3, 7, 17, 23, 25], L49304 = [1, 3, 7, 17, 25, 25], L49340 = [1, 3, 7, 19, 23, 25], L49341 = [1, 3, 7, 19, 25, 25], L49547 = [1, 3, 8, 9, 16, 22], L50077 = [1, 3, 9, 10, 11, 19], L50078 = [1, 3, 9, 10, 11, 20], L50085 = [1, 3, 9, 10, 13, 20], L50124 = [1, 3, 9, 11, 17, 25], L50125 = [1, 3, 9, 11, 19, 20], L50126 = [1, 3, 9, 11, 19, 25], L50129 = [1, 3, 9, 11, 23, 25], L50130 = [1, 3, 9, 11, 25, 25], L50150 = [1, 3, 9, 13, 25, 25], L50689 = [1, 3, 10, 19, 20, 21], L50824 = [1, 3, 11, 13, 19, 25], L50905 = [1, 3, 11, 15, 19, 25], L50998 = [1, 3, 11, 21, 23, 25], L51832 = [1, 3, 15, 19, 21, 25], L52123 = [1, 3, 19, 21, 25, 25], L53588 = [1, 4, 5, 5, 14, 21], L54098 = [1, 4, 5, 10, 14, 21], L54307 = [1, 4, 5, 14, 15, 21], L54331 = [1, 4, 5, 14, 20, 21], L54337 = [1, 4, 5, 14, 21, 25], L54826 = [1, 4, 6, 9, 11, 14], L54828 = [1, 4, 6, 9, 11, 16], L54829 = [1, 4, 6, 9, 11, 19], L54831 = [1, 4, 6, 9, 11, 21], L54832 = [1, 4, 6, 9, 11, 24], L54851 = [1, 4, 6, 9, 14, 16], L54853 = [1, 4, 6, 9, 14, 21], L54854 = [1, 4, 6, 9, 14, 24], L54865 = [1, 4, 6, 9, 16, 19], L54867 = [1, 4, 6, 9, 16, 21], L54869 = [1, 4, 6, 9, 16, 24], L54872 = [1, 4, 6, 9, 19, 21], L54874 = [1, 4, 6, 9, 19, 24], L54882 = [1, 4, 6, 9, 21, 24], L54996 = [1, 4, 6, 11, 14, 19], L54998 = [1, 4, 6, 11, 14, 21], L54999 = [1, 4, 6, 11, 14, 24], L55015 = [1, 4, 6, 11, 19, 21], L55016 = [1, 4, 6, 11, 19, 24], L55022 = [1, 4, 6, 11, 21, 24], L55145 = [1, 4, 6, 14, 16, 19], L55147 = [1, 4, 6, 14, 16, 21], L55159 = [1, 4, 6, 14, 19, 21], L55169 = [1, 4, 6, 14, 21, 24], L55235 = [1, 4, 6, 16, 19, 21], L55237 = [1, 4, 6, 16, 19, 24], L56263 = [1, 4, 9, 11, 16, 19], L56266 = [1, 4, 9, 11, 16, 24], L56270 = [1, 4, 9, 11, 19, 24], L56276 = [1, 4, 9, 11, 21, 24], L56383 = [1, 4, 9, 16, 19, 21], L56385 = [1, 4, 9, 16, 19, 24], L56491 = [1, 4, 10, 10, 14, 21], L56700 = [1, 4, 10, 14, 15, 21], L56724 = [1, 4, 10, 14, 20, 21], L56730 = [1, 4, 10, 14, 21, 25], L56934 = [1, 4, 11, 14, 16, 19], L57001 = [1, 4, 11, 16, 19, 24], L57463 = [1, 4, 14, 15, 15, 21], L57487 = [1, 4, 14, 15, 20, 21], L57493 = [1, 4, 14, 15, 21, 25], L57564 = [1, 4, 14, 20, 20, 21], L57570 = [1, 4, 14, 20, 21, 25], L57582 = [1, 4, 14, 21, 25, 25], L58149 = [1, 5, 5, 6, 9, 24], L59158 = [1, 5, 6, 9, 10, 24], L59181 = [1, 5, 6, 9, 15, 24], L59196 = [1, 5, 6, 9, 20, 24], L59205 = [1, 5, 6, 9, 24, 25], L59695 = [1, 5, 7, 9, 11, 15], L60435 = [1, 5, 9, 11, 19, 21], L63089 = [1, 6, 9, 10, 10, 24], L63110 = [1, 6, 9, 10, 15, 24], L63125 = [1, 6, 9, 10, 20, 24], L63134 = [1, 6, 9, 10, 24, 25], L63189 = [1, 6, 9, 15, 15, 24], L63204 = [1, 6, 9, 15, 20, 24], L63213 = [1, 6, 9, 15, 24, 25], L63246 = [1, 6, 9, 20, 20, 24], L63255 = [1, 6, 9, 20, 24, 25], L63270 = [1, 6, 9, 24, 25, 25], L64555 = [1, 7, 9, 10, 11, 20], L64586 = [1, 7, 9, 11, 25, 25], L66459 = [1, 9, 10, 11, 19, 21], L66539 = [1, 9, 11, 15, 19, 21], L66548 = [1, 9, 11, 19, 20, 21], L66550 = [1, 9, 11, 19, 21, 25], L70786 = [2, 4, 5, 6, 14, 24], L70797 = [2, 4, 5, 6, 16, 24], L70800 = [2, 4, 5, 6, 18, 22], L70801 = [2, 4, 5, 6, 18, 24], L70823 = [2, 4, 5, 8, 12, 18], L70825 = [2, 4, 5, 8, 12, 22], L70837 = [2, 4, 5, 8, 15, 22], L70900 = [2, 4, 5, 12, 14, 15], L70906 = [2, 4, 5, 12, 15, 16], L70907 = [2, 4, 5, 12, 15, 18], L70909 = [2, 4, 5, 12, 15, 22], L70924 = [2, 4, 5, 14, 15, 16], L70959 = [2, 4, 5, 16, 18, 24], L70962 = [2, 4, 5, 16, 20, 22], L70995 = [2, 4, 6, 8, 22, 25], L71007 = [2, 4, 6, 10, 15, 22], L71009 = [2, 4, 6, 10, 16, 25], L71013 = [2, 4, 6, 10, 24, 25], L71015 = [2, 4, 6, 12, 14, 25], L71016 = [2, 4, 6, 12, 16, 25], L71017 = [2, 4, 6, 12, 18, 25], L71019 = [2, 4, 6, 12, 22, 25], L71020 = [2, 4, 6, 12, 24, 25], L71027 = [2, 4, 6, 14, 16, 25], L71028 = [2, 4, 6, 14, 18, 25], L71030 = [2, 4, 6, 14, 22, 25], L71031 = [2, 4, 6, 14, 24, 25], L71050 = [2, 4, 6, 16, 24, 25], L71053 = [2, 4, 6, 18, 22, 25], L71054 = [2, 4, 6, 18, 24, 25], L71064 = [2, 4, 8, 10, 14, 25], L71069 = [2, 4, 8, 10, 24, 25], L71071 = [2, 4, 8, 14, 16, 25], L71076 = [2, 4, 8, 18, 20, 25], L71082 = [2, 4, 8, 22, 25, 25], L71118 = [2, 4, 10, 14, 16, 25], L71151 = [2, 4, 12, 14, 15, 16], L71152 = [2, 4, 12, 14, 15, 20], L71154 = [2, 4, 12, 14, 16, 25], L71156 = [2, 4, 12, 14, 22, 25], L71157 = [2, 4, 12, 14, 25, 25], L71164 = [2, 4, 12, 15, 16, 20], L71176 = [2, 4, 12, 16, 22, 25], L71177 = [2, 4, 12, 16, 25, 25], L71180 = [2, 4, 12, 18, 25, 25], L71184 = [2, 4, 12, 22, 25, 25], L71196 = [2, 4, 14, 16, 25, 25], L71406 = [2, 5, 6, 8, 10, 14], L71414 = [2, 5, 6, 8, 15, 18], L71492 = [2, 5, 8, 12, 18, 22], L71520 = [2, 5, 10, 10, 10, 18], L71533 = [2, 5, 10, 10, 18, 20], L71557 = [2, 5, 10, 18, 20, 20], L71592 = [2, 5, 18, 20, 20, 20],
90
EMILIO A. LAURET
Table 4. (continued) n = 6 q 51
I {0}
indexes of I-isospectral families {660, 983}, {1488, 1490}, {1491, 1492}, {5452, 7278}, {7453, 7557}, {8986, 8988, 8990}, {8995, 8997}, {8998, 9001}, {8999, 9000}, {29081, 29114}, {29706, 30668}, {32822, 32848}, {33826, 33853}, {34230, 41793}, {42413, 42718}, {46423, 46425, 46426, 46427, 46429}, {46428, 46432, 46434}, {46430, 46435}, {46440, 46442}, {46443, 46446}, {46444, 46445} {0, 1} {8989, 8991}, {46425, 46426}, {46433, 46436}
L71608 = [2, 6, 8, 18, 25, 25], L71634 = [2, 8, 10, 10, 10, 15], L71639 = [2, 8, 10, 10, 15, 20], L71656 = [2, 8, 10, 15, 20, 20], L71671 = [2, 8, 12, 15, 18, 22], L71677 = [2, 8, 12, 18, 22, 25], L71691 = [2, 8, 15, 20, 20, 20]. q = 51 : L660 = [0, 0, 1, 2, 10, 23], L983 = [0, 0, 1, 4, 5, 20], L1488 = [0, 0, 3, 6, 15, 17], L1490 = [0, 0, 3, 6, 17, 18], L1491 = [0, 0, 3, 6, 17, 21], L1492 = [0, 0, 3, 9, 12, 17], L5452 = [0, 1, 2, 10, 17, 23], L7278 = [0, 1, 4, 5, 17, 20], L7453 = [0, 1, 4, 7, 19, 23], L7557 = [0, 1, 4, 10, 19, 22], L8986 = [0, 3, 6, 9, 15, 17], L8988 = [0, 3, 6, 9, 17, 18], L8989 = [0, 3, 6, 9, 17, 21], L8990 = [0, 3, 6, 9, 17, 24], L8991 = [0, 3, 6, 12, 15, 17], L8995 = [0, 3, 6, 15, 17, 17], L8997 = [0, 3, 6, 17, 17, 18], L8998 = [0, 3, 6, 17, 17, 21], L8999 = [0, 3, 6, 17, 18, 21], L9000 = [0, 3, 9, 12, 15, 17], L9001 = [0, 3, 9, 12, 17, 17], L29081 = [1, 2, 4, 5, 8, 23], L29114 = [1, 2, 4, 5, 10, 25], L29706 = [1, 2, 4, 11, 14, 22], L30668 = [1, 2, 5, 10, 11, 14], L32822 = [1, 2, 8, 9, 13, 21], L32848 = [1, 2, 8, 9, 16, 21], L33826 = [1, 2, 9, 15, 19, 21], L33853 = [1, 2, 9, 16, 18, 21], L34230 = [1, 2, 10, 17, 17, 23], L41793 = [1, 4, 5, 17, 17, 20], L42413 = [1, 4, 7, 17, 19, 23], L42718 = [1, 4, 10, 17, 19, 22], L46423 = [3, 6, 9, 12, 15, 17], L46425 = [3, 6, 9, 12, 17, 18], L46426 = [3, 6, 9, 12, 17, 21], L46427 = [3, 6, 9, 12, 17, 24], L46428 = [3, 6, 9, 15, 17, 17], L46429 = [3, 6, 9, 15, 17, 18], L46430 = [3, 6, 9, 15, 17, 24], L46432 = [3, 6, 9, 17, 17, 18], L46433 = [3, 6, 9, 17, 17, 21], L46434 = [3, 6, 9, 17, 17, 24], L46435 = [3, 6, 9, 17, 18, 21], L46436 = [3, 6, 12, 15, 17, 17], L46440 = [3, 6, 15, 17, 17, 17], L46442 = [3, 6, 17, 17, 17, 18], L46443 = [3, 6, 17, 17, 17, 21], L46444 = [3, 6, 17, 17, 18, 21], L46445 = [3, 9, 12, 15, 17, 17], L46446 = [3, 9, 12, 17, 17, 17]. q = 52 : L88 = [0, 0, 0, 1, 3, 19], L121 = [0, 0, 0, 1, 5, 9], L122 = [0, 0, 0, 1, 5, 11], L130 = [0, 0, 0, 1, 5, 23], L955 = [0, 0, 1, 3, 5, 15], L957 = [0, 0, 1, 3, 5, 17], L959 = [0, 0, 1, 3, 5, 19], L970 = [0, 0, 1, 3, 7, 11], L973 = [0, 0, 1, 3, 7, 15], L1036 = [0, 0, 1, 3, 11, 23], L1059 = [0, 0, 1, 3, 13, 19], L1082 = [0, 0, 1, 3, 15, 21], L1083 = [0, 0, 1, 3, 15, 23], L1107 = [0, 0, 1, 3, 19, 21], L1112 = [0, 0, 1, 3, 19, 26], L1376 = [0, 0, 1, 5, 7, 11], L1382 = [0, 0, 1, 5, 7, 23], L1398 = [0, 0, 1, 5, 9, 11], L1400 = [0, 0, 1, 5, 9, 13], L1405 = [0, 0, 1, 5, 9, 26], L1407 = [0, 0, 1, 5, 11, 13], L1413 = [0, 0, 1, 5, 11, 26], L1428 = [0, 0, 1, 5, 13, 23], L1460 = [0, 0, 1, 5, 23, 26], L2141 = [0, 0, 2, 6, 10, 13], L2143 = [0, 0, 2, 6, 13, 14], L2145 = [0, 0, 2, 6, 13, 18], L2147 = [0, 0, 2, 6, 13, 22], L2196 = [0, 0, 4, 8, 12, 13], L2198 = [0, 0, 4, 8, 13, 16], L2199 = [0, 0, 4, 8, 13, 20], L2202 = [0, 0, 4, 12, 13, 16], L3469 = [0, 1, 1, 5, 5, 21], L3473 = [0, 1, 1, 5, 5, 25], L6343 = [0, 1, 2, 5, 16, 21], L6347 = [0, 1, 2, 5, 16, 25], L8066 = [0, 1, 3, 5, 9, 15], L8069 = [0, 1, 3, 5, 9, 19], L8073 = [0, 1, 3, 5, 9, 23], L8082 = [0, 1, 3, 5, 11, 17], L8107 = [0, 1, 3, 5, 13, 15], L8109 = [0, 1, 3, 5, 13, 17], L8111 = [0, 1, 3, 5, 13, 19], L8134 = [0, 1, 3, 5, 15, 19], L8138 = [0, 1, 3, 5, 15, 26], L8150 = [0, 1, 3, 5, 17, 21], L8152 = [0, 1, 3, 5, 17, 23], L8155 = [0, 1, 3, 5, 17, 26], L8166 = [0, 1, 3, 5, 19, 21], L8170 = [0, 1, 3, 5, 19, 26], L8218 = [0, 1, 3, 7, 9, 19], L8220 = [0, 1, 3, 7, 9, 21], L8222 = [0, 1, 3, 7, 9, 23], L8241 = [0, 1, 3, 7, 11, 13], L8244 = [0, 1, 3, 7, 11, 17], L8247 = [0, 1, 3, 7, 11, 23], L8249 = [0, 1, 3, 7, 11, 25], L8250 = [0, 1, 3, 7, 11, 26], L8266 = [0, 1, 3, 7, 13, 15], L8280 = [0, 1, 3, 7, 15, 25], L8281 = [0, 1, 3, 7, 15, 26], L8293 = [0, 1, 3, 7, 17, 23], L8295 = [0, 1, 3, 7, 17, 25], L8512 = [0, 1, 3, 9, 11, 17], L8681 = [0, 1, 3, 11, 13, 23], L8721 = [0, 1, 3, 11, 23, 26], L8830 = [0, 1, 3, 13, 13, 19], L8853 = [0, 1, 3, 13, 15, 21], L8854 = [0, 1, 3, 13, 15, 23], L8878 = [0, 1, 3, 13, 19, 21], L8883 = [0, 1, 3, 13, 19, 26], L9002 = [0, 1, 3, 15, 21, 26], L9004 = [0, 1, 3, 15, 23, 26], L9113 = [0, 1, 3, 19, 21, 26], L9125 = [0, 1, 3, 19, 26, 26], L9424 = [0, 1, 4, 5, 6, 21], L9427 = [0, 1, 4, 5, 6, 25], L10723 = [0, 1, 5, 7, 11, 13], L10727 = [0, 1, 5, 7, 11, 26], L10739 = [0, 1, 5, 7, 13, 23], L10756 = [0, 1, 5, 7, 23, 26], L10801 = [0, 1, 5, 8, 14, 21], L10805 = [0, 1, 5, 8, 14, 25], L10838 = [0, 1, 5, 9, 11, 13], L10841 = [0, 1, 5, 9, 11, 26], L10848 = [0, 1, 5, 9, 13, 13], L10853 = [0, 1, 5, 9, 13, 26], L10867 = [0, 1, 5, 9, 26, 26], L10875 = [0, 1, 5, 11, 13, 13], L10881 = [0, 1, 5, 11, 13, 26], L10901 =
APPENDIX
91
Table 4. (continued) n = 6 q I indexes of I-isospectral families 52 {0} {88, 121}, {122, 130}, {955, 957}, {959, 970, 973}, {1059, 1400}, {1082, 1376}, {1107, 1382, 1398}, {1112, 1405}, {1407, 1428}, {1413, 1460}, {2141, 2145}, {2143, 2147}, {2196, 2198}, {2199, 2202}, {3469, 3473}, {6343, 6347}, {8066, 8069}, {8073, 8152}, {8082, 8220}, {8107, 8109}, {8111, 8241, 8266}, {8134, 8244}, {8138, 8155}, {8150, 8218}, {8166, 8247}, {8170, 8250, 8281}, {8222, 8293}, {8249, 8280}, {8295, 8512}, {8830, 10848}, {8853, 10723}, {8878, 10739, 10838}, {8883, 10853}, {9002, 10727}, {9113, 10756, 10841}, {9125, 10867}, {9424, 9427}, {10801, 10805}, {10875, 10944}, {10881, 10976}, {10901, 11070}, {13842, 13869}, {13857, 13918}, {13871, 13872}, {13874, 13884},
[0, 1, 5, 11, 26, 26], L10944 = [0, 1, 5, 13, 13, 23], L10976 = [0, 1, 5, 13, 23, 26], L11070 = [0, 1, 5, 23, 26, 26], L13842 = [0, 2, 4, 13, 14, 16], L13857 = [0, 2, 4, 13, 20, 22], L13869 = [0, 2, 6, 8, 13, 16], L13871 = [0, 2, 6, 8, 13, 20], L13872 = [0, 2, 6, 8, 13, 24], L13874 = [0, 2, 6, 10, 13, 13], L13875 = [0, 2, 6, 10, 13, 14], L13877 = [0, 2, 6, 10, 13, 18], L13878 = [0, 2, 6, 10, 13, 22], L13880 = [0, 2, 6, 10, 13, 26], L13882 = [0, 2, 6, 13, 13, 14], L13884 = [0, 2, 6, 13, 13, 18], L13886 = [0, 2, 6, 13, 13, 22], L13891 = [0, 2, 6, 13, 14, 26], L13897 = [0, 2, 6, 13, 18, 26], L13903 = [0, 2, 6, 13, 22, 26], L13918 = [0, 2, 8, 10, 13, 16], L14059 = [0, 4, 8, 12, 13, 13], L14060 = [0, 4, 8, 12, 13, 16], L14061 = [0, 4, 8, 12, 13, 20], L14062 = [0, 4, 8, 12, 13, 24], L14063 = [0, 4, 8, 12, 13, 26], L14065 = [0, 4, 8, 13, 13, 16], L14066 = [0, 4, 8, 13, 13, 20], L14068 = [0, 4, 8, 13, 16, 26], L14069 = [0, 4, 8, 13, 20, 26], L14072 = [0, 4, 12, 13, 13, 16], L14074 = [0, 4, 12, 13, 16, 26], L25108 = [1, 1, 5, 5, 13, 21], L25112 = [1, 1, 5, 5, 13, 25], L25162 = [1, 1, 5, 5, 21, 26], L25175 = [1, 1, 5, 5, 25, 26], L43524 = [1, 2, 5, 13, 16, 21], L43528 = [1, 2, 5, 13, 16, 25], L43751 = [1, 2, 5, 16, 21, 26], L43762 = [1, 2, 5, 16, 25, 26], L52382 = [1, 3, 5, 7, 9, 23], L52384 = [1, 3, 5, 7, 9, 25], L52388 = [1, 3, 5, 7, 11, 15], L52390 = [1, 3, 5, 7, 11, 17], L52392 = [1, 3, 5, 7, 11, 19], L52395 = [1, 3, 5, 7, 11, 23], L52397 = [1, 3, 5, 7, 11, 25], L52427 = [1, 3, 5, 7, 15, 17], L52429 = [1, 3, 5, 7, 15, 19], L52430 = [1, 3, 5, 7, 15, 21], L52445 = [1, 3, 5, 7, 17, 19], L52448 = [1, 3, 5, 7, 17, 23], L52450 = [1, 3, 5, 7, 17, 25], L52646 = [1, 3, 5, 9, 11, 15], L52648 = [1, 3, 5, 9, 11, 17], L52649 = [1, 3, 5, 9, 11, 19], L52651 = [1, 3, 5, 9, 11, 23], L52657 = [1, 3, 5, 9, 13, 15], L52660 = [1, 3, 5, 9, 13, 19], L52664 = [1, 3, 5, 9, 13, 23], L52680 = [1, 3, 5, 9, 15, 17], L52681 = [1, 3, 5, 9, 15, 23], L52682 = [1, 3, 5, 9, 15, 25], L52683 = [1, 3, 5, 9, 15, 26], L52700 = [1, 3, 5, 9, 19, 21], L52702 = [1, 3, 5, 9, 19, 25], L52703 = [1, 3, 5, 9, 19, 26], L52712 = [1, 3, 5, 9, 21, 23], L52722 = [1, 3, 5, 9, 23, 25], L52723 = [1, 3, 5, 9, 23, 26], L52745 = [1, 3, 5, 11, 13, 17], L52765 = [1, 3, 5, 11, 15, 17], L52781 = [1, 3, 5, 11, 17, 21], L52783 = [1, 3, 5, 11, 17, 25], L52784 = [1, 3, 5, 11, 17, 26], L52915 = [1, 3, 5, 13, 13, 15], L52917 = [1, 3, 5, 13, 13, 17], L52919 = [1, 3, 5, 13, 13, 19], L52942 = [1, 3, 5, 13, 15, 19], L52946 = [1, 3, 5, 13, 15, 26], L52958 = [1, 3, 5, 13, 17, 21], L52960 = [1, 3, 5, 13, 17, 23], L52963 = [1, 3, 5, 13, 17, 26], L52974 = [1, 3, 5, 13, 19, 21], L52978 = [1, 3, 5, 13, 19, 26], L53080 = [1, 3, 5, 15, 17, 23], L53091 = [1, 3, 5, 15, 19, 26], L53099 = [1, 3, 5, 15, 26, 26], L53158 = [1, 3, 5, 17, 21, 23], L53161 = [1, 3, 5, 17, 21, 26], L53168 = [1, 3, 5, 17, 23, 25], L53169 = [1, 3, 5, 17, 23, 26], L53174 = [1, 3, 5, 17, 26, 26], L53224 = [1, 3, 5, 19, 21, 26], L53232 = [1, 3, 5, 19, 26, 26], L53443 = [1, 3, 7, 9, 11, 17], L53445 = [1, 3, 7, 9, 11, 23], L53451 = [1, 3, 7, 9, 13, 19], L53453 = [1, 3, 7, 9, 13, 21], L53455 = [1, 3, 7, 9, 13, 23], L53472 = [1, 3, 7, 9, 19, 21], L53476 = [1, 3, 7, 9, 19, 26], L53484 = [1, 3, 7, 9, 21, 23], L53485 = [1, 3, 7, 9, 21, 26], L53491 = [1, 3, 7, 9, 23, 26], L53611 = [1, 3, 7, 11, 13, 13], L53614 = [1, 3, 7, 11, 13, 17], L53617 = [1, 3, 7, 11, 13, 23], L53619 = [1, 3, 7, 11, 13, 25], L53620 = [1, 3, 7, 11, 13, 26], L53635 = [1, 3, 7, 11, 17, 25], L53636 = [1, 3, 7, 11, 17, 26], L53650 = [1, 3, 7, 11, 23, 26], L53654 = [1, 3, 7, 11, 25, 26], L53655 = [1, 3, 7, 11, 26, 26], L53742 = [1, 3, 7, 13, 13, 15], L53756 = [1, 3, 7, 13, 15, 25], L53757 = [1, 3, 7, 13, 15, 26], L53769 = [1, 3, 7, 13, 17, 23], L53771 = [1, 3, 7, 13, 17, 25], L53817 = [1, 3, 7, 15, 25, 26], L53818 = [1, 3, 7, 15, 26, 26], L53874 = [1, 3, 7, 17, 23, 26], L53878 = [1, 3, 7, 17, 25, 26],
92
EMILIO A. LAURET
Table 4. (continued) n = 6 q I indexes of I-isospectral families 52 {0} {13875, 13877, 13878}, {13880, 13897}, {13882, 13886}, {13891, 13903}, (cont.) {14059, 14065}, {14060, 14061, 14062}, {14063, 14068}, {14066, 14072}, {14069, 14074}, {25108, 25112}, {25162, 25175}, {43524, 43528}, {43751, 43762}, {52382, 52392}, {52384, 52388}, {52390, 52427, 52649}, {52395, 52646}, {52397, 52445}, {52429, 52448, 52648, 52680}, {52430, 52682}, {52450, 52651, 52702, 53080}, {52657, 52660}, {52664, 52960}, {52681, 53443}, {52683, 52703}, {52700, 52765}, {52723, 53169}, {52745, 53453}, {52781, 53472}, {52783, 53445}, {52784, 53485}, {52915, 52917}, {52919, 53611, 53742}, {52942, 53614}, {52946, 52963}, {52958, 53451}, {52974, 53617}, {52978, 53620, 53757}, {53091, 53636}, {53099, 53174}, {53161, 53476}, {53224, 53650}, {53232, 53655, 53818}, {53455, 53769}, {53484, 53635}, {53491, 53874}, {53619, 53756}, {53654, 53817}, {53771, 54977}, {53878, 54990}, {54452, 59374}, {55444, 64483}, {56372, 65238}, {56395, 64788}, {56420, 64832, 65207}, {56425, 65243}, {56544, 64792}, {56655, 64849, 65210},
L54452 = [1, 3, 8, 12, 15, 16], L54977 = [1, 3, 9, 11, 13, 17], L54990 = [1, 3, 9, 11, 17, 26], L55444 = [1, 3, 10, 14, 15, 18], L55722 = [1, 3, 11, 13, 13, 23], L55762 = [1, 3, 11, 13, 23, 26], L55898 = [1, 3, 11, 23, 26, 26], L56372 = [1, 3, 13, 13, 13, 19], L56395 = [1, 3, 13, 13, 15, 21], L56396 = [1, 3, 13, 13, 15, 23], L56420 = [1, 3, 13, 13, 19, 21], L56425 = [1, 3, 13, 13, 19, 26], L56544 = [1, 3, 13, 15, 21, 26], L56546 = [1, 3, 13, 15, 23, 26], L56655 = [1, 3, 13, 19, 21, 26], L56667 = [1, 3, 13, 19, 26, 26], L57071 = [1, 3, 15, 21, 26, 26], L57074 = [1, 3, 15, 23, 26, 26], L57422 = [1, 3, 19, 21, 26, 26], L57444 = [1, 3, 19, 26, 26, 26], L59126 = [1, 4, 5, 6, 13, 21], L59129 = [1, 4, 5, 6, 13, 25], L59163 = [1, 4, 5, 6, 21, 26], L59171 = [1, 4, 5, 6, 25, 26], L59374 = [1, 4, 5, 9, 12, 20], L64483 = [1, 5, 6, 9, 14, 22], L64788 = [1, 5, 7, 11, 13, 13], L64792 = [1, 5, 7, 11, 13, 26], L64801 = [1, 5, 7, 11, 26, 26], L64832 = [1, 5, 7, 13, 13, 23], L64849 = [1, 5, 7, 13, 23, 26], L64885 = [1, 5, 7, 23, 26, 26], L65049 = [1, 5, 8, 13, 14, 21], L65053 = [1, 5, 8, 13, 14, 25], L65112 = [1, 5, 8, 14, 21, 26], L65122 = [1, 5, 8, 14, 25, 26], L65207 = [1, 5, 9, 11, 13, 13], L65210 = [1, 5, 9, 11, 13, 26], L65216 = [1, 5, 9, 11, 26, 26], L65238 = [1, 5, 9, 13, 13, 13], L65243 = [1, 5, 9, 13, 13, 26], L65257 = [1, 5, 9, 13, 26, 26], L65287 = [1, 5, 9, 26, 26, 26], L65316 = [1, 5, 11, 13, 13, 13], L65322 = [1, 5, 11, 13, 13, 26], L65342 = [1, 5, 11, 13, 26, 26], L65392 = [1, 5, 11, 26, 26, 26], L65519 = [1, 5, 13, 13, 13, 23], L65551 = [1, 5, 13, 13, 23, 26], L65645 = [1, 5, 13, 23, 26, 26], L65870 = [1, 5, 23, 26, 26, 26], L75230 = [2, 4, 6, 13, 18, 24], L75291 = [2, 4, 8, 13, 20, 22], L75301 = [2, 4, 10, 12, 13, 14], L75305 = [2, 4, 10, 12, 13, 24], L75351 = [2, 4, 12, 13, 14, 16], L75382 = [2, 4, 13, 13, 14, 16], L75397 = [2, 4, 13, 13, 20, 22], L75408 = [2, 4, 13, 14, 16, 26], L75432 = [2, 4, 13, 18, 20, 22], L75433 = [2, 4, 13, 18, 20, 24], L75445 = [2, 4, 13, 20, 22, 26], L75467 = [2, 6, 8, 10, 13, 16], L75473 = [2, 6, 8, 13, 13, 16], L75475 = [2, 6, 8, 13, 13, 20], L75476 = [2, 6, 8, 13, 13, 24], L75485 = [2, 6, 8, 13, 16, 26], L75490 = [2, 6, 8, 13, 20, 26], L75492 = [2, 6, 8, 13, 24, 26], L75494 = [2, 6, 10, 13, 13, 13], L75495 = [2, 6, 10, 13, 13, 14], L75497 = [2, 6, 10, 13, 13, 18], L75498 = [2, 6, 10, 13, 13, 22], L75500 = [2, 6, 10, 13, 13, 26], L75503 = [2, 6, 10, 13, 14, 26], L75508 = [2, 6, 10, 13, 18, 26], L75509 = [2, 6, 10, 13, 22, 26], L75512 = [2, 6, 10, 13, 26, 26], L75514 = [2, 6, 13, 13, 13, 14], L75516 = [2, 6, 13, 13, 13, 18], L75518 = [2, 6, 13, 13, 13, 22], L75523 = [2, 6, 13, 13, 14, 26], L75529 = [2, 6, 13, 13, 18, 26], L75535 = [2, 6, 13, 13, 22, 26], L75544 = [2, 6, 13, 14, 26, 26], L75559 = [2, 6, 13, 18, 26, 26], L75571 = [2, 6, 13, 22, 26, 26], L75620 = [2, 8, 10, 13, 13, 16], L75625 = [2, 8, 10, 13, 16, 26], L75975 = [4, 8, 12, 13, 13, 13], L75976 = [4, 8, 12, 13, 13, 16], L75977 = [4, 8, 12, 13, 13, 20], L75978 = [4, 8, 12, 13, 13, 24], L75979 = [4, 8, 12, 13, 13, 26], L75981 = [4, 8, 12, 13, 16, 26], L75982 = [4, 8, 12, 13, 20, 26], L75983 = [4, 8, 12, 13, 24, 26], L75984 = [4, 8, 12, 13, 26, 26], L75986 = [4, 8, 13, 13, 13, 16], L75987 = [4, 8, 13, 13, 13, 20], L75989 = [4, 8, 13, 13, 16, 26], L75990 = [4, 8, 13, 13, 20, 26],
APPENDIX
93
Table 4. (continued) n = 6 q 52 (cont.)
I {0}
indexes of I-isospectral families {56667, 65257}, {57071, 64801}, {57422, 64885, 65216}, {57444, 65287}, {59126, 59129}, {59163, 59171}, {65049, 65053}, {65112, 65122}, {65316, 65519}, {65322, 65551}, {65342, 65645}, {65392, 65870}, {75230, 75301}, {75291, 75305}, {75351, 75433}, {75382, 75473}, {75397, 75620}, {75408, 75485}, {75432, 75467}, {75445, 75625}, {75475, 75476}, {75490, 75492}, {75494, 75516}, {75495, 75497, 75498}, {75500, 75529}, {75503, 75508, 75509}, {75512, 75559}, {75514, 75518}, {75523, 75535}, {75544, 75571}, {75975, 75986}, {75976, 75977, 75978}, {75979, 75989}, {75981, 75982, 75983}, {75984, 75992}, {75987, 75996}, {75990, 75998}, {75993, 76000} {0, 1} {1036, 1083}, {8681, 8854}, {8721, 9004}, {13877, 13878}, {14060, 14061}, {52448, 52680}, {52702, 53080}, {52712, 53158}, {52722, 53168}, {55722, 56396}, {55762, 56546}, {55898, 57074}, {75497, 75498}, {75508, 75509}, {75976, 75977}, {75981, 75982} {0, 1, 2, 3} {52427, 52649}
L75992 = [4, 8, 13, 16, 26, 26], L75993 = [4, 8, 13, 20, 26, 26], L75996 = [4, 12, 13, 13, 13, 16], L75998 = [4, 12, 13, 13, 16, 26], L76000 = [4, 12, 13, 16, 26, 26]. q = 53 : L34774 = [1, 4, 11, 15, 24, 25], L34777 = [1, 4, 11, 17, 24, 25]. q = 54 : L1437 = [0, 0, 1, 4, 7, 17], L1439 = [0, 0, 1, 4, 7, 19], L1645 = [0, 0, 1, 5, 7, 17], L1650 = [0, 0, 1, 5, 7, 25], L1682 = [0, 0, 1, 5, 11, 13], L1706 = [0, 0, 1, 5, 13, 17], L1748 = [0, 0, 1, 5, 19, 23], L2082 = [0, 0, 1, 8, 10, 17], L2084 = [0, 0, 1, 8, 10, 19], L9152 = [0, 1, 2, 13, 17, 23], L10317 = [0, 1, 3, 5, 11, 23], L10349 = [0, 1, 3, 5, 13, 25], L10390 = [0, 1, 3, 5, 17, 25], L10716 = [0, 1, 3, 7, 11, 13], L10751 = [0, 1, 3, 7, 13, 25], L10875 = [0, 1, 3, 8, 10, 17], L10877 = [0, 1, 3, 8, 10, 19], L11358 = [0, 1, 3, 11, 19, 23], L12600 = [0, 1, 4, 7, 11, 17], L12647 = [0, 1, 4, 7, 17, 18], L12655 = [0, 1, 4, 7, 18, 19], L13801 = [0, 1, 5, 6, 11, 19], L13804 = [0, 1, 5, 6, 11, 25], L13830 = [0, 1, 5, 6, 13, 25], L13916 = [0, 1, 5, 7, 9, 17], L13921 = [0, 1, 5, 7, 9, 25], L13925 = [0, 1, 5, 7, 11, 17], L13927 = [0, 1, 5, 7, 11, 19], L13928 = [0, 1, 5, 7, 11, 23], L13930 = [0, 1, 5, 7, 11, 25], L13940 = [0, 1, 5, 7, 12, 25], L13943 = [0, 1, 5, 7, 13, 17], L13945 = [0, 1, 5, 7, 13, 19], L13947 = [0, 1, 5, 7, 13, 23], L13949 = [0, 1, 5, 7, 13, 25], L13958 = [0, 1, 5, 7, 17, 18], L13961 = [0, 1, 5, 7, 17, 25], L13962 = [0, 1, 5, 7, 17, 27], L13967 = [0, 1, 5, 7, 18, 25], L13976 = [0, 1, 5, 7, 25, 27], L14102 = [0, 1, 5, 9, 11, 13], L14126 = [0, 1, 5, 9, 13, 17], L14168 = [0, 1, 5, 9, 19, 23], L14194 = [0, 1, 5, 11, 13, 18], L14195 = [0, 1, 5, 11, 13, 19], L14196 = [0, 1, 5, 11, 13, 27], L14326 = [0, 1, 5, 13, 17, 18], L14332 = [0, 1, 5, 13, 17, 27], L14477 = [0, 1, 5, 18, 19, 23], L14508 = [0, 1, 5, 19, 23, 27], L14892 = [0, 1, 6, 8, 10, 17], L14894 = [0, 1, 6, 8, 10, 19], L16249 = [0, 1, 8, 9, 10, 17], L16251 = [0, 1, 8, 9, 10, 19], L16369 = [0, 1, 8, 10, 12, 17], L16371 = [0, 1, 8, 10, 12, 19], L16398 = [0, 1, 8, 10, 15, 17], L16400 = [0, 1, 8, 10, 15, 19], L16416 = [0, 1, 8, 10, 17, 18], L16418 = [0, 1, 8, 10, 17, 21], L16420 = [0, 1, 8, 10, 17, 24], L16422 = [0, 1, 8, 10, 17, 27], L16424 = [0, 1, 8, 10, 18, 19], L16432 = [0, 1, 8, 10, 19, 21], L16433 = [0, 1, 8, 10, 19, 24], L16434 = [0, 1, 8, 10, 19, 27], L19970 = [0, 2, 3, 4, 8, 20], L19990 = [0, 2, 3, 4, 10, 14], L20337 = [0, 2, 3, 10, 22, 26], L20406 = [0, 2, 3, 14, 22, 26], L20533 = [0, 2, 4, 8, 9, 22], L20541 = [0, 2, 4, 8, 22, 27], L20556 = [0, 2, 4, 9, 10, 14], L20559 = [0, 2, 4, 9, 10, 20], L20572 = [0, 2, 4, 9, 14, 16], L20574 = [0, 2, 4, 9, 14, 20], L20603 = [0, 2, 4, 10, 14, 27], L20606 = [0, 2, 4, 10, 20, 27], L20633 = [0, 2, 4, 14, 16, 27], L20635 = [0, 2, 4, 14, 20, 27], L54417 = [1, 2, 4, 10, 22, 25], L56131 = [1, 2, 5, 10, 16, 22], L58930 = [1, 2, 7, 8, 16, 20], L59295 = [1, 2, 7, 10, 20, 25], L60627 = [1, 2, 8, 11, 16, 25], L62644 = [1, 2, 10, 11, 16, 20], L64892 = [1, 2, 13, 17, 18, 23], L66300 = [1, 2, 17, 22, 23, 25], L68091 = [1, 3, 3, 8, 10, 17], L68093 = [1, 3, 3, 8, 10, 19], L71384 = [1, 3, 5, 7, 11, 21], L71405 = [1, 3, 5, 7, 13, 15], L71459 = [1, 3, 5, 7, 19, 23], L71681 = [1, 3, 5, 9, 11, 23], L71713 = [1, 3, 5, 9, 13, 25], L71754 = [1, 3, 5, 9, 17, 25], L71825 = [1, 3, 5, 11, 13, 17], L71847 = [1, 3, 5, 11, 15, 17], L71849 = [1, 3, 5, 11, 15, 19], L71867 =
94
EMILIO A. LAURET
Table 4. (continued) n = 6 q I indexes of I-isospectral families 53 {0} {34774, 34777} 54 {0} {1437, 1439}, {1645, 1650, 1682}, {1706, 1748}, {2082, 2084}, {9152, 12600}, {10317, 10716}, {10349, 10390}, {10751, 11358}, {10875, 10877}, {12647, 12655}, {13801, 13804}, {13830, 13940}, {13916, 13921, 14102}, {13925, 13945}, {13927, 13928}, {13943, 13949, 13961, 14195}, {13958, 13967, 14194}, {13962, 13976, 14196}, {14126, 14168}, {14326, 14477}, {14332, 14508}, {14892, 14894}, {16249, 16251}, {16369, 16371}, {16398, 16400}, {16416, 16424}, {16418, 16432}, {16420, 16433}, {16422, 16434}, {19970, 19990}, {20337, 20406}, {20533, 20556, 20559}, {20541, 20603, 20606}, {20572, 20574}, {20633, 20635}, {54417, 56131}, {58930, 62644}, {59295, 60627}, {64892, 84643}, {66300, 91162}, {68091, 68093}, {71384, 71405}, {71459, 71825}, {71681, 74195}, {71713, 71754}, {71847, 71849}, {71867, 71882}, {71876, 74458}, {71885, 74457}, {71901, 74463}, {72079, 72308}, {72094, 74691}, {72109, 72331}, {72311, 74471}, {72394, 74695}, {72396, 74613}, {72947, 72949}, {74230, 76365},
[1, 3, 5, 11, 17, 21], L71876 = [1, 3, 5, 11, 18, 23], L71882 = [1, 3, 5, 11, 19, 21], L71885 = [1, 3, 5, 11, 19, 25], L71901 = [1, 3, 5, 11, 23, 27], L72079 = [1, 3, 5, 13, 18, 25], L72094 = [1, 3, 5, 13, 21, 23], L72109 = [1, 3, 5, 13, 25, 27], L72308 = [1, 3, 5, 17, 18, 25], L72311 = [1, 3, 5, 17, 19, 21], L72331 = [1, 3, 5, 17, 25, 27], L72394 = [1, 3, 5, 19, 21, 23], L72396 = [1, 3, 5, 19, 21, 25], L72947 = [1, 3, 6, 8, 10, 17], L72949 = [1, 3, 6, 8, 10, 19], L74195 = [1, 3, 7, 9, 11, 13], L74230 = [1, 3, 7, 9, 13, 25], L74457 = [1, 3, 7, 11, 13, 17], L74458 = [1, 3, 7, 11, 13, 18], L74463 = [1, 3, 7, 11, 13, 27], L74471 = [1, 3, 7, 11, 15, 25], L74613 = [1, 3, 7, 13, 15, 17], L74631 = [1, 3, 7, 13, 17, 21], L74642 = [1, 3, 7, 13, 18, 25], L74661 = [1, 3, 7, 13, 23, 25], L74666 = [1, 3, 7, 13, 25, 27], L74691 = [1, 3, 7, 15, 17, 19], L74695 = [1, 3, 7, 15, 17, 25], L74922 = [1, 3, 7, 21, 23, 25], L75172 = [1, 3, 8, 9, 10, 17], L75174 = [1, 3, 8, 9, 10, 19], L75334 = [1, 3, 8, 10, 12, 17], L75336 = [1, 3, 8, 10, 12, 19], L75369 = [1, 3, 8, 10, 15, 17], L75371 = [1, 3, 8, 10, 15, 19], L75389 = [1, 3, 8, 10, 17, 18], L75391 = [1, 3, 8, 10, 17, 21], L75393 = [1, 3, 8, 10, 17, 24], L75396 = [1, 3, 8, 10, 17, 27], L75398 = [1, 3, 8, 10, 18, 19], L75407 = [1, 3, 8, 10, 19, 21], L75408 = [1, 3, 8, 10, 19, 24], L75409 = [1, 3, 8, 10, 19, 27], L76365 = [1, 3, 9, 11, 19, 23], L77766 = [1, 3, 11, 13, 23, 25], L77915 = [1, 3, 11, 18, 19, 23], L77942 = [1, 3, 11, 19, 23, 27], L82706 = [1, 4, 5, 17, 19, 26], L84643 = [1, 4, 7, 11, 17, 18], L84862 = [1, 4, 7, 17, 18, 18], L84887 = [1, 4, 7, 18, 18, 19], L87062 = [1, 4, 10, 13, 17, 19], L90095 = [1, 5, 6, 9, 11, 19], L90098 = [1, 5, 6, 9, 11, 25], L90124 = [1, 5, 6, 9, 13, 25], L90235 = [1, 5, 6, 11, 18, 19], L90238 = [1, 5, 6, 11, 18, 25], L90245 = [1, 5, 6, 11, 19, 27], L90254 = [1, 5, 6, 11, 25, 27], L90274 = [1, 5, 6, 12, 13, 17], L90279 = [1, 5, 6, 12, 13, 23], L90304 = [1, 5, 6, 12, 17, 19], L90381 = [1, 5, 6, 13, 18, 25], L90396 = [1, 5, 6, 13, 23, 24], L90401 = [1, 5, 6, 13, 25, 27], L90511 = [1, 5, 6, 17, 19, 24], L90577 = [1, 5, 6, 19, 23, 24], L90722 = [1, 5, 7, 9, 9, 17], L90727 = [1, 5, 7, 9, 9, 25], L90731 = [1, 5, 7, 9, 11, 17], L90733 = [1, 5, 7, 9, 11, 19], L90734 = [1, 5, 7, 9, 11, 23], L90736 = [1, 5, 7, 9, 11, 25], L90746 = [1, 5, 7, 9, 12, 25], L90749 = [1, 5, 7, 9, 13, 17], L90751 = [1, 5, 7, 9, 13, 19], L90753 = [1, 5, 7, 9, 13, 23], L90755 = [1, 5, 7, 9, 13, 25], L90764 = [1, 5, 7, 9, 17, 18], L90767 = [1, 5, 7, 9, 17, 25], L90768 = [1, 5, 7, 9, 17, 27], L90773 = [1, 5, 7, 9, 18, 25], L90782 = [1, 5, 7, 9, 25, 27], L90785 = [1, 5, 7, 11, 13, 17], L90787 = [1, 5, 7, 11, 13, 19], L90789 = [1, 5, 7, 11, 13, 25], L90797 = [1, 5, 7, 11, 17, 18], L90798 = [1, 5, 7, 11, 17, 19], L90799 = [1, 5, 7, 11, 17, 23], L90801 = [1, 5, 7, 11, 17, 25], L90802 = [1, 5, 7, 11, 17, 27], L90804 = [1, 5, 7, 11, 18, 19], L90805 = [1, 5, 7, 11, 18, 23], L90807 = [1, 5, 7, 11, 18, 25], L90810 = [1, 5, 7, 11, 19, 27], L90811 = [1, 5, 7, 11, 23, 25], L90812 = [1, 5, 7, 11, 23, 27], L90815 = [1, 5, 7, 11, 25, 27], L90850 = [1, 5, 7, 12, 18, 25], L90860 = [1, 5, 7, 12, 25, 27], L90869 = [1, 5, 7, 13, 17, 18], L90870 = [1, 5, 7, 13, 17, 19], L90873 = [1, 5, 7, 13, 17, 27], L90875 = [1, 5, 7, 13, 18, 19], L90877 = [1, 5, 7, 13, 18, 23], L90879 = [1, 5, 7, 13, 18, 25], L90881 = [1, 5, 7, 13, 19, 27], L90886 =
APPENDIX
95
Table 4. (continued) n = 6 q I indexes of I-isospectral families 54 {0} {74631, 74922}, {74642, 77915}, {74661, 77766}, {74666, 77942}, {75172, 75174}, (cont.) {75334, 75336}, {75369, 75371}, {75389, 75398}, {75391, 75407}, {75393, 75408}, {75396, 75409}, {82706, 87062}, {84862, 84887}, {90095, 90098}, {90124, 90746}, {90235, 90238}, {90245, 90254}, {90274, 90577}, {90279, 90396}, {90304, 90511}, {90381, 90850}, {90401, 90860}, {90722, 90727, 91498}, {90731, 90751}, {90733, 90734}, {90749, 90755, 90767, 91591}, {90764, 90773, 91590}, {90768, 90782, 91592}, {90785, 90787, 90799}, {90789, 90798, 90811}, {90797, 90875}, {90802, 90881}, {90804, 90805}, {90810, 90812}, {90869, 90879, 90919, 91970}, {90873, 90889, 90927, 91972}, {90916, 90933, 91969}, {90920, 90942, 91971}, {90928, 90956, 91973}, {91522, 91564}, {91722, 91873}, {91728, 91904}, {92467, 92918}, {92473, 92949}, {92490, 93025}, {93469, 93471}, {94955, 94957}, {95077, 95079}, {95108, 95110}, {95126, 95134}, {95128, 95142}, {95130, 95143}, {95132, 95144}, {100612, 100614}, {100732, 100734}, {100761, 100763}, {100779, 100787}, {100781, 100795}, {100783, 100796}, {100785, 100797}, {101330, 101332}, {101359, 101361}, {101377, 101385}, {101379, 101393}, {101381, 101394}, {101383, 101395}, {101510, 101512}, {101528, 101536}, {101530, 101544}, {101532, 101545}, {101534, 101546}, {101611, 101636},
[1, 5, 7, 13, 23, 27], L90889 = [1, 5, 7, 13, 25, 27], L90916 = [1, 5, 7, 17, 18, 18], L90919 = [1, 5, 7, 17, 18, 25], L90920 = [1, 5, 7, 17, 18, 27], L90927 = [1, 5, 7, 17, 25, 27], L90928 = [1, 5, 7, 17, 27, 27], L90933 = [1, 5, 7, 18, 18, 25], L90942 = [1, 5, 7, 18, 25, 27], L90956 = [1, 5, 7, 25, 27, 27], L91162 = [1, 5, 8, 11, 13, 16], L91498 = [1, 5, 9, 9, 11, 13], L91522 = [1, 5, 9, 9, 13, 17], L91564 = [1, 5, 9, 9, 19, 23], L91590 = [1, 5, 9, 11, 13, 18], L91591 = [1, 5, 9, 11, 13, 19], L91592 = [1, 5, 9, 11, 13, 27], L91722 = [1, 5, 9, 13, 17, 18], L91728 = [1, 5, 9, 13, 17, 27], L91873 = [1, 5, 9, 18, 19, 23], L91904 = [1, 5, 9, 19, 23, 27], L91969 = [1, 5, 11, 13, 18, 18], L91970 = [1, 5, 11, 13, 18, 19], L91971 = [1, 5, 11, 13, 18, 27], L91972 = [1, 5, 11, 13, 19, 27], L91973 = [1, 5, 11, 13, 27, 27], L92467 = [1, 5, 13, 17, 18, 18], L92473 = [1, 5, 13, 17, 18, 27], L92490 = [1, 5, 13, 17, 27, 27], L92918 = [1, 5, 18, 18, 19, 23], L92949 = [1, 5, 18, 19, 23, 27], L93025 = [1, 5, 19, 23, 27, 27], L93469 = [1, 6, 6, 8, 10, 17], L93471 = [1, 6, 6, 8, 10, 19], L94955 = [1, 6, 8, 9, 10, 17], L94957 = [1, 6, 8, 9, 10, 19], L95077 = [1, 6, 8, 10, 12, 17], L95079 = [1, 6, 8, 10, 12, 19], L95108 = [1, 6, 8, 10, 15, 17], L95110 = [1, 6, 8, 10, 15, 19], L95126 = [1, 6, 8, 10, 17, 18], L95128 = [1, 6, 8, 10, 17, 21], L95130 = [1, 6, 8, 10, 17, 24], L95132 = [1, 6, 8, 10, 17, 27], L95134 = [1, 6, 8, 10, 18, 19], L95142 = [1, 6, 8, 10, 19, 21], L95143 = [1, 6, 8, 10, 19, 24], L95144 = [1, 6, 8, 10, 19, 27], L100612 = [1, 8, 9, 9, 10, 17], L100614 = [1, 8, 9, 9, 10, 19], L100732 = [1, 8, 9, 10, 12, 17], L100734 = [1, 8, 9, 10, 12, 19], L100761 = [1, 8, 9, 10, 15, 17], L100763 = [1, 8, 9, 10, 15, 19], L100779 = [1, 8, 9, 10, 17, 18], L100781 = [1, 8, 9, 10, 17, 21], L100783 = [1, 8, 9, 10, 17, 24], L100785 = [1, 8, 9, 10, 17, 27], L100787 = [1, 8, 9, 10, 18, 19], L100795 = [1, 8, 9, 10, 19, 21], L100796 = [1, 8, 9, 10, 19, 24], L100797 = [1, 8, 9, 10, 19, 27], L101330 = [1, 8, 10, 12, 12, 17], L101332 = [1, 8, 10, 12, 12, 19], L101359 = [1, 8, 10, 12, 15, 17], L101361 = [1, 8, 10, 12, 15, 19], L101377 = [1, 8, 10, 12, 17, 18], L101379 = [1, 8, 10, 12, 17, 21], L101381 = [1, 8, 10, 12, 17, 24], L101383 = [1, 8, 10, 12, 17, 27], L101385 = [1, 8, 10, 12, 18, 19], L101393 = [1, 8, 10, 12, 19, 21], L101394 = [1, 8, 10, 12, 19, 24], L101395 = [1, 8, 10, 12, 19, 27], L101510 = [1, 8, 10, 15, 15, 17], L101512 = [1, 8, 10, 15, 15, 19], L101528 = [1, 8, 10, 15, 17, 18], L101530 = [1, 8, 10, 15, 17, 21], L101532 = [1, 8, 10, 15, 17, 24], L101534 = [1, 8, 10, 15, 17, 27], L101536 = [1, 8, 10, 15, 18, 19], L101544 = [1, 8, 10, 15, 19, 21], L101545 = [1, 8, 10, 15, 19, 24], L101546 = [1, 8, 10, 15, 19, 27], L101611 = [1, 8, 10, 17, 18, 18], L101613 = [1, 8, 10, 17, 18, 21], L101615 = [1, 8, 10, 17, 18, 24], L101617 = [1, 8, 10, 17, 18, 27], L101622 = [1, 8, 10, 17, 21, 21], L101624 = [1, 8, 10, 17, 21, 24], L101626 = [1, 8, 10, 17, 21, 27], L101630 = [1, 8, 10, 17, 24, 24],
96
EMILIO A. LAURET
Table 4. (continued) n = 6 q 54 (cont.)
I {0}
indexes of I-isospectral families {101613, 101644}, {101615, 101645}, {101617, 101646}, {101622, 101672}, {101624, 101673}, {101626, 101674}, {101630, 101675}, {101632, 101676}, {101634, 101677}, {115538, 115626}, {115589, 115707}, {115599, 115713}, {115809, 115830}, {115813, 115833}, {115853, 115881}, {116227, 116956, 116996}, {116791, 116860}, {117024, 117237}, {117051, 117247}, {117495, 117498}, {117516, 117538}, {117551, 117554}, {117586, 117625}, {117640, 117715, 117718}, {117643, 117644}, {117646, 117647, 117651, 117656}, {117662, 117769, 117777}, {117665, 117768}, {117666, 117771}, {117669, 117772, 117780}, {117673, 117674}, {117676, 117677, 117681, 117686}, {117692, 117914, 117922}, {117695, 117913}, {117696, 117916}, {117699, 117917, 117925}, {117731, 117733}, {117831, 117837}, {117835, 117842}, {118024, 118030}, {118028, 118035} {0, 1} {13961, 14195}, {90767, 91591}, {90919, 91970}, {90927, 91972}, {117646, 117647}, {117676, 117677} {0, 1, 2} {13930, 13947}, {90736, 90753}, {90789, 90798}, {90801, 90870}, {90807, 90877}, {90815, 90886}, {117654, 117770}, {117684, 117915}
L101632 = [1, 8, 10, 17, 24, 27], L101634 = [1, 8, 10, 17, 27, 27], L101636 = [1, 8, 10, 18, 18, 19], L101644 = [1, 8, 10, 18, 19, 21], L101645 = [1, 8, 10, 18, 19, 24], L101646 = [1, 8, 10, 18, 19, 27], L101672 = [1, 8, 10, 19, 21, 21], L101673 = [1, 8, 10, 19, 21, 24], L101674 = [1, 8, 10, 19, 21, 27], L101675 = [1, 8, 10, 19, 24, 24], L101676 = [1, 8, 10, 19, 24, 27], L101677 = [1, 8, 10, 19, 27, 27], L115538 = [2, 3, 4, 8, 9, 20], L115589 = [2, 3, 4, 8, 18, 20], L115599 = [2, 3, 4, 8, 20, 27], L115626 = [2, 3, 4, 9, 10, 14], L115707 = [2, 3, 4, 10, 14, 18], L115713 = [2, 3, 4, 10, 14, 27], L115809 = [2, 3, 4, 14, 15, 16], L115813 = [2, 3, 4, 14, 15, 22], L115830 = [2, 3, 4, 14, 20, 21], L115833 = [2, 3, 4, 14, 21, 22], L115853 = [2, 3, 4, 15, 16, 20], L115881 = [2, 3, 4, 16, 20, 21], L116227 = [2, 3, 6, 10, 20, 22], L116791 = [2, 3, 9, 10, 22, 26], L116860 = [2, 3, 9, 14, 22, 26], L116956 = [2, 3, 10, 12, 14, 22], L116996 = [2, 3, 10, 14, 24, 26], L117024 = [2, 3, 10, 18, 22, 26], L117051 = [2, 3, 10, 22, 26, 27], L117237 = [2, 3, 14, 18, 22, 26], L117247 = [2, 3, 14, 22, 26, 27], L117495 = [2, 4, 6, 9, 10, 20], L117498 = [2, 4, 6, 9, 10, 26], L117516 = [2, 4, 6, 9, 14, 26], L117538 = [2, 4, 6, 9, 20, 26], L117551 = [2, 4, 6, 10, 20, 27], L117554 = [2, 4, 6, 10, 26, 27], L117586 = [2, 4, 6, 14, 26, 27], L117625 = [2, 4, 6, 20, 26, 27], L117640 = [2, 4, 8, 9, 9, 22], L117643 = [2, 4, 8, 9, 10, 14], L117644 = [2, 4, 8, 9, 10, 16], L117646 = [2, 4, 8, 9, 10, 20], L117647 = [2, 4, 8, 9, 10, 22], L117651 = [2, 4, 8, 9, 14, 16], L117654 = [2, 4, 8, 9, 14, 22], L117656 = [2, 4, 8, 9, 14, 26], L117662 = [2, 4, 8, 9, 18, 22], L117665 = [2, 4, 8, 9, 20, 22], L117666 = [2, 4, 8, 9, 20, 24], L117669 = [2, 4, 8, 9, 22, 27], L117673 = [2, 4, 8, 10, 14, 27], L117674 = [2, 4, 8, 10, 16, 27], L117676 = [2, 4, 8, 10, 20, 27], L117677 = [2, 4, 8, 10, 22, 27], L117681 = [2, 4, 8, 14, 16, 27], L117684 = [2, 4, 8, 14, 22, 27], L117686 = [2, 4, 8, 14, 26, 27], L117692 = [2, 4, 8, 18, 22, 27], L117695 = [2, 4, 8, 20, 22, 27], L117696 = [2, 4, 8, 20, 24, 27], L117699 = [2, 4, 8, 22, 27, 27], L117715 = [2, 4, 9, 9, 10, 14], L117718 = [2, 4, 9, 9, 10, 20], L117731 = [2, 4, 9, 9, 14, 16], L117733 = [2, 4, 9, 9, 14, 20], L117768 = [2, 4, 9, 10, 14, 16], L117769 = [2, 4, 9, 10, 14, 18], L117770 = [2, 4, 9, 10, 14, 22], L117771 = [2, 4, 9, 10, 14, 24], L117772 = [2, 4, 9, 10, 14, 27], L117777 = [2, 4, 9, 10, 18, 20], L117780 = [2, 4, 9, 10, 20, 27], L117831 = [2, 4, 9, 14, 16, 18], L117835 = [2, 4, 9, 14, 16, 27], L117837 = [2, 4, 9, 14, 18, 20], L117842 = [2, 4, 9, 14, 20, 27], L117913 = [2, 4, 10, 14, 16, 27], L117914 = [2, 4, 10, 14, 18, 27], L117915 = [2, 4, 10, 14, 22, 27], L117916 = [2, 4, 10, 14, 24, 27], L117917 = [2, 4, 10, 14, 27, 27], L117922 = [2, 4, 10, 18, 20, 27], L117925 = [2, 4, 10, 20, 27, 27], L118024 = [2, 4, 14, 16, 18, 27], L118028 = [2, 4, 14, 16, 27, 27], L118030 = [2, 4, 14, 18, 20, 27], L118035 = [2, 4, 14, 20, 27, 27]. q = 55 : L1592 = [0, 0, 5, 10, 11, 15], L1593 = [0, 0, 5, 10, 11, 20], L7532 = [0, 1, 3, 8, 12, 19], L7551 = [0, 1, 3, 8, 14, 21], L9833 = [0, 1, 10, 12, 21, 23], L9943 = [0, 1, 11, 11, 22, 22], L10162 =
APPENDIX
97
Table 4. (continued) n = 6 q 55
I {0}
indexes of I-isospectral families {1592, 1593}, {7532, 7551}, {10162, 10163}, {10166, 10167}, {42128, 42187}, {46301, 46321}, {47468, 47487}, {47609, 47630}, {47616, 47680}, {47629, 47695}, {47633, 47700}, {50169, 50176}, {50172, 50389}, {50186, 50193}, {55704, 55705}, {55708, 55709} {0, 1} {50201, 50386} {2, 3, 4} {9833, 54990}, {9943, 10172}, {30138, 54856}, {42232, 53500}, {42792, 55078}, {47693, 55071}, {48163, 55081}
[0, 5, 10, 11, 11, 15], L10163 = [0, 5, 10, 11, 11, 20], L10166 = [0, 5, 10, 11, 15, 22], L10167 = [0, 5, 10, 11, 20, 22], L10172 = [0, 5, 11, 11, 22, 22], L30138 = [1, 1, 10, 12, 21, 23], L42128 = [1, 2, 9, 12, 13, 21], L42187 = [1, 2, 9, 12, 23, 24], L42232 = [1, 2, 9, 13, 20, 24], L42792 = [1, 2, 10, 12, 21, 23], L46301 = [1, 3, 5, 8, 12, 19], L46321 = [1, 3, 5, 8, 14, 21], L47468 = [1, 3, 8, 10, 12, 19], L47487 = [1, 3, 8, 10, 14, 21], L47609 = [1, 3, 8, 12, 14, 21], L47616 = [1, 3, 8, 12, 15, 19], L47629 = [1, 3, 8, 12, 19, 20], L47630 = [1, 3, 8, 12, 19, 21], L47633 = [1, 3, 8, 12, 19, 25], L47680 = [1, 3, 8, 14, 15, 21], L47693 = [1, 3, 8, 14, 19, 25], L47695 = [1, 3, 8, 14, 20, 21], L47700 = [1, 3, 8, 14, 21, 25], L48163 = [1, 3, 10, 12, 21, 23], L50169 = [1, 4, 6, 9, 14, 16], L50172 = [1, 4, 6, 9, 14, 21], L50176 = [1, 4, 6, 9, 14, 26], L50186 = [1, 4, 6, 9, 16, 19], L50193 = [1, 4, 6, 9, 19, 24], L50201 = [1, 4, 6, 9, 21, 24], L50386 = [1, 4, 6, 14, 16, 19], L50389 = [1, 4, 6, 14, 16, 24], L53500 = [1, 5, 10, 12, 21, 23], L54856 = [1, 10, 10, 12, 21, 23], L54990 = [1, 10, 11, 12, 21, 23], L55071 = [1, 10, 12, 15, 21, 23], L55078 = [1, 10, 12, 20, 21, 23], L55081 = [1, 10, 12, 21, 23, 25], L55704 = [5, 10, 11, 11, 11, 15], L55705 = [5, 10, 11, 11, 11, 20], L55708 = [5, 10, 11, 11, 15, 22], L55709 = [5, 10, 11, 11, 20, 22]. q = 56 : L91 = [0, 0, 0, 1, 3, 13], L93 = [0, 0, 0, 1, 3, 15], L100 = [0, 0, 0, 1, 3, 23], L134 = [0, 0, 0, 1, 5, 11], L983 = [0, 0, 1, 2, 13, 15], L995 = [0, 0, 1, 2, 13, 27], L1196 = [0, 0, 1, 3, 9, 17], L1200 = [0, 0, 1, 3, 9, 23], L1251 = [0, 0, 1, 3, 13, 14], L1254 = [0, 0, 1, 3, 13, 17], L1262 = [0, 0, 1, 3, 13, 28], L1264 = [0, 0, 1, 3, 14, 15], L1271 = [0, 0, 1, 3, 14, 23], L1283 = [0, 0, 1, 3, 15, 23], L1287 = [0, 0, 1, 3, 15, 28], L1347 = [0, 0, 1, 3, 23, 28], L1671 = [0, 0, 1, 5, 9, 13], L1678 = [0, 0, 1, 5, 9, 25], L1681 = [0, 0, 1, 5, 11, 14], L1686 = [0, 0, 1, 5, 11, 28], L1859 = [0, 0, 1, 6, 13, 15], L1866 = [0, 0, 1, 6, 13, 27], L2193 = [0, 0, 1, 8, 16, 24], L2279 = [0, 0, 1, 9, 15, 17], L2283 = [0, 0, 1, 9, 15, 25], L2337 = [0, 0, 1, 10, 13, 15], L2342 = [0, 0, 1, 10, 13, 27], L2786 = [0, 0, 2, 6, 7, 10], L2789 = [0, 0, 2, 6, 7, 18], L2919 = [0, 0, 7, 8, 16, 24], L5341 = [0, 1, 1, 8, 16, 24], L7084 = [0, 1, 2, 2, 13, 15], L7096 = [0, 1, 2, 2, 13, 27], L7706 = [0, 1, 2, 4, 13, 15], L7718 = [0, 1, 2, 4, 13, 27], L8223 = [0, 1, 2, 6, 13, 15], L8234 = [0, 1, 2, 6, 13, 27], L8671 = [0, 1, 2, 8, 13, 15], L8683 = [0, 1, 2, 8, 13, 27], L8720 = [0, 1, 2, 8, 16, 24], L9002 = [0, 1, 2, 10, 13, 15], L9013 = [0, 1, 2, 10, 13, 27], L9258 = [0, 1, 2, 12, 13, 15], L9270 = [0, 1, 2, 12, 13, 27], L9379 = [0, 1, 2, 13, 14, 15], L9391 = [0, 1, 2, 13, 14, 27], L9393 = [0, 1, 2, 13, 15, 16], L9395 = [0, 1, 2, 13, 15, 18], L9397 = [0, 1, 2, 13, 15, 20], L9399 = [0, 1, 2, 13, 15, 22], L9401 = [0, 1, 2, 13, 15, 24], L9405 = [0, 1, 2, 13, 15, 28], L9417 = [0, 1, 2, 13, 16, 27], L9434 = [0, 1, 2, 13, 18, 27], L9451 = [0, 1, 2, 13, 20, 27], L9463 = [0, 1, 2, 13, 22, 27], L9471 = [0, 1, 2, 13, 24, 27], L9475 = [0, 1, 2, 13, 27, 28], L10294 = [0, 1, 3, 5, 9, 13], L10296 = [0, 1, 3, 5, 9, 15], L10298 = [0, 1, 3, 5, 9, 17], L10312 = [0, 1, 3, 5, 11, 15], L10344 = [0, 1, 3, 5, 13, 17], L10373 = [0, 1, 3, 5, 15, 19], L10395 = [0, 1, 3, 5, 17, 21], L10510 = [0, 1, 3, 7, 9, 19], L10518 = [0, 1, 3, 7, 9, 27], L10573 = [0, 1, 3, 7, 13, 17], L10575 = [0, 1, 3, 7, 13, 19], L10577 = [0, 1, 3, 7, 13, 21], L10581 = [0, 1, 3, 7, 13, 27], L10603 = [0, 1, 3, 7, 15, 21], L10659 = [0, 1, 3, 7, 21, 23], L10823 = [0, 1, 3, 8, 16, 24], L10915 = [0, 1, 3, 9, 11, 25], L10924 = [0, 1, 3, 9, 13, 27], L10928 = [0, 1, 3, 9, 14, 17], L10932 = [0, 1, 3, 9, 14, 23], L10948 = [0, 1, 3, 9, 17, 28], L10965 = [0, 1, 3, 9, 23, 28], L11131 = [0, 1, 3, 11, 13, 17], L11136 = [0, 1, 3, 11, 13, 25], L11152 = [0, 1, 3, 11, 15, 17], L11335 = [0, 1, 3, 13, 14, 14], L11338 = [0, 1, 3, 13, 14, 17], L11346 = [0, 1, 3, 13, 14, 28], L11348 = [0, 1, 3, 13, 15, 17], L11369 = [0, 1, 3, 13, 17, 28], L11403 = [0, 1, 3, 13, 28, 28], L11405 = [0, 1, 3, 14, 14, 15], L11412 = [0, 1, 3, 14, 14, 23], L11424 = [0, 1, 3, 14, 15, 23], L11428 = [0, 1, 3, 14, 15, 28], L11488 = [0, 1, 3, 14, 23, 28], L11519 = [0, 1, 3, 15, 17, 27], L11543 = [0, 1, 3, 15, 21, 27], L11554 = [0, 1, 3, 15, 23, 28], L11561 = [0, 1, 3, 15, 28, 28], L11838 = [0, 1, 3, 23, 28, 28], L12416 = [0, 1, 4, 6, 13, 15],
98
EMILIO A. LAURET
Table 4. (continued) n = 6 q I indexes of I-isospectral families 56 {0} {91, 93}, {100, 134}, {983, 995}, {1196, 1200}, {1251, 1264}, {1254, 1671}, {1262, 1287}, {1271, 1681}, {1283, 1678}, {1347, 1686}, {1859, 1866}, {2279, 2283}, {2337, 2342}, {2786, 2789}, {7084, 7096}, {7706, 7718}, {8223, 8234}, {8671, 8683}, {9002, 9013}, {9258, 9270}, {9379, 9391}, {9393, 9417}, {9395, 9434}, {9397, 9451}, {9399, 9463}, {9401, 9471}, {9405, 9475}, {10294, 10296}, {10298, 10312}, {10344, 10373}, {10395, 10575}, {10510, 10518}, {10573, 13845}, {10577, 10603}, {10581, 11543}, {10659, 13859}, {10915, 10924}, {10928, 10932}, {10948, 10965}, {11131, 11136, 11152}, L12423 = [0, 1, 4, 6, 13, 27], L12819 = [0, 1, 4, 8, 16, 24], L13027 = [0, 1, 4, 10, 13, 15], L13033 = [0, 1, 4, 10, 13, 27], L13253 = [0, 1, 4, 12, 20, 28], L13845 = [0, 1, 5, 7, 9, 13], L13855 = [0, 1, 5, 7, 11, 13], L13859 = [0, 1, 5, 7, 11, 21], L13861 = [0, 1, 5, 7, 11, 25], L14019 = [0, 1, 5, 8, 16, 24], L14076 = [0, 1, 5, 9, 13, 14], L14079 = [0, 1, 5, 9, 13, 28], L14086 = [0, 1, 5, 9, 14, 25], L14116 = [0, 1, 5, 9, 25, 28], L14120 = [0, 1, 5, 11, 14, 14], L14125 = [0, 1, 5, 11, 14, 28], L14139 = [0, 1, 5, 11, 28, 28], L14546 = [0, 1, 6, 6, 13, 15], L14553 = [0, 1, 6, 6, 13, 27], L14864 = [0, 1, 6, 8, 13, 15], L14871 = [0, 1, 6, 8, 13, 27], L14902 = [0, 1, 6, 8, 16, 24], L15052 = [0, 1, 6, 10, 13, 15], L15059 = [0, 1, 6, 10, 13, 27], L15144 = [0, 1, 6, 12, 13, 15], L15151 = [0, 1, 6, 12, 13, 27], L15223 = [0, 1, 6, 13, 14, 15], L15230 = [0, 1, 6, 13, 14, 27], L15232 = [0, 1, 6, 13, 15, 16], L15233 = [0, 1, 6, 13, 15, 18], L15234 = [0, 1, 6, 13, 15, 20], L15237 = [0, 1, 6, 13, 15, 24], L15239 = [0, 1, 6, 13, 15, 28], L15246 = [0, 1, 6, 13, 16, 27], L15252 = [0, 1, 6, 13, 18, 27], L15258 = [0, 1, 6, 13, 20, 27], L15266 = [0, 1, 6, 13, 24, 27], L15268 = [0, 1, 6, 13, 27, 28], L15838 = [0, 1, 7, 8, 16, 24], L15925 = [0, 1, 7, 9, 15, 17], L15929 = [0, 1, 7, 9, 15, 25], L16526 = [0, 1, 8, 8, 16, 24], L16628 = [0, 1, 8, 9, 16, 24], L16691 = [0, 1, 8, 10, 13, 15], L16696 = [0, 1, 8, 10, 13, 27], L16722 = [0, 1, 8, 10, 16, 24], L16809 = [0, 1, 8, 12, 16, 24], L16865 = [0, 1, 8, 13, 16, 24], L16900 = [0, 1, 8, 14, 16, 24], L16961 = [0, 1, 8, 15, 16, 24], L16983 = [0, 1, 8, 16, 16, 24], L16991 = [0, 1, 8, 16, 17, 24], L17000 = [0, 1, 8, 16, 18, 24], L17007 = [0, 1, 8, 16, 20, 24], L17015 = [0, 1, 8, 16, 21, 24], L17021 = [0, 1, 8, 16, 22, 24], L17028 = [0, 1, 8, 16, 24, 24], L17029 = [0, 1, 8, 16, 24, 26], L17030 = [0, 1, 8, 16, 24, 27], L17031 = [0, 1, 8, 16, 24, 28], L17298 = [0, 1, 9, 14, 15, 17], L17302 = [0, 1, 9, 14, 15, 25], L17328 = [0, 1, 9, 15, 17, 21], L17330 = [0, 1, 9, 15, 17, 28], L17334 = [0, 1, 9, 15, 21, 25], L17340 = [0, 1, 9, 15, 25, 28], L17424 = [0, 1, 10, 10, 13, 15], L17429 = [0, 1, 10, 10, 13, 27], L17505 = [0, 1, 10, 12, 13, 15], L17510 = [0, 1, 10, 12, 13, 27], L17573 = [0, 1, 10, 13, 14, 15], L17578 = [0, 1, 10, 13, 14, 27], L17580 = [0, 1, 10, 13, 15, 16], L17582 = [0, 1, 10, 13, 15, 20], L17583 = [0, 1, 10, 13, 15, 24], L17585 = [0, 1, 10, 13, 15, 28], L17590 = [0, 1, 10, 13, 16, 27], L17597 = [0, 1, 10, 13, 20, 27], L17600 = [0, 1, 10, 13, 24, 27], L17602 = [0, 1, 10, 13, 27, 28], L19208 = [0, 2, 6, 7, 7, 10], L19211 = [0, 2, 6, 7, 7, 18], L19229 = [0, 2, 6, 7, 10, 14], L19231 = [0, 2, 6, 7, 10, 18], L19232 = [0, 2, 6, 7, 10, 21], L19233 = [0, 2, 6, 7, 10, 22], L19235 = [0, 2, 6, 7, 10, 28], L19238 = [0, 2, 6, 7, 14, 18], L19252 = [0, 2, 6, 7, 18, 21], L19253 = [0, 2, 6, 7, 18, 28], L19371 = [0, 2, 7, 8, 16, 24], L19606 = [0, 4, 7, 8, 12, 16], L19609 = [0, 4, 7, 8, 12, 24], L19619 = [0, 4, 7, 8, 16, 24], L19638 = [0, 4, 7, 12, 20, 28], L19651 = [0, 4, 7, 14, 21, 28], L19688 = [0, 7, 7, 8, 16, 24], L19706 = [0, 7, 8, 8, 16, 24], L19717 = [0, 7, 8, 14, 16, 24], L19719 = [0, 7, 8, 14, 21, 28], L19721 = [0, 7, 8, 16, 21, 24], L19723 = [0, 7, 8, 16, 24, 28], L32643 = [1, 1, 4, 12, 20, 28], L49328 = [1, 2, 2, 2, 13, 15], L49340 = [1, 2, 2, 2, 13, 27], L49952 = [1, 2, 2, 4, 13, 15], L49964 = [1, 2, 2, 4, 13, 27], L50479 = [1, 2, 2, 6, 13, 15], L50491 = [1, 2, 2, 6, 13, 27], L50937 = [1, 2, 2, 8, 13, 15], L50949 = [1, 2, 2, 8, 13, 27], L51291 = [1, 2, 2, 10, 13, 15], L51303 = [1, 2, 2, 10, 13, 27], L51572 = [1, 2, 2, 12, 13, 15], L51584 = [1, 2, 2, 12, 13, 27], L51695 = [1, 2, 2, 13, 14, 15], L51707 = [1, 2, 2, 13, 14, 27], L51709 = [1, 2, 2, 13, 15, 16], L51711 = [1, 2, 2, 13, 15, 18], L51713 = [1, 2, 2, 13, 15, 20], L51715 = [1, 2, 2, 13, 15, 22], L51717 = [1, 2, 2, 13, 15, 24], L51719 = [1, 2, 2, 13, 15, 26], L51721 = [1, 2, 2, 13, 15, 28], L51733 = [1, 2, 2, 13, 16, 27], L51754 = [1, 2, 2, 13, 18, 27], L51771 = [1, 2, 2, 13, 20, 27], L51785 = [1, 2, 2, 13, 22, 27], L51794 =
APPENDIX
99
Table 4. (continued) n = 6 q I indexes of I-isospectral families 56 {0} {11335, 11405}, {11338, 14076}, {11346, 11428}, {11348, 11519}, {11369, 14079}, (cont.) {11403, 11561}, {11412, 14120}, {11424, 14086}, {11488, 14125}, {11554, 14116}, {11838, 14139}, {12416, 12423}, {13027, 13033}, {13855, 13861}, {14546, 14553}, {14864, 14871}, {15052, 15059}, {15144, 15151}, {15223, 15230}, {15232, 15246}, {15233, 15252}, {15234, 15258}, {15237, 15266}, {15239, 15268}, {15925, 15929}, {16691, 16696}, {17298, 17302}, {17328, 17334}, {17330, 17340}, {17424, 17429},
[1, 2, 2, 13, 24, 27], L51799 = [1, 2, 2, 13, 26, 27], L51801 = [1, 2, 2, 13, 27, 28], L55125 = [1, 2, 4, 4, 13, 15], L55137 = [1, 2, 4, 4, 13, 27], L55646 = [1, 2, 4, 6, 13, 15], L55658 = [1, 2, 4, 6, 13, 27], L56101 = [1, 2, 4, 8, 13, 15], L56113 = [1, 2, 4, 8, 13, 27], L56449 = [1, 2, 4, 10, 13, 15], L56460 = [1, 2, 4, 10, 13, 27], L56724 = [1, 2, 4, 12, 13, 15], L56736 = [1, 2, 4, 12, 13, 27], L56813 = [1, 2, 4, 12, 20, 28], L56845 = [1, 2, 4, 13, 14, 15], L56857 = [1, 2, 4, 13, 14, 27], L56859 = [1, 2, 4, 13, 15, 16], L56861 = [1, 2, 4, 13, 15, 18], L56863 = [1, 2, 4, 13, 15, 20], L56865 = [1, 2, 4, 13, 15, 22], L56867 = [1, 2, 4, 13, 15, 24], L56871 = [1, 2, 4, 13, 15, 28], L56883 = [1, 2, 4, 13, 16, 27], L56901 = [1, 2, 4, 13, 18, 27], L56918 = [1, 2, 4, 13, 20, 27], L56930 = [1, 2, 4, 13, 22, 27], L56938 = [1, 2, 4, 13, 24, 27], L56942 = [1, 2, 4, 13, 27, 28], L58274 = [1, 2, 5, 9, 17, 26], L59507 = [1, 2, 6, 6, 13, 15], L59518 = [1, 2, 6, 6, 13, 27], L59942 = [1, 2, 6, 8, 13, 15], L59953 = [1, 2, 6, 8, 13, 27], L60280 = [1, 2, 6, 10, 13, 15], L60290 = [1, 2, 6, 10, 13, 27], L60531 = [1, 2, 6, 12, 13, 15], L60542 = [1, 2, 6, 12, 13, 27], L60638 = [1, 2, 6, 13, 14, 15], L60649 = [1, 2, 6, 13, 14, 27], L60651 = [1, 2, 6, 13, 15, 16], L60653 = [1, 2, 6, 13, 15, 18], L60655 = [1, 2, 6, 13, 15, 20], L60657 = [1, 2, 6, 13, 15, 22], L60659 = [1, 2, 6, 13, 15, 24], L60660 = [1, 2, 6, 13, 15, 26], L60662 = [1, 2, 6, 13, 15, 28], L60673 = [1, 2, 6, 13, 16, 27], L60690 = [1, 2, 6, 13, 18, 27], L60705 = [1, 2, 6, 13, 20, 27], L60717 = [1, 2, 6, 13, 22, 27], L60724 = [1, 2, 6, 13, 24, 27], L60726 = [1, 2, 6, 13, 26, 27], L60728 = [1, 2, 6, 13, 27, 28], L62289 = [1, 2, 7, 13, 15, 21], L62353 = [1, 2, 7, 13, 21, 27], L62994 = [1, 2, 8, 8, 13, 15], L63006 = [1, 2, 8, 8, 13, 27], L63325 = [1, 2, 8, 10, 13, 15], L63336 = [1, 2, 8, 10, 13, 27], L63583 = [1, 2, 8, 12, 13, 15], L63595 = [1, 2, 8, 12, 13, 27], L63704 = [1, 2, 8, 13, 14, 15], L63716 = [1, 2, 8, 13, 14, 27], L63718 = [1, 2, 8, 13, 15, 16], L63720 = [1, 2, 8, 13, 15, 18], L63722 = [1, 2, 8, 13, 15, 20], L63724 = [1, 2, 8, 13, 15, 22], L63726 = [1, 2, 8, 13, 15, 24], L63730 = [1, 2, 8, 13, 15, 28], L63742 = [1, 2, 8, 13, 16, 27], L63760 = [1, 2, 8, 13, 18, 27], L63777 = [1, 2, 8, 13, 20, 27], L63789 = [1, 2, 8, 13, 22, 27], L63797 = [1, 2, 8, 13, 24, 27], L63801 = [1, 2, 8, 13, 27, 28], L64554 = [1, 2, 9, 11, 23, 26], L65257 = [1, 2, 10, 10, 13, 15], L65268 = [1, 2, 10, 10, 13, 27], L65499 = [1, 2, 10, 12, 13, 15], L65510 = [1, 2, 10, 12, 13, 27], L65615 = [1, 2, 10, 13, 14, 15], L65626 = [1, 2, 10, 13, 14, 27], L65628 = [1, 2, 10, 13, 15, 16], L65630 = [1, 2, 10, 13, 15, 18], L65632 = [1, 2, 10, 13, 15, 20], L65634 = [1, 2, 10, 13, 15, 22], L65635 = [1, 2, 10, 13, 15, 24], L65637 = [1, 2, 10, 13, 15, 26], L65639 = [1, 2, 10, 13, 15, 28], L65650 = [1, 2, 10, 13, 16, 27], L65666 = [1, 2, 10, 13, 18, 27], L65681 = [1, 2, 10, 13, 20, 27], L65691 = [1, 2, 10, 13, 22, 27], L65696 = [1, 2, 10, 13, 24, 27], L65700 = [1, 2, 10, 13, 26, 27], L65702 = [1, 2, 10, 13, 27, 28], L66794 = [1, 2, 12, 12, 13, 15], L66806 = [1, 2, 12, 12, 13, 27], L66915 = [1, 2, 12, 13, 14, 15], L66927 = [1, 2, 12, 13, 14, 27], L66929 = [1, 2, 12, 13, 15, 16], L66931 = [1, 2, 12, 13, 15, 18], L66933 = [1, 2, 12, 13, 15, 20], L66935 = [1, 2, 12, 13, 15, 22], L66937 = [1, 2, 12, 13, 15, 24], L66941 = [1, 2, 12, 13, 15, 28], L66953 = [1, 2, 12, 13, 16, 27], L66970 = [1, 2, 12, 13, 18, 27], L66987 = [1, 2, 12, 13, 20, 27], L66999 = [1, 2, 12, 13, 22, 27], L67007 = [1, 2, 12, 13, 24, 27], L67011 = [1, 2, 12, 13, 27, 28], L67508 = [1, 2, 13, 14, 14, 15], L67520 = [1, 2, 13, 14, 14, 27], L67522 = [1, 2, 13, 14, 15, 16], L67524 = [1, 2, 13, 14, 15, 18], L67526 = [1, 2, 13, 14, 15, 20], L67528 = [1, 2, 13, 14, 15, 22], L67530 = [1, 2, 13, 14, 15, 24], L67534 = [1, 2, 13, 14, 15, 28], L67546 = [1, 2, 13, 14, 16, 27], L67563 = [1, 2, 13, 14, 18, 27], L67580 = [1, 2, 13, 14, 20, 27], L67592 = [1, 2, 13, 14, 22, 27], L67600 = [1, 2, 13, 14, 24, 27], L67604 = [1, 2, 13, 14, 27, 28], L67606 = [1, 2, 13, 15, 16, 16], L67608 = [1, 2, 13, 15, 16, 18], L67610 = [1, 2, 13, 15, 16, 20], L67612 = [1, 2, 13, 15, 16, 22], L67614 = [1, 2, 13, 15, 16, 24], L67618 = [1, 2, 13, 15, 16, 28], L67627 = [1, 2, 13, 15, 18, 18], L67628 = [1, 2, 13, 15, 18, 20], L67630 =
100
EMILIO A. LAURET
Table 4. (continued) n = 6 q I indexes of I-isospectral families 56 {0} {17505, 17510}, {17573, 17578}, {17580, 17590}, {17582, 17597}, {17583, 17600}, (cont.) {17585, 17602}, {19208, 19211}, {19229, 19238}, {19232, 19252}, {19235, 19253}, {19606, 19609}, {49328, 49340}, {49952, 49964}, {50479, 50491}, {50937, 50949}, {51291, 51303}, {51572, 51584}, {51695, 51707}, {51709, 51733}, {51711, 51754}, {51713, 51771}, {51715, 51785}, {51717, 51794}, {51719, 51799}, {51721, 51801}, {55125, 55137}, {55646, 55658}, {56101, 56113}, {56449, 56460}, {56724, 56736}, {56845, 56857}, {56859, 56883}, {56861, 56901}, {56863, 56918}, {56865, 56930}, {56867, 56938}, {56871, 56942}, {58274, 64554}, {59507, 59518}, {59942, 59953}, {60280, 60290}, {60531, 60542}, {60638, 60649}, {60651, 60673}, {60653, 60690}, {60655, 60705}, {60657, 60717}, {60659, 60724}, {60660, 60726}, {60662, 60728}, {62289, 62353}, {62994, 63006}, {63325, 63336}, {63583, 63595}, {63704, 63716}, {63718, 63742}, {63720, 63760}, {63722, 63777}, {63724, 63789}, {63726, 63797},
[1, 2, 13, 15, 18, 22], L67632 = [1, 2, 13, 15, 18, 24], L67635 = [1, 2, 13, 15, 18, 28], L67643 = [1, 2, 13, 15, 20, 20], L67645 = [1, 2, 13, 15, 20, 22], L67647 = [1, 2, 13, 15, 20, 24], L67651 = [1, 2, 13, 15, 20, 28], L67658 = [1, 2, 13, 15, 22, 22], L67660 = [1, 2, 13, 15, 22, 24], L67663 = [1, 2, 13, 15, 22, 28], L67667 = [1, 2, 13, 15, 24, 24], L67671 = [1, 2, 13, 15, 24, 28], L67676 = [1, 2, 13, 15, 28, 28], L67688 = [1, 2, 13, 16, 16, 27], L67705 = [1, 2, 13, 16, 18, 27], L67722 = [1, 2, 13, 16, 20, 27], L67734 = [1, 2, 13, 16, 22, 27], L67742 = [1, 2, 13, 16, 24, 27], L67746 = [1, 2, 13, 16, 27, 28], L67787 = [1, 2, 13, 18, 18, 27], L67795 = [1, 2, 13, 18, 20, 27], L67807 = [1, 2, 13, 18, 22, 27], L67814 = [1, 2, 13, 18, 24, 27], L67817 = [1, 2, 13, 18, 27, 28], L67856 = [1, 2, 13, 20, 20, 27], L67868 = [1, 2, 13, 20, 22, 27], L67876 = [1, 2, 13, 20, 24, 27], L67880 = [1, 2, 13, 20, 27, 28], L67905 = [1, 2, 13, 22, 22, 27], L67912 = [1, 2, 13, 22, 24, 27], L67915 = [1, 2, 13, 22, 27, 28], L67925 = [1, 2, 13, 24, 24, 27], L67929 = [1, 2, 13, 24, 27, 28], L67933 = [1, 2, 13, 27, 28, 28], L70290 = [1, 3, 4, 7, 12, 19], L70374 = [1, 3, 4, 7, 19, 20], L70753 = [1, 3, 4, 9, 20, 23], L70968 = [1, 3, 4, 11, 13, 17], L70993 = [1, 3, 4, 11, 15, 17], L71091 = [1, 3, 4, 12, 13, 19], L71092 = [1, 3, 4, 12, 13, 20], L71119 = [1, 3, 4, 12, 15, 20], L71170 = [1, 3, 4, 12, 20, 23], L71175 = [1, 3, 4, 12, 20, 28], L71875 = [1, 3, 5, 7, 9, 17], L71887 = [1, 3, 5, 7, 11, 13], L71921 = [1, 3, 5, 7, 13, 17], L71972 = [1, 3, 5, 7, 17, 19], L71996 = [1, 3, 5, 7, 19, 27], L72233 = [1, 3, 5, 9, 11, 15], L72239 = [1, 3, 5, 9, 11, 23], L72241 = [1, 3, 5, 9, 11, 25], L72243 = [1, 3, 5, 9, 11, 27], L72245 = [1, 3, 5, 9, 13, 14], L72246 = [1, 3, 5, 9, 13, 15], L72248 = [1, 3, 5, 9, 13, 17], L72249 = [1, 3, 5, 9, 13, 19], L72251 = [1, 3, 5, 9, 13, 21], L72255 = [1, 3, 5, 9, 13, 25], L72256 = [1, 3, 5, 9, 13, 27], L72257 = [1, 3, 5, 9, 13, 28], L72259 = [1, 3, 5, 9, 14, 15], L72261 = [1, 3, 5, 9, 14, 17], L72273 = [1, 3, 5, 9, 15, 17], L72274 = [1, 3, 5, 9, 15, 19], L72277 = [1, 3, 5, 9, 15, 25], L72279 = [1, 3, 5, 9, 15, 28], L72294 = [1, 3, 5, 9, 17, 23], L72296 = [1, 3, 5, 9, 17, 25], L72298 = [1, 3, 5, 9, 17, 27], L72299 = [1, 3, 5, 9, 17, 28], L72322 = [1, 3, 5, 9, 21, 27], L72364 = [1, 3, 5, 11, 13, 15], L72366 = [1, 3, 5, 11, 13, 17], L72370 = [1, 3, 5, 11, 13, 21], L72372 = [1, 3, 5, 11, 13, 25], L72376 = [1, 3, 5, 11, 14, 15], L72392 = [1, 3, 5, 11, 15, 19], L72393 = [1, 3, 5, 11, 15, 21], L72394 = [1, 3, 5, 11, 15, 23], L72396 = [1, 3, 5, 11, 15, 27], L72397 = [1, 3, 5, 11, 15, 28], L72412 = [1, 3, 5, 11, 17, 21], L72428 = [1, 3, 5, 11, 19, 21], L72429 = [1, 3, 5, 11, 19, 23], L72431 = [1, 3, 5, 11, 19, 25], L72592 = [1, 3, 5, 13, 14, 17], L72606 = [1, 3, 5, 13, 15, 19], L72629 = [1, 3, 5, 13, 17, 27], L72630 = [1, 3, 5, 13, 17, 28], L72640 = [1, 3, 5, 13, 19, 21], L72694 = [1, 3, 5, 14, 15, 19], L72716 = [1, 3, 5, 14, 17, 21], L72793 = [1, 3, 5, 15, 17, 21], L72794 = [1, 3, 5, 15, 17, 23], L72809 = [1, 3, 5, 15, 19, 28], L72814 = [1, 3, 5, 15, 21, 27], L72930 = [1, 3, 5, 17, 21, 28], L72998 = [1, 3, 5, 19, 21, 23], L73216 = [1, 3, 7, 7, 9, 19], L73224 = [1, 3, 7, 7, 9, 27], L73279 = [1, 3, 7, 7, 13, 17], L73559 = [1, 3, 7, 8, 19, 24], L73624 = [1, 3, 7, 9, 11, 17], L73639 = [1, 3, 7, 9, 13, 25], L73645 = [1, 3, 7, 9, 14, 19], L73653 = [1, 3, 7, 9, 14, 27], L73667 = [1, 3, 7, 9, 17, 21], L73681 = [1, 3, 7, 9, 19, 28], L73691 = [1, 3, 7, 9, 21, 23], L73705 = [1, 3, 7, 9, 23, 27], L73717 = [1, 3, 7, 9, 27, 28], L73892 = [1, 3, 7, 11, 13, 17], L73894 = [1, 3, 7, 11, 13, 19], L73898 = [1, 3, 7, 11, 13, 25], L73899 = [1, 3, 7, 11, 13, 27], L74117 = [1, 3, 7, 13, 14, 17],
APPENDIX
101
Table 4. (continued) n = 6 q I indexes of I-isospectral families 56 {0} {63730, 63801}, {65257, 65268}, {65499, 65510}, {65615, 65626}, {65628, 65650}, (cont.) {65630, 65666}, {65632, 65681}, {65634, 65691}, {65635, 65696}, {65637, 65700}, {65639, 65702}, {66794, 66806}, {66915, 66927}, {66929, 66953}, {66931, 66970}, {66933, 66987}, {66935, 66999}, {66937, 67007}, {66941, 67011}, {67508, 67520}, {67522, 67546}, {67524, 67563}, {67526, 67580}, {67528, 67592}, {67530, 67600}, {67534, 67604}, {67606, 67688}, {67608, 67705}, {67610, 67722}, {67612, 67734}, {67614, 67742}, {67618, 67746}, {67627, 67787}, {67628, 67795}, {67630, 67807}, {67632, 67814}, {67635, 67817}, {67643, 67856}, {67645, 67868}, {67647, 67876}, {67651, 67880}, {67658, 67905}, {67660, 67912}, {67663, 67915}, {67667, 67925}, {67671, 67929}, {67676, 67933}, {70290, 70374}, {70753, 71091}, {70968, 70993}, {71092, 71119}, {71170, 82459}, {71875, 71887}, {71921, 71972}, {72233, 72248}, {72239, 72246}, {72241, 72274}, {72243, 72277}, {72245, 72259}, {72249, 72364}, {72251, 72393}, {72255, 72298, 72394}, {72256, 72366}, {72257, 72279}, {72261, 72376}, {72273, 72392}, {72294, 72372, 72429, 72606}, {72296, 72431}, {72299, 72397}, {72370, 72428, 72640}, {72396, 72629}, {72412, 72814}, {72592, 72694}, {72630, 72809},
L74119 = [1, 3, 7, 13, 14, 19], L74121 = [1, 3, 7, 13, 14, 21], L74125 = [1, 3, 7, 13, 14, 27], L74128 = [1, 3, 7, 13, 15, 17], L74151 = [1, 3, 7, 13, 17, 21], L74153 = [1, 3, 7, 13, 17, 25], L74154 = [1, 3, 7, 13, 17, 27], L74155 = [1, 3, 7, 13, 17, 28], L74167 = [1, 3, 7, 13, 19, 28], L74180 = [1, 3, 7, 13, 21, 28], L74192 = [1, 3, 7, 13, 27, 28], L74214 = [1, 3, 7, 14, 15, 21], L74270 = [1, 3, 7, 14, 21, 23], L74319 = [1, 3, 7, 15, 17, 27], L74345 = [1, 3, 7, 15, 21, 23], L74349 = [1, 3, 7, 15, 21, 28], L74402 = [1, 3, 7, 16, 19, 24], L74622 = [1, 3, 7, 21, 23, 28], L74951 = [1, 3, 8, 9, 16, 17], L74989 = [1, 3, 8, 9, 23, 24], L75178 = [1, 3, 8, 11, 13, 17], L75201 = [1, 3, 8, 11, 15, 17], L75429 = [1, 3, 8, 13, 16, 24], L75588 = [1, 3, 8, 15, 16, 24], L75702 = [1, 3, 8, 16, 23, 24], L76048 = [1, 3, 9, 11, 13, 19], L76057 = [1, 3, 9, 11, 14, 25], L76078 = [1, 3, 9, 11, 25, 28], L76088 = [1, 3, 9, 13, 14, 27], L76106 = [1, 3, 9, 13, 27, 28], L76110 = [1, 3, 9, 14, 14, 17], L76114 = [1, 3, 9, 14, 14, 23], L76130 = [1, 3, 9, 14, 17, 28], L76147 = [1, 3, 9, 14, 23, 28], L76197 = [1, 3, 9, 17, 28, 28], L76239 = [1, 3, 9, 23, 28, 28], L77065 = [1, 3, 11, 12, 13, 17], L77086 = [1, 3, 11, 12, 15, 17], L77146 = [1, 3, 11, 13, 14, 17], L77151 = [1, 3, 11, 13, 14, 25], L77157 = [1, 3, 11, 13, 15, 21], L77163 = [1, 3, 11, 13, 16, 17], L77171 = [1, 3, 11, 13, 17, 20], L77172 = [1, 3, 11, 13, 17, 24], L77175 = [1, 3, 11, 13, 17, 28], L77191 = [1, 3, 11, 13, 21, 25], L77199 = [1, 3, 11, 13, 25, 28], L77215 = [1, 3, 11, 14, 15, 17], L77273 = [1, 3, 11, 15, 16, 17], L77278 = [1, 3, 11, 15, 17, 20], L77280 = [1, 3, 11, 15, 17, 24], L77282 = [1, 3, 11, 15, 17, 28], L78137 = [1, 3, 13, 14, 14, 14], L78140 = [1, 3, 13, 14, 14, 17], L78148 = [1, 3, 13, 14, 14, 28], L78150 = [1, 3, 13, 14, 15, 17], L78171 = [1, 3, 13, 14, 17, 28], L78205 = [1, 3, 13, 14, 28, 28], L78219 = [1, 3, 13, 15, 17, 28], L78306 = [1, 3, 13, 17, 28, 28], L78409 = [1, 3, 13, 28, 28, 28], L78411 = [1, 3, 14, 14, 14, 15], L78418 = [1, 3, 14, 14, 14, 23], L78430 = [1, 3, 14, 14, 15, 23], L78434 = [1, 3, 14, 14, 15, 28], L78494 = [1, 3, 14, 14, 23, 28], L78525 = [1, 3, 14, 15, 17, 27], L78549 = [1, 3, 14, 15, 21, 27], L78560 = [1, 3, 14, 15, 23, 28], L78567 = [1, 3, 14, 15, 28, 28], L78844 = [1, 3, 14, 23, 28, 28], L78949 = [1, 3, 15, 17, 21, 27], L78960 = [1, 3, 15, 17, 27, 28], L79057 = [1, 3, 15, 21, 27, 28], L79082 = [1, 3, 15, 23, 28, 28], L79092 = [1, 3, 15, 28, 28, 28], L80023 = [1, 3, 23, 28, 28, 28], L80620 = [1, 4, 4, 6, 13, 15], L80627 = [1, 4, 4, 6, 13, 27], L81243 = [1, 4, 4, 10, 13, 15], L81249 = [1, 4, 4, 10, 13, 27], L81490 = [1, 4, 4, 12, 20, 28], L82459 = [1, 4, 5, 11, 12, 20], L82584 = [1, 4, 5, 12, 20, 28], L83080 = [1, 4, 6, 6, 13, 15], L83087 = [1, 4, 6, 6, 13, 27], L83435 = [1, 4, 6, 8, 13, 15], L83442 = [1, 4, 6, 8, 13, 27], L83659 = [1, 4, 6, 10, 13, 15], L83666 = [1, 4, 6, 10, 13, 27], L83813 = [1, 4, 6, 12, 13, 15], L83820 = [1, 4, 6, 12, 13, 27], L83878 = [1, 4, 6, 12, 20, 28], L83904 = [1, 4, 6, 13, 14, 15], L83911 = [1, 4, 6, 13, 14, 27],
102
EMILIO A. LAURET
Table 4. (continued) n = 6 q I indexes of I-isospectral families 56 {0} {72716, 74119}, {72793, 90557}, {72794, 76048}, {72930, 74167}, {72998, 73624}, (cont.) {73216, 73224}, {73279, 90336}, {73559, 74402}, {73639, 73705}, {73645, 73653}, {73667, 73691}, {73681, 73717}, {73892, 73898}, {73894, 90561}, {73899, 74128, 74319, 77157}, {74117, 90574}, {74121, 74214}, {74125, 78549}, {74151, 90576}, {74153, 77191}, {74154, 78949}, {74155, 90578}, {74180, 74349}, {74192, 79057}, {74270, 90630}, {74345, 90600}, {74622, 90653}, {74951, 74989}, {75178, 75201}, {75429, 75588}, {75702, 91196}, {76057, 76088}, {76078, 76106}, {76110, 76114}, {76130, 76147}, {76197, 76239}, {77065, 77086}, {77146, 77151, 77215}, {77163, 77273}, {77171, 77278}, {77172, 77280}, {77175, 77199, 77282}, {78137, 78411}, {78140, 91604}, {78148, 78434}, {78150, 78525}, {78171, 91607}, {78205, 78567}, {78219, 78960}, {78306, 91613}, {78409, 79092}, {78418, 91740}, {78430, 91620}, {78494, 91745}, {78560, 91650}, {78844, 91759}, {79082, 91735}, {80023, 91789}, {80620, 80627}, {81243, 81249}, {83080, 83087}, {83435, 83442}, {83659, 83666}, {83813, 83820}, {83904, 83911}, {83913, 83927}, {83914, 83933}, {83915, 83939}, {83918, 83947}, {83920, 83949},
L83913 = [1, 4, 6, 13, 15, 16], L83914 = [1, 4, 6, 13, 15, 18], L83915 = [1, 4, 6, 13, 15, 20], L83918 = [1, 4, 6, 13, 15, 24], L83920 = [1, 4, 6, 13, 15, 28], L83927 = [1, 4, 6, 13, 16, 27], L83933 = [1, 4, 6, 13, 18, 27], L83939 = [1, 4, 6, 13, 20, 27], L83947 = [1, 4, 6, 13, 24, 27], L83949 = [1, 4, 6, 13, 27, 28], L85051 = [1, 4, 7, 12, 20, 28], L85832 = [1, 4, 8, 10, 13, 15], L85838 = [1, 4, 8, 10, 13, 27], L86065 = [1, 4, 8, 12, 20, 28], L86661 = [1, 4, 9, 12, 17, 23], L86671 = [1, 4, 9, 12, 20, 28], L86686 = [1, 4, 9, 12, 23, 25], L86989 = [1, 4, 10, 10, 13, 15], L86995 = [1, 4, 10, 10, 13, 27], L87160 = [1, 4, 10, 12, 13, 15], L87165 = [1, 4, 10, 12, 13, 27], L87207 = [1, 4, 10, 12, 20, 28], L87228 = [1, 4, 10, 13, 14, 15], L87234 = [1, 4, 10, 13, 14, 27], L87236 = [1, 4, 10, 13, 15, 16], L87238 = [1, 4, 10, 13, 15, 20], L87239 = [1, 4, 10, 13, 15, 24], L87242 = [1, 4, 10, 13, 15, 28], L87248 = [1, 4, 10, 13, 16, 27], L87256 = [1, 4, 10, 13, 20, 27], L87260 = [1, 4, 10, 13, 24, 27], L87263 = [1, 4, 10, 13, 27, 28], L87919 = [1, 4, 12, 12, 20, 28], L87961 = [1, 4, 12, 13, 20, 28], L88015 = [1, 4, 12, 14, 20, 28], L88048 = [1, 4, 12, 15, 20, 28], L88087 = [1, 4, 12, 16, 20, 28], L88120 = [1, 4, 12, 17, 20, 28], L88145 = [1, 4, 12, 18, 20, 28], L88176 = [1, 4, 12, 20, 20, 28], L88181 = [1, 4, 12, 20, 21, 28], L88186 = [1, 4, 12, 20, 22, 28], L88190 = [1, 4, 12, 20, 24, 28], L88193 = [1, 4, 12, 20, 26, 28], L88194 = [1, 4, 12, 20, 27, 28], L88195 = [1, 4, 12, 20, 28, 28], L90336 = [1, 5, 7, 7, 9, 13], L90557 = [1, 5, 7, 9, 11, 13], L90561 = [1, 5, 7, 9, 11, 25], L90574 = [1, 5, 7, 9, 13, 14], L90576 = [1, 5, 7, 9, 13, 21], L90578 = [1, 5, 7, 9, 13, 28], L90600 = [1, 5, 7, 9, 21, 25], L90621 = [1, 5, 7, 11, 13, 14], L90626 = [1, 5, 7, 11, 13, 28], L90630 = [1, 5, 7, 11, 14, 21], L90632 = [1, 5, 7, 11, 14, 25], L90653 = [1, 5, 7, 11, 21, 28], L90659 = [1, 5, 7, 11, 25, 28], L91196 = [1, 5, 8, 11, 16, 24], L91604 = [1, 5, 9, 13, 14, 14], L91607 = [1, 5, 9, 13, 14, 28], L91613 = [1, 5, 9, 13, 28, 28], L91620 = [1, 5, 9, 14, 14, 25], L91650 = [1, 5, 9, 14, 25, 28], L91735 = [1, 5, 9, 25, 28, 28], L91740 = [1, 5, 11, 14, 14, 14], L91745 = [1, 5, 11, 14, 14, 28], L91759 = [1, 5, 11, 14, 28, 28], L91789 = [1, 5, 11, 28, 28, 28], L92906 = [1, 6, 6, 6, 13, 15], L92913 = [1, 6, 6, 6, 13, 27], L93225 = [1, 6, 6, 8, 13, 15], L93232 = [1, 6, 6, 8, 13, 27], L93414 = [1, 6, 6, 10, 13, 15], L93421 = [1, 6, 6, 10, 13, 27], L93508 = [1, 6, 6, 12, 13, 15], L93515 = [1, 6, 6, 12, 13, 27], L93588 = [1, 6, 6, 13, 14, 15], L93595 = [1, 6, 6, 13, 14, 27], L93597 = [1, 6, 6, 13, 15, 16], L93598 = [1, 6, 6, 13, 15, 18], L93599 = [1, 6, 6, 13, 15, 20], L93601 = [1, 6, 6, 13, 15, 22], L93602 = [1, 6, 6, 13, 15, 24], L93604 = [1, 6, 6, 13, 15, 28], L93611 = [1, 6, 6, 13, 16, 27], L93618 = [1, 6, 6, 13, 18, 27], L93624 = [1, 6, 6, 13, 20, 27], L93632 = [1, 6, 6, 13, 22, 27], L93635 = [1, 6, 6, 13, 24, 27], L93637 = [1, 6, 6, 13, 27, 28], L94575 = [1, 6, 7, 13, 15, 21], L94604 = [1, 6, 7, 13, 21, 27], L95007 = [1, 6, 8, 8, 13, 15], L95014 = [1, 6, 8, 8, 13, 27], L95195 = [1, 6, 8, 10, 13, 15], L95202 = [1, 6, 8, 10, 13, 27], L95289 = [1, 6, 8, 12, 13, 15], L95296 = [1, 6, 8, 12, 13, 27], L95369 = [1, 6, 8, 13, 14, 15], L95376 = [1, 6, 8, 13, 14, 27],
APPENDIX
103
Table 4. (continued) n = 6 q I indexes of I-isospectral families 56 {0} {85832, 85838}, {86661, 86686}, {86989, 86995}, {87160, 87165}, {87228, 87234}, (cont.) {87236, 87248}, {87238, 87256}, {87239, 87260}, {87242, 87263}, {90621, 90632}, {90626, 90659}, {92906, 92913}, {93225, 93232}, {93414, 93421}, {93508, 93515}, {93588, 93595}, {93597, 93611}, {93598, 93618}, {93599, 93624}, {93601, 93632}, {93602, 93635}, {93604, 93637}, {94575, 94604}, {95007, 95014}, {95195, 95202}, {95289, 95296}, {95369, 95376}, {95378, 95392}, {95379, 95398}, {95380, 95404}, {95383, 95412}, {95385, 95414}, {96049, 96056}, {96133, 96140}, {96204, 96211}, {96213, 96227}, {96214, 96234}, {96215, 96240}, {96217, 96246}, {96218, 96249}, {96220, 96251}, {96532, 96539}, {96611, 96618}, {96620, 96634}, {96621, 96640}, {96622, 96646}, {96625, 96654}, {96627, 96656}, {96928, 96935}, {96937, 96951}, {96938, 96957}, {96939, 96963}, {96942, 96971}, {96944, 96973}, {96975, 97012}, {96976, 97018}, {96977, 97024}, {96980, 97032}, {96982, 97034}, {96983, 97040}, {96984, 97045}, {96986, 97051}, {96988, 97053}, {96989, 97059}, {96992, 97067}, {96994, 97069}, {97001, 97081}, {97003, 97083}, {97005, 97085}, {98423, 98427}, {99837, 99841}, {99867, 99873}, {99869, 99879}, {100129, 100152}, {101921, 101926}, L95378 = [1, 6, 8, 13, 15, 16], L95379 = [1, 6, 8, 13, 15, 18], L95380 = [1, 6, 8, 13, 15, 20], L95383 = [1, 6, 8, 13, 15, 24], L95385 = [1, 6, 8, 13, 15, 28], L95392 = [1, 6, 8, 13, 16, 27], L95398 = [1, 6, 8, 13, 18, 27], L95404 = [1, 6, 8, 13, 20, 27], L95412 = [1, 6, 8, 13, 24, 27], L95414 = [1, 6, 8, 13, 27, 28], L96049 = [1, 6, 10, 10, 13, 15], L96056 = [1, 6, 10, 10, 13, 27], L96133 = [1, 6, 10, 12, 13, 15], L96140 = [1, 6, 10, 12, 13, 27], L96204 = [1, 6, 10, 13, 14, 15], L96211 = [1, 6, 10, 13, 14, 27], L96213 = [1, 6, 10, 13, 15, 16], L96214 = [1, 6, 10, 13, 15, 18], L96215 = [1, 6, 10, 13, 15, 20], L96217 = [1, 6, 10, 13, 15, 22], L96218 = [1, 6, 10, 13, 15, 24], L96220 = [1, 6, 10, 13, 15, 28], L96227 = [1, 6, 10, 13, 16, 27], L96234 = [1, 6, 10, 13, 18, 27], L96240 = [1, 6, 10, 13, 20, 27], L96246 = [1, 6, 10, 13, 22, 27], L96249 = [1, 6, 10, 13, 24, 27], L96251 = [1, 6, 10, 13, 27, 28], L96532 = [1, 6, 12, 12, 13, 15], L96539 = [1, 6, 12, 12, 13, 27], L96611 = [1, 6, 12, 13, 14, 15], L96618 = [1, 6, 12, 13, 14, 27], L96620 = [1, 6, 12, 13, 15, 16], L96621 = [1, 6, 12, 13, 15, 18], L96622 = [1, 6, 12, 13, 15, 20], L96625 = [1, 6, 12, 13, 15, 24], L96627 = [1, 6, 12, 13, 15, 28], L96634 = [1, 6, 12, 13, 16, 27], L96640 = [1, 6, 12, 13, 18, 27], L96646 = [1, 6, 12, 13, 20, 27], L96654 = [1, 6, 12, 13, 24, 27], L96656 = [1, 6, 12, 13, 27, 28], L96928 = [1, 6, 13, 14, 14, 15], L96935 = [1, 6, 13, 14, 14, 27], L96937 = [1, 6, 13, 14, 15, 16], L96938 = [1, 6, 13, 14, 15, 18], L96939 = [1, 6, 13, 14, 15, 20], L96942 = [1, 6, 13, 14, 15, 24], L96944 = [1, 6, 13, 14, 15, 28], L96951 = [1, 6, 13, 14, 16, 27], L96957 = [1, 6, 13, 14, 18, 27], L96963 = [1, 6, 13, 14, 20, 27], L96971 = [1, 6, 13, 14, 24, 27], L96973 = [1, 6, 13, 14, 27, 28], L96975 = [1, 6, 13, 15, 16, 16], L96976 = [1, 6, 13, 15, 16, 18], L96977 = [1, 6, 13, 15, 16, 20], L96980 = [1, 6, 13, 15, 16, 24], L96982 = [1, 6, 13, 15, 16, 28], L96983 = [1, 6, 13, 15, 18, 18], L96984 = [1, 6, 13, 15, 18, 20], L96986 = [1, 6, 13, 15, 18, 24], L96988 = [1, 6, 13, 15, 18, 28], L96989 = [1, 6, 13, 15, 20, 20], L96992 = [1, 6, 13, 15, 20, 24], L96994 = [1, 6, 13, 15, 20, 28], L97001 = [1, 6, 13, 15, 24, 24], L97003 = [1, 6, 13, 15, 24, 28], L97005 = [1, 6, 13, 15, 28, 28], L97012 = [1, 6, 13, 16, 16, 27], L97018 = [1, 6, 13, 16, 18, 27], L97024 = [1, 6, 13, 16, 20, 27], L97032 = [1, 6, 13, 16, 24, 27], L97034 = [1, 6, 13, 16, 27, 28], L97040 = [1, 6, 13, 18, 18, 27], L97045 = [1, 6, 13, 18, 20, 27], L97051 = [1, 6, 13, 18, 24, 27], L97053 = [1, 6, 13, 18, 27, 28], L97059 = [1, 6, 13, 20, 20, 27], L97067 = [1, 6, 13, 20, 24, 27], L97069 = [1, 6, 13, 20, 27, 28], L97081 = [1, 6, 13, 24, 24, 27], L97083 = [1, 6, 13, 24, 27, 28], L97085 = [1, 6, 13, 27, 28, 28], L98423 = [1, 7, 7, 9, 15, 17], L98427 = [1, 7, 7, 9, 15, 25], L99837 = [1, 7, 9, 14, 15, 17], L99841 = [1, 7, 9, 14, 15, 25], L99867 = [1, 7, 9, 15, 17, 21], L99869 = [1, 7, 9, 15, 17, 28], L99873 = [1, 7, 9, 15, 21, 25], L99879 = [1, 7, 9, 15, 25, 28], L100129 = [1, 7, 10, 13, 15, 21], L100152 = [1, 7, 10, 13, 21, 27], L101921 = [1, 8, 8, 10, 13, 15], L101926 = [1, 8, 8, 10, 13, 27], L102616 = [1, 8, 9, 15, 16, 17], L102620 = [1, 8, 9, 15, 16, 25], L102770 = [1, 8, 10, 10, 13, 15], L102775 = [1, 8, 10, 10, 13, 27], L102859 = [1, 8, 10, 12, 13, 15], L102864 =
104
EMILIO A. LAURET
Table 4. (continued) n = 6 q I indexes of I-isospectral families 56 {0} {102616, 102620}, {102770, 102775}, {102859, 102864}, {102927, 102932}, (cont.) {102934, 102944}, {102936, 102951}, {102937, 102954}, {102939, 102956}, {104910, 104914}, {104940, 104946}, {104942, 104952}, {105008, 105017}, {105010, 105023}, {105013, 105031}, {105165, 105170}, {105246, 105251}, {105314, 105319}, {105321, 105331}, {105322, 105336}, {105323, 105340}, {105324, 105343}, {105326, 105345}, {105590, 105595}, {105658, 105663}, {105665, 105675}, {105667, 105682}, {105668, 105685}, {105670, 105687}, {105918, 105923}, {105925, 105935}, {105927, 105942}, {105928, 105945}, {105930, 105947}, {105949, 105972}, {105951, 105979}, {105952, 105982}, {105954, 105984}, {105959, 105994}, {105960, 105997}, {105962, 105999}, {105963, 106002}, {105965, 106004}, {105967, 106006}, {110727, 110735}, {111131, 111134}, {111152, 111161}, {111155, 111175}, {111158, 111176}, {111212, 111225}, {111254, 111278}, {111257, 111292}, {111260, 111293}, {111271, 111337}, {111275, 111338}, {112351, 112354}, {112456, 112459}, {112463, 112468}, {112465, 112470}
[1, 8, 10, 12, 13, 27], L102927 = [1, 8, 10, 13, 14, 15], L102932 = [1, 8, 10, 13, 14, 27], L102934 = [1, 8, 10, 13, 15, 16], L102936 = [1, 8, 10, 13, 15, 20], L102937 = [1, 8, 10, 13, 15, 24], L102939 = [1, 8, 10, 13, 15, 28], L102944 = [1, 8, 10, 13, 16, 27], L102951 = [1, 8, 10, 13, 20, 27], L102954 = [1, 8, 10, 13, 24, 27], L102956 = [1, 8, 10, 13, 27, 28], L104910 = [1, 9, 14, 14, 15, 17], L104914 = [1, 9, 14, 14, 15, 25], L104940 = [1, 9, 14, 15, 17, 21], L104942 = [1, 9, 14, 15, 17, 28], L104946 = [1, 9, 14, 15, 21, 25], L104952 = [1, 9, 14, 15, 25, 28], L105008 = [1, 9, 15, 17, 21, 21], L105010 = [1, 9, 15, 17, 21, 28], L105013 = [1, 9, 15, 17, 28, 28], L105017 = [1, 9, 15, 21, 21, 25], L105023 = [1, 9, 15, 21, 25, 28], L105031 = [1, 9, 15, 25, 28, 28], L105165 = [1, 10, 10, 10, 13, 15], L105170 = [1, 10, 10, 10, 13, 27 L105246 = [1, 10, 10, 12, 13, 15], L105251 = [1, 10, 10, 12, 13, 27], L105314 = [1, 10, 10, 13, 14, 15], L105319 = [1, 10, 10, 13, 14, 27], L105321 = [1, 10, 10, 13, 15, 16], L105322 = [1, 10, 10, 13, 15, 18], L105323 = [1, 10, 10, 13, 15, 20], L105324 = [1, 10, 10, 13, 15, 24], L105326 = [1, 10, 10, 13, 15, 28], L105331 = [1, 10, 10, 13, 16, 27], L105336 = [1, 10, 10, 13, 18, 27], L105340 = [1, 10, 10, 13, 20, 27], L105343 = [1, 10, 10, 13, 24, 27], L105345 = [1, 10, 10, 13, 27, 28], L105590 = [1, 10, 12, 12, 13, 15], L105595 = [1, 10, 12, 12, 13, 27], L105658 = [1, 10, 12, 13, 14, 15], L105663 = [1, 10, 12, 13, 14, 27], L105665 = [1, 10, 12, 13, 15, 16], L105667 = [1, 10, 12, 13, 15, 20], L105668 = [1, 10, 12, 13, 15, 24], L105670 = [1, 10, 12, 13, 15, 28], L105675 = [1, 10, 12, 13, 16, 27], L105682 = [1, 10, 12, 13, 20, 27], L105685 = [1, 10, 12, 13, 24, 27], L105687 = [1, 10, 12, 13, 27, 28], L105918 = [1, 10, 13, 14, 14, 15], L105923 = [1, 10, 13, 14, 14, 27], L105925 = [1, 10, 13, 14, 15, 16], L105927 = [1, 10, 13, 14, 15, 20], L105928 = [1, 10, 13, 14, 15, 24], L105930 = [1, 10, 13, 14, 15, 28], L105935 = [1, 10, 13, 14, 16, 27], L105942 = [1, 10, 13, 14, 20, 27], L105945 = [1, 10, 13, 14, 24, 27], L105947 = [1, 10, 13, 14, 27, 28], L105949 = [1, 10, 13, 15, 16, 16], L105951 = [1, 10, 13, 15, 16, 20], L105952 = [1, 10, 13, 15, 16, 24], L105954 = [1, 10, 13, 15, 16, 28], L105959 = [1, 10, 13, 15, 20, 20], L105960 = [1, 10, 13, 15, 20, 24], L105962 = [1, 10, 13, 15, 20, 28], L105963 = [1, 10, 13, 15, 24, 24], L105965 = [1, 10, 13, 15, 24, 28], L105967 = [1, 10, 13, 15, 28, 28], L105972 = [1, 10, 13, 16, 16, 27], L105979 = [1, 10, 13, 16, 20, 27], L105982 = [1, 10, 13, 16, 24, 27], L105984 = [1, 10, 13, 16, 27, 28], L105994 = [1, 10, 13, 20, 20, 27], L105997 = [1, 10, 13, 20, 24, 27], L105999 = [1, 10, 13, 20, 27, 28], L106002 = [1, 10, 13, 24, 24, 27], L106004 = [1, 10, 13, 24, 27, 28], L106006 = [1, 10, 13, 27, 28, 28], L110727 = [2, 4, 6, 7, 10, 20], L110735 = [2, 4, 6, 7, 12, 18], L111011 = [2, 4, 7, 12, 20, 28], L111131 = [2, 6, 7, 7, 7, 10], L111134 = [2, 6, 7, 7, 7, 18], L111152 = [2, 6, 7, 7, 10, 14], L111154 = [2, 6, 7, 7, 10, 18], L111155 = [2, 6, 7, 7, 10, 21], L111156 = [2, 6, 7, 7, 10, 22], L111158 = [2, 6, 7, 7, 10, 28], L111161 = [2, 6, 7, 7, 14, 18], L111175 = [2, 6, 7, 7, 18, 21], L111176 = [2, 6, 7, 7, 18, 28], L111212 = [2, 6, 7, 8, 10, 24], L111225 = [2, 6, 7, 8, 16, 18], L111254 =
APPENDIX
105
Table 4. (continued) n = 6 q I indexes of I-isospectral families 56 {0, 1} {19231, 19233}, {71996, 72322}, {72298, 72394}, {72372, 72606}, (cont.) {73899, 74128}, {74319, 77157}, {111154, 111156}, {111256, 111258}, {111266, 111269}, {111268, 111272} {5} {2193, 2919, 16526, 16983, 17028, 19706}, {5341, 15838, 16628, 16961, 16991, 19688}, {8720, 14902, 16722, 16900, 17000, 17021, 17029, 19371, 19717}, {10823, 14019, 16865, 17015, 17030, 19721}, {12819, 16809, 17007, 17031, 19619, 19723}, {13253, 19638, 86065, 88087, 88190, 112467}, {32643, 85051, 86671, 88048, 88120, 112384}, {56813, 83878, 87207, 88015, 88145, 88186, 88193, 111011, 112520}, {71175, 82584, 87961, 88181, 88194, 112528}, {81490, 87919, 88176, 88195, 112256, 112529} {4, 5} {19651, 19719} [2, 6, 7, 10, 14, 14], L111256 = [2, 6, 7, 10, 14, 18], L111257 = [2, 6, 7, 10, 14, 21], L111258 = [2, 6, 7, 10, 14, 22], L111260 = [2, 6, 7, 10, 14, 28], L111266 = [2, 6, 7, 10, 18, 21], L111268 = [2, 6, 7, 10, 18, 28], L111269 = [2, 6, 7, 10, 21, 22], L111271 = [2, 6, 7, 10, 21, 28], L111272 = [2, 6, 7, 10, 22, 28], L111275 = [2, 6, 7, 10, 28, 28], L111278 = [2, 6, 7, 14, 14, 18], L111292 = [2, 6, 7, 14, 18, 21], L111293 = [2, 6, 7, 14, 18, 28], L111337 = [2, 6, 7, 18, 21, 28], L111338 = [2, 6, 7, 18, 28, 28], L112256 = [4, 4, 7, 12, 20, 28], L112351 = [4, 7, 7, 8, 12, 16], L112354 = [4, 7, 7, 8, 12, 24], L112384 = [4, 7, 7, 12, 20, 28], L112456 = [4, 7, 8, 12, 14, 16], L112459 = [4, 7, 8, 12, 14, 24], L112463 = [4, 7, 8, 12, 16, 21], L112465 = [4, 7, 8, 12, 16, 28], L112467 = [4, 7, 8, 12, 20, 28], L112468 = [4, 7, 8, 12, 21, 24], L112470 = [4, 7, 8, 12, 24, 28], L112520 = [4, 7, 12, 14, 20, 28], L112528 = [4, 7, 12, 20, 21, 28], L112529 = [4, 7, 12, 20, 28, 28]. q = 57 : L2001 = [0, 0, 3, 6, 19, 21], L2003 = [0, 0, 3, 9, 12, 19], L6211 = [0, 1, 2, 4, 7, 25], L6228 = [0, 1, 2, 4, 8, 25], L12332 = [0, 1, 7, 12, 26, 27], L12373 = [0, 1, 7, 18, 20, 27], L13275 = [0, 3, 6, 9, 15, 19], L13276 = [0, 3, 6, 9, 18, 19], L13279 = [0, 3, 6, 9, 19, 24], L13280 = [0, 3, 6, 9, 19, 27], L13281 = [0, 3, 6, 12, 15, 19], L13284 = [0, 3, 6, 12, 19, 24], L13289 = [0, 3, 6, 18, 19, 24], L13291 = [0, 3, 6, 19, 19, 21], L13294 = [0, 3, 9, 12, 15, 19], L13295 = [0, 3, 9, 12, 19, 19], L44464 = [1, 2, 4, 7, 8, 25], L44556 = [1, 2, 4, 7, 14, 16], L44564 = [1, 2, 4, 7, 14, 25], L44567 = [1, 2, 4, 7, 14, 28], L44620 = [1, 2, 4, 7, 19, 25], L44750 = [1, 2, 4, 8, 19, 25], L72907 = [1, 7, 12, 19, 26, 27], L72999 = [1, 7, 18, 19, 20, 27], L75246 = [3, 6, 9, 12, 15, 19], L75247 = [3, 6, 9, 12, 18, 19], L75249 = [3, 6, 9, 12, 19, 21], L75251 = [3, 6, 9, 12, 19, 27], L75252 = [3, 6, 9, 15, 18, 19], L75253 = [3, 6, 9, 15, 19, 19], L75254 = [3, 6, 9, 15, 19, 21], L75255 = [3, 6, 9, 15, 19, 27], L75256 = [3, 6, 9, 18, 19, 19], L75257 = [3, 6, 9, 18, 19, 21], L75258 = [3, 6, 9, 18, 19, 24], L75261 = [3, 6, 9, 19, 19, 24], L75262 = [3, 6, 9, 19, 19, 27], L75263 = [3, 6, 9, 19, 21, 24], L75264 = [3, 6, 9, 19, 21, 27], L75265 = [3, 6, 12, 15, 19, 19], L75269 = [3, 6, 12, 19, 19, 24], L75271 = [3, 6, 15, 18, 19, 24], L75275 = [3, 6, 18, 19, 19, 24], L75277 = [3, 6, 19, 19, 19, 21], L75280 = [3, 9, 12, 15, 19, 19], L75281 = [3, 9, 12, 19, 19, 19]. q = 58 : L1280 = [0, 0, 1, 3, 13, 21], L1309 = [0, 0, 1, 3, 15, 23], L1693 = [0, 0, 1, 5, 7, 25], L1717 = [0, 0, 1, 5, 9, 23], L11197 = [0, 1, 3, 7, 21, 25], L11210 = [0, 1, 3, 7, 23, 25], L11987 = [0, 1, 3, 13, 21, 25], L11988 = [0, 1, 3, 13, 21, 27], L11990 = [0, 1, 3, 13, 21, 29], L12179 = [0, 1, 3, 15, 23, 29], L14647 = [0, 1, 5, 7, 25, 29], L14792 = [0, 1, 5, 9, 23, 29], L16408 = [0, 1, 7, 9, 11, 15], L18971 = [0, 2, 4, 8, 22, 29], L18979 = [0, 2, 4, 10, 20, 29], L19041 = [0, 2, 8, 10, 14, 29], L19042 = [0, 2, 8, 10, 26, 29], L70134 = [1, 2, 9, 20, 26, 27], L78283 = [1, 3, 5, 7, 13, 27], L78337 = [1, 3, 5, 7, 19, 25], L78583 = [1, 3, 5, 9, 11, 17], L78586 = [1, 3, 5, 9, 11, 21], L78629 = [1, 3, 5, 9, 15, 27], L78756 = [1, 3, 5, 11, 15, 23], L78760 = [1, 3, 5, 11, 15, 27], L78774 = [1, 3, 5, 11, 17, 19], L78791 = [1, 3, 5, 11, 19, 23], L78807 = [1, 3, 5, 11, 23, 27], L78979 = [1, 3, 5, 13, 15, 21], L78998 = [1, 3, 5, 13, 17, 19], L79018 = [1, 3, 5, 13, 19, 23], L79036 =
106
EMILIO A. LAURET
Table 4. (continued) n = 6 q 57
I {0}
indexes of I-isospectral families {2001, 2003}, {6211, 6228}, {12332, 12373}, {13275, 13276, 13280}, {13279, 13281, 13284}, {13289, 13294}, {13291, 13295}, {44464, 44567}, {44556, 44564}, {44620, 44750}, {72907, 72999}, {75246, 75247}, {75249, 75251, 75254, 75257}, {75252, 75255, 75258, 75264}, {75253, 75256, 75262}, {75261, 75265, 75269}, {75263, 75271}, {75275, 75280}, {75277, 75281} {0, 1} {75255, 75258} 58 {0} {1280, 1309}, {1693, 1717}, {11197, 11210}, {11987, 11988, 16408}, {11990, 12179}, {14647, 14792}, {18971, 18979}, {19041, 19042}, {70134, 82109}, {78283, 78629}, {78337, 79846}, {78583, 78586}, {78756, 78998}, {78760, 79352}, {78774, 79843}, {78791, 79855}, {78807, 78979, 79230}, {79018, 79337}, {79036, 79201}, {79049, 79351}, {79215, 79886, 79913}, {79849, 80099}, {79884, 79911}, {80106, 80382}, {80292, 80337}, {80346, 85627}, {80384, 80577}, {80662, 80710}, {83554, 85618}, {84842, 84844, 104731}, {84847, 85666}, {89708, 91840}, {91654, 91784}, {97568, 98168}, {113022, 113053, 113058}, {113072, 113099}, {113126, 113157}, {113210, 113211} 59 {0} {8276, 8406}, {42279, 42621, 42634} [1, 3, 5, 13, 21, 25], L79049 = [1, 3, 5, 13, 23, 27], L79201 = [1, 3, 5, 15, 17, 27], L79215 = [1, 3, 5, 15, 19, 27], L79230 = [1, 3, 5, 15, 23, 27], L79337 = [1, 3, 5, 17, 19, 27], L79351 = [1, 3, 5, 17, 21, 25], L79352 = [1, 3, 5, 17, 21, 27], L79843 = [1, 3, 7, 9, 11, 17], L79846 = [1, 3, 7, 9, 11, 21], L79849 = [1, 3, 7, 9, 11, 27], L79855 = [1, 3, 7, 9, 13, 21], L79884 = [1, 3, 7, 9, 19, 25], L79886 = [1, 3, 7, 9, 19, 27], L79911 = [1, 3, 7, 9, 23, 25], L79913 = [1, 3, 7, 9, 23, 27], L80099 = [1, 3, 7, 11, 13, 15], L80106 = [1, 3, 7, 11, 13, 27], L80292 = [1, 3, 7, 13, 15, 25], L80337 = [1, 3, 7, 13, 23, 25], L80346 = [1, 3, 7, 13, 25, 27], L80382 = [1, 3, 7, 15, 19, 23], L80384 = [1, 3, 7, 15, 19, 25], L80577 = [1, 3, 7, 19, 23, 25], L80662 = [1, 3, 7, 21, 25, 29], L80710 = [1, 3, 7, 23, 25, 29], L82109 = [1, 3, 9, 10, 20, 26], L83554 = [1, 3, 11, 13, 17, 21], L84842 = [1, 3, 13, 21, 25, 29], L84844 = [1, 3, 13, 21, 27, 29], L84847 = [1, 3, 13, 21, 29, 29], L85618 = [1, 3, 15, 21, 23, 25], L85627 = [1, 3, 15, 21, 25, 27], L85666 = [1, 3, 15, 23, 29, 29], L89708 = [1, 4, 5, 22, 25, 28], L91654 = [1, 4, 7, 13, 24, 28], L91784 = [1, 4, 7, 20, 22, 23], L91840 = [1, 4, 7, 24, 25, 28], L97568 = [1, 5, 7, 25, 29, 29], L98168 = [1, 5, 9, 23, 29, 29], L104731 = [1, 7, 9, 11, 15, 29], L113022 = [2, 4, 6, 16, 26, 29], L113053 = [2, 4, 8, 14, 16, 29], L113058 = [2, 4, 8, 14, 28, 29], L113072 = [2, 4, 8, 22, 29, 29], L113099 = [2, 4, 10, 20, 29, 29], L113126 = [2, 4, 14, 16, 18, 29], L113157 = [2, 4, 20, 22, 24, 29], L113210 = [2, 8, 10, 14, 29, 29], L113211 = [2, 8, 10, 26, 29, 29]. q = 59 : L8276 = [0, 1, 3, 7, 22, 27], L8406 = [0, 1, 3, 9, 13, 20], L42279 = [1, 2, 4, 5, 16, 27], L42621 = [1, 2, 4, 8, 15, 16], L42634 = [1, 2, 4, 8, 15, 29].
APPENDIX
107
6. Computational results for dimension 13 q = 3 : L3 = [0, 0, 0, 1, 1, 1, 1], L4 = [0, 0, 1, 1, 1, 1, 1]. q = 5 : L7 = [0, 0, 0, 1, 1, 2, 2], L10 = [0, 0, 1, 1, 1, 2, 2], L13 = [0, 1, 1, 1, 1, 2, 2], L14 = [0, 1, 1, 1, 2, 2, 2]. q = 6 : L33 = [0, 0, 1, 1, 2, 2, 3], L36 = [0, 0, 1, 2, 2, 2, 2], L41 = [0, 0, 2, 2, 2, 2, 3], L50 = [0, 1, 1, 1, 1, 3, 3], L52 = [0, 1, 1, 1, 2, 2, 3], L56 = [0, 1, 1, 2, 2, 2, 3], L57 = [0, 1, 1, 2, 2, 3, 3], L76 = [1, 1, 1, 1, 1, 3, 3], L79 = [1, 1, 1, 1, 2, 3, 3], L80 = [1, 1, 1, 1, 3, 3, 3]. q = 8 : L27 = [0, 0, 0, 1, 2, 3, 4], L45 = [0, 0, 1, 1, 2, 3, 4], L53 = [0, 0, 1, 2, 2, 3, 4], L55 = [0, 0, 1, 2, 3, 4, 4], L73 = [0, 1, 1, 1, 2, 3, 4], L75 = [0, 1, 1, 1, 3, 3, 3], L85 = [0, 1, 1, 2, 3, 3, 4], L86 = [0, 1, 1, 2, 3, 4, 4], L96 = [0, 1, 2, 2, 3, 4, 4], L98 = [0, 1, 2, 3, 4, 4, 4], L132 = [1, 1, 1, 3, 3, 3, 4]. q = 9 : L21 = [0, 0, 0, 1, 2, 3, 4], L36 = [0, 0, 1, 1, 2, 3, 4], L40 = [0, 0, 1, 2, 3, 3, 4], L56 = [0, 1, 1, 1, 2, 3, 4], L62 = [0, 1, 1, 2, 2, 3, 4], L63 = [0, 1, 1, 2, 2, 4, 4], L65 = [0, 1, 1, 2, 3, 3, 4], L69 = [0, 1, 2, 3, 3, 3, 4], L104 = [1, 1, 2, 2, 3, 4, 4]. q = 10 : L82 = [0, 0, 1, 1, 3, 3, 5], L96 = [0, 0, 1, 2, 2, 4, 4], L99 = [0, 0, 1, 2, 3, 4, 5], L114 = [0, 0, 2, 2, 4, 4, 5], L146 = [0, 1, 1, 1, 3, 3, 5], L161 = [0, 1, 1, 2, 2, 4, 4], L165 = [0, 1, 1, 2, 3, 3, 5], L167 = [0, 1, 1, 2, 3, 4, 5], L173 = [0, 1, 1, 3, 3, 5, 5], L189 = [0, 1, 2, 2, 2, 4, 4], L192 = [0, 1, 2, 2, 3, 4, 4], L193 = [0, 1, 2, 2, 3, 4, 5], L195 = [0, 1, 2, 2, 4, 4, 4], L196 = [0, 1, 2, 2, 4, 4, 5], L199 = [0, 1, 2, 3, 4, 5, 5], L216 = [0, 2, 2, 2, 4, 4, 5], L219 = [0, 2, 2, 4, 4, 5, 5], L251 = [1, 1, 1, 1, 3, 3, 5], L271 = [1, 1, 1, 2, 3, 3, 5], L279 = [1, 1, 1, 3, 3, 3, 5], L281 = [1, 1, 1, 3, 3, 4, 5], L282 = [1, 1, 1, 3, 3, 5, 5], L303 = [1, 1, 2, 2, 3, 3, 5], L311 = [1, 1, 2, 3, 3, 4, 5], L312 = [1, 1, 2, 3, 3, 5, 5], L322 = [1, 1, 3, 3, 5, 5, 5]. q = 11 : L9 = [0, 0, 0, 0, 1, 2, 3], L10 = [0, 0, 0, 0, 1, 2, 4], L50 = [0, 0, 1, 2, 3, 4, 5], L91 = [0, 1, 1, 2, 3, 4, 5], L153 = [1, 1, 2, 2, 3, 3, 4], L154 = [1, 1, 2, 2, 3, 3, 5], L155 = [1, 1, 2, 2, 3, 4, 4]. q = 12 : L198 = [0, 0, 1, 3, 4, 4, 5], L204 = [0, 0, 1, 4, 4, 4, 4], L239 = [0, 0, 3, 4, 4, 4, 4], L340 = [0, 1, 1, 3, 3, 5, 5], L344 = [0, 1, 1, 3, 4, 4, 5], L385 = [0, 1, 2, 2, 3, 5, 6], L389 = [0, 1, 2, 2, 4, 4, 6], L404 = [0, 1, 2, 3, 4, 4, 5], L429 = [0, 1, 3, 3, 4, 4, 5], L436 = [0, 1, 3, 4, 4, 4, 5], L438 = [0, 1, 3, 4, 4, 5, 6], L472 = [0, 2, 2, 3, 4, 4, 6], L603 = [1, 1, 1, 3, 3, 5, 5], L653 = [1, 1, 2, 2, 3, 5, 6], L671 = [1, 1, 2, 3, 3, 5, 5], L702 = [1, 1, 3, 3, 3, 5, 5], L708 = [1, 1, 3, 3, 4, 5, 5], L711 = [1, 1, 3, 3, 5, 5, 6], L754 = [1, 2, 2, 2, 2, 6, 6], Table 5. n = 7 q 3 5 6 8
I {2, 5} {4} {2, 5} {6} {2, 3, 6} {5} {2, 5} {5, 6} {2, 5, 6} {4}
indexes of I-isospectral families {3, 4} {7, 10, 13, 14} {33, 56}, {36, 41}, {50, 79}, {52, 57}, {76, 80} {27, 55, 98}, {45, 86}, {73, 85}, {53, 96}, {75, 132} 9 {36, 56, 62, 65}, {63, 104} {21, 40, 69}, {36, 65}, {56, 62} {40, 69} 10 {82, 165, 303, 311}, {96, 114, 189, 195, 216}, {99, 193}, {146, 173, 271, 281, 312}, {161, 192, 196, 219}, {167, 199}, {251, 279, 282, 322} 11 {0} {9, 10}, {153, 154, 155} {3, 4, 5, 6} {50, 91} 12 {2, 5} {198, 436}, {204, 239}, {340, 708}, {344, 429}, {385, 783}, {389, 472}, {404, 438}, {603, 702}, {653, 778}, {671, 711}, {754, 890}, {762, 785}
108
EMILIO A. LAURET
Table 5. (continued) n = 7 q 13
I {0} {0, 1} 14 {0}
indexes of I-isospectral families {11, 12}, {13, 14}, {34, 35, 36}, {271, 273} {34, 35} {66, 68}, {198, 200}, {479, 481}, {806, 810}, {975, 979}, {1017, 1019} 15 {0} {18, 20}, {66, 72}, {175, 187}, {179, 191}, {408, 427}, {413, 433}, {686, 710}, {838, 868}, {846, 874}, {852, 882} {2} {402, 403}, {4} {177, 403, 830, 842}, {190, 212, 425, 432, 458}, {331, 411, 713, 732, 841}, {353, 399, 428, 431, 461}, {589, 684, 725, 730, 850} {2, 5} {199, 443}, {202, 213}, {371, 793}, {373, 444}, {404, 842}, {407, 434}, {641, 794}, {715, 832}, {726, 774} L762 = [1, 2, 2, 2, 3, 5, 6], L778 = [1, 2, 2, 3, 3, 5, 6], L783 = [1, 2, 2, 3, 4, 5, 6], L785 = [1, 2, 2, 3, 5, 6, 6], L890 = [2, 2, 2, 2, 3, 6, 6]. q = 13 : L11 = [0, 0, 0, 0, 1, 2, 3], L12 = [0, 0, 0, 0, 1, 2, 4], L13 = [0, 0, 0, 0, 1, 2, 5], L14 = [0, 0, 0, 0, 1, 3, 4], L34 = [0, 0, 0, 1, 2, 3, 4], L35 = [0, 0, 0, 1, 2, 3, 5], L36 = [0, 0, 0, 1, 2, 3, 6], L271 = [1, 1, 2, 2, 3, 3, 5], L273 = [1, 1, 2, 2, 3, 4, 4]. q = 14 : L66 = [0, 0, 0, 1, 2, 3, 4], L68 = [0, 0, 0, 1, 2, 3, 6], L198 = [0, 0, 1, 2, 3, 4, 7], L200 = [0, 0, 1, 2, 3, 6, 7], L479 = [0, 1, 2, 3, 4, 7, 7], L481 = [0, 1, 2, 3, 6, 7, 7], L806 = [1, 1, 2, 3, 3, 4, 5], L810 = [1, 1, 2, 3, 3, 5, 6], L975 = [1, 2, 2, 3, 4, 4, 6], L979 = [1, 2, 2, 3, 4, 6, 6], L1017 = [1, 2, 3, 4, 7, 7, 7], L1019 = [1, 2, 3, 6, 7, 7, 7]. q = 15 : L18 = [0, 0, 0, 0, 1, 2, 6], L20 = [0, 0, 0, 0, 1, 3, 4], L66 = [0, 0, 0, 1, 2, 5, 6], L72 = [0, 0, 0, 1, 3, 4, 5], L175 = [0, 0, 1, 2, 3, 6, 6], L177 = [0, 0, 1, 2, 4, 5, 7], L179 = [0, 0, 1, 2, 5, 5, 6], L187 = [0, 0, 1, 3, 3, 4, 6], L190 = [0, 0, 1, 3, 3, 6, 6], L191 = [0, 0, 1, 3, 4, 5, 5], L199 = [0, 0, 1, 4, 5, 5, 6], L202 = [0, 0, 1, 5, 5, 5, 5], L212 = [0, 0, 3, 3, 5, 6, 6], L213 = [0, 0, 3, 5, 5, 5, 5], L331 = [0, 1, 1, 2, 4, 5, 7], L353 = [0, 1, 1, 3, 3, 6, 6], L371 = [0, 1, 1, 4, 4, 6, 6], L373 = [0, 1, 1, 4, 5, 5, 6], L399 = [0, 1, 2, 3, 3, 6, 6], L402 = [0, 1, 2, 3, 4, 5, 6], L403 = [0, 1, 2, 3, 4, 5, 7], L404 = [0, 1, 2, 3, 4, 6, 7], L407 = [0, 1, 2, 3, 5, 5, 7], L408 = [0, 1, 2, 3, 5, 6, 6], L411 = [0, 1, 2, 4, 5, 5, 7], L413 = [0, 1, 2, 5, 5, 5, 6], L425 = [0, 1, 3, 3, 3, 6, 6], L427 = [0, 1, 3, 3, 4, 5, 6], L428 = [0, 1, 3, 3, 4, 6, 6], L431 = [0, 1, 3, 3, 5, 6, 6], L432 = [0, 1, 3, 3, 6, 6, 6], L433 = [0, 1, 3, 4, 5, 5, 5], L434 = [0, 1, 3, 4, 5, 5, 6], L443 = [0, 1, 4, 5, 5, 5, 6], L444 = [0, 1, 4, 5, 5, 6, 6], L458 = [0, 3, 3, 3, 5, 6, 6], L461 = [0, 3, 3, 5, 5, 6, 6], L589 = [1, 1, 1, 2, 4, 5, 7], L641 = [1, 1, 1, 4, 4, 6, 6], L684 = [1, 1, 2, 2, 4, 5, 7], L686 = [1, 1, 2, 2, 4, 6, 7], L710 = [1, 1, 2, 3, 4, 4, 7], L713 = [1, 1, 2, 3, 4, 5, 7], L715 = [1, 1, 2, 3, 4, 6, 7], L725 = [1, 1, 2, 4, 4, 5, 7], L726 = [1, 1, 2, 4, 4, 6, 6], L730 = [1, 1, 2, 4, 5, 5, 7], L732 = [1, 1, 2, 4, 5, 6, 7], L774 = [1, 1, 3, 4, 4, 6, 6], L793 = [1, 1, 4, 4, 5, 6, 6], L794 = [1, 1, 4, 4, 6, 6, 6], L830 = [1, 2, 3, 3, 4, 5, 7], L832 = [1, 2, 3, 3, 4, 6, 7], L838 = [1, 2, 3, 3, 6, 6, 6], L841 = [1, 2, 3, 4, 5, 5, 7], L842 = [1, 2, 3, 4, 5, 6, 7], L846 = [1, 2, 3, 5, 5, 6, 6], L850 = [1, 2, 4, 5, 5, 5, 7], L852 = [1, 2, 5, 5, 5, 5, 6], L868 = [1, 3, 3, 3, 4, 6, 6], L874 = [1, 3, 3, 4, 5, 5, 6], L882 = [1, 3, 4, 5, 5, 5, 5]. q = 16 : L78 = [0, 0, 0, 1, 2, 3, 5], L80 = [0, 0, 0, 1, 2, 3, 7], L96 = [0, 0, 0, 1, 3, 5, 7], L180 = [0, 0, 1, 1, 3, 3, 5], L181 = [0, 0, 1, 1, 3, 3, 7], L189 = [0, 0, 1, 1, 3, 5, 7], L233 = [0, 0, 1, 2, 2, 3, 5], L235 = [0, 0, 1, 2, 2, 3, 7], L250 = [0, 0, 1, 2, 3, 4, 5], L252 = [0, 0, 1, 2, 3, 4, 7], L255 = [0, 0, 1, 2, 3, 5, 7], L256 = [0, 0, 1, 2, 3, 5, 8], L258 = [0, 0, 1, 2, 3, 7, 8], L268 = [0, 0, 1, 2, 4, 6, 8], L282 = [0, 0, 1, 3, 4, 5, 7], L283 = [0, 0, 1, 3, 4, 5, 8], L285 = [0, 0, 1, 3, 5, 7, 8], L390 = [0, 1, 1, 1, 3, 5, 7], L472 = [0, 1, 1, 2, 3, 5, 7], L491 = [0, 1, 1, 2, 4, 6, 8], L512 = [0, 1, 1, 3, 3, 4, 5], L513 = [0, 1, 1, 3, 3, 4, 7], L516 = [0, 1, 1, 3, 3, 5, 7], L517 = [0, 1, 1, 3, 3, 5, 8], L518 = [0, 1, 1, 3, 3, 7, 8], L526 = [0, 1, 1, 3, 4, 5, 7], L535 = [0, 1, 1, 3, 5, 6, 7], L537 = [0, 1, 1, 3, 5, 7, 7], L538 = [0, 1, 1, 3, 5, 7, 8], L604 = [0, 1, 2, 2, 2, 3, 5], L606 = [0, 1, 2, 2, 2, 3, 7],
APPENDIX
109
Table 5. (continued) n = 7 q 16
I {0}
indexes of I-isospectral families {78, 80}, {180, 181}, {233, 235}, {250, 252}, {256, 258}, {512, 513}, {517, 518}, {604, 606}, {621, 623}, {625, 629}, {627, 631}, {655, 657}, {661, 663}, {668, 670}, {1155, 1158}, {1248, 1249}, {1253, 1254}, {1259, 1260}, {1391, 1393}, {1408, 1410}, {1412, 1416}, {1414, 1418}, {1443, 1445}, {1447, 1451}, {1449, 1453}, {1457, 1461}, {1459, 1463}, {1498, 1500}, {1504, 1506}, {1511, 1513}, {1518, 1520} {3} {283, 708}, {6} {96, 285, 710, 1575}, {189, 538, 1298}, {255, 667, 1517}, {268, 688}, {282, 707, 1572}, {390, 537, 994, 1297}, {472, 535, 1184, 1295}, {491, 687}, {516, 1252, 1258}, {526, 1280}, {626, 665, 1458, 1515}, {642, 686}, {660, 1510}, {704, 1569}, {826, 993}, {910, 991, 1183, 1294}, {964, 988, 1256}, {979, 1279}, {1109, 1181, 1292}, {1156, 1178}, {1170, 1277}, {1413, 1456}, {1448, 1508} {2, 3, 6} {665, 1515} 17 {0} {16, 17}, {18, 19}, {55, 56, 58}, {62, 63}, {156, 157, 158, 159, 160}, {161, 162}, {376, 377, 378, 379} {0, 1} {57, 59}, {157, 158}, {376, 377, 378} {0, 1, 2} {377, 378} L621 = [0, 1, 2, 2, 3, 4, 5], L623 = [0, 1, 2, 2, 3, 4, 7], L625 = [0, 1, 2, 2, 3, 5, 6], L626 = [0, 1, 2, 2, 3, 5, 7], L627 = [0, 1, 2, 2, 3, 5, 8], L629 = [0, 1, 2, 2, 3, 6, 7], L631 = [0, 1, 2, 2, 3, 7, 8], L642 = [0, 1, 2, 2, 4, 6, 8], L655 = [0, 1, 2, 3, 4, 4, 5], L657 = [0, 1, 2, 3, 4, 4, 7], L660 = [0, 1, 2, 3, 4, 5, 7], L661 = [0, 1, 2, 3, 4, 5, 8], L663 = [0, 1, 2, 3, 4, 7, 8], L665 = [0, 1, 2, 3, 5, 6, 7], L667 = [0, 1, 2, 3, 5, 7, 8], L668 = [0, 1, 2, 3, 5, 8, 8], L670 = [0, 1, 2, 3, 7, 8, 8], L686 = [0, 1, 2, 4, 6, 6, 8], L687 = [0, 1, 2, 4, 6, 7, 8], L688 = [0, 1, 2, 4, 6, 8, 8], L704 = [0, 1, 3, 4, 4, 5, 7], L707 = [0, 1, 3, 4, 5, 7, 8], L708 = [0, 1, 3, 4, 5, 8, 8], L710 = [0, 1, 3, 5, 7, 8, 8], L826 = [1, 1, 1, 1, 3, 5, 7], L910 = [1, 1, 1, 2, 3, 5, 7], L964 = [1, 1, 1, 3, 3, 5, 7], L979 = [1, 1, 1, 3, 4, 5, 7], L988 = [1, 1, 1, 3, 5, 5, 7], L991 = [1, 1, 1, 3, 5, 6, 7], L993 = [1, 1, 1, 3, 5, 7, 7], L994 = [1, 1, 1, 3, 5, 7, 8], L1109 = [1, 1, 2, 2, 3, 5, 7], L1155 = [1, 1, 2, 3, 3, 5, 6], L1156 = [1, 1, 2, 3, 3, 5, 7], L1158 = [1, 1, 2, 3, 3, 6, 7], L1170 = [1, 1, 2, 3, 4, 5, 7], L1178 = [1, 1, 2, 3, 5, 5, 7], L1181 = [1, 1, 2, 3, 5, 6, 7], L1183 = [1, 1, 2, 3, 5, 7, 7], L1184 = [1, 1, 2, 3, 5, 7, 8], L1248 = [1, 1, 3, 3, 4, 4, 5], L1249 = [1, 1, 3, 3, 4, 4, 7], L1252 = [1, 1, 3, 3, 4, 5, 7], L1253 = [1, 1, 3, 3, 4, 5, 8], L1254 = [1, 1, 3, 3, 4, 7, 8], L1256 = [1, 1, 3, 3, 5, 5, 7], L1258 = [1, 1, 3, 3, 5, 7, 8], L1259 = [1, 1, 3, 3, 5, 8, 8], L1260 = [1, 1, 3, 3, 7, 8, 8], L1277 = [1, 1, 3, 4, 5, 6, 7], L1279 = [1, 1, 3, 4, 5, 7, 7], L1280 = [1, 1, 3, 4, 5, 7, 8], L1292 = [1, 1, 3, 5, 6, 6, 7], L1294 = [1, 1, 3, 5, 6, 7, 7], L1295 = [1, 1, 3, 5, 6, 7, 8], L1297 = [1, 1, 3, 5, 7, 7, 8], L1298 = [1, 1, 3, 5, 7, 8, 8], L1391 = [1, 2, 2, 2, 2, 3, 5], L1393 = [1, 2, 2, 2, 2, 3, 7], L1408 = [1, 2, 2, 2, 3, 4, 5], L1410 = [1, 2, 2, 2, 3, 4, 7], L1412 = [1, 2, 2, 2, 3, 5, 6], L1413 = [1, 2, 2, 2, 3, 5, 7], L1414 = [1, 2, 2, 2, 3, 5, 8], L1416 = [1, 2, 2, 2, 3, 6, 7], L1418 = [1, 2, 2, 2, 3, 7, 8], L1443 = [1, 2, 2, 3, 4, 4, 5], L1445 = [1, 2, 2, 3, 4, 4, 7], L1447 = [1, 2, 2, 3, 4, 5, 6], L1448 = [1, 2, 2, 3, 4, 5, 7], L1449 = [1, 2, 2, 3, 4, 5, 8], L1451 = [1, 2, 2, 3, 4, 6, 7], L1453 = [1, 2, 2, 3, 4, 7, 8], L1456 = [1, 2, 2, 3, 5, 6, 7], L1457 = [1, 2, 2, 3, 5, 6, 8], L1458 = [1, 2, 2, 3, 5, 7, 8], L1459 = [1, 2, 2, 3, 5, 8, 8], L1461 = [1, 2, 2, 3, 6, 7, 8], L1463 = [1, 2, 2, 3, 7, 8, 8], L1498 = [1, 2, 3, 4, 4, 4, 5], L1500 = [1, 2, 3, 4, 4, 4, 7], L1504 = [1, 2, 3, 4, 4, 5, 8], L1506 = [1, 2, 3, 4, 4, 7, 8], L1508 = [1, 2, 3, 4, 5, 6, 7], L1510 = [1, 2, 3, 4, 5, 7, 8], L1511 = [1, 2, 3, 4, 5, 8, 8], L1513 = [1, 2, 3, 4, 7, 8, 8], L1515 = [1, 2, 3, 5, 6, 7, 8], L1517 = [1, 2, 3, 5, 7, 8, 8], L1518 = [1, 2, 3, 5, 8, 8, 8], L1520 = [1, 2, 3, 7, 8, 8, 8], L1569 = [1, 3, 4, 4, 5, 7, 8], L1572 = [1, 3, 4, 5, 7, 8, 8], L1575 = [1, 3, 5, 7, 8, 8, 8]. q = 17 : L16 = [0, 0, 0, 0, 1, 2, 5], L17 = [0, 0, 0, 0, 1, 2, 6], L18 = [0, 0, 0, 0, 1, 2, 7], L19 = [0, 0, 0, 0, 1, 3, 4], L55 = [0, 0, 0, 1, 2, 3, 5], L56 = [0, 0, 0, 1, 2, 3, 6], L57 = [0, 0, 0, 1, 2, 3, 7], L58 = [0, 0, 0, 1, 2, 3, 8], L59 = [0, 0, 0, 1, 2, 4, 5], L62 = [0, 0, 0, 1, 2, 6, 7], L63 = [0, 0, 0, 1, 3, 4, 5], L156 =
110
EMILIO A. LAURET
Table 5. (continued) n = 7 q 18
I {0}
indexes of I-isospectral families {117, 119}, {407, 409}, {429, 434}, {432, 437}, {1182, 1184}, {1204, 1209}, {1207, 1212}, {1251, 1260}, {1254, 1263}, {1258, 1267}, {2304, 2311}, {2905, 2911}, {2985, 2987}, {3007, 3012}, {3010, 3015}, {3054, 3063}, {3057, 3066}, {3061, 3070}, {3136, 3149}, {3139, 3152}, {3143, 3156}, {3147, 3161} {5} {956, 2260, 2494, 2525, 2530}, {1143, 1246, 1264, 1529, 1544}, {1943, 2446, 2518, 2531}, {2, 5} {537, 1446}, {1027, 2658}, {1255, 3140}, {1379, 1448}, {1568, 3677}, {2517, 2661}, {3058, 3144}, {3614, 3636}, {3668, 3679} {5, 6} {435, 1261}, {498, 1381, 3356}, {603, 612, 1575, 1587}, {861, 1253}, {956, 2525}, {1143, 1246, 1264}, {1210, 1265}, {1219, 3078}, {1340, 1383, 3289, 3358}, {1529, 1544}, {1566, 1577, 1589}, {1943, 2518}, {2260, 2494, 2530}, {2446, 2531}, {2879, 3059}, {3022, 3080}, {3248, 3291, 3360} {2, 5, 6} {1340, 3289}, {1575, 1587}, {3248, 3291}
[0, 0, 1, 2, 3, 4, 5], L157 = [0, 0, 1, 2, 3, 4, 6], L158 = [0, 0, 1, 2, 3, 4, 7], L159 = [0, 0, 1, 2, 3, 4, 8], L160 = [0, 0, 1, 2, 3, 5, 6], L161 = [0, 0, 1, 2, 3, 5, 8], L162 = [0, 0, 1, 2, 3, 6, 7], L376 = [0, 1, 2, 3, 4, 5, 6], L377 = [0, 1, 2, 3, 4, 5, 7], L378 = [0, 1, 2, 3, 4, 5, 8], L379 = [0, 1, 2, 3, 4, 6, 8]. q = 18 : L117 = [0, 0, 0, 1, 2, 4, 5], L119 = [0, 0, 0, 1, 2, 4, 7], L407 = [0, 0, 1, 2, 3, 4, 5], L409 = [0, 0, 1, 2, 3, 4, 7], L429 = [0, 0, 1, 2, 4, 5, 6], L432 = [0, 0, 1, 2, 4, 5, 9], L434 = [0, 0, 1, 2, 4, 6, 7], L435 = [0, 0, 1, 2, 4, 6, 8], L437 = [0, 0, 1, 2, 4, 7, 9], L498 = [0, 0, 1, 3, 5, 7, 9], L537 = [0, 0, 1, 5, 6, 6, 7], L603 = [0, 0, 2, 3, 4, 6, 8], L612 = [0, 0, 2, 4, 6, 8, 9], L861 = [0, 1, 1, 2, 4, 6, 8], L956 = [0, 1, 1, 3, 5, 7, 9], L1027 = [0, 1, 1, 5, 5, 7, 7], L1143 = [0, 1, 2, 2, 4, 6, 8], L1182 = [0, 1, 2, 3, 3, 4, 5], L1184 = [0, 1, 2, 3, 3, 4, 7], L1204 = [0, 1, 2, 3, 4, 5, 6], L1207 = [0, 1, 2, 3, 4, 5, 9], L1209 = [0, 1, 2, 3, 4, 6, 7], L1210 = [0, 1, 2, 3, 4, 6, 8], L1212 = [0, 1, 2, 3, 4, 7, 9], L1219 = [0, 1, 2, 3, 5, 7, 9], L1246 = [0, 1, 2, 4, 4, 6, 8], L1251 = [0, 1, 2, 4, 5, 6, 6], L1253 = [0, 1, 2, 4, 5, 6, 8], L1254 = [0, 1, 2, 4, 5, 6, 9], L1255 = [0, 1, 2, 4, 5, 7, 8], L1258 = [0, 1, 2, 4, 5, 9, 9], L1260 = [0, 1, 2, 4, 6, 6, 7], L1261 = [0, 1, 2, 4, 6, 6, 8], L1263 = [0, 1, 2, 4, 6, 7, 9], L1264 = [0, 1, 2, 4, 6, 8, 8], L1265 = [0, 1, 2, 4, 6, 8, 9], L1267 = [0, 1, 2, 4, 7, 9, 9], L1340 = [0, 1, 3, 3, 5, 7, 9], L1379 = [0, 1, 3, 5, 6, 6, 7], L1381 = [0, 1, 3, 5, 6, 7, 9], L1383 = [0, 1, 3, 5, 7, 9, 9], L1446 = [0, 1, 5, 6, 6, 6, 7], L1448 = [0, 1, 5, 6, 6, 7, 9], L1529 = [0, 2, 2, 3, 4, 6, 8], L1544 = [0, 2, 2, 4, 6, 8, 9], L1566 = [0, 2, 3, 3, 4, 6, 8], L1568 = [0, 2, 3, 3, 4, 8, 9], L1575 = [0, 2, 3, 4, 6, 6, 8], L1577 = [0, 2, 3, 4, 6, 8, 9], L1587 = [0, 2, 4, 6, 6, 8, 9], L1589 = [0, 2, 4, 6, 8, 9, 9], L1943 = [1, 1, 1, 3, 5, 7, 9], L2260 = [1, 1, 2, 3, 5, 7, 9], L2304 = [1, 1, 2, 4, 5, 5, 7], L2311 = [1, 1, 2, 4, 5, 7, 7], L2446 = [1, 1, 3, 3, 5, 7, 9], L2494 = [1, 1, 3, 4, 5, 7, 9], L2517 = [1, 1, 3, 5, 5, 7, 7], L2518 = [1, 1, 3, 5, 5, 7, 9], L2525 = [1, 1, 3, 5, 6, 7, 9], L2530 = [1, 1, 3, 5, 7, 8, 9], L2531 = [1, 1, 3, 5, 7, 9, 9], L2658 = [1, 1, 5, 5, 6, 7, 7], L2661 = [1, 1, 5, 5, 7, 7, 9], L2879 = [1, 2, 2, 3, 5, 7, 9], L2905 = [1, 2, 2, 4, 4, 5, 8], L2911 = [1, 2, 2, 4, 4, 7, 8], L2985 = [1, 2, 3, 3, 3, 4, 5], L2987 = [1, 2, 3, 3, 3, 4, 7], L3007 = [1, 2, 3, 3, 4, 5, 6], L3010 = [1, 2, 3, 3, 4, 5, 9], L3012 = [1, 2, 3, 3, 4, 6, 7], L3015 = [1, 2, 3, 3, 4, 7, 9], L3022 = [1, 2, 3, 3, 5, 7, 9], L3054 = [1, 2, 3, 4, 5, 6, 6], L3057 = [1, 2, 3, 4, 5, 6, 9], L3058 = [1, 2, 3, 4, 5, 7, 8], L3059 = [1, 2, 3, 4, 5, 7, 9], L3061 = [1, 2, 3, 4, 5, 9, 9], L3063 = [1, 2, 3, 4, 6, 6, 7], L3066 = [1, 2, 3, 4, 6, 7, 9], L3070 = [1, 2, 3, 4, 7, 9, 9], L3078 = [1, 2, 3, 5, 6, 7, 9], L3080 = [1, 2, 3, 5, 7, 9, 9], L3136 = [1, 2, 4, 5, 6, 6, 6], L3139 = [1, 2, 4, 5, 6, 6, 9], L3140 = [1, 2, 4, 5, 6, 7, 8], L3143 = [1, 2, 4, 5, 6, 9, 9], L3144 = [1, 2, 4, 5, 7, 8, 9], L3147 = [1, 2, 4, 5, 9, 9, 9], L3149 = [1, 2, 4, 6, 6, 6, 7], L3152 = [1, 2, 4, 6, 6, 7, 9], L3156 = [1, 2, 4, 6, 7, 9, 9], L3161 = [1, 2, 4, 7, 9, 9, 9], L3248 = [1, 3, 3, 3, 5, 7, 9], L3289 = [1, 3, 3, 5, 6, 7, 9], L3291 = [1, 3, 3, 5, 7, 9, 9], L3356 = [1, 3, 5, 6, 6, 7, 9], L3358 = [1, 3, 5, 6, 7, 9, 9], L3360 = [1, 3, 5, 7, 9, 9, 9], L3614 = [2, 2, 3, 4, 4, 8, 8], L3636 = [2, 2, 4, 4, 8, 8, 9], L3668 = [2, 3, 3, 3, 4, 8, 9], L3677 = [2, 3, 3, 4, 6, 8, 9], L3679 = [2, 3, 3, 4, 8, 9, 9].
APPENDIX
111
Table 5. (continued) n = 7 q 19
I {0}
indexes of I-isospectral families {19, 21}, {67, 68, 71}, {70, 72, 74}, {77, 79}, {209, 210}, {211, 213, 215, 217}, {214, 216, 218, 220}, {219, 222}, {548, 549, 550, 551, 552, 553, 554}, {555, 556, 557}, {1269, 1270, 1271, 1272} {0, 1} {216, 218}, {550, 551}, {552, 554}, {555, 557}, {1269, 1270, 1271} {0, 1, 2, 3} {1270, 1271} 20 {0} {355, 357}, {505, 507}, {1175, 1177}, {1182, 1186}, {1574, 1576}, {1584, 1588}, {3014, 3016}, {3305, 3309}, {3315, 3317}, {3322, 3326}, {3334, 3340}, {3988, 3990}, {3999, 4001}, {4205, 4209}, {4215, 4217}, {4225, 4229}, {4242, 4248} {4} {608, 1774, 4562, 4592}, {634, 779, 1826, 1854, 2116}, {1227, 1793, 3381, 3453, 4586}, {1285, 1763, 1840, 1855, 2122}, {1547, 2053, 4099, 4162, 5059}, {1600, 1798, 4224, 4273, 4594}, {1643, 1849, 1856, 2072, 2125}, {1671, 2084}, {2597, 3321, 3430, 3455, 4615}, {2973, 4032, 4138, 4163, 5077}, {3069, 3444, 3456, 4260, 4620}, {3967, 4159, 4164, 5025, 5085}, {4023, 4267, 4275, 4626} {4, 5, 6} {1600, 4594}, {2597, 3455} q = 19 : L19 = [0, 0, 0, 0, 1, 2, 7], L21 = [0, 0, 0, 0, 1, 3, 4], L67 = [0, 0, 0, 1, 2, 3, 5], L68 = [0, 0, 0, 1, 2, 3, 6], L70 = [0, 0, 0, 1, 2, 3, 8], L71 = [0, 0, 0, 1, 2, 3, 9], L72 = [0, 0, 0, 1, 2, 4, 5], L74 = [0, 0, 0, 1, 2, 4, 8], L77 = [0, 0, 0, 1, 2, 6, 8], L79 = [0, 0, 0, 1, 3, 4, 5], L209 = [0, 0, 1, 2, 3, 4, 5], L210 = [0, 0, 1, 2, 3, 4, 6], L211 = [0, 0, 1, 2, 3, 4, 7], L213 = [0, 0, 1, 2, 3, 4, 9], L214 = [0, 0, 1, 2, 3, 5, 6], L215 = [0, 0, 1, 2, 3, 5, 7], L216 = [0, 0, 1, 2, 3, 5, 9], L217 = [0, 0, 1, 2, 3, 6, 7], L218 = [0, 0, 1, 2, 3, 6, 8], L219 = [0, 0, 1, 2, 3, 7, 8], L220 = [0, 0, 1, 2, 3, 7, 9], L222 = [0, 0, 1, 2, 5, 6, 8], L548 = [0, 1, 2, 3, 4, 5, 6], L549 = [0, 1, 2, 3, 4, 5, 7], L550 = [0, 1, 2, 3, 4, 5, 8], L551 = [0, 1, 2, 3, 4, 5, 9], L552 = [0, 1, 2, 3, 4, 6, 7], L553 = [0, 1, 2, 3, 4, 6, 8], L554 = [0, 1, 2, 3, 4, 6, 9], L555 = [0, 1, 2, 3, 4, 7, 9], L556 = [0, 1, 2, 3, 5, 6, 9], L557 = [0, 1, 2, 3, 5, 7, 8], L1269 = [1, 2, 3, 4, 5, 6, 7], L1270 = [1, 2, 3, 4, 5, 6, 8], L1271 = [1, 2, 3, 4, 5, 6, 9], L1272 = [1, 2, 3, 4, 5, 8, 9]. q = 20 : L355 = [0, 0, 1, 1, 3, 3, 7], L357 = [0, 0, 1, 1, 3, 3, 9], L505 = [0, 0, 1, 2, 3, 4, 7], L507 = [0, 0, 1, 2, 3, 4, 9], L608 = [0, 0, 1, 3, 5, 7, 9], L634 = [0, 0, 1, 4, 4, 8, 8], L779 = [0, 0, 4, 4, 5, 8, 8], L1175 = [0, 1, 1, 3, 3, 5, 7], L1177 = [0, 1, 1, 3, 3, 5, 9], L1182 = [0, 1, 1, 3, 3, 7, 10], L1186 = [0, 1, 1, 3, 3, 9, 10], L1227 = [0, 1, 1, 3, 5, 7, 9], L1285 = [0, 1, 1, 4, 4, 8, 8], L1547 = [0, 1, 2, 2, 6, 6, 10], L1574 = [0, 1, 2, 3, 4, 5, 7], L1576 = [0, 1, 2, 3, 4, 5, 9], L1584 = [0, 1, 2, 3, 4, 7, 10], L1588 = [0, 1, 2, 3, 4, 9, 10], L1600 = [0, 1, 2, 3, 5, 7, 9], L1643 = [0, 1, 2, 4, 4, 8, 8], L1671 = [0, 1, 2, 4, 6, 8, 10], L1763 = [0, 1, 3, 4, 4, 8, 8], L1774 = [0, 1, 3, 4, 5, 7, 9], L1793 = [0, 1, 3, 5, 5, 7, 9], L1798 = [0, 1, 3, 5, 7, 9, 10], L1826 = [0, 1, 4, 4, 4, 8, 8], L1840 = [0, 1, 4, 4, 5, 8, 8], L1849 = [0, 1, 4, 4, 6, 8, 8], L1854 = [0, 1, 4, 4, 8, 8, 8], L1855 = [0, 1, 4, 4, 8, 8, 9], L1856 = [0, 1, 4, 4, 8, 8, 10], L2053 = [0, 2, 2, 5, 6, 6, 10], L2072 = [0, 2, 4, 4, 5, 8, 8], L2084 = [0, 2, 4, 5, 6, 8, 10], L2116 = [0, 4, 4, 4, 5, 8, 8], L2122 = [0, 4, 4, 5, 5, 8, 8], L2125 = [0, 4, 4, 5, 8, 8, 10], L2597 = [1, 1, 1, 3, 5, 7, 9], L2973 = [1, 1, 2, 2, 6, 6, 10], L3014 = [1, 1, 2, 3, 3, 6, 7], L3016 = [1, 1, 2, 3, 3, 6, 9], L3069 = [1, 1, 2, 3, 5, 7, 9], L3305 = [1, 1, 3, 3, 4, 7, 8], L3309 = [1, 1, 3, 3, 4, 8, 9], L3315 = [1, 1, 3, 3, 5, 5, 7], L3317 = [1, 1, 3, 3, 5, 5, 9], L3321 = [1, 1, 3, 3, 5, 7, 9], L3322 = [1, 1, 3, 3, 5, 7, 10], L3326 = [1, 1, 3, 3, 5, 9, 10], L3334 = [1, 1, 3, 3, 7, 10, 10], L3340 = [1, 1, 3, 3, 9, 10, 10], L3381 = [1, 1, 3, 4, 5, 7, 9], L3430 = [1, 1, 3, 5, 5, 7, 9], L3444 = [1, 1, 3, 5, 6, 7, 9], L3453 = [1, 1, 3, 5, 7, 8, 9], L3455 = [1, 1, 3, 5, 7, 9, 9], L3456 = [1, 1, 3, 5, 7, 9, 10], L3967 = [1, 2, 2, 2, 6, 6, 10], L3988 = [1, 2, 2, 3, 4, 4, 7], L3990 = [1, 2, 2, 3, 4, 4, 9], L3999 = [1, 2, 2, 3, 4, 6, 7], L4001 = [1, 2, 2, 3, 4, 6, 9], L4023 = [1, 2, 2, 3, 5, 7, 9], L4032 = [1, 2, 2, 3, 6, 6, 10], L4099 = [1, 2, 2, 4, 6, 6, 10], L4138 = [1, 2, 2, 5, 6, 6, 10], L4159 = [1, 2, 2, 6, 6, 6, 10],
112
EMILIO A. LAURET
Table 5. (continued) n = 7 q 21
I {0}
indexes of I-isospectral families {110, 112}, {121, 135}, {384, 389}, {385, 387}, {390, 394}, {391, 402}, {401, 459}, {404, 408}, {426, 462}, {1150, 1155, 1165}, {1157, 1168}, {1158, 1164}, {1169, 1179}, {1170, 1190}, {1189, 1298}, {1194, 1200}, {1231, 1304}, {2946, 2959}, {2988, 3001}, {2992, 3000, 3016}, {3004, 3021}, {3005, 3015}, {3022, 3041}, {3023, 3054}, {3039, 3194}, {3053, 3233}, {3060, 3067}, {3115, 3241} {0, 1} {1171, 1183}, {2987, 2989}, {3024, 3045} {2} {2988, 2989}, {2, 5} {500, 1360}, {506, 526}, {1077, 2847}, {1083, 1353}, {1211, 3084}, {1215, 1322}, {1230, 1362}, {2036, 2838}, {2392, 3079}, {2419, 2852}, {2605, 3086}, {2662, 2747}, {2996, 3018}
L4162 = [1, 2, 2, 6, 6, 8, 10], L4163 = [1, 2, 2, 6, 6, 9, 10], L4164 = [1, 2, 2, 6, 6, 10, 10], L4205 = [1, 2, 3, 4, 4, 7, 8], L4209 = [1, 2, 3, 4, 4, 8, 9], L4215 = [1, 2, 3, 4, 5, 5, 7], L4217 = [1, 2, 3, 4, 5, 5, 9], L4224 = [1, 2, 3, 4, 5, 7, 9], L4225 = [1, 2, 3, 4, 5, 7, 10], L4229 = [1, 2, 3, 4, 5, 9, 10], L4242 = [1, 2, 3, 4, 7, 10, 10], L4248 = [1, 2, 3, 4, 9, 10, 10], L4260 = [1, 2, 3, 5, 5, 7, 9], L4267 = [1, 2, 3, 5, 6, 7, 9], L4273 = [1, 2, 3, 5, 7, 8, 9], L4275 = [1, 2, 3, 5, 7, 9, 10], L4562 = [1, 3, 4, 4, 5, 7, 9], L4586 = [1, 3, 4, 5, 5, 7, 9], L4592 = [1, 3, 4, 5, 7, 8, 9], L4594 = [1, 3, 4, 5, 7, 9, 10], L4615 = [1, 3, 5, 5, 5, 7, 9], L4620 = [1, 3, 5, 5, 7, 9, 10], L4626 = [1, 3, 5, 7, 9, 10, 10], L5025 = [2, 2, 2, 5, 6, 6, 10], L5059 = [2, 2, 4, 5, 6, 6, 10], L5077 = [2, 2, 5, 5, 6, 6, 10], L5085 = [2, 2, 5, 6, 6, 10, 10]. q = 21 : L110 = [0, 0, 0, 1, 2, 4, 5], L112 = [0, 0, 0, 1, 2, 4, 8], L121 = [0, 0, 0, 1, 2, 6, 9], L135 = [0, 0, 0, 1, 3, 4, 6], L384 = [0, 0, 1, 2, 3, 4, 8], L385 = [0, 0, 1, 2, 3, 4, 9], L387 = [0, 0, 1, 2, 3, 5, 6], L389 = [0, 0, 1, 2, 3, 5, 8], L390 = [0, 0, 1, 2, 3, 5, 9], L391 = [0, 0, 1, 2, 3, 5, 10], L394 = [0, 0, 1, 2, 3, 6, 8], L401 = [0, 0, 1, 2, 3, 8, 9], L402 = [0, 0, 1, 2, 3, 8, 10], L404 = [0, 0, 1, 2, 4, 5, 7], L408 = [0, 0, 1, 2, 4, 7, 8], L426 = [0, 0, 1, 2, 6, 7, 9], L459 = [0, 0, 1, 3, 4, 5, 6], L462 = [0, 0, 1, 3, 4, 6, 7], L500 = [0, 0, 1, 6, 7, 7, 8], L506 = [0, 0, 1, 7, 7, 7, 7], L526 = [0, 0, 3, 7, 7, 7, 7], L1077 = [0, 1, 1, 6, 6, 8, 8], L1083 = [0, 1, 1, 6, 7, 7, 8], L1150 = [0, 1, 2, 3, 4, 5, 9], L1155 = [0, 1, 2, 3, 4, 6, 10], L1157 = [0, 1, 2, 3, 4, 7, 8], L1158 = [0, 1, 2, 3, 4, 7, 9], L1164 = [0, 1, 2, 3, 5, 6, 7], L1165 = [0, 1, 2, 3, 5, 6, 8], L1168 = [0, 1, 2, 3, 5, 7, 8], L1169 = [0, 1, 2, 3, 5, 7, 9], L1170 = [0, 1, 2, 3, 5, 7, 10], L1171 = [0, 1, 2, 3, 5, 8, 9], L1179 = [0, 1, 2, 3, 6, 7, 8], L1183 = [0, 1, 2, 3, 6, 8, 10], L1189 = [0, 1, 2, 3, 7, 8, 9], L1190 = [0, 1, 2, 3, 7, 8, 10], L1194 = [0, 1, 2, 4, 5, 7, 7], L1200 = [0, 1, 2, 4, 7, 7, 8], L1211 = [0, 1, 2, 5, 6, 8, 9], L1215 = [0, 1, 2, 5, 7, 7, 9], L1230 = [0, 1, 2, 6, 7, 7, 8], L1231 = [0, 1, 2, 6, 7, 7, 9], L1298 = [0, 1, 3, 4, 5, 6, 7], L1304 = [0, 1, 3, 4, 6, 7, 7], L1322 = [0, 1, 3, 6, 7, 7, 8], L1353 = [0, 1, 6, 6, 7, 7, 8], L1360 = [0, 1, 6, 7, 7, 7, 8], L1362 = [0, 1, 6, 7, 7, 8, 9], L2036 = [1, 1, 1, 6, 6, 8, 8], L2392 = [1, 1, 2, 5, 6, 8, 9], L2419 = [1, 1, 2, 6, 6, 8, 8], L2605 = [1, 1, 3, 4, 6, 8, 10], L2662 = [1, 1, 3, 6, 6, 8, 8], L2747 = [1, 1, 4, 6, 6, 8, 8], L2838 = [1, 1, 6, 6, 6, 8, 8], L2847 = [1, 1, 6, 6, 7, 8, 8], L2852 = [1, 1, 6, 6, 8, 8, 9], L2946 = [1, 2, 3, 3, 4, 8, 9], L2959 = [1, 2, 3, 3, 5, 8, 9], L2987 = [1, 2, 3, 4, 5, 6, 8], L2988 = [1, 2, 3, 4, 5, 6, 9], L2989 = [1, 2, 3, 4, 5, 6, 10], L2992 = [1, 2, 3, 4, 5, 7, 9], L2996 = [1, 2, 3, 4, 5, 9, 10], L3000 = [1, 2, 3, 4, 6, 7, 10], L3001 = [1, 2, 3, 4, 6, 8, 9], L3004 = [1, 2, 3, 4, 7, 7, 8], L3005 = [1, 2, 3, 4, 7, 7, 9], L3015 = [1, 2, 3, 5, 6, 7, 7], L3016 = [1, 2, 3, 5, 6, 7, 8], L3018 = [1, 2, 3, 5, 6, 8, 9], L3021 = [1, 2, 3, 5, 7, 7, 8], L3022 = [1, 2, 3, 5, 7, 7, 9], L3023 = [1, 2, 3, 5, 7, 7, 10], L3024 = [1, 2, 3, 5, 7, 8, 9], L3039 = [1, 2, 3, 6, 6, 9, 9], L3041 = [1, 2, 3, 6, 7, 7, 8], L3045 = [1, 2, 3, 6, 7, 8, 10], L3053 = [1, 2, 3, 7, 7, 8, 9], L3054 = [1, 2, 3, 7, 7, 8, 10], L3060 = [1, 2, 4, 5, 7, 7, 7], L3067 = [1, 2, 4, 7, 7, 7, 8], L3079 = [1, 2, 5, 6, 6, 8, 9], L3084 = [1, 2, 5, 6, 7, 8, 9], L3086 = [1, 2, 5, 6, 8, 9, 9], L3115 = [1, 2, 6, 7, 7, 7, 9], L3194 = [1, 3, 3, 4, 6, 6, 9], L3233 = [1, 3, 4, 5, 6, 7, 7], L3241 = [1, 3, 4, 6, 7, 7, 7]. q = 22 : L33 = [0, 0, 0, 0, 1, 3, 5], L34 = [0, 0, 0, 0, 1, 3, 7], L166 = [0, 0, 0, 1, 2, 8, 9], L177 = [0, 0, 0, 1, 3, 4, 8], L182 = [0, 0, 0, 1, 3, 5, 11], L184 = [0, 0, 0, 1, 3, 7, 11], L242 = [0, 0, 0, 2, 4, 6, 11], L243 = [0, 0, 0, 2, 4, 8, 11], L567 = [0, 0, 1, 2, 3, 4, 9], L570 = [0, 0, 1, 2, 3, 5, 6], L577 = [0, 0, 1, 2, 3, 6, 8], L582 = [0, 0, 1, 2, 3, 7, 10], L600 = [0, 0, 1, 2, 4, 5, 6], L623 = [0, 0, 1, 2, 5, 6, 7], L624 = [0, 0, 1, 2, 5, 6, 8],
APPENDIX
113
Table 5. (continued) n = 7 q 22
I {0}
indexes of I-isospectral families {33, 34}, {166, 177}, {182, 184}, {242, 243}, {567, 570}, {577, 600}, {582, 623}, {624, 641}, {662, 686}, {694, 697}, {818, 819}, {1880, 1882}, {1881, 1883, 1885, 1887}, {1886, 1888}, {1892, 1913}, {1898, 1904}, {1899, 1907}, {1903, 1908}, {1922, 1976}, {1924, 1979}, {1932, 2027}, {1977, 1982}, {2030, 2063}, {2099, 2142}, {2152, 2156}, {2379, 2380}, {4049, 4051, 4060}, {5345, 5347, 5352}, {5346, 5348, 5361}, {5350, 5357, 5362}, {5353, 5358}, {5355, 5363, 5366}, {5356, 5359, 5364, 5369}, {5368, 5371}, {5374, 5385, 5401}, {5376, 5400, 5413}, {5379, 5415}, {5391, 5402}, {5392, 5405}, {5398, 5406}, {5428, 5536}, {5431, 5541}, {5442, 5624}, {5539, 5546}, {5629, 5687}, {5742, 5811}, {5823, 5828}, {6204, 6205} {0, 1} {5347, 5352}, {5355, 5363} {3, 4, 5, 6} {1996, 2377}, {2147, 5407}, {4232, 5817}
L641 = [0, 0, 1, 2, 6, 7, 10], L662 = [0, 0, 1, 2, 8, 9, 11], L686 = [0, 0, 1, 3, 4, 8, 11], L694 = [0, 0, 1, 3, 5, 11, 11], L697 = [0, 0, 1, 3, 7, 11, 11], L818 = [0, 0, 2, 4, 6, 11, 11], L819 = [0, 0, 2, 4, 8, 11, 11], L1880 = [0, 1, 2, 3, 4, 5, 7], L1881 = [0, 1, 2, 3, 4, 5, 8], L1882 = [0, 1, 2, 3, 4, 5, 9], L1883 = [0, 1, 2, 3, 4, 5, 10], L1885 = [0, 1, 2, 3, 4, 6, 7], L1886 = [0, 1, 2, 3, 4, 6, 8], L1887 = [0, 1, 2, 3, 4, 6, 9], L1888 = [0, 1, 2, 3, 4, 6, 10], L1892 = [0, 1, 2, 3, 4, 7, 10], L1898 = [0, 1, 2, 3, 4, 9, 10], L1899 = [0, 1, 2, 3, 4, 9, 11], L1903 = [0, 1, 2, 3, 5, 6, 7], L1904 = [0, 1, 2, 3, 5, 6, 8], L1907 = [0, 1, 2, 3, 5, 6, 11], L1908 = [0, 1, 2, 3, 5, 7, 8], L1913 = [0, 1, 2, 3, 5, 8, 10], L1922 = [0, 1, 2, 3, 6, 8, 9], L1924 = [0, 1, 2, 3, 6, 8, 11], L1932 = [0, 1, 2, 3, 7, 10, 11], L1976 = [0, 1, 2, 4, 5, 6, 7], L1977 = [0, 1, 2, 4, 5, 6, 8], L1979 = [0, 1, 2, 4, 5, 6, 11], L1982 = [0, 1, 2, 4, 5, 8, 10], L1996 = [0, 1, 2, 4, 6, 8, 10], L2027 = [0, 1, 2, 5, 6, 7, 11], L2030 = [0, 1, 2, 5, 6, 8, 11], L2063 = [0, 1, 2, 6, 7, 10, 11], L2099 = [0, 1, 2, 8, 9, 11, 11], L2142 = [0, 1, 3, 4, 8, 11, 11], L2147 = [0, 1, 3, 5, 7, 9, 11], L2152 = [0, 1, 3, 5, 11, 11, 11], L2156 = [0, 1, 3, 7, 11, 11, 11], L2377 = [0, 2, 4, 6, 8, 10, 11], L2379 = [0, 2, 4, 6, 11, 11, 11], L2380 = [0, 2, 4, 8, 11, 11, 11], L4049 = [1, 1, 3, 3, 5, 5, 9], L4051 = [1, 1, 3, 3, 5, 7, 7], L4060 = [1, 1, 3, 3, 5, 9, 9], L4232 = [1, 1, 3, 5, 7, 9, 11], L5345 = [1, 2, 3, 4, 5, 6, 7], L5346 = [1, 2, 3, 4, 5, 6, 8], L5347 = [1, 2, 3, 4, 5, 6, 9], L5348 = [1, 2, 3, 4, 5, 6, 10], L5350 = [1, 2, 3, 4, 5, 7, 8], L5352 = [1, 2, 3, 4, 5, 7, 10], L5353 = [1, 2, 3, 4, 5, 7, 11], L5355 = [1, 2, 3, 4, 5, 8, 10], L5356 = [1, 2, 3, 4, 5, 8, 11], L5357 = [1, 2, 3, 4, 5, 9, 10], L5358 = [1, 2, 3, 4, 5, 9, 11], L5359 = [1, 2, 3, 4, 5, 10, 11], L5361 = [1, 2, 3, 4, 6, 7, 8], L5362 = [1, 2, 3, 4, 6, 7, 9], L5363 = [1, 2, 3, 4, 6, 7, 10], L5364 = [1, 2, 3, 4, 6, 7, 11], L5366 = [1, 2, 3, 4, 6, 8, 9], L5368 = [1, 2, 3, 4, 6, 8, 11], L5369 = [1, 2, 3, 4, 6, 9, 11], L5371 = [1, 2, 3, 4, 6, 10, 11], L5374 = [1, 2, 3, 4, 7, 8, 10], L5376 = [1, 2, 3, 4, 7, 9, 10], L5379 = [1, 2, 3, 4, 7, 10, 11], L5385 = [1, 2, 3, 4, 8, 9, 10], L5391 = [1, 2, 3, 4, 9, 10, 11], L5392 = [1, 2, 3, 4, 9, 11, 11], L5398 = [1, 2, 3, 5, 6, 7, 11], L5400 = [1, 2, 3, 5, 6, 8, 9], L5401 = [1, 2, 3, 5, 6, 8, 10], L5402 = [1, 2, 3, 5, 6, 8, 11], L5405 = [1, 2, 3, 5, 6, 11, 11], L5406 = [1, 2, 3, 5, 7, 8, 11], L5407 = [1, 2, 3, 5, 7, 9, 11], L5413 = [1, 2, 3, 5, 8, 9, 10], L5415 = [1, 2, 3, 5, 8, 10, 11], L5428 = [1, 2, 3, 6, 8, 9, 11], L5431 = [1, 2, 3, 6, 8, 11, 11], L5442 = [1, 2, 3, 7, 10, 11, 11], L5536 = [1, 2, 4, 5, 6, 7, 11], L5539 = [1, 2, 4, 5, 6, 8, 11], L5541 = [1, 2, 4, 5, 6, 11, 11], L5546 = [1, 2, 4, 5, 8, 10, 11], L5624 = [1, 2, 5, 6, 7, 11, 11], L5629 = [1, 2, 5, 6, 8, 11, 11], L5687 = [1, 2, 6, 7, 10, 11, 11], L5742 = [1, 2, 8, 9, 11, 11, 11], L5811 = [1, 3, 4, 8, 11, 11, 11], L5817 = [1, 3, 5, 7, 9, 11, 11], L5823 = [1, 3, 5, 11, 11, 11, 11], L5828 = [1, 3, 7, 11, 11, 11, 11], L6204 = [2, 4, 6, 11, 11, 11, 11], L6205 = [2, 4, 8, 11, 11, 11, 11]. q = 23 : L102 = [0, 0, 0, 1, 2, 4, 5], L104 = [0, 0, 0, 1, 2, 4, 8], L108 = [0, 0, 0, 1, 2, 5, 7], L110 = [0, 0, 0, 1, 2, 5, 9], L114 = [0, 0, 0, 1, 2, 6, 10], L121 = [0, 0, 0, 1, 3, 4, 9], L357 = [0, 0, 1, 2, 3, 4, 7], L358 = [0, 0, 1, 2, 3, 4, 8], L361 = [0, 0, 1, 2, 3, 4, 11], L362 = [0, 0, 1, 2, 3, 5, 6], L365 = [0, 0, 1, 2, 3, 5, 9], L368 = [0, 0, 1, 2, 3, 6, 7], L369 = [0, 0, 1, 2, 3, 6, 8], L371 = [0, 0, 1, 2, 3, 6, 10], L373 = [0, 0, 1, 2, 3, 7, 9], L376 = [0, 0, 1, 2, 3, 8, 10], L378 = [0, 0, 1, 2, 3, 9, 10], L383 = [0, 0, 1, 2, 4, 5, 11], L385 = [0, 0, 1, 2, 4, 7, 11], L386 = [0, 0, 1, 2, 4, 9, 10], L388 = [0, 0, 1, 2, 5, 6, 8], L390 = [0, 0, 1, 2, 5, 6, 10], L391 = [0, 0, 1, 2, 6, 7, 10],
114
EMILIO A. LAURET
Table 5. (continued) n = 7 q 23
I {0}
indexes of I-isospectral families {102, 104}, {108, 110}, {114, 121}, {357, 358}, {361, 362}, {365, 369}, {368, 371, 373}, {376, 378, 386, 392}, {383, 385}, {388, 390}, {391, 396}, {1085, 1086, 1090}, {1087, 1089, 1092, 1093, 1094, 1100}, {1088, 1091}, {1095, 1105}, {1097, 1102, 1103, 1104, 1106, 1107, 1108}, {1099, 1117}, {1101, 1112, 1113, 1114, 1120}, {1109, 1110, 1111, 1118}, {1119, 1124}, {2863, 2864, 2865, 2867, 2869}, {2866, 2868, 2873, 2877, 2881}, {2870, 2872, 2874, 2876, 2880, 2883}, {2871, 2875, 2878, 2879, 2882, 2884, 2885, 2886, 2888, 2889}, {2887, 2891, 2892} {0, 1} {1092, 1094}, {1102, 1108}, {2875, 2885, 2886}, {2882, 2888}
L392 = [0, 0, 1, 2, 6, 8, 9], L396 = [0, 0, 1, 3, 4, 5, 7], L1085 = [0, 1, 2, 3, 4, 5, 8], L1086 = [0, 1, 2, 3, 4, 5, 9], L1087 = [0, 1, 2, 3, 4, 5, 10], L1088 = [0, 1, 2, 3, 4, 5, 11], L1089 = [0, 1, 2, 3, 4, 6, 7], L1090 = [0, 1, 2, 3, 4, 6, 8], L1091 = [0, 1, 2, 3, 4, 6, 9], L1092 = [0, 1, 2, 3, 4, 6, 10], L1093 = [0, 1, 2, 3, 4, 6, 11], L1094 = [0, 1, 2, 3, 4, 7, 8], L1095 = [0, 1, 2, 3, 4, 7, 9], L1097 = [0, 1, 2, 3, 4, 7, 11], L1099 = [0, 1, 2, 3, 4, 8, 10], L1100 = [0, 1, 2, 3, 4, 8, 11], L1101 = [0, 1, 2, 3, 4, 9, 10], L1102 = [0, 1, 2, 3, 4, 9, 11], L1103 = [0, 1, 2, 3, 5, 6, 7], L1104 = [0, 1, 2, 3, 5, 6, 8], L1105 = [0, 1, 2, 3, 5, 6, 9], L1106 = [0, 1, 2, 3, 5, 6, 10], L1107 = [0, 1, 2, 3, 5, 7, 8], L1108 = [0, 1, 2, 3, 5, 7, 10], L1109 = [0, 1, 2, 3, 5, 7, 11], L1110 = [0, 1, 2, 3, 5, 8, 9], L1111 = [0, 1, 2, 3, 5, 8, 11], L1112 = [0, 1, 2, 3, 5, 9, 10], L1113 = [0, 1, 2, 3, 5, 9, 11], L1114 = [0, 1, 2, 3, 6, 7, 9], L1117 = [0, 1, 2, 3, 6, 8, 11], L1118 = [0, 1, 2, 3, 6, 9, 10], L1119 = [0, 1, 2, 3, 8, 9, 10], L1120 = [0, 1, 2, 3, 8, 9, 11], L1124 = [0, 1, 2, 6, 8, 9, 10], L2863 = [1, 2, 3, 4, 5, 6, 7], L2864 = [1, 2, 3, 4, 5, 6, 8], L2865 = [1, 2, 3, 4, 5, 6, 9], L2866 = [1, 2, 3, 4, 5, 6, 10], L2867 = [1, 2, 3, 4, 5, 6, 11], L2868 = [1, 2, 3, 4, 5, 7, 8], L2869 = [1, 2, 3, 4, 5, 7, 9], L2870 = [1, 2, 3, 4, 5, 7, 10], L2871 = [1, 2, 3, 4, 5, 7, 11], L2872 = [1, 2, 3, 4, 5, 8, 9], L2873 = [1, 2, 3, 4, 5, 8, 10], L2874 = [1, 2, 3, 4, 5, 8, 11], L2875 = [1, 2, 3, 4, 5, 9, 11], L2876 = [1, 2, 3, 4, 5, 10, 11], L2877 = [1, 2, 3, 4, 6, 7, 8], L2878 = [1, 2, 3, 4, 6, 7, 9], L2879 = [1, 2, 3, 4, 6, 7, 11], L2880 = [1, 2, 3, 4, 6, 8, 9], L2881 = [1, 2, 3, 4, 6, 8, 11], L2882 = [1, 2, 3, 4, 6, 9, 10], L2883 = [1, 2, 3, 4, 6, 9, 11], L2884 = [1, 2, 3, 4, 7, 8, 10], L2885 = [1, 2, 3, 4, 7, 9, 10], L2886 = [1, 2, 3, 4, 7, 9, 11], L2887 = [1, 2, 3, 4, 8, 9, 10], L2888 = [1, 2, 3, 4, 8, 9, 11], L2889 = [1, 2, 3, 5, 6, 7, 8], L2891 = [1, 2, 3, 5, 7, 8, 11], L2892 = [1, 2, 3, 5, 8, 9, 11]. q = 24 : L41 = [0, 0, 0, 0, 1, 3, 5], L43 = [0, 0, 0, 0, 1, 3, 7], L213 = [0, 0, 0, 1, 2, 5, 7], L217 = [0, 0, 0, 1, 2, 5, 11], L254 = [0, 0, 0, 1, 3, 4, 5], L256 = [0, 0, 0, 1, 3, 4, 7], L262 = [0, 0, 0, 1, 3, 5, 6], L264 = [0, 0, 0, 1, 3, 5, 8], L267 = [0, 0, 0, 1, 3, 5, 12], L269 = [0, 0, 0, 1, 3, 6, 7], L275 = [0, 0, 0, 1, 3, 7, 8], L277 = [0, 0, 0, 1, 3, 7, 12], L846 = [0, 0, 1, 2, 2, 5, 7], L850 = [0, 0, 1, 2, 2, 5, 11], L899 = [0, 0, 1, 2, 3, 5, 10], L911 = [0, 0, 1, 2, 3, 7, 10], L938 = [0, 0, 1, 2, 4, 5, 7], L942 = [0, 0, 1, 2, 4, 5, 11], L969 = [0, 0, 1, 2, 5, 6, 7], L973 = [0, 0, 1, 2, 5, 6, 11], L975 = [0, 0, 1, 2, 5, 7, 8], L979 = [0, 0, 1, 2, 5, 7, 12], L983 = [0, 0, 1, 2, 5, 8, 11], L988 = [0, 0, 1, 2, 5, 11, 12], L1071 = [0, 0, 1, 3, 3, 5, 9], L1082 = [0, 0, 1, 3, 3, 7, 9], L1099 = [0, 0, 1, 3, 4, 4, 5], L1101 = [0, 0, 1, 3, 4, 4, 7], L1107 = [0, 0, 1, 3, 4, 5, 6], L1109 = [0, 0, 1, 3, 4, 5, 8], L1112 = [0, 0, 1, 3, 4, 5, 12], L1114 = [0, 0, 1, 3, 4, 6, 7], L1120 = [0, 0, 1, 3, 4, 7, 8], L1122 = [0, 0, 1, 3, 4, 7, 12], L1137 = [0, 0, 1, 3, 5, 6, 6], L1139 = [0, 0, 1, 3, 5, 6, 8], L1142 = [0, 0, 1, 3, 5, 6, 12], L1147 = [0, 0, 1, 3, 5, 8, 8], L1150 = [0, 0, 1, 3, 5, 8, 12], L1153 = [0, 0, 1, 3, 5, 12, 12], L1155 = [0, 0, 1, 3, 6, 6, 7], L1161 = [0, 0, 1, 3, 6, 7, 8], L1163 = [0, 0, 1, 3, 6, 7, 12], L1172 = [0, 0, 1, 3, 6, 9, 12], L1178 = [0, 0, 1, 3, 7, 8, 8], L1180 = [0, 0, 1, 3, 7, 8, 12], L1183 = [0, 0, 1, 3, 7, 12, 12], L1389 = [0, 0, 1, 7, 8, 8, 9], L1398 = [0, 0, 1, 8, 8, 8, 8], L1534 = [0, 0, 2, 3, 6, 9, 12], L1606 = [0, 0, 3, 4, 6, 9, 12], L1622 = [0, 0, 3, 6, 8, 9, 12], L1624 = [0, 0, 3, 8, 8, 8, 8], L2380 = [0, 1, 1, 3, 5, 5, 11], L2389 = [0, 1, 1, 3, 5, 7, 7], L2431 = [0, 1, 1, 3, 6, 9, 12], L2817 = [0, 1, 1, 7, 7, 9, 9], L2821 = [0, 1, 1, 7, 8, 8, 9], L2942 = [0, 1, 2, 2, 2, 5, 7], L2946 = [0, 1, 2, 2, 2, 5, 11], L3034 = [0, 1, 2, 2, 4, 5, 7], L3038 = [0, 1, 2, 2, 4, 5, 11], L3065 = [0, 1, 2, 2, 5, 6, 7], L3069 = [0, 1, 2, 2, 5, 6, 11], L3071 = [0, 1, 2, 2, 5, 7, 8], L3073 = [0, 1, 2, 2, 5, 7, 10], L3075 = [0, 1, 2, 2, 5, 7, 12], L3079 = [0, 1, 2, 2, 5, 8, 11], L3085 = [0, 1, 2, 2, 5, 10, 11], L3087 = [0, 1, 2, 2, 5, 11, 12], L3103 = [0, 1, 2, 2, 6, 8, 11], L3214 = [0, 1, 2, 3, 4, 5, 10], L3226 = [0, 1, 2, 3, 4, 7, 10], L3247 = [0, 1, 2, 3, 5, 6, 10],
APPENDIX
115
Table 5. (continued) n = 7 q I indexes of I-isospectral families 24 {0} {41, 43}, {213, 217}, {254, 256}, {262, 269}, {264, 275}, {267, 277}, {846, 850}, {899, 911}, {938, 942}, {969, 973}, {975, 983}, {979, 988}, {1071, 1082}, {1099, 1101}, {1107, 1114}, {1109, 1120}, {1112, 1122}, {1137, 1155}, {1139, 1161}, {1142, 1163}, {1147, 1178}, {1150, 1180}, {1153, 1183}, {2942, 2946}, {3034, 3038}, {3065, 3069}, {3071, 3079}, {3073, 3085}, {3075, 3087}, {3214, 3226}, {3247, 3277}, {3251, 3262}, {3257, 3296}, {3265, 3302}, {3344, 3348}, {3375, 3379}, {3381, 3389}, {3385, 3394}, {3456, 3460}, {3462, 3470}, {3466, 3475}, {3477, 3491}, {3481, 3496}, {3487, 3502}, {3685, 3696}, {3715, 3739}, {3723, 3756}, {3728, 3759}, {3792, 3794}, {3800, 3807}, {3802, 3813}, {3805, 3815}, {3830, 3848}, {3832, 3854}, {3835, 3856}, {3840, 3871}, {3843, 3873}, {3846, 3876}, {3906, 3942}, {3908, 3948}, {3911, 3950}, {3916, 3965}, {3919, 3967}, {3922, 3970}, {3931, 4000}, {3934, 4002}, {3937, 4005}, {3940, 4009}, {7644, 7684}, {8917, 8921}, {9009, 9013}, {9040, 9044}, {9046, 9054}, {9048, 9060}, {9050, 9062}, {9226, 9237}, {9239, 9278}, {9322, 9326}, {9353, 9357}, {9359, 9367}, {9361, 9373}, {9363, 9375}, {9438, 9442}, {9444, 9452}, {9446, 9458}, {9448, 9460}, {9462, 9478}, {9464, 9484}, {9466, 9486}, {9472, 9494}, {9474, 9496}, {9734, 9773}, {9822, 9834}, {9855, 9885}, {9859, 9870}, {9865, 9904}, {9873, 9910}, {9946, 10011}, {9950, 9961},
L3251 = [0, 1, 2, 3, 5, 7, 9], L3257 = [0, 1, 2, 3, 5, 8, 10], L3262 = [0, 1, 2, 3, 5, 9, 11], L3265 = [0, 1, 2, 3, 5, 10, 12], L3277 = [0, 1, 2, 3, 6, 7, 10], L3288 = [0, 1, 2, 3, 6, 9, 12], L3296 = [0, 1, 2, 3, 7, 8, 10], L3302 = [0, 1, 2, 3, 7, 10, 12], L3344 = [0, 1, 2, 4, 4, 5, 7], L3348 = [0, 1, 2, 4, 4, 5, 11], L3375 = [0, 1, 2, 4, 5, 6, 7], L3379 = [0, 1, 2, 4, 5, 6, 11], L3381 = [0, 1, 2, 4, 5, 7, 8], L3385 = [0, 1, 2, 4, 5, 7, 12], L3389 = [0, 1, 2, 4, 5, 8, 11], L3394 = [0, 1, 2, 4, 5, 11, 12], L3456 = [0, 1, 2, 5, 6, 6, 7], L3460 = [0, 1, 2, 5, 6, 6, 11], L3462 = [0, 1, 2, 5, 6, 7, 8], L3466 = [0, 1, 2, 5, 6, 7, 12], L3470 = [0, 1, 2, 5, 6, 8, 11], L3475 = [0, 1, 2, 5, 6, 11, 12], L3477 = [0, 1, 2, 5, 7, 8, 8], L3481 = [0, 1, 2, 5, 7, 8, 12], L3487 = [0, 1, 2, 5, 7, 12, 12], L3491 = [0, 1, 2, 5, 8, 8, 11], L3496 = [0, 1, 2, 5, 8, 11, 12], L3502 = [0, 1, 2, 5, 11, 12, 12], L3533 = [0, 1, 2, 6, 7, 9, 10], L3539 = [0, 1, 2, 6, 8, 8, 10], L3546 = [0, 1, 2, 6, 8, 10, 11], L3564 = [0, 1, 2, 7, 8, 8, 9], L3685 = [0, 1, 3, 3, 4, 5, 9], L3696 = [0, 1, 3, 3, 4, 7, 9], L3715 = [0, 1, 3, 3, 5, 6, 9], L3723 = [0, 1, 3, 3, 5, 8, 9], L3728 = [0, 1, 3, 3, 5, 9, 12], L3739 = [0, 1, 3, 3, 6, 7, 9], L3749 = [0, 1, 3, 3, 6, 9, 12], L3756 = [0, 1, 3, 3, 7, 8, 9], L3759 = [0, 1, 3, 3, 7, 9, 12], L3792 = [0, 1, 3, 4, 4, 4, 5], L3794 = [0, 1, 3, 4, 4, 4, 7], L3800 = [0, 1, 3, 4, 4, 5, 6], L3802 = [0, 1, 3, 4, 4, 5, 8], L3804 = [0, 1, 3, 4, 4, 5, 11], L3805 = [0, 1, 3, 4, 4, 5, 12], L3807 = [0, 1, 3, 4, 4, 6, 7], L3813 = [0, 1, 3, 4, 4, 7, 8], L3814 = [0, 1, 3, 4, 4, 7, 9], L3815 = [0, 1, 3, 4, 4, 7, 12], L3830 = [0, 1, 3, 4, 5, 6, 6], L3832 = [0, 1, 3, 4, 5, 6, 8], L3835 = [0, 1, 3, 4, 5, 6, 12], L3840 = [0, 1, 3, 4, 5, 8, 8], L3842 = [0, 1, 3, 4, 5, 8, 11], L3843 = [0, 1, 3, 4, 5, 8, 12], L3846 = [0, 1, 3, 4, 5, 12, 12], L3848 = [0, 1, 3, 4, 6, 6, 7], L3854 = [0, 1, 3, 4, 6, 7, 8], L3856 = [0, 1, 3, 4, 6, 7, 12], L3865 = [0, 1, 3, 4, 6, 9, 12], L3871 = [0, 1, 3, 4, 7, 8, 8], L3872 = [0, 1, 3, 4, 7, 8, 9], L3873 = [0, 1, 3, 4, 7, 8, 12], L3876 = [0, 1, 3, 4, 7, 12, 12], L3906 = [0, 1, 3, 5, 6, 6, 6], L3908 = [0, 1, 3, 5, 6, 6, 8], L3911 = [0, 1, 3, 5, 6, 6, 12], L3916 = [0, 1, 3, 5, 6, 8, 8], L3919 = [0, 1, 3, 5, 6, 8, 12], L3920 = [0, 1, 3, 5, 6, 9, 12], L3922 = [0, 1, 3, 5, 6, 12, 12], L3927 = [0, 1, 3, 5, 7, 9, 11], L3931 = [0, 1, 3, 5, 8, 8, 8], L3933 = [0, 1, 3, 5, 8, 8, 11], L3934 = [0, 1, 3, 5, 8, 8, 12], L3937 = [0, 1, 3, 5, 8, 12, 12], L3940 = [0, 1, 3, 5, 12, 12, 12] L3942 = [0, 1, 3, 6, 6, 6, 7], L3948 = [0, 1, 3, 6, 6, 7, 8], L3950 = [0, 1, 3, 6, 6, 7, 12], L3965 = [0, 1, 3, 6, 7, 8, 8], L3967 = [0, 1, 3, 6, 7, 8, 12], L3969 = [0, 1, 3, 6, 7, 9, 12], L3970 = [0, 1, 3, 6, 7, 12, 12], L3979 = [0, 1, 3, 6, 8, 9, 12], L3987 = [0, 1, 3, 6, 9, 9, 12], L3990 = [0, 1, 3, 6, 9, 10, 12], L3991 = [0, 1, 3, 6, 9, 11, 12], L3992 = [0, 1, 3, 6, 9, 12, 12], L4000 = [0, 1, 3, 7, 8, 8, 8], L4001 = [0, 1, 3, 7, 8, 8, 9], L4002 = [0, 1, 3, 7, 8, 8, 12],
116
EMILIO A. LAURET
Table 5. (continued) n = 7 q I indexes of I-isospectral families 24 {0} {9956, 10030}, {9964, 10036}, {9968, 9987}, {9975, 9996}, (cont.) {9982, 10070}, {9990, 10076}, {9999, 10084}, {10148, 10152}, {10179, 10183}, {10185, 10193}, {10189, 10198}, {10260, 10264}, {10266, 10274}, {10270, 10279}, {10281, 10295}, {10285, 10300}, {10291, 10306}, {10429, 10433}, {10435, 10443}, {10439, 10448}, {10450, 10464}, {10454, 10469}, {10460, 10475}, {10477, 10498}, {10481, 10503}, {10487, 10509}, {10494, 10516}, {10836, 10868}, {10913, 10924}, {10943, 10967}, {10951, 10984}, {10956, 10987}, {11022, 11069}, {11030, 11086}, {11035, 11089}, {11048, 11122}, {11053, 11125}, {11058, 11129}, {11186, 11188}, {11194, 11201}, {11196, 11207}, {11199, 11209}, {11224, 11242}, {11226, 11248}, {11229, 11250}, {11234, 11265}, {11237, 11267}, {11240, 11270}, {11300, 11336}, {11302, 11342}, {11305, 11344}, {11310, 11359}, {11313, 11361}, {11316, 11364}, {11325, 11394}, {11328, 11396}, {11331, 11399}, {11334, 11403}, {11455, 11516}, {11457, 11522}, {11460, 11524}, {11465, 11539}, {11468, 11541}, {11471, 11544}, {11480, 11574}, {11483, 11576}, {11486, 11579}, {11489, 11583}, {11502, 11635}, {11505, 11637}, {11508, 11640}, {11511, 11644}, {11514, 11649} L4005 = [0, 1, 3, 7, 8, 12, 12], L4009 = [0, 1, 3, 7, 12, 12, 12], L4134 = [0, 1, 4, 4, 7, 9, 12], L4140 = [0, 1, 4, 4, 8, 8, 12], L4237 = [0, 1, 4, 7, 8, 8, 9], L4378 = [0, 1, 6, 7, 8, 8, 9], L4433 = [0, 1, 7, 8, 8, 8, 9], L4435 = [0, 1, 7, 8, 8, 9, 9], L4436 = [0, 1, 7, 8, 8, 9, 12], L4611 = [0, 2, 2, 3, 6, 9, 12], L4735 = [0, 2, 3, 4, 6, 9, 12], L4742 = [0, 2, 3, 4, 8, 9, 10], L4765 = [0, 2, 3, 6, 8, 8, 10], L4768 = [0, 2, 3, 6, 8, 9, 12], L4771 = [0, 2, 3, 6, 9, 10, 12], L4772 = [0, 2, 3, 6, 9, 12, 12], L4850 = [0, 3, 3, 4, 6, 9, 12], L4869 = [0, 3, 3, 6, 8, 9, 12], L4901 = [0, 3, 4, 4, 6, 9, 12], L4905 = [0, 3, 4, 4, 8, 8, 12], L4917 = [0, 3, 4, 6, 6, 9, 12], L4922 = [0, 3, 4, 6, 8, 9, 12], L4924 = [0, 3, 4, 6, 9, 12, 12], L4942 = [0, 3, 6, 6, 8, 9, 12], L4947 = [0, 3, 6, 8, 8, 9, 12], L4949 = [0, 3, 6, 8, 9, 12, 12], L6203 = [1, 1, 1, 7, 7, 9, 9], L6722 = [1, 1, 2, 3, 5, 9, 10], L7043 = [1, 1, 2, 5, 7, 11, 11], L7118 = [1, 1, 2, 6, 7, 9, 10], L7164 = [1, 1, 2, 7, 7, 9, 9], L7525 = [1, 1, 3, 4, 5, 5, 11], L7534 = [1, 1, 3, 4, 5, 7, 7], L7639 = [1, 1, 3, 5, 5, 6, 11], L7644 = [1, 1, 3, 5, 5, 7, 11], L7648 = [1, 1, 3, 5, 5, 8, 11], L7652 = [1, 1, 3, 5, 5, 11, 12], L7661 = [1, 1, 3, 5, 6, 7, 7], L7682 = [1, 1, 3, 5, 7, 7, 8], L7684 = [1, 1, 3, 5, 7, 7, 11], L7685 = [1, 1, 3, 5, 7, 7, 12], L7693 = [1, 1, 3, 5, 7, 9, 11], L7818 = [1, 1, 3, 7, 7, 9, 9], L8034 = [1, 1, 4, 4, 7, 9, 12], L8245 = [1, 1, 4, 7, 7, 9, 9], L8446 = [1, 1, 5, 7, 7, 9, 9], L8478 = [1, 1, 5, 7, 10, 11, 11], L8626 = [1, 1, 6, 7, 7, 9, 9], L8723 = [1, 1, 7, 7, 8, 9, 9], L8726 = [1, 1, 7, 7, 9, 9, 9], L8727 = [1, 1, 7, 7, 9, 9, 12], L8917 = [1, 2, 2, 2, 2, 5, 7], L8921 = [1, 2, 2, 2, 2, 5, 11], L9009 = [1, 2, 2, 2, 4, 5, 7], L9013 = [1, 2, 2, 2, 4, 5, 11], L9040 = [1, 2, 2, 2, 5, 6, 7], L9044 = [1, 2, 2, 2, 5, 6, 11], L9046 = [1, 2, 2, 2, 5, 7, 8], L9048 = [1, 2, 2, 2, 5, 7, 10], L9050 = [1, 2, 2, 2, 5, 7, 12], L9054 = [1, 2, 2, 2, 5, 8, 11], L9060 = [1, 2, 2, 2, 5, 10, 11], L9062 = [1, 2, 2, 2, 5, 11, 12], L9226 = [1, 2, 2, 3, 5, 7, 9], L9237 = [1, 2, 2, 3, 5, 9, 11], L9239 = [1, 2, 2, 3, 5, 10, 10], L9278 = [1, 2, 2, 3, 7, 10, 10], L9322 = [1, 2, 2, 4, 4, 5, 7], L9326 = [1, 2, 2, 4, 4, 5, 11], L9353 = [1, 2, 2, 4, 5, 6, 7], L9357 = [1, 2, 2, 4, 5, 6, 11], L9359 = [1, 2, 2, 4, 5, 7, 8], L9361 = [1, 2, 2, 4, 5, 7, 10], L9363 = [1, 2, 2, 4, 5, 7, 12], L9367 = [1, 2, 2, 4, 5, 8, 11], L9373 = [1, 2, 2, 4, 5, 10, 11], L9375 = [1, 2, 2, 4, 5, 11, 12], L9438 = [1, 2, 2, 5, 6, 6, 7], L9442 = [1, 2, 2, 5, 6, 6, 11], L9444 = [1, 2, 2, 5, 6, 7, 8], L9446 = [1, 2, 2, 5, 6, 7, 10], L9448 = [1, 2, 2, 5, 6, 7, 12], L9452 = [1, 2, 2, 5, 6, 8, 11], L9458 = [1, 2, 2, 5, 6, 10, 11], L9460 = [1, 2, 2, 5, 6, 11, 12], L9462 = [1, 2, 2, 5, 7, 8, 8], L9464 = [1, 2, 2, 5, 7, 8, 10], L9466 = [1, 2, 2, 5, 7, 8, 12], L9472 = [1, 2, 2, 5, 7, 10, 12], L9474 = [1, 2, 2, 5, 7, 12, 12], L9478 = [1, 2, 2, 5, 8, 8, 11], L9484 = [1, 2, 2, 5, 8, 10, 11], L9486 = [1, 2, 2, 5, 8, 11, 12], L9494 = [1, 2, 2, 5, 10, 11, 12], L9496 = [1, 2, 2, 5, 11, 12, 12], L9517 = [1, 2, 2, 6, 6, 10, 10], L9527 = [1, 2, 2, 6, 7, 9, 10], L9734 = [1, 2, 3, 3, 5, 9, 10], L9773 = [1, 2, 3, 3, 7, 9, 10], L9822 = [1, 2, 3, 4, 4, 5, 10], L9834 = [1, 2, 3, 4, 4, 7, 10],
APPENDIX
117
Table 5. (continued) n = 7 q 24 (cont.)
I {0, 1} {2}
indexes of I-isospectral families {2380, 2389}, {7525, 7534}, {7639, 7661}, {7648, 7682}, {7652, 7685} {3804, 3814}, {3842, 3872}, {3927, 11321}, {11330, 11398}, {11494, 11498}, {11507, 11639} {4} {3103, 3546}, {6722, 9973}, {10363, 12096} {2, 5} {1389, 4433}, {1398, 1624}, {2817, 8723}, {2821, 4435}, {3533, 10582}, {3539, 4765}, {3564, 4378}, {3927, 11494}, {3933, 4001}, {4134, 11910}, {4140, 4905}, {4237, 4436}, {6203, 8726}, {7118, 10587}, {7164, 8626}, {7693, 11043}, {7818, 8446}, {8034, 11913}, {8245, 8727}, {9517, 12811}, {9527, 10547}, {9963, 10034}, {9974, 11476}, {10221, 13056}, {10230, 11878}, {10337, 10589}, {11239, 11269}, {11321, 11498}, {11766, 13372}, {11804, 11914} {4, 5} {7043, 8478} {6} {1172, 3992}, {1534, 4772}, {1606, 1622, 4924, 4949}, {2431, 3991}, {3288, 3990}, {3749, 3987}, {3865, 3979}, {3920, 3969}, {4611, 4771}, {4735, 4768}, {4850, 4869}, {4901, 4922, 4947} {2, 3, 6} {3927, 11498}, {4742, 13103}, {4917, 4942}, {11321, 11494}, {13062, 13099}, {13239, 13259}
L9855 = [1, 2, 3, 4, 5, 6, 10], L9859 = [1, 2, 3, 4, 5, 7, 9], L9865 = [1, 2, 3, 4, 5, 8, 10], L9870 = [1, 2, 3, 4, 5, 9, 11], L9873 = [1, 2, 3, 4, 5, 10, 12], L9885 = [1, 2, 3, 4, 6, 7, 10], L9904 = [1, 2, 3, 4, 7, 8, 10], L9910 = [1, 2, 3, 4, 7, 10, 12], L9946 = [1, 2, 3, 5, 6, 6, 10], L9950 = [1, 2, 3, 5, 6, 7, 9], L9956 = [1, 2, 3, 5, 6, 8, 10], L9961 = [1, 2, 3, 5, 6, 9, 11], L9963 = [1, 2, 3, 5, 6, 10, 11], L9964 = [1, 2, 3, 5, 6, 10, 12], L9968 = [1, 2, 3, 5, 7, 8, 9], L9973 = [1, 2, 3, 5, 7, 9, 10], L9974 = [1, 2, 3, 5, 7, 9, 11], L9975 = [1, 2, 3, 5, 7, 9, 12], L9982 = [1, 2, 3, 5, 8, 8, 10], L9987 = [1, 2, 3, 5, 8, 9, 11], L9990 = [1, 2, 3, 5, 8, 10, 12], L9996 = [1, 2, 3, 5, 9, 11, 12], L9999 = [1, 2, 3, 5, 10, 12, 12], L10011 = [1, 2, 3, 6, 6, 7, 10], L10030 = [1, 2, 3, 6, 7, 8, 10], L10034 = [1, 2, 3, 6, 7, 9, 10], L10036 = [1, 2, 3, 6, 7, 10, 12], L10070 = [1, 2, 3, 7, 8, 8, 10], L10076 = [1, 2, 3, 7, 8, 10, 12], L10084 = [1, 2, 3, 7, 10, 12, 12], L10148 = [1, 2, 4, 4, 4, 5, 7], L10152 = [1, 2, 4, 4, 4, 5, 11], L10179 = [1, 2, 4, 4, 5, 6, 7], L10183 = [1, 2, 4, 4, 5, 6, 11], L10185 = [1, 2, 4, 4, 5, 7, 8], L10189 = [1, 2, 4, 4, 5, 7, 12], L10193 = [1, 2, 4, 4, 5, 8, 11], L10198 = [1, 2, 4, 4, 5, 11, 12], L10221 = [1, 2, 4, 4, 6, 10, 12], L10230 = [1, 2, 4, 4, 7, 9, 12], L10260 = [1, 2, 4, 5, 6, 6, 7], L10264 = [1, 2, 4, 5, 6, 6, 11], L10266 = [1, 2, 4, 5, 6, 7, 8], L10270 = [1, 2, 4, 5, 6, 7, 12], L10274 = [1, 2, 4, 5, 6, 8, 11], L10279 = [1, 2, 4, 5, 6, 11, 12], L10281 = [1, 2, 4, 5, 7, 8, 8], L10285 = [1, 2, 4, 5, 7, 8, 12], L10291 = [1, 2, 4, 5, 7, 12, 12], L10295 = [1, 2, 4, 5, 8, 8, 11], L10300 = [1, 2, 4, 5, 8, 11, 12], L10306 = [1, 2, 4, 5, 11, 12, 12], L10337 = [1, 2, 4, 6, 7, 9, 10], L10363 = [1, 2, 4, 6, 10, 11, 12], L10429 = [1, 2, 5, 6, 6, 6, 7], L10433 = [1, 2, 5, 6, 6, 6, 11], L10435 = [1, 2, 5, 6, 6, 7, 8], L10439 = [1, 2, 5, 6, 6, 7, 12], L10443 = [1, 2, 5, 6, 6, 8, 11], L10448 = [1, 2, 5, 6, 6, 11, 12], L10450 = [1, 2, 5, 6, 7, 8, 8], L10454 = [1, 2, 5, 6, 7, 8, 12], L10460 = [1, 2, 5, 6, 7, 12, 12], L10464 = [1, 2, 5, 6, 8, 8, 11], L10469 = [1, 2, 5, 6, 8, 11, 12], L10475 = [1, 2, 5, 6, 11, 12, 12], L10477 = [1, 2, 5, 7, 8, 8, 8], L10481 = [1, 2, 5, 7, 8, 8, 12], L10487 = [1, 2, 5, 7, 8, 12, 12], L10494 = [1, 2, 5, 7, 12, 12, 12], L10498 = [1, 2, 5, 8, 8, 8, 11], L10503 = [1, 2, 5, 8, 8, 11, 12], L10509 = [1, 2, 5, 8, 11, 12, 12], L10516 = [1, 2, 5, 11, 12, 12, 12], L10547 = [1, 2, 6, 6, 7, 9, 10], L10582 = [1, 2, 6, 7, 8, 9, 10], L10587 = [1, 2, 6, 7, 9, 9, 10], L10589 = [1, 2, 6, 7, 9, 10, 12], L10836 = [1, 3, 3, 3, 5, 9, 9], L10868 = [1, 3, 3, 3, 7, 9, 9], L10913 = [1, 3, 3, 4, 4, 5, 9], L10924 = [1, 3, 3, 4, 4, 7, 9], L10943 = [1, 3, 3, 4, 5, 6, 9], L10951 = [1, 3, 3, 4, 5, 8, 9], L10956 = [1, 3, 3, 4, 5, 9, 12], L10967 = [1, 3, 3, 4, 6, 7, 9], L10984 = [1, 3, 3, 4, 7, 8, 9], L10987 = [1, 3, 3, 4, 7, 9, 12], L11022 = [1, 3, 3, 5, 6, 6, 9], L11030 = [1, 3, 3, 5, 6, 8, 9], L11035 = [1, 3, 3, 5, 6, 9, 12], L11043 = [1, 3, 3, 5, 7, 9, 11], L11048 = [1, 3, 3, 5, 8, 8, 9], L11053 = [1, 3, 3, 5, 8, 9, 12], L11058 = [1, 3, 3, 5, 9, 12, 12], L11069 = [1, 3, 3, 6, 6, 7, 9], L11086 = [1, 3, 3, 6, 7, 8, 9], L11089 = [1, 3, 3, 6, 7, 9, 12], L11122 = [1, 3, 3, 7, 8, 8, 9], L11125 = [1, 3, 3, 7, 8, 9, 12], L11129 = [1, 3, 3, 7, 9, 12, 12], L11186 =
118
EMILIO A. LAURET
Table 5. (continued) n = 7 q I indexes of I-isospectral families 25 {0} {133, 146}, {141, 142}, {143, 145, 157}, {499, 514}, {504, 508}, {509, 511}, {510, 513, 516, 524}, {515, 519, 521}, {523, 563}, {529, 534}, {538, 554}, {565, 567}, {1406, 1411}, {1456, 1463}, {1655, 1660}, {1657, 1658}, {1661, 1663, 1671}, {1662, 1666}, {1664, 1668}, {1665, 1688}, {1670, 1674, 1707}, {1673, 1706, 1711, 1712, 1717}, {1677, 1691}, {1687, 1715}, {1696, 1724}, {1699, 1722}, {1719, 1740, 1774}, {1747, 1783}, {1775, 1777}, {1779, 1782, 1815}, {4321, 4326}, {4339, 4347}, {4393, 4400}, {4455, 4465}, {4750, 4752}, {4751, 4753}, {4756, 4776}, {4762, 4792}, {4765, 4838}, {4768, 4769, 4771, 4772, 4773, 4774, 4775, 4778}, {4780, 4782, 4827, 4835}, {4785, 4789}, {4787, 4840}, {4795, 4830, 4831}, {4817, 4871}, {4819, 4826}, {4820, 4869}, {4829, 4834}, {4832, 4837, 4842, 4851}, {4839, 4845, 4848}, {4846, 4855}, {4850, 4948}, {4886, 4895}, {4899, 4938}, {4951, 4953} [1, 3, 4, 4, 4, 4, 5], L11188 = [1, 3, 4, 4, 4, 4, 7], L11194 = [1, 3, 4, 4, 4, 5, 6], L11196 = [1, 3, 4, 4, 4, 5, 8], L11199 = [1, 3, 4, 4, 4, 5, 12], L11201 = [1, 3, 4, 4, 4, 6, 7], L11207 = [1, 3, 4, 4, 4, 7, 8], L11209 = [1, 3, 4, 4, 4, 7, 12], L11224 = [1, 3, 4, 4, 5, 6, 6], L11226 = [1, 3, 4, 4, 5, 6, 8], L11229 = [1, 3, 4, 4, 5, 6, 12], L11234 = [1, 3, 4, 4, 5, 8, 8], L11237 = [1, 3, 4, 4, 5, 8, 12], L11239 = [1, 3, 4, 4, 5, 11, 12], L11240 = [1, 3, 4, 4, 5, 12, 12], L11242 = [1, 3, 4, 4, 6, 6, 7], L11248 = [1, 3, 4, 4, 6, 7, 8], L11250 = [1, 3, 4, 4, 6, 7, 12], L11265 = [1, 3, 4, 4, 7, 8, 8], L11267 = [1, 3, 4, 4, 7, 8, 12], L11269 = [1, 3, 4, 4, 7, 9, 12], L11270 = [1, 3, 4, 4, 7, 12, 12], L11300 = [1, 3, 4, 5, 6, 6, 6], L11302 = [1, 3, 4, 5, 6, 6, 8], L11305 = [1, 3, 4, 5, 6, 6, 12], L11310 = [1, 3, 4, 5, 6, 8, 8], L11313 = [1, 3, 4, 5, 6, 8, 12], L11316 = [1, 3, 4, 5, 6, 12, 12], L11321 = [1, 3, 4, 5, 7, 9, 11], L11325 = [1, 3, 4, 5, 8, 8, 8], L11328 = [1, 3, 4, 5, 8, 8, 12], L11330 = [1, 3, 4, 5, 8, 11, 12], L11331 = [1, 3, 4, 5, 8, 12, 12], L11334 = [1, 3, 4, 5, 12, 12, 12], L11336 = [1, 3, 4, 6, 6, 6, 7], L11342 = [1, 3, 4, 6, 6, 7, 8], L11344 = [1, 3, 4, 6, 6, 7, 12], L11359 = [1, 3, 4, 6, 7, 8, 8], L11361 = [1, 3, 4, 6, 7, 8, 12], L11364 = [1, 3, 4, 6, 7, 12, 12], L11394 = [1, 3, 4, 7, 8, 8, 8], L11396 = [1, 3, 4, 7, 8, 8, 12], L11398 = [1, 3, 4, 7, 8, 9, 12], L11399 = [1, 3, 4, 7, 8, 12, 12], L11403 = [1, 3, 4, 7, 12, 12, 12], L11455 = [1, 3, 5, 6, 6, 6, 6], L11457 = [1, 3, 5, 6, 6, 6, 8], L11460 = [1, 3, 5, 6, 6, 6, 12], L11465 = [1, 3, 5, 6, 6, 8, 8], L11468 = [1, 3, 5, 6, 6, 8, 12], L11471 = [1, 3, 5, 6, 6, 12, 12], L11476 = [1, 3, 5, 6, 7, 9, 11], L11480 = [1, 3, 5, 6, 8, 8, 8], L11483 = [1, 3, 5, 6, 8, 8, 12], L11486 = [1, 3, 5, 6, 8, 12, 12], L11489 = [1, 3, 5, 6, 12, 12, 12], L11494 = [1, 3, 5, 7, 8, 9, 11], L11498 = [1, 3, 5, 7, 9, 11, 12], L11502 = [1, 3, 5, 8, 8, 8, 8], L11505 = [1, 3, 5, 8, 8, 8, 12], L11507 = [1, 3, 5, 8, 8, 11, 12], L11508 = [1, 3, 5, 8, 8, 12, 12], L11511 = [1, 3, 5, 8, 12, 12, 12], L11514 = [1, 3, 5, 12, 12, 12, 12], L11516 = [1, 3, 6, 6, 6, 6, 7], L11522 = [1, 3, 6, 6, 6, 7, 8], L11524 = [1, 3, 6, 6, 6, 7, 12], L11539 = [1, 3, 6, 6, 7, 8, 8], L11541 = [1, 3, 6, 6, 7, 8, 12], L11544 = [1, 3, 6, 6, 7, 12, 12], L11574 = [1, 3, 6, 7, 8, 8, 8], L11576 = [1, 3, 6, 7, 8, 8, 12], L11579 = [1, 3, 6, 7, 8, 12, 12], L11583 = [1, 3, 6, 7, 12, 12, 12], L11635 = [1, 3, 7, 8, 8, 8, 8], L11637 = [1, 3, 7, 8, 8, 8, 12], L11639 = [1, 3, 7, 8, 8, 9, 12], L11640 = [1, 3, 7, 8, 8, 12, 12], L11644 = [1, 3, 7, 8, 12, 12, 12], L11649 = [1, 3, 7, 12, 12, 12, 12], L11766 = [1, 4, 4, 4, 4, 12, 12], L11804 = [1, 4, 4, 4, 7, 9, 12], L11878 = [1, 4, 4, 6, 7, 9, 12], L11910 = [1, 4, 4, 7, 8, 9, 12], L11913 = [1, 4, 4, 7, 9, 9, 12], L11914 = [1, 4, 4, 7, 9, 12, 12], L12096 = [1, 4, 6, 10, 10, 11, 12], L12811 = [2, 2, 3, 6, 6, 10, 10], L13056 = [2, 3, 4, 4, 6, 10, 12], L13062 = [2, 3, 4, 4, 8, 9, 10], L13099 = [2, 3, 4, 8, 8, 9, 10], L13103 = [2, 3, 4, 8, 9, 10, 12], L13239 = [3, 3, 3, 4, 9, 9, 9], L13259 = [3, 3, 3, 8, 9, 9, 9], L13372 = [3, 4, 4, 4, 4, 12, 12]. q = 25 : L133 = [0, 0, 0, 1, 2, 4, 11], L141 = [0, 0, 0, 1, 2, 6, 7], L142 = [0, 0, 0, 1, 2, 6, 8], L143 = [0, 0, 0, 1, 2, 6, 9], L145 = [0, 0, 0, 1, 2, 6, 11], L146 = [0, 0, 0, 1, 2, 7, 8], L157 = [0, 0, 0, 1, 3, 4, 9], L499 = [0, 0, 1, 2, 3, 4, 11], L504 = [0, 0, 1, 2, 3, 5, 8], L508 = [0, 0, 1, 2, 3, 5, 12], L509 = [0, 0, 1, 2, 3, 6, 7], L510 = [0, 0, 1, 2, 3, 6, 8], L511 = [0, 0, 1, 2, 3, 6, 9], L513 = [0, 0, 1, 2, 3, 6, 11], L514 = [0, 0, 1, 2, 3, 6, 12], L515 = [0, 0, 1, 2, 3, 7, 8], L516 = [0, 0, 1, 2, 3, 7, 9], L518 = [0, 0, 1, 2, 3, 7, 11], L519 = [0, 0, 1, 2, 3, 7, 12],
APPENDIX
119
Table 5. (continued) n = 7 q 25 (cont.)
I {0, 1}
indexes of I-isospectral families {518, 535}, {519, 521}, {1674, 1707}, {1712, 1717}, {4330, 4332}, {4340, 4348}, {4755, 4757}, {4763, 4828}, {4772, 4773, 4774, 4778}, {4782, 4835}, {4795, 4831}, {4844, 4896}, {4845, 4848} {0, 1, 2} {4772, 4778} {4} {605, 1841, 1846, 5018, 5023, 5028}, {615, 1856, 1859}, {1458, 4395, 4459}, {1526, 1838, 1858}, {1718, 4841, 4865}, {1772, 1827, 1857}, {2824, 4337, 4456}, {3533, 4777, 4783}, {3654, 4098, 4440, 4449, 4461} {0, 3, 4} {4841, 4865} {0, 1, 2, 3, 4} {4777, 4783}
L521 = [0, 0, 1, 2, 3, 8, 12], L523 = [0, 0, 1, 2, 3, 9, 11], L524 = [0, 0, 1, 2, 3, 9, 12], L529 = [0, 0, 1, 2, 4, 5, 7], L534 = [0, 0, 1, 2, 4, 5, 12], L535 = [0, 0, 1, 2, 4, 7, 8], L538 = [0, 0, 1, 2, 4, 9, 10], L554 = [0, 0, 1, 2, 5, 7, 8], L563 = [0, 0, 1, 2, 6, 7, 8], L565 = [0, 0, 1, 2, 6, 7, 11], L567 = [0, 0, 1, 2, 6, 8, 11], L605 = [0, 0, 1, 4, 6, 9, 11], L615 = [0, 0, 1, 5, 5, 10, 10], L1406 = [0, 1, 1, 4, 4, 6, 11], L1411 = [0, 1, 1, 4, 4, 9, 11], L1456 = [0, 1, 1, 4, 6, 9, 9], L1458 = [0, 1, 1, 4, 6, 9, 11], L1463 = [0, 1, 1, 4, 6, 11, 11], L1526 = [0, 1, 1, 5, 5, 10, 10], L1655 = [0, 1, 2, 3, 4, 5, 11], L1657 = [0, 1, 2, 3, 4, 6, 7], L1658 = [0, 1, 2, 3, 4, 6, 8], L1660 = [0, 1, 2, 3, 4, 6, 10], L1661 = [0, 1, 2, 3, 4, 6, 11], L1662 = [0, 1, 2, 3, 4, 6, 12], L1663 = [0, 1, 2, 3, 4, 7, 8], L1664 = [0, 1, 2, 3, 4, 7, 9], L1665 = [0, 1, 2, 3, 4, 7, 10], L1666 = [0, 1, 2, 3, 4, 7, 11], L1668 = [0, 1, 2, 3, 4, 8, 9], L1670 = [0, 1, 2, 3, 4, 8, 11], L1671 = [0, 1, 2, 3, 4, 8, 12], L1673 = [0, 1, 2, 3, 4, 9, 11], L1674 = [0, 1, 2, 3, 4, 9, 12], L1677 = [0, 1, 2, 3, 4, 10, 12], L1687 = [0, 1, 2, 3, 5, 6, 8], L1688 = [0, 1, 2, 3, 5, 6, 9], L1691 = [0, 1, 2, 3, 5, 6, 12], L1696 = [0, 1, 2, 3, 5, 7, 12], L1699 = [0, 1, 2, 3, 5, 8, 12], L1706 = [0, 1, 2, 3, 6, 7, 8], L1707 = [0, 1, 2, 3, 6, 7, 9], L1711 = [0, 1, 2, 3, 6, 8, 12], L1712 = [0, 1, 2, 3, 6, 9, 11], L1715 = [0, 1, 2, 3, 6, 10, 12], L1717 = [0, 1, 2, 3, 7, 8, 11], L1718 = [0, 1, 2, 3, 7, 8, 12], L1719 = [0, 1, 2, 3, 7, 9, 10], L1722 = [0, 1, 2, 3, 7, 10, 12], L1724 = [0, 1, 2, 3, 8, 10, 12], L1740 = [0, 1, 2, 4, 5, 7, 12], L1747 = [0, 1, 2, 4, 5, 10, 11], L1772 = [0, 1, 2, 5, 5, 10, 10], L1774 = [0, 1, 2, 5, 6, 7, 8], L1775 = [0, 1, 2, 5, 6, 7, 10], L1777 = [0, 1, 2, 5, 6, 8, 10], L1779 = [0, 1, 2, 5, 6, 9, 10], L1782 = [0, 1, 2, 5, 6, 10, 11], L1783 = [0, 1, 2, 5, 7, 8, 10], L1815 = [0, 1, 3, 4, 5, 9, 10], L1827 = [0, 1, 3, 5, 5, 10, 10], L1838 = [0, 1, 4, 5, 5, 10, 10], L1841 = [0, 1, 4, 5, 6, 9, 11], L1846 = [0, 1, 4, 6, 9, 10, 11], L1856 = [0, 1, 5, 5, 5, 10, 10], L1857 = [0, 1, 5, 5, 7, 10, 10], L1858 = [0, 1, 5, 5, 9, 10, 10], L1859 = [0, 1, 5, 5, 10, 10, 10], L2824 = [1, 1, 1, 4, 6, 9, 11], L3533 = [1, 1, 2, 3, 7, 8, 12], L3654 = [1, 1, 2, 4, 6, 9, 11], L4098 = [1, 1, 3, 4, 6, 9, 11], L4321 = [1, 1, 4, 4, 5, 6, 11], L4326 = [1, 1, 4, 4, 5, 9, 11], L4330 = [1, 1, 4, 4, 6, 6, 9], L4332 = [1, 1, 4, 4, 6, 6, 11], L4337 = [1, 1, 4, 4, 6, 9, 11], L4339 = [1, 1, 4, 4, 6, 10, 11], L4340 = [1, 1, 4, 4, 6, 11, 11], L4347 = [1, 1, 4, 4, 9, 10, 11], L4348 = [1, 1, 4, 4, 9, 11, 11], L4393 = [1, 1, 4, 5, 6, 9, 9], L4395 = [1, 1, 4, 5, 6, 9, 11], L4400 = [1, 1, 4, 5, 6, 11, 11], L4440 = [1, 1, 4, 6, 7, 9, 11], L4449 = [1, 1, 4, 6, 8, 9, 11], L4455 = [1, 1, 4, 6, 9, 9, 10], L4456 = [1, 1, 4, 6, 9, 9, 11], L4459 = [1, 1, 4, 6, 9, 10, 11], L4461 = [1, 1, 4, 6, 9, 11, 12], L4465 = [1, 1, 4, 6, 10, 11, 11], L4750 = [1, 2, 3, 4, 5, 6, 11], L4751 = [1, 2, 3, 4, 5, 6, 12], L4752 = [1, 2, 3, 4, 5, 7, 8], L4753 = [1, 2, 3, 4, 5, 7, 9], L4755 = [1, 2, 3, 4, 5, 7, 11], L4756 = [1, 2, 3, 4, 5, 7, 12], L4757 = [1, 2, 3, 4, 5, 8, 9], L4762 = [1, 2, 3, 4, 5, 9, 11], L4763 = [1, 2, 3, 4, 5, 9, 12], L4765 = [1, 2, 3, 4, 5, 10, 11], L4768 = [1, 2, 3, 4, 6, 7, 8], L4769 = [1, 2, 3, 4, 6, 7, 9], L4771 = [1, 2, 3, 4, 6, 7, 11], L4772 = [1, 2, 3, 4, 6, 7, 12], L4773 = [1, 2, 3, 4, 6, 8, 9], L4774 = [1, 2, 3, 4, 6, 8, 11], L4775 = [1, 2, 3, 4, 6, 8, 12], L4776 = [1, 2, 3, 4, 6, 9, 10], L4777 = [1, 2, 3, 4, 6, 9, 11], L4778 = [1, 2, 3, 4, 6, 9, 12], L4780 = [1, 2, 3, 4, 6, 10, 11], L4782 = [1, 2, 3, 4, 7, 8, 10], L4783 = [1, 2, 3, 4, 7, 8, 12], L4785 = [1, 2, 3, 4, 7, 9, 12], L4787 = [1, 2, 3, 4, 7, 10, 12], L4789 = [1, 2, 3, 4, 8, 9, 11], L4792 = [1, 2, 3, 4, 8, 10, 12], L4795 = [1, 2, 3, 4, 9, 10, 12], L4817 = [1, 2, 3, 5, 5, 7, 12], L4819 = [1, 2, 3, 5, 5, 8, 10], L4820 = [1, 2, 3, 5, 5, 8, 12], L4826 = [1, 2, 3, 5, 5, 10, 12], L4827 = [1, 2, 3, 5, 6, 7, 8], L4828 = [1, 2, 3, 5, 6, 7, 9], L4829 = [1, 2, 3, 5, 6, 7, 10], L4830 = [1, 2, 3, 5, 6, 7, 11], L4831 = [1, 2, 3, 5, 6, 8, 9], L4832 = [1, 2, 3, 5, 6, 8, 10], L4834 = [1, 2, 3, 5, 6, 9, 10],
120
EMILIO A. LAURET
Table 5. (continued) n = 7 q 26
I {0}
indexes of I-isospectral families {39, 42}, {40, 44}, {218, 244}, {233, 282}, {246, 247}, {249, 251, 252}, {254, 263}, {257, 269}, {360, 361}, {362, 364}, {902, 961}, {952, 965}, {994, 1045}, {1020, 1088}, {1044, 1077}, {1057, 1181}, {1093, 1095}, {1099, 1104, 1105}, {1108, 1129}, {1114, 1141}, {1352, 1353, 1354}, {1355, 1356}, {1357, 1359}, {3289, 3351}, {3298, 3317}, {3323, 3345}, {3334, 3372}, {3352, 3470}, {3359, 3501}, {3368, 3661}, {3400, 3575}, {3405, 3578}, {3485, 3500}, {3544, 3586}, {3557, 3589}, {3660, 3766}, {3716, 3857}, {3764, 3835}, {3786, 4052}, {3866, 3869}, {3875, 3885, 3886}, {3890, 3931}, {3900, 3951}, {4385, 4386, 4387}, {4388, 4389}, {4390, 4392}, {7493, 7495}, {7534, 7541}, {10497, 10500, 10504}, {10501, 10503}, {10509, 10527}, {10514, 10608}, {10516, 10525}, {10524, 10531}, {10532, 10534}, {10541, 10617}, {10550, 10614}, {10551, 10552, 10963}, {10553, 10694}, {10560, 10572}, {10571, 10610}, {10578, 10615}, {10579, 10623}, {10587, 10648}, {10609, 10620}, {10630, 10679}, {10637, 10680}, {10646, 10962}, {10661, 10739}, {10675, 10974}, {10696, 11049}, {10698, 10977}, {10712, 11050}, {10730, 10971}, {10731, 11365}, {10774, 11133}, {10793, 11195}, {10800, 11199}, {11005, 11048}, {11046, 11061}, {11134, 11215}, {11156, 11219}, {11362, 11547}, {11461, 11714}, {11544, 11677}, {11577, 12077}, {11659, 11661}, {11727, 11731}, {11738, 11754, 11755}, {11760, 11831}, {11775, 11861}, {12670, 12671, 12672}, {12673, 12674}, {12675, 12677} {0, 1} {251, 252}, {1104, 1105}, {1352, 1353}, {3885, 3886}, {4385, 4386}, {10517, 10536}, {10554, 10616}, {11754, 11755}, {12670, 12671}
L4835 = [1, 2, 3, 5, 6, 9, 11], L4837 = [1, 2, 3, 5, 6, 10, 11], L4838 = [1, 2, 3, 5, 6, 10, 12], L4839 = [1, 2, 3, 5, 7, 8, 10], L4840 = [1, 2, 3, 5, 7, 8, 11], L4841 = [1, 2, 3, 5, 7, 8, 12], L4842 = [1, 2, 3, 5, 7, 9, 10], L4844 = [1, 2, 3, 5, 7, 10, 11], L4845 = [1, 2, 3, 5, 7, 10, 12], L4846 = [1, 2, 3, 5, 8, 9, 12], L4848 = [1, 2, 3, 5, 8, 10, 12], L4850 = [1, 2, 3, 5, 9, 10, 11], L4851 = [1, 2, 3, 5, 9, 10, 12], L4855 = [1, 2, 3, 6, 7, 8, 10], L4865 = [1, 2, 3, 7, 8, 10, 12], L4869 = [1, 2, 3, 7, 10, 10, 12], L4871 = [1, 2, 3, 8, 10, 10, 12], L4886 = [1, 2, 4, 5, 5, 7, 10], L4895 = [1, 2, 4, 5, 5, 10, 12], L4896 = [1, 2, 4, 5, 7, 8, 10], L4899 = [1, 2, 4, 5, 9, 10, 10], L4938 = [1, 2, 5, 5, 7, 8, 10], L4948 = [1, 2, 5, 6, 7, 8, 10], L4951 = [1, 2, 5, 6, 7, 10, 11], L4953 = [1, 2, 5, 6, 8, 10, 11], L5018 = [1, 4, 5, 5, 6, 9, 11], L5023 = [1, 4, 5, 6, 9, 10, 11], L5028 = [1, 4, 6, 9, 10, 10, 11]. q = 26 : L39 = [0, 0, 0, 0, 1, 3, 5], L40 = [0, 0, 0, 0, 1, 3, 7], L42 = [0, 0, 0, 0, 1, 3, 9], L44 = [0, 0, 0, 0, 1, 3, 11], L218 = [0, 0, 0, 1, 2, 7, 8], L233 = [0, 0, 0, 1, 2, 10, 11], L244 = [0, 0, 0, 1, 3, 4, 8], L246 = [0, 0, 0, 1, 3, 4, 10], L247 = [0, 0, 0, 1, 3, 4, 12], L249 = [0, 0, 0, 1, 3, 5, 7], L251 = [0, 0, 0, 1, 3, 5, 9], L252 = [0, 0, 0, 1, 3, 5, 11], L254 = [0, 0, 0, 1, 3, 5, 13], L257 = [0, 0, 0, 1, 3, 7, 13], L263 = [0, 0, 0, 1, 3, 9, 13], L269 = [0, 0, 0, 1, 3, 11, 13], L282 = [0, 0, 0, 1, 4, 5, 8], L360 = [0, 0, 0, 2, 4, 6, 13], L361 = [0, 0, 0, 2, 4, 8, 13], L362 = [0, 0, 0, 2, 4, 10, 13], L364 = [0, 0, 0, 2, 6, 8, 13], L902 = [0, 0, 1, 2, 3, 9, 12], L952 = [0, 0, 1, 2, 4, 10, 11], L961 = [0, 0, 1, 2, 5, 6, 7], L965 = [0, 0, 1, 2, 5, 6, 12], L994 = [0, 0, 1, 2, 6, 7, 8], L1020 = [0, 0, 1, 2, 7, 8, 13], L1044 = [0, 0, 1, 2, 9, 10, 11], L1045 = [0, 0, 1, 2, 9, 10, 12], L1057 = [0, 0, 1, 2, 10, 11, 13], L1077 = [0, 0, 1, 3, 4, 5, 8], L1088 = [0, 0, 1, 3, 4, 8, 13], L1093 = [0, 0, 1, 3, 4, 10, 13], L1095 = [0, 0, 1, 3, 4, 12, 13], L1099 = [0, 0, 1, 3, 5, 7, 13], L1104 = [0, 0, 1, 3, 5, 9, 13], L1105 = [0, 0, 1, 3, 5, 11, 13], L1108 = [0, 0, 1, 3, 5, 13, 13], L1114 = [0, 0, 1, 3, 7, 13, 13], L1129 = [0, 0, 1, 3, 9, 13, 13], L1141 = [0, 0, 1, 3, 11, 13, 13], L1181 = [0, 0, 1, 4, 5, 8, 13], L1352 = [0, 0, 2, 4, 6, 8, 13], L1353 = [0, 0, 2, 4, 6, 10, 13], L1354 = [0, 0, 2, 4, 6, 12, 13], L1355 = [0, 0, 2, 4, 6, 13, 13], L1356 = [0, 0, 2, 4, 8, 13, 13], L1357 = [0, 0, 2, 4, 10, 13, 13], L1359 =
APPENDIX
121
[0, 0, 2, 6, 8, 13, 13], L3289 = [0, 1, 2, 3, 4, 7, 8], L3298 = [0, 1, 2, 3, 4, 8, 11], L3317 = [0, 1, 2, 3, 5, 6, 10], L3323 = [0, 1, 2, 3, 5, 7, 10], L3334 = [0, 1, 2, 3, 5, 9, 12], L3345 = [0, 1, 2, 3, 6, 7, 9], L3351 = [0, 1, 2, 3, 6, 8, 9], L3352 = [0, 1, 2, 3, 6, 8, 10], L3359 = [0, 1, 2, 3, 6, 10, 11], L3368 = [0, 1, 2, 3, 7, 8, 10], L3372 = [0, 1, 2, 3, 7, 9, 10], L3400 = [0, 1, 2, 3, 9, 10, 12], L3405 = [0, 1, 2, 3, 9, 12, 13], L3470 = [0, 1, 2, 4, 5, 6, 12], L3485 = [0, 1, 2, 4, 5, 10, 12], L3500 = [0, 1, 2, 4, 6, 7, 8], L3501 = [0, 1, 2, 4, 6, 7, 9], L3544 = [0, 1, 2, 4, 9, 10, 11], L3557 = [0, 1, 2, 4, 10, 11, 13], L3575 = [0, 1, 2, 5, 6, 7, 8], L3578 = [0, 1, 2, 5, 6, 7, 13], L3586 = [0, 1, 2, 5, 6, 11, 12], L3589 = [0, 1, 2, 5, 6, 12, 13], L3660 = [0, 1, 2, 6, 7, 8, 13], L3661 = [0, 1, 2, 6, 7, 9, 10], L3716 = [0, 1, 2, 7, 8, 13, 13], L3764 = [0, 1, 2, 9, 10, 11, 13], L3766 = [0, 1, 2, 9, 10, 12, 13], L3786 = [0, 1, 2, 10, 11, 13, 13], L3835 = [0, 1, 3, 4, 5, 8, 13], L3857 = [0, 1, 3, 4, 8, 13, 13], L3866 = [0, 1, 3, 4, 10, 13, 13], L3869 = [0, 1, 3, 4, 12, 13, 13], L3875 = [0, 1, 3, 5, 7, 13, 13], L3885 = [0, 1, 3, 5, 9, 13, 13], L3886 = [0, 1, 3, 5, 11, 13, 13], L3890 = [0, 1, 3, 5, 13, 13, 13], L3900 = [0, 1, 3, 7, 13, 13, 13], L3931 = [0, 1, 3, 9, 13, 13, 13], L3951 = [0, 1, 3, 11, 13, 13, 13], L4052 = [0, 1, 4, 5, 8, 13, 13], L4385 = [0, 2, 4, 6, 8, 13, 13], L4386 = [0, 2, 4, 6, 10, 13, 13], L4387 = [0, 2, 4, 6, 12, 13, 13], L4388 = [0, 2, 4, 6, 13, 13, 13], L4389 = [0, 2, 4, 8, 13, 13, 13], L4390 = [0, 2, 4, 10, 13, 13, 13], L4392 = [0, 2, 6, 8, 13, 13, 13], L7493 = [1, 1, 3, 3, 4, 9, 10], L7495 = [1, 1, 3, 3, 4, 9, 12], L7534 = [1, 1, 3, 3, 5, 11, 11], L7541 = [1, 1, 3, 3, 7, 7, 9], L10497 = [1, 2, 3, 4, 5, 6, 11], L10500 = [1, 2, 3, 4, 5, 7, 8], L10501 = [1, 2, 3, 4, 5, 7, 9], L10503 = [1, 2, 3, 4, 5, 7, 11], L10504 = [1, 2, 3, 4, 5, 7, 12], L10509 = [1, 2, 3, 4, 5, 8, 11], L10514 = [1, 2, 3, 4, 5, 9, 12], L10516 = [1, 2, 3, 4, 5, 10, 11], L10517 = [1, 2, 3, 4, 5, 10, 12], L10524 = [1, 2, 3, 4, 6, 7, 8], L10525 = [1, 2, 3, 4, 6, 7, 9], L10527 = [1, 2, 3, 4, 6, 7, 11], L10531 = [1, 2, 3, 4, 6, 8, 9], L10532 = [1, 2, 3, 4, 6, 8, 10], L10534 = [1, 2, 3, 4, 6, 8, 12], L10536 = [1, 2, 3, 4, 6, 9, 10], L10541 = [1, 2, 3, 4, 6, 10, 11], L10550 = [1, 2, 3, 4, 7, 8, 9], L10551 = [1, 2, 3, 4, 7, 8, 10], L10552 = [1, 2, 3, 4, 7, 8, 12], L10553 = [1, 2, 3, 4, 7, 8, 13], L10554 = [1, 2, 3, 4, 7, 9, 10], L10560 = [1, 2, 3, 4, 7, 10, 12], L10571 = [1, 2, 3, 4, 8, 9, 11], L10572 = [1, 2, 3, 4, 8, 9, 12], L10578 = [1, 2, 3, 4, 8, 11, 12], L10579 = [1, 2, 3, 4, 8, 11, 13], L10587 = [1, 2, 3, 4, 9, 11, 12], L10608 = [1, 2, 3, 5, 6, 7, 8], L10609 = [1, 2, 3, 5, 6, 7, 9], L10610 = [1, 2, 3, 5, 6, 7, 10], L10614 = [1, 2, 3, 5, 6, 8, 9], L10615 = [1, 2, 3, 5, 6, 8, 10], L10616 = [1, 2, 3, 5, 6, 8, 11], L10617 = [1, 2, 3, 5, 6, 8, 12], L10620 = [1, 2, 3, 5, 6, 9, 11], L10623 = [1, 2, 3, 5, 6, 10, 13], L10630 = [1, 2, 3, 5, 7, 8, 10], L10637 = [1, 2, 3, 5, 7, 10, 13], L10646 = [1, 2, 3, 5, 8, 9, 12], L10648 = [1, 2, 3, 5, 8, 10, 11], L10661 = [1, 2, 3, 5, 9, 12, 13], L10675 = [1, 2, 3, 6, 7, 8, 10], L10679 = [1, 2, 3, 6, 7, 9, 10], L10680 = [1, 2, 3, 6, 7, 9, 13], L10694 = [1, 2, 3, 6, 8, 9, 13], L10696 = [1, 2, 3, 6, 8, 10, 11], L10698 = [1, 2, 3, 6, 8, 10, 13], L10712 = [1, 2, 3, 6, 10, 11, 13], L10730 = [1, 2, 3, 7, 8, 10, 12], L10731 = [1, 2, 3, 7, 8, 10, 13], L10739 = [1, 2, 3, 7, 9, 10, 13], L10774 = [1, 2, 3, 8, 10, 11, 12], L10793 = [1, 2, 3, 9, 10, 12, 13], L10800 = [1, 2, 3, 9, 12, 13, 13], L10962 = [1, 2, 4, 5, 6, 7, 9], L10963 = [1, 2, 4, 5, 6, 7, 10], L10971 = [1, 2, 4, 5, 6, 9, 12], L10974 = [1, 2, 4, 5, 6, 11, 12], L10977 = [1, 2, 4, 5, 6, 12, 13], L11005 = [1, 2, 4, 5, 10, 12, 13], L11046 = [1, 2, 4, 6, 7, 8, 10], L11048 = [1, 2, 4, 6, 7, 8, 13], L11049 = [1, 2, 4, 6, 7, 9, 10], L11050 = [1, 2, 4, 6, 7, 9, 13], L11061 = [1, 2, 4, 6, 8, 10, 11], L11133 = [1, 2, 4, 9, 10, 11, 12], L11134 = [1, 2, 4, 9, 10, 11, 13], L11156 = [1, 2, 4, 10, 11, 13, 13] L11195 = [1, 2, 5, 6, 7, 8, 13], L11199 = [1, 2, 5, 6, 7, 13, 13], L11215 = [1, 2, 5, 6, 11, 12, 13], L11219 = [1, 2, 5, 6, 12, 13, 13], L11362 = [1, 2, 6, 7, 8, 13, 13], L11365 = [1, 2, 6, 7, 9, 10, 13], L11461 = [1, 2, 7, 8, 13, 13, 13], L11544 = [1, 2, 9, 10, 11, 13, 13], L11547 = [1, 2, 9, 10, 12, 13, 13], L11577 = [1, 2, 10, 11, 13, 13, 13], L11659 = [1, 3, 4, 4, 10, 10, 12], L11661 = [1, 3, 4, 4, 10, 12, 12], L11677 = [1, 3, 4, 5, 8, 13, 13], L11714 = [1, 3, 4, 8, 13, 13, 13], L11727 = [1, 3, 4, 10, 13, 13, 13], L11731 = [1, 3, 4, 12, 13, 13, 13], L11738 = [1, 3, 5, 7, 13, 13, 13], L11754 = [1, 3, 5, 9, 13, 13, 13], L11755 = [1, 3, 5, 11, 13, 13, 13], L11760 = [1, 3, 5, 13, 13, 13, 1 L11775 = [1, 3, 7, 13, 13, 13, 13], L11831 = [1, 3, 9, 13, 13, 13, 13], L11861 = [1, 3, 11, 13, 13, 13, 13], L12077 = [1, 4, 5, 8, 13, 13, 13], L12670 = [2, 4, 6, 8, 13, 13, 13], L12671 = [2, 4, 6, 10, 13, 13, 13], L12672 = [2, 4, 6, 12, 13, 13, 13], L12673 = [2, 4, 6, 13, 13, 13, 13], L12674 = [2, 4, 8, 13, 13, 13, 13], L12675 = [2, 4, 10, 13, 13, 13, 13], L12677 = [2, 6, 8, 13, 13, 13, 13]. q = 27 : L162 = [0, 0, 0, 1, 2, 4, 11], L165 = [0, 0, 0, 1, 2, 5, 7], L168 = [0, 0, 0, 1, 2, 5, 10], L177 = [0, 0, 0, 1, 2, 7, 8], L179 = [0, 0, 0, 1, 2, 7, 10], L687 = [0, 0, 1, 2, 3, 5, 10], L690 = [0, 0, 1, 2, 3, 5, 13], L704 = [0, 0, 1, 2, 3, 7, 13], L716 = [0, 0, 1, 2, 3, 10, 13], L720 = [0, 0, 1, 2, 4, 5, 7], L721 = [0, 0, 1, 2, 4, 5, 8], L723 = [0, 0, 1, 2, 4, 5, 10], L724 = [0, 0, 1, 2, 4, 5, 11], L727 = [0, 0, 1, 2, 4, 7, 8], L730 = [0, 0, 1, 2, 4, 7, 11], L732 = [0, 0, 1, 2, 4, 7, 13], L736 = [0, 0, 1, 2, 4, 9, 11], L738 = [0, 0, 1, 2, 4, 10, 11], L739 = [0, 0, 1, 2, 4, 10, 12],
122
EMILIO A. LAURET
Table 5. (continued) n = 7 q I indexes of I-isospectral families 27 {0} {162, 165, 168}, {177, 179}, {687, 690}, {704, 716}, {720, 721}, {723, 724, 727, 732}, {736, 749, 755}, {738, 748}, {739, 751}, {781, 786}, {2478, 2483}, {2480, 2481}, {2487, 2489}, {2492, 2507}, {2496, 2511}, {2504, 2563}, {2525, 2561}, {2528, 2531}, {2574, 2593}, {2575, 2699}, {2576, 2705}, {2583, 2710}, {2602, 2604, 2610}, {2603, 2608}, {2605, 2611, 2617}, {2613, 2614, 2620, 2625}, {2618, 2649}, {2633, 2661, 2669}, {2635, 2659}, {2636, 2663}, {2724, 2733}, {7662, 7800}, {7710, 7711}, {7718, 7723, 7744}, {7728, 7748}, {7731, 7746, 7761}, {7737, 7739}, {7738, 7743}, {7752, 7756}, {7754, 7805, 7807}, {7755, 7809, 7819}, {7758, 7764}, {7767, 7791}, {7776, 7810}, {7779, 7811}, {7788, 7910}, {7793, 8041}, {7813, 7821}, {7825, 7913}, {7833, 7899}, {7838, 7908}, {7843, 7846}, {7886, 7891}, {7923, 8128}, {7924, 8129}, {7930, 7954}, {7931, 8126}, {7932, 8136}, {7942, 8144}, {7967, 7971, 7981}, {7968, 7969, 7975}, {7970, 7979}, {7972, 7982, 7988}, {7984, 7985, 7993, 7998}, {7989, 8040}, {8010, 8057, 8067}, {8012, 8054}, {8013, 8059}, {8164, 8177} L748 = [0, 0, 1, 2, 5, 7, 8], L749 = [0, 0, 1, 2, 5, 7, 9], L750 = [0, 0, 1, 2, 5, 7, 11], L751 = [0, 0, 1, 2, 5, 7, 12], L755 = [0, 0, 1, 2, 5, 9, 10], L781 = [0, 0, 1, 2, 7, 8, 9], L786 = [0, 0, 1, 2, 7, 9, 10], L880 = [0, 0, 1, 3, 6, 9, 12], L937 = [0, 0, 1, 8, 9, 9, 10], L1909 = [0, 1, 1, 3, 6, 9, 12], L2363 = [0, 1, 1, 8, 8, 10, 10], L2478 = [0, 1, 2, 3, 4, 5, 12], L2480 = [0, 1, 2, 3, 4, 6, 7], L2481 = [0, 1, 2, 3, 4, 6, 8], L2483 = [0, 1, 2, 3, 4, 6, 10], L2487 = [0, 1, 2, 3, 4, 7, 8], L2489 = [0, 1, 2, 3, 4, 7, 10], L2492 = [0, 1, 2, 3, 4, 7, 13], L2496 = [0, 1, 2, 3, 4, 8, 12], L2504 = [0, 1, 2, 3, 4, 10, 12], L2507 = [0, 1, 2, 3, 4, 11, 13], L2511 = [0, 1, 2, 3, 5, 6, 8], L2525 = [0, 1, 2, 3, 5, 8, 12], L2528 = [0, 1, 2, 3, 5, 9, 10], L2531 = [0, 1, 2, 3, 5, 9, 13], L2557 = [0, 1, 2, 3, 6, 9, 12], L2561 = [0, 1, 2, 3, 6, 10, 13], L2563 = [0, 1, 2, 3, 6, 11, 13], L2574 = [0, 1, 2, 3, 7, 9, 13], L2575 = [0, 1, 2, 3, 7, 10, 12], L2576 = [0, 1, 2, 3, 7, 11, 12], L2583 = [0, 1, 2, 3, 8, 10, 12], L2593 = [0, 1, 2, 3, 9, 10, 13], L2602 = [0, 1, 2, 4, 5, 7, 8], L2603 = [0, 1, 2, 4, 5, 7, 9], L2604 = [0, 1, 2, 4, 5, 7, 10], L2605 = [0, 1, 2, 4, 5, 7, 11], L2607 = [0, 1, 2, 4, 5, 7, 13], L2608 = [0, 1, 2, 4, 5, 8, 9], L2609 = [0, 1, 2, 4, 5, 8, 10], L2610 = [0, 1, 2, 4, 5, 8, 11], L2611 = [0, 1, 2, 4, 5, 8, 13], L2613 = [0, 1, 2, 4, 5, 9, 10], L2614 = [0, 1, 2, 4, 5, 9, 11], L2617 = [0, 1, 2, 4, 5, 10, 13], L2618 = [0, 1, 2, 4, 5, 11, 12], L2620 = [0, 1, 2, 4, 7, 8, 9], L2623 = [0, 1, 2, 4, 7, 9, 11], L2625 = [0, 1, 2, 4, 7, 9, 13], L2633 = [0, 1, 2, 4, 9, 9, 11], L2635 = [0, 1, 2, 4, 9, 10, 11], L2636 = [0, 1, 2, 4, 9, 10, 12], L2649 = [0, 1, 2, 5, 6, 7, 8], L2659 = [0, 1, 2, 5, 7, 8, 9], L2661 = [0, 1, 2, 5, 7, 9, 9], L2662 = [0, 1, 2, 5, 7, 9, 11], L2663 = [0, 1, 2, 5, 7, 9, 12], L2669 = [0, 1, 2, 5, 9, 9, 10], L2699 = [0, 1, 2, 6, 7, 8, 12], L2705 = [0, 1, 2, 6, 7, 11, 12], L2710 = [0, 1, 2, 6, 8, 10, 12], L2724 = [0, 1, 2, 7, 8, 9, 9], L2728 = [0, 1, 2, 7, 8, 10, 11], L2733 = [0, 1, 2, 7, 9, 9, 10], L2846 = [0, 1, 3, 3, 6, 9, 12], L2886 = [0, 1, 3, 4, 6, 9, 12], L2901 = [0, 1, 3, 5, 6, 9, 12], L2913 = [0, 1, 3, 6, 6, 9, 12], L2917 = [0, 1, 3, 6, 8, 9, 12], L2918 = [0, 1, 3, 6, 8, 10, 12], L2921 = [0, 1, 3, 6, 9, 9, 12], L2922 = [0, 1, 3, 6, 9, 12, 12], L2935 = [0, 1, 3, 8, 9, 9, 10], L2990 = [0, 1, 6, 8, 9, 9, 10], L3002 = [0, 1, 8, 9, 9, 9, 10], L3004 = [0, 1, 8, 9, 9, 10, 12], L6577 = [1, 1, 3, 8, 8, 10, 10], L7331 = [1, 1, 6, 8, 8, 10, 10], L7438 = [1, 1, 8, 8, 9, 10, 10], L7441 = [1, 1, 8, 8, 10, 10, 12], L7662 = [1, 2, 3, 3, 6, 11, 13], L7710 = [1, 2, 3, 4, 5, 6, 10], L7711 = [1, 2, 3, 4, 5, 6, 11], L7718 = [1, 2, 3, 4, 5, 7, 12], L7719 = [1, 2, 3, 4, 5, 7, 13], L7721 = [1, 2, 3, 4, 5, 8, 10], L7723 = [1, 2, 3, 4, 5, 8, 12], L7728 = [1, 2, 3, 4, 5, 9, 12], L7731 = [1, 2, 3, 4, 5, 10, 12], L7732 = [1, 2, 3, 4, 5, 10, 13], L7734 = [1, 2, 3, 4, 5, 11, 13], L7737 = [1, 2, 3, 4, 6, 7, 8], L7738 = [1, 2, 3, 4, 6, 7, 9], L7739 = [1, 2, 3, 4, 6, 7, 10], L7743 = [1, 2, 3, 4, 6, 8, 9], L7744 = [1, 2, 3, 4, 6, 8, 11], L7746 = [1, 2, 3, 4, 6, 8, 13], L7748 = [1, 2, 3, 4, 6, 9, 10], L7752 = [1, 2, 3, 4, 6, 10, 11], L7754 = [1, 2, 3, 4, 6, 10, 13], L7755 = [1, 2, 3, 4, 6, 11, 12], L7756 = [1, 2, 3, 4, 6, 11, 13], L7758 = [1, 2, 3, 4, 7, 8, 9], L7759 = [1, 2, 3, 4, 7, 8, 10], L7760 = [1, 2, 3, 4, 7, 8, 11], L7761 = [1, 2, 3, 4, 7, 8, 12], L7764 = [1, 2, 3, 4, 7, 9, 10], L7767 = [1, 2, 3, 4, 7, 9, 13], L7776 = [1, 2, 3, 4, 8, 9, 12],
APPENDIX
123
Table 5. (continued) n = 7 q 27 (cont.)
I {0, 1}
indexes of I-isospectral families {723, 724}, {2613, 2614}, {7719, 7721}, {7732, 7759}, {7734, 7760}, {7780, 7832}, {7984, 7985} {0, 1, 2} {730, 750}, {2607, 2609}, {2611, 2617}, {2623, 2662}, {7968, 7969}, {7974, 7980}, {7982, 7988}, {7996, 8058} {2, 5} {937, 3002}, {2363, 7438}, {2728, 8168}, {2918, 8500}, {2935, 2990, 3004}, {6577, 7331, 7441}, {7922, 8127, 8172}, {8397, 8491, 8502} {5, 6} {880, 2921}, {1909, 2917}, {2557, 2886, 2901}, {2846, 2913, 2922}
L7779 = [1, 2, 3, 4, 8, 10, 12], L7780 = [1, 2, 3, 4, 8, 10, 13], L7788 = [1, 2, 3, 4, 9, 10, 12], L7791 = [1, 2, 3, 4, 9, 11, 13], L7793 = [1, 2, 3, 4, 10, 11, 12], L7800 = [1, 2, 3, 5, 6, 6, 8], L7805 = [1, 2, 3, 5, 6, 7, 8], L7807 = [1, 2, 3, 5, 6, 7, 10], L7809 = [1, 2, 3, 5, 6, 7, 12], L7810 = [1, 2, 3, 5, 6, 8, 9], L7811 = [1, 2, 3, 5, 6, 8, 10], L7813 = [1, 2, 3, 5, 6, 8, 13], L7819 = [1, 2, 3, 5, 6, 10, 12], L7821 = [1, 2, 3, 5, 6, 11, 13], L7825 = [1, 2, 3, 5, 7, 8, 12], L7832 = [1, 2, 3, 5, 7, 10, 11], L7833 = [1, 2, 3, 5, 7, 11, 12], L7838 = [1, 2, 3, 5, 8, 9, 12], L7843 = [1, 2, 3, 5, 9, 9, 10], L7846 = [1, 2, 3, 5, 9, 9, 13], L7886 = [1, 2, 3, 6, 7, 8, 12], L7891 = [1, 2, 3, 6, 7, 10, 12], L7899 = [1, 2, 3, 6, 8, 10, 13], L7908 = [1, 2, 3, 6, 9, 10, 13], L7910 = [1, 2, 3, 6, 9, 11, 13], L7913 = [1, 2, 3, 6, 10, 11, 13], L7922 = [1, 2, 3, 7, 8, 10, 11], L7923 = [1, 2, 3, 7, 8, 10, 12], L7924 = [1, 2, 3, 7, 8, 11, 12], L7930 = [1, 2, 3, 7, 9, 9, 13], L7931 = [1, 2, 3, 7, 9, 10, 12], L7932 = [1, 2, 3, 7, 9, 11, 12], L7942 = [1, 2, 3, 8, 9, 10, 12], L7954 = [1, 2, 3, 9, 9, 10, 13], L7967 = [1, 2, 4, 5, 7, 8, 9], L7968 = [1, 2, 4, 5, 7, 8, 10], L7969 = [1, 2, 4, 5, 7, 8, 11], L7970 = [1, 2, 4, 5, 7, 9, 9], L7971 = [1, 2, 4, 5, 7, 9, 10], L7972 = [1, 2, 4, 5, 7, 9, 11], L7974 = [1, 2, 4, 5, 7, 9, 13], L7975 = [1, 2, 4, 5, 7, 10, 13], L7979 = [1, 2, 4, 5, 8, 9, 9], L7980 = [1, 2, 4, 5, 8, 9, 10], L7981 = [1, 2, 4, 5, 8, 9, 11], L7982 = [1, 2, 4, 5, 8, 9, 13], L7984 = [1, 2, 4, 5, 9, 9, 10], L7985 = [1, 2, 4, 5, 9, 9, 11], L7988 = [1, 2, 4, 5, 9, 10, 13], L7989 = [1, 2, 4, 5, 9, 11, 12], L7993 = [1, 2, 4, 7, 8, 9, 9], L7996 = [1, 2, 4, 7, 9, 9, 11], L7998 = [1, 2, 4, 7, 9, 9, 13], L8010 = [1, 2, 4, 9, 9, 9, 11], L8012 = [1, 2, 4, 9, 9, 10, 11], L8013 = [1, 2, 4, 9, 9, 10, 12], L8040 = [1, 2, 5, 6, 7, 8, 9], L8041 = [1, 2, 5, 6, 7, 8, 12], L8054 = [1, 2, 5, 7, 8, 9, 9], L8057 = [1, 2, 5, 7, 9, 9, 9], L8058 = [1, 2, 5, 7, 9, 9, 11], L8059 = [1, 2, 5, 7, 9, 9, 12], L8067 = [1, 2, 5, 9, 9, 9, 10], L8126 = [1, 2, 6, 7, 8, 9, 12], L8127 = [1, 2, 6, 7, 8, 10, 11], L8128 = [1, 2, 6, 7, 8, 10, 12], L8129 = [1, 2, 6, 7, 8, 11, 12], L8136 = [1, 2, 6, 7, 9, 11, 12], L8144 = [1, 2, 6, 8, 9, 10, 12], L8164 = [1, 2, 7, 8, 9, 9, 9], L8168 = [1, 2, 7, 8, 9, 10, 11], L8172 = [1, 2, 7, 8, 10, 11, 12], L8177 = [1, 2, 7, 9, 9, 9, 10], L8397 = [1, 3, 3, 6, 8, 10, 12], L8491 = [1, 3, 6, 6, 8, 10, 12], L8500 = [1, 3, 6, 8, 9, 10, 12], L8502 = [1, 3, 6, 8, 10, 12, 12]. q = 28 : L43 = [0, 0, 0, 0, 1, 3, 5], L46 = [0, 0, 0, 0, 1, 3, 9], L299 = [0, 0, 0, 1, 3, 5, 7], L301 = [0, 0, 0, 1, 3, 5, 9], L302 = [0, 0, 0, 1, 3, 5, 11], L304 = [0, 0, 0, 1, 3, 5, 14], L307 = [0, 0, 0, 1, 3, 7, 9], L319 = [0, 0, 0, 1, 3, 9, 14], L1134 = [0, 0, 1, 2, 3, 5, 10], L1141 = [0, 0, 1, 2, 3, 6, 9], L1399 = [0, 0, 1, 3, 4, 5, 12], L1411 = [0, 0, 1, 3, 4, 8, 9], L1433 = [0, 0, 1, 3, 5, 7, 7], L1435 = [0, 0, 1, 3, 5, 7, 9], L1436 = [0, 0, 1, 3, 5, 7, 11], L1438 = [0, 0, 1, 3, 5, 7, 14], L1444 = [0, 0, 1, 3, 5, 9, 14], L1445 = [0, 0, 1, 3, 5, 11, 14], L1448 = [0, 0, 1, 3, 5, 14, 14], L1451 = [0, 0, 1, 3, 7, 7, 9], L1463 = [0, 0, 1, 3, 7, 9, 14], L1496 = [0, 0, 1, 3, 9, 14, 14], L1915 = [0, 0, 2, 4, 6, 7, 8], L1917 = [0, 0, 2, 4, 6, 7, 12], L3023 = [0, 1, 1, 3, 3, 9, 11], L3113 = [0, 1, 1, 3, 5, 5, 13], L4538 = [0, 1, 2, 3, 4, 9, 11], L4558 = [0, 1, 2, 3, 5, 6, 10], L4561 = [0, 1, 2, 3, 5, 6, 13], L4566 = [0, 1, 2, 3, 5, 7, 10], L4572 = [0, 1, 2, 3, 5, 8, 9], L4578 = [0, 1, 2, 3, 5, 9, 10], L4585 = [0, 1, 2, 3, 5, 10, 14], L4596 = [0, 1, 2, 3, 6, 7, 9], L4609 = [0, 1, 2, 3, 6, 9, 10], L4611 = [0, 1, 2, 3, 6, 9, 14], L4942 = [0, 1, 2, 5, 6, 8, 12], L5084 = [0, 1, 2, 6, 8, 9, 12], L5337 = [0, 1, 3, 4, 5, 7, 12], L5342 = [0, 1, 3, 4, 5, 8, 11], L5343 = [0, 1, 3, 4, 5, 8, 12], L5347 = [0, 1, 3, 4, 5, 9, 12], L5354 = [0, 1, 3, 4, 5, 12, 14], L5366 = [0, 1, 3, 4, 7, 8, 9], L5394 = [0, 1, 3, 4, 8, 9, 12], L5396 = [0, 1, 3, 4, 8, 9, 14], L5438 = [0, 1, 3, 5, 7, 7, 7], L5440 = [0, 1, 3, 5, 7, 7, 9], L5441 = [0, 1, 3, 5, 7, 7, 11], L5443 = [0, 1, 3, 5, 7, 7, 14], L5449 = [0, 1, 3, 5, 7, 9, 14], L5450 = [0, 1, 3, 5, 7, 11, 14], L5453 = [0, 1, 3, 5, 7, 14, 14], L5464 = [0, 1, 3, 5, 9, 14, 14], L5465 = [0, 1, 3, 5, 11, 14, 14], L5469 = [0, 1, 3, 5, 14, 14, 14], L5472 = [0, 1, 3, 7, 7, 7, 9], L5484 = [0, 1, 3, 7, 7, 9, 14], L5517 = [0, 1, 3, 7, 9, 14, 14], L5587 = [0, 1, 3, 9, 14, 14, 14], L6566 = [0, 2, 4, 6, 7, 7, 8], L6568 =
124
EMILIO A. LAURET
Table 5. (continued) n = 7 q 28
I {0}
indexes of I-isospectral families {43, 46}, {299, 307}, {304, 319}, {1134, 1141}, {1399, 1411}, {1433, 1451}, {1438, 1463}, {1448, 1496}, {1915, 1917}, {3023, 3113}, {4538, 4572}, {4558, 4609}, {4561, 4578}, {4566, 4596}, {4585, 4611}, {5337, 5366}, {5342, 5347}, {5354, 5396}, {5438, 5472}, {5443, 5484}, {5453, 5517}, {5469, 5587}, {6566, 6568}, {6573, 6575}, {10811, 10813}, {10832, 10834}, {10848, 10927}, {10868, 11246}, {10922, 11255}, {10923, 11263}, {11253, 11258}, {15331, 15338}, {15354, 15362}, {15394, 15509}, {15425, 16085}, {15436, 15483}, {15440, 15541}, {15474, 15595}, {15477, 15515}, {15487, 15493}, {15498, 15554}, {15503, 15582}, {15522, 15597}, {15538, 15546}, {15567, 15635}, {17360, 17418}, {17365, 17370}, {17366, 17446}, {17377, 17448}, {17384, 17386}, {17390, 17397}, {17392, 17509}, {17406, 17511}, {17581, 17637}, {17586, 17649}, {17596, 17682}, {17612, 17752}, {17634, 17879}, {19944, 19946}, {19951, 19953}, {19961, 19963} {0, 1} {301, 302}, {1435, 1436}, {1444, 1445}, {4942, 5084}, {5440, 5441}, {5449, 5450}, {5464, 5465}, {15423, 16088}, {15486, 15490}, {16485, 16779}, {16508, 16827}, {17385, 17388}, {17583, 17584}, {17592, 17593}, {17607, 17608}, {17628, 17629} {0, 6} {5343, 5394}, {15492, 15633}
[0, 2, 4, 6, 7, 7, 12], L6573 = [0, 2, 4, 6, 7, 8, 14], L6575 = [0, 2, 4, 6, 7, 12, 14], L10811 = [1, 1, 3, 3, 5, 5, 11], L10813 = [1, 1, 3, 3, 5, 5, 13], L10832 = [1, 1, 3, 3, 5, 9, 11], L10834 = [1, 1, 3, 3, 5, 9, 13], L10848 = [1, 1, 3, 3, 5, 13, 13], L10868 = [1, 1, 3, 3, 7, 9, 11], L10922 = [1, 1, 3, 3, 9, 11, 13], L10923 = [1, 1, 3, 3, 9, 11, 14], L10927 = [1, 1, 3, 3, 9, 13, 13], L11246 = [1, 1, 3, 5, 5, 7, 13], L11253 = [1, 1, 3, 5, 5, 9, 11], L11255 = [1, 1, 3, 5, 5, 9, 13], L11258 = [1, 1, 3, 5, 5, 11, 13], L11263 = [1, 1, 3, 5, 5, 13, 14], L15331 = [1, 2, 3, 4, 5, 9, 13], L15338 = [1, 2, 3, 4, 5, 11, 13], L15354 = [1, 2, 3, 4, 6, 8, 9], L15362 = [1, 2, 3, 4, 6, 9, 12], L15394 = [1, 2, 3, 4, 7, 9, 11], L15423 = [1, 2, 3, 4, 8, 10, 11], L15425 = [1, 2, 3, 4, 8, 10, 13], L15436 = [1, 2, 3, 4, 9, 10, 12], L15440 = [1, 2, 3, 4, 9, 11, 14], L15474 = [1, 2, 3, 5, 6, 7, 10], L15477 = [1, 2, 3, 5, 6, 7, 13], L15483 = [1, 2, 3, 5, 6, 8, 12], L15486 = [1, 2, 3, 5, 6, 9, 10], L15487 = [1, 2, 3, 5, 6, 9, 11], L15490 = [1, 2, 3, 5, 6, 10, 11], L15492 = [1, 2, 3, 5, 6, 10, 14], L15493 = [1, 2, 3, 5, 6, 11, 13], L15498 = [1, 2, 3, 5, 6, 13, 14], L15503 = [1, 2, 3, 5, 7, 7, 10], L15509 = [1, 2, 3, 5, 7, 8, 9], L15515 = [1, 2, 3, 5, 7, 9, 10], L15522 = [1, 2, 3, 5, 7, 10, 14], L15538 = [1, 2, 3, 5, 8, 9, 11], L15541 = [1, 2, 3, 5, 8, 9, 14], L15546 = [1, 2, 3, 5, 8, 11, 13], L15554 = [1, 2, 3, 5, 9, 10, 14], L15567 = [1, 2, 3, 5, 10, 14, 14], L15582 = [1, 2, 3, 6, 7, 7, 9], L15595 = [1, 2, 3, 6, 7, 9, 10], L15597 = [1, 2, 3, 6, 7, 9, 14], L15633 = [1, 2, 3, 6, 9, 10, 14], L15635 = [1, 2, 3, 6, 9, 14, 14], L16085 = [1, 2, 4, 5, 6, 8, 9], L16088 = [1, 2, 4, 5, 6, 8, 13], L16485 = [1, 2, 5, 6, 7, 8, 12], L16508 = [1, 2, 5, 6, 8, 12, 14], L16779 = [1, 2, 6, 7, 8, 9, 12], L16827 = [1, 2, 6, 8, 9, 12, 14], L17360 = [1, 3, 4, 5, 7, 7, 12], L17365 = [1, 3, 4, 5, 7, 8, 11], L17366 = [1, 3, 4, 5, 7, 8, 12], L17370 = [1, 3, 4, 5, 7, 9, 12], L17377 = [1, 3, 4, 5, 7, 12, 14], L17384 = [1, 3, 4, 5, 8, 9, 11], L17385 = [1, 3, 4, 5, 8, 9, 12], L17386 = [1, 3, 4, 5, 8, 9, 13], L17388 = [1, 3, 4, 5, 8, 11, 12], L17390 = [1, 3, 4, 5, 8, 11, 14], L17392 = [1, 3, 4, 5, 8, 12, 14], L17397 = [1, 3, 4, 5, 9, 12, 14], L17406 = [1, 3, 4, 5, 12, 14, 14], L17418 = [1, 3, 4, 7, 7, 8, 9], L17446 = [1, 3, 4, 7, 8, 9, 12], L17448 = [1, 3, 4, 7, 8, 9, 14], L17509 = [1, 3, 4, 8, 9, 12, 14], L17511 = [1, 3, 4, 8, 9, 14, 14], L17581 = [1, 3, 5, 7, 7, 7, 7], L17583 = [1, 3, 5, 7, 7, 7, 9], L17584 = [1, 3, 5, 7, 7, 7, 11], L17586 = [1, 3, 5, 7, 7, 7, 14], L17592 = [1, 3, 5, 7, 7, 9, 14], L17593 = [1, 3, 5, 7, 7, 11, 14], L17596 = [1, 3, 5, 7, 7, 14, 14], L17607 = [1, 3, 5, 7, 9, 14, 14], L17608 = [1, 3, 5, 7, 11, 14, 14], L17612 = [1, 3, 5, 7, 14, 14, 14], L17628 = [1, 3, 5, 9, 14, 14, 14], L17629 = [1, 3, 5, 11, 14, 14, 14], L17634 = [1, 3, 5, 14, 14, 14, 14], L17637 = [1, 3, 7, 7, 7, 7, 9], L17649 = [1, 3, 7, 7, 7, 9, 14], L17682 = [1, 3, 7, 7, 9, 14, 14], L17752 = [1, 3, 7, 9, 14, 14, 14], L17879 = [1, 3, 9, 14, 14, 14, 14], L19944 =
APPENDIX
125
Table 5. (continued) n = 7 q I indexes of I-isospectral families 29 {0} {164, 171}, {215, 216}, {728, 750, 755}, {799, 815}, {2582, 2589}, {2591, 2608, 2611}, {2593, 2630}, {2597, 2644}, {2601, 2637}, {2610, 2638}, {2617, 2628}, {2622, 2635}, {2632, 2639, 2645}, {2650, 2698}, {2672, 2712}, {2677, 2692}, {2678, 2735}, {2713, 2745}, {2723, 2726}, {2725, 2755}, {2727, 2740}, {2728, 2772}, {2767, 2769}, {8080, 8081}, {8087, 8106}, {8090, 8112}, {8094, 8118}, {8097, 8101, 8123, 8131}, {8100, 8163, 8182}, {8102, 8129}, {8107, 8124}, {8109, 8113}, {8110, 8115, 8116, 8133}, {8120, 8141, 8184}, {8128, 8183, 8189, 8190, 8192}, {8132, 8137}, {8139, 8166, 8174}, {8142, 8197}, {8144, 8159}, {8146, 8160, 8234}, {8147, 8208}, {8150, 8188}, {8152, 8156, 8194, 8222}, {8154, 8248}, {8155, 8195}, {8161, 8187}, {8172, 8201, 8227, 8240}, {8179, 8180}, {8198, 8239, 8256}, {8206, 8217}, {8209, 8270}, {8210, 8223}, {8211, 8274, 8299, 8301, 8306}, {8214, 8254}, {8218, 8225}, {8224, 8245}, {8229, 8305}, {8235, 8241}, {8243, 8250}, {8260, 8279}, {8261, 8287}, {8268, 8300}, {8275, 8298}, {8277, 8303, 8311} [2, 4, 6, 7, 7, 7, 8], L19946 = [2, 4, 6, 7, 7, 7, 12], L19951 = [2, 4, 6, 7, 7, 8, 14], L19953 = [2, 4, 6, 7, 7, 12, 14], L19961 = [2, 4, 6, 7, 8, 14, 14], L19963 = [2, 4, 6, 7, 12, 14, 14]. q = 29 : L164 = [0, 0, 0, 1, 2, 4, 11], L171 = [0, 0, 0, 1, 2, 5, 10], L215 = [0, 0, 0, 1, 4, 5, 7], L216 = [0, 0, 0, 1, 4, 5, 13], L728 = [0, 0, 1, 2, 3, 8, 13], L750 = [0, 0, 1, 2, 4, 7, 8], L755 = [0, 0, 1, 2, 4, 7, 14], L799 = [0, 0, 1, 2, 7, 8, 9], L815 = [0, 0, 1, 2, 10, 11, 12], L2582 = [0, 1, 2, 3, 4, 7, 13], L2589 = [0, 1, 2, 3, 4, 8, 14], L2591 = [0, 1, 2, 3, 4, 9, 11], L2593 = [0, 1, 2, 3, 4, 9, 13], L2597 = [0, 1, 2, 3, 4, 10, 13], L2601 = [0, 1, 2, 3, 4, 11, 14], L2608 = [0, 1, 2, 3, 5, 6, 11], L2610 = [0, 1, 2, 3, 5, 6, 13], L2611 = [0, 1, 2, 3, 5, 6, 14], L2617 = [0, 1, 2, 3, 5, 7, 13], L2622 = [0, 1, 2, 3, 5, 8, 12], L2628 = [0, 1, 2, 3, 5, 9, 14], L2630 = [0, 1, 2, 3, 5, 10, 12], L2632 = [0, 1, 2, 3, 5, 10, 14], L2635 = [0, 1, 2, 3, 5, 11, 14], L2637 = [0, 1, 2, 3, 5, 12, 14], L2638 = [0, 1, 2, 3, 6, 7, 8], L2639 = [0, 1, 2, 3, 6, 7, 9], L2644 = [0, 1, 2, 3, 6, 7, 14], L2645 = [0, 1, 2, 3, 6, 8, 9], L2650 = [0, 1, 2, 3, 6, 8, 14], L2672 = [0, 1, 2, 3, 7, 11, 13], L2677 = [0, 1, 2, 3, 8, 9, 12], L2678 = [0, 1, 2, 3, 8, 9, 13], L2692 = [0, 1, 2, 3, 10, 11, 12], L2698 = [0, 1, 2, 4, 5, 7, 9], L2712 = [0, 1, 2, 4, 5, 11, 12], L2713 = [0, 1, 2, 4, 5, 11, 13], L2723 = [0, 1, 2, 4, 7, 12, 13], L2725 = [0, 1, 2, 4, 10, 11, 12], L2726 = [0, 1, 2, 4, 10, 11, 13], L2727 = [0, 1, 2, 4, 10, 12, 13], L2728 = [0, 1, 2, 4, 11, 12, 13], L2735 = [0, 1, 2, 5, 6, 8, 10], L2740 = [0, 1, 2, 5, 6, 11, 13], L2745 = [0, 1, 2, 5, 7, 10, 11], L2755 = [0, 1, 2, 6, 7, 8, 11], L2767 = [0, 1, 2, 7, 8, 12, 13], L2769 = [0, 1, 2, 7, 10, 12, 13], L2772 = [0, 1, 2, 10, 11, 12, 13], L8080 = [1, 2, 3, 4, 5, 7, 11], L8081 = [1, 2, 3, 4, 5, 7, 12], L8087 = [1, 2, 3, 4, 5, 8, 12], L8090 = [1, 2, 3, 4, 5, 9, 10], L8094 = [1, 2, 3, 4, 5, 9, 14], L8097 = [1, 2, 3, 4, 5, 10, 13], L8100 = [1, 2, 3, 4, 5, 11, 13], L8101 = [1, 2, 3, 4, 5, 11, 14], L8102 = [1, 2, 3, 4, 5, 12, 13], L8106 = [1, 2, 3, 4, 6, 7, 9], L8107 = [1, 2, 3, 4, 6, 7, 10], L8109 = [1, 2, 3, 4, 6, 7, 12], L8110 = [1, 2, 3, 4, 6, 7, 13], L8112 = [1, 2, 3, 4, 6, 8, 9], L8113 = [1, 2, 3, 4, 6, 8, 11], L8115 = [1, 2, 3, 4, 6, 8, 13], L8116 = [1, 2, 3, 4, 6, 8, 14], L8118 = [1, 2, 3, 4, 6, 9, 11], L8120 = [1, 2, 3, 4, 6, 9, 13], L8123 = [1, 2, 3, 4, 6, 10, 12], L8124 = [1, 2, 3, 4, 6, 10, 13], L8128 = [1, 2, 3, 4, 6, 11, 14], L8129 = [1, 2, 3, 4, 6, 12, 13], L8131 = [1, 2, 3, 4, 7, 8, 9], L8132 = [1, 2, 3, 4, 7, 8, 10], L8133 = [1, 2, 3, 4, 7, 8, 11], L8137 = [1, 2, 3, 4, 7, 9, 10], L8139 = [1, 2, 3, 4, 7, 9, 13], L8141 = [1, 2, 3, 4, 7, 10, 11], L8142 = [1, 2, 3, 4, 7, 10, 12], L8144 = [1, 2, 3, 4, 7, 10, 14], L8146 = [1, 2, 3, 4, 7, 11, 13], L8147 = [1, 2, 3, 4, 7, 12, 13], L8150 = [1, 2, 3, 4, 8, 9, 11], L8152 = [1, 2, 3, 4, 8, 9, 13], L8154 = [1, 2, 3, 4, 8, 10, 11], L8155 = [1, 2, 3, 4, 8, 10, 12], L8156 = [1, 2, 3, 4, 8, 10, 13], L8159 = [1, 2, 3, 4, 8, 11, 13], L8160 = [1, 2, 3, 4, 8, 11, 14], L8161 = [1, 2, 3, 4, 8, 12, 14], L8163 = [1, 2, 3, 4, 9, 10, 13], L8166 = [1, 2, 3, 4, 9, 11, 13], L8172 = [1, 2, 3, 4, 10, 11, 14], L8174 = [1, 2, 3, 4, 10, 12, 14], L8179 = [1, 2, 3, 5, 6, 7, 10], L8180 = [1, 2, 3, 5, 6, 7, 11], L8182 = [1, 2, 3, 5, 6, 7, 13], L8183 = [1, 2, 3, 5, 6, 7, 14], L8184 = [1, 2, 3, 5, 6, 8, 9], L8187 = [1, 2, 3, 5, 6, 8, 12], L8188 = [1, 2, 3, 5, 6, 8, 14], L8189 = [1, 2, 3, 5, 6, 9, 10], L8190 = [1, 2, 3, 5, 6, 9, 11], L8192 = [1, 2, 3, 5, 6, 9, 14],
126
EMILIO A. LAURET
Table 5. (continued) n = 7 q I indexes of I-isospectral families 30 {0} {55, 59}, {423, 427}, {444, 463}, {448, 469}, {800, 815}, {805, 837}, {1814, 1820}, {1817, 1819}, {2140, 2155}, {2241, 2245}, {2262, 2281}, {2266, 2287}, {2311, 2334}, {2354, 2413}, {2358, 2419}, {2366, 2431}, {3413, 3463}, {3520, 3560}, {3532, 3586}, {3535, 3588}, {3547, 3644}, {3550, 3646}, {7672, 8282}, {7780, 7786}, {7783, 7785}, {7873, 7888}, {7874, 7896}, {7878, 7898}, {7885, 7887}, {7892, 7897}, {8886, 8901}, {8978, 9030}, {8982, 9036}, {9326, 9330}, {9347, 9366}, {9351, 9372}, {9396, 9419}, {9439, 9498}, {9443, 9504}, {9451, 9516}, {9594, 9659}, {9602, 9671}, {9712, 9854}, {9716, 9860}, {9724, 9872}, {9736, 9892}, {12669, 12778}, {12718, 12856}, {12721, 12858}, {12960, 13051}, {12972, 13077}, {12975, 13079}, {12991, 13128}, {13001, 13144}, {13004, 13146}, {13008, 13149}, {13024, 13241}, {13034, 13269}, {13037, 13271}, {13041, 13274}, {20406, 20498}, {27061, 27073}, {27066, 27114}, {27070, 27072}, {27083, 27113}, {27419, 29191},
L8194 = [1, 2, 3, 5, 6, 10, 12], L8195 = [1, 2, 3, 5, 6, 10, 14], L8197 = [1, 2, 3, 5, 6, 11, 14], L8198 = [1, 2, 3, 5, 6, 12, 13], L8201 = [1, 2, 3, 5, 7, 8, 10], L8206 = [1, 2, 3, 5, 7, 9, 14], L8208 = [1, 2, 3, 5, 7, 10, 13], L8209 = [1, 2, 3, 5, 7, 10, 14], L8210 = [1, 2, 3, 5, 7, 11, 12], L8211 = [1, 2, 3, 5, 7, 11, 13], L8214 = [1, 2, 3, 5, 8, 9, 12], L8217 = [1, 2, 3, 5, 8, 10, 12], L8218 = [1, 2, 3, 5, 8, 10, 14], L8222 = [1, 2, 3, 5, 9, 10, 12], L8223 = [1, 2, 3, 5, 9, 10, 13], L8224 = [1, 2, 3, 5, 9, 11, 12], L8225 = [1, 2, 3, 5, 9, 11, 14], L8227 = [1, 2, 3, 5, 9, 12, 14], L8229 = [1, 2, 3, 5, 10, 11, 13], L8234 = [1, 2, 3, 5, 11, 12, 14], L8235 = [1, 2, 3, 6, 7, 8, 9], L8239 = [1, 2, 3, 6, 7, 8, 13], L8240 = [1, 2, 3, 6, 7, 9, 10], L8241 = [1, 2, 3, 6, 7, 9, 13], L8243 = [1, 2, 3, 6, 7, 10, 12], L8245 = [1, 2, 3, 6, 7, 11, 13], L8248 = [1, 2, 3, 6, 7, 12, 14], L8250 = [1, 2, 3, 6, 8, 10, 11], L8254 = [1, 2, 3, 6, 8, 11, 14], L8256 = [1, 2, 3, 6, 8, 12, 14], L8260 = [1, 2, 3, 7, 8, 9, 13], L8261 = [1, 2, 3, 7, 8, 10, 11], L8268 = [1, 2, 3, 7, 10, 11, 12], L8270 = [1, 2, 3, 7, 10, 12, 14], L8274 = [1, 2, 3, 8, 9, 11, 14], L8275 = [1, 2, 3, 8, 9, 12, 13], L8277 = [1, 2, 3, 8, 10, 11, 12], L8279 = [1, 2, 3, 8, 10, 11, 14], L8287 = [1, 2, 4, 5, 7, 9, 14], L8298 = [1, 2, 4, 10, 11, 12, 13], L8299 = [1, 2, 5, 6, 7, 8, 9], L8300 = [1, 2, 5, 6, 7, 8, 10], L8301 = [1, 2, 5, 6, 7, 8, 11], L8303 = [1, 2, 5, 6, 7, 10, 11], L8305 = [1, 2, 5, 6, 7, 11, 13], L8306 = [1, 2, 5, 6, 8, 10, 11], L8311 = [1, 2, 6, 7, 8, 10, 11]. q = 30 : L55 = [0, 0, 0, 0, 1, 3, 7], L59 = [0, 0, 0, 0, 1, 3, 11], L423 = [0, 0, 0, 1, 3, 5, 7], L427 = [0, 0, 0, 1, 3, 5, 11], L444 = [0, 0, 0, 1, 3, 7, 10], L448 = [0, 0, 0, 1, 3, 7, 15], L463 = [0, 0, 0, 1, 3, 10, 11], L469 = [0, 0, 0, 1, 3, 11, 15], L800 = [0, 0, 0, 2, 4, 5, 12], L805 = [0, 0, 0, 2, 4, 12, 15], L815 = [0, 0, 0, 2, 5, 6, 8], L837 = [0, 0, 0, 2, 6, 8, 15], L1814 = [0, 0, 1, 2, 4, 7, 8], L1817 = [0, 0, 1, 2, 4, 7, 11], L1819 = [0, 0, 1, 2, 4, 7, 13], L1820 = [0, 0, 1, 2, 4, 7, 14], L2140 = [0, 0, 1, 3, 3, 7, 9], L2155 = [0, 0, 1, 3, 3, 9, 11], L2241 = [0, 0, 1, 3, 5, 5, 7], L2245 = [0, 0, 1, 3, 5, 5, 11], L2262 = [0, 0, 1, 3, 5, 7, 10], L2266 = [0, 0, 1, 3, 5, 7, 15], L2281 = [0, 0, 1, 3, 5, 10, 11], L2287 = [0, 0, 1, 3, 5, 11, 15], L2311 = [0, 0, 1, 3, 6, 7, 12], L2334 = [0, 0, 1, 3, 6, 11, 12], L2354 = [0, 0, 1, 3, 7, 10, 10], L2358 = [0, 0, 1, 3, 7, 10, 15], L2366 = [0, 0, 1, 3, 7, 15, 15], L2413 = [0, 0, 1, 3, 10, 10, 11], L2419 = [0, 0, 1, 3, 10, 11, 15], L2431 = [0, 0, 1, 3, 11, 15, 15], L2781 = [0, 0, 1, 5, 7, 11, 13], L2886 = [0, 0, 1, 6, 6, 12, 12], L3073 = [0, 0, 1, 9, 10, 10, 11], L3098 = [0, 0, 1, 10, 10, 10, 10], L3413 = [0, 0, 2, 3, 4, 9, 12], L3463 = [0, 0, 2, 3, 6, 8, 9], L3520 = [0, 0, 2, 4, 5, 5, 12], L3532 = [0, 0, 2, 4, 5, 10, 12], L3535 = [0, 0, 2, 4, 5, 12, 15], L3547 = [0, 0, 2, 4, 10, 12, 15], L3550 = [0, 0, 2, 4, 12, 15, 15], L3560 = [0, 0, 2, 5, 5, 6, 8], L3586 = [0, 0, 2, 5, 6, 8, 10], L3588 = [0, 0, 2, 5, 6, 8, 15], L3644 = [0, 0, 2, 6, 8, 10, 15], L3646 = [0, 0, 2, 6, 8, 15, 15], L3821 = [0, 0, 3, 10, 10, 10, 10], L3852 = [0, 0, 5, 6, 6, 12, 12], L6047 = [0, 1, 1, 5, 7, 11, 13], L6212 = [0, 1, 1, 6, 6, 12, 12], L6616 = [0, 1, 1, 9, 9, 11, 11], L6631 = [0, 1, 1, 9, 10, 10, 11], L7411 = [0, 1, 2, 3, 4, 7, 14], L7416 = [0, 1, 2, 3, 4, 8, 11], L7672 = [0, 1, 2, 3, 11, 12, 14], L7780 = [0, 1, 2, 4, 5, 7, 8], L7783 = [0, 1, 2, 4, 5, 7, 11],
APPENDIX
127
Table 5. (continued) n = 7 q I indexes of I-isospectral families 30 {0} {27892, 29813}, {27922, 29817}, {28238, 28244}, {28241, 28243}, (cont.) {28331, 28346}, {28332, 28354}, {28336, 28356}, {28343, 28345}, {28350, 28355}, {28502, 28504}, {28503, 28524}, {28518, 28523}, {28635, 28668}, {28636, 28676}, {28640, 28678}, {28644, 28690}, {28649, 28692}, {28665, 28667}, {28672, 28677}, {28681, 29824}, {28684, 28691}, {31027, 31075}, {31398, 31413}, {31490, 31542}, {31494, 31548}, {31651, 31707}, {31777, 31911}, {31781, 31917}, {31789, 31929}, {32760, 32764}, {32781, 32800}, {32785, 32806}, {32830, 32853}, {32873, 32932}, {32877, 32938}, {32885, 32950}, {33028, 33093}, {33036, 33105}, {33146, 33288}, {33150, 33294}, {33158, 33306}, {33170, 33326}, {33419, 33490}, {33540, 33691}, {33548, 33703}, {33560, 33723}, {33795, 34088}, {33799, 34094}, {33807, 34106}, {33819, 34126}, {33835, 34156}, {40902, 41051}, {41182, 41409}, {41231, 41487}, {41234, 41489}, {41294, 41613}, {41336, 41651}, {41339, 41653}, {41343, 41656}, {41822, 42004}, {41834, 42030}, {41837, 42032}, {41853, 42081}, {41863, 42097}, {41866, 42099}, {41870, 42102}, {41903, 42203}, {41908, 42206}, {41920, 42238}, {41923, 42240}, {41927, 42243}, {41932, 42247}, {41965, 42419}, {41970, 42422}, {41982, 42474}, {41985, 42476}, {41989, 42479}, {41994, 42483}
L7785 = [0, 1, 2, 4, 5, 7, 13], L7786 = [0, 1, 2, 4, 5, 7, 14], L7873 = [0, 1, 2, 4, 7, 8, 10], L7874 = [0, 1, 2, 4, 7, 8, 11], L7878 = [0, 1, 2, 4, 7, 8, 15], L7885 = [0, 1, 2, 4, 7, 10, 11], L7887 = [0, 1, 2, 4, 7, 10, 13], L7888 = [0, 1, 2, 4, 7, 10, 14], L7890 = [0, 1, 2, 4, 7, 11, 12], L7892 = [0, 1, 2, 4, 7, 11, 15], L7896 = [0, 1, 2, 4, 7, 13, 14], L7897 = [0, 1, 2, 4, 7, 13, 15], L7898 = [0, 1, 2, 4, 7, 14, 15], L7915 = [0, 1, 2, 4, 8, 10, 14], L8122 = [0, 1, 2, 5, 7, 11, 13], L8272 = [0, 1, 2, 6, 6, 12, 12], L8282 = [0, 1, 2, 6, 7, 8, 9], L8284 = [0, 1, 2, 6, 7, 8, 11], L8517 = [0, 1, 2, 8, 9, 11, 12], L8530 = [0, 1, 2, 8, 10, 10, 12], L8591 = [0, 1, 2, 9, 10, 10, 11], L8886 = [0, 1, 3, 3, 5, 7, 9], L8901 = [0, 1, 3, 3, 5, 9, 11], L8978 = [0, 1, 3, 3, 7, 9, 10], L8982 = [0, 1, 3, 3, 7, 9, 15], L9028 = [0, 1, 3, 3, 9, 9, 15], L9030 = [0, 1, 3, 3, 9, 10, 11], L9036 = [0, 1, 3, 3, 9, 11, 15], L9326 = [0, 1, 3, 5, 5, 5, 7], L9330 = [0, 1, 3, 5, 5, 5, 11], L9347 = [0, 1, 3, 5, 5, 7, 10], L9351 = [0, 1, 3, 5, 5, 7, 15], L9366 = [0, 1, 3, 5, 5, 10, 11], L9372 = [0, 1, 3, 5, 5, 11, 15], L9396 = [0, 1, 3, 5, 6, 7, 12], L9419 = [0, 1, 3, 5, 6, 11, 12], L9439 = [0, 1, 3, 5, 7, 10, 10], L9443 = [0, 1, 3, 5, 7, 10, 15], L9445 = [0, 1, 3, 5, 7, 11, 13], L9451 = [0, 1, 3, 5, 7, 15, 15], L9498 = [0, 1, 3, 5, 10, 10, 11], L9504 = [0, 1, 3, 5, 10, 11, 15], L9516 = [0, 1, 3, 5, 11, 15, 15], L9572 = [0, 1, 3, 6, 6, 12, 12], L9594 = [0, 1, 3, 6, 7, 10, 12], L9602 = [0, 1, 3, 6, 7, 12, 15], L9647 = [0, 1, 3, 6, 9, 12, 15], L9659 = [0, 1, 3, 6, 10, 11, 12], L9671 = [0, 1, 3, 6, 11, 12, 15], L9709 = [0, 1, 3, 7, 9, 11, 13], L9712 = [0, 1, 3, 7, 10, 10, 10], L9715 = [0, 1, 3, 7, 10, 10, 13], L9716 = [0, 1, 3, 7, 10, 10, 15], L9724 = [0, 1, 3, 7, 10, 15, 15], L9736 = [0, 1, 3, 7, 15, 15, 15], L9828 = [0, 1, 3, 9, 10, 10, 11], L9854 = [0, 1, 3, 10, 10, 10, 11], L9860 = [0, 1, 3, 10, 10, 11, 15], L9872 = [0, 1, 3, 10, 11, 15, 15], L9892 = [0, 1, 3, 11, 15, 15, 1 L10360 = [0, 1, 4, 6, 6, 12, 12], L10412 = [0, 1, 4, 6, 9, 11, 14], L10423 = [0, 1, 4, 6, 10, 10, 14], L10552 = [0, 1, 4, 9, 10, 10, 11], L10730 = [0, 1, 5, 5, 7, 11, 13], L10766 = [0, 1, 5, 5, 9, 11, 15], L10777 = [0, 1, 5, 5, 10, 10, 15], L10835 = [0, 1, 5, 6, 6, 12, 12], L10854 = [0, 1, 5, 6, 7, 11, 13], L10940 = [0, 1, 5, 7, 10, 11, 13], L10943 = [0, 1, 5, 7, 11, 13, 15], L11022 = [0, 1, 5, 9, 10, 10, 11], L11128 = [0, 1, 6, 6, 6, 12, 12], L11149 = [0, 1, 6, 6, 7, 12, 12], L11169 = [0, 1, 6, 6, 8, 12, 12], L11188 = [0, 1, 6, 6, 9, 12, 12], L11202 = [0, 1, 6, 6, 10, 12, 12], L11211 = [0, 1, 6, 6, 11, 12, 12], L11214 = [0, 1, 6, 6, 12, 12, 12], L11215 = [0, 1, 6, 6, 12, 12, 14], L11216 = [0, 1, 6, 6, 12, 12, 15] L11332 = [0, 1, 6, 9, 10, 10, 11], L11580 = [0, 1, 9, 9, 10, 10, 11], L11606 = [0, 1, 9, 10, 10, 10, 11], L11610 = [0, 1, 9, 10, 10, 11, 12], L11611 = [0, 1, 9, 10, 10, 11, 15], L12622 = [0, 2, 3, 3, 9, 9, 15], L12669 = [0, 2, 3, 4, 5, 9, 12],
128
EMILIO A. LAURET
Table 5. (continued) n = 7 q I 30 {0, 1} (cont.) {2} {4}
indexes of I-isospectral families {7411, 7416}, {7890, 8284}, {26972, 26977}, {27079, 27107}, {27091, 27115}, {28348, 29193}, {28670, 29819}, {28682, 29825} {33144, 33162} {2781, 10854, 36563, 36665}, {2886, 3852, 11128, 11214, 13701}, {6047, 10730, 22399, 22623, 36270}, {6212, 10835, 11149, 11211, 13684}, {7915, 12996, 28546, 28744, 41893}, {8122, 10940, 29209, 29375, 36660}, {8272, 10360, 11169, 11202, 11215, 13137, 13707}, {9028, 13471, 31700, 31906, 42872}, {9445, 10943, 33032, 33160, 36667}, {9572, 11188, 11216, 13578, 13710}, {9647, 13584}, {12622, 13504, 41064, 41118, 42934}, {12710, 13029, 41283, 41324, 41955}, {12850, 13250, 13256, 13626, 13729}, {12873, 13632}, {15950, 22195, 22534, 22620, 36146}, {18050, 28373, 28639, 28741, 41858}, {18298, 21313, 22560, 22607, 22626, 29031, 36356}, {19475, 31540, 31776, 31903, 42838}, {20048, 22587, 22627, 32879, 36359}, {25592, 28156, 28707, 28738, 28746, 39937, 41913}, {25814, 28349, 29335, 29367, 36841}, {26817, 31332, 31846, 31901, 31908, 41000, 42890}, {27110, 28724, 28747, 41223, 41915}, {27330, 29354, 29377, 33152, 36844}, {31079, 31896, 31909, 42749, 42891}, {31501, 33143, 33162, 36847}, {39334, 40903, 41093, 41116, 42952}, {39475, 40037, 40046, 41321, 41975}, {40801, 41113, 41119, 42784, 42953}, {40894, 41315, 41326, 41977}
L12710 = [0, 2, 3, 4, 8, 10, 14], L12718 = [0, 2, 3, 4, 9, 10, 12], L12721 = [0, 2, 3, 4, 9, 12, 15], L12778 = [0, 2, 3, 5, 6, 8, 9], L12850 = [0, 2, 3, 6, 6, 12, 12], L12856 = [0, 2, 3, 6, 8, 9, 10], L12858 = [0, 2, 3, 6, 8, 9, 15], L12873 = [0, 2, 3, 6, 9, 12, 15], L12902 = [0, 2, 3, 8, 10, 10, 12], L12960 = [0, 2, 4, 5, 5, 5, 12], L12972 = [0, 2, 4, 5, 5, 10, 12], L12975 = [0, 2, 4, 5, 5, 12, 15], L12991 = [0, 2, 4, 5, 6, 12, 12], L12996 = [0, 2, 4, 5, 8, 10, 14], L13001 = [0, 2, 4, 5, 10, 10, 12], L13004 = [0, 2, 4, 5, 10, 12, 15], L13008 = [0, 2, 4, 5, 12, 15, 15], L13024 = [0, 2, 4, 6, 12, 12, 15], L13029 = [0, 2, 4, 8, 10, 14, 15], L13034 = [0, 2, 4, 10, 10, 12, 15], L13037 = [0, 2, 4, 10, 12, 15, 1 L13041 = [0, 2, 4, 12, 15, 15, 15], L13051 = [0, 2, 5, 5, 5, 6, 8], L13077 = [0, 2, 5, 5, 6, 8, 10], L13079 = [0, 2, 5, 5, 6, 8, 15], L13098 = [0, 2, 5, 5, 8, 12, 15], L13112 = [0, 2, 5, 5, 10, 10, 15], L13128 = [0, 2, 5, 6, 6, 8, 12], L13137 = [0, 2, 5, 6, 6, 12, 12], L13144 = [0, 2, 5, 6, 8, 10, 10], L13146 = [0, 2, 5, 6, 8, 10, 15], L13149 = [0, 2, 5, 6, 8, 15, 15], L13181 = [0, 2, 5, 8, 10, 10, 12], L13241 = [0, 2, 6, 6, 8, 12, 15], L13250 = [0, 2, 6, 6, 9, 12, 12], L13256 = [0, 2, 6, 6, 12, 12, 15], L13269 = [0, 2, 6, 8, 10, 10, 15], L13271 = [0, 2, 6, 8, 10, 15, 15], L13274 = [0, 2, 6, 8, 15, 15, 15], L13316 = [0, 2, 8, 9, 10, 10, 12], L13326 = [0, 2, 8, 10, 10, 12, 15], L13471 = [0, 3, 3, 5, 9, 9, 15], L13504 = [0, 3, 3, 9, 9, 10, 15], L13559 = [0, 3, 5, 5, 10, 10, 15], L13578 = [0, 3, 5, 6, 6, 12, 12], L13584 = [0, 3, 5, 6, 9, 12, 15], L13626 = [0, 3, 6, 6, 10, 12, 12], L13632 = [0, 3, 6, 9, 10, 12, 15], L13684 = [0, 5, 5, 6, 6, 12, 12], L13689 = [0, 5, 5, 6, 10, 10, 15], L13701 = [0, 5, 6, 6, 6, 12, 12], L13707 = [0, 5, 6, 6, 10, 12, 12], L13710 = [0, 5, 6, 6, 12, 12, 15], L13729 = [0, 6, 6, 10, 12, 12, 15], L15950 = [1, 1, 1, 5, 7, 11, 13], L16593 = [1, 1, 1, 9, 9, 11, 11], L18050 = [1, 1, 2, 4, 8, 10, 14], L18298 = [1, 1, 2, 5, 7, 11, 13], L18840 = [1, 1, 2, 8, 9, 11, 12], L18919 = [1, 1, 2, 9, 9, 11, 11], L19475 = [1, 1, 3, 3, 9, 9, 15], L20048 = [1, 1, 3, 5, 7, 11, 13], L20406 = [1, 1, 3, 7, 7, 11, 13], L20464 = [1, 1, 3, 7, 9, 11, 13], L20498 = [1, 1, 3, 7, 11, 11, 13], L20652 = [1, 1, 3, 9, 9, 11, 11], L21313 = [1, 1, 4, 5, 7, 11, 13], L21580 = [1, 1, 4, 6, 9, 11, 14], L21887 = [1, 1, 4, 9, 9, 11, 11], L22195 = [1, 1, 5, 5, 7, 11, 13], L22258 = [1, 1, 5, 5, 9, 11, 15], L22399 = [1, 1, 5, 6, 7, 11, 13], L22534 = [1, 1, 5, 7, 7, 11, 13], L22560 = [1, 1, 5, 7, 8, 11, 13], L22587 = [1, 1, 5, 7, 9, 11, 13], L22607 = [1, 1, 5, 7, 10, 11, 13], L22620 = [1, 1, 5, 7, 11, 11, 13], L22623 = [1, 1, 5, 7, 11, 12, 13], L22626 = [1, 1, 5, 7, 11, 13, 14], L22627 = [1, 1, 5, 7, 11, 13, 15], L22764 = [1, 1, 5, 9, 9, 11, 11], L23376 = [1, 1, 6, 9, 9, 11, 11], L23682 = [1, 1, 7, 9, 9, 11, 11], L24110 = [1, 1, 9, 9, 9, 11, 11],
APPENDIX
129
Table 5. (continued) n = 7 q I indexes of I-isospectral families 30 {2, 5} {3073, 11606}, {3098, 3821}, {6616, 24130}, {6631, 11580}, {8517, 30373}, (cont.) {8530, 13316}, {8591, 11610}, {9709, 33789}, {9715, 9828}, {10412, 35621}, {10423, 12902}, {10552, 11332}, {10766, 36443}, {10777, 13559}, {11022, 11611}, {13098, 42137}, {13112, 13689}, {13181, 13326}, {16593, 24110}, {18840, 30356}, {18919, 24144}, {20464, 31783}, {20652, 23682}, {21580, 35607}, {21887, 23376}, {22258, 36430}, {22764, 24145}, {26236, 40509}, {26258, 30384}, {27650, 32526}, {27669, 33533}, {27754, 30148}, {28553, 41286}, {28572, 35630}, {28726, 29915}, {29063, 42131}, {29085, 36451}, {29426, 30385}, {32884, 32924}, {33143, 33792}, {34639, 39719}, {34688, 35476}, {35000, 41434}, {35049, 36308}, {35171, 35632}, {36095, 42997}, {36182, 36452}, {40176, 42140}, {40291, 40515}, {41855, 42101}, {41895, 41957}, {42022, 43242}, {42051, 42141}
L24130 = [1, 1, 9, 9, 10, 11, 11], L24144 = [1, 1, 9, 9, 11, 11, 12], L24145 = [1, 1, 9, 9, 11, 11, 15], L25592 = [1, 2, 2, 4, 8, 10, 14], L25814 = [1, 2, 2, 5, 7, 11, 13], L26236 = [1, 2, 2, 8, 8, 12, 12], L26258 = [1, 2, 2, 8, 9, 11, 12], L26817 = [1, 2, 3, 3, 9, 9, 15], L26972 = [1, 2, 3, 4, 5, 7, 14], L26977 = [1, 2, 3, 4, 5, 8, 11], L27061 = [1, 2, 3, 4, 7, 8, 9], L27066 = [1, 2, 3, 4, 7, 8, 14], L27070 = [1, 2, 3, 4, 7, 9, 11], L27072 = [1, 2, 3, 4, 7, 9, 13], L27073 = [1, 2, 3, 4, 7, 9, 14], L27079 = [1, 2, 3, 4, 7, 10, 14], L27083 = [1, 2, 3, 4, 7, 11, 14], L27091 = [1, 2, 3, 4, 7, 14, 15], L27107 = [1, 2, 3, 4, 8, 10, 11], L27110 = [1, 2, 3, 4, 8, 10, 14], L27113 = [1, 2, 3, 4, 8, 11, 13], L27114 = [1, 2, 3, 4, 8, 11, 14], L27115 = [1, 2, 3, 4, 8, 11, 15], L27330 = [1, 2, 3, 5, 7, 11, 13], L27419 = [1, 2, 3, 5, 11, 12, 14], L27650 = [1, 2, 3, 7, 8, 12, 13], L27669 = [1, 2, 3, 7, 9, 11, 13], L27754 = [1, 2, 3, 8, 9, 11, 12], L27892 = [1, 2, 3, 10, 11, 12, 14], L27922 = [1, 2, 3, 11, 12, 14, 15], L28156 = [1, 2, 4, 4, 8, 10, 14], L28238 = [1, 2, 4, 5, 5, 7, 8], L28241 = [1, 2, 4, 5, 5, 7, 11], L28243 = [1, 2, 4, 5, 5, 7, 13], L28244 = [1, 2, 4, 5, 5, 7, 14], L28331 = [1, 2, 4, 5, 7, 8, 10], L28332 = [1, 2, 4, 5, 7, 8, 11], L28336 = [1, 2, 4, 5, 7, 8, 15], L28343 = [1, 2, 4, 5, 7, 10, 11], L28345 = [1, 2, 4, 5, 7, 10, 13], L28346 = [1, 2, 4, 5, 7, 10, 14], L28348 = [1, 2, 4, 5, 7, 11, 12], L28349 = [1, 2, 4, 5, 7, 11, 13], L28350 = [1, 2, 4, 5, 7, 11, 15], L28354 = [1, 2, 4, 5, 7, 13, 14], L28355 = [1, 2, 4, 5, 7, 13, 15], L28356 = [1, 2, 4, 5, 7, 14, 15], L28373 = [1, 2, 4, 5, 8, 10, 14], L28502 = [1, 2, 4, 6, 7, 8, 11], L28503 = [1, 2, 4, 6, 7, 8, 12], L28504 = [1, 2, 4, 6, 7, 8, 13], L28518 = [1, 2, 4, 6, 7, 11, 12], L28523 = [1, 2, 4, 6, 7, 12, 13], L28524 = [1, 2, 4, 6, 7, 12, 14], L28546 = [1, 2, 4, 6, 8, 10, 14], L28553 = [1, 2, 4, 6, 8, 12, 14], L28572 = [1, 2, 4, 6, 9, 11, 14], L28635 = [1, 2, 4, 7, 8, 10, 10], L28636 = [1, 2, 4, 7, 8, 10, 11], L28639 = [1, 2, 4, 7, 8, 10, 14], L28640 = [1, 2, 4, 7, 8, 10, 15], L28644 = [1, 2, 4, 7, 8, 11, 15], L28649 = [1, 2, 4, 7, 8, 15, 15], L28665 = [1, 2, 4, 7, 10, 10, 11], L28667 = [1, 2, 4, 7, 10, 10, 13], L28668 = [1, 2, 4, 7, 10, 10, 14], L28670 = [1, 2, 4, 7, 10, 11, 12], L28672 = [1, 2, 4, 7, 10, 11, 15], L28676 = [1, 2, 4, 7, 10, 13, 14], L28677 = [1, 2, 4, 7, 10, 13, 15] L28678 = [1, 2, 4, 7, 10, 14, 15], L28681 = [1, 2, 4, 7, 11, 12, 13], L28682 = [1, 2, 4, 7, 11, 12, 15], L28684 = [1, 2, 4, 7, 11, 15, 15], L28690 = [1, 2, 4, 7, 13, 14, 15], L28691 = [1, 2, 4, 7, 13, 15, 15], L28692 = [1, 2, 4, 7, 14, 15, 15] L28707 = [1, 2, 4, 8, 8, 10, 14], L28724 = [1, 2, 4, 8, 9, 10, 14], L28726 = [1, 2, 4, 8, 9, 11, 12], L28738 = [1, 2, 4, 8, 10, 10, 14], L28741 = [1, 2, 4, 8, 10, 11, 14], L28744 = [1, 2, 4, 8, 10, 12, 14], L28746 = [1, 2, 4, 8, 10, 14, 14] L28747 = [1, 2, 4, 8, 10, 14, 15], L29031 = [1, 2, 5, 5, 7, 11, 13], L29063 = [1, 2, 5, 5, 8, 12, 15], L29085 = [1, 2, 5, 5, 9, 11, 15], L29191 = [1, 2, 5, 6, 7, 8, 9], L29193 = [1, 2, 5, 6, 7, 8, 11], L29209 = [1, 2, 5, 6, 7, 11, 13], L29335 = [1, 2, 5, 7, 8, 11, 13], L29354 = [1, 2, 5, 7, 9, 11, 13], L29367 = [1, 2, 5, 7, 10, 11, 13], L29375 = [1, 2, 5, 7, 11, 12, 13], L29377 = [1, 2, 5, 7, 11, 13, 15], L29426 = [1, 2, 5, 8, 9, 11, 12], L29813 = [1, 2, 6, 7, 8, 9, 10], L29817 = [1, 2, 6, 7, 8, 9, 15], L29819 = [1, 2, 6, 7, 8, 10, 11], L29824 = [1, 2, 6, 7, 8, 11, 13], L29825 = [1, 2, 6, 7, 8, 11, 15], L29915 = [1, 2, 6, 8, 9, 11, 12], L30148 = [1, 2, 7, 8, 9, 11, 12], L30356 = [1, 2, 8, 9, 9, 11, 12], L30373 = [1, 2, 8, 9, 10, 11, 12], L30384 = [1, 2, 8, 9, 11, 12, 12], L30385 = [1, 2, 8, 9, 11, 12, 15], L31027 = [1, 3, 3, 3, 7, 9, 9], L31075 = [1, 3, 3, 3, 9, 9, 11], L31079 = [1, 3, 3, 3, 9, 9, 15], L31332 = [1, 3, 3, 4, 9, 9, 15],
130
EMILIO A. LAURET
L31398 = [1, 3, 3, 5, 5, 7, 9], L31413 = [1, 3, 3, 5, 5, 9, 11], L31490 = [1, 3, 3, 5, 7, 9, 10], L31494 = [1, 3, 3, 5, 7, 9, 15], L31501 = [1, 3, 3, 5, 7, 11, 13], L31540 = [1, 3, 3, 5, 9, 9, 15], L31542 = [1, 3, 3, 5, 9, 10, 11], L31548 = [1, 3, 3, 5, 9, 11, 15], L31651 = [1, 3, 3, 6, 7, 9, 12], L31700 = [1, 3, 3, 6, 9, 9, 15], L31707 = [1, 3, 3, 6, 9, 11, 12], L31776 = [1, 3, 3, 7, 9, 9, 15], L31777 = [1, 3, 3, 7, 9, 10, 10], L31781 = [1, 3, 3, 7, 9, 10, 15], L31783 = [1, 3, 3, 7, 9, 11, 13], L31789 = [1, 3, 3, 7, 9, 15, 15], L31846 = [1, 3, 3, 8, 9, 9, 15], L31896 = [1, 3, 3, 9, 9, 9, 15], L31901 = [1, 3, 3, 9, 9, 10, 15], L31903 = [1, 3, 3, 9, 9, 11, 15], L31906 = [1, 3, 3, 9, 9, 12, 15], L31908 = [1, 3, 3, 9, 9, 14, 15], L31909 = [1, 3, 3, 9, 9, 15, 15], L31911 = [1, 3, 3, 9, 10, 10, 11], L31917 = [1, 3, 3, 9, 10, 11, 15], L31929 = [1, 3, 3, 9, 11, 15, 15], L32526 = [1, 3, 4, 6, 9, 11, 14], L32760 = [1, 3, 5, 5, 5, 5, 7], L32764 = [1, 3, 5, 5, 5, 5, 11], L32781 = [1, 3, 5, 5, 5, 7, 10], L32785 = [1, 3, 5, 5, 5, 7, 15], L32800 = [1, 3, 5, 5, 5, 10, 11], L32806 = [1, 3, 5, 5, 5, 11, 15], L32830 = [1, 3, 5, 5, 6, 7, 12], L32853 = [1, 3, 5, 5, 6, 11, 12], L32873 = [1, 3, 5, 5, 7, 10, 10], L32877 = [1, 3, 5, 5, 7, 10, 15], L32879 = [1, 3, 5, 5, 7, 11, 13], L32884 = [1, 3, 5, 5, 7, 13, 15], L32885 = [1, 3, 5, 5, 7, 15, 15], L32924 = [1, 3, 5, 5, 9, 11, 15], L32932 = [1, 3, 5, 5, 10, 10, 11], L32938 = [1, 3, 5, 5, 10, 11, 15], L32950 = [1, 3, 5, 5, 11, 15, 15], L33028 = [1, 3, 5, 6, 7, 10, 12], L33032 = [1, 3, 5, 6, 7, 11, 13], L33036 = [1, 3, 5, 6, 7, 12, 15], L33093 = [1, 3, 5, 6, 10, 11, 12], L33105 = [1, 3, 5, 6, 11, 12, 15], L33143 = [1, 3, 5, 7, 9, 11, 13], L33144 = [1, 3, 5, 7, 9, 11, 15], L33146 = [1, 3, 5, 7, 10, 10, 10], L33150 = [1, 3, 5, 7, 10, 10, 15], L33152 = [1, 3, 5, 7, 10, 11, 13], L33158 = [1, 3, 5, 7, 10, 15, 15], L33160 = [1, 3, 5, 7, 11, 12, 13] L33162 = [1, 3, 5, 7, 11, 13, 15], L33170 = [1, 3, 5, 7, 15, 15, 15], L33288 = [1, 3, 5, 10, 10, 10, 11], L33294 = [1, 3, 5, 10, 10, 11, 15], L33306 = [1, 3, 5, 10, 11, 15, 15], L33326 = [1, 3, 5, 11, 15, 15, 15], L33419 = [1, 3, 6, 6, 7, 12, 12], L33490 = [1, 3, 6, 6, 11, 12, 12], L33533 = [1, 3, 6, 7, 9, 11, 13], L33540 = [1, 3, 6, 7, 10, 10, 12], L33548 = [1, 3, 6, 7, 10, 12, 15], L33560 = [1, 3, 6, 7, 12, 15, 15], L33691 = [1, 3, 6, 10, 10, 11, 12], L33703 = [1, 3, 6, 10, 11, 12, 15], L33723 = [1, 3, 6, 11, 12, 15, 15], L33789 = [1, 3, 7, 9, 10, 11, 13], L33792 = [1, 3, 7, 9, 11, 13, 15], L33795 = [1, 3, 7, 10, 10, 10, 10], L33799 = [1, 3, 7, 10, 10, 10, 15], L33807 = [1, 3, 7, 10, 10, 15, 15], L33819 = [1, 3, 7, 10, 15, 15, 15], L33835 = [1, 3, 7, 15, 15, 15, 15], L34088 = [1, 3, 10, 10, 10, 10, 11], L34094 = [1, 3, 10, 10, 10, 11, 15], L34106 = [1, 3, 10, 10, 11, 15, 15], L34126 = [1, 3, 10, 11, 15, 15, 15], L34156 = [1, 3, 11, 15, 15, 15, 15], L34639 = [1, 4, 4, 6, 6, 14, 14], L34688 = [1, 4, 4, 6, 9, 11, 14], L35000 = [1, 4, 5, 5, 6, 14, 15], L35049 = [1, 4, 5, 5, 9, 11, 15], L35171 = [1, 4, 5, 6, 9, 11, 14], L35476 = [1, 4, 6, 6, 9, 11, 14], L35607 = [1, 4, 6, 9, 9, 11, 14], L35621 = [1, 4, 6, 9, 10, 11, 14], L35630 = [1, 4, 6, 9, 11, 12, 14], L35632 = [1, 4, 6, 9, 11, 14, 15], L36095 = [1, 5, 5, 5, 5, 15, 15], L36146 = [1, 5, 5, 5, 7, 11, 13], L36182 = [1, 5, 5, 5, 9, 11, 15], L36270 = [1, 5, 5, 6, 7, 11, 13], L36308 = [1, 5, 5, 6, 9, 11, 15], L36356 = [1, 5, 5, 7, 10, 11, 13], L36359 = [1, 5, 5, 7, 11, 13, 15], L36430 = [1, 5, 5, 9, 9, 11, 15], L36443 = [1, 5, 5, 9, 10, 11, 15], L36451 = [1, 5, 5, 9, 11, 12, 15], L36452 = [1, 5, 5, 9, 11, 15, 15], L36563 = [1, 5, 6, 6, 7, 11, 13], L36660 = [1, 5, 6, 7, 10, 11, 13], L36665 = [1, 5, 6, 7, 11, 12, 13], L36667 = [1, 5, 6, 7, 11, 13, 15], L36841 = [1, 5, 7, 10, 10, 11, 13 L36844 = [1, 5, 7, 10, 11, 13, 15], L36847 = [1, 5, 7, 11, 13, 15, 15], L39334 = [2, 2, 3, 3, 9, 9, 15], L39475 = [2, 2, 3, 4, 8, 10, 14], L39719 = [2, 2, 3, 8, 8, 12, 12], L39937 = [2, 2, 4, 5, 8, 10, 14], L40037 = [2, 2, 4, 8, 9, 10, 14], L40046 = [2, 2, 4, 8, 10, 14, 15], L40176 = [2, 2, 5, 5, 8, 12, 15], L40291 = [2, 2, 5, 8, 8, 12, 12], L40509 = [2, 2, 8, 8, 9, 12, 12], L40515 = [2, 2, 8, 8, 12, 12, 15], L40801 = [2, 3, 3, 3, 9, 9, 15], L40894 = [2, 3, 3, 4, 8, 10, 14], L40902 = [2, 3, 3, 4, 9, 9, 12], L40903 = [2, 3, 3, 4, 9, 9, 15], L41000 = [2, 3, 3, 5, 9, 9, 15], L41051 = [2, 3, 3, 6, 8, 9, 9], L41064 = [2, 3, 3, 6, 9, 9, 15], L41093 = [2, 3, 3, 8, 9, 9, 15], L41113 = [2, 3, 3, 9, 9, 9, 15], L41116 = [2, 3, 3, 9, 9, 10, 15], L41118 = [2, 3, 3, 9, 9, 12, 15], L41119 = [2, 3, 3, 9, 9, 15, 15], L41182 = [2, 3, 4, 5, 5, 9, 12], L41223 = [2, 3, 4, 5, 8, 10, 14], L41231 = [2, 3, 4, 5, 9, 10, 12], L41234 = [2, 3, 4, 5, 9, 12, 15], L41283 = [2, 3, 4, 6, 8, 10, 14], L41286 = [2, 3, 4, 6, 8, 12, 14], L41294 = [2, 3, 4, 6, 9, 12, 12], L41315 = [2, 3, 4, 8, 9, 10, 14], L41321 = [2, 3, 4, 8, 10, 10, 14], L41324 = [2, 3, 4, 8, 10, 12, 14], L41326 = [2, 3, 4, 8, 10, 14, 15], L41336 = [2, 3, 4, 9, 10, 10, 12], L41339 = [2, 3, 4, 9, 10, 12, 15], L41343 = [2, 3, 4, 9, 12, 15, 15], L41409 = [2, 3, 5, 5, 6, 8, 9], L41434 = [2, 3, 5, 5, 8, 12, 15], L41487 = [2, 3, 5, 6, 8, 9, 10], L41489 = [2, 3, 5, 6, 8, 9, 15], L41613 = [2, 3, 6, 6, 8, 9, 12], L41651 = [2, 3, 6, 8, 9, 10, 10], L41653 = [2, 3, 6, 8, 9, 10, 15], L41656 = [2, 3, 6, 8, 9, 15, 15], L41822 = [2, 4, 5, 5, 5, 5, 12], L41834 = [2, 4, 5, 5, 5, 10, 12], L41837 = [2, 4, 5, 5, 5, 12, 15], L41853 = [2, 4, 5, 5, 6, 12, 12], L41855 = [2, 4, 5, 5, 6, 14, 15], L41858 = [2, 4, 5, 5, 8, 10, 14], L41863 = [2, 4, 5, 5, 10, 10, 12], L41866 = [2, 4, 5, 5, 10, 12, 15], L41870 = [2, 4, 5, 5, 12, 15, 15], L41893 = [2, 4, 5, 6, 8, 10, 14], L41895 = [2, 4, 5, 6, 8, 12, 14], L41903 = [2, 4, 5, 6, 10, 12, 12], L41908 = [2, 4, 5, 6, 12, 12, 15], L41913 =
APPENDIX
131
Table 5. (continued) n = 7 q 31
I {0}
indexes of I-isospectral families {874, 910}, {969, 983, 992}, {1014, 1017}, {3311, 3319}, {3323, 3384}, {3344, 3348}, {3364, 3380}, {3396, 3468}, {3409, 3496}, {3437, 3575}, {3460, 3550}, {3498, 3546}, {3544, 3596}, {10988, 10990}, {10995, 11001, 11002}, {11013, 11016, 11104}, {11024, 11031}, {11036, 11101}, {11041, 11069}, {11050, 11110}, {11057, 11195}, {11060, 11120}, {11062, 11074, 11117}, {11065, 11192}, {11068, 11123}, {11073, 11149}, {11075, 11197}, {11085, 11090}, {11086, 11121, 11190, 11196}, {11102, 11116}, {11107, 11115, 11131}, {11112, 11127}, {11124, 11289}, {11129, 11186}, {11140, 11168}, {11144, 11231}, {11148, 11171, 11308, 11317}, {11157, 11219}, {11169, 11191}, {11176, 11209}, {11182, 11334}, {11183, 11232}, {11184, 11200}, {11203, 11214}, {11217, 11297}, {11220, 11306}, {11244, 11263, 11341}, {11250, 11257}, {11262, 11332}, {11277, 11328}, {11282, 11365}, {11360, 11370} {0, 1} {11008, 11010}
[2, 4, 5, 8, 10, 10, 14], L41915 = [2, 4, 5, 8, 10, 14, 15], L41920 = [2, 4, 5, 10, 10, 10, 12], L41923 = [2, 4, 5, 10, 10, 12, 1 L41927 = [2, 4, 5, 10, 12, 15, 15], L41932 = [2, 4, 5, 12, 15, 15, 15], L41955 = [2, 4, 6, 8, 10, 14, 15], L41957 = [2, 4, 6, 8, 12, 14, 15], L41965 = [2, 4, 6, 10, 12, 12, 15], L41970 = [2, 4, 6, 12, 12, 15, 15], L41975 = [2, 4, 8, 10, 10, 14, 15], L41977 = [2, 4, 8, 10, 14, 15, 15], L41982 = [2, 4, 10, 10, 10, 12, 15], L41985 = [2, 4, 10, 10, 12, 15, 15], L41989 = [2, 4, 10, 12, 15, 15, 15], L41994 = [2, 4, 12, 15, 15, 15, 15], L42004 = [2, 5, 5, 5, 5, 6, 8], L42022 = [2, 5, 5, 5, 5, 15, 15], L42030 = [2, 5, 5, 5, 6, 8, 10], L42032 = [2, 5, 5, 5, 6, 8, 15], L42051 = [2, 5, 5, 5, 8, 12, 15], L42081 = [2, 5, 5, 6, 6, 8, 12], L42097 = [2, 5, 5, 6, 8, 10, 10], L42099 = [2, 5, 5, 6, 8, 10, 15], L42101 = [2, 5, 5, 6, 8, 12, 15], L42102 = [2, 5, 5, 6, 8, 15, 15], L42131 = [2, 5, 5, 8, 9, 12, 15], L42137 = [2, 5, 5, 8, 10, 12, 15], L42140 = [2, 5, 5, 8, 12, 12, 15], L42141 = [2, 5, 5, 8, 12, 15, 15], L42203 = [2, 5, 6, 6, 8, 10, 12], L42206 = [2, 5, 6, 6, 8, 12, 15], L42238 = [2, 5, 6, 8, 10, 10, 10], L42240 = [2, 5, 6, 8, 10, 10, 15], L42243 = [2, 5, 6, 8, 10, 15, 15], L42247 = [2, 5, 6, 8, 15, 15, 15], L42419 = [2, 6, 6, 8, 10, 12, 15] L42422 = [2, 6, 6, 8, 12, 15, 15], L42474 = [2, 6, 8, 10, 10, 10, 15], L42476 = [2, 6, 8, 10, 10, 15, 15], L42479 = [2, 6, 8, 10, 15, 15, 15], L42483 = [2, 6, 8, 15, 15, 15, 15], L42749 = [3, 3, 3, 5, 9, 9, 15], L42784 = [3, 3, 3, 9, 9, 10, 15], L42838 = [3, 3, 5, 5, 9, 9, 15], L42872 = [3, 3, 5, 6, 9, 9, 15], L42890 = [3, 3, 5, 9, 9, 10, 15], L42891 = [3, 3, 5, 9, 9, 15, 15], L42934 = [3, 3, 6, 9, 9, 10, 15], L42952 = [3, 3, 9, 9, 10, 10, 15], L42953 = [3, 3, 9, 9, 10, 15, 15], L42997 = [3, 5, 5, 5, 5, 15, 15], L43242 = [5, 5, 5, 5, 6, 15, 15]. q = 31 : L874 = [0, 0, 1, 2, 3, 8, 11], L910 = [0, 0, 1, 2, 4, 7, 12], L969 = [0, 0, 1, 2, 6, 8, 14], L983 = [0, 0, 1, 2, 7, 9, 10], L992 = [0, 0, 1, 2, 8, 10, 13], L1014 = [0, 0, 1, 3, 4, 7, 9], L1017 = [0, 0, 1, 3, 4, 9, 10], L3311 = [0, 1, 2, 3, 4, 7, 14], L3319 = [0, 1, 2, 3, 4, 8, 15], L3323 = [0, 1, 2, 3, 4, 9, 13], L3344 = [0, 1, 2, 3, 5, 6, 11], L3348 = [0, 1, 2, 3, 5, 6, 15], L3364 = [0, 1, 2, 3, 5, 9, 11], L3380 = [0, 1, 2, 3, 5, 12, 15], L3384 = [0, 1, 2, 3, 6, 7, 9], L3396 = [0, 1, 2, 3, 6, 8, 14], L3409 = [0, 1, 2, 3, 6, 12, 14], L3437 = [0, 1, 2, 3, 8, 9, 11], L3460 = [0, 1, 2, 3, 9, 12, 14], L3468 = [0, 1, 2, 3, 10, 13, 15], L3496 = [0, 1, 2, 4, 5, 11, 15], L3498 = [0, 1, 2, 4, 5, 12, 14], L3544 = [0, 1, 2, 5, 6, 11, 14], L3546 = [0, 1, 2, 5, 7, 8, 9], L3550 = [0, 1, 2, 5, 7, 9, 10], L3575 = [0, 1, 2, 6, 7, 8, 14], L3596 = [0, 1, 2, 7, 8, 10, 13], L10988 = [1, 2, 3, 4, 5, 14, 15], L10990 = [1, 2, 3, 4, 6, 7, 9], L10995 = [1, 2, 3, 4, 6, 7, 14], L11001 = [1, 2, 3, 4, 6, 8, 14], L11002 = [1, 2, 3, 4, 6, 8, 15], L11008 = [1, 2, 3, 4, 6, 9, 15], L11010 = [1, 2, 3, 4, 6, 10, 12], L11013 = [1, 2, 3, 4, 6, 10, 15], L11016 = [1, 2, 3, 4, 6, 11, 14], L11024 = [1, 2, 3, 4, 7, 8, 10], L11031 = [1, 2, 3, 4, 7, 9, 11], L11036 = [1, 2, 3, 4, 7, 10, 11], L11041 = [1, 2, 3, 4, 7, 11, 13], L11050 = [1, 2, 3, 4, 8, 9, 11], L11057 = [1, 2, 3, 4, 8, 10, 13], L11060 = [1, 2, 3, 4, 8, 11, 12], L11062 = [1, 2, 3, 4, 8, 11, 14], L11065 = [1, 2, 3, 4, 8, 12, 14], L11068 = [1, 2, 3, 4, 9, 10, 12], L11069 = [1, 2, 3, 4, 9, 10, 13], L11073 = [1, 2, 3, 4, 9, 11, 14], L11074 = [1, 2, 3, 4, 9, 11, 15], L11075 = [1, 2, 3, 4, 9, 12, 13], L11085 =
132
EMILIO A. LAURET
[1, 2, 3, 4, 10, 12, 14], L11086 = [1, 2, 3, 4, 10, 12, 15], L11090 = [1, 2, 3, 4, 11, 12, 14], L11101 = [1, 2, 3, 5, 6, 7, 13], L11102 = [1, 2, 3, 5, 6, 7, 14], L11104 = [1, 2, 3, 5, 6, 8, 9], L11107 = [1, 2, 3, 5, 6, 8, 12], L11110 = [1, 2, 3, 5, 6, 8, 15], L11112 = [1, 2, 3, 5, 6, 9, 11], L11115 = [1, 2, 3, 5, 6, 9, 15], L11116 = [1, 2, 3, 5, 6, 10, 11], L11117 = [1, 2, 3, 5, 6, 10, 12], L11120 = [1, 2, 3, 5, 6, 10, 15], L11121 = [1, 2, 3, 5, 6, 11, 12], L11123 = [1, 2, 3, 5, 6, 11, 15], L11124 = [1, 2, 3, 5, 6, 12, 14], L11127 = [1, 2, 3, 5, 6, 13, 15], L11129 = [1, 2, 3, 5, 7, 8, 10], L11131 = [1, 2, 3, 5, 7, 8, 12], L11140 = [1, 2, 3, 5, 7, 10, 13], L11144 = [1, 2, 3, 5, 7, 11, 14], L11148 = [1, 2, 3, 5, 7, 13, 14], L11149 = [1, 2, 3, 5, 7, 13, 15], L11157 = [1, 2, 3, 5, 8, 10, 14], L11168 = [1, 2, 3, 5, 9, 11, 14], L11169 = [1, 2, 3, 5, 9, 11, 15], L11171 = [1, 2, 3, 5, 9, 12, 14], L11176 = [1, 2, 3, 5, 10, 11, 14], L11182 = [1, 2, 3, 5, 11, 12, 13], L11183 = [1, 2, 3, 5, 11, 12, 14], L11184 = [1, 2, 3, 5, 11, 12, 15], L11186 = [1, 2, 3, 5, 11, 13, 15] L11190 = [1, 2, 3, 6, 7, 8, 10], L11191 = [1, 2, 3, 6, 7, 8, 11], L11192 = [1, 2, 3, 6, 7, 8, 12], L11195 = [1, 2, 3, 6, 7, 9, 10], L11196 = [1, 2, 3, 6, 7, 9, 13], L11197 = [1, 2, 3, 6, 7, 9, 14], L11200 = [1, 2, 3, 6, 7, 10, 13], L11203 = [1, 2, 3, 6, 7, 11, 13], L11209 = [1, 2, 3, 6, 8, 9, 10], L11214 = [1, 2, 3, 6, 8, 10, 13], L11217 = [1, 2, 3, 6, 8, 11, 12], L11219 = [1, 2, 3, 6, 8, 11, 15], L11220 = [1, 2, 3, 6, 8, 12, 14], L11231 = [1, 2, 3, 6, 11, 13, 15], L11232 = [1, 2, 3, 7, 8, 9, 10], L11244 = [1, 2, 3, 7, 9, 10, 13], L11250 = [1, 2, 3, 7, 9, 13, 15], L11257 = [1, 2, 3, 7, 11, 13, 14], L11262 = [1, 2, 3, 8, 9, 10, 13], L11263 = [1, 2, 3, 8, 9, 10, 14], L11277 = [1, 2, 3, 8, 11, 12, 15], L11282 = [1, 2, 3, 9, 10, 12, 14], L11289 = [1, 2, 3, 10, 12, 13, 15], L11297 = [1, 2, 4, 5, 7, 9, 15], L11306 = [1, 2, 4, 5, 8, 9, 15], L11308 = [1, 2, 4, 5, 9, 10, 12], L11317 = [1, 2, 4, 5, 11, 12, 15], L11328 = [1, 2, 4, 7, 11, 13, 14], L11332 = [1, 2, 5, 6, 7, 8, 9], L11334 = [1, 2, 5, 6, 7, 8, 11], L11341 = [1, 2, 5, 6, 8, 9, 10], L11360 = [1, 2, 6, 7, 8, 9, 13], L11365 = [1, 2, 6, 7, 8, 13, 14], L11370 = [1, 2, 8, 9, 10, 12, 14]. q = 32 : L47 = [0, 0, 0, 0, 1, 3, 7], L49 = [0, 0, 0, 0, 1, 3, 9], L301 = [0, 0, 0, 1, 2, 7, 9], L307 = [0, 0, 0, 1, 2, 7, 15], L357 = [0, 0, 0, 1, 3, 5, 7], L359 = [0, 0, 0, 1, 3, 5, 9], L362 = [0, 0, 0, 1, 3, 5, 13], L366 = [0, 0, 0, 1, 3, 7, 8], L367 = [0, 0, 0, 1, 3, 7, 9], L371 = [0, 0, 0, 1, 3, 7, 16], L373 = [0, 0, 0, 1, 3, 8, 9], L382 = [0, 0, 0, 1, 3, 9, 16], L480 = [0, 0, 0, 1, 6, 7, 9], L483 = [0, 0, 0, 1, 6, 7, 15], L1151 = [0, 0, 1, 1, 7, 7, 9], L1154 = [0, 0, 1, 1, 7, 7, 15], L1396 = [0, 0, 1, 2, 2, 7, 9], L1402 = [0, 0, 1, 2, 2, 7, 15], L1459 = [0, 0, 1, 2, 3, 5, 10], L1468 = [0, 0, 1, 2, 3, 6, 9], L1503 = [0, 0, 1, 2, 3, 10, 13], L1505 = [0, 0, 1, 2, 3, 10, 15], L1561 = [0, 0, 1, 2, 4, 7, 9], L1567 = [0, 0, 1, 2, 4, 7, 15], L1610 = [0, 0, 1, 2, 5, 6, 11], L1614 = [0, 0, 1, 2, 5, 6, 15], L1652 = [0, 0, 1, 2, 5, 13, 14], L1670 = [0, 0, 1, 2, 6, 7, 9], L1672 = [0, 0, 1, 2, 6, 7, 11], L1675 = [0, 0, 1, 2, 6, 7, 15], L1686 = [0, 0, 1, 2, 6, 9, 11], L1692 = [0, 0, 1, 2, 6, 10, 14], L1708 = [0, 0, 1, 2, 7, 8, 9], L1714 = [0, 0, 1, 2, 7, 8, 15], L1716 = [0, 0, 1, 2, 7, 9, 10], L1718 = [0, 0, 1, 2, 7, 9, 12], L1722 = [0, 0, 1, 2, 7, 9, 16], L1726 = [0, 0, 1, 2, 7, 10, 15], L1734 = [0, 0, 1, 2, 7, 12, 15], L1739 = [0, 0, 1, 2, 7, 15, 16], L1811 = [0, 0, 1, 2, 11, 13, 14], L1855 = [0, 0, 1, 3, 4, 5, 13], L1860 = [0, 0, 1, 3, 4, 7, 9], L1862 = [0, 0, 1, 3, 4, 7, 12], L1877 = [0, 0, 1, 3, 4, 9, 12], L1887 = [0, 0, 1, 3, 4, 11, 13], L1904 = [0, 0, 1, 3, 5, 7, 8], L1905 = [0, 0, 1, 3, 5, 7, 9], L1906 = [0, 0, 1, 3, 5, 7, 11], L1908 = [0, 0, 1, 3, 5, 7, 13], L1909 = [0, 0, 1, 3, 5, 7, 16], L1911 = [0, 0, 1, 3, 5, 8, 9], L1914 = [0, 0, 1, 3, 5, 8, 13], L1918 = [0, 0, 1, 3, 5, 9, 11], L1919 = [0, 0, 1, 3, 5, 9, 16], L1922 = [0, 0, 1, 3, 5, 11, 15], L1925 = [0, 0, 1, 3, 5, 12, 13], L1929 = [0, 0, 1, 3, 5, 13, 15], L1930 = [0, 0, 1, 3, 5, 13, 16], L1936 = [0, 0, 1, 3, 7, 8, 8], L1937 = [0, 0, 1, 3, 7, 8, 9], L1941 = [0, 0, 1, 3, 7, 8, 16], L1943 = [0, 0, 1, 3, 7, 9, 16], L1952 = [0, 0, 1, 3, 7, 16, 16], L1954 = [0, 0, 1, 3, 8, 8, 9], L1963 = [0, 0, 1, 3, 8, 9, 16], L1987 = [0, 0, 1, 3, 9, 16, 16], L2119 = [0, 0, 1, 4, 6, 7, 9], L2122 = [0, 0, 1, 4, 6, 7, 15], L2173 = [0, 0, 1, 4, 8, 12, 16], L2253 = [0, 0, 1, 6, 6, 7, 9], L2256 = [0, 0, 1, 6, 6, 7, 15], L2283 = [0, 0, 1, 6, 7, 8, 9], L2286 = [0, 0, 1, 6, 7, 8, 15], L2289 = [0, 0, 1, 6, 7, 9, 12], L2291 = [0, 0, 1, 6, 7, 9, 16], L2295 = [0, 0, 1, 6, 7, 12, 15], L2297 = [0, 0, 1, 6, 7, 15, 16], L3726 = [0, 1, 1, 2, 6, 10, 14], L4694 = [0, 1, 1, 4, 7, 7, 9], L4697 = [0, 1, 1, 4, 7, 7, 15], L4773 = [0, 1, 1, 4, 8, 12, 16], L5417 = [0, 1, 1, 7, 7, 8, 9], L5420 = [0, 1, 1, 7, 7, 8, 15], L5423 = [0, 1, 1, 7, 7, 9, 12], L5426 = [0, 1, 1, 7, 7, 9, 16], L5429 = [0, 1, 1, 7, 7, 12, 15], L5433 = [0, 1, 1, 7, 7, 15, 16], L5970 = [0, 1, 2, 2, 2, 7, 9], L5976 = [0, 1, 2, 2, 2, 7, 15], L6137 = [0, 1, 2, 2, 4, 7, 9], L6143 = [0, 1, 2, 2, 4, 7, 15], L6254 = [0, 1, 2, 2, 6, 7, 9], L6260 = [0, 1, 2, 2, 6, 7, 15], L6281 = [0, 1, 2, 2, 6, 10, 14], L6301 = [0, 1, 2, 2, 7, 8, 9], L6307 = [0, 1, 2, 2, 7, 8, 15], L6309 = [0, 1, 2, 2, 7, 9, 10], L6311 = [0, 1, 2, 2, 7, 9, 12], L6313 = [0, 1, 2, 2, 7, 9, 14], L6315 = [0, 1, 2, 2, 7, 9, 16], L6321 = [0, 1, 2, 2, 7, 10, 15], L6330 = [0, 1, 2, 2, 7, 12, 15], L6335 = [0, 1, 2, 2, 7, 14, 15], L6337 = [0, 1, 2, 2, 7, 15, 16], L6553 = [0, 1, 2, 3, 5, 8, 10], L6560 = [0, 1, 2, 3, 5, 9, 10], L6572 = [0, 1, 2, 3, 5, 10, 16], L6593 = [0, 1, 2, 3, 6, 7, 10], L6596 = [0, 1, 2, 3, 6, 7, 14], L6600 = [0, 1, 2, 3, 6, 8, 9], L6608 = [0, 1, 2, 3, 6, 9, 10], L6609 = [0, 1, 2, 3, 6, 9, 11], L6611 = [0, 1, 2, 3, 6, 9, 14], L6612 = [0, 1, 2, 3, 6, 9, 16],
APPENDIX
133
Table 5. (continued) n = 7 q I indexes of I-isospectral families 32 {0} {47, 49}, {301, 307}, {357, 359}, {366, 373}, {371, 382}, {480, 483}, {1151, 1154}, {1396, 1402}, {1459, 1468}, {1503, 1614}, {1505, 1610}, {1561, 1567}, {1652, 1811}, {1670, 1675}, {1672, 1686}, {1708, 1714}, {1716, 1726}, {1718, 1734}, {1722, 1739}, {1862, 1877}, {1904, 1911}, {1905, 1906, 1908, 1918}, {1909, 1919}, {1922, 1929}, {1936, 1954}, {1941, 1963}, {1952, 1987}, {2119, 2122}, {2253, 2256}, {2283, 2286}, {2289, 2295}, {2291, 2297}, {4694, 4697}, {5417, 5420}, {5423, 5429}, {5426, 5433}, {5970, 5976}, {6137, 6143}, {6254, 6260}, {6301, 6307}, {6309, 6321}, {6311, 6330}, {6313, 6335}, {6315, 6337}, {6553, 6600}, {6560, 6609}, {6572, 6612}, {6593, 6611}, {6596, 6608}, {6620, 6646}, {6621, 6656}, {6657, 7151}, {6693, 7139}, {6695, 7135}, {6718, 7141}, {6729, 6993}, {6749, 7153}, {6750, 7163}, {6754, 7154}, {6829, 6835}, {6940, 6945}, {6984, 6990}, {6992, 7002}, {6994, 7010}, {6998, 7015}, {7221, 7587}, {7270, 7685}, {7290, 7295}, {7328, 7333}, {7330, 7365}, {7335, 7344}, {7337, 7350}, {7338, 7352}, {7340, 7354}, {7347, 7391}, {7434, 7440}, {7442, 7452}, {7444, 7460}, {7448, 7465}, {7467, 7488}, {7468, 7492}, {7471, 7495}, {7475, 7505}, {7479, 7510}, {7484, 7515}, {7794, 7795}, {7796, 7809}, {7797, 7798, 7808, 7810}, {7813, 7840}, {7815, 7823, 7839, 7850}, {7833, 7865}, {7849, 7901}, {7897, 7898}, {7956, 7972}, {7957, 7958, 7960, 7979}, {7961, 7980}, {7965, 7966, 7969, 7997}, {7970, 7998}, {7983, 7990}, {8005, 8019}, {8028, 8065}, {8033, 8074}, {8044, 8098}, {8063, 8149}, {8324, 8327}, {8481, 8484}, {8511, 8514}, {8517, 8523}, {8519, 8525}, {8782, 8785}, {8812, 8815}, {8817, 8823}, {8818, 8826}, {8820, 8828}, {8890, 8893}, {8896, 8902}, {8898, 8904}, {8909, 8918}, {8911, 8920}, {8913, 8922}, {15363, 15386}, {18131, 18134}, {18871, 18874}, {18877, 18883}, {18880, 18887}, {20496, 20503}, {21004, 21007}, {21010, 21016}, {21013, 21020}, {21025, 21035}, {21028, 21039}, {21032, 21043}, {22166, 22172}, {22333, 22339}, {22451, 22457}, {22498, 22504}, {22506, 22518}, {22508, 22527}, {22510, 22532}, {22512, 22534}, {23056, 23062}, {23174, 23180}, {23221, 23227}, {23229, 23241}, {23231, 23250}, {23233, 23255}, {23235, 23257}, {23594, 23599}, {23633, 23639}, {23641, 23653}, {23643, 23662}, {23645, 23667}, {23647, 23669}, {23754, 24707}, {23782, 23788}, {23790, 23802}, {23792, 23811}, {23794, 23816}, {23796, 23818}, {23820, 23847}, {23822, 23856}, {23824, 23860}, {23826, 23862}, {23831, 23875}, {23833, 23880}, {23835, 23882}, {23840, 23888}, {23842, 23890}, {24258, 24301}, {24260, 24307}, {24348, 24498}, {24415, 24531}, {24419, 24569}, {24441, 25540, 25552}, {24445, 25570}, {24447, 25562}, {24500, 24512, 24515}, {24501, 24513, 24516}, {24525, 24641}, {24527, 24535, 24643, 24650}, {24534, 24703}, {24551, 24558}, {24560, 24623, 24704}, {24561, 24622, 24708}, {24573, 24627}, {24576, 24637}, {24582, 24725}, {24589, 24734}, L6616 = [0, 1, 2, 3, 6, 10, 14], L6620 = [0, 1, 2, 3, 6, 11, 13], L6621 = [0, 1, 2, 3, 6, 11, 14], L6646 = [0, 1, 2, 3, 7, 9, 10], L6656 = [0, 1, 2, 3, 7, 10, 14], L6657 = [0, 1, 2, 3, 7, 10, 15], L6693 = [0, 1, 2, 3, 8, 10, 13],
134
EMILIO A. LAURET
Table 5. (continued) n = 7 q I indexes of I-isospectral families 32 {0} {24601, 24737}, {24620, 25555}, {24621, 24766}, {24624, 24767}, (cont.) {24646, 24792}, {24649, 24796}, {24656, 24771}, {24697, 24736}, {24700, 24733}, {24709, 24793, 25559}, {24712, 24770}, {24721, 24765}, {24745, 24837}, {24746, 24847}, {24797, 24871}, {24800, 24903}, {24848, 26258}, {24867, 26233}, {24868, 24900, 26222, 26229}, {24870, 26224}, {24904, 26291}, {24951, 26246}, {24953, 26242}, {24976, 26248}, {24987, 25884}, {25007, 26260}, {25008, 26270}, {25012, 26261}, {25065, 26273}, {25088, 25915}, {25131, 26295}, {25132, 26312}, {25138, 26296}, {25239, 25245}, {25350, 25355}, {25395, 25401}, {25403, 25413}, {25405, 25421}, {25409, 25426}, {25652, 26354}, {25686, 26120}, {25714, 25719}, {25752, 25757}, {25759, 25768}, {25761, 25774}, {25762, 25776}, {25764, 25778}, {25770, 25820}, {25875, 25881}, {25883, 25893}, {25885, 25901}, {25889, 25906}, {25908, 25929}, {25909, 25933}, {25912, 25936}, {25916, 25946}, {25920, 25951}, {25925, 25956}, {26405, 27164}, {26454, 27262}, {26533, 27428}, {26555, 26560}, {26593, 26598}, {26600, 26609}, {26602, 26615}, {26603, 26617}, {26605, 26619}, {26700, 26705}, {26702, 26778}, {26707, 26716}, {26709, 26722}, {26710, 26724}, {26712, 26726}, {26719, 26804}, {26728, 26745}, {26729, 26749}, {26732, 26752}, {26735, 26759}, {26736, 26761}, {26738, 26763}, {26740, 26765}, {26742, 26767}, {26756, 26856}, {26930, 26936}, {26938, 26948}, {26940, 26956}, {26944, 26961}, {26963, 26984}, {26964, 26988}, {26967, 26991}, {26971, 27001}, {26975, 27006}, {26980, 27011}, {27013, 27048}, {27014, 27052}, {27017, 27055}, {27018, 27059}, {27021, 27062}, {27024, 27065}, {27030, 27077}, {27034, 27082}, {27039, 27087}, {27044, 27092}, {27554, 27555}, {27557, 27558, 27568, 27570}, {27573, 27600},
L6695 = [0, 1, 2, 3, 8, 10, 15], L6718 = [0, 1, 2, 3, 9, 10, 14], L6729 = [0, 1, 2, 3, 9, 12, 15], L6749 = [0, 1, 2, 3, 10, 13, 15], L6750 = [0, 1, 2, 3, 10, 13, 16], L6754 = [0, 1, 2, 3, 10, 15, 16], L6829 = [0, 1, 2, 4, 4, 7, 9], L6835 = [0, 1, 2, 4, 4, 7, 15], L6940 = [0, 1, 2, 4, 6, 7, 9], L6945 = [0, 1, 2, 4, 6, 7, 15], L6965 = [0, 1, 2, 4, 6, 10, 14], L6984 = [0, 1, 2, 4, 7, 8, 9], L6990 = [0, 1, 2, 4, 7, 8, 15], L6992 = [0, 1, 2, 4, 7, 9, 10], L6993 = [0, 1, 2, 4, 7, 9, 11], L6994 = [0, 1, 2, 4, 7, 9, 12], L6998 = [0, 1, 2, 4, 7, 9, 16], L7002 = [0, 1, 2, 4, 7, 10, 15], L7010 = [0, 1, 2, 4, 7, 12, 15], L7015 = [0, 1, 2, 4, 7, 15, 16], L7045 = [0, 1, 2, 4, 8, 12, 16], L7135 = [0, 1, 2, 5, 6, 8, 11], L7139 = [0, 1, 2, 5, 6, 8, 15], L7141 = [0, 1, 2, 5, 6, 9, 10], L7148 = [0, 1, 2, 5, 6, 10, 14], L7151 = [0, 1, 2, 5, 6, 11, 13], L7153 = [0, 1, 2, 5, 6, 11, 15], L7154 = [0, 1, 2, 5, 6, 11, 16], L7163 = [0, 1, 2, 5, 6, 15, 16], L7221 = [0, 1, 2, 5, 8, 13, 14], L7270 = [0, 1, 2, 5, 13, 14, 16], L7290 = [0, 1, 2, 6, 6, 7, 9], L7295 = [0, 1, 2, 6, 6, 7, 15], L7312 = [0, 1, 2, 6, 6, 10, 14], L7328 = [0, 1, 2, 6, 7, 8, 9], L7330 = [0, 1, 2, 6, 7, 8, 11], L7333 = [0, 1, 2, 6, 7, 8, 15], L7335 = [0, 1, 2, 6, 7, 9, 10], L7337 = [0, 1, 2, 6, 7, 9, 12], L7338 = [0, 1, 2, 6, 7, 9, 14], L7340 = [0, 1, 2, 6, 7, 9, 16], L7343 = [0, 1, 2, 6, 7, 10, 14], L7344 = [0, 1, 2, 6, 7, 10, 15], L7347 = [0, 1, 2, 6, 7, 11, 16], L7350 = [0, 1, 2, 6, 7, 12, 15], L7352 = [0, 1, 2, 6, 7, 14, 15], L7354 = [0, 1, 2, 6, 7, 15, 16], L7365 = [0, 1, 2, 6, 8, 9, 11], L7371 = [0, 1, 2, 6, 8, 10, 14], L7391 = [0, 1, 2, 6, 9, 11, 16], L7399 = [0, 1, 2, 6, 10, 10, 14], L7403 = [0, 1, 2, 6, 10, 12, 14], L7406 = [0, 1, 2, 6, 10, 14, 14], L7407 = [0, 1, 2, 6, 10, 14, 15], L7408 = [0, 1, 2, 6, 10, 14, 16], L7434 = [0, 1, 2, 7, 8, 8, 9], L7440 = [0, 1, 2, 7, 8, 8, 15], L7442 = [0, 1, 2, 7, 8, 9, 10], L7444 = [0, 1, 2, 7, 8, 9, 12],
APPENDIX
135
Table 5. (continued) n = 7 q I indexes of I-isospectral families 32 {0} {27575, 27583, 27599, 27611}, {27607, 27663}, {27660, 27661}, (cont.) {27726, 27727}, {27728, 27756}, {27729, 27730, 27755, 27757}, {27733, 27737, 27741, 27777}, {27736, 27739}, {27742, 27780}, {27744, 27745, 27779, 27781}, {27760, 27829}, {27762, 27770, 27828, 27839}, {27785, 27800}, {27789, 27851}, {27793, 27810, 27850, 27870}, {27822, 27885}, {27838, 27921}, {27869, 27990}, {27917, 27918}, {27986, 27987}, {28089, 28116}, {28090, 28091, 28093, 28123}, {28094, 28124}, {28098, 28099, 28102, 28141}, {28103, 28142}, {28108, 28109, 28113, 28172}, {28114, 28173}, {28127, 28134}, {28149, 28163}, {28184, 28207}, {28218, 28284}, {28223, 28293}, {28234, 28317}, {28253, 28368}, {28282, 28462}, {28698, 28701}, {28864, 28867}, {28894, 28897}, {28900, 28906}, {28902, 28908}, {29211, 29214}, {29241, 29244}, {29246, 29252}, {29247, 29255}, {29249, 29257}, {29319, 29322}, {29325, 29331}, {29327, 29333}, {29338, 29347}, {29340, 29349}, {29342, 29351}, {29811, 29814}, {29841, 29844}, {29846, 29852}, {29847, 29855}, {29849, 29857}, {29920, 29923}, {29925, 29931}, {29926, 29934}, {29928, 29936}, {29939, 29950}, {29941, 29952}, {29942, 29955}, {29944, 29957}, {29946, 29959}, {30083, 30086}, {30089, 30095}, {30091, 30097}, {30102, 30111}, {30104, 30113}, {30106, 30115}, {30122, 30134}, {30124, 30136}, {30126, 30138}, {30128, 30140} L7448 = [0, 1, 2, 7, 8, 9, 16], L7452 = [0, 1, 2, 7, 8, 10, 15], L7460 = [0, 1, 2, 7, 8, 12, 15], L7465 = [0, 1, 2, 7, 8, 15, 16], L7467 = [0, 1, 2, 7, 9, 10, 10], L7468 = [0, 1, 2, 7, 9, 10, 12], L7471 = [0, 1, 2, 7, 9, 10, 16], L7475 = [0, 1, 2, 7, 9, 12, 12], L7479 = [0, 1, 2, 7, 9, 12, 16], L7484 = [0, 1, 2, 7, 9, 16, 16], L7488 = [0, 1, 2, 7, 10, 10, 15], L7492 = [0, 1, 2, 7, 10, 12, 15], L7495 = [0, 1, 2, 7, 10, 15, 16], L7505 = [0, 1, 2, 7, 12, 12, 15], L7510 = [0, 1, 2, 7, 12, 15, 16], L7515 = [0, 1, 2, 7, 15, 16, 16], L7587 = [0, 1, 2, 8, 11, 13, 14], L7685 = [0, 1, 2, 11, 13, 14, 16], L7743 = [0, 1, 3, 4, 4, 5, 13], L7748 = [0, 1, 3, 4, 4, 7, 9], L7776 = [0, 1, 3, 4, 4, 11, 13], L7794 = [0, 1, 3, 4, 5, 7, 9], L7795 = [0, 1, 3, 4, 5, 7, 11], L7796 = [0, 1, 3, 4, 5, 7, 12], L7797 = [0, 1, 3, 4, 5, 7, 13], L7798 = [0, 1, 3, 4, 5, 7, 15], L7804 = [0, 1, 3, 4, 5, 8, 13], L7808 = [0, 1, 3, 4, 5, 9, 11], L7809 = [0, 1, 3, 4, 5, 9, 12], L7810 = [0, 1, 3, 4, 5, 9, 15], L7813 = [0, 1, 3, 4, 5, 11, 13], L7815 = [0, 1, 3, 4, 5, 11, 15], L7818 = [0, 1, 3, 4, 5, 12, 13], L7823 = [0, 1, 3, 4, 5, 13, 15], L7824 = [0, 1, 3, 4, 5, 13, 16], L7831 = [0, 1, 3, 4, 7, 8, 9], L7833 = [0, 1, 3, 4, 7, 8, 12], L7838 = [0, 1, 3, 4, 7, 9, 12], L7839 = [0, 1, 3, 4, 7, 9, 13], L7840 = [0, 1, 3, 4, 7, 9, 15], L7841 = [0, 1, 3, 4, 7, 9, 16], L7849 = [0, 1, 3, 4, 7, 12, 16], L7850 = [0, 1, 3, 4, 7, 13, 15], L7865 = [0, 1, 3, 4, 8, 9, 12], L7875 = [0, 1, 3, 4, 8, 11, 13], L7883 = [0, 1, 3, 4, 8, 12, 16], L7897 = [0, 1, 3, 4, 9, 11, 13], L7898 = [0, 1, 3, 4, 9, 11, 15], L7901 = [0, 1, 3, 4, 9, 12, 16], L7925 = [0, 1, 3, 4, 11, 13, 16], L7956 = [0, 1, 3, 5, 7, 8, 8], L7957 = [0, 1, 3, 5, 7, 8, 9], L7958 = [0, 1, 3, 5, 7, 8, 11], L7960 = [0, 1, 3, 5, 7, 8, 13], L7961 = [0, 1, 3, 5, 7, 8, 16], L7962 = [0, 1, 3, 5, 7, 9, 11], L7963 = [0, 1, 3, 5, 7, 9, 13], L7965 = [0, 1, 3, 5, 7, 9, 16], L7966 = [0, 1, 3, 5, 7, 11, 16], L7969 = [0, 1, 3, 5, 7, 13, 16], L7970 = [0, 1, 3, 5, 7, 16, 16], L7972 = [0, 1, 3, 5, 8, 8, 9], L7975 = [0, 1, 3, 5, 8, 8, 13], L7979 = [0, 1, 3, 5, 8, 9, 11], L7980 = [0, 1, 3, 5, 8, 9, 16], L7983 = [0, 1, 3, 5, 8, 11, 15], L7986 = [0, 1, 3, 5, 8, 12, 13], L7990 = [0, 1, 3, 5, 8, 13, 15], L7991 = [0, 1, 3, 5, 8, 13, 16], L7997 = [0, 1, 3, 5, 9, 11, 16], L7998 = [0, 1, 3, 5, 9, 16, 16], L8005 = [0, 1, 3, 5, 11, 15, 16], L8008 = [0, 1, 3, 5, 12, 12, 13], L8012 = [0, 1, 3, 5, 12, 13, 16], L8019 = [0, 1, 3, 5, 13, 15, 16], L8020 = [0, 1, 3, 5, 13, 16, 16], L8028 = [0, 1, 3, 7, 8, 8, 8], L8029 = [0, 1, 3, 7, 8, 8, 9], L8033 = [0, 1, 3, 7, 8, 8, 16], L8035 = [0, 1, 3, 7, 8, 9, 16], L8044 = [0, 1, 3, 7, 8, 16, 16], L8047 = [0, 1, 3, 7, 9, 16, 16], L8063 =
136
EMILIO A. LAURET
Table 5. (continued) n = 7 q 32 (cont.)
I {0, 1}
indexes of I-isospectral families {362, 367}, {1855, 1860}, {1887, 1925}, {1906, 1908}, {1914, 1937}, {1930, 1943}, {7743, 7748}, {7776, 8008}, {7804, 7831}, {7818, 7838}, {7824, 7841}, {7875, 7986}, {7925, 8012}, {7958, 7960}, {7962, 7963}, {7966, 7969}, {7975, 8029}, {7991, 8035}, {8020, 8047}, {24500, 24512}, {24538, 24653}, {24561, 24708}, {27503, 27508}, {27536, 28187}, {27564, 27591}, {27578, 27598}, {27584, 27601}, {27637, 28152}, {27689, 27796}, {27694, 28191}, {27732, 27734}, {27735, 27738}, {27737, 27741}, {27743, 27778}, {27751, 27820}, {27765, 27827}, {27771, 27830}, {27788, 27849}, {27801, 27848}, {27811, 27852}, {27895, 28130}, {27945, 28156}, {28040, 28197}, {28091, 28093}, {28095, 28096}, {28099, 28102}, {28105, 28106}, {28109, 28113}, {28119, 28219}, {28135, 28225}, {28164, 28237}, {28208, 28257} {0, 1, 2} {24763, 24799} {6} {1692, 7408, 26891}, {2173, 8651}, {3726, 7407, 15299, 26890}, {4773, 8650}, {6281, 7406, 23747, 26889}, {6616, 7148, 24788, 26285}, {6965, 7403, 25844, 26884}, {7045, 8649}, {7312, 7399, 26674, 26875}, {7343, 26751}, {7371, 26821}, {7883, 8455}, {8379, 8646}, {8544, 8635}, {10518, 15298}, {13524, 15297, 23746, 26888}, {14060, 15294, 24787}, {14508, 15291, 25843, 26883}, {14847, 15286, 24783}, {15124, 15281, 26673, 26874}, {15177, 15255, 26730}, {15221, 26820}, {22478, 23745, 26887}, {22832, 23743, 24786, 26198}, {23201, 23740, 25842, 26882}, {23408, 23736, 24775, 26284}, {23617, 23731, 26672, 26873}, {23652, 23713}, {23690, 26819}, {24310, 24780, 25560, 25840}, {24521, 24710, 24764, 26226}, {24741, 26255}, {25375, 25837, 26879}, {25736, 25833, 26669, 26870}, {25767, 26748}, {25798, 26816}, {26577, 26665, 26866}, {26608, 26653}, {26636, 26812} {2, 3, 6} {8594, 29490}, {28977, 29488} {0, 5, 6} {24710, 24764}
[0, 1, 3, 7, 16, 16, 16], L8065 = [0, 1, 3, 8, 8, 8, 9], L8074 = [0, 1, 3, 8, 8, 9, 16], L8098 = [0, 1, 3, 8, 9, 16, 16], L8149 = [0, 1, 3, 9, 16, 16, 16], L8324 = [0, 1, 4, 4, 6, 7, 9], L8327 = [0, 1, 4, 4, 6, 7, 15], L8379 = [0, 1, 4, 4, 8, 12, 16], L8455 = [0, 1, 4, 5, 8, 12, 16], L8481 = [0, 1, 4, 6, 6, 7, 9], L8484 = [0, 1, 4, 6, 6, 7, 15], L8511 = [0, 1, 4, 6, 7, 8, 9], L8514 = [0, 1, 4, 6, 7, 8, 15], L8517 = [0, 1, 4, 6, 7, 9, 12], L8519 = [0, 1, 4, 6, 7, 9, 16], L8523 = [0, 1, 4, 6, 7, 12, 15], L8525 = [0, 1, 4, 6, 7, 15, 16], L8544 = [0, 1, 4, 6, 8, 12, 16], L8594 = [0, 1, 4, 7, 9, 12, 15], L8635 = [0, 1, 4, 8, 10, 12, 16], L8646 = [0, 1, 4, 8, 12, 12, 16], L8649 = [0, 1, 4, 8, 12, 14, 16], L8650 = [0, 1, 4, 8, 12, 15, 16], L8651 = [0, 1, 4, 8, 12, 16, 16], L8782 = [0, 1, 6, 6, 6, 7, 9], L8785 = [0, 1, 6, 6, 6, 7, 15], L8812 = [0, 1, 6, 6, 7, 8, 9], L8815 = [0, 1, 6, 6, 7, 8, 15], L8817 = [0, 1, 6, 6, 7, 9, 10], L8818 = [0, 1, 6, 6, 7, 9, 12], L8820 = [0, 1, 6, 6, 7, 9, 16], L8823 = [0, 1, 6, 6, 7, 10, 15], L8826 = [0, 1, 6, 6, 7, 12, 15], L8828 = [0, 1, 6, 6, 7, 15, 16], L8890 = [0, 1, 6, 7, 8, 8, 9], L8893 = [0, 1, 6, 7, 8, 8, 15], L8896 = [0, 1, 6, 7, 8, 9, 12], L8898 = [0, 1, 6, 7, 8, 9, 16], L8902 = [0, 1, 6, 7, 8, 12, 15], L8904 = [0, 1, 6, 7, 8, 15, 16], L8909 = [0, 1, 6, 7, 9, 12, 12], L8911 = [0, 1, 6, 7, 9, 12, 16], L8913 = [0, 1, 6, 7, 9, 16, 16], L8918 = [0, 1, 6, 7, 12, 12, 15], L8920 = [0, 1, 6, 7, 12, 15, 16], L8922 = [0, 1, 6, 7, 15, 16, 16], L10518 = [1, 1, 1, 2, 6, 10, 14], L13524 = [1, 1, 2, 2, 6, 10, 14], L14060 = [1, 1, 2, 3, 6, 10, 14], L14508 = [1, 1, 2, 4, 6, 10, 14], L14847 = [1, 1, 2, 5, 6, 10, 14], L15124 = [1, 1, 2, 6, 6, 10, 14], L15177 = [1, 1, 2, 6, 7, 10, 14], L15221 = [1, 1, 2, 6, 8, 10, 14], L15255 = [1, 1, 2, 6, 9, 10, 14], L15281 = [1, 1, 2, 6, 10, 10, 14], L15286 = [1, 1, 2, 6, 10, 11, 14], L15291 = [1, 1, 2, 6, 10, 12, 14], L15294 = [1, 1, 2, 6, 10, 13, 14]
APPENDIX
137
L15297 = [1, 1, 2, 6, 10, 14, 14], L15298 = [1, 1, 2, 6, 10, 14, 15], L15299 = [1, 1, 2, 6, 10, 14, 16], L15363 = [1, 1, 2, 7, 7, 9, 14], L15386 = [1, 1, 2, 7, 7, 14, 15], L18131 = [1, 1, 4, 4, 7, 7, 9], L18134 = [1, 1, 4, 4, 7, 7, 15], L18871 = [1, 1, 4, 7, 7, 8, 9], L18874 = [1, 1, 4, 7, 7, 8, 15], L18877 = [1, 1, 4, 7, 7, 9, 12], L18880 = [1, 1, 4, 7, 7, 9, 16], L18883 = [1, 1, 4, 7, 7, 12, 15], L18887 = [1, 1, 4, 7, 7, 15, 16], L20496 = [1, 1, 6, 7, 7, 9, 10], L20503 = [1, 1, 6, 7, 7, 10, 15], L21004 = [1, 1, 7, 7, 8, 8, 9], L21007 = [1, 1, 7, 7, 8, 8, 15], L21010 = [1, 1, 7, 7, 8, 9, 12], L21013 = [1, 1, 7, 7, 8, 9, 16], L21016 = [1, 1, 7, 7, 8, 12, 15], L21020 = [1, 1, 7, 7, 8, 15, 16], L21025 = [1, 1, 7, 7, 9, 12, 12], L21028 = [1, 1, 7, 7, 9, 12, 16], L21032 = [1, 1, 7, 7, 9, 16, 16], L21035 = [1, 1, 7, 7, 12, 12, 15], L21039 = [1, 1, 7, 7, 12, 15, 16], L21043 = [1, 1, 7, 7, 15, 16, 16], L22166 = [1, 2, 2, 2, 2, 7, 9], L22172 = [1, 2, 2, 2, 2, 7, 15], L22333 = [1, 2, 2, 2, 4, 7, 9], L22339 = [1, 2, 2, 2, 4, 7, 15], L22451 = [1, 2, 2, 2, 6, 7, 9], L22457 = [1, 2, 2, 2, 6, 7, 15], L22478 = [1, 2, 2, 2, 6, 10, 14], L22498 = [1, 2, 2, 2, 7, 8, 9], L22504 = [1, 2, 2, 2, 7, 8, 15], L22506 = [1, 2, 2, 2, 7, 9, 10], L22508 = [1, 2, 2, 2, 7, 9, 12], L22510 = [1, 2, 2, 2, 7, 9, 14], L22512 = [1, 2, 2, 2, 7, 9, 16], L22518 = [1, 2, 2, 2, 7, 10, 15], L22527 = [1, 2, 2, 2, 7, 12, 15], L22532 = [1, 2, 2, 2, 7, 14, 15], L22534 = [1, 2, 2, 2, 7, 15, 16], L22832 = [1, 2, 2, 3, 6, 10, 14], L23056 = [1, 2, 2, 4, 4, 7, 9], L23062 = [1, 2, 2, 4, 4, 7, 15], L23174 = [1, 2, 2, 4, 6, 7, 9], L23180 = [1, 2, 2, 4, 6, 7, 15], L23201 = [1, 2, 2, 4, 6, 10, 14], L23221 = [1, 2, 2, 4, 7, 8, 9], L23227 = [1, 2, 2, 4, 7, 8, 15], L23229 = [1, 2, 2, 4, 7, 9, 10], L23231 = [1, 2, 2, 4, 7, 9, 12], L23233 = [1, 2, 2, 4, 7, 9, 14], L23235 = [1, 2, 2, 4, 7, 9, 16], L23241 = [1, 2, 2, 4, 7, 10, 15], L23250 = [1, 2, 2, 4, 7, 12, 15], L23255 = [1, 2, 2, 4, 7, 14, 15], L23257 = [1, 2, 2, 4, 7, 15, 16], L23408 = [1, 2, 2, 5, 6, 10, 14], L23594 = [1, 2, 2, 6, 6, 7, 9], L23599 = [1, 2, 2, 6, 6, 7, 15], L23617 = [1, 2, 2, 6, 6, 10, 14], L23633 = [1, 2, 2, 6, 7, 8, 9], L23639 = [1, 2, 2, 6, 7, 8, 15], L23641 = [1, 2, 2, 6, 7, 9, 10], L23643 = [1, 2, 2, 6, 7, 9, 12], L23645 = [1, 2, 2, 6, 7, 9, 14], L23647 = [1, 2, 2, 6, 7, 9, 16], L23652 = [1, 2, 2, 6, 7, 10, 14], L23653 = [1, 2, 2, 6, 7, 10, 15], L23662 = [1, 2, 2, 6, 7, 12, 15], L23667 = [1, 2, 2, 6, 7, 14, 15], L23669 = [1, 2, 2, 6, 7, 15, 16], L23690 = [1, 2, 2, 6, 8, 10, 14], L23713 = [1, 2, 2, 6, 9, 10, 14], L23731 = [1, 2, 2, 6, 10, 10, 14], L23736 = [1, 2, 2, 6, 10, 11, 14], L23740 = [1, 2, 2, 6, 10, 12, 14], L23743 = [1, 2, 2, 6, 10, 13, 14], L23745 = [1, 2, 2, 6, 10, 14, 14], L23746 = [1, 2, 2, 6, 10, 14, 15], L23747 = [1, 2, 2, 6, 10, 14, 16] L23754 = [1, 2, 2, 6, 11, 13, 14], L23782 = [1, 2, 2, 7, 8, 8, 9], L23788 = [1, 2, 2, 7, 8, 8, 15], L23790 = [1, 2, 2, 7, 8, 9, 10], L23792 = [1, 2, 2, 7, 8, 9, 12], L23794 = [1, 2, 2, 7, 8, 9, 14], L23796 = [1, 2, 2, 7, 8, 9, 16], L23802 = [1, 2, 2, 7, 8, 10, 15], L23811 = [1, 2, 2, 7, 8, 12, 15], L23816 = [1, 2, 2, 7, 8, 14, 15], L23818 = [1, 2, 2, 7, 8, 15, 16], L23820 = [1, 2, 2, 7, 9, 10, 10], L23822 = [1, 2, 2, 7, 9, 10, 12], L23824 = [1, 2, 2, 7, 9, 10, 14], L23826 = [1, 2, 2, 7, 9, 10, 16], L23831 = [1, 2, 2, 7, 9, 12, 12], L23833 = [1, 2, 2, 7, 9, 12, 14], L23835 = [1, 2, 2, 7, 9, 12, 16], L23840 = [1, 2, 2, 7, 9, 14, 16], L23842 = [1, 2, 2, 7, 9, 16, 16], L23847 = [1, 2, 2, 7, 10, 10, 15], L23856 = [1, 2, 2, 7, 10, 12, 15], L23860 = [1, 2, 2, 7, 10, 14, 15], L23862 = [1, 2, 2, 7, 10, 15, 16], L23875 = [1, 2, 2, 7, 12, 12, 15], L23880 = [1, 2, 2, 7, 12, 14, 15], L23882 = [1, 2, 2, 7, 12, 15, 16], L23888 = [1, 2, 2, 7, 14, 15, 16] L23890 = [1, 2, 2, 7, 15, 16, 16], L24258 = [1, 2, 3, 4, 5, 10, 12], L24260 = [1, 2, 3, 4, 5, 10, 14], L24301 = [1, 2, 3, 4, 6, 9, 12], L24307 = [1, 2, 3, 4, 6, 10, 11], L24310 = [1, 2, 3, 4, 6, 10, 14], L24348 = [1, 2, 3, 4, 7, 10, 11], L24415 = [1, 2, 3, 4, 9, 10, 14], L24419 = [1, 2, 3, 4, 9, 11, 13], L24441 = [1, 2, 3, 4, 10, 11, 14], L24445 = [1, 2, 3, 4, 10, 12, 13], L24447 = [1, 2, 3, 4, 10, 12, 15], L24498 = [1, 2, 3, 5, 6, 7, 12], L24500 = [1, 2, 3, 5, 6, 7, 14], L24501 = [1, 2, 3, 5, 6, 7, 15], L24512 = [1, 2, 3, 5, 6, 9, 10], L24513 = [1, 2, 3, 5, 6, 9, 11], L24515 = [1, 2, 3, 5, 6, 9, 14], L24516 = [1, 2, 3, 5, 6, 9, 15], L24521 = [1, 2, 3, 5, 6, 10, 14], L24525 = [1, 2, 3, 5, 6, 11, 13], L24527 = [1, 2, 3, 5, 6, 11, 15], L24531 = [1, 2, 3, 5, 6, 12, 14], L24534 = [1, 2, 3, 5, 6, 13, 14], L24535 = [1, 2, 3, 5, 6, 13, 15], L24538 = [1, 2, 3, 5, 6, 14, 15], L24551 = [1, 2, 3, 5, 7, 9, 10], L24558 = [1, 2, 3, 5, 7, 10, 11], L24560 = [1, 2, 3, 5, 7, 10, 13], L24561 = [1, 2, 3, 5, 7, 10, 14], L24569 = [1, 2, 3, 5, 7, 12, 13], L24573 = [1, 2, 3, 5, 7, 13, 14], L24576 = [1, 2, 3, 5, 7, 14, 15], L24582 = [1, 2, 3, 5, 8, 8, 10], L24589 = [1, 2, 3, 5, 8, 9, 10], L24601 = [1, 2, 3, 5, 8, 10, 16], L24620 = [1, 2, 3, 5, 9, 10, 12], L24621 = [1, 2, 3, 5, 9, 10, 13], L24622 = [1, 2, 3, 5, 9, 10, 14], L24623 = [1, 2, 3, 5, 9, 10, 15], L24624 = [1, 2, 3, 5, 9, 10, 16], L24627 = [1, 2, 3, 5, 9, 11, 14], L24637 = [1, 2, 3, 5, 9, 14, 15], L24641 = [1, 2, 3, 5, 10, 11, 13], L24643 = [1, 2, 3, 5, 10, 11, 15], L24646 = [1, 2, 3, 5, 10, 12, 13], L24649 = [1, 2, 3, 5, 10, 13, 14], L24650 = [1, 2, 3, 5, 10, 13, 15], L24653 = [1, 2, 3, 5, 10, 14, 15] L24656 = [1, 2, 3, 5, 10, 16, 16], L24697 = [1, 2, 3, 6, 7, 8, 10], L24700 = [1, 2, 3, 6, 7, 8, 14], L24703 = [1, 2, 3, 6, 7, 9, 10], L24704 = [1, 2, 3, 6, 7, 9, 11], L24707 = [1, 2, 3, 6, 7, 10, 10], L24708 = [1, 2, 3, 6, 7, 10, 11], L24709 = [1, 2, 3, 6, 7, 10, 12], L24710 = [1, 2, 3, 6, 7, 10, 14], L24712 = [1, 2, 3, 6, 7, 10, 16], L24721 =
138
EMILIO A. LAURET
[1, 2, 3, 6, 7, 14, 16], L24725 = [1, 2, 3, 6, 8, 8, 9], L24733 = [1, 2, 3, 6, 8, 9, 10], L24734 = [1, 2, 3, 6, 8, 9, 11], L24736 = [1, 2, 3, 6, 8, 9, 14], L24737 = [1, 2, 3, 6, 8, 9, 16], L24741 = [1, 2, 3, 6, 8, 10, 14], L24745 = [1, 2, 3, 6, 8, 11, 13], L24746 = [1, 2, 3, 6, 8, 11, 14], L24763 = [1, 2, 3, 6, 9, 10, 13], L24764 = [1, 2, 3, 6, 9, 10, 14], L24765 = [1, 2, 3, 6, 9, 10, 16], L24766 = [1, 2, 3, 6, 9, 11, 13], L24767 = [1, 2, 3, 6, 9, 11, 16], L24770 = [1, 2, 3, 6, 9, 14, 16], L24771 = [1, 2, 3, 6, 9, 16, 16], L24775 = [1, 2, 3, 6, 10, 10, 14], L24780 = [1, 2, 3, 6, 10, 12, 14], L24783 = [1, 2, 3, 6, 10, 13, 14], L24786 = [1, 2, 3, 6, 10, 14, 14], L24787 = [1, 2, 3, 6, 10, 14, 15], L24788 = [1, 2, 3, 6, 10, 14, 16], L24792 = [1, 2, 3, 6, 11, 12, 13], L24793 = [1, 2, 3, 6, 11, 12, 14], L24796 = [1, 2, 3, 6, 11, 13, 14] L24797 = [1, 2, 3, 6, 11, 13, 16], L24799 = [1, 2, 3, 6, 11, 14, 15], L24800 = [1, 2, 3, 6, 11, 14, 16], L24837 = [1, 2, 3, 7, 8, 9, 10], L24847 = [1, 2, 3, 7, 8, 10, 14], L24848 = [1, 2, 3, 7, 8, 10, 15], L24867 = [1, 2, 3, 7, 9, 10, 12], L24868 = [1, 2, 3, 7, 9, 10, 13], L24870 = [1, 2, 3, 7, 9, 10, 15], L24871 = [1, 2, 3, 7, 9, 10, 16], L24900 = [1, 2, 3, 7, 10, 13, 15], L24903 = [1, 2, 3, 7, 10, 14, 16], L24904 = [1, 2, 3, 7, 10, 15, 16], L24951 = [1, 2, 3, 8, 8, 10, 13], L24953 = [1, 2, 3, 8, 8, 10, 15], L24976 = [1, 2, 3, 8, 9, 10, 14], L24987 = [1, 2, 3, 8, 9, 12, 15], L25007 = [1, 2, 3, 8, 10, 13, 15], L25008 = [1, 2, 3, 8, 10, 13, 16], L25012 = [1, 2, 3, 8, 10, 15, 16], L25065 = [1, 2, 3, 9, 10, 14, 16] L25088 = [1, 2, 3, 9, 12, 15, 16], L25131 = [1, 2, 3, 10, 13, 15, 16], L25132 = [1, 2, 3, 10, 13, 16, 16], L25138 = [1, 2, 3, 10, 15, 16, 16], L25239 = [1, 2, 4, 4, 4, 7, 9], L25245 = [1, 2, 4, 4, 4, 7, 15], L25350 = [1, 2, 4, 4, 6, 7, 9], L25355 = [1, 2, 4, 4, 6, 7, 15], L25375 = [1, 2, 4, 4, 6, 10, 14], L25395 = [1, 2, 4, 4, 7, 8, 9], L25401 = [1, 2, 4, 4, 7, 8, 15], L25403 = [1, 2, 4, 4, 7, 9, 10], L25405 = [1, 2, 4, 4, 7, 9, 12], L25409 = [1, 2, 4, 4, 7, 9, 16], L25413 = [1, 2, 4, 4, 7, 10, 15], L25421 = [1, 2, 4, 4, 7, 12, 15], L25426 = [1, 2, 4, 4, 7, 15, 16], L25540 = [1, 2, 4, 5, 6, 7, 14], L25552 = [1, 2, 4, 5, 6, 9, 10], L25555 = [1, 2, 4, 5, 6, 9, 13], L25559 = [1, 2, 4, 5, 6, 10, 13], L25560 = [1, 2, 4, 5, 6, 10, 14], L25562 = [1, 2, 4, 5, 6, 11, 12], L25570 = [1, 2, 4, 5, 6, 12, 15], L25652 = [1, 2, 4, 5, 9, 11, 13], L25686 = [1, 2, 4, 5, 12, 13, 14], L25714 = [1, 2, 4, 6, 6, 7, 9], L25719 = [1, 2, 4, 6, 6, 7, 15], L25736 = [1, 2, 4, 6, 6, 10, 14], L25752 = [1, 2, 4, 6, 7, 8, 9], L25757 = [1, 2, 4, 6, 7, 8, 15], L25759 = [1, 2, 4, 6, 7, 9, 10], L25761 = [1, 2, 4, 6, 7, 9, 12], L25762 = [1, 2, 4, 6, 7, 9, 14], L25764 = [1, 2, 4, 6, 7, 9, 16], L25767 = [1, 2, 4, 6, 7, 10, 14], L25768 = [1, 2, 4, 6, 7, 10, 15], L25770 = [1, 2, 4, 6, 7, 11, 12], L25774 = [1, 2, 4, 6, 7, 12, 15], L25776 = [1, 2, 4, 6, 7, 14, 15], L25778 = [1, 2, 4, 6, 7, 15, 16], L25798 = [1, 2, 4, 6, 8, 10, 14], L25820 = [1, 2, 4, 6, 9, 11, 12], L25833 = [1, 2, 4, 6, 10, 10, 14], L25837 = [1, 2, 4, 6, 10, 12, 14], L25840 = [1, 2, 4, 6, 10, 13, 14], L25842 = [1, 2, 4, 6, 10, 14, 14], L25843 = [1, 2, 4, 6, 10, 14, 15], L25844 = [1, 2, 4, 6, 10, 14, 16], L25875 = [1, 2, 4, 7, 8, 8, 9], L25881 = [1, 2, 4, 7, 8, 8, 15], L25883 = [1, 2, 4, 7, 8, 9, 10], L25884 = [1, 2, 4, 7, 8, 9, 11], L25885 = [1, 2, 4, 7, 8, 9, 12], L25889 = [1, 2, 4, 7, 8, 9, 16], L25893 = [1, 2, 4, 7, 8, 10, 15], L25901 = [1, 2, 4, 7, 8, 12, 15], L25906 = [1, 2, 4, 7, 8, 15, 16], L25908 = [1, 2, 4, 7, 9, 10, 10], L25909 = [1, 2, 4, 7, 9, 10, 12], L25912 = [1, 2, 4, 7, 9, 10, 16], L25915 = [1, 2, 4, 7, 9, 11, 16], L25916 = [1, 2, 4, 7, 9, 12, 12], L25920 = [1, 2, 4, 7, 9, 12, 16], L25925 = [1, 2, 4, 7, 9, 16, 16], L25929 = [1, 2, 4, 7, 10, 10, 15], L25933 = [1, 2, 4, 7, 10, 12, 15], L25936 = [1, 2, 4, 7, 10, 15, 16], L25946 = [1, 2, 4, 7, 12, 12, 15], L25951 = [1, 2, 4, 7, 12, 15, 16], L25956 = [1, 2, 4, 7, 15, 16, 16], L26120 = [1, 2, 4, 11, 12, 13, 14], L26198 = [1, 2, 5, 6, 6, 10, 14] L26222 = [1, 2, 5, 6, 7, 9, 11], L26224 = [1, 2, 5, 6, 7, 9, 15], L26226 = [1, 2, 5, 6, 7, 10, 14], L26229 = [1, 2, 5, 6, 7, 11, 15], L26233 = [1, 2, 5, 6, 7, 12, 15], L26242 = [1, 2, 5, 6, 8, 8, 11], L26246 = [1, 2, 5, 6, 8, 8, 15], L26248 = [1, 2, 5, 6, 8, 9, 10], L26255 = [1, 2, 5, 6, 8, 10, 14], L26258 = [1, 2, 5, 6, 8, 11, 13], L26260 = [1, 2, 5, 6, 8, 11, 15], L26261 = [1, 2, 5, 6, 8, 11, 16], L26270 = [1, 2, 5, 6, 8, 15, 16], L26273 = [1, 2, 5, 6, 9, 10, 16], L26284 = [1, 2, 5, 6, 10, 14, 14], L26285 = [1, 2, 5, 6, 10, 14, 16], L26291 = [1, 2, 5, 6, 11, 13, 16], L26295 = [1, 2, 5, 6, 11, 15, 16], L26296 = [1, 2, 5, 6, 11, 16, 16], L26312 = [1, 2, 5, 6, 15, 16, 16], L26354 = [1, 2, 5, 7, 11, 12, 13] L26405 = [1, 2, 5, 8, 8, 13, 14], L26454 = [1, 2, 5, 8, 13, 14, 16], L26533 = [1, 2, 5, 13, 14, 16, 16], L26555 = [1, 2, 6, 6, 6, 7, 9], L26560 = [1, 2, 6, 6, 6, 7, 15], L26577 = [1, 2, 6, 6, 6, 10, 14], L26593 = [1, 2, 6, 6, 7, 8, 9], L26598 = [1, 2, 6, 6, 7, 8, 15], L26600 = [1, 2, 6, 6, 7, 9, 10], L26602 = [1, 2, 6, 6, 7, 9, 12], L26603 = [1, 2, 6, 6, 7, 9, 14], L26605 = [1, 2, 6, 6, 7, 9, 16], L26608 = [1, 2, 6, 6, 7, 10, 14], L26609 = [1, 2, 6, 6, 7, 10, 15], L26615 = [1, 2, 6, 6, 7, 12, 15], L26617 = [1, 2, 6, 6, 7, 14, 15], L26619 = [1, 2, 6, 6, 7, 15, 16], L26636 = [1, 2, 6, 6, 8, 10, 14], L26653 = [1, 2, 6, 6, 9, 10, 14], L26665 = [1, 2, 6, 6, 10, 10, 14], L26669 = [1, 2, 6, 6, 10, 12, 14], L26672 = [1, 2, 6, 6, 10, 14, 14], L26673 = [1, 2, 6, 6, 10, 14, 15], L26674 = [1, 2, 6, 6, 10, 14, 16], L26700 = [1, 2, 6, 7, 8, 8, 9], L26702 = [1, 2, 6, 7, 8, 8, 11], L26705 = [1, 2, 6, 7, 8, 8, 15], L26707 = [1, 2, 6, 7, 8, 9, 10], L26709 = [1, 2, 6, 7, 8, 9, 12], L26710 = [1, 2, 6, 7, 8, 9, 14], L26712 = [1, 2, 6, 7, 8, 9, 16], L26716 =
APPENDIX
139
[1, 2, 6, 7, 8, 10, 15], L26719 = [1, 2, 6, 7, 8, 11, 16], L26722 = [1, 2, 6, 7, 8, 12, 15], L26724 = [1, 2, 6, 7, 8, 14, 15], L26726 = [1, 2, 6, 7, 8, 15, 16], L26728 = [1, 2, 6, 7, 9, 10, 10], L26729 = [1, 2, 6, 7, 9, 10, 12], L26730 = [1, 2, 6, 7, 9, 10, 14], L26732 = [1, 2, 6, 7, 9, 10, 16], L26735 = [1, 2, 6, 7, 9, 12, 12], L26736 = [1, 2, 6, 7, 9, 12, 14], L26738 = [1, 2, 6, 7, 9, 12, 16], L26740 = [1, 2, 6, 7, 9, 14, 16], L26742 = [1, 2, 6, 7, 9, 16, 16], L26745 = [1, 2, 6, 7, 10, 10, 15], L26748 = [1, 2, 6, 7, 10, 12, 14], L26749 = [1, 2, 6, 7, 10, 12, 15], L26751 = [1, 2, 6, 7, 10, 14, 16] L26752 = [1, 2, 6, 7, 10, 15, 16], L26756 = [1, 2, 6, 7, 11, 16, 16], L26759 = [1, 2, 6, 7, 12, 12, 15], L26761 = [1, 2, 6, 7, 12, 14, 15], L26763 = [1, 2, 6, 7, 12, 15, 16], L26765 = [1, 2, 6, 7, 14, 15, 16], L26767 = [1, 2, 6, 7, 15, 16, 16] L26778 = [1, 2, 6, 8, 8, 9, 11], L26804 = [1, 2, 6, 8, 9, 11, 16], L26812 = [1, 2, 6, 8, 10, 10, 14], L26816 = [1, 2, 6, 8, 10, 12, 14], L26819 = [1, 2, 6, 8, 10, 14, 14], L26820 = [1, 2, 6, 8, 10, 14, 15], L26821 = [1, 2, 6, 8, 10, 14, 16] L26856 = [1, 2, 6, 9, 11, 16, 16], L26866 = [1, 2, 6, 10, 10, 10, 14], L26870 = [1, 2, 6, 10, 10, 12, 14], L26873 = [1, 2, 6, 10, 10, 14, 14], L26874 = [1, 2, 6, 10, 10, 14, 15], L26875 = [1, 2, 6, 10, 10, 14, 16], L26879 = [1, 2, 6, 10, 12, 12, 14], L26882 = [1, 2, 6, 10, 12, 14, 14], L26883 = [1, 2, 6, 10, 12, 14, 15], L26884 = [1, 2, 6, 10, 12, 14, 16], L26887 = [1, 2, 6, 10, 14, 14, 14], L26888 = [1, 2, 6, 10, 14, 14, 15], L26889 = [1, 2, 6, 10, 14, 14, 16], L26890 = [1, 2, 6, 10, 14, 15, 16], L26891 = [1, 2, 6, 10, 14, 16, 16], L26930 = [1, 2, 7, 8, 8, 8, 9], L26936 = [1, 2, 7, 8, 8, 8, 15], L26938 = [1, 2, 7, 8, 8, 9, 10], L26940 = [1, 2, 7, 8, 8, 9, 12], L26944 = [1, 2, 7, 8, 8, 9, 16], L26948 = [1, 2, 7, 8, 8, 10, 15], L26956 = [1, 2, 7, 8, 8, 12, 15], L26961 = [1, 2, 7, 8, 8, 15, 16], L26963 = [1, 2, 7, 8, 9, 10, 10], L26964 = [1, 2, 7, 8, 9, 10, 12], L26967 = [1, 2, 7, 8, 9, 10, 16], L26971 = [1, 2, 7, 8, 9, 12, 12], L26975 = [1, 2, 7, 8, 9, 12, 16], L26980 = [1, 2, 7, 8, 9, 16, 16], L26984 = [1, 2, 7, 8, 10, 10, 15], L26988 = [1, 2, 7, 8, 10, 12, 15], L26991 = [1, 2, 7, 8, 10, 15, 16], L27001 = [1, 2, 7, 8, 12, 12, 15], L27006 = [1, 2, 7, 8, 12, 15, 16], L27011 = [1, 2, 7, 8, 15, 16, 16], L27013 = [1, 2, 7, 9, 10, 10, 10] L27014 = [1, 2, 7, 9, 10, 10, 12], L27017 = [1, 2, 7, 9, 10, 10, 16], L27018 = [1, 2, 7, 9, 10, 12, 12], L27021 = [1, 2, 7, 9, 10, 12, 16], L27024 = [1, 2, 7, 9, 10, 16, 16], L27030 = [1, 2, 7, 9, 12, 12, 12], L27034 = [1, 2, 7, 9, 12, 12, 16] L27039 = [1, 2, 7, 9, 12, 16, 16], L27044 = [1, 2, 7, 9, 16, 16, 16], L27048 = [1, 2, 7, 10, 10, 10, 15], L27052 = [1, 2, 7, 10, 10, 12, 15], L27055 = [1, 2, 7, 10, 10, 15, 16], L27059 = [1, 2, 7, 10, 12, 12, 15], L27062 = [1, 2, 7, 10, 12, 15, 16], L27065 = [1, 2, 7, 10, 15, 16, 16], L27077 = [1, 2, 7, 12, 12, 12, 15], L27082 = [1, 2, 7, 12, 12, 15, 16], L27087 = [1, 2, 7, 12, 15, 16, 16], L27092 = [1, 2, 7, 15, 16, 16, 16], L27164 = [1, 2, 8, 8, 11, 13, 14], L27262 = [1, 2, 8, 11, 13, 14, 16], L27428 = [1, 2, 11, 13, 14, 16, 16], L27503 = [1, 3, 4, 4, 4, 5, 13], L27508 = [1, 3, 4, 4, 4, 7, 9], L27536 = [1, 3, 4, 4, 4, 11, 13], L27554 = [1, 3, 4, 4, 5, 7, 9], L27555 = [1, 3, 4, 4, 5, 7, 11], L27557 = [1, 3, 4, 4, 5, 7, 13], L27558 = [1, 3, 4, 4, 5, 7, 15], L27564 = [1, 3, 4, 4, 5, 8, 13], L27568 = [1, 3, 4, 4, 5, 9, 11], L27570 = [1, 3, 4, 4, 5, 9, 15], L27573 = [1, 3, 4, 4, 5, 11, 13], L27575 = [1, 3, 4, 4, 5, 11, 15], L27578 = [1, 3, 4, 4, 5, 12, 13], L27583 = [1, 3, 4, 4, 5, 13, 15], L27584 = [1, 3, 4, 4, 5, 13, 16], L27591 = [1, 3, 4, 4, 7, 8, 9], L27598 = [1, 3, 4, 4, 7, 9, 12], L27599 = [1, 3, 4, 4, 7, 9, 13], L27600 = [1, 3, 4, 4, 7, 9, 15], L27601 = [1, 3, 4, 4, 7, 9, 16], L27607 = [1, 3, 4, 4, 7, 12, 12], L27611 = [1, 3, 4, 4, 7, 13, 15], L27637 = [1, 3, 4, 4, 8, 11, 13], L27660 = [1, 3, 4, 4, 9, 11, 13], L27661 = [1, 3, 4, 4, 9, 11, 15], L27663 = [1, 3, 4, 4, 9, 12, 12], L27689 = [1, 3, 4, 4, 11, 12, 13], L27694 = [1, 3, 4, 4, 11, 13, 16], L27726 = [1, 3, 4, 5, 7, 8, 9], L27727 = [1, 3, 4, 5, 7, 8, 11], L27728 = [1, 3, 4, 5, 7, 8, 12], L27729 = [1, 3, 4, 5, 7, 8, 13], L27730 = [1, 3, 4, 5, 7, 8, 15], L27732 = [1, 3, 4, 5, 7, 9, 11], L27733 = [1, 3, 4, 5, 7, 9, 12], L27734 = [1, 3, 4, 5, 7, 9, 13], L27735 = [1, 3, 4, 5, 7, 9, 15], L27736 = [1, 3, 4, 5, 7, 9, 16], L27737 = [1, 3, 4, 5, 7, 11, 12], L27738 = [1, 3, 4, 5, 7, 11, 13], L27739 = [1, 3, 4, 5, 7, 11, 16], L27741 = [1, 3, 4, 5, 7, 12, 13], L27742 = [1, 3, 4, 5, 7, 12, 16], L27743 = [1, 3, 4, 5, 7, 13, 15], L27744 = [1, 3, 4, 5, 7, 13, 16], L27745 = [1, 3, 4, 5, 7, 15, 16], L27751 = [1, 3, 4, 5, 8, 8, 13], L27755 = [1, 3, 4, 5, 8, 9, 11], L27756 = [1, 3, 4, 5, 8, 9, 12], L27757 = [1, 3, 4, 5, 8, 9, 15], L27760 = [1, 3, 4, 5, 8, 11, 13], L27762 = [1, 3, 4, 5, 8, 11, 15], L27765 = [1, 3, 4, 5, 8, 12, 13], L27770 = [1, 3, 4, 5, 8, 13, 15], L27771 = [1, 3, 4, 5, 8, 13, 16], L27777 = [1, 3, 4, 5, 9, 11, 12], L27778 = [1, 3, 4, 5, 9, 11, 15], L27779 = [1, 3, 4, 5, 9, 11, 16], L27780 = [1, 3, 4, 5, 9, 12, 16], L27781 = [1, 3, 4, 5, 9, 15, 16], L27785 = [1, 3, 4, 5, 11, 12, 15], L27788 = [1, 3, 4, 5, 11, 13, 15], L27789 = [1, 3, 4, 5, 11, 13, 16], L27793 = [1, 3, 4, 5, 11, 15, 16], L27796 = [1, 3, 4, 5, 12, 12, 13], L27800 = [1, 3, 4, 5, 12, 13, 15], L27801 = [1, 3, 4, 5, 12, 13, 16] L27810 = [1, 3, 4, 5, 13, 15, 16], L27811 = [1, 3, 4, 5, 13, 16, 16], L27820 = [1, 3, 4, 7, 8, 8, 9], L27822 = [1, 3, 4, 7, 8, 8, 12], L27827 = [1, 3, 4, 7, 8, 9, 12], L27828 = [1, 3, 4, 7, 8, 9, 13], L27829 = [1, 3, 4, 7, 8, 9, 15], L27830 = [1, 3, 4, 7, 8, 9, 16], L27838 = [1, 3, 4, 7, 8, 12, 16], L27839 = [1, 3, 4, 7, 8, 13, 15], L27848 =
140
EMILIO A. LAURET
[1, 3, 4, 7, 9, 12, 16], L27849 = [1, 3, 4, 7, 9, 13, 15], L27850 = [1, 3, 4, 7, 9, 13, 16], L27851 = [1, 3, 4, 7, 9, 15, 16], L27852 = [1, 3, 4, 7, 9, 16, 16], L27869 = [1, 3, 4, 7, 12, 16, 16], L27870 = [1, 3, 4, 7, 13, 15, 16], L27885 = [1, 3, 4, 8, 8, 9, 12], L27895 = [1, 3, 4, 8, 8, 11, 13], L27917 = [1, 3, 4, 8, 9, 11, 13], L27918 = [1, 3, 4, 8, 9, 11, 15], L27921 = [1, 3, 4, 8, 9, 12, 16], L27945 = [1, 3, 4, 8, 11, 13, 16], L27986 = [1, 3, 4, 9, 11, 13, 16], L27987 = [1, 3, 4, 9, 11, 15, 16], L27990 = [1, 3, 4, 9, 12, 16, 16], L28040 = [1, 3, 4, 11, 13, 16, 16], L28089 = [1, 3, 5, 7, 8, 8, 8], L28090 = [1, 3, 5, 7, 8, 8, 9], L28091 = [1, 3, 5, 7, 8, 8, 11], L28093 = [1, 3, 5, 7, 8, 8, 13], L28094 = [1, 3, 5, 7, 8, 8, 16], L28095 = [1, 3, 5, 7, 8, 9, 11], L28096 = [1, 3, 5, 7, 8, 9, 13], L28098 = [1, 3, 5, 7, 8, 9, 16], L28099 = [1, 3, 5, 7, 8, 11, 16], L28102 = [1, 3, 5, 7, 8, 13, 16], L28103 = [1, 3, 5, 7, 8, 16, 16], L28105 = [1, 3, 5, 7, 9, 11, 16], L28106 = [1, 3, 5, 7, 9, 13, 16], L28108 = [1, 3, 5, 7, 9, 16, 16], L28109 = [1, 3, 5, 7, 11, 16, 16], L28113 = [1, 3, 5, 7, 13, 16, 16], L28114 = [1, 3, 5, 7, 16, 16, 16], L28116 = [1, 3, 5, 8, 8, 8, 9], L28119 = [1, 3, 5, 8, 8, 8, 13], L28123 = [1, 3, 5, 8, 8, 9, 11], L28124 = [1, 3, 5, 8, 8, 9, 16], L28127 = [1, 3, 5, 8, 8, 11, 15], L28130 = [1, 3, 5, 8, 8, 12, 13], L28134 = [1, 3, 5, 8, 8, 13, 15], L28135 = [1, 3, 5, 8, 8, 13, 16], L28141 = [1, 3, 5, 8, 9, 11, 16], L28142 = [1, 3, 5, 8, 9, 16, 16], L28149 = [1, 3, 5, 8, 11, 15, 16], L28152 = [1, 3, 5, 8, 12, 12, 13], L28156 = [1, 3, 5, 8, 12, 13, 16], L28163 = [1, 3, 5, 8, 13, 15, 16], L28164 = [1, 3, 5, 8, 13, 16, 16], L28172 = [1, 3, 5, 9, 11, 16, 16], L28173 = [1, 3, 5, 9, 16, 16, 16], L28184 = [1, 3, 5, 11, 15, 16, 16], L28187 = [1, 3, 5, 12, 12, 12, 1 L28191 = [1, 3, 5, 12, 12, 13, 16], L28197 = [1, 3, 5, 12, 13, 16, 16], L28207 = [1, 3, 5, 13, 15, 16, 16], L28208 = [1, 3, 5, 13, 16, 16, 16], L28218 = [1, 3, 7, 8, 8, 8, 8], L28219 = [1, 3, 7, 8, 8, 8, 9], L28223 = [1, 3, 7, 8, 8, 8, 16], L28225 = [1, 3, 7, 8, 8, 9, 16], L28234 = [1, 3, 7, 8, 8, 16, 16], L28237 = [1, 3, 7, 8, 9, 16, 16], L28253 = [1, 3, 7, 8, 16, 16, 16], L28257 = [1, 3, 7, 9, 16, 16, 16], L28282 = [1, 3, 7, 16, 16, 16, 16], L28284 = [1, 3, 8, 8, 8, 8, 9], L28293 = [1, 3, 8, 8, 8, 9, 16], L28317 = [1, 3, 8, 8, 9, 16, 16], L28368 = [1, 3, 8, 9, 16, 16, 16], L28462 = [1, 3, 9, 16, 16, 16, 16], L28698 = [1, 4, 4, 4, 6, 7, 9], L28701 = [1, 4, 4, 4, 6, 7, 15], L28864 = [1, 4, 4, 6, 6, 7, 9], L28867 = [1, 4, 4, 6, 6, 7, 15], L28894 = [1, 4, 4, 6, 7, 8, 9], L28897 = [1, 4, 4, 6, 7, 8, 15], L28900 = [1, 4, 4, 6, 7, 9, 12], L28902 = [1, 4, 4, 6, 7, 9, 16], L28906 = [1, 4, 4, 6, 7, 12, 15], L28908 = [1, 4, 4, 6, 7, 15, 16], L28977 = [1, 4, 4, 7, 9, 12, 15], L29211 = [1, 4, 6, 6, 6, 7, 9], L29214 = [1, 4, 6, 6, 6, 7, 15], L29241 = [1, 4, 6, 6, 7, 8, 9], L29244 = [1, 4, 6, 6, 7, 8, 15], L29246 = [1, 4, 6, 6, 7, 9, 10], L29247 = [1, 4, 6, 6, 7, 9, 12], L29249 = [1, 4, 6, 6, 7, 9, 16], L29252 = [1, 4, 6, 6, 7, 10, 15], L29255 = [1, 4, 6, 6, 7, 12, 15], L29257 = [1, 4, 6, 6, 7, 15, 16], L29319 = [1, 4, 6, 7, 8, 8, 9], L29322 = [1, 4, 6, 7, 8, 8, 15], L29325 = [1, 4, 6, 7, 8, 9, 12], L29327 = [1, 4, 6, 7, 8, 9, 16], L29331 = [1, 4, 6, 7, 8, 12, 15], L29333 = [1, 4, 6, 7, 8, 15, 16], L29338 = [1, 4, 6, 7, 9, 12, 12], L29340 = [1, 4, 6, 7, 9, 12, 16], L29342 = [1, 4, 6, 7, 9, 16, 16], L29347 = [1, 4, 6, 7, 12, 12, 15], L29349 = [1, 4, 6, 7, 12, 15, 16], L29351 = [1, 4, 6, 7, 15, 16, 16], L29488 = [1, 4, 7, 9, 12, 12, 15] L29490 = [1, 4, 7, 9, 12, 15, 16], L29811 = [1, 6, 6, 6, 6, 7, 9], L29814 = [1, 6, 6, 6, 6, 7, 15], L29841 = [1, 6, 6, 6, 7, 8, 9], L29844 = [1, 6, 6, 6, 7, 8, 15], L29846 = [1, 6, 6, 6, 7, 9, 10], L29847 = [1, 6, 6, 6, 7, 9, 12], L29849 = [1, 6, 6, 6, 7, 9, 16], L29852 = [1, 6, 6, 6, 7, 10, 15], L29855 = [1, 6, 6, 6, 7, 12, 15], L29857 = [1, 6, 6, 6, 7, 15, 16], L29920 = [1, 6, 6, 7, 8, 8, 9], L29923 = [1, 6, 6, 7, 8, 8, 15], L29925 = [1, 6, 6, 7, 8, 9, 10], L29926 = [1, 6, 6, 7, 8, 9, 12], L29928 = [1, 6, 6, 7, 8, 9, 16], L29931 = [1, 6, 6, 7, 8, 10, 15], L29934 = [1, 6, 6, 7, 8, 12, 15], L29936 = [1, 6, 6, 7, 8, 15, 16], L29939 = [1, 6, 6, 7, 9, 10, 12], L29941 = [1, 6, 6, 7, 9, 10, 16], L29942 = [1, 6, 6, 7, 9, 12, 12], L29944 = [1, 6, 6, 7, 9, 12, 16], L29946 = [1, 6, 6, 7, 9, 16, 16], L29950 = [1, 6, 6, 7, 10, 12, 15], L29952 = [1, 6, 6, 7, 10, 15, 16], L29955 = [1, 6, 6, 7, 12, 12, 15], L29957 = [1, 6, 6, 7, 12, 15, 16] L29959 = [1, 6, 6, 7, 15, 16, 16], L30083 = [1, 6, 7, 8, 8, 8, 9], L30086 = [1, 6, 7, 8, 8, 8, 15], L30089 = [1, 6, 7, 8, 8, 9, 12], L30091 = [1, 6, 7, 8, 8, 9, 16], L30095 = [1, 6, 7, 8, 8, 12, 15], L30097 = [1, 6, 7, 8, 8, 15, 16], L30102 = [1, 6, 7, 8, 9, 12, 12], L30104 = [1, 6, 7, 8, 9, 12, 16], L30106 = [1, 6, 7, 8, 9, 16, 16], L30111 = [1, 6, 7, 8, 12, 12, 15], L30113 = [1, 6, 7, 8, 12, 15, 16], L30115 = [1, 6, 7, 8, 15, 16, 16], L30122 = [1, 6, 7, 9, 12, 12, 12] L30124 = [1, 6, 7, 9, 12, 12, 16], L30126 = [1, 6, 7, 9, 12, 16, 16], L30128 = [1, 6, 7, 9, 16, 16, 16], L30134 = [1, 6, 7, 12, 12, 12, 15], L30136 = [1, 6, 7, 12, 12, 15, 16], L30138 = [1, 6, 7, 12, 15, 16, 16], L30140 = [1, 6, 7, 15, 16, 16, 16]. q = 33 : L41 = [0, 0, 0, 0, 1, 2, 14], L56 = [0, 0, 0, 0, 1, 4, 5], L250 = [0, 0, 0, 1, 2, 4, 13], L257 = [0, 0, 0, 1, 2, 5, 10], L261 = [0, 0, 0, 1, 2, 5, 14], L273 = [0, 0, 0, 1, 2, 7, 8], L301 = [0, 0, 0, 1, 2, 11, 14], L387 = [0, 0, 0, 1, 4, 5, 11], L490 = [0, 0, 0, 3, 6, 9, 11], L492 = [0, 0, 0, 3, 6, 11, 12], L1354 = [0, 0, 1, 2, 4, 7, 14], L1376 = [0, 0, 1, 2, 4, 11, 13], L1402 = [0, 0, 1, 2, 5, 7, 13], L1416 = [0, 0, 1, 2, 5, 10, 11], L1421 =
APPENDIX
141
Table 5. (continued) n = 7 q 33
I {0}
indexes of I-isospectral families {41, 56}, {250, 257}, {261, 273}, {301, 387}, {490, 492}, {1354, 1402}, {1376, 1416}, {1421, 1481}, {1460, 1752}, {1563, 1855}, {2077, 2080}, {5519, 5617}, {5762, 6785}, {5807, 5811, 5816}, {5813, 5814}, {5839, 5994}, {5866, 6008}, {5926, 6049}, {6055, 6239}, {6185, 6996}, {6425, 7189}, {7606, 7610}, {20231, 20248}, {20249, 20279}, {20321, 20672}, {20333, 20676}, {20405, 20419}, {20500, 20544}, {20571, 21940}, {20725, 20739}, {20767, 20885, 21490}, {20938, 23488}, {21036, 23459}, {21108, 21113, 21124}, {21110, 21111, 21136, 21147}, {21125, 21138, 21187}, {21129, 21146, 21152}, {21135, 21211}, {21149, 21150}, {21199, 21572}, {21252, 21534}, {21273, 21600}, {21399, 21686}, {21498, 21559}, {21693, 22137}, {22033, 23879}, {22494, 24194}, {23453, 23469}, {23502, 23823}, {24906, 24910} {0, 1} {5826, 5846}, {21113, 21124}, {21182, 21224} {2, 5} {2034, 7527}, {2043, 2082}, {5265, 19505}, {5269, 7529}, {6369, 22399}, {6377, 7438}, {6401, 7502}, {7052, 23964}, {7059, 7530}, {7122, 7254}, {11244, 19508}, {13872, 22406}, {13939, 19395}, {15810, 23969}, {15972, 19191}, {16945, 23239}, {17207, 19509}, {17615, 22362}, {17974, 18667}, {20895, 23971}, {20907, 23523}, {20986, 22233}, {21254, 22023}, {21265, 23845}, {21340, 22409} {3, 4, 5, 6} {7005, 7608}
[0, 0, 1, 2, 5, 11, 14], L1460 = [0, 0, 1, 2, 6, 9, 15], L1481 = [0, 0, 1, 2, 7, 8, 11], L1563 = [0, 0, 1, 2, 11, 11, 14], L1752 = [0, 0, 1, 3, 6, 9, 10], L1855 = [0, 0, 1, 4, 5, 11, 11], L2034 = [0, 0, 1, 10, 11, 11, 12], L2043 = [0, 0, 1, 11, 11, 11, 11], L2077 = [0, 0, 3, 6, 9, 11, 11], L2080 = [0, 0, 3, 6, 11, 11, 12], L2082 = [0, 0, 3, 11, 11, 11, 11], L5265 = [0, 1, 1, 10, 10, 12, 12], L5269 = [0, 1, 1, 10, 11, 11, 12], L5519 = [0, 1, 2, 3, 4, 10, 15], L5617 = [0, 1, 2, 3, 6, 8, 10], L5762 = [0, 1, 2, 3, 10, 12, 15], L5807 = [0, 1, 2, 4, 5, 7, 14], L5811 = [0, 1, 2, 4, 5, 8, 10], L5813 = [0, 1, 2, 4, 5, 8, 13], L5814 = [0, 1, 2, 4, 5, 8, 14], L5816 = [0, 1, 2, 4, 5, 8, 16], L5826 = [0, 1, 2, 4, 5, 10, 13], L5839 = [0, 1, 2, 4, 5, 13, 14], L5846 = [0, 1, 2, 4, 7, 8, 13], L5866 = [0, 1, 2, 4, 7, 11, 14], L5926 = [0, 1, 2, 4, 11, 11, 13], L5994 = [0, 1, 2, 5, 7, 8, 10], L6008 = [0, 1, 2, 5, 7, 11, 13], L6049 = [0, 1, 2, 5, 10, 11, 11], L6055 = [0, 1, 2, 5, 11, 11, 14], L6185 = [0, 1, 2, 6, 9, 11, 15], L6239 = [0, 1, 2, 7, 8, 11, 11], L6369 = [0, 1, 2, 9, 10, 12, 13], L6377 = [0, 1, 2, 9, 11, 11, 13], L6401 = [0, 1, 2, 10, 11, 11, 12], L6425 = [0, 1, 2, 11, 11, 11, 14] L6785 = [0, 1, 3, 4, 6, 7, 15], L6996 = [0, 1, 3, 6, 9, 10, 11], L7005 = [0, 1, 3, 6, 9, 12, 15], L7052 = [0, 1, 3, 8, 10, 12, 14], L7059 = [0, 1, 3, 8, 11, 11, 14], L7122 = [0, 1, 3, 10, 11, 11, 12], L7189 = [0, 1, 4, 5, 11, 11, 11], L7254 = [0, 1, 4, 7, 11, 11, 15], L7438 = [0, 1, 6, 10, 11, 11, 12], L7502 = [0, 1, 9, 10, 11, 11, 12], L7527 = [0, 1, 10, 11, 11, 11, 12], L7529 = [0, 1, 10, 11, 11, 12, 12], L7530 = [0, 1, 10, 11, 11, 12, 15], L7606 = [0, 3, 6, 9, 11, 11, 11], L7608 = [0, 3, 6, 9, 11, 12, 15], L7610 = [0, 3, 6, 11, 11, 11, 12], L11244 = [1, 1, 1, 10, 10, 12, 12 L13872 = [1, 1, 2, 9, 10, 12, 13], L13939 = [1, 1, 2, 10, 10, 12, 12], L15810 = [1, 1, 3, 8, 10, 12, 14], L15972 = [1, 1, 3, 10, 10, 12, 12], L16945 = [1, 1, 4, 7, 10, 12, 15], L17207 = [1, 1, 4, 10, 10, 12, 12], L17615 = [1, 1, 5, 6, 10, 12, 16], L17974 = [1, 1, 5, 10, 10, 12, 12], L18667 = [1, 1, 6, 10, 10, 12, 12], L19191 = [1, 1, 8, 10, 10, 12, 12], L19395 = [1, 1, 9, 10, 10, 12, 12], L19505 = [1, 1, 10, 10, 11, 12, 12], L19508 = [1, 1, 10, 10, 12, 12, 12], L19509 = [1, 1, 10, 10, 12, 12, 15], L20231 = [1, 2, 3, 4, 7, 8, 10], L20248 = [1, 2, 3, 4, 7, 10, 13], L20249 = [1, 2, 3, 4, 7, 10, 14], L20279 = [1, 2, 3, 4, 8, 10, 13], L20321 = [1, 2, 3, 4, 9, 12, 15], L20333 = [1, 2, 3, 4, 10, 11, 15], L20405 = [1, 2, 3, 5, 6, 8, 15], L20419 = [1, 2, 3, 5, 6, 10, 15], L20500 = [1, 2, 3, 5, 8, 13, 16], L20544 = [1, 2, 3, 5, 10, 13, 14], L20571 = [1, 2, 3, 5, 12, 13, 15], L20672 = [1, 2, 3, 6, 8, 9, 12], L20676 = [1, 2, 3, 6, 8, 10, 11], L20725 = [1, 2, 3, 6, 9, 13, 15], L20739 = [1, 2, 3, 6, 10, 12, 15], L20767 = [1, 2, 3, 6, 12, 13, 14], L20885 = [1, 2, 3, 8, 9, 10, 15], L20895 = [1, 2, 3, 8, 9, 13, 14], L20907 = [1, 2, 3, 8, 10, 12, 14],
142
EMILIO A. LAURET
L20938 = [1, 2, 3, 8, 12, 13, 15], L20986 = [1, 2, 3, 9, 10, 12, 13], L21036 = [1, 2, 3, 10, 11, 12, 15], L21108 = [1, 2, 4, 5, 7, 8, 10], L21110 = [1, 2, 4, 5, 7, 8, 13], L21111 = [1, 2, 4, 5, 7, 8, 14], L21113 = [1, 2, 4, 5, 7, 8, 16], L21124 = [1, 2, 4, 5, 7, 10, 14], L21125 = [1, 2, 4, 5, 7, 10, 16], L21129 = [1, 2, 4, 5, 7, 11, 14], L21135 = [1, 2, 4, 5, 7, 12, 16], L21136 = [1, 2, 4, 5, 7, 13, 14], L21138 = [1, 2, 4, 5, 7, 13, 16], L21146 = [1, 2, 4, 5, 8, 10, 11], L21147 = [1, 2, 4, 5, 8, 10, 16], L21149 = [1, 2, 4, 5, 8, 11, 13], L21150 = [1, 2, 4, 5, 8, 11, 14], L21152 = [1, 2, 4, 5, 8, 11, 16], L21182 = [1, 2, 4, 5, 10, 11, 13], L21187 = [1, 2, 4, 5, 10, 13, 16], L21199 = [1, 2, 4, 5, 11, 13, 14], L21211 = [1, 2, 4, 5, 12, 13, 16], L21224 = [1, 2, 4, 7, 8, 11, 13], L21252 = [1, 2, 4, 7, 9, 12, 15], L21254 = [1, 2, 4, 7, 9, 13, 15], L21265 = [1, 2, 4, 7, 10, 12, 15], L21273 = [1, 2, 4, 7, 11, 11, 14], L21340 = [1, 2, 4, 9, 10, 12, 13], L21399 = [1, 2, 4, 11, 11, 11, 13], L21490 = [1, 2, 5, 6, 7, 9, 12], L21498 = [1, 2, 5, 6, 7, 12, 15], L21534 = [1, 2, 5, 6, 9, 12, 13], L21559 = [1, 2, 5, 6, 12, 13, 15], L21572 = [1, 2, 5, 7, 8, 10, 11], L21600 = [1, 2, 5, 7, 11, 11, 13], L21686 = [1, 2, 5, 10, 11, 11, 11], L21693 = [1, 2, 5, 11, 11, 11, 14], L21940 = [1, 2, 6, 8, 9, 10, 15], L22023 = [1, 2, 6, 9, 10, 12, 13], L22033 = [1, 2, 6, 9, 11, 11, 15], L22137 = [1, 2, 7, 8, 11, 11, 11], L22233 = [1, 2, 8, 9, 10, 12, 13] L22362 = [1, 2, 9, 9, 10, 12, 13], L22399 = [1, 2, 9, 10, 11, 12, 13], L22406 = [1, 2, 9, 10, 12, 12, 13], L22409 = [1, 2, 9, 10, 12, 13, 15], L22494 = [1, 2, 11, 11, 11, 11, 14], L23239 = [1, 3, 3, 8, 10, 12, 14], L23453 = [1, 3, 4, 6, 7, 9, 15], L23459 = [1, 3, 4, 6, 7, 11, 15], L23469 = [1, 3, 4, 6, 9, 10, 12], L23488 = [1, 3, 4, 6, 10, 14, 15], L23502 = [1, 3, 4, 6, 12, 14, 15], L23523 = [1, 3, 4, 7, 10, 12, 15], L23823 = [1, 3, 6, 7, 8, 12, 15], L23845 = [1, 3, 6, 8, 10, 12, 14], L23879 = [1, 3, 6, 9, 10, 11, 11], L23964 = [1, 3, 8, 10, 11, 12, 14], L23969 = [1, 3, 8, 10, 12, 12, 14], L23971 = [1, 3, 8, 10, 12, 14, 15], L24194 = [1, 4, 5, 11, 11, 11, 11], L24906 = [3, 6, 9, 11, 11, 11, 11], L24910 = [3, 6, 11, 11, 11, 11, 12]. q = 34 : L51 = [0, 0, 0, 0, 1, 3, 7], L53 = [0, 0, 0, 0, 1, 3, 9], L56 = [0, 0, 0, 0, 1, 3, 13], L74 = [0, 0, 0, 0, 1, 5, 7], L413 = [0, 0, 0, 1, 3, 5, 9], L414 = [0, 0, 0, 1, 3, 5, 11], L416 = [0, 0, 0, 1, 3, 5, 13], L418 = [0, 0, 0, 1, 3, 5, 15], L422 = [0, 0, 0, 1, 3, 7, 9], L424 = [0, 0, 0, 1, 3, 7, 11], L426 = [0, 0, 0, 1, 3, 7, 15], L428 = [0, 0, 0, 1, 3, 7, 17], L439 = [0, 0, 0, 1, 3, 9, 17], L456 = [0, 0, 0, 1, 3, 13, 17], L540 = [0, 0, 0, 1, 5, 7, 17], L568 = [0, 0, 0, 1, 6, 9, 10], L571 = [0, 0, 0, 1, 6, 9, 14], L582 = [0, 0, 0, 1, 6, 12, 13], L590 = [0, 0, 0, 1, 6, 14, 15], L682 = [0, 0, 0, 2, 4, 10, 17], L683 = [0, 0, 0, 2, 4, 12, 17], L684 = [0, 0, 0, 2, 4, 14, 17], L686 = [0, 0, 0, 2, 6, 8, 17], L1876 = [0, 0, 1, 2, 4, 8, 9], L1882 = [0, 0, 1, 2, 4, 8, 15], L1888 = [0, 0, 1, 2, 4, 9, 13], L1890 = [0, 0, 1, 2, 4, 9, 15], L2322 = [0, 0, 1, 3, 5, 7, 9], L2323 = [0, 0, 1, 3, 5, 7, 11], L2325 = [0, 0, 1, 3, 5, 7, 13], L2326 = [0, 0, 1, 3, 5, 7, 15], L2337 = [0, 0, 1, 3, 5, 9, 11], L2338 = [0, 0, 1, 3, 5, 9, 13], L2340 = [0, 0, 1, 3, 5, 9, 17], L2342 = [0, 0, 1, 3, 5, 11, 15], L2344 = [0, 0, 1, 3, 5, 11, 17], L2351 = [0, 0, 1, 3, 5, 13, 17], L2356 = [0, 0, 1, 3, 5, 15, 17], L2369 = [0, 0, 1, 3, 7, 9, 17], L2376 = [0, 0, 1, 3, 7, 11, 17], L2382 = [0, 0, 1, 3, 7, 15, 17], L2385 = [0, 0, 1, 3, 7, 17, 17], L2422 = [0, 0, 1, 3, 9, 17, 17], L2476 = [0, 0, 1, 3, 13, 17, 17], L2756 = [0, 0, 1, 5, 7, 17, 17], L2852 = [0, 0, 1, 6, 9, 10, 12], L2855 = [0, 0, 1, 6, 9, 10, 15], L2856 = [0, 0, 1, 6, 9, 10, 17], L2858 = [0, 0, 1, 6, 9, 12, 13], L2865 = [0, 0, 1, 6, 9, 14, 17], L2875 = [0, 0, 1, 6, 10, 12, 13], L2895 = [0, 0, 1, 6, 12, 13, 17], L2912 = [0, 0, 1, 6, 14, 15, 17], L3122 = [0, 0, 2, 4, 6, 10, 17], L3123 = [0, 0, 2, 4, 6, 12, 17], L3124 = [0, 0, 2, 4, 6, 14, 17], L3125 = [0, 0, 2, 4, 6, 16, 17], L3127 = [0, 0, 2, 4, 8, 10, 17], L3131 = [0, 0, 2, 4, 10, 17, 17], L3132 = [0, 0, 2, 4, 12, 14, 17], L3133 = [0, 0, 2, 4, 12, 17, 17], L3134 = [0, 0, 2, 4, 14, 17, 17], L3136 = [0, 0, 2, 6, 8, 10, 17], L3137 = [0, 0, 2, 6, 8, 17, 17], L8482 = [0, 1, 2, 3, 8, 15, 16], L8556 = [0, 1, 2, 3, 11, 14, 16], L8584 = [0, 1, 2, 3, 13, 14, 16], L8818 = [0, 1, 2, 4, 6, 13, 15], L8886 = [0, 1, 2, 4, 8, 9, 13], L8890 = [0, 1, 2, 4, 8, 9, 17], L8909 = [0, 1, 2, 4, 8, 13, 15], L8916 = [0, 1, 2, 4, 8, 15, 17], L8937 = [0, 1, 2, 4, 9, 13, 17], L8941 = [0, 1, 2, 4, 9, 15, 17], L8990 = [0, 1, 2, 4, 12, 13, 15], L9003 = [0, 1, 2, 4, 13, 14, 15], L9072 = [0, 1, 2, 5, 6, 11, 16], L9533 = [0, 1, 2, 7, 8, 9, 10], L9556 = [0, 1, 2, 7, 8, 15, 16], L9726 = [0, 1, 2, 8, 11, 15, 16], L10268 = [0, 1, 3, 5, 7, 9, 11], L10269 = [0, 1, 3, 5, 7, 9, 13], L10270 = [0, 1, 3, 5, 7, 9, 15], L10271 = [0, 1, 3, 5, 7, 9, 17], L10272 = [0, 1, 3, 5, 7, 11, 13], L10274 = [0, 1, 3, 5, 7, 11, 17], L10280 = [0, 1, 3, 5, 7, 13, 17], L10282 = [0, 1, 3, 5, 7, 15, 17], L10314 = [0, 1, 3, 5, 9, 11, 17], L10316 = [0, 1, 3, 5, 9, 13, 17], L10319 = [0, 1, 3, 5, 9, 17, 17], L10324 = [0, 1, 3, 5, 11, 15, 17], L10327 = [0, 1, 3, 5, 11, 17, 17], L10344 = [0, 1, 3, 5, 13, 17, 17], L10353 = [0, 1, 3, 5, 15, 17, 17], L10386 = [0, 1, 3, 7, 9, 17, 17], L10403 = [0, 1, 3, 7, 11, 17, 17], L10415 = [0, 1, 3, 7, 15, 17, 17], L10419 = [0, 1, 3, 7, 17, 17, 17], L10516 = [0, 1, 3, 9, 17, 17, 17], L10646 = [0, 1, 3, 13, 17, 17, 17], L11409 = [0, 1, 5, 7, 17, 17, 17], L11677 = [0, 1, 6, 9, 10, 12, 13], L11679 = [0, 1, 6, 9, 10, 12, 15], L11680 = [0, 1, 6, 9, 10, 12, 17] L11686 = [0, 1, 6, 9, 10, 15, 17], L11687 = [0, 1, 6, 9, 10, 17, 17], L11693 = [0, 1, 6, 9, 12, 13, 17], L11700 =
APPENDIX
143
Table 5. (continued) n = 7 q 34
I {0}
indexes of I-isospectral families {51, 53}, {56, 74}, {413, 416}, {414, 418, 422}, {428, 439}, {456, 540}, {568, 571}, {582, 590}, {682, 683}, {684, 686}, {1876, 1882}, {1888, 1890}, {2322, 2325}, {2323, 2326, 2337, 2338, 2342}, {2340, 2351}, {2344, 2356, 2369}, {2385, 2422}, {2476, 2756}, {2852, 2875}, {2855, 2858}, {2856, 2865}, {2895, 2912}, {3122, 3123, 3125}, {3131, 3133}, {3132, 3136}, {3134, 3137}, {8482, 8818}, {8556, 9072}, {8584, 9533}, {8886, 8909}, {8890, 8916}, {8937, 8941}, {8990, 9726}, {9003, 9556}, {10268, 10269, 10270, 10272}, {10271, 10280}, {10274, 10282, 10314, 10316, 10324}, {10319, 10344}, {10327, 10353, 10386}, {10419, 10516}, {10646, 11409}, {11680, 11728}, {11686, 11693}, {11687, 11700}, {11767, 11796}, {12245, 12246, 12247, 12248, 12250}, {12251, 12253}, {12252, 12254, 12256}, {12262, 12264}, {12263, 12267}, {12265, 12268}, {32741, 33011}, {32756, 32785}, {32836, 34452}, {33355, 34455}, {33402, 34262}, {33428, 34554}, {33452, 34599}, {33644, 35296}, {33704, 36514}, {34489, 34499}, {34553, 35986}, {34799, 34859}, {34805, 34870}, {34920, 34926}, {35052, 36957}, {35077, 36565}, {35306, 36129}, {36069, 37227}, {38185, 38186, 38187, 38189}, {38188, 38204}, {38192, 38207, 38278, 38281, 38294}, {38285, 38330}, {38298, 38344, 38415}, {38474, 38691}, {38956, 40752}, {41383, 41468}, {41389, 41399}, {41390, 41406}, {41534, 41578}, {42478, 42479, 42480, 42482}, {42481, 42483, 42484, 42485, 42487}, {42488, 42490}, {42489, 42491, 42493}, {42499, 42501}, {42500, 42504}, {42502, 42505} {0, 1} {424, 426}, {2326, 2337}, {2376, 2382}, {3124, 3127}, {10269, 10270, 10272}, {10282, 10314}, {10403, 10415}, {11677, 11679}, {12246, 12247}, {12255, 12258}, {38186, 38187, 38189}, {38207, 38278}, {38449, 38469}, {41380, 41382}, {42478, 42479, 42480}, {42483, 42484}, {42492, 42495} {0, 1, 2} {10270, 10272}, {38187, 38189}, {42479, 42480}
[0, 1, 6, 9, 14, 17, 17], L11728 = [0, 1, 6, 10, 12, 13, 17], L11767 = [0, 1, 6, 12, 13, 17, 17], L11796 = [0, 1, 6, 14, 15, 17, 17], L12245 = [0, 2, 4, 6, 8, 10, 17], L12246 = [0, 2, 4, 6, 8, 12, 17], L12247 = [0, 2, 4, 6, 8, 14, 17], L12248 = [0, 2, 4, 6, 8, 16, 17], L12250 = [0, 2, 4, 6, 10, 12, 17], L12251 = [0, 2, 4, 6, 10, 16, 17], L12252 = [0, 2, 4, 6, 10, 17, 17], L12253 = [0, 2, 4, 6, 12, 14, 17], L12254 = [0, 2, 4, 6, 12, 17, 17], L12255 = [0, 2, 4, 6, 14, 17, 17] L12256 = [0, 2, 4, 6, 16, 17, 17], L12258 = [0, 2, 4, 8, 10, 17, 17], L12262 = [0, 2, 4, 10, 17, 17, 17], L12263 = [0, 2, 4, 12, 14, 17, 17], L12264 = [0, 2, 4, 12, 17, 17, 17], L12265 = [0, 2, 4, 14, 17, 17, 17], L12267 = [0, 2, 6, 8, 10, 17, 17], L12268 = [0, 2, 6, 8, 17, 17, 17], L32741 = [1, 2, 3, 5, 6, 14, 15], L32756 = [1, 2, 3, 5, 7, 8, 15], L32785 = [1, 2, 3, 5, 7, 13, 14], L32836 = [1, 2, 3, 5, 8, 15, 16], L33011 = [1, 2, 3, 6, 8, 9, 11], L33355 = [1, 2, 3, 8, 9, 12, 16], L33402 = [1, 2, 3, 8, 11, 13, 15], L33428 = [1, 2, 3, 8, 12, 15, 16], L33452 = [1, 2, 3, 8, 15, 16, 17], L33644 = [1, 2, 3, 11, 14, 16, 17], L33704 = [1, 2, 3, 13, 14, 16, 17], L34262 = [1, 2, 4, 5, 9, 11, 13], L34452 = [1, 2, 4, 6, 7, 13, 15], L34455 = [1, 2, 4, 6, 7, 15, 16], L34489 = [1, 2, 4, 6, 8, 12, 13], L34499 = [1, 2, 4, 6, 8, 14, 15], L34553 = [1, 2, 4, 6, 10, 13, 14], L34554 = [1, 2, 4, 6, 10, 13, 15], L34599 = [1, 2, 4, 6, 13, 15, 17], L34799 = [1, 2, 4, 8, 9, 13, 17], L34805 = [1, 2, 4, 8, 9, 17, 17], L34859 = [1, 2, 4, 8, 13, 15, 17], L34870 = [1, 2, 4, 8, 15, 17, 17], L34920 = [1, 2, 4, 9, 13, 17, 17], L34926 = [1, 2, 4, 9, 15, 17, 17], L35052 = [1, 2, 4, 12, 13, 15, 17], L35077 = [1, 2, 4, 13, 14, 15, 17], L35296 = [1, 2, 5, 6, 11, 16, 17], L35306 = [1, 2, 5, 6, 12, 13, 16], L35986 = [1, 2, 6, 7, 8, 10, 12] L36069 = [1, 2, 6, 7, 13, 15, 16], L36129 = [1, 2, 6, 8, 9, 11, 14], L36514 = [1, 2, 7, 8, 9, 10, 17], L36565 = [1, 2, 7, 8, 15, 16, 17], L36957 = [1, 2, 8, 11, 15, 16, 17], L37227 = [1, 2, 10, 11, 13, 15, 16], L38185 = [1, 3, 5, 7, 9, 11, 17], L38186 = [1, 3, 5, 7, 9, 13, 17], L38187 = [1, 3, 5, 7, 9, 15, 17], L38188 = [1, 3, 5, 7, 9, 17, 17], L38189 = [1, 3, 5, 7, 11, 13, 17], L38192 = [1, 3, 5, 7, 11, 17, 17], L38204 = [1, 3, 5, 7, 13, 17, 17], L38207 =
144
EMILIO A. LAURET
Table 5. (continued) n = 7 q 35
I {0}
indexes of I-isospectral families {396, 401}, {1451, 1512, 1516}, {1622, 1708}, {1623, 1626}, {1633, 1707}, {1977, 1982}, {1984, 1994}, {6350, 6469, 6474}, {6352, 6471}, {6472, 6488}, {6484, 6606}, {6489, 6586, 6611}, {6568, 6601}, {6575, 6607}, {6605, 7165}, {6637, 6964}, {6948, 6951}, {7164, 7173}, {7166, 7183}, {7169, 7182}, {7956, 7969}, {8025, 8030}, {8032, 8042}, {8046, 8063}, {24032, 24036, 24045}, {24051, 24126, 24127, 24128}, {24054, 24145}, {24055, 24058, 24132, 24141}, {24059, 24170}, {24147, 24150}, {24153, 24175, 24182, 24651, 24663}, {24174, 24223}, {24178, 24652}, {24186, 24242}, {24222, 24654}, {24226, 24237}, {24238, 24672}, {24642, 24814}, {24667, 24671, 24724}, {24694, 24827}, {24815, 24838}, {24842, 25456, 25467}, {24945, 24984}, {25737, 25740}, {25953, 25962}, {25955, 25972}, {25958, 25971}, {25991, 26196}, {26224, 26325}, {26391, 26805}, {26398, 26411}, {26432, 26802}, {26437, 26493}, {26483, 26504}, {26485, 26514}, {26488, 26513}, {26494, 26531}, {26500, 26530}, {28095, 28108}, {28109, 28112}, {28111, 28130}, {28116, 28138}, {28238, 28243}, {28245, 28255}, {28259, 28276}, {28281, 28307} {0, 1} {24036, 24045}, {24835, 24913} {4} {2151, 8376, 28877, 28900}, {2184, 2251, 8437, 8461, 8559}, {5543, 8398, 22031, 22284, 28901}, {5730, 8368, 8443, 8462, 8549}, {7066, 8394, 26127, 26257, 28896}, {7185, 8255, 26415, 26533, 28675}, {7294, 7812, 8080, 8290, 8454, 8457, 8560}, {12204, 21907, 22180, 22287, 28934}, {15439, 25992, 26192, 26259, 28925}, {15726, 21086, 22207, 22272, 22288, 26534, 28697}, {17519, 25974, 26496, 26526, 28542}, {18151, 19777, 22239, 22260, 22289, 25855, 28929}, {24203, 24511, 24674, 25339, 26244, 26516, 28693} {0, 3, 4} {26244, 26516}
[1, 3, 5, 7, 15, 17, 17], L38278 = [1, 3, 5, 9, 11, 17, 17], L38281 = [1, 3, 5, 9, 13, 17, 17], L38285 = [1, 3, 5, 9, 17, 17, 17] L38294 = [1, 3, 5, 11, 15, 17, 17], L38298 = [1, 3, 5, 11, 17, 17, 17], L38330 = [1, 3, 5, 13, 17, 17, 17], L38344 = [1, 3, 5, 15, 17, 17, 17], L38415 = [1, 3, 7, 9, 17, 17, 17], L38449 = [1, 3, 7, 11, 17, 17, 17], L38469 = [1, 3, 7, 15, 17, 17, 17], L38474 = [1, 3, 7, 17, 17, 17, 17], L38691 = [1, 3, 9, 17, 17, 17, 17], L38956 = [1, 3, 13, 17, 17, 17, 17], L40752 = [1, 5, 7, 17, 17, 17, 17], L41380 = [1, 6, 9, 10, 12, 13, 17], L41382 = [1, 6, 9, 10, 12, 15, 17], L41383 = [1, 6, 9, 10, 12, 17, 17], L41389 = [1, 6, 9, 10, 15, 17, 17], L41390 = [1, 6, 9, 10, 17, 17, 17], L41399 = [1, 6, 9, 12, 13, 17, 17], L41406 = [1, 6, 9, 14, 17, 17, 17], L41468 = [1, 6, 10, 12, 13, 17, 17], L41534 = [1, 6, 12, 13, 17, 17, 17], L41578 = [1, 6, 14, 15, 17, 17, 17], L42478 = [2, 4, 6, 8, 10, 12, 17], L42479 = [2, 4, 6, 8, 10, 14, 17], L42480 = [2, 4, 6, 8, 10, 16, 17], L42481 = [2, 4, 6, 8, 10, 17, 17], L42482 = [2, 4, 6, 8, 12, 16, 17], L42483 = [2, 4, 6, 8, 12, 17, 17], L42484 = [2, 4, 6, 8, 14, 17, 17] L42485 = [2, 4, 6, 8, 16, 17, 17], L42487 = [2, 4, 6, 10, 12, 17, 17], L42488 = [2, 4, 6, 10, 16, 17, 17], L42489 = [2, 4, 6, 10, 17, 17, 17], L42490 = [2, 4, 6, 12, 14, 17, 17], L42491 = [2, 4, 6, 12, 17, 17, 17], L42492 = [2, 4, 6, 14, 17, 17, 17], L42493 = [2, 4, 6, 16, 17, 17, 17], L42495 = [2, 4, 8, 10, 17, 17, 17], L42499 = [2, 4, 10, 17, 17, 17, 17], L42500 = [2, 4, 12, 14, 17, 17, 17], L42501 = [2, 4, 12, 17, 17, 17, 17], L42502 = [2, 4, 14, 17, 17, 17, 17], L42504 = [2, 6, 8, 10, 17, 17, 17], L42505 = [2, 6, 8, 17, 17, 17, 17]. q = 35 : L396 = [0, 0, 0, 1, 4, 6, 9], L401 = [0, 0, 0, 1, 4, 6, 16], L1451 = [0, 0, 1, 2, 3, 8, 16], L1512 = [0, 0, 1, 2, 4, 8, 9], L1516 = [0, 0, 1, 2, 4, 8, 16], L1622 = [0, 0, 1, 2, 6, 7, 16], L1623 = [0, 0, 1, 2, 6, 8, 9],
APPENDIX
145
L1626 = [0, 0, 1, 2, 6, 8, 12], L1633 = [0, 0, 1, 2, 6, 9, 12], L1707 = [0, 0, 1, 2, 8, 9, 12], L1708 = [0, 0, 1, 2, 8, 9, 14], L1977 = [0, 0, 1, 4, 6, 7, 9], L1982 = [0, 0, 1, 4, 6, 7, 16], L1984 = [0, 0, 1, 4, 6, 9, 14], L1994 = [0, 0, 1, 4, 6, 14, 16], L2151 = [0, 0, 1, 6, 8, 13, 15], L2184 = [0, 0, 1, 7, 7, 14, 14], L2251 = [0, 0, 5, 7, 7, 14, 14], L5543 = [0, 1, 1, 6, 8, 13, 15], L5730 = [0, 1, 1, 7, 7, 14, 14], L6350 = [0, 1, 2, 3, 4, 11, 16], L6352 = [0, 1, 2, 3, 4, 12, 13], L6469 = [0, 1, 2, 3, 6, 8, 17], L6471 = [0, 1, 2, 3, 6, 9, 11], L6472 = [0, 1, 2, 3, 6, 9, 13], L6474 = [0, 1, 2, 3, 6, 9, 16], L6484 = [0, 1, 2, 3, 6, 11, 13], L6488 = [0, 1, 2, 3, 6, 11, 17], L6489 = [0, 1, 2, 3, 6, 12, 13], L6568 = [0, 1, 2, 3, 8, 10, 11], L6575 = [0, 1, 2, 3, 8, 11, 13], L6586 = [0, 1, 2, 3, 8, 13, 16], L6601 = [0, 1, 2, 3, 9, 10, 16], L6605 = [0, 1, 2, 3, 9, 11, 16], L6606 = [0, 1, 2, 3, 9, 11, 17], L6607 = [0, 1, 2, 3, 9, 12, 13], L6611 = [0, 1, 2, 3, 9, 12, 17], L6637 = [0, 1, 2, 3, 10, 12, 15], L6948 = [0, 1, 2, 5, 6, 8, 9], L6951 = [0, 1, 2, 5, 6, 8, 12], L6964 = [0, 1, 2, 5, 6, 10, 11], L7066 = [0, 1, 2, 5, 9, 12, 16], L7164 = [0, 1, 2, 6, 8, 9, 10], L7165 = [0, 1, 2, 6, 8, 9, 11], L7166 = [0, 1, 2, 6, 8, 9, 12], L7169 = [0, 1, 2, 6, 8, 9, 15], L7173 = [0, 1, 2, 6, 8, 10, 12], L7182 = [0, 1, 2, 6, 8, 12, 15], L7183 = [0, 1, 2, 6, 8, 12, 16], L7185 = [0, 1, 2, 6, 8, 13, 15], L7294 = [0, 1, 2, 7, 7, 14, 14], L7812 = [0, 1, 3, 7, 7, 14, 14], L7956 = [0, 1, 4, 5, 6, 9, 15], L7969 = [0, 1, 4, 5, 6, 15, 16], L8025 = [0, 1, 4, 6, 7, 7, 9], L8030 = [0, 1, 4, 6, 7, 7, 16], L8032 = [0, 1, 4, 6, 7, 9, 14], L8042 = [0, 1, 4, 6, 7, 14, 16], L8046 = [0, 1, 4, 6, 9, 14, 14], L8063 = [0, 1, 4, 6, 14, 14, 16], L8080 = [0, 1, 4, 7, 7, 14, 14], L8255 = [0, 1, 5, 6, 8, 13, 15], L8290 = [0, 1, 5, 7, 7, 14, 14], L8368 = [0, 1, 6, 7, 7, 14, 14], L8376 = [0, 1, 6, 7, 8, 13, 15], L8394 = [0, 1, 6, 8, 10, 13, 15], L8398 = [0, 1, 6, 8, 13, 15, 15], L8437 = [0, 1, 7, 7, 7, 14, 14], L8443 = [0, 1, 7, 7, 8, 14, 14], L8454 = [0, 1, 7, 7, 10, 14, 14], L8457 = [0, 1, 7, 7, 11, 14, 14], L8461 = [0, 1, 7, 7, 14, 14, 14], L8462 = [0, 1, 7, 7, 14, 14, 15], L8549 = [0, 5, 5, 7, 7, 14, 14], L8559 = [0, 5, 7, 7, 7, 14, 14], L8560 = [0, 5, 7, 7, 10, 14, 14], L12204 = [1, 1, 1, 6, 8, 13, 15], L15439 = [1, 1, 2, 5, 9, 12, 16], L15726 = [1, 1, 2, 6, 8, 13, 15], L17519 = [1, 1, 3, 4, 10, 11, 17], L18151 = [1, 1, 3, 6, 8, 13, 15], L19777 = [1, 1, 4, 6, 8, 13, 15], L21086 = [1, 1, 5, 6, 8, 13, 15], L21907 = [1, 1, 6, 6, 8, 13, 15], L22031 = [1, 1, 6, 7, 8, 13, 15], L22180 = [1, 1, 6, 8, 8, 13, 15], L22207 = [1, 1, 6, 8, 9, 13, 15], L22239 = [1, 1, 6, 8, 10, 13, 15], L22260 = [1, 1, 6, 8, 11, 13, 15], L22272 = [1, 1, 6, 8, 12, 13, 15], L22284 = [1, 1, 6, 8, 13, 14, 15], L22287 = [1, 1, 6, 8, 13, 15, 15], L22288 = [1, 1, 6, 8, 13, 15, 16] L22289 = [1, 1, 6, 8, 13, 15, 17], L24032 = [1, 2, 3, 4, 6, 9, 13], L24036 = [1, 2, 3, 4, 6, 9, 17], L24045 = [1, 2, 3, 4, 6, 11, 12], L24051 = [1, 2, 3, 4, 6, 12, 13], L24054 = [1, 2, 3, 4, 6, 12, 16], L24055 = [1, 2, 3, 4, 6, 12, 17], L24058 = [1, 2, 3, 4, 6, 13, 16], L24059 = [1, 2, 3, 4, 6, 13, 17], L24126 = [1, 2, 3, 4, 8, 9, 11], L24127 = [1, 2, 3, 4, 8, 9, 12], L24128 = [1, 2, 3, 4, 8, 9, 13], L24132 = [1, 2, 3, 4, 8, 9, 17], L24141 = [1, 2, 3, 4, 8, 11, 12], L24145 = [1, 2, 3, 4, 8, 11, 16], L24147 = [1, 2, 3, 4, 8, 12, 13], L24150 = [1, 2, 3, 4, 8, 12, 17], L24153 = [1, 2, 3, 4, 8, 13, 16], L24170 = [1, 2, 3, 4, 9, 11, 12], L24174 = [1, 2, 3, 4, 9, 11, 17], L24175 = [1, 2, 3, 4, 9, 12, 13], L24178 = [1, 2, 3, 4, 9, 12, 16], L24182 = [1, 2, 3, 4, 9, 13, 16], L24186 = [1, 2, 3, 4, 9, 14, 17], L24203 = [1, 2, 3, 4, 10, 11, 17], L24222 = [1, 2, 3, 4, 11, 12, 16], L24223 = [1, 2, 3, 4, 11, 12, 17], L24226 = [1, 2, 3, 4, 11, 13, 16] L24237 = [1, 2, 3, 4, 12, 13, 16], L24238 = [1, 2, 3, 4, 12, 13, 17], L24242 = [1, 2, 3, 4, 12, 14, 17], L24511 = [1, 2, 3, 5, 9, 12, 16], L24642 = [1, 2, 3, 6, 7, 13, 17], L24651 = [1, 2, 3, 6, 8, 9, 11], L24652 = [1, 2, 3, 6, 8, 9, 13], L24654 = [1, 2, 3, 6, 8, 9, 16], L24663 = [1, 2, 3, 6, 8, 11, 12], L24667 = [1, 2, 3, 6, 8, 11, 17], L24671 = [1, 2, 3, 6, 8, 12, 16], L24672 = [1, 2, 3, 6, 8, 12, 17], L24674 = [1, 2, 3, 6, 8, 13, 15], L24694 = [1, 2, 3, 6, 9, 14, 16], L24724 = [1, 2, 3, 6, 11, 13, 17], L24814 = [1, 2, 3, 7, 8, 9, 12], L24815 = [1, 2, 3, 7, 8, 9, 13], L24827 = [1, 2, 3, 7, 8, 11, 13], L24835 = [1, 2, 3, 7, 8, 12, 17], L24838 = [1, 2, 3, 7, 8, 13, 16], L24842 = [1, 2, 3, 7, 8, 14, 16], L24913 = [1, 2, 3, 7, 12, 13, 17], L24945 = [1, 2, 3, 8, 9, 12, 13], L24984 = [1, 2, 3, 8, 11, 13, 17], L25339 = [1, 2, 4, 5, 9, 12, 16], L25456 = [1, 2, 4, 7, 8, 9, 14], L25467 = [1, 2, 4, 7, 8, 14, 16], L25737 = [1, 2, 5, 5, 6, 8, 9], L25740 = [1, 2, 5, 5, 6, 8, 12], L25855 = [1, 2, 5, 5, 9, 12, 16], L25953 = [1, 2, 5, 6, 8, 9, 10], L25955 = [1, 2, 5, 6, 8, 9, 12], L25958 = [1, 2, 5, 6, 8, 9, 15], L25962 = [1, 2, 5, 6, 8, 10, 12], L25971 = [1, 2, 5, 6, 8, 12, 15], L25972 = [1, 2, 5, 6, 8, 12, 16], L25974 = [1, 2, 5, 6, 8, 13, 15], L25991 = [1, 2, 5, 6, 9, 12, 15], L25992 = [1, 2, 5, 6, 9, 12, 16], L26127 = [1, 2, 5, 7, 9, 12, 16], L26192 = [1, 2, 5, 8, 9, 12, 16], L26196 = [1, 2, 5, 8, 9, 15, 16], L26224 = [1, 2, 5, 8, 12, 15, 16], L26244 = [1, 2, 5, 9, 10, 12, 16], L26257 = [1, 2, 5, 9, 12, 14, 16], L26259 = [1, 2, 5, 9, 12, 15, 16], L26325 = [1, 2, 5, 12, 13, 15, 16], L26391 = [1, 2, 6, 7, 7, 14, 16], L26398 = [1, 2, 6, 7, 8, 9, 14], L26411 = [1, 2, 6, 7, 8, 12, 14], L26415 = [1, 2, 6, 7, 8, 13, 15], L26432 = [1, 2, 6, 7, 9, 12, 14], L26437 = [1, 2, 6, 7, 9, 13, 16], L26483 = [1, 2, 6, 8, 9, 10, 10], L26485 = [1, 2, 6, 8, 9, 10, 12], L26488 = [1, 2, 6, 8, 9, 10, 15], L26493 = [1, 2, 6, 8, 9, 12, 14], L26494 = [1, 2, 6, 8, 9, 12, 15], L26496 = [1, 2, 6, 8, 9, 13, 15], L26500 =
146
EMILIO A. LAURET
Table 5. (continued) n = 7 q I indexes of I-isospectral families 36 {0} {2665, 2669}, {3318, 3320}, {3323, 3344}, {3775, 3780}, {5169, 5171}, {5320, 5322}, {12325, 12335}, {13059, 13402}, {13327, 13331}, {13405, 13409}, {13415, 13429}, {13419, 13440}, {15034, 15036}, {15039, 15060}, {15536, 15652}, {15928, 15930}, {15933, 15954}, {15988, 15990}, {15993, 16065}, {15995, 16002}, {16000, 16007}, {16005, 16092}, {16013, 16095}, {17544, 17549}, {17597, 17625}, {17606, 17632}, {17613, 17634}, {21471, 21473}, {21674, 21676}, {21712, 21714}, {21718, 21724}, {21720, 21728}, {21722, 21729}, {22091, 22093}, {22121, 22123}, {22126, 22131}, {22129, 22134}, {39965, 39967}, {39986, 39988}, {39997, 40074}, {40713, 40725}, {51539, 51798}, {51666, 51676}, {51732, 51755}, {51839, 51849},
[1, 2, 6, 8, 9, 15, 15], L26504 = [1, 2, 6, 8, 10, 10, 12], L26513 = [1, 2, 6, 8, 10, 12, 15], L26514 = [1, 2, 6, 8, 10, 12, 16], L26516 = [1, 2, 6, 8, 10, 13, 15], L26526 = [1, 2, 6, 8, 12, 13, 15], L26530 = [1, 2, 6, 8, 12, 15, 15], L26531 = [1, 2, 6, 8, 12, 15, 16], L26533 = [1, 2, 6, 8, 13, 14, 15], L26534 = [1, 2, 6, 8, 13, 15, 15], L26802 = [1, 2, 7, 8, 9, 12, 14], L26805 = [1, 2, 7, 8, 9, 14, 14], L28095 = [1, 4, 5, 6, 7, 9, 15], L28108 = [1, 4, 5, 6, 7, 15, 16], L28109 = [1, 4, 5, 6, 9, 10, 11], L28111 = [1, 4, 5, 6, 9, 10, 15], L28112 = [1, 4, 5, 6, 9, 10, 16], L28116 = [1, 4, 5, 6, 9, 14, 15], L28130 = [1, 4, 5, 6, 10, 15, 16], L28138 = [1, 4, 5, 6, 14, 15, 16], L28238 = [1, 4, 6, 7, 7, 7, 9], L28243 = [1, 4, 6, 7, 7, 7, 16], L28245 = [1, 4, 6, 7, 7, 9, 14], L28255 = [1, 4, 6, 7, 7, 14, 16], L28259 = [1, 4, 6, 7, 9, 14, 14], L28276 = [1, 4, 6, 7, 14, 14, 16], L28281 = [1, 4, 6, 9, 14, 14, 14], L28307 = [1, 4, 6, 14, 14, 14, 16], L28542 = [1, 5, 5, 6, 8, 13, 15], L28675 = [1, 5, 6, 7, 8, 13, 15], L28693 = [1, 5, 6, 8, 10, 13, 15], L28697 = [1, 5, 6, 8, 13, 15, 15], L28877 = [1, 6, 7, 7, 8, 13, 15], L28896 = [1, 6, 7, 8, 10, 13, 15], L28900 = [1, 6, 7, 8, 13, 14, 15], L28901 = [1, 6, 7, 8, 13, 15, 15], L28925 = [1, 6, 8, 10, 10, 13, 15], L28929 = [1, 6, 8, 10, 13, 15, 15], L28934 = [1, 6, 8, 13, 15, 15, 15]. q = 36 : L542 = [0, 0, 0, 1, 3, 5, 17], L559 = [0, 0, 0, 1, 3, 7, 11], L2665 = [0, 0, 1, 2, 5, 7, 10], L2669 = [0, 0, 1, 2, 5, 7, 14], L3120 = [0, 0, 1, 3, 3, 5, 17], L3137 = [0, 0, 1, 3, 3, 7, 11], L3314 = [0, 0, 1, 3, 5, 6, 17], L3318 = [0, 0, 1, 3, 5, 7, 11], L3320 = [0, 0, 1, 3, 5, 7, 13], L3323 = [0, 0, 1, 3, 5, 7, 17], L3341 = [0, 0, 1, 3, 5, 9, 17], L3344 = [0, 0, 1, 3, 5, 11, 13], L3352 = [0, 0, 1, 3, 5, 12, 17], L3368 = [0, 0, 1, 3, 5, 17, 18], L3385 = [0, 0, 1, 3, 6, 7, 11], L3450 = [0, 0, 1, 3, 7, 9, 11], L3461 = [0, 0, 1, 3, 7, 11, 12], L3463 = [0, 0, 1, 3, 7, 11, 18], L3775 = [0, 0, 1, 4, 5, 7, 16], L3780 = [0, 0, 1, 4, 5, 8, 11], L3962 = [0, 0, 1, 4, 8, 12, 16], L4858 = [0, 0, 1, 11, 12, 12, 13 L5169 = [0, 0, 2, 3, 4, 8, 10], L5171 = [0, 0, 2, 3, 4, 8, 14], L5320 = [0, 0, 2, 4, 8, 9, 10], L5322 = [0, 0, 2, 4, 8, 9, 14], L5516 = [0, 0, 3, 4, 8, 12, 16], L5585 = [0, 0, 4, 8, 9, 12, 16], L8917 = [0, 1, 1, 4, 8, 12, 16], L10949 = [0, 1, 1, 11, 11, 13, 13], L12325 = [0, 1, 2, 3, 5, 10, 11], L12335 = [0, 1, 2, 3, 5, 11, 14], L13059 = [0, 1, 2, 4, 7, 11, 13], L13127 = [0, 1, 2, 4, 8, 12, 16], L13327 = [0, 1, 2, 5, 6, 7, 10], L13331 = [0, 1, 2, 5, 6, 7, 14], L13402 = [0, 1, 2, 5, 7, 8, 17], L13405 = [0, 1, 2, 5, 7, 9, 10], L13409 = [0, 1, 2, 5, 7, 9, 14], L13415 = [0, 1, 2, 5, 7, 10, 12], L13419 = [0, 1, 2, 5, 7, 10, 18], L13429 = [0, 1, 2, 5, 7, 12, 14], L13440 = [0, 1, 2, 5, 7, 14, 18], L13917 = [0, 1, 2, 6, 10, 14, 18], L14579 = [0, 1, 2, 10, 11, 13, 14], L14836 = [0, 1, 3, 3, 3, 5, 17], L14853 = [0, 1, 3, 3, 3, 7, 11], L15030 = [0, 1, 3, 3, 5, 6, 17], L15034 = [0, 1, 3, 3, 5, 7, 11], L15036 = [0, 1, 3, 3, 5, 7, 13], L15039 = [0, 1, 3, 3, 5, 7, 17], L15057 = [0, 1, 3, 3, 5, 9, 17], L15060 = [0, 1, 3, 3, 5, 11, 13], L15069 = [0, 1, 3, 3, 5, 12, 17], L15082 = [0, 1, 3, 3, 5, 15, 17], L15087 = [0, 1, 3, 3, 5, 17, 18], L15104 = [0, 1, 3, 3, 6, 7, 11], L15171 = [0, 1, 3, 3, 7, 9, 11], L15184 = [0, 1, 3, 3, 7, 11, 12], L15185 = [0, 1, 3, 3, 7, 11, 15], L15187 = [0, 1, 3, 3, 7, 11, 18], L15536 = [0, 1, 3, 4, 5, 11, 16], L15652 = [0, 1, 3, 4, 7, 8, 13], L15732 = [0, 1, 3, 4, 8, 12, 16], L15924 = [0, 1, 3, 5, 6, 6, 17], L15928 = [0, 1, 3, 5, 6, 7, 11], L15930 = [0, 1, 3, 5, 6, 7, 13], L15933 = [0, 1, 3, 5, 6, 7, 17], L15951 = [0, 1, 3, 5, 6, 9, 17], L15954 = [0, 1, 3, 5, 6, 11, 13], L15962 = [0, 1, 3, 5, 6, 12, 17], L15978 = [0, 1, 3, 5, 6, 17, 18], L15988 = [0, 1, 3, 5, 7, 9, 11], L15990 = [0, 1, 3, 5, 7, 9, 13], L15993 = [0, 1, 3, 5, 7, 9, 17], L15995 = [0, 1, 3, 5, 7, 11, 12], L15996 = [0, 1, 3, 5, 7, 11, 13], L15999 = [0, 1, 3, 5, 7, 11, 17], L16000 =
APPENDIX
147
Table 5. (continued) n = 7 q I indexes of I-isospectral families 36 {0} {51880, 51911}, {51885, 51923}, {53982, 54036}, {53990, 54002}, {54057, 54626}, (cont.) {54065, 54621}, {54155, 57802}, {54159, 54779}, {54348, 55558}, {54671, 55825}, {54736, 55842}, {54745, 55854}, {54922, 54957}, {55483, 55487}, {55561, 55565}, {55571, 55585}, {55575, 55596}, {55833, 55846}, {55857, 55861}, {55867, 55881}, {55871, 55892}, {55902, 55911}, {55906, 55940}, {55910, 55951}, {55916, 55972}, {59922, 59924}, {59927, 59948}, {60823, 60825}, {60828, 60849}, {60887, 60889}, {60892, 60969}, {60894, 60901}, {60896, 60906}, {60899, 60907}, {60904, 60999}, {60910, 61003}, {60915, 61004}, {62592, 62915}, {62653, 62681}, {62721, 63189}, {62752, 63204}, {62763, 63209}, {63965, 63967}, {63970, 63991}, {64025, 64027}, {64030, 64102}, {64032, 64039}, {64037, 64044}, {64042, 64129}, {64050, 64132}, {64214, 64216}, {64219, 64412}, {64221, 64228}, {64226, 64233}, {64231, 64439},
[0, 1, 3, 5, 7, 11, 18], L16002 = [0, 1, 3, 5, 7, 12, 13], L16005 = [0, 1, 3, 5, 7, 12, 17], L16007 = [0, 1, 3, 5, 7, 13, 18], L16013 = [0, 1, 3, 5, 7, 17, 18], L16062 = [0, 1, 3, 5, 9, 9, 17], L16065 = [0, 1, 3, 5, 9, 11, 13], L16073 = [0, 1, 3, 5, 9, 12, 17], L16089 = [0, 1, 3, 5, 9, 17, 18], L16092 = [0, 1, 3, 5, 11, 12, 13], L16095 = [0, 1, 3, 5, 11, 13, 18], L16104 = [0, 1, 3, 5, 12, 12, 17], L16120 = [0, 1, 3, 5, 12, 17, 18], L16149 = [0, 1, 3, 5, 17, 18, 18], L16166 = [0, 1, 3, 6, 6, 7, 11], L16231 = [0, 1, 3, 6, 7, 9, 11], L16242 = [0, 1, 3, 6, 7, 11, 12], L16244 = [0, 1, 3, 6, 7, 11, 18], L16463 = [0, 1, 3, 7, 9, 9, 11], L16474 = [0, 1, 3, 7, 9, 11, 12], L16476 = [0, 1, 3, 7, 9, 11, 18], L16504 = [0, 1, 3, 7, 11, 12, 12], L16506 = [0, 1, 3, 7, 11, 12, 18], L16509 = [0, 1, 3, 7, 11, 18, 18], L16778 = [0, 1, 3, 9, 11, 13, 15] L16919 = [0, 1, 3, 11, 12, 12, 13], L17357 = [0, 1, 4, 4, 8, 12, 16], L17544 = [0, 1, 4, 5, 6, 7, 16], L17549 = [0, 1, 4, 5, 6, 8, 11], L17597 = [0, 1, 4, 5, 7, 9, 16], L17606 = [0, 1, 4, 5, 7, 12, 16], L17613 = [0, 1, 4, 5, 7, 16, 18], L17625 = [0, 1, 4, 5, 8, 9, 11], L17632 = [0, 1, 4, 5, 8, 11, 12], L17634 = [0, 1, 4, 5, 8, 11, 18], L17638 = [0, 1, 4, 5, 8, 12, 16], L17873 = [0, 1, 4, 6, 8, 12, 16], L18146 = [0, 1, 4, 8, 8, 12, 16], L18193 = [0, 1, 4, 8, 9, 12, 16], L18227 = [0, 1, 4, 8, 10, 12, 16], L18246 = [0, 1, 4, 8, 11, 12, 16], L18249 = [0, 1, 4, 8, 11, 13, 16], L18260 = [0, 1, 4, 8, 12, 12, 16], L18268 = [0, 1, 4, 8, 12, 14, 16], L18272 = [0, 1, 4, 8, 12, 15, 16], L18274 = [0, 1, 4, 8, 12, 16, 16] L18275 = [0, 1, 4, 8, 12, 16, 17], L18276 = [0, 1, 4, 8, 12, 16, 18], L18817 = [0, 1, 5, 7, 11, 13, 17], L19167 = [0, 1, 6, 6, 11, 13, 18], L19591 = [0, 1, 6, 11, 12, 12, 13], L20372 = [0, 1, 9, 11, 12, 12, 13], L20659 = [0, 1, 11, 12, 12, 12, 13], L20662 = [0, 1, 11, 12, 12, 13, 15], L20663 = [0, 1, 11, 12, 12, 13, 18], L21471 = [0, 2, 3, 3, 4, 8, 10], L21473 = [0, 2, 3, 3, 4, 8, 14], L21674 = [0, 2, 3, 4, 6, 8, 10], L21676 = [0, 2, 3, 4, 6, 8, 14], L21712 = [0, 2, 3, 4, 8, 9, 10], L21714 = [0, 2, 3, 4, 8, 9, 14], L21718 = [0, 2, 3, 4, 8, 10, 12], L21720 = [0, 2, 3, 4, 8, 10, 15], L21722 = [0, 2, 3, 4, 8, 10, 18], L21724 = [0, 2, 3, 4, 8, 12, 14], L21726 = [0, 2, 3, 4, 8, 12, 16], L21728 = [0, 2, 3, 4, 8, 14, 15], L21729 = [0, 2, 3, 4, 8, 14, 18], L21875 = [0, 2, 3, 6, 10, 14, 18], L21981 = [0, 2, 3, 9, 10, 14, 15], L22002 = [0, 2, 3, 10, 12, 12, 14], L22091 = [0, 2, 4, 6, 8, 9, 10], L22093 = [0, 2, 4, 6, 8, 9, 14], L22121 = [0, 2, 4, 8, 9, 9, 10], L22123 = [0, 2, 4, 8, 9, 9, 14], L22126 = [0, 2, 4, 8, 9, 10, 12], L22129 = [0, 2, 4, 8, 9, 10, 18], L22131 = [0, 2, 4, 8, 9, 12, 14], L22132 = [0, 2, 4, 8, 9, 12, 16], L22134 = [0, 2, 4, 8, 9, 14, 18], L22240 = [0, 2, 6, 9, 10, 14, 18], L22327 = [0, 2, 9, 10, 12, 12, 14], L22448 = [0, 3, 3, 4, 8, 12, 16], L22547 = [0, 3, 4, 4, 8, 12, 16], L22605 = [0, 3, 4, 6, 8, 12, 16], L22634 = [0, 3, 4, 8, 9, 12, 16], L22636 = [0, 3, 4, 8, 9, 15, 16], L22642 = [0, 3, 4, 8, 12, 12, 16], L22644 = [0, 3, 4, 8, 12, 15, 16], L22646 = [0, 3, 4, 8, 12, 16, 18], L22734 = [0, 4, 4, 8, 9, 12, 16], L22774 = [0, 4, 6, 8, 9, 12, 16], L22793 = [0, 4, 8, 9, 9, 12, 16], L22798 = [0, 4, 8, 9, 12, 12, 16], L22800 = [0, 4, 8, 9, 12, 16, 18], L32066 = [1, 1, 2, 6, 10, 14, 18], L36814 = [1, 1, 3, 11, 11, 13, 13], L39965 = [1, 1, 5, 5, 7, 7, 11], L39967 = [1, 1, 5, 5, 7, 7, 13], L39986 = [1, 1, 5, 5, 7, 11, 13], L39988 = [1, 1, 5, 5, 7, 11, 17], L39997 = [1, 1, 5, 5, 7, 13, 17], L40074 = [1, 1, 5, 5, 11, 13, 17], L40713 = [1, 1, 5, 7, 11, 11, 13], L40725 = [1, 1, 5, 7, 11, 13, 13], L43045 = [1, 1, 6, 11, 11, 13, 13], L45369 = [1, 1, 9, 11, 11, 13, 13], L46006 = [1, 1, 11, 11, 12, 13, 13], L46012 = [1, 1, 11, 11, 13, 13, 15], L46013 = [1, 1, 11, 11, 13, 13, 18], L49316 = [1, 2, 2, 6, 10, 14, 18], L51539 = [1, 2, 3, 4, 11, 13, 17], L51666 = [1, 2, 3, 5, 6, 10, 11], L51676 = [1, 2, 3, 5, 6, 11, 14],
148
EMILIO A. LAURET
Table 5. (continued) n = 7 q I indexes of I-isospectral families 36 {0} {64239, 64442}, {64241, 64256}, {64246, 64261}, {64254, 64269}, {64259, 64499}, (cont.) {64267, 64502}, {64277, 64506}, {68707, 68712}, {68760, 68788}, {68769, 68795}, {68776, 68797}, {68899, 68901}, {68918, 68998}, {68927, 69005}, {68934, 69007}, {68947, 69026}, {68954, 69028}, {68961, 69030}, {78620, 78622}, {78825, 78827}, {78864, 78866}, {78870, 78876}, {78872, 78880}, {78874, 78881}, {79424, 79426}, {79462, 79464}, {79468, 79474}, {79470, 79478}, {79472, 79479}, {79569, 79571}, {79575, 79581}, {79577, 79585}, {79579, 79586}, {79592, 79605}, {79594, 79609}, {79596, 79610}, {79601, 79616}, {79603, 79617}, {80404, 80406}, {80434, 80436}, {80439, 80444}, {80442, 80447}, {80511, 80513}, {80516, 80521}, {80519, 80524}, {80528, 80537}, {80531, 80540}, {80535, 80544}
L51732 = [1, 2, 3, 5, 7, 10, 15], L51755 = [1, 2, 3, 5, 7, 14, 15], L51757 = [1, 2, 3, 5, 7, 14, 17], L51798 = [1, 2, 3, 5, 8, 11, 13], L51839 = [1, 2, 3, 5, 9, 10, 11], L51849 = [1, 2, 3, 5, 9, 11, 14], L51880 = [1, 2, 3, 5, 10, 11, 12], L51881 = [1, 2, 3, 5, 10, 11, 13], L51885 = [1, 2, 3, 5, 10, 11, 18], L51900 = [1, 2, 3, 5, 10, 14, 17], L51911 = [1, 2, 3, 5, 11, 12, 14], L51923 = [1, 2, 3, 5, 11, 14, 18], L52289 = [1, 2, 3, 6, 10, 14, 18], L52502 = [1, 2, 3, 7, 10, 11, 14] L53056 = [1, 2, 3, 10, 11, 13, 14], L53982 = [1, 2, 4, 5, 7, 10, 16], L53990 = [1, 2, 4, 5, 7, 11, 17], L54002 = [1, 2, 4, 5, 7, 13, 17], L54036 = [1, 2, 4, 5, 8, 10, 11], L54057 = [1, 2, 4, 5, 8, 13, 14], L54065 = [1, 2, 4, 5, 8, 14, 17], L54155 = [1, 2, 4, 5, 11, 13, 15], L54159 = [1, 2, 4, 5, 11, 14, 16], L54348 = [1, 2, 4, 6, 7, 11, 13], L54513 = [1, 2, 4, 6, 10, 14, 18], L54621 = [1, 2, 4, 7, 8, 10, 11], L54626 = [1, 2, 4, 7, 8, 10, 17], L54671 = [1, 2, 4, 7, 9, 11, 13], L54736 = [1, 2, 4, 7, 11, 12, 13], L54745 = [1, 2, 4, 7, 11, 13, 18], L54779 = [1, 2, 4, 7, 13, 14, 16], L54922 = [1, 2, 4, 8, 10, 11, 13], L54957 = [1, 2, 4, 8, 11, 13, 14], L55483 = [1, 2, 5, 6, 6, 7, 10], L55487 = [1, 2, 5, 6, 6, 7, 14], L55558 = [1, 2, 5, 6, 7, 8, 17], L55561 = [1, 2, 5, 6, 7, 9, 10], L55565 = [1, 2, 5, 6, 7, 9, 14], L55571 = [1, 2, 5, 6, 7, 10, 12], L55575 = [1, 2, 5, 6, 7, 10, 18], L55585 = [1, 2, 5, 6, 7, 12, 14], L55596 = [1, 2, 5, 6, 7, 14, 18], L55719 = [1, 2, 5, 6, 10, 14, 18], L55825 = [1, 2, 5, 7, 8, 9, 17], L55833 = [1, 2, 5, 7, 8, 11, 13], L55842 = [1, 2, 5, 7, 8, 12, 17], L55846 = [1, 2, 5, 7, 8, 13, 17], L55854 = [1, 2, 5, 7, 8, 17, 18], L55857 = [1, 2, 5, 7, 9, 9, 10], L55861 = [1, 2, 5, 7, 9, 9, 14], L55867 = [1, 2, 5, 7, 9, 10, 12], L55871 = [1, 2, 5, 7, 9, 10, 18], L55881 = [1, 2, 5, 7, 9, 12, 14], L55892 = [1, 2, 5, 7, 9, 14, 18], L55902 = [1, 2, 5, 7, 10, 11, 13], L55906 = [1, 2, 5, 7, 10, 12, 12], L55910 = [1, 2, 5, 7, 10, 12, 18], L55911 = [1, 2, 5, 7, 10, 13, 17], L55916 = [1, 2, 5, 7, 10, 18, 18], L55940 = [1, 2, 5, 7, 12, 12, 14], L55951 = [1, 2, 5, 7, 12, 14, 18], L55972 = [1, 2, 5, 7, 14, 18, 18], L56804 = [1, 2, 6, 6, 10, 14, 18] L57187 = [1, 2, 6, 8, 10, 14, 18], L57345 = [1, 2, 6, 9, 10, 14, 18], L57451 = [1, 2, 6, 10, 10, 14, 18], L57466 = [1, 2, 6, 10, 11, 13, 14], L57470 = [1, 2, 6, 10, 11, 14, 18], L57490 = [1, 2, 6, 10, 12, 14, 18], L57506 = [1, 2, 6, 10, 14, 14, 18], L57509 = [1, 2, 6, 10, 14, 15, 18], L57512 = [1, 2, 6, 10, 14, 16, 18], L57513 = [1, 2, 6, 10, 14, 17, 18], L57514 = [1, 2, 6, 10, 14, 18, 18], L57802 = [1, 2, 7, 8, 11, 13, 15], L58956 = [1, 2, 9, 10, 11, 13, 14], L59269 = [1, 2, 10, 11, 12, 13, 14], L59280 = [1, 2, 10, 11, 13, 14, 15], L59281 = [1, 2, 10, 11, 13, 14, 18], L59724 = [1, 3, 3, 3, 3, 5, 17], L59741 = [1, 3, 3, 3, 3, 7, 11], L59918 = [1, 3, 3, 3, 5, 6, 17], L59922 = [1, 3, 3, 3, 5, 7, 11], L59924 = [1, 3, 3, 3, 5, 7, 13], L59927 = [1, 3, 3, 3, 5, 7, 17], L59945 = [1, 3, 3, 3, 5, 9, 17], L59948 = [1, 3, 3, 3, 5, 11, 13], L59957 = [1, 3, 3, 3, 5, 12, 17], L59970 = [1, 3, 3, 3, 5, 15, 17], L59975 = [1, 3, 3, 3, 5, 17, 18], L59992 = [1, 3, 3, 3, 6, 7, 11], L60059 = [1, 3, 3, 3, 7, 9, 11], L60072 = [1, 3, 3, 3, 7, 11, 12], L60073 = [1, 3, 3, 3, 7, 11, 15], L60075 = [1, 3, 3, 3, 7, 11, 18], L60216 = [1, 3, 3, 3, 11, 13, 15], L60819 = [1, 3, 3, 5, 6, 6, 17], L60823 = [1, 3, 3, 5, 6, 7, 11], L60825 = [1, 3, 3, 5, 6, 7, 13], L60828 = [1, 3, 3, 5, 6, 7, 17], L60846 = [1, 3, 3, 5, 6, 9, 17], L60849 = [1, 3, 3, 5, 6, 11, 13], L60858 = [1, 3, 3, 5, 6, 12, 17], L60871 = [1, 3, 3, 5, 6, 15, 17], L60876 = [1, 3, 3, 5, 6, 17, 18], L60887 = [1, 3, 3, 5, 7, 9, 11], L60889 = [1, 3, 3, 5, 7, 9, 13], L60892 = [1, 3, 3, 5, 7, 9, 17], L60894 = [1, 3, 3, 5, 7, 11, 12], L60895 = [1, 3, 3, 5, 7, 11, 13], L60896 = [1, 3, 3, 5, 7, 11, 15], L60898 = [1, 3, 3, 5, 7, 11, 17], L60899 = [1, 3, 3, 5, 7, 11, 18], L60901 = [1, 3, 3, 5, 7, 12, 13], L60904 = [1, 3, 3, 5, 7, 12, 17], L60906 = [1, 3, 3, 5, 7, 13, 15], L60907 = [1, 3, 3, 5, 7, 13, 18], L60910 = [1, 3, 3, 5, 7, 15, 17], L60915 = [1, 3, 3, 5, 7, 17, 18], L60966 = [1, 3, 3, 5, 9, 9, 17], L60969 =
APPENDIX
149
Table 5. (continued) n = 7 q I indexes of I-isospectral families 36 {0, 1} {542, 559}, {3120, 3137}, {3314, 3385}, {3341, 3450}, {3352, 3461}, (cont.) {3368, 3463}, {14836, 14853}, {15030, 15104}, {15057, 15171}, {15069, 15184}, {15082, 15185}, {15087, 15187}, {15924, 16166}, {15951, 16231}, {15962, 16242}, {15978, 16244}, {15996, 15999}, {16062, 16463}, {16073, 16474}, {16089, 16476}, {16104, 16504}, {16120, 16506}, {16149, 16509}, {51757, 51881}, {51900, 52502}, {59724, 59741}, {59918, 59992}, {59945, 60059}, {59957, 60072}, {59970, 60073}, {59975, 60075}, {60819, 61087}, {60846, 61154}, {60858, 61167}, {60871, 61168}, {60876, 61170}, {60895, 60898}, {60966, 61401}, {60978, 61414}, {60996, 61417}, {61015, 61455}, {61028, 61456}, {61033, 61458}, {61063, 61460}, {61070, 61463}, {62657, 63200}, {62705, 63201}, {63961, 64622}, {63988, 64687}, {63999, 64698}, {64015, 64700}, {64033, 64036}, {64099, 64919}, {64110, 64930}, {64126, 64932}, {64141, 64960}, {64157, 64962}, {64186, 64965}, {64222, 64225}, {64242, 64245}, {64249, 64253}, {64409, 65569}, {64420, 65580}, {64436, 65582}, {64451, 65610}, {64467, 65612}, {64496, 65615}, {64516, 65672}, {64532, 65674}, {64561, 65677}, {64605, 65681}
[1, 3, 3, 5, 9, 11, 13], L60978 = [1, 3, 3, 5, 9, 12, 17], L60991 = [1, 3, 3, 5, 9, 15, 17], L60996 = [1, 3, 3, 5, 9, 17, 18], L60999 = [1, 3, 3, 5, 11, 12, 13], L61003 = [1, 3, 3, 5, 11, 13, 15], L61004 = [1, 3, 3, 5, 11, 13, 18], L61015 = [1, 3, 3, 5, 12, 12, 17], L61028 = [1, 3, 3, 5, 12, 15, 17], L61033 = [1, 3, 3, 5, 12, 17, 18], L61063 = [1, 3, 3, 5, 15, 17, 18] L61070 = [1, 3, 3, 5, 17, 18, 18], L61087 = [1, 3, 3, 6, 6, 7, 11], L61154 = [1, 3, 3, 6, 7, 9, 11], L61167 = [1, 3, 3, 6, 7, 11, 12], L61168 = [1, 3, 3, 6, 7, 11, 15], L61170 = [1, 3, 3, 6, 7, 11, 18], L61401 = [1, 3, 3, 7, 9, 9, 11], L61414 = [1, 3, 3, 7, 9, 11, 12], L61415 = [1, 3, 3, 7, 9, 11, 15], L61417 = [1, 3, 3, 7, 9, 11, 18], L61455 = [1, 3, 3, 7, 11, 12, 12], L61456 = [1, 3, 3, 7, 11, 12, 15], L61458 = [1, 3, 3, 7, 11, 12, 18], L61460 = [1, 3, 3, 7, 11, 15, 18] L61463 = [1, 3, 3, 7, 11, 18, 18], L61742 = [1, 3, 3, 9, 11, 13, 15], L61893 = [1, 3, 3, 11, 13, 15, 15], L62592 = [1, 3, 4, 5, 6, 11, 16], L62653 = [1, 3, 4, 5, 7, 15, 16], L62657 = [1, 3, 4, 5, 7, 16, 17], L62681 = [1, 3, 4, 5, 8, 11, 15], L62705 = [1, 3, 4, 5, 8, 16, 17], L62721 = [1, 3, 4, 5, 9, 11, 16], L62752 = [1, 3, 4, 5, 11, 12, 16], L62763 = [1, 3, 4, 5, 11, 16, 18], L62915 = [1, 3, 4, 6, 7, 8, 13], L63189 = [1, 3, 4, 7, 8, 9, 13], L63200 = [1, 3, 4, 7, 8, 11, 13], L63201 = [1, 3, 4, 7, 8, 11, 16], L63204 = [1, 3, 4, 7, 8, 12, 13], L63209 = [1, 3, 4, 7, 8, 13, 18], L63466 = [1, 3, 4, 8, 11, 13, 16], L63961 = [1, 3, 5, 6, 6, 6, 17], L63965 = [1, 3, 5, 6, 6, 7, 11], L63967 = [1, 3, 5, 6, 6, 7, 13], L63970 = [1, 3, 5, 6, 6, 7, 17], L63988 = [1, 3, 5, 6, 6, 9, 17], L63991 = [1, 3, 5, 6, 6, 11, 13], L63999 = [1, 3, 5, 6, 6, 12, 17], L64015 = [1, 3, 5, 6, 6, 17, 18], L64025 = [1, 3, 5, 6, 7, 9, 11], L64027 = [1, 3, 5, 6, 7, 9, 13], L64030 = [1, 3, 5, 6, 7, 9, 17], L64032 = [1, 3, 5, 6, 7, 11, 12], L64033 = [1, 3, 5, 6, 7, 11, 13], L64036 = [1, 3, 5, 6, 7, 11, 17], L64037 = [1, 3, 5, 6, 7, 11, 18], L64039 = [1, 3, 5, 6, 7, 12, 13], L64042 = [1, 3, 5, 6, 7, 12, 17], L64044 = [1, 3, 5, 6, 7, 13, 18], L64050 = [1, 3, 5, 6, 7, 17, 18], L64099 = [1, 3, 5, 6, 9, 9, 17], L64102 = [1, 3, 5, 6, 9, 11, 13], L64110 = [1, 3, 5, 6, 9, 12, 17], L64126 = [1, 3, 5, 6, 9, 17, 18], L64129 = [1, 3, 5, 6, 11, 12, 13], L64132 = [1, 3, 5, 6, 11, 13, 18], L64141 = [1, 3, 5, 6, 12, 12, 17], L64157 = [1, 3, 5, 6, 12, 17, 18], L64186 = [1, 3, 5, 6, 17, 18, 18], L64214 = [1, 3, 5, 7, 9, 9, 11], L64216 = [1, 3, 5, 7, 9, 9, 13], L64219 = [1, 3, 5, 7, 9, 9, 17], L64221 = [1, 3, 5, 7, 9, 11, 12], L64222 = [1, 3, 5, 7, 9, 11, 13], L64225 = [1, 3, 5, 7, 9, 11, 17], L64226 = [1, 3, 5, 7, 9, 11, 18], L64228 = [1, 3, 5, 7, 9, 12, 13], L64231 = [1, 3, 5, 7, 9, 12, 17], L64233 = [1, 3, 5, 7, 9, 13, 18], L64239 = [1, 3, 5, 7, 9, 17, 18], L64241 = [1, 3, 5, 7, 11, 12, 12], L64242 = [1, 3, 5, 7, 11, 12, 13], L64245 = [1, 3, 5, 7, 11, 12, 17], L64246 = [1, 3, 5, 7, 11, 12, 18], L64248 = [1, 3, 5, 7, 11, 13, 17], L64249 = [1, 3, 5, 7, 11, 13, 18] L64253 = [1, 3, 5, 7, 11, 17, 18], L64254 = [1, 3, 5, 7, 11, 18, 18], L64256 = [1, 3, 5, 7, 12, 12, 13], L64259 = [1, 3, 5, 7, 12, 12, 17], L64261 = [1, 3, 5, 7, 12, 13, 18], L64267 = [1, 3, 5, 7, 12, 17, 18], L64269 = [1, 3, 5, 7, 13, 18, 18] L64277 = [1, 3, 5, 7, 17, 18, 18], L64409 = [1, 3, 5, 9, 9, 9, 17], L64412 = [1, 3, 5, 9, 9, 11, 13], L64420 = [1, 3, 5, 9, 9, 12, 17], L64436 = [1, 3, 5, 9, 9, 17, 18], L64439 = [1, 3, 5, 9, 11, 12, 13], L64442 = [1, 3, 5, 9, 11, 13, 18], L64451 = [1, 3, 5, 9, 12, 12, 17], L64467 = [1, 3, 5, 9, 12, 17, 18], L64496 = [1, 3, 5, 9, 17, 18, 18], L64499 =
150
EMILIO A. LAURET
Table 5. (continued) n = 7 q 36 (cont.)
I {3} {5} {2, 5}
indexes of I-isospectral families {60216, 61893} {17357, 18146, 18274, 22547, 22734}, {49316, 57451, 57506, 77826, 78354} {4858, 20659}, {10949, 46006}, {14579, 59269}, {16778, 66425}, {16919, 20372, 20662}, {18249, 70752}, {18817, 72018}, {19167, 72947}, {19591, 20663}, {21981, 80163}, {22002, 22327}, {22636, 81690}, {36814, 45369, 46012}, {43045, 46013}, {53056, 58956, 59280}, {57466, 59281}, {61742, 66281, 66430}, {63466, 70599, 70760}, {64248, 72005}, {64837, 72812, 72952}, {65234, 66431}, {69741, 70762}, {71824, 72021}, {72519, 72953}, {78031, 78500}, {79154, 80139}, 79598, 80532}, {79924, 80167}, {81264, 81682}, {81505, 81889}, {81605, 81955}, {81632, 81694} {0, 1, 6} {60991, 61415} {5, 6} {3962, 18260}, {5516, 5585, 22642, 22798}, {8917, 18246}, {13127, 18227, 18268}, {13917, 57490}, {15732, 18193, 18272}, {17357, 18146, 18274}, {17638, 18275}, {17873, 18276}, {21726, 22132}, {21875, 22240, 79949, 80772}, {22448, 22634, 22644, 22793}, {22547, 22734}, {22605, 22646, 22774, 22800}, {32066, 57470}, {49316, 57451, 57506}, {52289, 57345, 57509}, {54513, 57187, 57512}, {55719, 57513}, {56804, 57514}, {77826, 78354}, {79037, 79925, 79952, 80757}, {79514, 80472}, {79818, 79953, 80683, 80774} {2, 5, 6} {22642, 22798}, {79818, 80683}
[1, 3, 5, 11, 12, 12, 13], L64502 = [1, 3, 5, 11, 12, 13, 18], L64506 = [1, 3, 5, 11, 13, 18, 18], L64516 = [1, 3, 5, 12, 12, 12, 17], L64532 = [1, 3, 5, 12, 12, 17, 18], L64561 = [1, 3, 5, 12, 17, 18, 18], L64605 = [1, 3, 5, 17, 18, 18, 18], L64622 = [1, 3, 6, 6, 6, 7, 11], L64687 = [1, 3, 6, 6, 7, 9, 11], L64698 = [1, 3, 6, 6, 7, 11, 12], L64700 = [1, 3, 6, 6, 7, 11, 18], L64837 = [1, 3, 6, 6, 11, 13, 18], L64919 = [1, 3, 6, 7, 9, 9, 11], L64930 = [1, 3, 6, 7, 9, 11, 12], L64932 = [1, 3, 6, 7, 9, 11, 18], L64960 = [1, 3, 6, 7, 11, 12, 12], L64962 = [1, 3, 6, 7, 11, 12, 18], L64965 = [1, 3, 6, 7, 11, 18, 18], L65234 = [1, 3, 6, 9, 11, 13, 15], L65569 = [1, 3, 7, 9, 9, 9, 11], L65580 = [1, 3, 7, 9, 9, 11, 12], L65582 = [1, 3, 7, 9, 9, 11, 18], L65610 = [1, 3, 7, 9, 11, 12, 12], L65612 = [1, 3, 7, 9, 11, 12, 18], L65615 = [1, 3, 7, 9, 11, 18, 18], L65672 = [1, 3, 7, 11, 12, 12, 12], L65674 = [1, 3, 7, 11, 12, 12, 18], L65677 = [1, 3, 7, 11, 12, 18, 18], L65681 = [1, 3, 7, 11, 18, 18, 18], L66281 = [1, 3, 9, 9, 11, 13, 15], L66425 = [1, 3, 9, 11, 12, 13, 15], L66430 = [1, 3, 9, 11, 13, 15, 15], L66431 = [1, 3, 9, 11, 13, 15, 18], L68707 = [1, 4, 5, 6, 6, 7, 16], L68712 = [1, 4, 5, 6, 6, 8, 11], L68760 = [1, 4, 5, 6, 7, 9, 16], L68769 = [1, 4, 5, 6, 7, 12, 16], L68776 = [1, 4, 5, 6, 7, 16, 18], L68788 = [1, 4, 5, 6, 8, 9, 11], L68795 = [1, 4, 5, 6, 8, 11, 12], L68797 = [1, 4, 5, 6, 8, 11, 18], L68899 = [1, 4, 5, 7, 8, 11, 13], L68901 = [1, 4, 5, 7, 8, 11, 17], L68918 = [1, 4, 5, 7, 9, 9, 16], L68927 = [1, 4, 5, 7, 9, 12, 16], L68934 = [1, 4, 5, 7, 9, 16, 18], L68947 = [1, 4, 5, 7, 12, 12, 16], L68954 = [1, 4, 5, 7, 12, 16, 18], L68961 = [1, 4, 5, 7, 16, 18, 18], L68998 = [1, 4, 5, 8, 9, 9, 11], L69005 = [1, 4, 5, 8, 9, 11, 12], L69007 = [1, 4, 5, 8, 9, 11, 18], L69026 = [1, 4, 5, 8, 11, 12, 12], L69028 = [1, 4, 5, 8, 11, 12, 18], L69030 = [1, 4, 5, 8, 11, 18, 18], L69741 = [1, 4, 6, 8, 11, 13, 16], L70599 = [1, 4, 8, 9, 11, 13, 16], L70752 = [1, 4, 8, 11, 12, 13, 16], L70760 = [1, 4, 8, 11, 13, 15, 16], L70762 = [1, 4, 8, 11, 13, 16, 18], L71824 = [1, 5, 6, 7, 11, 13, 17], L72005 = [1, 5, 7, 9, 11, 13, 17], L72018 = [1, 5, 7, 11, 12, 13, 17], L72021 = [1, 5, 7, 11, 13, 17, 1 L72519 = [1, 6, 6, 6, 11, 13, 18], L72812 = [1, 6, 6, 9, 11, 13, 18], L72947 = [1, 6, 6, 11, 12, 13, 18], L72952 = [1, 6, 6, 11, 13, 15, 18], L72953 = [1, 6, 6, 11, 13, 18, 18], L77826 = [2, 2, 3, 6, 10, 14, 18], L78031 = [2, 2, 3, 10, 10, 14, 14], L78354 = [2, 2, 6, 9, 10, 14, 18], L78500 = [2, 2, 9, 10, 10, 14, 14], L78620 =
APPENDIX
151
Table 5. (continued) n = 7 q 37
I {0}
indexes of I-isospectral families {341, 342}, {1508, 1522, 1526}, {7100, 7119}, {7434, 7437}, {25130, 25195}, {25212, 25357}, {25600, 26130}, {25658, 25680}, {25967, 26470}, {26570, 26652}, {26577, 26682}, {26579, 26590} {0, 1} {7432, 7435}, {26701, 26702}
[2, 3, 3, 3, 4, 8, 10], L78622 = [2, 3, 3, 3, 4, 8, 14], L78825 = [2, 3, 3, 4, 6, 8, 10], L78827 = [2, 3, 3, 4, 6, 8, 14], L78864 = [2, 3, 3, 4, 8, 9, 10], L78866 = [2, 3, 3, 4, 8, 9, 14], L78870 = [2, 3, 3, 4, 8, 10, 12], L78872 = [2, 3, 3, 4, 8, 10, 15], L78874 = [2, 3, 3, 4, 8, 10, 18], L78876 = [2, 3, 3, 4, 8, 12, 14], L78880 = [2, 3, 3, 4, 8, 14, 15], L78881 = [2, 3, 3, 4, 8, 14, 18], L79037 = [2, 3, 3, 6, 10, 14, 18], L79154 = [2, 3, 3, 9, 10, 14, 15], L79424 = [2, 3, 4, 6, 6, 8, 10], L79426 = [2, 3, 4, 6, 6, 8, 14], L79462 = [2, 3, 4, 6, 8, 9, 10], L79464 = [2, 3, 4, 6, 8, 9, 14], L79468 = [2, 3, 4, 6, 8, 10, 12], L79470 = [2, 3, 4, 6, 8, 10, 15], L79472 = [2, 3, 4, 6, 8, 10, 18], L79474 = [2, 3, 4, 6, 8, 12, 14], L79478 = [2, 3, 4, 6, 8, 14, 15], L79479 = [2, 3, 4, 6, 8, 14, 18], L79514 = [2, 3, 4, 6, 10, 14, 18], L79569 = [2, 3, 4, 8, 9, 9, 10], L79571 = [2, 3, 4, 8, 9, 9, 14], L79575 = [2, 3, 4, 8, 9, 10, 12], L79577 = [2, 3, 4, 8, 9, 10, 15], L79579 = [2, 3, 4, 8, 9, 10, 18], L79581 = [2, 3, 4, 8, 9, 12, 14], L79585 = [2, 3, 4, 8, 9, 14, 15], L79586 = [2, 3, 4, 8, 9, 14, 18], L79592 = [2, 3, 4, 8, 10, 12, 12], L79594 = [2, 3, 4, 8, 10, 12, 15], L79596 = [2, 3, 4, 8, 10, 12, 18], L79598 = [2, 3, 4, 8, 10, 14, 16], L79601 = [2, 3, 4, 8, 10, 15, 18], L79603 = [2, 3, 4, 8, 10, 18, 18] L79605 = [2, 3, 4, 8, 12, 12, 14], L79609 = [2, 3, 4, 8, 12, 14, 15], L79610 = [2, 3, 4, 8, 12, 14, 18], L79616 = [2, 3, 4, 8, 14, 15, 18], L79617 = [2, 3, 4, 8, 14, 18, 18], L79818 = [2, 3, 6, 6, 10, 14, 18], L79924 = [2, 3, 6, 9, 10, 14, 15] L79925 = [2, 3, 6, 9, 10, 14, 18], L79949 = [2, 3, 6, 10, 12, 14, 18], L79952 = [2, 3, 6, 10, 14, 15, 18], L79953 = [2, 3, 6, 10, 14, 18, 18], L80139 = [2, 3, 9, 9, 10, 14, 15], L80163 = [2, 3, 9, 10, 12, 14, 15], L80167 = [2, 3, 9, 10, 14, 15, 18], L80404 = [2, 4, 6, 6, 8, 9, 10], L80406 = [2, 4, 6, 6, 8, 9, 14], L80434 = [2, 4, 6, 8, 9, 9, 10], L80436 = [2, 4, 6, 8, 9, 9, 14], L80439 = [2, 4, 6, 8, 9, 10, 12], L80442 = [2, 4, 6, 8, 9, 10, 18], L80444 = [2, 4, 6, 8, 9, 12, 14], L80447 = [2, 4, 6, 8, 9, 14, 18], L80472 = [2, 4, 6, 9, 10, 14, 18], L80511 = [2, 4, 8, 9, 9, 9, 10], L80513 = [2, 4, 8, 9, 9, 9, 14], L80516 = [2, 4, 8, 9, 9, 10, 12], L80519 = [2, 4, 8, 9, 9, 10, 18], L80521 = [2, 4, 8, 9, 9, 12, 14], L80524 = [2, 4, 8, 9, 9, 14, 18], L80528 = [2, 4, 8, 9, 10, 12, 12], L80531 = [2, 4, 8, 9, 10, 12, 18], L80532 = [2, 4, 8, 9, 10, 14, 16], L80535 = [2, 4, 8, 9, 10, 18, 18], L80537 = [2, 4, 8, 9, 12, 12, 14] L80540 = [2, 4, 8, 9, 12, 14, 18], L80544 = [2, 4, 8, 9, 14, 18, 18], L80683 = [2, 6, 6, 9, 10, 14, 18], L80757 = [2, 6, 9, 9, 10, 14, 18], L80772 = [2, 6, 9, 10, 12, 14, 18], L80774 = [2, 6, 9, 10, 14, 18, 18], L81264 = [3, 3, 4, 8, 9, 15, 16], L81505 = [3, 4, 4, 8, 8, 16, 16], L81605 = [3, 4, 6, 6, 8, 16, 18], L81632 = [3, 4, 6, 8, 9, 15, 16], L81682 = [3, 4, 8, 9, 9, 15, 16], L81690 = [3, 4, 8, 9, 12, 15, 16], L81694 = [3, 4, 8, 9, 15, 16, 18], L81889 = [4, 4, 8, 8, 9, 16, 16], L81955 = [4, 6, 6, 8, 9, 16, 18]. q = 37 : L341 = [0, 0, 0, 1, 3, 4, 11], L342 = [0, 0, 0, 1, 3, 4, 12], L1508 = [0, 0, 1, 2, 4, 5, 16], L1522 = [0, 0, 1, 2, 4, 8, 9], L1526 = [0, 0, 1, 2, 4, 8, 16], L7100 = [0, 1, 2, 5, 7, 10, 11], L7119 = [0, 1, 2, 5, 8, 10, 13], L7432 = [0, 1, 3, 4, 7, 9, 16], L7434 = [0, 1, 3, 4, 7, 10, 12], L7435 = [0, 1, 3, 4, 7, 12, 16], L7437 = [0, 1, 3, 4, 9, 10, 12], L25130 = [1, 2, 3, 4, 7, 12, 15], L25195 = [1, 2, 3, 4, 9, 10, 14], L25212 = [1, 2, 3, 4, 9, 13, 14], L25357 = [1, 2, 3, 5, 6, 14, 16], L25600 = [1, 2, 3, 6, 7, 13, 17], L25658 = [1, 2, 3, 6, 9, 13, 14], L25680 = [1, 2, 3, 6, 10, 13, 18], L25967 = [1, 2, 3, 9, 13, 15, 17], L26130 = [1, 2, 4, 5, 10, 11, 12], L26470 = [1, 2, 5, 12, 14, 15, 17 L26570 = [1, 2, 6, 9, 10, 15, 16], L26577 = [1, 2, 6, 9, 11, 15, 17], L26579 = [1, 2, 6, 9, 12, 14, 15], L26590 = [1, 2, 6, 9, 14, 15, 17], L26652 = [1, 2, 8, 9, 12, 14, 17], L26682 = [1, 2, 9, 11, 15, 16, 17], L26701 = [1, 3, 4, 7, 9, 10, 12] L26702 = [1, 3, 4, 7, 9, 10, 16]. q = 38 : L60 = [0, 0, 0, 0, 1, 3, 11], L63 = [0, 0, 0, 0, 1, 3, 15], L511 = [0, 0, 0, 1, 3, 5, 13], L513 = [0, 0, 0, 1, 3, 5, 15], L515 = [0, 0, 0, 1, 3, 5, 17], L523 = [0, 0, 0, 1, 3, 7, 13], L539 = [0, 0, 0, 1, 3, 9, 11], L553 = [0, 0, 0, 1, 3, 11, 15], L554 = [0, 0, 0, 1, 3, 11, 17], L556 = [0, 0, 0, 1, 3, 11, 19], L573 = [0, 0, 0, 1, 3, 15, 19], L682 = [0, 0, 0, 1, 5, 7, 9], L767 = [0, 0, 0, 1, 7, 8, 12], L769 = [0, 0, 0, 1, 7, 8, 18], L895 = [0, 0, 0, 2, 4, 14, 19], L898 = [0, 0, 0, 2, 6, 8, 19], L3182 = [0, 0, 1, 3, 5, 7, 11], L3184 = [0, 0, 1, 3, 5, 7, 13], L3185 = [0, 0, 1, 3, 5, 7, 15], L3187 = [0, 0, 1, 3, 5, 7, 17], L3200 = [0, 0, 1, 3, 5, 9, 11], L3201 = [0, 0, 1, 3, 5, 9, 13], L3203 = [0, 0, 1, 3, 5, 9, 15],
152
EMILIO A. LAURET
Table 5. (continued) n = 7 q 38
I {0}
indexes of I-isospectral families {60, 63}, {511, 513}, {515, 523, 539}, {553, 554, 682}, {556, 573}, {767, 769}, {895, 898}, {3182, 3185}, {3184, 3187, 3200, 3203}, {3201, 3205, 3209, 3220}, {3222, 3231}, {3230, 3251}, {3237, 3270, 3334}, {3392, 3394, 3882}, {3397, 3451}, {4150, 4155}, {4475, 4476, 4479}, {4478, 4481, 4483}, {4488, 4494}, {4491, 4495}, {13213, 13265}, {13710, 14226}, {15534, 15536, 15543}, {15535, 15538, 15541, 15542, 15553, 15556, 15611}, {15545, 15557}, {15555, 15563, 15613, 15621}, {15615, 15625, 15636, 15670}, {15673, 15696}, {15695, 15754}, {15708, 15802, 15992}, {16163, 16166, 17634}, {16170, 16300}, {18327, 18336}, {19086, 19087}, {19088, 19090, 19093, 19096}, {19092, 19094, 19097, 19100}, {19095, 19098, 19103}, {19099, 19110}, {19102, 19106, 19108}, {19114, 19120}, {19117, 19121}, {43772, 43776}, {52993, 52995}, {56838, 56984}, {58310, 59967}, {59904, 59929}, {63322, 63332}, {63337, 63338, 63339, 63341}, {63340, 63344, 63357}, {63343, 63348, 63355, 63356, 63383, 63387, 63531}, {63360, 63388}, {63386, 63400, 63534, 63549}, {63537, 63555, 63578, 63658}, {63662, 63708}, {63707, 63845}, {63728, 63944, 64415}, {64825, 64829, 68583}, {64834, 65099}, {66909, 66911}, {70110, 70115}, {70150, 70164}, {71778, 71779, 71780, 71781, 71783, 71784, 71785}, {71782, 71786}, {71787, 71792, 71794}, {71788, 71790, 71795, 71798}, {71793, 71796, 71799, 71802}, {71797, 71800, 71805}, {71801, 71812}, {71804, 71808, 71810}, {71816, 71822}, {71819, 71823} {0, 1} {3201, 3205}, {15536, 15543}, {15538, 15541}, {15553, 15611}, {15615, 15625}, {19094, 19097}, {63338, 63339, 63341}, {63344, 63357}, {63348, 63355}, {63383, 63531}, {63537, 63555}, {71780, 71781}, {71783, 71785}, {71787, 71794}, {71796, 71799} {0, 1, 2, 3} {63339, 63341}
L3205 = [0, 0, 1, 3, 5, 9, 17], L3209 = [0, 0, 1, 3, 5, 11, 15], L3220 = [0, 0, 1, 3, 5, 13, 17], L3222 = [0, 0, 1, 3, 5, 13, 19], L3230 = [0, 0, 1, 3, 5, 15, 17], L3231 = [0, 0, 1, 3, 5, 15, 19], L3237 = [0, 0, 1, 3, 5, 17, 19], L3251 = [0, 0, 1, 3, 7, 9, 13], L3270 = [0, 0, 1, 3, 7, 13, 19], L3334 = [0, 0, 1, 3, 9, 11, 19], L3392 = [0, 0, 1, 3, 11, 15, 19], L3394 = [0, 0, 1, 3, 11, 17, 19], L3397 = [0, 0, 1, 3, 11, 19, 19], L3451 = [0, 0, 1, 3, 15, 19, 19], L3882 = [0, 0, 1, 5, 7, 9, 19], L4150 = [0, 0, 1, 7, 8, 12, 19], L4155 = [0, 0, 1, 7, 8, 18, 19], L4475 = [0, 0, 2, 4, 6, 10, 19], L4476 = [0, 0, 2, 4, 6, 12, 19], L4478 = [0, 0, 2, 4, 6, 16, 19], L4479 = [0, 0, 2, 4, 6, 18, 19], L4481 = [0, 0, 2, 4, 8, 10, 19], L4483 = [0, 0, 2, 4, 8, 16, 19], L4488 = [0, 0, 2, 4, 12, 16, 19], L4491 = [0, 0, 2, 4, 14, 19, 19], L4494 = [0, 0, 2, 6, 8, 10, 19], L4495 = [0, 0, 2, 6, 8, 19, 19], L13213 = [0, 1, 2, 4, 10, 11, 17], L13265 = [0, 1, 2, 4, 11, 15, 16], L13710 = [0, 1, 2, 5, 14, 15, 18], L14226 = [0, 1, 2, 7, 9, 10, 12], L15534 = [0, 1, 3, 5, 7, 9, 11], L15535 = [0, 1, 3, 5, 7, 9, 13], L15536 = [0, 1, 3, 5, 7, 9, 15], L15538 = [0, 1, 3, 5, 7, 9, 17], L15541 = [0, 1, 3, 5, 7, 11, 13], L15542 = [0, 1, 3, 5, 7, 11, 15], L15543 = [0, 1, 3, 5, 7, 11, 17], L15545 = [0, 1, 3, 5, 7, 11, 19], L15553 = [0, 1, 3, 5, 7, 13, 17], L15555 = [0, 1, 3, 5, 7, 13, 19], L15556 = [0, 1, 3, 5, 7, 15, 17], L15557 = [0, 1, 3, 5, 7, 15, 19], L15563 = [0, 1, 3, 5, 7, 17, 19], L15611 = [0, 1, 3, 5, 9, 11, 13], L15613 = [0, 1, 3, 5, 9, 11, 19], L15615 = [0, 1, 3, 5, 9, 13, 19], L15621 = [0, 1, 3, 5, 9, 15, 19], L15625 = [0, 1, 3, 5, 9, 17, 19], L15636 = [0, 1, 3, 5, 11, 15, 19], L15670 = [0, 1, 3, 5, 13, 17, 19], L15673 = [0, 1, 3, 5, 13, 19, 19], L15695 = [0, 1, 3, 5, 15, 17, 19], L15696 = [0, 1, 3, 5, 15, 19, 19], L15708 = [0, 1, 3, 5, 17, 19, 19], L15754 = [0, 1, 3, 7, 9, 13, 19], L15802 = [0, 1, 3, 7, 13, 19, 19], L15992 = [0, 1, 3, 9, 11, 19, 19], L16163 = [0, 1, 3, 11, 15, 19, 19], L16166 = [0, 1, 3, 11, 17, 19, 19], L16170 = [0, 1, 3, 11, 19, 19, 19], L16300 = [0, 1, 3, 15, 19, 19, 19], L17634 = [0, 1, 5, 7, 9, 19, 19], L18327 = [0, 1, 7, 8, 12, 19, 19], L18336 = [0, 1, 7, 8, 18, 19, 19], L19086 = [0, 2, 4, 6, 8, 10, 19],
APPENDIX
153
L19087 = [0, 2, 4, 6, 8, 12, 19], L19088 = [0, 2, 4, 6, 8, 14, 19], L19090 = [0, 2, 4, 6, 8, 18, 19], L19092 = [0, 2, 4, 6, 10, 12, 19], L19093 = [0, 2, 4, 6, 10, 14, 19], L19094 = [0, 2, 4, 6, 10, 18, 19], L19095 = [0, 2, 4, 6, 10, 19, 19] L19096 = [0, 2, 4, 6, 12, 14, 19], L19097 = [0, 2, 4, 6, 12, 16, 19], L19098 = [0, 2, 4, 6, 12, 19, 19], L19099 = [0, 2, 4, 6, 14, 16, 19], L19100 = [0, 2, 4, 6, 14, 18, 19], L19102 = [0, 2, 4, 6, 16, 19, 19], L19103 = [0, 2, 4, 6, 18, 19, 19] L19106 = [0, 2, 4, 8, 10, 19, 19], L19108 = [0, 2, 4, 8, 16, 19, 19], L19110 = [0, 2, 4, 10, 12, 16, 19], L19114 = [0, 2, 4, 12, 16, 19, 19], L19117 = [0, 2, 4, 14, 19, 19, 19], L19120 = [0, 2, 6, 8, 10, 19, 19], L19121 = [0, 2, 6, 8, 19, 19, 19], L43772 = [1, 1, 7, 7, 8, 11, 12], L43776 = [1, 1, 7, 7, 8, 11, 18], L52993 = [1, 2, 3, 5, 7, 11, 14], L52995 = [1, 2, 3, 5, 7, 11, 16], L56838 = [1, 2, 4, 10, 11, 17, 19], L56984 = [1, 2, 4, 11, 15, 16, 19], L58310 = [1, 2, 5, 14, 15, 18, 19], L59904 = [1, 2, 7, 8, 12, 14, 16], L59929 = [1, 2, 7, 8, 14, 16, 18], L59967 = [1, 2, 7, 9, 10, 12, 19 L63322 = [1, 3, 5, 7, 8, 12, 17], L63332 = [1, 3, 5, 7, 8, 17, 18], L63337 = [1, 3, 5, 7, 9, 11, 13], L63338 = [1, 3, 5, 7, 9, 11, 15], L63339 = [1, 3, 5, 7, 9, 11, 17], L63340 = [1, 3, 5, 7, 9, 11, 19], L63341 = [1, 3, 5, 7, 9, 13, 15], L63343 = [1, 3, 5, 7, 9, 13, 19], L63344 = [1, 3, 5, 7, 9, 15, 19], L63348 = [1, 3, 5, 7, 9, 17, 19], L63355 = [1, 3, 5, 7, 11, 13, 19], L63356 = [1, 3, 5, 7, 11, 15, 19], L63357 = [1, 3, 5, 7, 11, 17, 19], L63360 = [1, 3, 5, 7, 11, 19, 19] L63383 = [1, 3, 5, 7, 13, 17, 19], L63386 = [1, 3, 5, 7, 13, 19, 19], L63387 = [1, 3, 5, 7, 15, 17, 19], L63388 = [1, 3, 5, 7, 15, 19, 19], L63400 = [1, 3, 5, 7, 17, 19, 19], L63531 = [1, 3, 5, 9, 11, 13, 19], L63534 = [1, 3, 5, 9, 11, 19, 19] L63537 = [1, 3, 5, 9, 13, 19, 19], L63549 = [1, 3, 5, 9, 15, 19, 19], L63555 = [1, 3, 5, 9, 17, 19, 19], L63578 = [1, 3, 5, 11, 15, 19, 19], L63658 = [1, 3, 5, 13, 17, 19, 19], L63662 = [1, 3, 5, 13, 19, 19, 19], L63707 = [1, 3, 5, 15, 17, 19, 19], L63708 = [1, 3, 5, 15, 19, 19, 19], L63728 = [1, 3, 5, 17, 19, 19, 19], L63845 = [1, 3, 7, 9, 13, 19, 19], L63944 = [1, 3, 7, 13, 19, 19, 19], L64415 = [1, 3, 9, 11, 19, 19, 19], L64825 = [1, 3, 11, 15, 19, 19, 19], L64829 = [1, 3, 11, 17, 19, 19, 19], L64834 = [1, 3, 11, 19, 19, 19, 19], L65099 = [1, 3, 15, 19, 19, 19, 19], L66909 = [1, 4, 6, 7, 8, 10, 12], L66911 = [1, 4, 6, 7, 8, 10, 18], L68583 = [1, 5, 7, 9, 19, 19, 19] L70110 = [1, 7, 8, 8, 12, 12, 18], L70115 = [1, 7, 8, 8, 12, 18, 18], L70150 = [1, 7, 8, 12, 19, 19, 19], L70164 = [1, 7, 8, 18, 19, 19, 19], L71778 = [2, 4, 6, 8, 10, 12, 19], L71779 = [2, 4, 6, 8, 10, 14, 19], L71780 = [2, 4, 6, 8, 10, 16, 19 L71781 = [2, 4, 6, 8, 10, 18, 19], L71782 = [2, 4, 6, 8, 10, 19, 19], L71783 = [2, 4, 6, 8, 12, 14, 19], L71784 = [2, 4, 6, 8, 12, 16, 19], L71785 = [2, 4, 6, 8, 12, 18, 19], L71786 = [2, 4, 6, 8, 12, 19, 19], L71787 = [2, 4, 6, 8, 14, 18, 19] L71788 = [2, 4, 6, 8, 14, 19, 19], L71790 = [2, 4, 6, 8, 18, 19, 19], L71792 = [2, 4, 6, 10, 12, 18, 19], L71793 = [2, 4, 6, 10, 12, 19, 19], L71794 = [2, 4, 6, 10, 14, 16, 19], L71795 = [2, 4, 6, 10, 14, 19, 19], L71796 = [2, 4, 6, 10, 18, 19, 19], L71797 = [2, 4, 6, 10, 19, 19, 19], L71798 = [2, 4, 6, 12, 14, 19, 19], L71799 = [2, 4, 6, 12, 16, 19, 19], L71800 = [2, 4, 6, 12, 19, 19, 19], L71801 = [2, 4, 6, 14, 16, 19, 19], L71802 = [2, 4, 6, 14, 18, 19, 19], L71804 = [2, 4, 6, 16, 19, 19, 19], L71805 = [2, 4, 6, 18, 19, 19, 19], L71808 = [2, 4, 8, 10, 19, 19, 19], L71810 = [2, 4, 8, 16, 19, 19, 19], L71812 = [2, 4, 10, 12, 16, 19, 19], L71816 = [2, 4, 12, 16, 19, 19, 19], L71819 = [2, 4, 14, 19, 19, 19, 19], L71822 = [2, 6, 8, 10, 19, 19, 19], L71823 = [2, 6, 8, 19, 19, 19, 19]. q = 39 : L405 = [0, 0, 0, 1, 2, 10, 17], L553 = [0, 0, 0, 1, 4, 5, 11], L745 = [0, 0, 0, 3, 6, 9, 13], L746 = [0, 0, 0, 3, 6, 12, 13], L748 = [0, 0, 0, 3, 6, 13, 15], L749 = [0, 0, 0, 3, 9, 12, 13], L2273 = [0, 0, 1, 2, 5, 14, 16], L2424 = [0, 0, 1, 2, 8, 10, 14], L2517 = [0, 0, 1, 2, 10, 13, 17], L2766 = [0, 0, 1, 3, 4, 9, 17], L2771 = [0, 0, 1, 3, 4, 10, 14], L2782 = [0, 0, 1, 3, 4, 12, 14], L2794 = [0, 0, 1, 3, 4, 14, 17], L3119 = [0, 0, 1, 4, 5, 11, 13], L3529 = [0, 0, 1, 12, 13, 13, 14], L3544 = [0, 0, 1, 13, 13, 13, 13], L3600 = [0, 0, 3, 6, 9, 12, 13], L3601 = [0, 0, 3, 6, 9, 13, 13], L3602 = [0, 0, 3, 6, 9, 13, 15], L3603 = [0, 0, 3, 6, 9, 13, 18], L3604 = [0, 0, 3, 6, 12, 13, 13], L3606 = [0, 0, 3, 6, 13, 13, 15], L3607 = [0, 0, 3, 9, 12, 13, 13], L3609 = [0, 0, 3, 13, 13, 13, 13], L9724 = [0, 1, 1, 12, 12, 14, 14], L9743 = [0, 1, 1, 12, 13, 13, 14], L10701 = [0, 1, 2, 4, 5, 7, 17], L10710 = [0, 1, 2, 4, 5, 8, 16], L10730 = [0, 1, 2, 4, 5, 10, 17], L10757 = [0, 1, 2, 4, 5, 14, 17], L10759 = [0, 1, 2, 4, 5, 14, 19], L10771 = [0, 1, 2, 4, 7, 8, 11], L10773 = [0, 1, 2, 4, 7, 8, 14], L10775 = [0, 1, 2, 4, 7, 8, 17], L10788 = [0, 1, 2, 4, 7, 10, 11], L10803 = [0, 1, 2, 4, 7, 11, 19], L10827 = [0, 1, 2, 4, 7, 16, 17], L11293 = [0, 1, 2, 5, 13, 14, 16], L11661 = [0, 1, 2, 7, 8, 10, 11], L11849 = [0, 1, 2, 8, 10, 13, 14], L12124 = [0, 1, 2, 10, 13, 13, 17], L12169 = [0, 1, 2, 11, 12, 14, 15 L12178 = [0, 1, 2, 11, 13, 13, 15], L12224 = [0, 1, 2, 12, 13, 13, 14], L13034 = [0, 1, 3, 4, 9, 13, 17], L13058 = [0, 1, 3, 4, 10, 13, 14], L13088 = [0, 1, 3, 4, 12, 13, 14], L13108 = [0, 1, 3, 4, 13, 14, 17], L13385 = [0, 1, 3, 6, 7, 10, 15], L13412 = [0, 1, 3, 6, 8, 10, 18], L13764 = [0, 1, 3, 10, 12, 14, 16], L13774 = [0, 1, 3, 10, 13, 13, 16], L13854 = [0, 1, 3, 12, 13, 13, 14], L13964 = [0, 1, 4, 5, 11, 13, 13], L14152 = [0, 1, 4, 9, 13, 13, 17], L14337 = [0, 1, 5, 8, 12, 14, 18
154
EMILIO A. LAURET
Table 5. (continued) n = 7 q 39
I {0}
indexes of I-isospectral families {405, 553}, {745, 746}, {748, 749}, {2273, 2424}, {2517, 3119}, {2766, 2782}, {2771, 2794}, {3600, 3602, 3603}, {3601, 3604}, {3606, 3607}, {10701, 10710}, {10730, 10771}, {10757, 10803}, {10759, 10773}, {10775, 10788}, {10827, 11661}, {11293, 11849}, {12124, 13964}, {13034, 13088}, {13058, 13108}, {13385, 13412}, {14982, 14985, 14986}, {14984, 14987}, {14989, 14990}, {43236, 43331}, {44896, 44901}, {44899, 44903, 44981}, {44908, 44936, 45062}, {44909, 44953}, {44923, 44966}, {44928, 45041}, {45054, 45171}, {45083, 45259}, {45126, 45281}, {45128, 45177}, {45179, 45237}, {45240, 45287}, {45333, 47759}, {45532, 47144}, {45591, 46327}, {46657, 48223}, {48875, 53554}, {49946, 49971}, {51589, 51703}, {51643, 51735}, {52445, 52498}, {55472, 55476, 55477}, {55475, 55478}, {55480, 55481} {0, 1} {3600, 3602}, {14982, 14985}, {51554, 51555}, {55472, 55476} {2, 5} {3529, 14849}, {3544, 3609}, {9724, 41392}, {9743, 14833}, {12169, 48960}, {12178, 14611}, {12224, 14852}, {13764, 53198}, {13774, 14774}, {13854, 14152}, {14337, 54267}, {14341, 14853}, {21918, 41367}, {27258, 48948}, {27363, 41410}, {31449, 53185}, {31680, 40956}, {34216, 50914}, {34586, 40658}, {36029, 54262}, {36578, 41411}, {37533, 48967}, {38323, 39336}, {44551, 54176}, {44577, 53206}, {44657, 48775}, {45507, 47561}, {45528, 52623}, {45677, 48606}, {46355, 53208}, {46370, 52016}, {46573, 48968}, {51559, 51578}
L14341 = [0, 1, 5, 8, 13, 13, 18], L14611 = [0, 1, 6, 12, 13, 13, 14], L14774 = [0, 1, 9, 12, 13, 13, 14], L14833 = [0, 1, 12, 12, 13, 13, 14], L14849 = [0, 1, 12, 13, 13, 13, 14], L14852 = [0, 1, 12, 13, 13, 14, 15], L14853 = [0, 1, 12, 13, 13, 14, 18], L14982 = [0, 3, 6, 9, 12, 13, 13], L14984 = [0, 3, 6, 9, 13, 13, 13], L14985 = [0, 3, 6, 9, 13, 13, 15], L14986 = [0, 3, 6, 9, 13, 13, 18], L14987 = [0, 3, 6, 12, 13, 13, 13], L14989 = [0, 3, 6, 13, 13, 13, 15], L14990 = [0, 3, 9, 12, 13, 13, 13], L21918 = [1, 1, 1, 12, 12, 14, 14], L27258 = [1, 1, 2, 11, 12, 14, 15], L27363 = [1, 1, 2, 12, 12, 14, 14], L31449 = [1, 1, 3, 10, 12, 14, 16], L31680 = [1, 1, 3, 12, 12, 14, 14], L34216 = [1, 1, 4, 9, 12, 14, 17], L34586 = [1, 1, 4, 12, 12, 14, 14], L36029 = [1, 1, 5, 8, 12, 14, 18], L36578 = [1, 1, 5, 12, 12, 14, 14], L37533 = [1, 1, 6, 7, 12, 14, 19], L38323 = [1, 1, 6, 12, 12, 14, 1 L39336 = [1, 1, 7, 12, 12, 14, 14], L40658 = [1, 1, 9, 12, 12, 14, 14], L40956 = [1, 1, 10, 12, 12, 14, 14], L41367 = [1, 1, 12, 12, 12, 14, 14], L41392 = [1, 1, 12, 12, 13, 14, 14], L41410 = [1, 1, 12, 12, 14, 14, 15], L41411 = [1, 1, 12, 12, 14, 14, 18], L43236 = [1, 2, 3, 5, 8, 11, 16], L43331 = [1, 2, 3, 5, 10, 11, 14], L44551 = [1, 2, 3, 10, 11, 15, 16], L44577 = [1, 2, 3, 10, 12, 14, 16], L44657 = [1, 2, 3, 11, 12, 14, 15], L44896 = [1, 2, 4, 5, 7, 10, 11], L44899 = [1, 2, 4, 5, 7, 10, 14], L44901 = [1, 2, 4, 5, 7, 10, 17], L44903 = [1, 2, 4, 5, 7, 10, 19], L44908 = [1, 2, 4, 5, 7, 11, 16], L44909 = [1, 2, 4, 5, 7, 11, 17], L44923 = [1, 2, 4, 5, 7, 13, 17], L44928 = [1, 2, 4, 5, 7, 14, 19], L44936 = [1, 2, 4, 5, 7, 16, 19], L44953 = [1, 2, 4, 5, 8, 10, 17], L44966 = [1, 2, 4, 5, 8, 13, 16], L44981 = [1, 2, 4, 5, 8, 16, 19], L45041 = [1, 2, 4, 5, 10, 11, 14], L45054 = [1, 2, 4, 5, 10, 13, 17], L45062 = [1, 2, 4, 5, 10, 16, 19], L45083 = [1, 2, 4, 5, 11, 14, 19], L45126 = [1, 2, 4, 5, 13, 14, 17], L45128 = [1, 2, 4, 5, 13, 14, 19] L45171 = [1, 2, 4, 7, 8, 11, 13], L45177 = [1, 2, 4, 7, 8, 13, 14], L45179 = [1, 2, 4, 7, 8, 13, 17], L45237 = [1, 2, 4, 7, 10, 11, 13], L45240 = [1, 2, 4, 7, 10, 11, 17], L45259 = [1, 2, 4, 7, 10, 14, 19], L45281 = [1, 2, 4, 7, 11, 13, 19] L45287 = [1, 2, 4, 7, 11, 16, 17], L45333 = [1, 2, 4, 7, 13, 16, 17], L45507 = [1, 2, 4, 9, 11, 15, 17], L45528 = [1, 2, 4, 9, 12, 14, 17], L45532 = [1, 2, 4, 9, 12, 15, 17], L45591 = [1, 2, 4, 10, 11, 14, 17], L45677 = [1, 2, 4, 11, 12, 14, 1 L46327 = [1, 2, 5, 8, 10, 11, 16], L46355 = [1, 2, 5, 8, 11, 15, 18], L46370 = [1, 2, 5, 8, 12, 14, 18], L46573 = [1, 2, 5, 11, 12, 14, 15], L46657 = [1, 2, 5, 13, 13, 14, 16], L47144 = [1, 2, 6, 7, 11, 12, 15], L47561 = [1, 2, 6, 11, 12, 14, 15], L47759 = [1, 2, 7, 8, 10, 11, 13], L48223 = [1, 2, 8, 10, 13, 13, 14], L48606 = [1, 2, 9, 11, 12, 14, 15], L48775 = [1, 2, 10, 11, 12, 14, 15], L48875 = [1, 2, 10, 13, 13, 13, 17], L48948 = [1, 2, 11, 12, 12, 14, 15], L48960 = [1, 2, 11, 12, 13, 14, 15], L48967 = [1, 2, 11, 12, 14, 15, 15], L48968 =
APPENDIX
155
Table 5. (continued) n = 7 q I indexes of I-isospectral families 40 {0} {63, 65}, {70, 94}, {524, 532}, {612, 614}, {624, 647}, {625, 649}, {628, 846}, {633, 652}, {657, 847}, {689, 851}, {943, 948}, {2915, 2923}, {3105, 3422}, {3107, 3416}, {3203, 3211}, {3438, 3446}, {3586, 3594}, {3654, 3662}, {3664, 3680}, {3666, 3690}, {3668, 3700}, {3672, 3704}, {3939, 3962}, {3991, 4606}, {4047, 4071}, {4050, 4073}, {4052, 4070}, {4079, 4081}, {4095, 4108}, {4116, 5045}, {4142, 4214}, {4148, 4149, 4152}, {4154, 4272}, {4155, 4274}, {4158, 5197}, {4163, 4277}, {4166, 4280}, {4176, 4190}, {4183, 5200}, {4196, 4285}, {4254, 5193}, {4290, 5201}, {4322, 5205}, {4433, 5215}, {4711, 4716}, {5463, 5468}, {5547, 5552}, {5594, 5599}, {5601, 5610}, {5603, 5619}, {5605, 5621}, {15060, 15068}, {15350, 15358}, {15589, 15597}, {15754, 15762}, {15823, 15831}, {15833, 15849}, {15835, 15862}, {15837, 15872}, {15839, 15877}, {15841, 15879}, {16522, 16582}, {16675, 17960}, {16728, 18499}, {16730, 18493}, {16771, 18517}, {16868, 18519}, {16869, 18540}, {16873, 18520}, {16993, 17001}, {17229, 17237}, {17268, 18728}, {17388, 17396}, {17456, 17464}, {17466, 17482}, {17468, 17492}, {17470, 17502}, {17474, 17506}, {18110, 18140}, {18409, 18416}, {18487, 18523}, {18556, 18564}, {18621, 18629}, {18631, 18645}, {18633, 18656}, {18635, 18666}, {18636, 18669}, {18638, 18671}, {19134, 19142}, {19202, 19210}, {19212, 19228}, {19214, 19238}, {19216, 19248}, {19220, 19252}, {19453, 19461}, {19463, 19479}, {19465, 19489}, {19467, 19499}, {19471, 19503}, {19505, 19545}, {19507, 19555}, {19509, 19565}, {19513, 19569}, {19518, 19584}, {19520, 19592}, {19523, 19595}, {19528, 19612}, {19532, 19616}, {19537, 19620}, {20348, 20357}, {20412, 20429}, {20416, 20559}, {20420, 20550}, {20428, 20566}, {20434, 23038}, {20439, 20569}, {20447, 21008}, {20613, 23044}, {20700, 23053}, {20819, 20843}, {20864, 20876}, {20921, 20922, 20926}, {20925, 20939, 20942, 21064}, {20929, 21057}, {20932, 21059}, {20934, 21056}, {20940, 21070}, {20943, 21072}, {20956, 24546}, {20961, 21080}, {20969, 21069}, {21012, 21024}, {21090, 21092}, {21106, 21119}, {21127, 24550}, {21168, 21215}, {21247, 24557}, {21300, 21316}, {21303, 21361}, {21310, 21575}, {21317, 21581}, {21331, 25129}, {21340, 21588}, {21350, 21351, 21354}, {21360, 21363, 21368}, {21370, 21776}, {21371, 21778}, {21374, 25150}, {21379, 21781},
[1, 2, 11, 12, 14, 15, 18], L49946 = [1, 3, 3, 4, 9, 10, 14], L49971 = [1, 3, 3, 4, 9, 14, 17], L50914 = [1, 3, 3, 10, 12, 14, 16 L51554 = [1, 3, 4, 9, 10, 14, 16], L51555 = [1, 3, 4, 9, 10, 14, 17], L51559 = [1, 3, 4, 9, 10, 16, 17], L51578 = [1, 3, 4, 9, 12, 14, 17], L51589 = [1, 3, 4, 9, 13, 13, 17], L51643 = [1, 3, 4, 10, 13, 13, 14], L51703 = [1, 3, 4, 12, 13, 13, 1 L51735 = [1, 3, 4, 13, 13, 14, 17], L52016 = [1, 3, 5, 8, 12, 14, 18], L52445 = [1, 3, 6, 7, 10, 13, 15], L52498 = [1, 3, 6, 8, 10, 13, 18], L52623 = [1, 3, 6, 10, 12, 14, 16], L53185 = [1, 3, 10, 12, 12, 14, 16], L53198 = [1, 3, 10, 12, 13, 14, 16], L53206 = [1, 3, 10, 12, 14, 15, 16], L53208 = [1, 3, 10, 12, 14, 16, 18], L53554 = [1, 4, 5, 11, 13, 13, 13], L54176 = [1, 5, 6, 8, 12, 14, 18], L54262 = [1, 5, 8, 12, 12, 14, 18], L54267 = [1, 5, 8, 12, 13, 14, 18], L55472 = [3, 6, 9, 12, 13, 13, 13], L55475 = [3, 6, 9, 13, 13, 13, 13], L55476 = [3, 6, 9, 13, 13, 13, 15], L55477 = [3, 6, 9, 13, 13, 13, 18], L55478 = [3, 6, 12, 13, 13, 13, 13], L55480 = [3, 6, 13, 13, 13, 13, 15], L55481 = [3, 9, 12, 13, 13, 13, 13]. q = 40 : L63 = [0, 0, 0, 0, 1, 3, 7], L65 = [0, 0, 0, 0, 1, 3, 9], L70 = [0, 0, 0, 0, 1, 3, 15], L94 = [0, 0, 0, 0, 1, 5, 7], L524 = [0, 0, 0, 1, 2, 9, 11], L532 = [0, 0, 0, 1, 2, 9, 19], L612 = [0, 0, 0, 1, 3, 5, 11], L614 = [0, 0, 0, 1, 3, 5, 13], L624 = [0, 0, 0, 1, 3, 7, 10], L625 = [0, 0, 0, 1, 3, 7, 11], L628 = [0, 0, 0, 1, 3, 7, 15],
156
EMILIO A. LAURET
Table 5. (continued) n = 7 q I indexes of I-isospectral families 40 {0} {21382, 21784}, {21392, 21406}, {21399, 25153}, {21412, 21789}, {21418, 21793}, (cont.) {21450, 21486}, {21469, 25158}, {21494, 21800}, {21628, 25134}, {21743, 25145}, {21805, 25159}, {21837, 25163}, {21948, 25173}, {22235, 25193}, {22530, 22535}, {23344, 23349}, {23435, 23440}, {23482, 23487}, {23489, 23498}, {23491, 23507}, {23493, 23509}, {24961, 24976}, {25842, 25847}, {25926, 25931}, {25973, 25978}, {25980, 25989}, {25981, 25994}, {25982, 26000}, {25984, 26002}, {26207, 26212}, {26254, 26259}, {26261, 26270}, {26263, 26279}, {26265, 26281}, {26403, 26408}, {26410, 26419}, {26412, 26428}, {26414, 26430}, {26432, 26449}, {26434, 26458}, {26436, 26460}, {26440, 26475}, {26442, 26477}, {26444, 26479}, {28395, 28398}, {28650, 28653}, {67089, 67097}, {67379, 67387}, {67618, 67626}, {67784, 67792}, {67853, 67861}, {67863, 67879}, {67865, 67892}, {67867, 67902}, {67869, 67907}, {67871, 67909}, {69059, 69067}, {69298, 69306}, {69464, 69472}, {69533, 69541}, {69543, 69559}, {69545, 69572}, {69547, 69582}, {69549, 69587}, {69551, 69589}, {70226, 70259}, {70543, 70551}, {70706, 70714}, {70775, 70783}, {70785, 70801}, {70787, 70814}, {70789, 70824}, {70791, 70829}, {70793, 70831}, {71410, 71418}, {71479, 71487}, {71489, 71505}, {71491, 71518}, {71493, 71528}, {71495, 71533}, {71497, 71535}, {71748, 71756}, {71758, 71774}, {71760, 71787}, {71762, 71797}, {71764, 71802}, {71766, 71804}, {71806, 71852}, {71808, 71865}, {71810, 71875}, {71812, 71880}, {71814, 71882}, {71821, 71907}, {71823, 71917}, {71825, 71921}, {71827, 71923}, {71833, 71942}, {71835, 71947}, {71837, 71949}, {71842, 71954}, {71844, 71956}, {73242, 73306}, {73280, 77731}, {73282, 77725}, {73806, 73999}, {74031, 80267}, {74033, 80252}, {74041, 80256}, {74108, 74111}, {74126, 74130}, {74127, 74131, 74275}, {74146, 74273}, {74148, 74168, 74271, 74291}, {74151, 74214}, {74153, 74283}, {74268, 74278}, {74367, 74618}, {74368, 74643}, {74369, 74642}, {74386, 74443}, {74437, 80243}, {74463, 80261}, {74637, 74734}, {74659, 75316}, {74699, 75029}, {74816, 80484}, {74822, 75098}, {74842, 75945}, {75189, 82554}, {75191, 82536}, {75289, 80690}, {75322, 75418, 82575, 82591}, {75324, 82579}, L633 = [0, 0, 0, 1, 3, 7, 20], L647 = [0, 0, 0, 1, 3, 9, 10], L649 = [0, 0, 0, 1, 3, 9, 13], L652 = [0, 0, 0, 1, 3, 9, 20], L657 = [0, 0, 0, 1, 3, 10, 15], L689 = [0, 0, 0, 1, 3, 15, 20], L846 = [0, 0, 0, 1, 5, 7, 9], L847 = [0, 0, 0, 1, 5, 7, 10], L851 = [0, 0, 0, 1, 5, 7, 20], L943 = [0, 0, 0, 1, 6, 9, 11], L948 = [0, 0, 0, 1, 6, 9, 19], L2915 = [0, 0, 1, 2, 2, 9, 11], L2923 = [0, 0, 1, 2, 2, 9, 19], L3105 = [0, 0, 1, 2, 3, 14, 17], L3107 = [0, 0, 1, 2, 3, 14, 19], L3203 = [0, 0, 1, 2, 4, 9, 11], L3211 = [0, 0, 1, 2, 4, 9, 19], L3416 = [0, 0, 1, 2, 6, 7, 13], L3422 = [0, 0, 1, 2, 6, 7, 19], L3438 = [0, 0, 1, 2, 6, 9, 11], L3446 = [0, 0, 1, 2, 6, 9, 19], L3586 = [0, 0, 1, 2, 8, 9, 11], L3594 = [0, 0, 1, 2, 8, 9, 19], L3654 = [0, 0, 1, 2, 9, 10, 11], L3662 = [0, 0, 1, 2, 9, 10, 19], L3664 = [0, 0, 1, 2, 9, 11, 12], L3666 = [0, 0, 1, 2, 9, 11, 14], L3668 = [0, 0, 1, 2, 9, 11, 16], L3672 = [0, 0, 1, 2, 9, 11, 20], L3680 = [0, 0, 1, 2, 9, 12, 19], L3690 = [0, 0, 1, 2, 9, 14, 19], L3700 = [0, 0, 1, 2, 9, 16, 19], L3704 = [0, 0, 1, 2, 9, 19, 20], L3939 = [0, 0, 1, 3, 4, 7, 12], L3962 = [0, 0, 1, 3, 4, 9, 12], L3991 = [0, 0, 1, 3, 4, 12, 15], L4047 = [0, 0, 1, 3, 5, 7, 11], L4050 = [0, 0, 1, 3, 5, 7, 15], L4052 = [0, 0, 1, 3, 5, 7, 17], L4070 = [0, 0, 1, 3, 5, 9, 11], L4071 = [0, 0, 1, 3, 5, 9, 13], L4073 = [0, 0, 1, 3, 5, 9, 15], L4079 = [0, 0, 1, 3, 5, 10, 11], L4081 = [0, 0, 1, 3, 5, 10, 13], L4095 = [0, 0, 1, 3, 5, 11, 20], L4108 = [0, 0, 1, 3, 5, 13, 20], L4116 = [0, 0, 1, 3, 5, 15, 15], L4142 = [0, 0, 1, 3, 7, 8, 16], L4148 = [0, 0, 1, 3, 7, 9, 11], L4149 = [0, 0, 1, 3, 7, 9, 13], L4152 = [0, 0, 1, 3, 7, 9, 19], L4154 = [0, 0, 1, 3, 7, 10, 10], L4155 = [0, 0, 1, 3, 7, 10, 11], L4158 = [0, 0, 1, 3, 7, 10, 15], L4163 = [0, 0, 1, 3, 7, 10, 20], L4166 = [0, 0, 1, 3, 7, 11, 20], L4176 = [0, 0, 1, 3, 7, 13, 19], L4183 = [0, 0, 1, 3, 7, 15, 20], L4190 = [0, 0, 1, 3, 7, 17, 19], L4196 = [0, 0, 1, 3, 7, 20, 20], L4214 = [0, 0, 1, 3, 8, 9, 16], L4254 = [0, 0, 1, 3, 8, 15, 16], L4272 =
APPENDIX
157
Table 5. (continued) n = 7 q I indexes of I-isospectral families 40 {0} {75438, 80727}, {75499, 82621}, {75501, 82615}, {75542, 82639}, {75639, 82641}, (cont.) {75640, 82662}, {75644, 82642}, {75708, 83430}, {75767, 82719}, {76031, 82723}, {76032, 82768}, {76038, 82724}, {76196, 76204}, {76432, 76440}, {76592, 76600}, {76660, 76668}, {76670, 76686}, {76672, 76696}, {76674, 76706}, {76678, 76710}, {77326, 77356}, {77625, 77632}, {77754, 77890}, {77775, 77783}, {77842, 77850}, {77852, 77867}, {77854, 77878}, {77856, 77888}, {77857, 77892}, {77859, 77894}, {77925, 83299}, {78022, 83431}, {78410, 78418}, {78478, 78486}, {78488, 78504}, {78490, 78514}, {78492, 78524}, {78496, 78528}, {78729, 78737}, {78739, 78755}, {78741, 78765}, {78743, 78775}, {78747, 78779}, {78781, 78821}, {78783, 78831}, {78785, 78841}, {78789, 78845}, {78794, 78860}, {78796, 78868}, {78799, 78871}, {78804, 78888}, {78808, 78892}, {78813, 78896}, {80224, 80260}, {80375, 80404}, {80990, 81020}, {81264, 81294}, {81308, 81365}, {81320, 81396}, {81326, 81413}, {81330, 81417}, {82086, 82093}, {82224, 82231}, {82282, 82289}, {82291, 82305}, {82293, 82314}, {82295, 82322}, {82296, 82324}, {82298, 82326}, {82571, 82645}, {82600, 82727}, {82604, 82882}, {82609, 82734}, {82784, 82792}, {82849, 82857}, {82859, 82873}, {82861, 82884}, {82863, 82894}, {82864, 82897}, {82866, 82899}, {83079, 83087}, {83089, 83103}, {83091, 83114}, {83093, 83124}, {83094, 83127}, {83096, 83129}, {83131, 83165}, {83133, 83174}, {83135, 83182}, {83136, 83184}, {83138, 83186}, {83142, 83201}, {83144, 83211}, {83147, 83215}, {83151, 83232}, {83152, 83235}, {83154, 83237}, {83156, 83240}, {83158, 83242}, {84512, 84520}, {84580, 84588}, {84590, 84606}, {84592, 84616}, {84594, 84626}, {84598, 84630}, {84831, 84839}, {84841, 84857}, {84843, 84867}, {84845, 84877}, {84849, 84881}, {84883, 84923}, {84885, 84933}, {84887, 84943}, {84891, 84947}, {84896, 84962}, {84898, 84970}, {84901, 84973}, {84906, 84990}, {84910, 84994}, {84915, 84998}, {85540, 85548}, {85550, 85566}, {85552, 85576}, {85554, 85586}, {85558, 85590}, {85592, 85632}, {85594, 85642}, {85596, 85652}, {85600, 85656}, {85605, 85671}, {85607, 85679}, {85610, 85682}, {85615, 85699}, {85619, 85703}, {85624, 85707}, {85709, 85799}, {85711, 85809}, {85713, 85819}, {85717, 85823}, {85722, 85838}, {85724, 85846}, {85727, 85849}, {85732, 85866}, {85736, 85870}, {85741, 85874}, {85751, 85896}, {85753, 85904}, {85756, 85907}, {85761, 85920}, {85764, 85923}, {85767, 85926}, {85777, 85953}, {85781, 85957}, {85786, 85961}, {85791, 85965}, {87464, 87481}, {87468, 87611}, {87484, 87618}, {87741, 94664}, {88007, 88148}, {88016, 88150}, {88018, 88140}, {88170, 88261}, {88188, 88197}, {88243, 88280}, {88288, 96235}, {88314, 89507}, {88411, 88428}, {88415, 88744}, {88434, 88753}, {88441, 88749}, {88443, 88457, 88748, 88774}, {88467, 88513}, {88471, 89003}, {88473, 88479, 88482}, {88485, 88552}, {88488, 88554}, {88496, 89039}, {88500, 89041}, [0, 0, 1, 3, 9, 10, 10], L4274 = [0, 0, 1, 3, 9, 10, 13], L4277 = [0, 0, 1, 3, 9, 10, 20], L4280 = [0, 0, 1, 3, 9, 13, 20], L4285 = [0, 0, 1, 3, 9, 20, 20], L4290 = [0, 0, 1, 3, 10, 10, 15], L4322 = [0, 0, 1, 3, 10, 15, 20], L4433 = [0, 0, 1, 3, 15, 20, 20], L4606 = [0, 0, 1, 4, 5, 7, 12], L4711 = [0, 0, 1, 4, 6, 9, 11], L4716 = [0, 0, 1, 4, 6, 9, 19], L5045 = [0, 0, 1, 5, 5, 7, 15], L5193 = [0, 0, 1, 5, 7, 8, 16], L5197 = [0, 0, 1, 5, 7, 9, 10], L5200 = [0, 0, 1, 5, 7, 9, 20], L5201 = [0, 0, 1, 5, 7, 10, 10], L5205 = [0, 0, 1, 5, 7, 10, 20], L5215 = [0, 0, 1, 5, 7, 20, 20], L5328 = [0, 0, 1, 5, 10, 15, 20], L5463 = [0, 0, 1, 6, 6, 9, 11], L5468 = [0, 0, 1, 6, 6, 9, 19], L5547 = [0, 0, 1, 6, 8, 9, 11], L5552 = [0, 0, 1, 6, 8, 9, 19], L5594 = [0, 0, 1, 6, 9, 10, 11], L5599 = [0, 0, 1, 6, 9, 10, 19], L5601 = [0, 0, 1, 6, 9, 11, 12], L5603 = [0, 0, 1, 6, 9, 11, 16], L5605 = [0, 0, 1, 6, 9, 11, 20], L5610 = [0, 0, 1, 6, 9, 12, 19],
158
EMILIO A. LAURET
Table 5. (continued) n = 7 q I indexes of I-isospectral families 40 {0} {88504, 88994}, {88512, 89010}, {88518, 96886}, {88523, 89013}, {88531, 90551}, (cont.) {88551, 89061}, {88567, 88581}, {88574, 96893}, {88587, 89066}, {88617, 90603}, {88887, 96867}, {89137, 96904}, {89224, 96913}, {89474, 96937}, {89708, 89732}, {89810, 89811, 89815}, {89818, 89946}, {89828, 89831, 89953}, {89829, 89959}, {89832, 89961}, {89845, 89968}, {89847, 89955}, {89995, 90007}, {90057, 90101}, {90141, 100625}, {90218, 90521}, {90235, 90529}, {90241, 90517}, {90254, 90255, 90259}, {90258, 90293, 90296, 90751}, {90261, 90264, 90270}, {90262, 90267, 90274}, {90266, 90271, 90280}, {90279, 90335, 90341, 90778}, {90283, 90744}, {90286, 90746}, {90288, 90743}, {90294, 90757}, {90297, 90759}, {90310, 101225}, {90315, 90767}, {90323, 90756}, {90337, 90790}, {90342, 90793}, {90366, 90393}, {90386, 101230}, {90399, 90811}, {90417, 90789}, {90555, 90567}, {90618, 90663}, {90699, 101213}, {90825, 90827}, {90841, 90854}, {90862, 101234}, {90903, 90950}, {90982, 101241}, {91075, 91204}, {91292, 101257}, {91373, 91389}, {91376, 91602}, {91409, 91998}, {91424, 91457}, {91427, 91586}, {91430, 91434, 91440}, {91437, 91494}, {91444, 91604}, {91451, 92197}, {91458, 92203}, {91472, 103021}, {91481, 92210}, {91496, 92218}, {91521, 91555}, {91541, 103029}, {91561, 92229}, {91575, 91576, 91579}, {91585, 91588, 91593}, {91601, 91606, 91613}, {91615, 92730}, {91616, 92732}, {91619, 103073}, {91624, 92735}, {91627, 92738}, {91637, 91651}, {91644, 103076}, {91657, 92743}, {91663, 92747}, {91695, 91731}, {91714, 103081}, {91739, 92754}, {91749, 92759}, {91823, 91895}, {91864, 103088}, {91905, 92768}, {92156, 103011}, {92269, 103034}, {92384, 103045}, {92678, 103067}, {92773, 103089}, {92805, 103093}, {92916, 103103}, {93203, 103123}, {93827, 103158}, {94142, 94147}, {94967, 94972}, {95059, 95064}, {95106, 95111}, {95113, 95122}, {95115, 95131}, {95117, 95133}, {96686, 96701}, {97701, 97706}, {97792, 97797}, {97839, 97844}, {97846, 97855}, {97847, 97860}, {97848, 97866}, {97850, 97868}, {98099, 98104}, {98146, 98151}, {98153, 98162}, {98155, 98171}, {98157, 98173}, {98295, 98300}, {98302, 98311}, {98304, 98320}, {98306, 98322}, {98324, 98341}, {98326, 98350}, {98328, 98352}, {98332, 98367}, {98334, 98369}, {98336, 98371}, {102087, 102104}, {102389, 102404}, {102557, 102572}, {102581, 102608}, {102589, 102625}, {102591, 102627}, {104690, 104695}, {104774, 104779}, {104821, 104826}, {104828, 104837}, {104829, 104842}, {104830, 104848}, {104832, 104850}, {105055, 105060}, {105102, 105107}, {105109, 105118}, {105110, 105123}, {105111, 105129}, {105113, 105131},
L5619 = [0, 0, 1, 6, 9, 16, 19], L5621 = [0, 0, 1, 6, 9, 19, 20], L5778 = [0, 0, 1, 7, 9, 15, 17], L5863 = [0, 0, 1, 8, 8, 16, 16], L6579 = [0, 0, 2, 5, 10, 15, 20], L6698 = [0, 0, 4, 5, 10, 15, 20], L6742 = [0, 0, 5, 8, 8, 16, 16], L6750 = [0, 0, 5, 8, 10, 15, 20], L12174 = [0, 1, 1, 5, 10, 15, 20], L13212 = [0, 1, 1, 7, 9, 15, 17], L13555 = [0, 1, 1, 8, 8, 16, 16], L15060 = [0, 1, 2, 2, 2, 9, 11], L15068 = [0, 1, 2, 2, 2, 9, 19], L15350 = [0, 1, 2, 2, 4, 9, 11], L15358 = [0, 1, 2, 2, 4, 9, 19], L15589 = [0, 1, 2, 2, 6, 9, 11], L15597 = [0, 1, 2, 2, 6, 9, 19], L15754 = [0, 1, 2, 2, 8, 9, 11], L15762 = [0, 1, 2, 2, 8, 9, 19], L15823 = [0, 1, 2, 2, 9, 10, 11], L15831 = [0, 1, 2, 2, 9, 10, 19], L15833 = [0, 1, 2, 2, 9, 11, 12], L15835 = [0, 1, 2, 2, 9, 11, 14], L15837 = [0, 1, 2, 2, 9, 11, 16], L15839 =
APPENDIX
159
Table 5. (continued) n = 7 q 40 (cont.)
I {0}
indexes of I-isospectral families {105254, 105259}, {105261, 105270}, {105262, 105275}, {105263, 105281}, {105265, 105283}, {105285, 105303}, {105286, 105308}, {105287, 105314}, {105289, 105316}, {105291, 105325}, {105293, 105327}, {105294, 105336}, {105296, 105338}, {105298, 105340}, {105815, 105820}, {105862, 105867}, {105869, 105878}, {105871, 105887}, {105873, 105889}, {106011, 106016}, {106018, 106027}, {106020, 106036}, {106022, 106038}, {106040, 106057}, {106042, 106066}, {106044, 106068}, {106048, 106083}, {106050, 106085}, {106052, 106087}, {106386, 106391}, {106393, 106402}, {106395, 106411}, {106397, 106413}, {106415, 106432}, {106417, 106441}, {106419, 106443}, {106423, 106458}, {106425, 106460}, {106427, 106462}, {106464, 106493}, {106466, 106502}, {106468, 106504}, {106472, 106519}, {106474, 106521}, {106476, 106523}, {106482, 106546}, {106484, 106548}, {106486, 106550}, {106488, 106552}, {110883, 110886}, {111040, 111043}, {111046, 111051}, {111049, 111056}, {111693, 111696}, {111823, 111826}, {111833, 111838}, {111836, 111843} {0, 1} {4149, 4152}, {20925, 20939}, {20942, 21064}, {21351, 21354}, {21363, 21368}, {87994, 88008}, {88012, 88141}, {88246, 88484}, {88479, 88482}, {88492, 89348}, {90202, 90216}, {90220, 90514}, {90258, 90293}, {90267, 90274}, {90277, 90333}, {90279, 90335}, {90296, 90751}, {90339, 90776}, {90341, 90778}, {91434, 91440}, {91576, 91579}, {91588, 91593}, {91606, 91613} {0, 1, 2} {16413, 16479}, {74308, 74609}, {74370, 74644} {0, 1, 2, 3} {90265, 90269}
[0, 1, 2, 2, 9, 11, 18], L15841 = [0, 1, 2, 2, 9, 11, 20], L15849 = [0, 1, 2, 2, 9, 12, 19], L15862 = [0, 1, 2, 2, 9, 14, 19], L15872 = [0, 1, 2, 2, 9, 16, 19], L15877 = [0, 1, 2, 2, 9, 18, 19], L15879 = [0, 1, 2, 2, 9, 19, 20], L16413 = [0, 1, 2, 3, 6, 11, 13], L16479 = [0, 1, 2, 3, 7, 9, 14], L16522 = [0, 1, 2, 3, 7, 14, 16], L16582 = [0, 1, 2, 3, 8, 11, 14], L16675 = [0, 1, 2, 3, 9, 15, 18], L16728 = [0, 1, 2, 3, 10, 14, 17], L16730 = [0, 1, 2, 3, 10, 14, 19], L16771 = [0, 1, 2, 3, 11, 14, 19], L16868 = [0, 1, 2, 3, 14, 17, 19], L16869 = [0, 1, 2, 3, 14, 17, 20], L16873 = [0, 1, 2, 3, 14, 19, 20] L16993 = [0, 1, 2, 4, 4, 9, 11], L17001 = [0, 1, 2, 4, 4, 9, 19], L17229 = [0, 1, 2, 4, 6, 9, 11], L17237 = [0, 1, 2, 4, 6, 9, 19], L17268 = [0, 1, 2, 4, 6, 13, 17], L17388 = [0, 1, 2, 4, 8, 9, 11], L17396 = [0, 1, 2, 4, 8, 9, 19], L17456 = [0, 1, 2, 4, 9, 10, 11], L17464 = [0, 1, 2, 4, 9, 10, 19], L17466 = [0, 1, 2, 4, 9, 11, 12], L17468 = [0, 1, 2, 4, 9, 11, 14], L17470 = [0, 1, 2, 4, 9, 11, 16], L17474 = [0, 1, 2, 4, 9, 11, 20], L17482 = [0, 1, 2, 4, 9, 12, 19], L17492 = [0, 1, 2, 4, 9, 14, 19], L17502 = [0, 1, 2, 4, 9, 16, 19], L17506 = [0, 1, 2, 4, 9, 19, 20], L17960 = [0, 1, 2, 5, 7, 9, 18], L18110 = [0, 1, 2, 5, 9, 11, 15], L18140 = [0, 1, 2, 5, 9, 15, 19], L18198 = [0, 1, 2, 5, 10, 15, 20], L18409 = [0, 1, 2, 6, 6, 9, 11], L18416 = [0, 1, 2, 6, 6, 9, 19], L18487 = [0, 1, 2, 6, 7, 9, 18], L18493 = [0, 1, 2, 6, 7, 10, 13], L18499 = [0, 1, 2, 6, 7, 10, 19], L18517 = [0, 1, 2, 6, 7, 13, 17], L18519 = [0, 1, 2, 6, 7, 13, 19], L18520 = [0, 1, 2, 6, 7, 13, 20], L18523 = [0, 1, 2, 6, 7, 14, 17], L18540 = [0, 1, 2, 6, 7, 19, 20], L18556 = [0, 1, 2, 6, 8, 9, 11], L18564 = [0, 1, 2, 6, 8, 9, 19], L18621 = [0, 1, 2, 6, 9, 10, 11], L18629 = [0, 1, 2, 6, 9, 10, 19], L18631 = [0, 1, 2, 6, 9, 11, 12], L18633 = [0, 1, 2, 6, 9, 11, 14], L18635 = [0, 1, 2, 6, 9, 11, 16], L18636 = [0, 1, 2, 6, 9, 11, 18], L18638 = [0, 1, 2, 6, 9, 11, 20], L18645 = [0, 1, 2, 6, 9, 12, 19], L18656 = [0, 1, 2, 6, 9, 14, 19], L18666 = [0, 1, 2, 6, 9, 16, 19], L18669 = [0, 1, 2, 6, 9, 18, 19], L18671 = [0, 1, 2, 6, 9, 19, 20], L18708 = [0, 1, 2, 6, 10, 14, 18], L18728 = [0, 1, 2, 6, 11, 12, 13], L18952 = [0, 1, 2, 7, 9, 15, 17], L19134 = [0, 1, 2, 8, 8, 9, 11], L19142 = [0, 1, 2, 8, 8, 9, 19], L19189 = [0, 1, 2, 8, 8, 16, 16], L19202 = [0, 1, 2, 8, 9, 10, 11], L19210 = [0, 1, 2, 8, 9, 10, 19], L19212 = [0, 1, 2, 8, 9, 11, 12], L19214 = [0, 1, 2, 8, 9, 11, 14], L19216 = [0, 1, 2, 8, 9, 11, 16], L19220 = [0, 1, 2, 8, 9, 11, 20], L19228 = [0, 1, 2, 8, 9, 12, 19], L19238 = [0, 1, 2, 8, 9, 14, 19], L19248 =
160
EMILIO A. LAURET
Table 5. (continued) n = 7 q 40 (cont.)
I {4}
indexes of I-isospectral families {5778, 26816, 107236, 107304}, {5863, 6742, 26995, 27123, 29422}, {13212, 26873, 61313, 61824, 107302}, {13555, 26801, 27021, 27117, 29393}, {18708, 28931, 82936, 83380, 112482}, {18952, 26868, 83802, 84085, 107294}, {19189, 26244, 27053, 27104, 27124, 28970, 29431}, {21153, 25155, 90605, 91042, 103026}, {21558, 25244, 27065, 27125, 29434}, {22598, 22691}, {22758, 29202, 95531, 95837, 113075}, {23653, 23828}, {23682, 26875, 98722, 98825, 107306}, {23804, 27085, 27126, 29302, 29437}, {23906, 29320}, {36174, 61064, 61603, 61819, 107409}, {42884, 82646, 83113, 83376, 112252}, {43343, 59207, 61659, 61799, 61828, 84081, 107402}, {47674, 90273, 90334, 90777, 101229}, {48720, 56587, 61702, 61772, 61829, 90047, 103083}, {51424, 95346, 95648, 95833, 113023}, {53189, 61745, 61830, 98822, 107411}, {56410, 56539}, {70871, 82360, 83279, 83370, 83384, 111107, 112513}, {71170, 82599, 84002, 84088, 107397}, {73930, 74647, 80715, 84030, 84070, 90888, 103078}, {74335, 80453, 83312, 83385, 112520}, {76806, 95189, 95722, 95829, 95840, 111611, 113103}, {77932, 83337, 83386, 111858, 112522}, {78203, 84054, 84089, 98808, 107404}, {87746, 94844, 95809, 95841, 113116}, {88247, 88491, 91044, 96896, 103085}, {90264, 90269}, {94371, 95823, 95842, 112945, 113117}, {95309, 98816, 98827, 107413}, {98762, 99231}, {107277, 107779} {6} {5328, 25581}, {6579, 29055}, {6698, 6750, 29345, 29449}, {12174, 25580}, {18198, 25579}, {21080, 21163}, {21132, 25167}, {21445, 91816}, {23190, 25576}, {24676, 25572}, {25015, 25559}, {25306, 25539}, {25426, 25516}, {28487, 29054}, {28726, 29053}, {28988, 29045}, {29197, 29344, 29430}, {29270, 29402}, {29314, 29341, 29448} {2, 3, 6} {25436, 103845}, {29000, 112674}, {29337, 29445}, {97238, 103843}, {103401, 103835}, {111956, 112672}, {112595, 112664}, {113196, 113464} {4, 5, 6} {70871, 83384}, {74283, 74375}, {82360, 83370}
[0, 1, 2, 8, 9, 16, 19], L19252 = [0, 1, 2, 8, 9, 19, 20], L19453 = [0, 1, 2, 9, 10, 10, 11], L19461 = [0, 1, 2, 9, 10, 10, 19], L19463 = [0, 1, 2, 9, 10, 11, 12], L19465 = [0, 1, 2, 9, 10, 11, 14], L19467 = [0, 1, 2, 9, 10, 11, 16], L19471 = [0, 1, 2, 9, 10, 11, 20], L19479 = [0, 1, 2, 9, 10, 12, 19], L19489 = [0, 1, 2, 9, 10, 14, 19], L19499 = [0, 1, 2, 9, 10, 16, 19] L19503 = [0, 1, 2, 9, 10, 19, 20], L19505 = [0, 1, 2, 9, 11, 12, 12], L19507 = [0, 1, 2, 9, 11, 12, 14], L19509 = [0, 1, 2, 9, 11, 12, 16], L19513 = [0, 1, 2, 9, 11, 12, 20], L19518 = [0, 1, 2, 9, 11, 14, 14], L19520 = [0, 1, 2, 9, 11, 14, 16] L19523 = [0, 1, 2, 9, 11, 14, 20], L19528 = [0, 1, 2, 9, 11, 16, 16], L19532 = [0, 1, 2, 9, 11, 16, 20], L19537 = [0, 1, 2, 9, 11, 20, 20], L19545 = [0, 1, 2, 9, 12, 12, 19], L19555 = [0, 1, 2, 9, 12, 14, 19], L19565 = [0, 1, 2, 9, 12, 16, 19] L19569 = [0, 1, 2, 9, 12, 19, 20], L19584 = [0, 1, 2, 9, 14, 14, 19], L19592 = [0, 1, 2, 9, 14, 16, 19], L19595 =
APPENDIX
161
[0, 1, 2, 9, 14, 19, 20], L19612 = [0, 1, 2, 9, 16, 16, 19], L19616 = [0, 1, 2, 9, 16, 19, 20], L19620 = [0, 1, 2, 9, 19, 20, 20] L20348 = [0, 1, 3, 4, 5, 11, 12], L20357 = [0, 1, 3, 4, 5, 12, 13], L20412 = [0, 1, 3, 4, 7, 9, 13], L20416 = [0, 1, 3, 4, 7, 9, 19], L20420 = [0, 1, 3, 4, 7, 10, 12], L20428 = [0, 1, 3, 4, 7, 11, 12], L20429 = [0, 1, 3, 4, 7, 11, 13], L20434 = [0, 1, 3, 4, 7, 12, 15], L20439 = [0, 1, 3, 4, 7, 12, 20], L20447 = [0, 1, 3, 4, 7, 15, 16], L20550 = [0, 1, 3, 4, 9, 10, 12], L20559 = [0, 1, 3, 4, 9, 11, 13], L20566 = [0, 1, 3, 4, 9, 12, 13], L20569 = [0, 1, 3, 4, 9, 12, 20], L20613 = [0, 1, 3, 4, 10, 12, 15], L20700 = [0, 1, 3, 4, 12, 15, 20], L20819 = [0, 1, 3, 5, 5, 7, 11], L20843 = [0, 1, 3, 5, 5, 9, 13], L20864 = [0, 1, 3, 5, 5, 11, 15], L20876 = [0, 1, 3, 5, 5, 13, 15], L20921 = [0, 1, 3, 5, 7, 9, 11], L20922 = [0, 1, 3, 5, 7, 9, 13], L20925 = [0, 1, 3, 5, 7, 9, 17], L20926 = [0, 1, 3, 5, 7, 9, 19], L20929 = [0, 1, 3, 5, 7, 10, 11], L20932 = [0, 1, 3, 5, 7, 10, 15], L20934 = [0, 1, 3, 5, 7, 10, 17], L20939 = [0, 1, 3, 5, 7, 11, 13], L20940 = [0, 1, 3, 5, 7, 11, 15], L20942 = [0, 1, 3, 5, 7, 11, 19], L20943 = [0, 1, 3, 5, 7, 11, 20], L20956 = [0, 1, 3, 5, 7, 15, 15], L20961 = [0, 1, 3, 5, 7, 15, 20], L20969 = [0, 1, 3, 5, 7, 17, 20], L21008 = [0, 1, 3, 5, 8, 11, 12], L21012 = [0, 1, 3, 5, 8, 11, 16], L21024 = [0, 1, 3, 5, 8, 13, 16], L21056 = [0, 1, 3, 5, 9, 10, 11], L21057 = [0, 1, 3, 5, 9, 10, 13], L21059 = [0, 1, 3, 5, 9, 10, 15], L21064 = [0, 1, 3, 5, 9, 11, 13], L21069 = [0, 1, 3, 5, 9, 11, 20], L21070 = [0, 1, 3, 5, 9, 13, 15], L21072 = [0, 1, 3, 5, 9, 13, 20], L21080 = [0, 1, 3, 5, 9, 15, 20], L21090 = [0, 1, 3, 5, 10, 10, 11], L21092 = [0, 1, 3, 5, 10, 10, 13], L21106 = [0, 1, 3, 5, 10, 11, 20], L21119 = [0, 1, 3, 5, 10, 13, 20] L21127 = [0, 1, 3, 5, 10, 15, 15], L21132 = [0, 1, 3, 5, 10, 15, 20], L21153 = [0, 1, 3, 5, 11, 13, 19], L21163 = [0, 1, 3, 5, 11, 15, 20], L21168 = [0, 1, 3, 5, 11, 20, 20], L21215 = [0, 1, 3, 5, 13, 20, 20], L21247 = [0, 1, 3, 5, 15, 15, 20] L21300 = [0, 1, 3, 7, 8, 9, 13], L21303 = [0, 1, 3, 7, 8, 9, 19], L21310 = [0, 1, 3, 7, 8, 10, 16], L21316 = [0, 1, 3, 7, 8, 11, 13], L21317 = [0, 1, 3, 7, 8, 11, 16], L21331 = [0, 1, 3, 7, 8, 15, 16], L21340 = [0, 1, 3, 7, 8, 16, 20], L21350 = [0, 1, 3, 7, 9, 10, 11], L21351 = [0, 1, 3, 7, 9, 10, 13], L21354 = [0, 1, 3, 7, 9, 10, 19], L21360 = [0, 1, 3, 7, 9, 11, 20], L21361 = [0, 1, 3, 7, 9, 13, 16], L21363 = [0, 1, 3, 7, 9, 13, 20], L21368 = [0, 1, 3, 7, 9, 19, 20], L21370 = [0, 1, 3, 7, 10, 10, 10], L21371 = [0, 1, 3, 7, 10, 10, 11], L21374 = [0, 1, 3, 7, 10, 10, 15], L21379 = [0, 1, 3, 7, 10, 10, 20], L21382 = [0, 1, 3, 7, 10, 11, 20], L21392 = [0, 1, 3, 7, 10, 13, 19], L21399 = [0, 1, 3, 7, 10, 15, 20] L21406 = [0, 1, 3, 7, 10, 17, 19], L21412 = [0, 1, 3, 7, 10, 20, 20], L21418 = [0, 1, 3, 7, 11, 20, 20], L21445 = [0, 1, 3, 7, 13, 17, 19], L21450 = [0, 1, 3, 7, 13, 19, 20], L21469 = [0, 1, 3, 7, 15, 20, 20], L21486 = [0, 1, 3, 7, 17, 19, 20] L21494 = [0, 1, 3, 7, 20, 20, 20], L21558 = [0, 1, 3, 8, 8, 16, 16], L21575 = [0, 1, 3, 8, 9, 10, 16], L21581 = [0, 1, 3, 8, 9, 13, 16], L21588 = [0, 1, 3, 8, 9, 16, 20], L21628 = [0, 1, 3, 8, 10, 15, 16], L21743 = [0, 1, 3, 8, 15, 16, 20], L21776 = [0, 1, 3, 9, 10, 10, 10], L21778 = [0, 1, 3, 9, 10, 10, 13], L21781 = [0, 1, 3, 9, 10, 10, 20], L21784 = [0, 1, 3, 9, 10, 13, 20], L21789 = [0, 1, 3, 9, 10, 20, 20], L21793 = [0, 1, 3, 9, 13, 20, 20], L21800 = [0, 1, 3, 9, 20, 20, 20] L21805 = [0, 1, 3, 10, 10, 10, 15], L21837 = [0, 1, 3, 10, 10, 15, 20], L21948 = [0, 1, 3, 10, 15, 20, 20], L22235 = [0, 1, 3, 15, 20, 20, 20], L22530 = [0, 1, 4, 4, 6, 9, 11], L22535 = [0, 1, 4, 4, 6, 9, 19], L22598 = [0, 1, 4, 4, 7, 12, 12], L22691 = [0, 1, 4, 4, 9, 12, 12], L22758 = [0, 1, 4, 4, 12, 12, 20], L23038 = [0, 1, 4, 5, 7, 9, 12], L23044 = [0, 1, 4, 5, 7, 10, 12], L23053 = [0, 1, 4, 5, 7, 12, 20], L23190 = [0, 1, 4, 5, 10, 15, 20], L23344 = [0, 1, 4, 6, 6, 9, 11], L23349 = [0, 1, 4, 6, 6, 9, 19], L23435 = [0, 1, 4, 6, 8, 9, 11], L23440 = [0, 1, 4, 6, 8, 9, 19], L23482 = [0, 1, 4, 6, 9, 10, 11], L23487 = [0, 1, 4, 6, 9, 10, 19], L23489 = [0, 1, 4, 6, 9, 11, 12], L23491 = [0, 1, 4, 6, 9, 11, 16], L23493 = [0, 1, 4, 6, 9, 11, 20], L23498 = [0, 1, 4, 6, 9, 12, 19], L23507 = [0, 1, 4, 6, 9, 16, 19], L23509 = [0, 1, 4, 6, 9, 19, 20], L23653 = [0, 1, 4, 7, 8, 12, 16], L23682 = [0, 1, 4, 7, 9, 15, 17], L23804 = [0, 1, 4, 8, 8, 16, 16], L23828 = [0, 1, 4, 8, 9, 12, 16], L23906 = [0, 1, 4, 8, 12, 16, 20], L24546 = [0, 1, 5, 5, 7, 9, 15], L24550 = [0, 1, 5, 5, 7, 10, 15], L24557 = [0, 1, 5, 5, 7, 15, 20], L24676 = [0, 1, 5, 5, 10, 15, 20], L24961 = [0, 1, 5, 6, 9, 11, 15], L24976 = [0, 1, 5, 6, 9, 15, 19], L25015 = [0, 1, 5, 6, 10, 15, 20], L25129 = [0, 1, 5, 7, 8, 9, 16], L25134 = [0, 1, 5, 7, 8, 10, 16], L25145 = [0, 1, 5, 7, 8, 16, 20], L25150 = [0, 1, 5, 7, 9, 10, 10], L25153 = [0, 1, 5, 7, 9, 10, 20], L25155 = [0, 1, 5, 7, 9, 15, 17], L25158 = [0, 1, 5, 7, 9, 20, 20], L25159 = [0, 1, 5, 7, 10, 10, 10], L25163 = [0, 1, 5, 7, 10, 10, 20], L25167 = [0, 1, 5, 7, 10, 15, 20], L25173 = [0, 1, 5, 7, 10, 20, 20], L25193 = [0, 1, 5, 7, 20, 20, 20], L25244 = [0, 1, 5, 8, 8, 16, 16], L25306 = [0, 1, 5, 8, 10, 15, 20], L25426 = [0, 1, 5, 9, 10, 15, 20], L25436 = [0, 1, 5, 9, 11, 15, 19], L25516 = [0, 1, 5, 10, 11, 15, 20], L25539 = [0, 1, 5, 10, 12, 15, 20], L25559 = [0, 1, 5, 10, 14, 15, 20], L25572 = [0, 1, 5, 10, 15, 15, 20], L25576 = [0, 1, 5, 10, 15, 16, 20], L25579 = [0, 1, 5, 10, 15, 18, 20], L25580 = [0, 1, 5, 10, 15, 19, 20], L25581 = [0, 1, 5, 10, 15, 20, 20], L25842 = [0, 1, 6, 6, 6, 9, 11], L25847 = [0, 1, 6, 6, 6, 9, 19], L25926 = [0, 1, 6, 6, 8, 9, 11], L25931 = [0, 1, 6, 6, 8, 9, 19], L25973 = [0, 1, 6, 6, 9, 10, 11], L25978 = [0, 1, 6, 6, 9, 10, 19], L25980 = [0, 1, 6, 6, 9, 11, 12],
162
EMILIO A. LAURET
L25981 = [0, 1, 6, 6, 9, 11, 14], L25982 = [0, 1, 6, 6, 9, 11, 16], L25984 = [0, 1, 6, 6, 9, 11, 20], L25989 = [0, 1, 6, 6, 9, 12, 19], L25994 = [0, 1, 6, 6, 9, 14, 19], L26000 = [0, 1, 6, 6, 9, 16, 19], L26002 = [0, 1, 6, 6, 9, 19, 20], L26207 = [0, 1, 6, 8, 8, 9, 11], L26212 = [0, 1, 6, 8, 8, 9, 19], L26244 = [0, 1, 6, 8, 8, 16, 16], L26254 = [0, 1, 6, 8, 9, 10, 11], L26259 = [0, 1, 6, 8, 9, 10, 19], L26261 = [0, 1, 6, 8, 9, 11, 12], L26263 = [0, 1, 6, 8, 9, 11, 16], L26265 = [0, 1, 6, 8, 9, 11, 20], L26270 = [0, 1, 6, 8, 9, 12, 19], L26279 = [0, 1, 6, 8, 9, 16, 19], L26281 = [0, 1, 6, 8, 9, 19, 20], L26403 = [0, 1, 6, 9, 10, 10, 11], L26408 = [0, 1, 6, 9, 10, 10, 19], L26410 = [0, 1, 6, 9, 10, 11, 12], L26412 = [0, 1, 6, 9, 10, 11, 16], L26414 = [0, 1, 6, 9, 10, 11, 20], L26419 = [0, 1, 6, 9, 10, 12, 19], L26428 = [0, 1, 6, 9, 10, 16, 19], L26430 = [0, 1, 6, 9, 10, 19, 20], L26432 = [0, 1, 6, 9, 11, 12, 12], L26434 = [0, 1, 6, 9, 11, 12, 16] L26436 = [0, 1, 6, 9, 11, 12, 20], L26440 = [0, 1, 6, 9, 11, 16, 16], L26442 = [0, 1, 6, 9, 11, 16, 20], L26444 = [0, 1, 6, 9, 11, 20, 20], L26449 = [0, 1, 6, 9, 12, 12, 19], L26458 = [0, 1, 6, 9, 12, 16, 19], L26460 = [0, 1, 6, 9, 12, 19, 20] L26475 = [0, 1, 6, 9, 16, 16, 19], L26477 = [0, 1, 6, 9, 16, 19, 20], L26479 = [0, 1, 6, 9, 19, 20, 20], L26801 = [0, 1, 7, 8, 8, 16, 16], L26816 = [0, 1, 7, 8, 9, 15, 17], L26868 = [0, 1, 7, 9, 10, 15, 17], L26873 = [0, 1, 7, 9, 15, 15, 17], L26875 = [0, 1, 7, 9, 15, 17, 20], L26995 = [0, 1, 8, 8, 8, 16, 16], L27021 = [0, 1, 8, 8, 9, 16, 16], L27053 = [0, 1, 8, 8, 10, 16, 16], L27065 = [0, 1, 8, 8, 11, 16, 16], L27085 = [0, 1, 8, 8, 12, 16, 16], L27104 = [0, 1, 8, 8, 14, 16, 16] L27117 = [0, 1, 8, 8, 15, 16, 16], L27123 = [0, 1, 8, 8, 16, 16, 16], L27124 = [0, 1, 8, 8, 16, 16, 18], L27125 = [0, 1, 8, 8, 16, 16, 19], L27126 = [0, 1, 8, 8, 16, 16, 20], L28395 = [0, 2, 2, 5, 6, 6, 14], L28398 = [0, 2, 2, 5, 6, 6, 18], L28487 = [0, 2, 2, 5, 10, 15, 20], L28650 = [0, 2, 4, 5, 6, 8, 14], L28653 = [0, 2, 4, 5, 6, 8, 18], L28726 = [0, 2, 4, 5, 10, 15, 20], L28931 = [0, 2, 5, 6, 10, 14, 18], L28970 = [0, 2, 5, 8, 8, 16, 16], L28988 = [0, 2, 5, 8, 10, 15, 20], L29000 = [0, 2, 5, 8, 12, 15, 18], L29045 = [0, 2, 5, 10, 12, 15, 20], L29053 = [0, 2, 5, 10, 15, 16, 20], L29054 = [0, 2, 5, 10, 15, 18, 20], L29055 = [0, 2, 5, 10, 15, 20, 20], L29197 = [0, 4, 4, 5, 10, 15, 20], L29202 = [0, 4, 4, 5, 12, 12, 20], L29270 = [0, 4, 5, 5, 10, 15, 20], L29302 = [0, 4, 5, 8, 8, 16, 16], L29314 = [0, 4, 5, 8, 10, 15, 20], L29320 = [0, 4, 5, 8, 12, 16, 20], L29337 = [0, 4, 5, 10, 10, 15, 20], L29341 = [0, 4, 5, 10, 12, 15, 2 L29344 = [0, 4, 5, 10, 15, 16, 20], L29345 = [0, 4, 5, 10, 15, 20, 20], L29393 = [0, 5, 5, 8, 8, 16, 16], L29402 = [0, 5, 5, 8, 10, 15, 20], L29422 = [0, 5, 8, 8, 8, 16, 16], L29430 = [0, 5, 8, 8, 10, 15, 20], L29431 = [0, 5, 8, 8, 10, 16, 16], L29434 = [0, 5, 8, 8, 15, 16, 16], L29437 = [0, 5, 8, 8, 16, 16, 20], L29445 = [0, 5, 8, 10, 10, 15, 20], L29448 = [0, 5, 8, 10, 15, 16, 20], L29449 = [0, 5, 8, 10, 15, 20, 20], L36174 = [1, 1, 1, 7, 9, 15, 17], L42884 = [1, 1, 2, 6, 10, 14, 18 L43343 = [1, 1, 2, 7, 9, 15, 17], L47674 = [1, 1, 3, 5, 11, 13, 19], L48720 = [1, 1, 3, 7, 9, 15, 17], L51424 = [1, 1, 4, 4, 12, 12, 20], L53189 = [1, 1, 4, 7, 9, 15, 17], L56410 = [1, 1, 5, 7, 7, 9, 17], L56539 = [1, 1, 5, 7, 9, 9, 17], L56587 = [1, 1, 5, 7, 9, 15, 17], L59207 = [1, 1, 6, 7, 9, 15, 17], L61064 = [1, 1, 7, 7, 9, 15, 17], L61313 = [1, 1, 7, 8, 9, 15, 17], L61603 = [1, 1, 7, 9, 9, 15, 17], L61659 = [1, 1, 7, 9, 10, 15, 17], L61702 = [1, 1, 7, 9, 11, 15, 17], L61745 = [1, 1, 7, 9, 12, 15, 17], L61772 = [1, 1, 7, 9, 13, 15, 17], L61799 = [1, 1, 7, 9, 14, 15, 17], L61819 = [1, 1, 7, 9, 15, 15, 17], L61824 = [1, 1, 7, 9, 15, 16, 17], L61828 = [1, 1, 7, 9, 15, 17, 18], L61829 = [1, 1, 7, 9, 15, 17, 19] L61830 = [1, 1, 7, 9, 15, 17, 20], L67089 = [1, 2, 2, 2, 2, 9, 11], L67097 = [1, 2, 2, 2, 2, 9, 19], L67379 = [1, 2, 2, 2, 4, 9, 11], L67387 = [1, 2, 2, 2, 4, 9, 19], L67618 = [1, 2, 2, 2, 6, 9, 11], L67626 = [1, 2, 2, 2, 6, 9, 19], L67784 = [1, 2, 2, 2, 8, 9, 11], L67792 = [1, 2, 2, 2, 8, 9, 19], L67853 = [1, 2, 2, 2, 9, 10, 11], L67861 = [1, 2, 2, 2, 9, 10, 19], L67863 = [1, 2, 2, 2, 9, 11, 12], L67865 = [1, 2, 2, 2, 9, 11, 14], L67867 = [1, 2, 2, 2, 9, 11, 16], L67869 = [1, 2, 2, 2, 9, 11, 18], L67871 = [1, 2, 2, 2, 9, 11, 20], L67879 = [1, 2, 2, 2, 9, 12, 19], L67892 = [1, 2, 2, 2, 9, 14, 19], L67902 = [1, 2, 2, 2, 9, 16, 19], L67907 = [1, 2, 2, 2, 9, 18, 19], L67909 = [1, 2, 2, 2, 9, 19, 20], L69059 = [1, 2, 2, 4, 4, 9, 11], L69067 = [1, 2, 2, 4, 4, 9, 19], L69298 = [1, 2, 2, 4, 6, 9, 11], L69306 = [1, 2, 2, 4, 6, 9, 19], L69464 = [1, 2, 2, 4, 8, 9, 11], L69472 = [1, 2, 2, 4, 8, 9, 19], L69533 = [1, 2, 2, 4, 9, 10, 11], L69541 = [1, 2, 2, 4, 9, 10, 19], L69543 = [1, 2, 2, 4, 9, 11, 12], L69545 = [1, 2, 2, 4, 9, 11, 14], L69547 = [1, 2, 2, 4, 9, 11, 16], L69549 = [1, 2, 2, 4, 9, 11, 18], L69551 = [1, 2, 2, 4, 9, 11, 20], L69559 = [1, 2, 2, 4, 9, 12, 19], L69572 = [1, 2, 2, 4, 9, 14, 19], L69582 = [1, 2, 2, 4, 9, 16, 19], L69587 = [1, 2, 2, 4, 9, 18, 19], L69589 = [1, 2, 2, 4, 9, 19, 20], L70226 = [1, 2, 2, 5, 9, 11, 15], L70259 = [1, 2, 2, 5, 9, 15, 19], L70543 = [1, 2, 2, 6, 6, 9, 11], L70551 = [1, 2, 2, 6, 6, 9, 19], L70706 = [1, 2, 2, 6, 8, 9, 11], L70714 = [1, 2, 2, 6, 8, 9, 19], L70775 = [1, 2, 2, 6, 9, 10, 11], L70783 = [1, 2, 2, 6, 9, 10, 19], L70785 = [1, 2, 2, 6, 9, 11, 12], L70787 = [1, 2, 2, 6, 9, 11, 14], L70789 = [1, 2, 2, 6, 9, 11, 16], L70791 = [1, 2, 2, 6, 9, 11, 18], L70793 = [1, 2, 2, 6, 9, 11, 20], L70801 = [1, 2, 2, 6, 9, 12, 19], L70814 = [1, 2, 2, 6, 9, 14, 19], L70824 = [1, 2, 2, 6, 9, 16, 19], L70829 = [1, 2, 2, 6, 9, 18, 19], L70831 = [1, 2, 2, 6, 9, 19, 20], L70871 = [1, 2, 2, 6, 10, 14, 18], L71170 = [1, 2, 2, 7, 9, 15, 17], L71410 =
APPENDIX
163
[1, 2, 2, 8, 8, 9, 11], L71418 = [1, 2, 2, 8, 8, 9, 19], L71479 = [1, 2, 2, 8, 9, 10, 11], L71487 = [1, 2, 2, 8, 9, 10, 19], L71489 = [1, 2, 2, 8, 9, 11, 12], L71491 = [1, 2, 2, 8, 9, 11, 14], L71493 = [1, 2, 2, 8, 9, 11, 16], L71495 = [1, 2, 2, 8, 9, 11, 18], L71497 = [1, 2, 2, 8, 9, 11, 20], L71505 = [1, 2, 2, 8, 9, 12, 19], L71518 = [1, 2, 2, 8, 9, 14, 19], L71528 = [1, 2, 2, 8, 9, 16, 19], L71533 = [1, 2, 2, 8, 9, 18, 19], L71535 = [1, 2, 2, 8, 9, 19, 20], L71748 = [1, 2, 2, 9, 10, 10, 11], L71756 = [1, 2, 2, 9, 10, 10, 19], L71758 = [1, 2, 2, 9, 10, 11, 12], L71760 = [1, 2, 2, 9, 10, 11, 14] L71762 = [1, 2, 2, 9, 10, 11, 16], L71764 = [1, 2, 2, 9, 10, 11, 18], L71766 = [1, 2, 2, 9, 10, 11, 20], L71774 = [1, 2, 2, 9, 10, 12, 19], L71787 = [1, 2, 2, 9, 10, 14, 19], L71797 = [1, 2, 2, 9, 10, 16, 19], L71802 = [1, 2, 2, 9, 10, 18, 19] L71804 = [1, 2, 2, 9, 10, 19, 20], L71806 = [1, 2, 2, 9, 11, 12, 12], L71808 = [1, 2, 2, 9, 11, 12, 14], L71810 = [1, 2, 2, 9, 11, 12, 16], L71812 = [1, 2, 2, 9, 11, 12, 18], L71814 = [1, 2, 2, 9, 11, 12, 20], L71821 = [1, 2, 2, 9, 11, 14, 14] L71823 = [1, 2, 2, 9, 11, 14, 16], L71825 = [1, 2, 2, 9, 11, 14, 18], L71827 = [1, 2, 2, 9, 11, 14, 20], L71833 = [1, 2, 2, 9, 11, 16, 16], L71835 = [1, 2, 2, 9, 11, 16, 18], L71837 = [1, 2, 2, 9, 11, 16, 20], L71842 = [1, 2, 2, 9, 11, 18, 20] L71844 = [1, 2, 2, 9, 11, 20, 20], L71852 = [1, 2, 2, 9, 12, 12, 19], L71865 = [1, 2, 2, 9, 12, 14, 19], L71875 = [1, 2, 2, 9, 12, 16, 19], L71880 = [1, 2, 2, 9, 12, 18, 19], L71882 = [1, 2, 2, 9, 12, 19, 20], L71907 = [1, 2, 2, 9, 14, 14, 19] L71917 = [1, 2, 2, 9, 14, 16, 19], L71921 = [1, 2, 2, 9, 14, 18, 19], L71923 = [1, 2, 2, 9, 14, 19, 20], L71942 = [1, 2, 2, 9, 16, 16, 19], L71947 = [1, 2, 2, 9, 16, 18, 19], L71949 = [1, 2, 2, 9, 16, 19, 20], L71954 = [1, 2, 2, 9, 18, 19, 20] L71956 = [1, 2, 2, 9, 19, 20, 20], L73242 = [1, 2, 3, 4, 11, 14, 18], L73280 = [1, 2, 3, 4, 12, 14, 17], L73282 = [1, 2, 3, 4, 12, 14, 19], L73306 = [1, 2, 3, 4, 13, 14, 18], L73806 = [1, 2, 3, 5, 9, 11, 14], L73930 = [1, 2, 3, 5, 11, 13, 19], L73999 = [1, 2, 3, 5, 13, 14, 17], L74031 = [1, 2, 3, 5, 14, 15, 17], L74033 = [1, 2, 3, 5, 14, 15, 19], L74041 = [1, 2, 3, 5, 14, 17, 19], L74108 = [1, 2, 3, 6, 7, 9, 14], L74111 = [1, 2, 3, 6, 7, 9, 18], L74126 = [1, 2, 3, 6, 7, 11, 13], L74127 = [1, 2, 3, 6, 7, 11, 14], L74130 = [1, 2, 3, 6, 7, 11, 17], L74131 = [1, 2, 3, 6, 7, 11, 18], L74146 = [1, 2, 3, 6, 7, 13, 17], L74148 = [1, 2, 3, 6, 7, 13, 19], L74151 = [1, 2, 3, 6, 7, 14, 16], L74153 = [1, 2, 3, 6, 7, 14, 18], L74168 = [1, 2, 3, 6, 7, 17, 19], L74214 = [1, 2, 3, 6, 8, 11, 18], L74268 = [1, 2, 3, 6, 9, 11, 13], L74271 = [1, 2, 3, 6, 9, 11, 17], L74273 = [1, 2, 3, 6, 9, 11, 19], L74275 = [1, 2, 3, 6, 9, 13, 14], L74278 = [1, 2, 3, 6, 9, 13, 19], L74283 = [1, 2, 3, 6, 9, 14, 18], L74291 = [1, 2, 3, 6, 9, 17, 19], L74308 = [1, 2, 3, 6, 10, 11, 13], L74335 = [1, 2, 3, 6, 10, 14, 18], L74367 = [1, 2, 3, 6, 11, 13, 17], L74368 = [1, 2, 3, 6, 11, 13, 18], L74369 = [1, 2, 3, 6, 11, 13, 19] L74370 = [1, 2, 3, 6, 11, 13, 20], L74375 = [1, 2, 3, 6, 11, 14, 18], L74386 = [1, 2, 3, 6, 11, 16, 18], L74437 = [1, 2, 3, 6, 13, 15, 17], L74443 = [1, 2, 3, 6, 13, 16, 18], L74463 = [1, 2, 3, 6, 14, 15, 18], L74609 = [1, 2, 3, 7, 9, 10, 14], L74618 = [1, 2, 3, 7, 9, 11, 14], L74637 = [1, 2, 3, 7, 9, 13, 18], L74642 = [1, 2, 3, 7, 9, 14, 17], L74643 = [1, 2, 3, 7, 9, 14, 18], L74644 = [1, 2, 3, 7, 9, 14, 20], L74647 = [1, 2, 3, 7, 9, 15, 17], L74659 = [1, 2, 3, 7, 9, 18, 19], L74699 = [1, 2, 3, 7, 10, 14, 16], L74734 = [1, 2, 3, 7, 11, 13, 18], L74816 = [1, 2, 3, 7, 14, 15, 17], L74822 = [1, 2, 3, 7, 14, 16, 20], L74842 = [1, 2, 3, 7, 15, 18, 19], L75029 = [1, 2, 3, 8, 10, 11, 14], L75098 = [1, 2, 3, 8, 11, 14, 20] L75189 = [1, 2, 3, 8, 14, 16, 17], L75191 = [1, 2, 3, 8, 14, 16, 19], L75289 = [1, 2, 3, 9, 10, 15, 18], L75316 = [1, 2, 3, 9, 11, 13, 18], L75322 = [1, 2, 3, 9, 11, 14, 17], L75324 = [1, 2, 3, 9, 11, 14, 19], L75418 = [1, 2, 3, 9, 14, 17, 19] L75438 = [1, 2, 3, 9, 15, 18, 20], L75499 = [1, 2, 3, 10, 10, 14, 17], L75501 = [1, 2, 3, 10, 10, 14, 19], L75542 = [1, 2, 3, 10, 11, 14, 19], L75639 = [1, 2, 3, 10, 14, 17, 19], L75640 = [1, 2, 3, 10, 14, 17, 20], L75644 = [1, 2, 3, 10, 14, 19, 20], L75708 = [1, 2, 3, 11, 12, 14, 18], L75767 = [1, 2, 3, 11, 14, 19, 20], L75945 = [1, 2, 3, 13, 15, 18, 19], L76031 = [1, 2, 3, 14, 17, 19, 20], L76032 = [1, 2, 3, 14, 17, 20, 20], L76038 = [1, 2, 3, 14, 19, 20, 20], L76196 = [1, 2, 4, 4, 4, 9, 11], L76204 = [1, 2, 4, 4, 4, 9, 19], L76432 = [1, 2, 4, 4, 6, 9, 11], L76440 = [1, 2, 4, 4, 6, 9, 19], L76592 = [1, 2, 4, 4, 8, 9, 11], L76600 = [1, 2, 4, 4, 8, 9, 19], L76660 = [1, 2, 4, 4, 9, 10, 11], L76668 = [1, 2, 4, 4, 9, 10, 19], L76670 = [1, 2, 4, 4, 9, 11, 12], L76672 = [1, 2, 4, 4, 9, 11, 14], L76674 = [1, 2, 4, 4, 9, 11, 16], L76678 = [1, 2, 4, 4, 9, 11, 20], L76686 = [1, 2, 4, 4, 9, 12, 19], L76696 = [1, 2, 4, 4, 9, 14, 19], L76706 = [1, 2, 4, 4, 9, 16, 19], L76710 = [1, 2, 4, 4, 9, 19, 20], L76806 = [1, 2, 4, 4, 12, 12, 20], L77326 = [1, 2, 4, 5, 9, 11, 15], L77356 = [1, 2, 4, 5, 9, 15, 19], L77625 = [1, 2, 4, 6, 6, 9, 11], L77632 = [1, 2, 4, 6, 6, 9, 19], L77725 = [1, 2, 4, 6, 7, 12, 13], L77731 = [1, 2, 4, 6, 7, 12, 19], L77754 = [1, 2, 4, 6, 7, 17, 18], L77775 = [1, 2, 4, 6, 8, 9, 11], L77783 = [1, 2, 4, 6, 8, 9, 19], L77842 = [1, 2, 4, 6, 9, 10, 11], L77850 = [1, 2, 4, 6, 9, 10, 19], L77852 = [1, 2, 4, 6, 9, 11, 12], L77854 = [1, 2, 4, 6, 9, 11, 14], L77856 = [1, 2, 4, 6, 9, 11, 16], L77857 = [1, 2, 4, 6, 9, 11, 18], L77859 = [1, 2, 4, 6, 9, 11, 20], L77867 = [1, 2, 4, 6, 9, 12, 19], L77878 = [1, 2, 4, 6, 9, 14, 19], L77888 = [1, 2, 4, 6, 9, 16, 19], L77890 = [1, 2, 4, 6, 9, 17, 18], L77892 = [1, 2, 4, 6, 9, 18, 19], L77894 = [1, 2, 4, 6, 9, 19, 20], L77925 = [1, 2, 4, 6, 10, 13, 17], L77932 = [1, 2, 4, 6, 10, 14, 18],
164
EMILIO A. LAURET
L78022 = [1, 2, 4, 6, 13, 17, 20], L78203 = [1, 2, 4, 7, 9, 15, 17], L78410 = [1, 2, 4, 8, 8, 9, 11], L78418 = [1, 2, 4, 8, 8, 9, 19], L78478 = [1, 2, 4, 8, 9, 10, 11], L78486 = [1, 2, 4, 8, 9, 10, 19], L78488 = [1, 2, 4, 8, 9, 11, 12], L78490 = [1, 2, 4, 8, 9, 11, 14], L78492 = [1, 2, 4, 8, 9, 11, 16], L78496 = [1, 2, 4, 8, 9, 11, 20], L78504 = [1, 2, 4, 8, 9, 12, 19], L78514 = [1, 2, 4, 8, 9, 14, 19], L78524 = [1, 2, 4, 8, 9, 16, 19], L78528 = [1, 2, 4, 8, 9, 19, 20], L78729 = [1, 2, 4, 9, 10, 10, 11], L78737 = [1, 2, 4, 9, 10, 10, 19], L78739 = [1, 2, 4, 9, 10, 11, 12], L78741 = [1, 2, 4, 9, 10, 11, 14], L78743 = [1, 2, 4, 9, 10, 11, 16], L78747 = [1, 2, 4, 9, 10, 11, 20], L78755 = [1, 2, 4, 9, 10, 12, 19] L78765 = [1, 2, 4, 9, 10, 14, 19], L78775 = [1, 2, 4, 9, 10, 16, 19], L78779 = [1, 2, 4, 9, 10, 19, 20], L78781 = [1, 2, 4, 9, 11, 12, 12], L78783 = [1, 2, 4, 9, 11, 12, 14], L78785 = [1, 2, 4, 9, 11, 12, 16], L78789 = [1, 2, 4, 9, 11, 12, 20] L78794 = [1, 2, 4, 9, 11, 14, 14], L78796 = [1, 2, 4, 9, 11, 14, 16], L78799 = [1, 2, 4, 9, 11, 14, 20], L78804 = [1, 2, 4, 9, 11, 16, 16], L78808 = [1, 2, 4, 9, 11, 16, 20], L78813 = [1, 2, 4, 9, 11, 20, 20], L78821 = [1, 2, 4, 9, 12, 12, 19] L78831 = [1, 2, 4, 9, 12, 14, 19], L78841 = [1, 2, 4, 9, 12, 16, 19], L78845 = [1, 2, 4, 9, 12, 19, 20], L78860 = [1, 2, 4, 9, 14, 14, 19], L78868 = [1, 2, 4, 9, 14, 16, 19], L78871 = [1, 2, 4, 9, 14, 19, 20], L78888 = [1, 2, 4, 9, 16, 16, 19] L78892 = [1, 2, 4, 9, 16, 19, 20], L78896 = [1, 2, 4, 9, 19, 20, 20], L80224 = [1, 2, 5, 6, 7, 9, 18], L80243 = [1, 2, 5, 6, 7, 11, 19], L80252 = [1, 2, 5, 6, 7, 13, 15], L80256 = [1, 2, 5, 6, 7, 13, 19], L80260 = [1, 2, 5, 6, 7, 14, 17], L80261 = [1, 2, 5, 6, 7, 14, 18], L80267 = [1, 2, 5, 6, 7, 15, 19], L80375 = [1, 2, 5, 6, 9, 11, 15], L80404 = [1, 2, 5, 6, 9, 15, 19], L80453 = [1, 2, 5, 6, 10, 14, 18], L80484 = [1, 2, 5, 6, 11, 13, 19], L80690 = [1, 2, 5, 7, 9, 10, 18], L80715 = [1, 2, 5, 7, 9, 15, 17], L80727 = [1, 2, 5, 7, 9, 18, 20], L80990 = [1, 2, 5, 8, 9, 11, 15], L81020 = [1, 2, 5, 8, 9, 15, 19], L81264 = [1, 2, 5, 9, 10, 11, 15], L81294 = [1, 2, 5, 9, 10, 15, 19], L81308 = [1, 2, 5, 9, 11, 12, 15], L81320 = [1, 2, 5, 9, 11, 14, 15], L81326 = [1, 2, 5, 9, 11, 15, 16], L81330 = [1, 2, 5, 9, 11, 15, 20], L81365 = [1, 2, 5, 9, 12, 15, 19], L81396 = [1, 2, 5, 9, 14, 15, 19], L81413 = [1, 2, 5, 9, 15, 16, 19], L81417 = [1, 2, 5, 9, 15, 19, 20] L82086 = [1, 2, 6, 6, 6, 9, 11], L82093 = [1, 2, 6, 6, 6, 9, 19], L82224 = [1, 2, 6, 6, 8, 9, 11], L82231 = [1, 2, 6, 6, 8, 9, 19], L82282 = [1, 2, 6, 6, 9, 10, 11], L82289 = [1, 2, 6, 6, 9, 10, 19], L82291 = [1, 2, 6, 6, 9, 11, 12], L82293 = [1, 2, 6, 6, 9, 11, 14], L82295 = [1, 2, 6, 6, 9, 11, 16], L82296 = [1, 2, 6, 6, 9, 11, 18], L82298 = [1, 2, 6, 6, 9, 11, 20], L82305 = [1, 2, 6, 6, 9, 12, 19], L82314 = [1, 2, 6, 6, 9, 14, 19], L82322 = [1, 2, 6, 6, 9, 16, 19], L82324 = [1, 2, 6, 6, 9, 18, 19], L82326 = [1, 2, 6, 6, 9, 19, 20], L82360 = [1, 2, 6, 6, 10, 14, 18], L82536 = [1, 2, 6, 7, 8, 13, 16], L82554 = [1, 2, 6, 7, 8, 16, 19], L82571 = [1, 2, 6, 7, 9, 10, 18], L82575 = [1, 2, 6, 7, 9, 11, 13], L82579 = [1, 2, 6, 7, 9, 11, 19], L82591 = [1, 2, 6, 7, 9, 13, 19], L82599 = [1, 2, 6, 7, 9, 15, 17], L82600 = [1, 2, 6, 7, 9, 15, 18], L82604 = [1, 2, 6, 7, 9, 16, 18], L82609 = [1, 2, 6, 7, 9, 18, 20], L82615 = [1, 2, 6, 7, 10, 10, 13], L82621 = [1, 2, 6, 7, 10, 10, 19], L82639 = [1, 2, 6, 7, 10, 13, 17], L82641 = [1, 2, 6, 7, 10, 13, 19], L82642 = [1, 2, 6, 7, 10, 13, 20], L82645 = [1, 2, 6, 7, 10, 14, 17], L82646 = [1, 2, 6, 7, 10, 14, 18], L82662 = [1, 2, 6, 7, 10, 19, 20] L82719 = [1, 2, 6, 7, 13, 17, 20], L82723 = [1, 2, 6, 7, 13, 19, 20], L82724 = [1, 2, 6, 7, 13, 20, 20], L82727 = [1, 2, 6, 7, 14, 15, 17], L82734 = [1, 2, 6, 7, 14, 17, 20], L82768 = [1, 2, 6, 7, 19, 20, 20], L82784 = [1, 2, 6, 8, 8, 9, 11], L82792 = [1, 2, 6, 8, 8, 9, 19], L82849 = [1, 2, 6, 8, 9, 10, 11], L82857 = [1, 2, 6, 8, 9, 10, 19], L82859 = [1, 2, 6, 8, 9, 11, 12], L82861 = [1, 2, 6, 8, 9, 11, 14], L82863 = [1, 2, 6, 8, 9, 11, 16], L82864 = [1, 2, 6, 8, 9, 11, 18], L82866 = [1, 2, 6, 8, 9, 11, 20], L82873 = [1, 2, 6, 8, 9, 12, 19], L82882 = [1, 2, 6, 8, 9, 14, 17], L82884 = [1, 2, 6, 8, 9, 14, 19], L82894 = [1, 2, 6, 8, 9, 16, 19], L82897 = [1, 2, 6, 8, 9, 18, 19], L82899 = [1, 2, 6, 8, 9, 19, 20], L82936 = [1, 2, 6, 8, 10, 14, 18], L83079 = [1, 2, 6, 9, 10, 10, 11], L83087 = [1, 2, 6, 9, 10, 10, 19], L83089 = [1, 2, 6, 9, 10, 11, 12], L83091 = [1, 2, 6, 9, 10, 11, 14], L83093 = [1, 2, 6, 9, 10, 11, 16], L83094 = [1, 2, 6, 9, 10, 11, 18] L83096 = [1, 2, 6, 9, 10, 11, 20], L83103 = [1, 2, 6, 9, 10, 12, 19], L83113 = [1, 2, 6, 9, 10, 14, 18], L83114 = [1, 2, 6, 9, 10, 14, 19], L83124 = [1, 2, 6, 9, 10, 16, 19], L83127 = [1, 2, 6, 9, 10, 18, 19], L83129 = [1, 2, 6, 9, 10, 19, 20] L83131 = [1, 2, 6, 9, 11, 12, 12], L83133 = [1, 2, 6, 9, 11, 12, 14], L83135 = [1, 2, 6, 9, 11, 12, 16], L83136 = [1, 2, 6, 9, 11, 12, 18], L83138 = [1, 2, 6, 9, 11, 12, 20], L83142 = [1, 2, 6, 9, 11, 14, 14], L83144 = [1, 2, 6, 9, 11, 14, 16] L83147 = [1, 2, 6, 9, 11, 14, 20], L83151 = [1, 2, 6, 9, 11, 16, 16], L83152 = [1, 2, 6, 9, 11, 16, 18], L83154 = [1, 2, 6, 9, 11, 16, 20], L83156 = [1, 2, 6, 9, 11, 18, 20], L83158 = [1, 2, 6, 9, 11, 20, 20], L83165 = [1, 2, 6, 9, 12, 12, 19] L83174 = [1, 2, 6, 9, 12, 14, 19], L83182 = [1, 2, 6, 9, 12, 16, 19], L83184 = [1, 2, 6, 9, 12, 18, 19], L83186 = [1, 2, 6, 9, 12, 19, 20], L83201 = [1, 2, 6, 9, 14, 14, 19], L83211 = [1, 2, 6, 9, 14, 16, 19], L83215 = [1, 2, 6, 9, 14, 19, 20] L83232 = [1, 2, 6, 9, 16, 16, 19], L83235 = [1, 2, 6, 9, 16, 18, 19], L83237 = [1, 2, 6, 9, 16, 19, 20], L83240 = [1, 2, 6, 9, 18, 19, 20], L83242 = [1, 2, 6, 9, 19, 20, 20], L83279 = [1, 2, 6, 10, 10, 14, 18], L83299 = [1, 2, 6, 10, 11, 12, 1 L83312 = [1, 2, 6, 10, 11, 14, 18], L83337 = [1, 2, 6, 10, 12, 14, 18], L83370 = [1, 2, 6, 10, 14, 14, 18],
APPENDIX
165
L83376 = [1, 2, 6, 10, 14, 15, 18], L83380 = [1, 2, 6, 10, 14, 16, 18], L83384 = [1, 2, 6, 10, 14, 18, 18], L83385 = [1, 2, 6, 10, 14, 18, 19], L83386 = [1, 2, 6, 10, 14, 18, 20], L83430 = [1, 2, 6, 11, 12, 13, 18], L83431 = [1, 2, 6, 11, 12, 13, 20], L83802 = [1, 2, 7, 8, 9, 15, 17], L84002 = [1, 2, 7, 9, 10, 15, 17], L84030 = [1, 2, 7, 9, 11, 15, 17], L84054 = [1, 2, 7, 9, 12, 15, 17], L84070 = [1, 2, 7, 9, 13, 15, 17], L84081 = [1, 2, 7, 9, 15, 15, 17] L84085 = [1, 2, 7, 9, 15, 16, 17], L84088 = [1, 2, 7, 9, 15, 17, 18], L84089 = [1, 2, 7, 9, 15, 17, 20], L84512 = [1, 2, 8, 8, 8, 9, 11], L84520 = [1, 2, 8, 8, 8, 9, 19], L84580 = [1, 2, 8, 8, 9, 10, 11], L84588 = [1, 2, 8, 8, 9, 10, 19], L84590 = [1, 2, 8, 8, 9, 11, 12], L84592 = [1, 2, 8, 8, 9, 11, 14], L84594 = [1, 2, 8, 8, 9, 11, 16], L84598 = [1, 2, 8, 8, 9, 11, 20], L84606 = [1, 2, 8, 8, 9, 12, 19], L84616 = [1, 2, 8, 8, 9, 14, 19], L84626 = [1, 2, 8, 8, 9, 16, 19], L84630 = [1, 2, 8, 8, 9, 19, 20], L84831 = [1, 2, 8, 9, 10, 10, 11], L84839 = [1, 2, 8, 9, 10, 10, 19], L84841 = [1, 2, 8, 9, 10, 11, 12], L84843 = [1, 2, 8, 9, 10, 11, 14], L84845 = [1, 2, 8, 9, 10, 11, 16], L84849 = [1, 2, 8, 9, 10, 11, 20] L84857 = [1, 2, 8, 9, 10, 12, 19], L84867 = [1, 2, 8, 9, 10, 14, 19], L84877 = [1, 2, 8, 9, 10, 16, 19], L84881 = [1, 2, 8, 9, 10, 19, 20], L84883 = [1, 2, 8, 9, 11, 12, 12], L84885 = [1, 2, 8, 9, 11, 12, 14], L84887 = [1, 2, 8, 9, 11, 12, 16] L84891 = [1, 2, 8, 9, 11, 12, 20], L84896 = [1, 2, 8, 9, 11, 14, 14], L84898 = [1, 2, 8, 9, 11, 14, 16], L84901 = [1, 2, 8, 9, 11, 14, 20], L84906 = [1, 2, 8, 9, 11, 16, 16], L84910 = [1, 2, 8, 9, 11, 16, 20], L84915 = [1, 2, 8, 9, 11, 20, 20] L84923 = [1, 2, 8, 9, 12, 12, 19], L84933 = [1, 2, 8, 9, 12, 14, 19], L84943 = [1, 2, 8, 9, 12, 16, 19], L84947 = [1, 2, 8, 9, 12, 19, 20], L84962 = [1, 2, 8, 9, 14, 14, 19], L84970 = [1, 2, 8, 9, 14, 16, 19], L84973 = [1, 2, 8, 9, 14, 19, 20] L84990 = [1, 2, 8, 9, 16, 16, 19], L84994 = [1, 2, 8, 9, 16, 19, 20], L84998 = [1, 2, 8, 9, 19, 20, 20], L85540 = [1, 2, 9, 10, 10, 10, 11], L85548 = [1, 2, 9, 10, 10, 10, 19], L85550 = [1, 2, 9, 10, 10, 11, 12], L85552 = [1, 2, 9, 10, 10, 11, 14], L85554 = [1, 2, 9, 10, 10, 11, 16], L85558 = [1, 2, 9, 10, 10, 11, 20], L85566 = [1, 2, 9, 10, 10, 12, 19], L85576 = [1, 2, 9, 10, 10, 14, 19], L85586 = [1, 2, 9, 10, 10, 16, 19], L85590 = [1, 2, 9, 10, 10, 19, 20], L85592 = [1, 2, 9, 10, 11, 12, 12], L85594 = [1, 2, 9, 10, 11, 12, 14], L85596 = [1, 2, 9, 10, 11, 12, 16], L85600 = [1, 2, 9, 10, 11, 12, 20], L85605 = [1, 2, 9, 10, 11, 14, 14], L85607 = [1, 2, 9, 10, 11, 14, 16], L85610 = [1, 2, 9, 10, 11, 14, 20], L85615 = [1, 2, 9, 10, 11, 16, 16], L85619 = [1, 2, 9, 10, 11, 16, 20], L85624 = [1, 2, 9, 10, 11, 20, 20], L85632 = [1, 2, 9, 10, 12, 12, 19], L85642 = [1, 2, 9, 10, 12, 14, 19], L85652 = [1, 2, 9, 10, 12, 16, 19], L85656 = [1, 2, 9, 10, 12, 19, 20], L85671 = [1, 2, 9, 10, 14, 14, 19], L85679 = [1, 2, 9, 10, 14, 16, 19], L85682 = [1, 2, 9, 10, 14, 19, 20], L85699 = [1, 2, 9, 10, 16, 16, 19], L85703 = [1, 2, 9, 10, 16, 19, 20], L85707 = [1, 2, 9, 10, 19, 20, 20], L85709 = [1, 2, 9, 11, 12, 12, 12], L85711 = [1, 2, 9, 11, 12, 12, 14], L85713 = [1, 2, 9, 11, 12, 12, 16], L85717 = [1, 2, 9, 11, 12, 12, 20], L85722 = [1, 2, 9, 11, 12, 14, 14], L85724 = [1, 2, 9, 11, 12, 14, 16], L85727 = [1, 2, 9, 11, 12, 14, 20], L85732 = [1, 2, 9, 11, 12, 16, 16], L85736 = [1, 2, 9, 11, 12, 16, 20], L85741 = [1, 2, 9, 11, 12, 20, 20], L85751 = [1, 2, 9, 11, 14, 14, 14], L85753 = [1, 2, 9, 11, 14, 14, 16], L85756 = [1, 2, 9, 11, 14, 14, 20], L85761 = [1, 2, 9, 11, 14, 16, 16], L85764 = [1, 2, 9, 11, 14, 16, 20], L85767 = [1, 2, 9, 11, 14, 20, 20], L85777 = [1, 2, 9, 11, 16, 16, 16], L85781 = [1, 2, 9, 11, 16, 16, 20], L85786 = [1, 2, 9, 11, 16, 20, 20], L85791 = [1, 2, 9, 11, 20, 20, 20], L85799 = [1, 2, 9, 12, 12, 12, 19], L85809 = [1, 2, 9, 12, 12, 14, 19], L85819 = [1, 2, 9, 12, 12, 16, 19], L85823 = [1, 2, 9, 12, 12, 19, 20], L85838 = [1, 2, 9, 12, 14, 14, 19], L85846 = [1, 2, 9, 12, 14, 16, 19], L85849 = [1, 2, 9, 12, 14, 19, 20], L85866 = [1, 2, 9, 12, 16, 16, 19], L85870 = [1, 2, 9, 12, 16, 19, 20], L85874 = [1, 2, 9, 12, 19, 20, 20], L85896 = [1, 2, 9, 14, 14, 14, 19], L85904 = [1, 2, 9, 14, 14, 16, 19], L85907 = [1, 2, 9, 14, 14, 19, 20], L85920 = [1, 2, 9, 14, 16, 16, 19], L85923 = [1, 2, 9, 14, 16, 19, 20], L85926 = [1, 2, 9, 14, 19, 20, 20], L85953 = [1, 2, 9, 16, 16, 16, 19], L85957 = [1, 2, 9, 16, 16, 19, 20], L85961 = [1, 2, 9, 16, 19, 20, 20], L85965 = [1, 2, 9, 19, 20, 20, 20], L87464 = [1, 3, 4, 4, 7, 9, 13], L87468 = [1, 3, 4, 4, 7, 9, 19], L87481 = [1, 3, 4, 4, 7, 11, 13], L87484 = [1, 3, 4, 4, 7, 12, 12], L87611 = [1, 3, 4, 4, 9, 11, 13], L87618 = [1, 3, 4, 4, 9, 12, 12], L87741 = [1, 3, 4, 4, 12, 12, 15], L87746 = [1, 3, 4, 4, 12, 12, 20], L87994 = [1, 3, 4, 5, 7, 9, 17], L88007 = [1, 3, 4, 5, 7, 11, 12], L88008 = [1, 3, 4, 5, 7, 11, 13], L88012 = [1, 3, 4, 5, 7, 11, 19], L88016 = [1, 3, 4, 5, 7, 12, 15], L88018 = [1, 3, 4, 5, 7, 12, 17], L88140 = [1, 3, 4, 5, 9, 11, 12], L88141 = [1, 3, 4, 5, 9, 11, 13], L88148 = [1, 3, 4, 5, 9, 12, 13], L88150 = [1, 3, 4, 5, 9, 12, 15], L88170 = [1, 3, 4, 5, 9, 16, 17], L88188 = [1, 3, 4, 5, 10, 11, 12], L88197 = [1, 3, 4, 5, 10, 12, 13], L88243 = [1, 3, 4, 5, 11, 12, 20], L88246 = [1, 3, 4, 5, 11, 13, 17], L88247 = [1, 3, 4, 5, 11, 13, 19] L88261 = [1, 3, 4, 5, 11, 16, 17], L88280 = [1, 3, 4, 5, 12, 13, 20], L88288 = [1, 3, 4, 5, 12, 15, 15], L88314 = [1, 3, 4, 5, 13, 16, 17], L88411 = [1, 3, 4, 7, 8, 9, 13], L88415 = [1, 3, 4, 7, 8, 9, 19], L88428 = [1, 3, 4, 7, 8, 11, 13],
166
EMILIO A. LAURET
L88434 = [1, 3, 4, 7, 8, 12, 16], L88441 = [1, 3, 4, 7, 8, 13, 17], L88443 = [1, 3, 4, 7, 8, 13, 19], L88457 = [1, 3, 4, 7, 8, 17, 19], L88467 = [1, 3, 4, 7, 9, 10, 13], L88471 = [1, 3, 4, 7, 9, 10, 19], L88473 = [1, 3, 4, 7, 9, 11, 12], L88479 = [1, 3, 4, 7, 9, 12, 13], L88482 = [1, 3, 4, 7, 9, 12, 19], L88484 = [1, 3, 4, 7, 9, 13, 15], L88485 = [1, 3, 4, 7, 9, 13, 16], L88488 = [1, 3, 4, 7, 9, 13, 20], L88491 = [1, 3, 4, 7, 9, 15, 17], L88492 = [1, 3, 4, 7, 9, 15, 19], L88496 = [1, 3, 4, 7, 9, 16, 19], L88500 = [1, 3, 4, 7, 9, 19, 20], L88504 = [1, 3, 4, 7, 10, 10, 12], L88512 = [1, 3, 4, 7, 10, 11, 12], L88513 = [1, 3, 4, 7, 10, 11, 13], L88518 = [1, 3, 4, 7, 10, 12, 15], L88523 = [1, 3, 4, 7, 10, 12, 20] L88531 = [1, 3, 4, 7, 10, 15, 16], L88551 = [1, 3, 4, 7, 11, 12, 20], L88552 = [1, 3, 4, 7, 11, 13, 16], L88554 = [1, 3, 4, 7, 11, 13, 20], L88567 = [1, 3, 4, 7, 12, 13, 19], L88574 = [1, 3, 4, 7, 12, 15, 20], L88581 = [1, 3, 4, 7, 12, 17, 19] L88587 = [1, 3, 4, 7, 12, 20, 20], L88617 = [1, 3, 4, 7, 15, 16, 20], L88744 = [1, 3, 4, 8, 9, 11, 13], L88748 = [1, 3, 4, 8, 9, 11, 17], L88749 = [1, 3, 4, 8, 9, 11, 19], L88753 = [1, 3, 4, 8, 9, 12, 16], L88774 = [1, 3, 4, 8, 9, 17, 19], L88887 = [1, 3, 4, 8, 12, 15, 16], L88994 = [1, 3, 4, 9, 10, 10, 12], L89003 = [1, 3, 4, 9, 10, 11, 13], L89010 = [1, 3, 4, 9, 10, 12, 13], L89013 = [1, 3, 4, 9, 10, 12, 20], L89039 = [1, 3, 4, 9, 11, 13, 16], L89041 = [1, 3, 4, 9, 11, 13, 20] L89061 = [1, 3, 4, 9, 12, 13, 20], L89066 = [1, 3, 4, 9, 12, 20, 20], L89137 = [1, 3, 4, 10, 10, 12, 15], L89224 = [1, 3, 4, 10, 12, 15, 20], L89348 = [1, 3, 4, 11, 13, 15, 19], L89474 = [1, 3, 4, 12, 15, 20, 20], L89507 = [1, 3, 4, 13, 15, 16, 17], L89708 = [1, 3, 5, 5, 5, 7, 11], L89732 = [1, 3, 5, 5, 5, 9, 13], L89810 = [1, 3, 5, 5, 7, 9, 11], L89811 = [1, 3, 5, 5, 7, 9, 13], L89815 = [1, 3, 5, 5, 7, 9, 19], L89818 = [1, 3, 5, 5, 7, 10, 11], L89828 = [1, 3, 5, 5, 7, 11, 13], L89829 = [1, 3, 5, 5, 7, 11, 15], L89831 = [1, 3, 5, 5, 7, 11, 19], L89832 = [1, 3, 5, 5, 7, 11, 20], L89845 = [1, 3, 5, 5, 7, 15, 15], L89847 = [1, 3, 5, 5, 7, 15, 17], L89946 = [1, 3, 5, 5, 9, 10, 13], L89953 = [1, 3, 5, 5, 9, 11, 13], L89955 = [1, 3, 5, 5, 9, 11, 15], L89959 = [1, 3, 5, 5, 9, 13, 15], L89961 = [1, 3, 5, 5, 9, 13, 20], L89968 = [1, 3, 5, 5, 9, 15, 15], L89995 = [1, 3, 5, 5, 10, 11, 15], L90007 = [1, 3, 5, 5, 10, 13, 15], L90047 = [1, 3, 5, 5, 11, 13, 19], L90057 = [1, 3, 5, 5, 11, 15, 20], L90101 = [1, 3, 5, 5, 13, 15, 20], L90141 = [1, 3, 5, 5, 15, 15, 15] L90202 = [1, 3, 5, 7, 8, 9, 17], L90216 = [1, 3, 5, 7, 8, 11, 13], L90218 = [1, 3, 5, 7, 8, 11, 16], L90220 = [1, 3, 5, 7, 8, 11, 19], L90235 = [1, 3, 5, 7, 8, 15, 16], L90241 = [1, 3, 5, 7, 8, 16, 17], L90254 = [1, 3, 5, 7, 9, 10, 11], L90255 = [1, 3, 5, 7, 9, 10, 13], L90258 = [1, 3, 5, 7, 9, 10, 17], L90259 = [1, 3, 5, 7, 9, 10, 19], L90261 = [1, 3, 5, 7, 9, 11, 13], L90262 = [1, 3, 5, 7, 9, 11, 15], L90264 = [1, 3, 5, 7, 9, 11, 17], L90265 = [1, 3, 5, 7, 9, 11, 19], L90266 = [1, 3, 5, 7, 9, 11, 20], L90267 = [1, 3, 5, 7, 9, 13, 15], L90269 = [1, 3, 5, 7, 9, 13, 17], L90270 = [1, 3, 5, 7, 9, 13, 19], L90271 = [1, 3, 5, 7, 9, 13, 20], L90273 = [1, 3, 5, 7, 9, 15, 17], L90274 = [1, 3, 5, 7, 9, 15, 19], L90277 = [1, 3, 5, 7, 9, 16, 17], L90279 = [1, 3, 5, 7, 9, 17, 20], L90280 = [1, 3, 5, 7, 9, 19, 20], L90283 = [1, 3, 5, 7, 10, 10, 11], L90286 = [1, 3, 5, 7, 10, 10, 15], L90288 = [1, 3, 5, 7, 10, 10, 17], L90293 = [1, 3, 5, 7, 10, 11, 13] L90294 = [1, 3, 5, 7, 10, 11, 15], L90296 = [1, 3, 5, 7, 10, 11, 19], L90297 = [1, 3, 5, 7, 10, 11, 20], L90310 = [1, 3, 5, 7, 10, 15, 15], L90315 = [1, 3, 5, 7, 10, 15, 20], L90323 = [1, 3, 5, 7, 10, 17, 20], L90333 = [1, 3, 5, 7, 11, 13, 16] L90334 = [1, 3, 5, 7, 11, 13, 19], L90335 = [1, 3, 5, 7, 11, 13, 20], L90337 = [1, 3, 5, 7, 11, 15, 20], L90339 = [1, 3, 5, 7, 11, 16, 19], L90341 = [1, 3, 5, 7, 11, 19, 20], L90342 = [1, 3, 5, 7, 11, 20, 20], L90366 = [1, 3, 5, 7, 13, 15, 19] L90386 = [1, 3, 5, 7, 15, 15, 20], L90393 = [1, 3, 5, 7, 15, 17, 19], L90399 = [1, 3, 5, 7, 15, 20, 20], L90417 = [1, 3, 5, 7, 17, 20, 20], L90514 = [1, 3, 5, 8, 9, 11, 13], L90517 = [1, 3, 5, 8, 9, 11, 16], L90521 = [1, 3, 5, 8, 9, 13, 16], L90529 = [1, 3, 5, 8, 9, 15, 16], L90551 = [1, 3, 5, 8, 10, 11, 12], L90555 = [1, 3, 5, 8, 10, 11, 16], L90567 = [1, 3, 5, 8, 10, 13, 16], L90603 = [1, 3, 5, 8, 11, 12, 20], L90605 = [1, 3, 5, 8, 11, 13, 19], L90618 = [1, 3, 5, 8, 11, 16, 20] L90663 = [1, 3, 5, 8, 13, 16, 20], L90699 = [1, 3, 5, 8, 15, 15, 16], L90743 = [1, 3, 5, 9, 10, 10, 11], L90744 = [1, 3, 5, 9, 10, 10, 13], L90746 = [1, 3, 5, 9, 10, 10, 15], L90751 = [1, 3, 5, 9, 10, 11, 13], L90756 = [1, 3, 5, 9, 10, 11, 20] L90757 = [1, 3, 5, 9, 10, 13, 15], L90759 = [1, 3, 5, 9, 10, 13, 20], L90767 = [1, 3, 5, 9, 10, 15, 20], L90776 = [1, 3, 5, 9, 11, 13, 16], L90777 = [1, 3, 5, 9, 11, 13, 19], L90778 = [1, 3, 5, 9, 11, 13, 20], L90789 = [1, 3, 5, 9, 11, 20, 20] L90790 = [1, 3, 5, 9, 13, 15, 20], L90793 = [1, 3, 5, 9, 13, 20, 20], L90811 = [1, 3, 5, 9, 15, 20, 20], L90825 = [1, 3, 5, 10, 10, 10, 11], L90827 = [1, 3, 5, 10, 10, 10, 13], L90841 = [1, 3, 5, 10, 10, 11, 20], L90854 = [1, 3, 5, 10, 10, 13, 20], L90862 = [1, 3, 5, 10, 10, 15, 15], L90888 = [1, 3, 5, 10, 11, 13, 19], L90903 = [1, 3, 5, 10, 11, 20, 20], L90950 = [1, 3, 5, 10, 13, 20, 20], L90982 = [1, 3, 5, 10, 15, 15, 20], L91042 = [1, 3, 5, 11, 13, 16, 19], L91044 = [1, 3, 5, 11, 13, 19, 20], L91075 = [1, 3, 5, 11, 20, 20, 20], L91204 = [1, 3, 5, 13, 20, 20, 20], L91292 = [1, 3, 5, 15, 15, 20, 20], L91373 = [1, 3, 7, 8, 8, 9, 13], L91376 = [1, 3, 7, 8, 8, 9, 19], L91389 = [1, 3, 7, 8, 8, 11, 13], L91409 = [1, 3, 7, 8, 8, 16, 16], L91424 = [1, 3, 7, 8, 9, 10, 13], L91427 = [1, 3, 7, 8, 9, 10, 19], L91430 = [1, 3, 7, 8, 9, 11, 16], L91434 = [1, 3, 7, 8, 9, 13, 16], L91437 = [1, 3, 7, 8, 9, 13, 20],
APPENDIX
167
L91440 = [1, 3, 7, 8, 9, 16, 19], L91444 = [1, 3, 7, 8, 9, 19, 20], L91451 = [1, 3, 7, 8, 10, 10, 16], L91457 = [1, 3, 7, 8, 10, 11, 13], L91458 = [1, 3, 7, 8, 10, 11, 16], L91472 = [1, 3, 7, 8, 10, 15, 16], L91481 = [1, 3, 7, 8, 10, 16, 20] L91494 = [1, 3, 7, 8, 11, 13, 20], L91496 = [1, 3, 7, 8, 11, 16, 20], L91521 = [1, 3, 7, 8, 13, 16, 19], L91541 = [1, 3, 7, 8, 15, 16, 20], L91555 = [1, 3, 7, 8, 16, 17, 19], L91561 = [1, 3, 7, 8, 16, 20, 20], L91575 = [1, 3, 7, 9, 10, 10, 11] L91576 = [1, 3, 7, 9, 10, 10, 13], L91579 = [1, 3, 7, 9, 10, 10, 19], L91585 = [1, 3, 7, 9, 10, 11, 20], L91586 = [1, 3, 7, 9, 10, 13, 16], L91588 = [1, 3, 7, 9, 10, 13, 20], L91593 = [1, 3, 7, 9, 10, 19, 20], L91601 = [1, 3, 7, 9, 11, 20, 20] L91602 = [1, 3, 7, 9, 13, 16, 16], L91604 = [1, 3, 7, 9, 13, 16, 20], L91606 = [1, 3, 7, 9, 13, 20, 20], L91613 = [1, 3, 7, 9, 19, 20, 20], L91615 = [1, 3, 7, 10, 10, 10, 10], L91616 = [1, 3, 7, 10, 10, 10, 11], L91619 = [1, 3, 7, 10, 10, 10, 15], L91624 = [1, 3, 7, 10, 10, 10, 20], L91627 = [1, 3, 7, 10, 10, 11, 20], L91637 = [1, 3, 7, 10, 10, 13, 19], L91644 = [1, 3, 7, 10, 10, 15, 20], L91651 = [1, 3, 7, 10, 10, 17, 19], L91657 = [1, 3, 7, 10, 10, 20, 20], L91663 = [1, 3, 7, 10, 11, 20, 20], L91695 = [1, 3, 7, 10, 13, 19, 20], L91714 = [1, 3, 7, 10, 15, 20, 20], L91731 = [1, 3, 7, 10, 17, 19, 20], L91739 = [1, 3, 7, 10, 20, 20, 20], L91749 = [1, 3, 7, 11, 20, 20, 20], L91816 = [1, 3, 7, 13, 17, 19, 20], L91823 = [1, 3, 7, 13, 19, 20, 20], L91864 = [1, 3, 7, 15, 20, 20, 20], L91895 = [1, 3, 7, 17, 19, 20, 20], L91905 = [1, 3, 7, 20, 20, 20, 20], L91998 = [1, 3, 8, 8, 9, 16, 16], L92156 = [1, 3, 8, 8, 15, 16, 16], L92197 = [1, 3, 8, 9, 10, 10, 16], L92203 = [1, 3, 8, 9, 10, 13, 16], L92210 = [1, 3, 8, 9, 10, 16, 20], L92218 = [1, 3, 8, 9, 13, 16, 20], L92229 = [1, 3, 8, 9, 16, 20, 20], L92269 = [1, 3, 8, 10, 10, 15, 16], L92384 = [1, 3, 8, 10, 15, 16, 20], L92678 = [1, 3, 8, 15, 16, 20, 20], L92730 = [1, 3, 9, 10, 10, 10, 10], L92732 = [1, 3, 9, 10, 10, 10, 13], L92735 = [1, 3, 9, 10, 10, 10, 20], L92738 = [1, 3, 9, 10, 10, 13, 20], L92743 = [1, 3, 9, 10, 10, 20, 20], L92747 = [1, 3, 9, 10, 13, 20, 20], L92754 = [1, 3, 9, 10, 20, 20, 20], L92759 = [1, 3, 9, 13, 20, 20, 20], L92768 = [1, 3, 9, 20, 20, 20, 20], L92773 = [1, 3, 10, 10, 10, 10, 15], L92805 = [1, 3, 10, 10, 10, 15, 20], L92916 = [1, 3, 10, 10, 15, 20, 20], L93203 = [1, 3, 10, 15, 20, 20, 20], L93827 = [1, 3, 15, 20, 20, 20, 20], L94142 = [1, 4, 4, 4, 6, 9, 11], L94147 = [1, 4, 4, 4, 6, 9, 19], L94371 = [1, 4, 4, 4, 12, 12, 20], L94664 = [1, 4, 4, 5, 7, 12, 12], L94844 = [1, 4, 4, 5, 12, 12, 20], L94967 = [1, 4, 4, 6, 6, 9, 11], L94972 = [1, 4, 4, 6, 6, 9, 19], L95059 = [1, 4, 4, 6, 8, 9, 11], L95064 = [1, 4, 4, 6, 8, 9, 19], L95106 = [1, 4, 4, 6, 9, 10, 11], L95111 = [1, 4, 4, 6, 9, 10, 19], L95113 = [1, 4, 4, 6, 9, 11, 12], L95115 = [1, 4, 4, 6, 9, 11, 16], L95117 = [1, 4, 4, 6, 9, 11, 20], L95122 = [1, 4, 4, 6, 9, 12, 19], L95131 = [1, 4, 4, 6, 9, 16, 19], L95133 = [1, 4, 4, 6, 9, 19, 20], L95189 = [1, 4, 4, 6, 12, 12, 20], L95309 = [1, 4, 4, 7, 9, 15, 17], L95346 = [1, 4, 4, 7, 12, 12, 20], L95531 = [1, 4, 4, 8, 12, 12, 20], L95648 = [1, 4, 4, 9, 12, 12, 20], L95722 = [1, 4, 4, 10, 12, 12, 20], L95809 = [1, 4, 4, 11, 12, 12, 20], L95823 = [1, 4, 4, 12, 12, 12, 20], L95829 = [1, 4, 4, 12, 12, 14, 20], L95833 = [1, 4, 4, 12, 12, 15, 20], L95837 = [1, 4, 4, 12, 12, 16, 20], L95840 = [1, 4, 4, 12, 12, 18, 20], L95841 = [1, 4, 4, 12, 12, 19, 20], L95842 = [1, 4, 4, 12, 12, 20, 20], L96235 = [1, 4, 5, 5, 7, 12, 15], L96686 = [1, 4, 5, 6, 9, 11, 15], L96701 = [1, 4, 5, 6, 9, 15, 19], L96867 = [1, 4, 5, 7, 8, 12, 16], L96886 = [1, 4, 5, 7, 9, 10, 12], L96893 = [1, 4, 5, 7, 9, 12, 20], L96896 = [1, 4, 5, 7, 9, 15, 17], L96904 = [1, 4, 5, 7, 10, 10, 12], L96913 = [1, 4, 5, 7, 10, 12, 20], L96937 = [1, 4, 5, 7, 12, 20, 20], L97238 = [1, 4, 5, 9, 11, 15, 19] L97701 = [1, 4, 6, 6, 6, 9, 11], L97706 = [1, 4, 6, 6, 6, 9, 19], L97792 = [1, 4, 6, 6, 8, 9, 11], L97797 = [1, 4, 6, 6, 8, 9, 19], L97839 = [1, 4, 6, 6, 9, 10, 11], L97844 = [1, 4, 6, 6, 9, 10, 19], L97846 = [1, 4, 6, 6, 9, 11, 12], L97847 = [1, 4, 6, 6, 9, 11, 14], L97848 = [1, 4, 6, 6, 9, 11, 16], L97850 = [1, 4, 6, 6, 9, 11, 20], L97855 = [1, 4, 6, 6, 9, 12, 19], L97860 = [1, 4, 6, 6, 9, 14, 19], L97866 = [1, 4, 6, 6, 9, 16, 19], L97868 = [1, 4, 6, 6, 9, 19, 20], L98099 = [1, 4, 6, 8, 8, 9, 11], L98104 = [1, 4, 6, 8, 8, 9, 19], L98146 = [1, 4, 6, 8, 9, 10, 11], L98151 = [1, 4, 6, 8, 9, 10, 19], L98153 = [1, 4, 6, 8, 9, 11, 12], L98155 = [1, 4, 6, 8, 9, 11, 16], L98157 = [1, 4, 6, 8, 9, 11, 20], L98162 = [1, 4, 6, 8, 9, 12, 19], L98171 = [1, 4, 6, 8, 9, 16, 19], L98173 = [1, 4, 6, 8, 9, 19, 20], L98295 = [1, 4, 6, 9, 10, 10, 11], L98300 = [1, 4, 6, 9, 10, 10, 19], L98302 = [1, 4, 6, 9, 10, 11, 12], L98304 = [1, 4, 6, 9, 10, 11, 16] L98306 = [1, 4, 6, 9, 10, 11, 20], L98311 = [1, 4, 6, 9, 10, 12, 19], L98320 = [1, 4, 6, 9, 10, 16, 19], L98322 = [1, 4, 6, 9, 10, 19, 20], L98324 = [1, 4, 6, 9, 11, 12, 12], L98326 = [1, 4, 6, 9, 11, 12, 16], L98328 = [1, 4, 6, 9, 11, 12, 20] L98332 = [1, 4, 6, 9, 11, 16, 16], L98334 = [1, 4, 6, 9, 11, 16, 20], L98336 = [1, 4, 6, 9, 11, 20, 20], L98341 = [1, 4, 6, 9, 12, 12, 19], L98350 = [1, 4, 6, 9, 12, 16, 19], L98352 = [1, 4, 6, 9, 12, 19, 20], L98367 = [1, 4, 6, 9, 16, 16, 19] L98369 = [1, 4, 6, 9, 16, 19, 20], L98371 = [1, 4, 6, 9, 19, 20, 20], L98722 = [1, 4, 7, 8, 9, 15, 17], L98762 = [1, 4, 7, 8, 12, 16, 20], L98808 = [1, 4, 7, 9, 10, 15, 17], L98816 = [1, 4, 7, 9, 12, 15, 17], L98822 = [1, 4, 7, 9, 15, 15, 17] L98825 = [1, 4, 7, 9, 15, 16, 17], L98827 = [1, 4, 7, 9, 15, 17, 20], L99231 = [1, 4, 8, 9, 12, 16, 20], L100625 =
168
EMILIO A. LAURET
[1, 5, 5, 5, 7, 15, 15], L101213 = [1, 5, 5, 7, 8, 15, 16], L101225 = [1, 5, 5, 7, 9, 10, 15], L101229 = [1, 5, 5, 7, 9, 15, 17], L101230 = [1, 5, 5, 7, 9, 15, 20], L101234 = [1, 5, 5, 7, 10, 10, 15], L101241 = [1, 5, 5, 7, 10, 15, 20], L101257 = [1, 5, 5, 7, 15, 20, 20], L102087 = [1, 5, 6, 6, 9, 11, 15], L102104 = [1, 5, 6, 6, 9, 15, 19], L102389 = [1, 5, 6, 8, 9, 11, 15], L102404 = [1, 5, 6, 8, 9, 15, 19], L102557 = [1, 5, 6, 9, 10, 11, 15], L102572 = [1, 5, 6, 9, 10, 15, 19], L102581 = [1, 5, 6, 9, 11, 12, 15], L102589 = [1, 5, 6, 9, 11, 15, 16], L102591 = [1, 5, 6, 9, 11, 15, 20], L102608 = [1, 5, 6, 9, 12, 15, 19], L102625 = [1, 5, 6, 9, 15, 16, 19], L102627 = [1, 5, 6, 9, 15, 19, 20], L103011 = [1, 5, 7, 8, 8, 16, 16], L103021 = [1, 5, 7, 8, 9, 10, 16], L103026 = [1, 5, 7, 8, 9, 15, 17], L103029 = [1, 5, 7, 8, 9, 16, 20], L103034 = [1, 5, 7, 8, 10, 10, 16], L103045 = [1, 5, 7, 8, 10, 16, 20], L103067 = [1, 5, 7, 8, 16, 20, 20], L103073 = [1, 5, 7, 9, 10, 10, 10], L103076 = [1, 5, 7, 9, 10, 10, 20], L103078 = [1, 5, 7, 9, 10, 15, 17], L103081 = [1, 5, 7, 9, 10, 20, 20], L103083 = [1, 5, 7, 9, 15, 15, 17], L103085 = [1, 5, 7, 9, 15, 17, 20], L103088 = [1, 5, 7, 9, 20, 20, 20], L103089 = [1, 5, 7, 10, 10, 10, 10], L103093 = [1, 5, 7, 10, 10, 10, 20], L103103 = [1, 5, 7, 10, 10, 20, 20], L103123 = [1, 5, 7, 10, 20, 20, 20], L103158 = [1, 5, 7, 20, 20, 20, 20], L103401 = [1, 5, 8, 9, 11, 15, 19], L103835 = [1, 5, 9, 11, 12, 15, 19], L103843 = [1, 5, 9, 11, 15, 16, 19], L103845 = [1, 5, 9, 11, 15, 19, 20], L104690 = [1, 6, 6, 6, 6, 9, 11], L104695 = [1, 6, 6, 6, 6, 9, 19], L104774 = [1, 6, 6, 6, 8, 9, 11], L104779 = [1, 6, 6, 6, 8, 9, 19], L104821 = [1, 6, 6, 6, 9, 10, 11], L104826 = [1, 6, 6, 6, 9, 10, 19], L104828 = [1, 6, 6, 6, 9, 11, 12], L104829 = [1, 6, 6, 6, 9, 11, 14], L104830 = [1, 6, 6, 6, 9, 11, 16], L104832 = [1, 6, 6, 6, 9, 11, 20], L104837 = [1, 6, 6, 6, 9, 12, 19], L104842 = [1, 6, 6, 6, 9, 14, 19], L104848 = [1, 6, 6, 6, 9, 16, 19], L104850 = [1, 6, 6, 6, 9, 19, 20], L105055 = [1, 6, 6, 8, 8, 9, 11], L105060 = [1, 6, 6, 8, 8, 9, 19], L105102 = [1, 6, 6, 8, 9, 10, 11], L105107 = [1, 6, 6, 8, 9, 10, 19], L105109 = [1, 6, 6, 8, 9, 11, 12], L105110 = [1, 6, 6, 8, 9, 11, 14], L105111 = [1, 6, 6, 8, 9, 11, 16], L105113 = [1, 6, 6, 8, 9, 11, 20], L105118 = [1, 6, 6, 8, 9, 12, 19], L105123 = [1, 6, 6, 8, 9, 14, 19], L105129 = [1, 6, 6, 8, 9, 16, 19], L105131 = [1, 6, 6, 8, 9, 19, 20], L105254 = [1, 6, 6, 9, 10, 10, 11], L105259 = [1, 6, 6, 9, 10, 10, 19], L105261 = [1, 6, 6, 9, 10, 11, 12], L105262 = [1, 6, 6, 9, 10, 11, 14], L105263 = [1, 6, 6, 9, 10, 11, 16], L105265 = [1, 6, 6, 9, 10, 11, 20], L105270 = [1, 6, 6, 9, 10, 12, 19], L105275 = [1, 6, 6, 9, 10, 14, 19], L105281 = [1, 6, 6, 9, 10, 16, 19], L105283 = [1, 6, 6, 9, 10, 19, 20], L105285 = [1, 6, 6, 9, 11, 12, 12], L105286 = [1, 6, 6, 9, 11, 12, 14], L105287 = [1, 6, 6, 9, 11, 12, 16], L105289 = [1, 6, 6, 9, 11, 12, 20], L105291 = [1, 6, 6, 9, 11, 14, 16], L105293 = [1, 6, 6, 9, 11, 14, 20], L105294 = [1, 6, 6, 9, 11, 16, 16], L105296 = [1, 6, 6, 9, 11, 16, 20], L105298 = [1, 6, 6, 9, 11, 20, 20], L105303 = [1, 6, 6, 9, 12, 12, 19], L105308 = [1, 6, 6, 9, 12, 14, 19], L105314 = [1, 6, 6, 9, 12, 16, 19], L105316 = [1, 6, 6, 9, 12, 19, 20], L105325 = [1, 6, 6, 9, 14, 16, 19], L105327 = [1, 6, 6, 9, 14, 19, 20], L105336 = [1, 6, 6, 9, 16, 16, 19], L105338 = [1, 6, 6, 9, 16, 19, 20], L105340 = [1, 6, 6, 9, 19, 20, 20], L105815 = [1, 6, 8, 8, 8, 9, 11], L105820 = [1, 6, 8, 8, 8, 9, 19], L105862 = [1, 6, 8, 8, 9, 10, 11], L105867 = [1, 6, 8, 8, 9, 10, 19], L105869 = [1, 6, 8, 8, 9, 11, 12], L105871 = [1, 6, 8, 8, 9, 11, 16], L105873 = [1, 6, 8, 8, 9, 11, 20], L105878 = [1, 6, 8, 8, 9, 12, 19], L105887 = [1, 6, 8, 8, 9, 16, 19], L105889 = [1, 6, 8, 8, 9, 19, 20], L106011 = [1, 6, 8, 9, 10, 10, 11], L106016 = [1, 6, 8, 9, 10, 10, 19], L106018 = [1, 6, 8, 9, 10, 11, 12], L106020 = [1, 6, 8, 9, 10, 11, 16], L106022 = [1, 6, 8, 9, 10, 11, 20], L106027 = [1, 6, 8, 9, 10, 12, 19], L106036 = [1, 6, 8, 9, 10, 16, 19], L106038 = [1, 6, 8, 9, 10, 19, 20], L106040 = [1, 6, 8, 9, 11, 12, 12], L106042 = [1, 6, 8, 9, 11, 12, 16], L106044 = [1, 6, 8, 9, 11, 12, 20], L106048 = [1, 6, 8, 9, 11, 16, 16], L106050 = [1, 6, 8, 9, 11, 16, 20], L106052 = [1, 6, 8, 9, 11, 20, 20], L106057 = [1, 6, 8, 9, 12, 12, 19], L106066 = [1, 6, 8, 9, 12, 16, 19], L106068 = [1, 6, 8, 9, 12, 19, 20], L106083 = [1, 6, 8, 9, 16, 16, 19], L106085 = [1, 6, 8, 9, 16, 19, 20], L106087 = [1, 6, 8, 9, 19, 20, 20], L106386 = [1, 6, 9, 10, 10, 10, 11], L106391 = [1, 6, 9, 10, 10, 10, 19], L106393 = [1, 6, 9, 10, 10, 11, 12], L106395 = [1, 6, 9, 10, 10, 11, 16], L106397 = [1, 6, 9, 10, 10, 11, 20], L106402 = [1, 6, 9, 10, 10, 12, 19], L106411 = [1, 6, 9, 10, 10, 16, 19], L106413 = [1, 6, 9, 10, 10, 19, 20], L106415 = [1, 6, 9, 10, 11, 12, 12], L106417 = [1, 6, 9, 10, 11, 12, 16], L106419 = [1, 6, 9, 10, 11, 12, 20], L106423 = [1, 6, 9, 10, 11, 16, 16], L106425 = [1, 6, 9, 10, 11, 16, 20], L106427 = [1, 6, 9, 10, 11, 20, 20], L106432 = [1, 6, 9, 10, 12, 12, 19], L106441 = [1, 6, 9, 10, 12, 16, 19], L106443 = [1, 6, 9, 10, 12, 19, 20], L106458 = [1, 6, 9, 10, 16, 16, 19], L106460 = [1, 6, 9, 10, 16, 19, 20], L106462 = [1, 6, 9, 10, 19, 20, 20], L106464 = [1, 6, 9, 11, 12, 12, 12], L106466 = [1, 6, 9, 11, 12, 12, 16], L106468 = [1, 6, 9, 11, 12, 12, 20], L106472 = [1, 6, 9, 11, 12, 16, 16], L106474 = [1, 6, 9, 11, 12, 16, 20], L106476 = [1, 6, 9, 11, 12, 20, 20], L106482 = [1, 6, 9, 11, 16, 16, 16], L106484 = [1, 6, 9, 11, 16, 16, 20], L106486 =
APPENDIX
169
Table 5. (continued) n = 7 q I indexes of I-isospectral families 41 {0} {1958, 1959}, {2061, 2141}, {2070, 2139}, {9870, 9876}, {10243, 10247}, {11329, 11333}, {11508, 11517}, {42611, 42613}, {42620, 42622, 42646}, {44330, 44337}
[1, 6, 9, 11, 16, 20, 20], L106488 = [1, 6, 9, 11, 20, 20, 20], L106493 = [1, 6, 9, 12, 12, 12, 19], L106502 = [1, 6, 9, 12, 12, 16, 19], L106504 = [1, 6, 9, 12, 12, 19, 20], L106519 = [1, 6, 9, 12, 16, 16, 19], L106521 = [1, 6, 9, 12, 16, 19, 20], L106523 = [1, 6, 9, 12, 19, 20, 20], L106546 = [1, 6, 9, 16, 16, 16, 19], L106548 = [1, 6, 9, 16, 16, 19, 20], L106550 = [1, 6, 9, 16, 19, 20, 20], L106552 = [1, 6, 9, 19, 20, 20, 20], L107236 = [1, 7, 8, 8, 9, 15, 17], L107277 = [1, 7, 8, 8, 16, 16, 20], L107294 = [1, 7, 8, 9, 10, 15, 17], L107302 = [1, 7, 8, 9, 15, 15, 17 L107304 = [1, 7, 8, 9, 15, 16, 17], L107306 = [1, 7, 8, 9, 15, 17, 20], L107397 = [1, 7, 9, 10, 10, 15, 17], L107402 = [1, 7, 9, 10, 15, 15, 17], L107404 = [1, 7, 9, 10, 15, 17, 20], L107409 = [1, 7, 9, 15, 15, 15, 17], L107411 = [1, 7, 9, 15, 15, 17, 20], L107413 = [1, 7, 9, 15, 17, 20, 20], L107779 = [1, 8, 8, 9, 16, 16, 20], L110883 = [2, 2, 5, 5, 6, 6, 14], L110886 = [2, 2, 5, 5, 6, 6, 18], L111040 = [2, 2, 5, 6, 6, 10, 14], L111043 = [2, 2, 5, 6, 6, 10, 18], L111046 = [2, 2, 5, 6, 6, 14, 15], L111049 = [2, 2, 5, 6, 6, 14, 20], L111051 = [2, 2, 5, 6, 6, 15, 18], L111056 = [2, 2, 5, 6, 6, 18, 20], L111107 = [2, 2, 5, 6, 10, 14, 18], L111611 = [2, 4, 4, 5, 12, 12, 20], L111693 = [2, 4, 5, 5, 6, 8, 14], L111696 = [2, 4, 5, 5, 6, 8, 18], L111823 = [2, 4, 5, 6, 8, 10, 14], L111826 = [2, 4, 5, 6, 8, 10, 18], L111833 = [2, 4, 5, 6, 8, 14, 15], L111836 = [2, 4, 5, 6, 8, 14, 20], L111838 = [2, 4, 5, 6, 8, 15, 18], L111843 = [2, 4, 5, 6, 8, 18, 20], L111858 = [2, 4, 5, 6, 10, 14, 18], L111956 = [2, 4, 5, 8, 12, 15, 18], L112252 = [2, 5, 5, 6, 10, 14, 18 L112482 = [2, 5, 6, 8, 10, 14, 18], L112513 = [2, 5, 6, 10, 10, 14, 18], L112520 = [2, 5, 6, 10, 14, 15, 18], L112522 = [2, 5, 6, 10, 14, 18, 20], L112595 = [2, 5, 8, 8, 12, 15, 18], L112664 = [2, 5, 8, 12, 12, 15, 18], L112672 = [2, 5, 8, 12, 15, 16, 18], L112674 = [2, 5, 8, 12, 15, 18, 20], L112945 = [4, 4, 4, 5, 12, 12, 20], L113023 = [4, 4, 5, 5, 12, 12, 20], L113075 = [4, 4, 5, 8, 12, 12, 20], L113103 = [4, 4, 5, 10, 12, 12, 20], L113116 = [4, 4, 5, 12, 12, 15, 20], L113117 = [4, 4, 5, 12, 12, 20, 20], L113196 = [4, 5, 5, 5, 15, 15, 15], L113464 = [5, 5, 5, 8, 15, 15, 15]. q = 41 : L1958 = [0, 0, 1, 2, 3, 9, 13], L1959 = [0, 0, 1, 2, 3, 9, 14], L2061 = [0, 0, 1, 2, 4, 9, 18], L2070 = [0, 0, 1, 2, 4, 10, 18], L2139 = [0, 0, 1, 2, 5, 8, 18], L2141 = [0, 0, 1, 2, 5, 9, 10], L9870 = [0, 1, 2, 3, 6, 13, 18], L9876 = [0, 1, 2, 3, 6, 14, 18], L10243 = [0, 1, 2, 4, 5, 9, 16], L10247 = [0, 1, 2, 4, 5, 9, 20], L11329 = [0, 1, 3, 4, 5, 12, 15], L11333 = [0, 1, 3, 4, 5, 14, 15], L11508 = [0, 1, 4, 5, 6, 13, 19], L11517 = [0, 1, 4, 5, 11, 16, 17], L42611 = [1, 2, 4, 5, 8, 9, 16], L42613 = [1, 2, 4, 5, 8, 9, 18], L42620 = [1, 2, 4, 5, 8, 10, 18], L42622 = [1, 2, 4, 5, 8, 10, 20], L42646 = [1, 2, 4, 5, 8, 16, 20], L44330 = [1, 3, 4, 7, 10, 11, 16], L44337 = [1, 3, 4, 7, 10, 13, 18]. q = 42 : L844 = [0, 0, 0, 1, 3, 11, 15], L874 = [0, 0, 0, 1, 3, 15, 17], L922 = [0, 0, 0, 1, 4, 5, 16], L925 = [0, 0, 0, 1, 4, 5, 20], L1081 = [0, 0, 0, 1, 5, 11, 13], L1084 = [0, 0, 0, 1, 5, 11, 17], L5483 = [0, 0, 1, 3, 5, 9, 13], L5487 = [0, 0, 1, 3, 5, 9, 17], L5489 = [0, 0, 1, 3, 5, 9, 19], L5493 = [0, 0, 1, 3, 5, 11, 13], L5495 = [0, 0, 1, 3, 5, 11, 15], L5499 = [0, 0, 1, 3, 5, 11, 19], L5512 = [0, 0, 1, 3, 5, 13, 15], L5513 = [0, 0, 1, 3, 5, 13, 17], L5515 = [0, 0, 1, 3, 5, 13, 19], L5528 = [0, 0, 1, 3, 5, 15, 19], L5727 = [0, 0, 1, 3, 7, 11, 15], L5757 = [0, 0, 1, 3, 7, 15, 17], L6005 = [0, 0, 1, 3, 11, 14, 15], L6015 = [0, 0, 1, 3, 11, 15, 21], L6096 = [0, 0, 1, 3, 14, 15, 17], L6132 = [0, 0, 1, 3, 15, 17, 21], L6345 = [0, 0, 1, 4, 5, 7, 16], L6348 = [0, 0, 1, 4, 5, 7, 20], L6389 = [0, 0, 1, 4, 5, 14, 16], L6392 = [0, 0, 1, 4, 5, 14, 20], L6398 = [0, 0, 1, 4, 5, 16, 21], L6404 = [0, 0, 1, 4, 5, 20, 21], L7070 = [0, 0, 1, 5, 7, 11, 13], L7073 = [0, 0, 1, 5, 7, 11, 17], L7183 = [0, 0, 1, 5, 11, 13, 14], L7185 = [0, 0, 1, 5, 11, 13, 21], L7188 = [0, 0, 1, 5, 11, 14, 17], L7194 = [0, 0, 1, 5, 11, 17, 21], L8879 = [0, 0, 1, 13, 14, 14, 15], L8898 = [0, 0, 1, 14, 14, 14, 14], L9688 = [0, 0, 2, 3, 6, 10, 20], L9935 = [0, 0, 2, 4, 6, 9, 10], L9957 = [0, 0, 2, 4, 7, 8, 10], L9959 = [0, 0, 2, 4, 7, 8, 16], L9977 = [0, 0, 2, 4, 7, 12, 18], L9988 = [0, 0, 2, 4, 8, 10, 21], L9990 = [0, 0, 2, 4, 8, 16, 21], L10027 = [0, 0, 2, 4, 12, 18, 21], L10085 = [0, 0, 2, 6, 7, 8, 12], L10123 = [0, 0, 2, 6, 8, 12, 21], L10605 = [0, 0, 3, 6, 7, 9, 12], L10608 = [0, 0, 3, 6, 7, 9, 18], L10623 = [0, 0, 3, 6, 9, 12, 14], L10626 = [0, 0, 3, 6, 9, 14, 18], L10707 = [0, 0, 3, 14, 14, 14, 14], L20476 = [0, 1, 1, 13, 13, 15, 15], L20483 = [0, 1, 1, 13, 14, 14, 15], L24294 = [0, 1, 2, 4, 11, 13, 19], L24916 = [0, 1, 2, 5, 10, 11, 13], L26658 = [0, 1, 2, 8, 10, 11, 16
170
EMILIO A. LAURET
Table 5. (continued) n = 7 q I indexes of I-isospectral families 42 {0} {844, 874}, {922, 925}, {1081, 1084}, {5483, 5487}, {5489, 5512}, {5493, 5515}, {5495, 5528}, {5499, 5513}, {5727, 5757}, {6005, 6096}, {6015, 6132}, {6345, 6348}, {6389, 6392}, {6398, 6404}, {7070, 7073}, {7183, 7188}, {7185, 7194}, {9688, 9935}, {9957, 9959}, {9977, 10085}, {9988, 9990}, {10027, 10123}, {10605, 10608}, {10623, 10626}, {24294, 24916}, {26658, 27527}, {30289, 30293}, {30295, 30318}, {30299, 30321}, {30301, 30334}, {30305, 30319}, {30442, 30479, 30585}, {30454, 30464}, {30460, 30481}, {30466, 30578}, {30487, 30586}, {30500, 30581}, {30505, 30594}, {30507, 30608}, {30511, 30579}, {30515, 30636}, {30527, 30589}, {31380, 31410}, {31658, 31749}, {31668, 31785}, {32728, 32975}, {32738, 33011}, {32765, 33101}, {34078, 34081}, {34122, 34125}, {34131, 34137}, {34290, 34293}, {34299, 34305}, {34317, 34326}, {36691, 36712}, {36825, 36828}, {36938, 36943}, {36940, 36949}, {37265, 37273}, {37267, 37279}, {37270, 37289}, {45862, 45868}, {46224, 46954}, {46904, 46917}, {46905, 46915}, {46918, 46923}, {46919, 46933}, {46932, 47455}, {46942, 46974}, {46943, 46972}, {46975, 46980}, {46976, 46990}, {46989, 47559}, {47005, 47007}, {47025, 47419}, {47036, 47041}, {47039, 47044}, {47095, 47459}, {47100, 47462}, {47118, 47123}, {47121, 47126}, {47221, 47565}, {47226, 47570}, {48803, 48806}, {48822, 48828}, {48825, 48831}, {48860, 48866}, {48863, 48869}, {76675, 76683}, {113166, 113170},
L27527 = [0, 1, 2, 10, 16, 17, 20], L27760 = [0, 1, 2, 12, 13, 15, 16], L27783 = [0, 1, 2, 12, 14, 14, 16], L27886 = [0, 1, 2, 13, 14, 14, 15], L30289 = [0, 1, 3, 5, 7, 9, 13], L30293 = [0, 1, 3, 5, 7, 9, 17], L30295 = [0, 1, 3, 5, 7, 9, 19], L30299 = [0, 1, 3, 5, 7, 11, 13], L30301 = [0, 1, 3, 5, 7, 11, 15], L30305 = [0, 1, 3, 5, 7, 11, 19], L30318 = [0, 1, 3, 5, 7, 13, 15], L30319 = [0, 1, 3, 5, 7, 13, 17], L30321 = [0, 1, 3, 5, 7, 13, 19], L30334 = [0, 1, 3, 5, 7, 15, 19], L30440 = [0, 1, 3, 5, 9, 11, 17], L30442 = [0, 1, 3, 5, 9, 11, 19], L30454 = [0, 1, 3, 5, 9, 13, 14], L30458 = [0, 1, 3, 5, 9, 13, 19], L30460 = [0, 1, 3, 5, 9, 13, 21], L30464 = [0, 1, 3, 5, 9, 14, 17], L30466 = [0, 1, 3, 5, 9, 14, 19], L30479 = [0, 1, 3, 5, 9, 17, 19], L30481 = [0, 1, 3, 5, 9, 17, 21], L30487 = [0, 1, 3, 5, 9, 19, 21], L30500 = [0, 1, 3, 5, 11, 13, 14], L30505 = [0, 1, 3, 5, 11, 13, 21], L30507 = [0, 1, 3, 5, 11, 14, 15], L30511 = [0, 1, 3, 5, 11, 14, 19], L30515 = [0, 1, 3, 5, 11, 15, 21], L30527 = [0, 1, 3, 5, 11, 19, 21], L30578 = [0, 1, 3, 5, 13, 14, 15] L30579 = [0, 1, 3, 5, 13, 14, 17], L30581 = [0, 1, 3, 5, 13, 14, 19], L30585 = [0, 1, 3, 5, 13, 15, 19], L30586 = [0, 1, 3, 5, 13, 15, 21], L30589 = [0, 1, 3, 5, 13, 17, 21], L30594 = [0, 1, 3, 5, 13, 19, 21], L30608 = [0, 1, 3, 5, 14, 15, 19] L30636 = [0, 1, 3, 5, 15, 19, 21], L31380 = [0, 1, 3, 7, 7, 11, 15], L31410 = [0, 1, 3, 7, 7, 15, 17], L31658 = [0, 1, 3, 7, 11, 14, 15], L31668 = [0, 1, 3, 7, 11, 15, 21], L31749 = [0, 1, 3, 7, 14, 15, 17], L31785 = [0, 1, 3, 7, 15, 17, 21] L32719 = [0, 1, 3, 11, 13, 15, 17], L32728 = [0, 1, 3, 11, 14, 14, 15], L32730 = [0, 1, 3, 11, 14, 14, 17], L32738 = [0, 1, 3, 11, 14, 15, 21], L32765 = [0, 1, 3, 11, 15, 21, 21], L32946 = [0, 1, 3, 13, 14, 14, 15], L32975 = [0, 1, 3, 14, 14, 15, 17], L33011 = [0, 1, 3, 14, 15, 17, 21], L33101 = [0, 1, 3, 15, 17, 21, 21], L34078 = [0, 1, 4, 5, 7, 7, 16], L34081 = [0, 1, 4, 5, 7, 7, 20], L34122 = [0, 1, 4, 5, 7, 14, 16], L34125 = [0, 1, 4, 5, 7, 14, 20], L34131 = [0, 1, 4, 5, 7, 16, 21], L34137 = [0, 1, 4, 5, 7, 20, 21], L34290 = [0, 1, 4, 5, 14, 14, 16], L34293 = [0, 1, 4, 5, 14, 14, 20], L34299 = [0, 1, 4, 5, 14, 16, 21], L34305 = [0, 1, 4, 5, 14, 20, 21], L34317 = [0, 1, 4, 5, 16, 21, 21], L34326 = [0, 1, 4, 5, 20, 21, 21], L35958 = [0, 1, 4, 10, 13, 15, 18], L35967 = [0, 1, 4, 10, 14, 14, 1 L36258 = [0, 1, 4, 13, 14, 14, 15], L36691 = [0, 1, 5, 6, 11, 12, 13], L36712 = [0, 1, 5, 6, 11, 17, 18], L36825 = [0, 1, 5, 7, 7, 11, 13], L36828 = [0, 1, 5, 7, 7, 11, 17], L36938 = [0, 1, 5, 7, 11, 13, 14], L36940 = [0, 1, 5, 7, 11, 13, 21], L36943 = [0, 1, 5, 7, 11, 14, 17], L36949 = [0, 1, 5, 7, 11, 17, 21], L37220 = [0, 1, 5, 9, 14, 14, 19], L37265 = [0, 1, 5, 11, 13, 14, 14], L37267 = [0, 1, 5, 11, 13, 14, 21], L37270 = [0, 1, 5, 11, 13, 21, 21], L37273 = [0, 1, 5, 11, 14, 14, 17], L37279 = [0, 1, 5, 11, 14, 17, 21], L37289 = [0, 1, 5, 11, 17, 21, 21], L38582 = [0, 1, 6, 8, 13, 15, 20], L38593 = [0, 1, 6, 8, 14, 14, 20], L39177 = [0, 1, 6, 13, 14, 14, 15], L39656 = [0, 1, 7, 7, 13, 15, 21
APPENDIX
171
Table 5. (continued) n = 7 q I indexes of I-isospectral families 42 {0} {113173, 113179}, {113176, 113180}, {113222, 113400}, {113378, 113380}, (cont.) {113486, 118006}, {114699, 117588}, {115069, 115107}, {116030, 118604}, {116047, 118607}, {118052, 118073}, {123174, 124043}, {125531, 128265}, {125543, 128397}, {132293, 132315}, {134287, 134400}, {136381, 136384}, {139191, 139221}, {139241, 139286}, {139462, 139466}, {139468, 139491}, {139472, 139494}, {139474, 139507}, {139478, 139492}, {139615, 139652, 139758}, {139627, 139637}, {139633, 139654}, {139639, 139751}, {139660, 139759}, {139673, 139754}, {139678, 139767}, {139680, 139781}, {139684, 139752}, {139688, 139809}, {139700, 139762}, {140189, 140201}, {140198, 140299, 140625}, {140213, 140336, 140641}, {140261, 140284}, {140267, 140301}, {140280, 140339}, {140286, 140618}, {140307, 140626}, {140351, 140642}, {140368, 140526}, {140394, 140621}, {140399, 140634}, {140409, 140657}, {140411, 140672}, {140415, 140619}, {140419, 140700}, {140431, 140629}, {140438, 140760}, {140462, 140648}, {142896, 143090},
L39665 = [0, 1, 7, 7, 14, 14, 21], L40461 = [0, 1, 7, 13, 14, 14, 15], L41363 = [0, 1, 8, 13, 14, 14, 15], L41960 = [0, 1, 9, 13, 14, 14, 15], L42625 = [0, 1, 12, 13, 14, 14, 15], L42771 = [0, 1, 13, 14, 14, 14, 15], L42774 = [0, 1, 13, 14, 14, 15, 15], L42775 = [0, 1, 13, 14, 14, 15, 18], L42776 = [0, 1, 13, 14, 14, 15, 21], L45862 = [0, 2, 3, 4, 8, 9, 16], L45868 = [0, 2, 3, 4, 8, 10, 15], L46224 = [0, 2, 3, 6, 10, 14, 20], L46750 = [0, 2, 3, 12, 14, 14, 16], L46904 = [0, 2, 4, 6, 7, 8, 16], L46905 = [0, 2, 4, 6, 7, 8, 18], L46915 = [0, 2, 4, 6, 7, 10, 12], L46917 = [0, 2, 4, 6, 7, 10, 16], L46918 = [0, 2, 4, 6, 7, 10, 18], L46919 = [0, 2, 4, 6, 7, 10, 20], L46923 = [0, 2, 4, 6, 7, 12, 16], L46932 = [0, 2, 4, 6, 7, 16, 18], L46933 = [0, 2, 4, 6, 7, 16, 20], L46942 = [0, 2, 4, 6, 8, 16, 21], L46943 = [0, 2, 4, 6, 8, 18, 21], L46954 = [0, 2, 4, 6, 9, 10, 14], L46972 = [0, 2, 4, 6, 10, 12, 21], L46974 = [0, 2, 4, 6, 10, 16, 21], L46975 = [0, 2, 4, 6, 10, 18, 21], L46976 = [0, 2, 4, 6, 10, 20, 21], L46980 = [0, 2, 4, 6, 12, 16, 21] L46989 = [0, 2, 4, 6, 16, 18, 21], L46990 = [0, 2, 4, 6, 16, 20, 21], L47005 = [0, 2, 4, 7, 7, 8, 10], L47007 = [0, 2, 4, 7, 7, 8, 16], L47025 = [0, 2, 4, 7, 7, 12, 18], L47036 = [0, 2, 4, 7, 8, 10, 14], L47039 = [0, 2, 4, 7, 8, 10, 21], L47041 = [0, 2, 4, 7, 8, 14, 16], L47044 = [0, 2, 4, 7, 8, 16, 21], L47095 = [0, 2, 4, 7, 12, 14, 18], L47100 = [0, 2, 4, 7, 12, 18, 21], L47118 = [0, 2, 4, 8, 10, 14, 21], L47121 = [0, 2, 4, 8, 10, 21, 21], L47123 = [0, 2, 4, 8, 14, 16, 21] L47126 = [0, 2, 4, 8, 16, 21, 21], L47221 = [0, 2, 4, 12, 14, 18, 21], L47226 = [0, 2, 4, 12, 18, 21, 21], L47419 = [0, 2, 6, 7, 7, 8, 12], L47455 = [0, 2, 6, 7, 8, 10, 12], L47459 = [0, 2, 6, 7, 8, 12, 14], L47462 = [0, 2, 6, 7, 8, 12, 21], L47559 = [0, 2, 6, 8, 10, 12, 21], L47565 = [0, 2, 6, 8, 12, 14, 21], L47570 = [0, 2, 6, 8, 12, 21, 21], L47854 = [0, 2, 7, 7, 12, 16, 21], L47862 = [0, 2, 7, 7, 14, 14, 21], L48010 = [0, 2, 7, 12, 14, 14, 16], L48225 = [0, 2, 9, 12, 14, 14, 16], L48345 = [0, 2, 12, 14, 14, 15, 16], L48348 = [0, 2, 12, 14, 14, 16, 21], L48803 = [0, 3, 6, 7, 7, 9, 12], L48806 = [0, 3, 6, 7, 7, 9, 18], L48822 = [0, 3, 6, 7, 9, 12, 14], L48825 = [0, 3, 6, 7, 9, 12, 21], L48828 = [0, 3, 6, 7, 9, 14, 18], L48831 = [0, 3, 6, 7, 9, 18, 21], L48860 = [0, 3, 6, 9, 12, 14, 14], L48863 = [0, 3, 6, 9, 12, 14, 21], L48866 = [0, 3, 6, 9, 14, 14, 18], L48869 = [0, 3, 6, 9, 14, 18, 21], L48937 = [0, 3, 7, 7, 14, 14, 21] L49121 = [0, 6, 7, 7, 14, 14, 21], L59263 = [1, 1, 1, 13, 13, 15, 15], L67826 = [1, 1, 2, 12, 13, 15, 16], L67979 = [1, 1, 2, 13, 13, 15, 15], L74690 = [1, 1, 3, 11, 13, 15, 17], L75049 = [1, 1, 3, 13, 13, 15, 15], L76675 = [1, 1, 4, 5, 5, 16, 17], L76683 = [1, 1, 4, 5, 5, 17, 20], L80080 = [1, 1, 4, 10, 13, 15, 18], L80677 = [1, 1, 4, 13, 13, 15, 15], L83790 = [1, 1, 5, 9, 13, 15, 19], L84709 = [1, 1, 5, 13, 13, 15, 15], L86950 = [1, 1, 6, 8, 13, 15, 20], L88255 = [1, 1, 6, 13, 13, 15, 15], L89165 = [1, 1, 7, 7, 13, 15, 21], L90967 = [1, 1, 7, 13, 13, 15, 1 L93021 = [1, 1, 8, 13, 13, 15, 15], L94532 = [1, 1, 9, 13, 13, 15, 15], L96250 = [1, 1, 11, 13, 13, 15, 15], L96821 = [1, 1, 12, 13, 13, 15, 15], L97194 = [1, 1, 13, 13, 14, 15, 15], L97200 = [1, 1, 13, 13, 15, 15, 15], L97201 = [1, 1, 13, 13, 15, 15, 18], L97202 = [1, 1, 13, 13, 15, 15, 21], L105285 = [1, 2, 2, 12, 12, 16, 16],
172
EMILIO A. LAURET
Table 5. (continued) n = 7 q I indexes of I-isospectral families 42 {0} {143469, 143499}, {143747, 143838}, {143757, 143874}, {144817, 145064}, (cont.) {144827, 145100}, {144854, 145190}, {148073, 148658}, {148083, 148694}, {148110, 148784}, {148165, 148969}, {150256, 150264}, {152780, 152787}, {152853, 152856}, {152897, 152900}, {152906, 152912}, {153065, 153068}, {153074, 153080}, {153092, 153101}, {153531, 153534}, {153540, 153546}, {153558, 153567}, {153586, 153598}, {160975, 160996}, {161313, 161352}, {161314, 161328}, {161315, 161327}, {161317, 161369}, {161561, 161564}, {161674, 161679}, {161676, 161685}, {162001, 162009}, {162003, 162015}, {162006, 162025}, {162774, 162785}, {162776, 162791}, {162779, 162801}, {162782, 162816}, {189384, 189448}, {189409, 189429}, {189586, 189592}, {189741, 189758}, {189744, 189761}, {189754, 189774}, {189762, 189780}, {189906, 190624}, {190617, 190620}, {190836, 192652}, {192459, 192472}, {192460, 192470}, {192473, 192478}, {192474, 192488}, {192487, 193885}, {192497, 192503, 192545}, {192506, 192549}, {192507, 192544}, {192512, 192554}, {192514, 192547}, {192550, 192566}, {192551, 192583}, {192556, 192572}, {192557, 192591}, {192582, 193989}, {192590, 193991}, {192601, 192607, 192693}, {192610, 192697}, {192611, 192692}, {192616, 192702}, {192618, 192695}, {192698, 192714}, {192699, 192731}, {192704, 192720}, {192705, 192739}, {192730, 194227}, {192738, 194229}, {192755, 192757}, {192775, 193849}, {192786, 192791}, {192789, 192794}, {192845, 193889}, {192850, 193892}, {192868, 192878}, {192871, 192881}, {192876, 192885}, {193006, 194000}, {193011, 194003}, {193018, 194008}, {193045, 193055}, {193048, 193058}, {193053, 193062}, {193268, 194243}, {193273, 194248}, {193280, 194255}, {197047, 197050}, {197066, 197072}, {197069, 197075}, {197107, 197117}, {197110, 197120}, {197114, 197123}, {197174, 197184}, {197177, 197187}, {197181, 197190}
L105313 = [1, 2, 2, 12, 13, 15, 16], L111334 = [1, 2, 3, 11, 12, 16, 17], L111361 = [1, 2, 3, 11, 13, 15, 17], L111538 = [1, 2, 3, 12, 13, 15, 16], L113166 = [1, 2, 4, 5, 8, 10, 16], L113170 = [1, 2, 4, 5, 8, 10, 20], L113173 = [1, 2, 4, 5, 8, 11, 13], L113176 = [1, 2, 4, 5, 8, 11, 16], L113179 = [1, 2, 4, 5, 8, 11, 19], L113180 = [1, 2, 4, 5, 8, 11, 20], L113222 = [1, 2, 4, 5, 8, 17, 20], L113378 = [1, 2, 4, 5, 11, 13, 17], L113380 = [1, 2, 4, 5, 11, 13, 19], L113400 = [1, 2, 4, 5, 11, 16, 20], L113486 = [1, 2, 4, 5, 13, 17, 20], L114699 = [1, 2, 4, 7, 11, 13, 19], L115069 = [1, 2, 4, 8, 10, 11, 16], L115107 = [1, 2, 4, 8, 10, 16, 19], L115841 = [1, 2, 4, 10, 12, 16, 18], L115869 = [1, 2, 4, 10, 13, 15, 18], L116030 = [1, 2, 4, 11, 13, 14, 19], L116047 = [1, 2, 4, 11, 13, 19, 21], L116173 = [1, 2, 4, 12, 13, 15, 16], L117588 = [1, 2, 5, 7, 10, 11, 13], L118006 = [1, 2, 5, 8, 10, 11, 13], L118052 = [1, 2, 5, 8, 11, 13, 17], L118073 = [1, 2, 5, 8, 11, 17, 19], L118444 = [1, 2, 5, 9, 12, 16, 19], L118472 = [1, 2, 5, 9, 13, 15, 19], L118604 = [1, 2, 5, 10, 11, 13, 14], L118607 = [1, 2, 5, 10, 11, 13, 21], L118884 = [1, 2, 5, 12, 13, 15, 16], L120957 = [1, 2, 6, 8, 12, 16, 20], L120979 = [1, 2, 6, 8, 13, 15, 20], L121947 = [1, 2, 6, 12, 13, 15, 16], L122850 = [1, 2, 7, 7, 12, 16, 21], L122878 = [1, 2, 7, 7, 13, 15, 21], L123174 = [1, 2, 7, 8, 10, 11, 16], L124043 = [1, 2, 7, 10, 16, 17, 20], L124276 = [1, 2, 7, 12, 13, 15, 16], L125531 = [1, 2, 8, 10, 11, 14, 16], L125543 = [1, 2, 8, 10, 11, 16, 21], L125841 = [1, 2, 8, 12, 13, 15, 16], L127058 = [1, 2, 9, 12, 13, 15, 16], L128265 = [1, 2, 10, 14, 16, 17, 20], L128397 = [1, 2, 10, 16, 17, 20, 21], L128506 = [1, 2, 11, 12, 13, 15, 16], L128866 = [1, 2, 12, 12, 13, 15, 16], L129000 = [1, 2, 12, 13, 14, 15, 16], L129022 = [1, 2, 12, 13, 15, 15, 16], L129028 = [1, 2, 12, 13, 15, 16, 18], L129029 = [1, 2, 12, 13, 15, 16, 21], L132293 = [1, 3, 3, 5, 9, 11, 13], L132315 = [1, 3, 3, 5, 9, 13, 19], L134287 = [1, 3, 3, 9, 11, 15, 15], L134400 = [1, 3, 3, 9, 15, 15, 17] L134755 = [1, 3, 3, 11, 13, 15, 17], L136381 = [1, 3, 4, 5, 9, 15, 16], L136384 = [1, 3, 4, 5, 9, 15, 20], L138290 =
APPENDIX
173
Table 5. (continued) n = 7 q I 42 {0, 1} (cont.) {2} {2, 5}
indexes of I-isospectral families {30440, 30458}, {139613, 139631}, {140190, 140191}, {140196, 140265}, {140209, 140277}, {192553, 192571}, {192701, 192719} {140191, 140201} {8879, 42771}, {8898, 10707}, {20476, 97194}, {20483, 42774}, {27760, 129000}, {27783, 48345}, {27886, 42625}, {32719, 148048}, {32730, 41960}, {32946, 37220}, {35958, 159341}, {35967, 46750}, {36258, 42775}, {38582, 167243}, {38593, 48225}, {39177, 41363}, {39656, 170306}, {39665, 48937}, {40461, 42776}, {47854, 194911}, {47862, 49121}, {48010, 48348}, {59263, 97200}, {67826, 129022}, {67979, 96821}, {74690, 148057}, {75049, 96250}, {80080, 159347}, {80677, 97201}, {83790, 134755}, {84709, 94532}, {86950, 167252}, {88255, 93021}, {89165, 170312}, {90967, 97202}, {105285, 187255}, {105313, 128866}, {111334, 158616}, {111361, 147970}, {111538, 128506}, {115841, 190672}, {115869, 159260}, {116173, 129028}, {118444, 142292}, {118472, 142917}, {118884, 127058}, {120957, 193146}, {120979, 167173}, {121947, 125841}, {122850, 194920}, {122878, 170240}, {124276, 129029}, {138290, 166872}, {138340, 159164}, {138461, 148060}, {140208, 140269}, {143765, 169976}, {143824, 161666}, {144808, 148061}, {151864, 183342}, {151953, 159349}, {154768, 189954}, {154840, 167255}, {155230, 157942}, {156015, 191154}, {156102, 170314}, {156816, 159350}, {164078, 186960}, {164238, 166679}, {165207, 194847}, {165375, 169777}, {165677, 167257}, {169278, 197256}, {169496, 170315}, {185777, 194897}, {186228, 187264}, {192836, 193955}, {192848, 194925}, {192969, 193231}, {194691, 197628}, {194747, 194926}
[1, 3, 4, 10, 11, 17, 18], L138340 = [1, 3, 4, 10, 13, 15, 18], L138461 = [1, 3, 4, 11, 13, 15, 17], L139191 = [1, 3, 5, 6, 9, 12, 17], L139221 = [1, 3, 5, 6, 9, 17, 18], L139241 = [1, 3, 5, 6, 11, 12, 19], L139286 = [1, 3, 5, 6, 12, 13, 17] L139462 = [1, 3, 5, 7, 7, 9, 13], L139466 = [1, 3, 5, 7, 7, 9, 17], L139468 = [1, 3, 5, 7, 7, 9, 19], L139472 = [1, 3, 5, 7, 7, 11, 13], L139474 = [1, 3, 5, 7, 7, 11, 15], L139478 = [1, 3, 5, 7, 7, 11, 19], L139491 = [1, 3, 5, 7, 7, 13, 15], L139492 = [1, 3, 5, 7, 7, 13, 17], L139494 = [1, 3, 5, 7, 7, 13, 19], L139507 = [1, 3, 5, 7, 7, 15, 19], L139613 = [1, 3, 5, 7, 9, 11, 17], L139615 = [1, 3, 5, 7, 9, 11, 19], L139627 = [1, 3, 5, 7, 9, 13, 14], L139631 = [1, 3, 5, 7, 9, 13, 19], L139633 = [1, 3, 5, 7, 9, 13, 21], L139637 = [1, 3, 5, 7, 9, 14, 17], L139639 = [1, 3, 5, 7, 9, 14, 19], L139652 = [1, 3, 5, 7, 9, 17, 19], L139654 = [1, 3, 5, 7, 9, 17, 21], L139660 = [1, 3, 5, 7, 9, 19, 21], L139673 = [1, 3, 5, 7, 11, 13, 14], L139678 = [1, 3, 5, 7, 11, 13, 21], L139680 = [1, 3, 5, 7, 11, 14, 15], L139684 = [1, 3, 5, 7, 11, 14, 19], L139688 = [1, 3, 5, 7, 11, 15, 21], L139700 = [1, 3, 5, 7, 11, 19, 21], L139751 = [1, 3, 5, 7, 13, 14, 15], L139752 = [1, 3, 5, 7, 13, 14, 17], L139754 = [1, 3, 5, 7, 13, 14, 19], L139758 = [1, 3, 5, 7, 13, 15, 19], L139759 = [1, 3, 5, 7, 13, 15, 21], L139762 = [1, 3, 5, 7, 13, 17, 21], L139767 = [1, 3, 5, 7, 13, 19, 21], L139781 = [1, 3, 5, 7, 14, 15, 19], L139809 = [1, 3, 5, 7, 15, 19, 21], L140189 = [1, 3, 5, 9, 11, 13, 15], L140190 = [1, 3, 5, 9, 11, 13, 17], L140191 = [1, 3, 5, 9, 11, 13, 19], L140196 = [1, 3, 5, 9, 11, 14, 17], L140198 = [1, 3, 5, 9, 11, 14, 19], L140201 = [1, 3, 5, 9, 11, 15, 17], L140208 = [1, 3, 5, 9, 11, 17, 19], L140209 = [1, 3, 5, 9, 11, 17, 21], L140213 = [1, 3, 5, 9, 11, 19, 21], L140261 = [1, 3, 5, 9, 13, 14, 14], L140265 = [1, 3, 5, 9, 13, 14, 19], L140267 = [1, 3, 5, 9, 13, 14, 21], L140269 = [1, 3, 5, 9, 13, 15, 19], L140277 = [1, 3, 5, 9, 13, 19, 21], L140280 = [1, 3, 5, 9, 13, 21, 21], L140284 = [1, 3, 5, 9, 14, 14, 17], L140286 = [1, 3, 5, 9, 14, 14, 19], L140299 = [1, 3, 5, 9, 14, 17, 19], L140301 = [1, 3, 5, 9, 14, 17, 21], L140307 = [1, 3, 5, 9, 14, 19, 21], L140336 = [1, 3, 5, 9, 17, 19, 21], L140339 = [1, 3, 5, 9, 17, 21, 21], L140351 = [1, 3, 5, 9, 19, 21, 21], L140368 = [1, 3, 5, 11, 12, 13, 18], L140394 = [1, 3, 5, 11, 13, 14, 14],
174
EMILIO A. LAURET
L140399 = [1, 3, 5, 11, 13, 14, 21], L140409 = [1, 3, 5, 11, 13, 21, 21], L140411 = [1, 3, 5, 11, 14, 14, 15], L140415 = [1, 3, 5, 11, 14, 14, 19], L140419 = [1, 3, 5, 11, 14, 15, 21], L140431 = [1, 3, 5, 11, 14, 19, 21], L140438 = [1, 3, 5, 11, 15, 21, 21], L140462 = [1, 3, 5, 11, 19, 21, 21], L140526 = [1, 3, 5, 12, 13, 18, 19], L140618 = [1, 3, 5, 13, 14, 14, 15], L140619 = [1, 3, 5, 13, 14, 14, 17], L140621 = [1, 3, 5, 13, 14, 14, 19], L140625 = [1, 3, 5, 13, 14, 15, 19], L140626 = [1, 3, 5, 13, 14, 15, 21], L140629 = [1, 3, 5, 13, 14, 17, 21], L140634 = [1, 3, 5, 13, 14, 19, 21], L140641 = [1, 3, 5, 13, 15, 19, 21], L140642 = [1, 3, 5, 13, 15, 21, 21], L140648 = [1, 3, 5, 13, 17, 21, 21], L140657 = [1, 3, 5, 13, 19, 21, 21], L140672 = [1, 3, 5, 14, 14, 15, 19], L140700 = [1, 3, 5, 14, 15, 19, 21], L140760 = [1, 3, 5, 15, 19, 21, 21], L142292 = [1, 3, 6, 8, 13, 15, 20], L142896 = [1, 3, 6, 11, 12, 15, 18], L142917 = [1, 3, 6, 11, 13, 15, 17], L143090 = [1, 3, 6, 12, 15, 17, 18], L143469 = [1, 3, 7, 7, 7, 11, 15], L143499 = [1, 3, 7, 7, 7, 15, 17], L143747 = [1, 3, 7, 7, 11, 14, 15], L143757 = [1, 3, 7, 7, 11, 15, 21], L143765 = [1, 3, 7, 7, 11, 17, 21], L143824 = [1, 3, 7, 7, 13, 15, 21], L143838 = [1, 3, 7, 7, 14, 15, 17], L143874 = [1, 3, 7, 7, 15, 17, 21], L144808 = [1, 3, 7, 11, 13, 15, 17], L144817 = [1, 3, 7, 11, 14, 14, 15], L144827 = [1, 3, 7, 11, 14, 15, 21], L144854 = [1, 3, 7, 11, 15, 21, 21], L145064 = [1, 3, 7, 14, 14, 15, 17], L145100 = [1, 3, 7, 14, 15, 17, 21], L145190 = [1, 3, 7, 15, 17, 21, 21], L147970 = [1, 3, 11, 12, 13, 15, 17], L148048 = [1, 3, 11, 13, 14, 15, 17], L148057 = [1, 3, 11, 13, 15, 15, 17], L148060 = [1, 3, 11, 13, 15, 17, 18], L148061 = [1, 3, 11, 13, 15, 17, 21], L148073 = [1, 3, 11, 14, 14, 14, 15], L148083 = [1, 3, 11, 14, 14, 15, 21], L148110 = [1, 3, 11, 14, 15, 21, 21], L148165 = [1, 3, 11, 15, 21, 21, 21], L148658 = [1, 3, 14, 14, 14, 15, 17], L148694 = [1, 3, 14, 14, 15, 17, 21], L148784 = [1, 3, 14, 15, 17, 21, 21], L148969 = [1, 3, 15, 17, 21, 21, 21], L150256 = [1, 4, 4, 5, 16, 16, 20], L150264 = [1, 4, 4, 5, 16, 20, 20], L151864 = [1, 4, 4, 10, 10, 18, 18], L151953 = [1, 4, 4, 10, 13, 15, 18], L152780 = [1, 4, 5, 6, 12, 16, 18], L152787 = [1, 4, 5, 6, 12, 18, 20], L152853 = [1, 4, 5, 7, 7, 7, 16], L152856 = [1, 4, 5, 7, 7, 7, 20], L152897 = [1, 4, 5, 7, 7, 14, 16], L152900 = [1, 4, 5, 7, 7, 14, 20], L152906 = [1, 4, 5, 7, 7, 16, 21], L152912 = [1, 4, 5, 7, 7, 20, 21], L153065 = [1, 4, 5, 7, 14, 14, 16], L153068 = [1, 4, 5, 7, 14, 14, 20], L153074 = [1, 4, 5, 7, 14, 16, 21], L153080 = [1, 4, 5, 7, 14, 20, 21], L153092 = [1, 4, 5, 7, 16, 21, 21], L153101 = [1, 4, 5, 7, 20, 21, 21], L153531 = [1, 4, 5, 14, 14, 14, 16], L153534 = [1, 4, 5, 14, 14, 14, 20], L153540 = [1, 4, 5, 14, 14, 16, 21], L153546 = [1, 4, 5, 14, 14, 20, 21], L153558 = [1, 4, 5, 14, 16, 21, 21], L153567 = [1, 4, 5, 14, 20, 21, 21], L153586 = [1, 4, 5, 16, 21, 21, 21], L153598 = [1, 4, 5, 20, 21, 21, 21], L154768 = [1, 4, 6, 8, 10, 18, 20], L154840 = [1, 4, 6, 8, 13, 15, 20], L155230 = [1, 4, 6, 10, 13, 15, 18], L156015 = [1, 4, 7, 7, 10, 18, 21], L156102 = [1, 4, 7, 7, 13, 15, 21], L156816 = [1, 4, 7, 10, 13, 15, 18], L157942 = [1, 4, 8, 10, 13, 15, 18], L158616 = [1, 4, 9, 10, 13, 15, 18], L159164 = [1, 4, 10, 11, 13, 15, 18], L159260 = [1, 4, 10, 12, 13, 15, 18], L159341 = [1, 4, 10, 13, 14, 15, 18], L159347 = [1, 4, 10, 13, 15, 15, 18], L159349 = [1, 4, 10, 13, 15, 18, 18], L159350 = [1, 4, 10, 13, 15, 18, 21], L160975 = [1, 5, 6, 7, 11, 12, 13], L160996 = [1, 5, 6, 7, 11, 17, 18], L161313 = [1, 5, 6, 11, 12, 13, 14], L161314 = [1, 5, 6, 11, 12, 13, 17], L161315 = [1, 5, 6, 11, 12, 13, 18], L161317 = [1, 5, 6, 11, 12, 13, 21], L161327 = [1, 5, 6, 11, 12, 17, 18], L161328 = [1, 5, 6, 11, 12, 17, 19], L161352 = [1, 5, 6, 11, 14, 17, 18], L161369 = [1, 5, 6, 11, 17, 18, 21], L161561 = [1, 5, 7, 7, 7, 11, 13], L161564 = [1, 5, 7, 7, 7, 11, 17], L161666 = [1, 5, 7, 7, 9, 19, 21], L161674 = [1, 5, 7, 7, 11, 13, 14], L161676 = [1, 5, 7, 7, 11, 13, 21] L161679 = [1, 5, 7, 7, 11, 14, 17], L161685 = [1, 5, 7, 7, 11, 17, 21], L162001 = [1, 5, 7, 11, 13, 14, 14], L162003 = [1, 5, 7, 11, 13, 14, 21], L162006 = [1, 5, 7, 11, 13, 21, 21], L162009 = [1, 5, 7, 11, 14, 14, 17], L162015 = [1, 5, 7, 11, 14, 17, 21], L162025 = [1, 5, 7, 11, 17, 21, 21], L162774 = [1, 5, 11, 13, 14, 14, 14], L162776 = [1, 5, 11, 13, 14, 14, 21], L162779 = [1, 5, 11, 13, 14, 21, 21], L162782 = [1, 5, 11, 13, 21, 21, 21], L162785 = [1, 5, 11, 14, 14, 14, 17], L162791 = [1, 5, 11, 14, 14, 17, 21], L162801 = [1, 5, 11, 14, 17, 21, 21], L162816 = [1, 5, 11, 17, 21, 21, 21], L164078 = [1, 6, 6, 8, 8, 20, 20], L164238 = [1, 6, 6, 8, 13, 15, 20], L165207 = [1, 6, 7, 7, 8, 20, 21], L165375 = [1, 6, 7, 7, 13, 15, 21], L165677 = [1, 6, 7, 8, 13, 15, 20], L166679 = [1, 6, 8, 8, 13, 15, 20], L166872 = [1, 6, 8, 9, 13, 15, 20], L167173 = [1, 6, 8, 12, 13, 15, 20], L167243 = [1, 6, 8, 13, 14, 15, 20], L167252 = [1, 6, 8, 13, 15, 15, 20], L167255 = [1, 6, 8, 13, 15, 18, 20], L167257 = [1, 6, 8, 13, 15, 20, 21], L169278 = [1, 7, 7, 7, 7, 21, 21], L169496 = [1, 7, 7, 7, 13, 15, 21], L169777 = [1, 7, 7, 8, 13, 15, 21], L169976 = [1, 7, 7, 9, 13, 15, 21], L170240 = [1, 7, 7, 12, 13, 15, 21], L170306 = [1, 7, 7, 13, 14, 15, 21], L170312 = [1, 7, 7, 13, 15, 15, 21], L170314 = [1, 7, 7, 13, 15, 18, 21], L170315 = [1, 7, 7, 13, 15, 21, 21], L183342 = [2, 2, 3, 12, 12, 16, 16], L185777 = [2, 2, 7, 7, 12, 16, 21], L186228 =
APPENDIX
175
[2, 2, 7, 12, 12, 16, 16], L186960 = [2, 2, 9, 12, 12, 16, 16], L187255 = [2, 2, 12, 12, 15, 16, 16], L187264 = [2, 2, 12, 12, 16, 16, 21], L189384 = [2, 3, 4, 6, 8, 15, 16], L189409 = [2, 3, 4, 6, 9, 10, 20], L189429 = [2, 3, 4, 6, 9, 16, 20], L189448 = [2, 3, 4, 6, 10, 15, 16], L189586 = [2, 3, 4, 7, 8, 9, 16], L189592 = [2, 3, 4, 7, 8, 10, 15], L189741 = [2, 3, 4, 8, 9, 10, 15], L189744 = [2, 3, 4, 8, 9, 10, 20], L189754 = [2, 3, 4, 8, 9, 14, 16], L189758 = [2, 3, 4, 8, 9, 15, 16], L189761 = [2, 3, 4, 8, 9, 16, 20], L189762 = [2, 3, 4, 8, 9, 16, 21], L189774 = [2, 3, 4, 8, 10, 14, 15], L189780 = [2, 3, 4, 8, 10, 15, 21], L189906 = [2, 3, 4, 9, 12, 15, 18], L189954 = [2, 3, 4, 10, 12, 16, 18], L190617 = [2, 3, 6, 8, 9, 10, 12], L190620 = [2, 3, 6, 8, 9, 10, 18], L190624 = [2, 3, 6, 8, 9, 12, 15], L190672 = [2, 3, 6, 8, 12, 16, 20], L190836 = [2, 3, 6, 10, 14, 14, 20], L191154 = [2, 3, 7, 7, 12, 16, 21], L192459 = [2, 4, 6, 7, 7, 8, 16], L192460 = [2, 4, 6, 7, 7, 8, 18], L192470 = [2, 4, 6, 7, 7, 10, 12], L192472 = [2, 4, 6, 7, 7, 10, 16], L192473 = [2, 4, 6, 7, 7, 10, 18], L192474 = [2, 4, 6, 7, 7, 10, 20], L192478 = [2, 4, 6, 7, 7, 12, 16], L192487 = [2, 4, 6, 7, 7, 16, 18], L192488 = [2, 4, 6, 7, 7, 16, 20], L192497 = [2, 4, 6, 7, 8, 10, 18], L192503 = [2, 4, 6, 7, 8, 12, 20], L192506 = [2, 4, 6, 7, 8, 14, 16], L192507 = [2, 4, 6, 7, 8, 14, 18], L192512 = [2, 4, 6, 7, 8, 16, 21], L192514 = [2, 4, 6, 7, 8, 18, 21], L192544 = [2, 4, 6, 7, 10, 12, 14], L192545 = [2, 4, 6, 7, 10, 12, 16], L192547 = [2, 4, 6, 7, 10, 12, 21 L192549 = [2, 4, 6, 7, 10, 14, 16], L192550 = [2, 4, 6, 7, 10, 14, 18], L192551 = [2, 4, 6, 7, 10, 14, 20], L192553 = [2, 4, 6, 7, 10, 16, 18], L192554 = [2, 4, 6, 7, 10, 16, 21], L192556 = [2, 4, 6, 7, 10, 18, 21], L192557 = [2, 4, 6, 7, 10, 20, 21], L192566 = [2, 4, 6, 7, 12, 14, 16], L192571 = [2, 4, 6, 7, 12, 16, 20], L192572 = [2, 4, 6, 7, 12, 16, 21], L192582 = [2, 4, 6, 7, 14, 16, 18], L192583 = [2, 4, 6, 7, 14, 16, 20], L192590 = [2, 4, 6, 7, 16, 18, 21], L192591 = [2, 4, 6, 7, 16, 20, 21], L192601 = [2, 4, 6, 8, 10, 18, 21], L192607 = [2, 4, 6, 8, 12, 20, 21], L192610 = [2, 4, 6, 8, 14, 16, 21], L192611 = [2, 4, 6, 8, 14, 18, 21], L192616 = [2, 4, 6, 8, 16, 21, 21], L192618 = [2, 4, 6, 8, 18, 21, 21], L192652 = [2, 4, 6, 9, 10, 14, 14], L192692 = [2, 4, 6, 10, 12, 14, 21], L192693 = [2, 4, 6, 10, 12, 16, 21], L192695 = [2, 4, 6, 10, 12, 21, 21], L192697 = [2, 4, 6, 10, 14, 16, 21], L192698 = [2, 4, 6, 10, 14, 18, 21], L192699 = [2, 4, 6, 10, 14, 20, 21], L192701 = [2, 4, 6, 10, 16, 18, 21], L192702 = [2, 4, 6, 10, 16, 21, 21], L192704 = [2, 4, 6, 10, 18, 21, 21], L192705 = [2, 4, 6, 10, 20, 21, 21], L192714 = [2, 4, 6, 12, 14, 16, 21], L192719 = [2, 4, 6, 12, 16, 20, 21], L192720 = [2, 4, 6, 12, 16, 21, 21], L192730 = [2, 4, 6, 14, 16, 18, 21], L192731 = [2, 4, 6, 14, 16, 20, 21], L192738 = [2, 4, 6, 16, 18, 21, 21], L192739 = [2, 4, 6, 16, 20, 21, 21], L192755 = [2, 4, 7, 7, 7, 8, 10], L192757 = [2, 4, 7, 7, 7, 8, 16], L192775 = [2, 4, 7, 7, 7, 12, 18], L192786 = [2, 4, 7, 7, 8, 10, 14], L192789 = [2, 4, 7, 7, 8, 10, 21], L192791 = [2, 4, 7, 7, 8, 14, 16], L192794 = [2, 4, 7, 7, 8, 16, 21], L192836 = [2, 4, 7, 7, 10, 18, 21], L192845 = [2, 4, 7, 7, 12, 14, 18], L192848 = [2, 4, 7, 7, 12, 16, 21], L192850 = [2, 4, 7, 7, 12, 18, 21], L192868 = [2, 4, 7, 8, 10, 14, 14], L192871 = [2, 4, 7, 8, 10, 14, 21], L192876 = [2, 4, 7, 8, 10, 21, 21], L192878 = [2, 4, 7, 8, 14, 14, 16], L192881 = [2, 4, 7, 8, 14, 16, 21], L192885 = [2, 4, 7, 8, 16, 21, 21], L192969 = [2, 4, 7, 10, 12, 16, 18], L193006 = [2, 4, 7, 12, 14, 14, 18], L193011 = [2, 4, 7, 12, 14, 18, 21], L193018 = [2, 4, 7, 12, 18, 21, 21], L193045 = [2, 4, 8, 10, 14, 14, 21], L193048 = [2, 4, 8, 10, 14, 21, 21], L193053 = [2, 4, 8, 10, 21, 21, 21], L193055 = [2, 4, 8, 14, 14, 16, 21], L193058 = [2, 4, 8, 14, 16, 21, 21], L193062 = [2, 4, 8, 16, 21, 21, 21], L193146 = [2, 4, 9, 10, 12, 16, 18], L193231 = [2, 4, 10, 12, 16, 18, 21], L193268 = [2, 4, 12, 14, 14, 18, 21], L193273 = [2, 4, 12, 14, 18, 21, 21], L193280 = [2, 4, 12, 18, 21, 21, 21], L193849 = [2, 6, 7, 7, 7, 8, 12], L193885 = [2, 6, 7, 7, 8, 10, 12], L193889 = [2, 6, 7, 7, 8, 12, 14], L193892 = [2, 6, 7, 7, 8, 12, 21], L193955 = [2, 6, 7, 7, 12, 16, 21], L193989 = [2, 6, 7, 8, 10, 12, 14], L193991 = [2, 6, 7, 8, 10, 12, 21 L194000 = [2, 6, 7, 8, 12, 14, 14], L194003 = [2, 6, 7, 8, 12, 14, 21], L194008 = [2, 6, 7, 8, 12, 21, 21], L194227 = [2, 6, 8, 10, 12, 14, 21], L194229 = [2, 6, 8, 10, 12, 21, 21], L194243 = [2, 6, 8, 12, 14, 14, 21], L194248 = [2, 6, 8, 12, 14, 21, 21], L194255 = [2, 6, 8, 12, 21, 21, 21], L194691 = [2, 7, 7, 7, 7, 21, 21], L194747 = [2, 7, 7, 7, 12, 16, 21], L194847 = [2, 7, 7, 9, 12, 16, 21], L194897 = [2, 7, 7, 12, 12, 16, 21], L194911 = [2, 7, 7, 12, 14, 16, 21], L194920 = [2, 7, 7, 12, 15, 16, 21], L194925 = [2, 7, 7, 12, 16, 18, 21], L194926 = [2, 7, 7, 12, 16, 21, 21], L197047 = [3, 6, 7, 7, 7, 9, 12], L197050 = [3, 6, 7, 7, 7, 9, 18], L197066 = [3, 6, 7, 7, 9, 12, 14], L197069 = [3, 6, 7, 7, 9, 12, 21], L197072 = [3, 6, 7, 7, 9, 14, 18], L197075 = [3, 6, 7, 7, 9, 18, 21], L197107 = [3, 6, 7, 9, 12, 14, 14], L197110 = [3, 6, 7, 9, 12, 14, 21], L197114 = [3, 6, 7, 9, 12, 21, 21], L197117 = [3, 6, 7, 9, 14, 14, 18], L197120 = [3, 6, 7, 9, 14, 18, 21], L197123 = [3, 6, 7, 9, 18, 21, 21], L197174 = [3, 6, 9, 12, 14, 14, 14], L197177 = [3, 6, 9, 12, 14, 14, 21], L197181 = [3, 6, 9, 12, 14, 21, 21],
176
EMILIO A. LAURET
Table 5. (continued) n = 7 q I indexes of I-isospectral families 43 {0} {502, 508}, {52063, 52090}
L197184 = [3, 6, 9, 14, 14, 14, 18], L197187 = [3, 6, 9, 14, 14, 18, 21], L197190 = [3, 6, 9, 14, 18, 21, 21], L197256 = [3, 7, 7, 7, 7, 21, 21], L197628 = [6, 7, 7, 7, 7, 21, 21]. q = 43 : L502 = [0, 0, 0, 1, 3, 8, 14], L508 = [0, 0, 0, 1, 3, 9, 14], L52063 = [1, 2, 3, 6, 7, 9, 21], L52090 = [1, 2, 3, 6, 7, 12, 18]. q = 44 : L66 = [0, 0, 0, 0, 1, 3, 7], L68 = [0, 0, 0, 0, 1, 3, 9], L72 = [0, 0, 0, 0, 1, 3, 13], L75 = [0, 0, 0, 0, 1, 3, 17], L100 = [0, 0, 0, 0, 1, 5, 7], L102 = [0, 0, 0, 0, 1, 5, 9], L694 = [0, 0, 0, 1, 3, 5, 13], L696 = [0, 0, 0, 1, 3, 5, 15], L707 = [0, 0, 0, 1, 3, 7, 11], L709 = [0, 0, 0, 1, 3, 7, 13], L713 = [0, 0, 0, 1, 3, 7, 19], L715 = [0, 0, 0, 1, 3, 7, 21], L716 = [0, 0, 0, 1, 3, 7, 22], L733 = [0, 0, 0, 1, 3, 9, 11], L734 = [0, 0, 0, 1, 3, 9, 13], L737 = [0, 0, 0, 1, 3, 9, 19], L738 = [0, 0, 0, 1, 3, 9, 22], L752 = [0, 0, 0, 1, 3, 11, 13], L755 = [0, 0, 0, 1, 3, 11, 17], L776 = [0, 0, 0, 1, 3, 13, 22], L796 = [0, 0, 0, 1, 3, 17, 22], L970 = [0, 0, 0, 1, 5, 7, 9], L971 = [0, 0, 0, 1, 5, 7, 11], L974 = [0, 0, 0, 1, 5, 7, 22], L985 = [0, 0, 0, 1, 5, 9, 11], L989 = [0, 0, 0, 1, 5, 9, 22], L1401 = [0, 0, 0, 2, 6, 10, 11], L1403 = [0, 0, 0, 2, 6, 11, 14], L1441 = [0, 0, 0, 4, 8, 11, 12], L1442 = [0, 0, 0, 4, 8, 11, 16], L4986 = [0, 0, 1, 3, 5, 7, 13], L4991 = [0, 0, 1, 3, 5, 7, 19], L4993 = [0, 0, 1, 3, 5, 7, 21], L5009 = [0, 0, 1, 3, 5, 9, 13], L5011 = [0, 0, 1, 3, 5, 9, 15], L5013 = [0, 0, 1, 3, 5, 9, 17], L5014 = [0, 0, 1, 3, 5, 9, 19], L5016 = [0, 0, 1, 3, 5, 9, 21], L5020 = [0, 0, 1, 3, 5, 11, 13], L5022 = [0, 0, 1, 3, 5, 11, 15], L5043 = [0, 0, 1, 3, 5, 13, 17], L5044 = [0, 0, 1, 3, 5, 13, 19], L5046 = [0, 0, 1, 3, 5, 13, 22], L5055 = [0, 0, 1, 3, 5, 15, 17], L5057 = [0, 0, 1, 3, 5, 15, 21], L5058 = [0, 0, 1, 3, 5, 15, 22], L5099 = [0, 0, 1, 3, 7, 9, 13], L5101 = [0, 0, 1, 3, 7, 9, 19], L5115 = [0, 0, 1, 3, 7, 11, 11], L5117 = [0, 0, 1, 3, 7, 11, 13], L5121 = [0, 0, 1, 3, 7, 11, 19], L5123 = [0, 0, 1, 3, 7, 11, 21], L5124 = [0, 0, 1, 3, 7, 11, 22], L5137 = [0, 0, 1, 3, 7, 13, 22], L5155 = [0, 0, 1, 3, 7, 19, 22], L5159 = [0, 0, 1, 3, 7, 21, 22], L5160 = [0, 0, 1, 3, 7, 22, 22], L5269 = [0, 0, 1, 3, 9, 11, 11], L5270 = [0, 0, 1, 3, 9, 11, 13], L5273 = [0, 0, 1, 3, 9, 11, 19], L5274 = [0, 0, 1, 3, 9, 11, 22], L5277 = [0, 0, 1, 3, 9, 13, 22], L5285 = [0, 0, 1, 3, 9, 19, 22], L5286 = [0, 0, 1, 3, 9, 22, 22], L5350 = [0, 0, 1, 3, 11, 11, 13], L5353 = [0, 0, 1, 3, 11, 11, 17], L5374 = [0, 0, 1, 3, 11, 13, 22], L5394 = [0, 0, 1, 3, 11, 17, 22], L5475 = [0, 0, 1, 3, 13, 22, 22], L5545 = [0, 0, 1, 3, 17, 22, 22], L6415 = [0, 0, 1, 5, 7, 9, 11], L6417 = [0, 0, 1, 5, 7, 9, 22], L6418 = [0, 0, 1, 5, 7, 11, 11], L6421 = [0, 0, 1, 5, 7, 11, 22], L6427 = [0, 0, 1, 5, 7, 22, 22], L6477 = [0, 0, 1, 5, 9, 11, 11], L6481 = [0, 0, 1, 5, 9, 11, 22], L6490 = [0, 0, 1, 5, 9, 22, 22], L7919 = [0, 0, 2, 4, 11, 16, 18], L7931 = [0, 0, 2, 6, 8, 11, 16], L7934 = [0, 0, 2, 6, 10, 11, 11], L7937 = [0, 0, 2, 6, 10, 11, 22], L7939 = [0, 0, 2, 6, 11, 11, 14], L7944 = [0, 0, 2, 6, 11, 14, 22], L8049 = [0, 0, 4, 8, 11, 11, 12], L8050 = [0, 0, 4, 8, 11, 11, 16], L8053 = [0, 0, 4, 8, 11, 12, 22], L8054 = [0, 0, 4, 8, 11, 16, 22], L24282 = [0, 1, 2, 6, 7, 13, 17], L24303 = [0, 1, 2, 6, 7, 17, 18], L24466 = [0, 1, 2, 6, 9, 15, 17], L24689 = [0, 1, 2, 6, 13, 17, 18], L24733 = [0, 1, 2, 6, 15, 17, 18], L26220 = [0, 1, 2, 10, 15, 18, 19], L27315 = [0, 1, 3, 4, 7, 12, 13] L27317 = [0, 1, 3, 4, 7, 12, 16], L27339 = [0, 1, 3, 4, 7, 16, 17], L27413 = [0, 1, 3, 4, 8, 12, 13], L27889 = [0, 1, 3, 5, 7, 9, 13], L27890 = [0, 1, 3, 5, 7, 9, 15], L27892 = [0, 1, 3, 5, 7, 9, 17], L27893 = [0, 1, 3, 5, 7, 9, 19], L27895 = [0, 1, 3, 5, 7, 9, 21], L27899 = [0, 1, 3, 5, 7, 11, 13], L27904 = [0, 1, 3, 5, 7, 11, 19], L27906 = [0, 1, 3, 5, 7, 11, 21], L27918 = [0, 1, 3, 5, 7, 13, 15], L27920 = [0, 1, 3, 5, 7, 13, 17], L27922 = [0, 1, 3, 5, 7, 13, 22], L27926 = [0, 1, 3, 5, 7, 15, 21], L27935 = [0, 1, 3, 5, 7, 17, 19], L27944 = [0, 1, 3, 5, 7, 19, 21], L27945 = [0, 1, 3, 5, 7, 19, 22], L27949 = [0, 1, 3, 5, 7, 21, 22], L28032 = [0, 1, 3, 5, 9, 11, 13], L28034 = [0, 1, 3, 5, 9, 11, 15], L28036 = [0, 1, 3, 5, 9, 11, 17], L28037 = [0, 1, 3, 5, 9, 11, 19], L28039 = [0, 1, 3, 5, 9, 11, 21], L28042 = [0, 1, 3, 5, 9, 13, 15], L28044 = [0, 1, 3, 5, 9, 13, 17], L28045 = [0, 1, 3, 5, 9, 13, 19], L28047 = [0, 1, 3, 5, 9, 13, 22], L28055 = [0, 1, 3, 5, 9, 15, 22], L28062 = [0, 1, 3, 5, 9, 17, 21], L28063 = [0, 1, 3, 5, 9, 17, 22], L28066 = [0, 1, 3, 5, 9, 19, 22], L28070 = [0, 1, 3, 5, 9, 21, 22], L28074 = [0, 1, 3, 5, 11, 11, 13], L28076 = [0, 1, 3, 5, 11, 11, 15], L28097 = [0, 1, 3, 5, 11, 13, 17], L28098 = [0, 1, 3, 5, 11, 13, 19], L28100 = [0, 1, 3, 5, 11, 13, 22], L28109 = [0, 1, 3, 5, 11, 15, 17], L28111 = [0, 1, 3, 5, 11, 15, 21], L28112 = [0, 1, 3, 5, 11, 15, 22], L28204 = [0, 1, 3, 5, 13, 17, 22] L28206 = [0, 1, 3, 5, 13, 19, 22], L28209 = [0, 1, 3, 5, 13, 22, 22], L28245 = [0, 1, 3, 5, 15, 17, 22], L28249 = [0, 1, 3, 5, 15, 21, 22], L28250 = [0, 1, 3, 5, 15, 22, 22], L28399 = [0, 1, 3, 7, 9, 11, 13], L28401 = [0, 1, 3, 7, 9, 11, 19],
APPENDIX
177
Table 5. (continued) n = 7 q I indexes of I-isospectral families 44 {0} {66, 68}, {72, 75, 100, 102}, {694, 696}, {707, 733}, {709, 970}, {716, 738}, {752, 755, 971, 985}, {776, 796, 974, 989}, {1401, 1403}, {1441, 1442}, {4986, 5011}, {4991, 5013}, {4993, 5009}, {5014, 5044}, {5016, 5055}, {5020, 5022}, {5043, 5099}, {5046, 5058}, {5057, 5101}, {5115, 5269}, {5117, 6415}, {5124, 5274}, {5137, 6417}, {5160, 5286}, {5350, 5353, 6418, 6477}, {5374, 5394, 6421, 6481}, {5475, 5545, 6427, 6490}, {7919, 7931}, {7934, 7939}, {7937, 7944}, {8049, 8050}, {8053, 8054}, {24282, 24466}, {24303, 24733}, {24689, 26220}, {27315, 27339}, {27317, 27413}, {27889, 27890, 27892, 27895}, {27893, 27918, 27920, 28042}, {27899, 28034}, {27904, 28036}, {27906, 28032}, {27922, 28055}, {27945, 28063}, {27949, 28047}, {28037, 28098}, {28039, 28109}, {28066, 28206}, {28070, 28245}, {28074, 28076}, {28097, 28399}, {28100, 28112}, {28111, 28401}, {28204, 28406}, {28209, 28250}, {28249, 28412}, {28473, 29083}, {28475, 33317}, {28482, 29088}, {28495, 33319}, {28518, 29100}, {28562, 33321}, {28614, 29122}, {28894, 31707}, {29360, 29363, 33322, 33509}, {29384, 29404, 33325, 33513}, {29485, 29555, 33331, 33522},
L28406 = [0, 1, 3, 7, 9, 13, 22], L28412 = [0, 1, 3, 7, 9, 19, 22], L28473 = [0, 1, 3, 7, 11, 11, 11], L28475 = [0, 1, 3, 7, 11, 11, 13], L28479 = [0, 1, 3, 7, 11, 11, 19], L28481 = [0, 1, 3, 7, 11, 11, 21], L28482 = [0, 1, 3, 7, 11, 11, 22] L28495 = [0, 1, 3, 7, 11, 13, 22], L28513 = [0, 1, 3, 7, 11, 19, 22], L28517 = [0, 1, 3, 7, 11, 21, 22], L28518 = [0, 1, 3, 7, 11, 22, 22], L28562 = [0, 1, 3, 7, 13, 22, 22], L28607 = [0, 1, 3, 7, 19, 22, 22], L28613 = [0, 1, 3, 7, 21, 22, 22] L28614 = [0, 1, 3, 7, 22, 22, 22], L28894 = [0, 1, 3, 8, 12, 13, 16], L29083 = [0, 1, 3, 9, 11, 11, 11], L29084 = [0, 1, 3, 9, 11, 11, 13], L29087 = [0, 1, 3, 9, 11, 11, 19], L29088 = [0, 1, 3, 9, 11, 11, 22], L29091 = [0, 1, 3, 9, 11, 13, 22] L29099 = [0, 1, 3, 9, 11, 19, 22], L29100 = [0, 1, 3, 9, 11, 22, 22], L29106 = [0, 1, 3, 9, 13, 22, 22], L29121 = [0, 1, 3, 9, 19, 22, 22], L29122 = [0, 1, 3, 9, 22, 22, 22], L29360 = [0, 1, 3, 11, 11, 11, 13], L29363 = [0, 1, 3, 11, 11, 11, 1 L29384 = [0, 1, 3, 11, 11, 13, 22], L29404 = [0, 1, 3, 11, 11, 17, 22], L29485 = [0, 1, 3, 11, 13, 22, 22], L29555 = [0, 1, 3, 11, 17, 22, 22], L29787 = [0, 1, 3, 13, 22, 22, 22], L29966 = [0, 1, 3, 17, 22, 22, 22], L31707 = [0, 1, 4, 7, 8, 12, 13], L32070 = [0, 1, 4, 8, 12, 16, 20], L33317 = [0, 1, 5, 7, 9, 11, 11], L33319 = [0, 1, 5, 7, 9, 11, 22], L33321 = [0, 1, 5, 7, 9, 22, 22], L33322 = [0, 1, 5, 7, 11, 11, 11], L33325 = [0, 1, 5, 7, 11, 11, 22], L33331 = [0, 1, 5, 7, 11, 22, 22], L33341 = [0, 1, 5, 7, 22, 22, 22], L33509 = [0, 1, 5, 9, 11, 11, 11], L33513 = [0, 1, 5, 9, 11, 11, 22], L33522 = [0, 1, 5, 9, 11, 22, 22], L33538 = [0, 1, 5, 9, 22, 22, 22], L37639 = [0, 2, 4, 6, 8, 11, 18], L37643 = [0, 2, 4, 6, 10, 11, 12], L37657 = [0, 2, 4, 6, 11, 12, 16], L37662 = [0, 2, 4, 6, 11, 14, 20], L37682 = [0, 2, 4, 8, 10, 11, 12], L37718 = [0, 2, 4, 10, 11, 12, 14], L37719 = [0, 2, 4, 10, 11, 12, 16], L37746 = [0, 2, 4, 11, 11, 16, 18], L37761 = [0, 2, 4, 11, 12, 14, 20], L37782 = [0, 2, 4, 11, 16, 18, 22], L37806 = [0, 2, 6, 8, 11, 11, 16], L37813 = [0, 2, 6, 8, 11, 16, 22], L37817 = [0, 2, 6, 10, 11, 11, 11], L37820 = [0, 2, 6, 10, 11, 11, 2 L37825 = [0, 2, 6, 10, 11, 22, 22], L37827 = [0, 2, 6, 11, 11, 11, 14], L37832 = [0, 2, 6, 11, 11, 14, 22], L37841 = [0, 2, 6, 11, 14, 22, 22], L38084 = [0, 4, 8, 11, 11, 11, 12], L38085 = [0, 4, 8, 11, 11, 11, 16], L38088 = [0, 4, 8, 11, 11, 12, 22], L38089 = [0, 4, 8, 11, 11, 16, 22], L38091 = [0, 4, 8, 11, 12, 16, 20], L38093 = [0, 4, 8, 11, 12, 22, 22], L38094 = [0, 4, 8, 11, 16, 22, 22], L104783 = [1, 2, 3, 5, 9, 10, 18], L104883 = [1, 2, 3, 5, 10, 13, 14], L105112 = [1, 2, 3, 5, 14, 15, 18], L105544 = [1, 2, 3, 6, 10, 13, 14], L105555 = [1, 2, 3, 6, 10, 14, 17], L105776 = [1, 2, 3, 6, 14, 17, 18], L105994 = [1, 2, 3, 7, 9, 10, 14], L106112 = [1, 2, 3, 7, 10, 14, 18], L107028 = [1, 2, 3, 9, 10, 14, 18], L107201 = [1, 2, 3, 9, 13, 15, 18], L107559 = [1, 2, 3, 10, 13, 17, 18], L113758 = [1, 2, 5, 6, 7, 10, 18], L113937 = [1, 2, 5, 6, 9, 10, 18], L113973 = [1, 2, 5, 6, 9, 14, 18] L113983 = [1, 2, 5, 6, 9, 15, 21], L114047 = [1, 2, 5, 6, 10, 18, 19], L114179 = [1, 2, 5, 6, 13, 15, 21], L114214 = [1, 2, 5, 6, 14, 18, 19], L114413 = [1, 2, 5, 7, 9, 10, 21], L114493 = [1, 2, 5, 7, 10, 14, 18], L114661 = [1, 2, 5, 7, 14, 18, 19
178
EMILIO A. LAURET
Table 5. (continued) n = 7 q I indexes of I-isospectral families 44 {0} {29787, 29966, 33341, 33538}, {37639, 37643}, {37657, 37682}, (cont.) {37662, 37718}, {37719, 37761}, {37746, 37806}, {37782, 37813}, {37817, 37827}, {37820, 37832}, {37825, 37841}, {38084, 38085}, {38088, 38089}, {38093, 38094}, {104783, 105112}, {104883, 105994}, {105544, 105555}, {105776, 114047, 114214}, {106112, 107028}, {107201, 114413}, {107559, 114661}, {113758, 113937}, {113973, 114493}, {113983, 114179}, {117309, 118051}, {117330, 118649}, {117405, 118161}, {117460, 119016}, {118605, 123545}, {118906, 123896}, {126804, 126849}, {127086, 127283}, {127222, 127719}, {127392, 127416}, {127394, 127837}, {127454, 127539}, {127463, 127921}, {127468, 127912}, {128045, 139444, 139445}, {128235, 129439}, {128950, 139298}, {129460, 129461, 129463, 129466}, {129464, 129514, 129516, 129996}, {129468, 129473, 129476, 129484}, {129470, 129471, 129475, 129477}, {129474, 129478, 129485, 129491}, {129487, 129591, 129595, 130032}, {129495, 129988}, {129500, 129990}, {129502, 129986}, {129518, 130009}, {129541, 130017}, {129545, 130001}, {129598, 130067}, {129600, 129601, 129607},
L117309 = [1, 2, 6, 7, 11, 13, 17], L117330 = [1, 2, 6, 7, 11, 17, 18], L117405 = [1, 2, 6, 7, 13, 17, 22], L117460 = [1, 2, 6, 7, 17, 18, 22], L118051 = [1, 2, 6, 9, 11, 15, 17], L118161 = [1, 2, 6, 9, 15, 17, 22], L118408 = [1, 2, 6, 10, 14, 18, 22], L118605 = [1, 2, 6, 11, 13, 17, 18], L118649 = [1, 2, 6, 11, 15, 17, 18], L118906 = [1, 2, 6, 13, 17, 18, 22], L119016 = [1, 2, 6, 15, 17, 18, 22], L123545 = [1, 2, 10, 11, 15, 18, 19], L123896 = [1, 2, 10, 15, 18, 19, 22], L126804 = [1, 3, 4, 5, 8, 15, 20], L126849 = [1, 3, 4, 5, 9, 12, 20], L127086 = [1, 3, 4, 5, 15, 16, 19], L127222 = [1, 3, 4, 7, 8, 12, 20], L127283 = [1, 3, 4, 7, 9, 12, 13], L127392 = [1, 3, 4, 7, 11, 12, 13], L127394 = [1, 3, 4, 7, 11, 12, 16], L127416 = [1, 3, 4, 7, 11, 16, 17], L127454 = [1, 3, 4, 7, 12, 13, 22], L127463 = [1, 3, 4, 7, 12, 16, 17], L127468 = [1, 3, 4, 7, 12, 16, 22], L127539 = [1, 3, 4, 7, 16, 17, 22], L127719 = [1, 3, 4, 8, 9, 12, 20], L127837 = [1, 3, 4, 8, 11, 12, 13], L127912 = [1, 3, 4, 8, 12, 13, 22 L127921 = [1, 3, 4, 8, 12, 15, 17], L128045 = [1, 3, 4, 8, 16, 17, 20], L128235 = [1, 3, 4, 9, 13, 15, 20], L128950 = [1, 3, 4, 12, 13, 17, 20], L129439 = [1, 3, 5, 7, 8, 16, 19], L129460 = [1, 3, 5, 7, 9, 11, 13], L129461 = [1, 3, 5, 7, 9, 11, 15], L129463 = [1, 3, 5, 7, 9, 11, 17], L129464 = [1, 3, 5, 7, 9, 11, 19], L129466 = [1, 3, 5, 7, 9, 11, 21], L129468 = [1, 3, 5, 7, 9, 13, 15], L129470 = [1, 3, 5, 7, 9, 13, 17], L129471 = [1, 3, 5, 7, 9, 13, 19], L129473 = [1, 3, 5, 7, 9, 13, 21], L129474 = [1, 3, 5, 7, 9, 13, 22], L129475 = [1, 3, 5, 7, 9, 15, 17], L129476 = [1, 3, 5, 7, 9, 15, 19], L129477 = [1, 3, 5, 7, 9, 15, 21], L129478 = [1, 3, 5, 7, 9, 15, 22], L129484 = [1, 3, 5, 7, 9, 17, 21], L129485 = [1, 3, 5, 7, 9, 17, 22], L129487 = [1, 3, 5, 7, 9, 19, 22], L129491 = [1, 3, 5, 7, 9, 21, 22], L129495 = [1, 3, 5, 7, 11, 11, 13], L129500 = [1, 3, 5, 7, 11, 11, 19], L129502 = [1, 3, 5, 7, 11, 11, 21], L129514 = [1, 3, 5, 7, 11, 13, 15], L129516 = [1, 3, 5, 7, 11, 13, 17], L129518 = [1, 3, 5, 7, 11, 13, 22], L129522 = [1, 3, 5, 7, 11, 15, 21], L129531 = [1, 3, 5, 7, 11, 17, 19], L129540 = [1, 3, 5, 7, 11, 19, 21], L129541 = [1, 3, 5, 7, 11, 19, 22], L129545 = [1, 3, 5, 7, 11, 21, 22], L129591 = [1, 3, 5, 7, 13, 15, 22], L129595 = [1, 3, 5, 7, 13, 17, 22], L129598 = [1, 3, 5, 7, 13, 22, 22], L129600 = [1, 3, 5, 7, 15, 17, 19], L129601 = [1, 3, 5, 7, 15, 17, 21], L129607 = [1, 3, 5, 7, 15, 19, 21], L129609 = [1, 3, 5, 7, 15, 21, 22], L129634 = [1, 3, 5, 7, 17, 19, 22], L129653 = [1, 3, 5, 7, 19, 21, 22], L129654 = [1, 3, 5, 7, 19, 22, 22], L129660 = [1, 3, 5, 7, 21, 22, 22], L129986 = [1, 3, 5, 9, 11, 11, 13], L129988 = [1, 3, 5, 9, 11, 11, 15], L129990 = [1, 3, 5, 9, 11, 11, 17], L129991 = [1, 3, 5, 9, 11, 11, 19], L129993 = [1, 3, 5, 9, 11, 11, 21], L129996 = [1, 3, 5, 9, 11, 13, 15], L129998 = [1, 3, 5, 9, 11, 13, 17], L129999 = [1, 3, 5, 9, 11, 13, 19], L130001 = [1, 3, 5, 9, 11, 13, 22], L130009 = [1, 3, 5, 9, 11, 15, 22], L130016 = [1, 3, 5, 9, 11, 17, 21], L130017 = [1, 3, 5, 9, 11, 17, 22],
APPENDIX
179
Table 5. (continued) n = 7 q I indexes of I-isospectral families 44 {0} {129654, 130085}, {129660, 130043}, {129991, 130124}, {129993, 130135}, (cont.) {130020, 130232}, {130024, 130271}, {130090, 130550}, {130096, 130655}, {130100, 130102}, {130123, 131119}, {130126, 130138}, {130137, 131121}, {130230, 131126}, {130235, 130276}, {130275, 131132}, {130547, 131141}, {130554, 130662}, {130661, 131153}, {131357, 133260}, {131359, 146271}, {131366, 133265}, {131379, 146273}, {131402, 133277}, {131446, 146275}, {131498, 133299}, {131607, 146277}, {131703, 133334}, {132582, 141914}, {132803, 132856}, {132805, 141943}, {134055, 134058, 146278, 146769}, {134079, 134099, 146281, 146773}, {134180, 134250, 146287, 146782}, {134482, 134661, 146297, 146798}, {135214, 135594, 146312, 146823}, {139288, 139453}, {139347, 139669}, {157562, 157564}, {157563, 157565, 157574, 157576}, {157571, 157593}, {157575, 157577}, {157581, 157609}, {157587, 157600}, {157588, 157603}, {157599, 157604}, {157623, 157704}, {157628, 157786}, {157642, 157710}, {157644, 157713}, {157652, 157803}, {157711, 157716}, {157787, 157850}, {157806, 157903}, {157835, 157987}, {157871, 157994}, {157939, 158006}, {158011, 158027}, {158014, 158032}, {158019, 158041}, {158025, 158055}, {158550, 158551}, {158554, 158555}, {158559, 158560}, {158564, 158565} L130020 L130038 L130067 L130090 L130102 L130126 L130138 L130235 L130276 L130554 L130662 L131126 L131153 L131363 L131379 L131402 L131497 L131694 L132582 L132856 L133264 L133276 L133298 L133333 L134058 L134180 L134661
= [1, 3, 5, 9, 11, 19, 22], L130024 = [1, 3, 5, 9, 11, 21, 22], L130032 = [1, 3, 5, 9, 13, 15, 22], = [1, 3, 5, 9, 13, 17, 22], L130040 = [1, 3, 5, 9, 13, 19, 22], L130043 = [1, 3, 5, 9, 13, 22, 22], = [1, 3, 5, 9, 15, 22, 22], L130084 = [1, 3, 5, 9, 17, 21, 22], L130085 = [1, 3, 5, 9, 17, 22, 22], = [1, 3, 5, 9, 19, 22, 22], L130096 = [1, 3, 5, 9, 21, 22, 22], L130100 = [1, 3, 5, 11, 11, 11, 13], = [1, 3, 5, 11, 11, 11, 15], L130123 = [1, 3, 5, 11, 11, 13, 17], L130124 = [1, 3, 5, 11, 11, 13, 19], = [1, 3, 5, 11, 11, 13, 22], L130135 = [1, 3, 5, 11, 11, 15, 17], L130137 = [1, 3, 5, 11, 11, 15, 21], = [1, 3, 5, 11, 11, 15, 22], L130230 = [1, 3, 5, 11, 13, 17, 22], L130232 = [1, 3, 5, 11, 13, 19, 22], = [1, 3, 5, 11, 13, 22, 22], L130271 = [1, 3, 5, 11, 15, 17, 22], L130275 = [1, 3, 5, 11, 15, 21, 22], = [1, 3, 5, 11, 15, 22, 22], L130547 = [1, 3, 5, 13, 17, 22, 22], L130550 = [1, 3, 5, 13, 19, 22, 22], = [1, 3, 5, 13, 22, 22, 22], L130655 = [1, 3, 5, 15, 17, 22, 22], L130661 = [1, 3, 5, 15, 21, 22, 22], = [1, 3, 5, 15, 22, 22, 22], L131119 = [1, 3, 7, 9, 11, 11, 13], L131121 = [1, 3, 7, 9, 11, 11, 19], = [1, 3, 7, 9, 11, 13, 22], L131132 = [1, 3, 7, 9, 11, 19, 22], L131141 = [1, 3, 7, 9, 13, 22, 22], = [1, 3, 7, 9, 19, 22, 22], L131357 = [1, 3, 7, 11, 11, 11, 11], L131359 = [1, 3, 7, 11, 11, 11, 13], = [1, 3, 7, 11, 11, 11, 19], L131365 = [1, 3, 7, 11, 11, 11, 21], L131366 = [1, 3, 7, 11, 11, 11, 22], = [1, 3, 7, 11, 11, 13, 22], L131397 = [1, 3, 7, 11, 11, 19, 22], L131401 = [1, 3, 7, 11, 11, 21, 22], = [1, 3, 7, 11, 11, 22, 22], L131446 = [1, 3, 7, 11, 13, 22, 22], L131491 = [1, 3, 7, 11, 19, 22, 22], = [1, 3, 7, 11, 21, 22, 22], L131498 = [1, 3, 7, 11, 22, 22, 22], L131607 = [1, 3, 7, 13, 22, 22, 22], = [1, 3, 7, 19, 22, 22, 22], L131702 = [1, 3, 7, 21, 22, 22, 22], L131703 = [1, 3, 7, 22, 22, 22, 22], = [1, 3, 8, 11, 12, 13, 16], L132803 = [1, 3, 8, 12, 13, 16, 20], L132805 = [1, 3, 8, 12, 13, 16, 22], = [1, 3, 8, 12, 16, 17, 20], L133260 = [1, 3, 9, 11, 11, 11, 11], L133261 = [1, 3, 9, 11, 11, 11, 13], = [1, 3, 9, 11, 11, 11, 19], L133265 = [1, 3, 9, 11, 11, 11, 22], L133268 = [1, 3, 9, 11, 11, 13, 22], = [1, 3, 9, 11, 11, 19, 22], L133277 = [1, 3, 9, 11, 11, 22, 22], L133283 = [1, 3, 9, 11, 13, 22, 22], = [1, 3, 9, 11, 19, 22, 22], L133299 = [1, 3, 9, 11, 22, 22, 22], L133309 = [1, 3, 9, 13, 22, 22, 22], = [1, 3, 9, 19, 22, 22, 22], L133334 = [1, 3, 9, 22, 22, 22, 22], L134055 = [1, 3, 11, 11, 11, 11, 13], = [1, 3, 11, 11, 11, 11, 17], L134079 = [1, 3, 11, 11, 11, 13, 22], L134099 = [1, 3, 11, 11, 11, 17, 22], = [1, 3, 11, 11, 13, 22, 22], L134250 = [1, 3, 11, 11, 17, 22, 22], L134482 = [1, 3, 11, 13, 22, 22, 22], = [1, 3, 11, 17, 22, 22, 22], L135214 = [1, 3, 13, 22, 22, 22, 22], L135594 = [1, 3, 17, 22, 22, 22, 22],
180
EMILIO A. LAURET
Table 5. (continued) n = 7 q 44 (cont.)
I {0, 1}
indexes of I-isospectral families {713, 734}, {715, 737}, {5121, 5270}, {5123, 5273}, {5155, 5277}, {5159, 5285}, {27892, 27895}, {27918, 27920}, {27926, 28045}, {27935, 28062}, {27944, 28044}, {28479, 29084}, {28481, 29087}, {28513, 29091}, {28517, 29099}, {28607, 29106}, {28613, 29121}, {129463, 129466}, {129470, 129471}, {129475, 129477}, {129485, 129491}, {129514, 129516}, {129522, 129999}, {129531, 130016}, {129540, 129998}, {129591, 129595}, {129609, 130040}, {129634, 130084}, {129653, 130038}, {131363, 133261}, {131365, 133264}, {131397, 133268}, {131401, 133276}, {131491, 133283}, {131497, 133298}, {131694, 133309}, {131702, 133333} {0, 1, 2} {129473, 129476} {3, 4, 5, 6} {32070, 38091}, {118408, 158020}
L139288 = [1, 4, 5, 7, 8, 12, 20], L139298 = [1, 4, 5, 7, 8, 19, 20], L139347 = [1, 4, 5, 7, 12, 16, 20], L139444 = [1, 4, 5, 8, 9, 12, 16], L139445 = [1, 4, 5, 8, 9, 12, 20], L139453 = [1, 4, 5, 8, 9, 16, 20], L139669 = [1, 4, 5, 9, 12, 16, 20], L141914 = [1, 4, 7, 8, 11, 12, 13], L141943 = [1, 4, 7, 8, 12, 13, 22], L146271 = [1, 5, 7, 9, 11, 11, 11], L146273 = [1, 5, 7, 9, 11, 11, 22], L146275 = [1, 5, 7, 9, 11, 22, 22], L146277 = [1, 5, 7, 9, 22, 22, 22], L146278 = [1, 5, 7, 11, 11, 11, 11], L146281 = [1, 5, 7, 11, 11, 11, 22], L146287 = [1, 5, 7, 11, 11, 22, 22], L146297 = [1, 5, 7, 11, 22, 22, 22], L146312 = [1, 5, 7, 22, 22, 22, 22], L146769 = [1, 5, 9, 11, 11, 11, 11], L146773 = [1, 5, 9, 11, 11, 11, 22], L146782 = [1, 5, 9, 11, 11, 22, 22], L146798 = [1, 5, 9, 11, 22, 22, 22], L146823 = [1, 5, 9, 22, 22, 22, 22], L157562 = [2, 4, 6, 8, 10, 11, 14], L157563 = [2, 4, 6, 8, 10, 11, 16], L157564 = [2, 4, 6, 8, 10, 11, 18], L157565 = [2, 4, 6, 8, 10, 11, 20], L157571 = [2, 4, 6, 8, 11, 11, 18], L157574 = [2, 4, 6, 8, 11, 12, 14], L157575 = [2, 4, 6, 8, 11, 12, 16], L157576 = [2, 4, 6, 8, 11, 12, 18], L157577 = [2, 4, 6, 8, 11, 12, 20], L157581 = [2, 4, 6, 8, 11, 14, 20], L157587 = [2, 4, 6, 8, 11, 18, 20], L157588 = [2, 4, 6, 8, 11, 18, 22], L157593 = [2, 4, 6, 10, 11, 11, 12], L157599 = [2, 4, 6, 10, 11, 12, 14], L157600 = [2, 4, 6, 10, 11, 12, 16], L157603 = [2, 4, 6, 10, 11, 12, 22], L157604 = [2, 4, 6, 10, 11, 14, 16], L157609 = [2, 4, 6, 10, 11, 16, 20], L157623 = [2, 4, 6, 11, 11, 12, 16], L157628 = [2, 4, 6, 11, 11, 14, 20], L157642 = [2, 4, 6, 11, 12, 16, 18], L157644 = [2, 4, 6, 11, 12, 16, 22], L157652 = [2, 4, 6, 11, 14, 20, 22], L157704 = [2, 4, 8, 10, 11, 11, 12], L157710 = [2, 4, 8, 10, 11, 12, 14], L157711 = [2, 4, 8, 10, 11, 12, 16], L157713 = [2, 4, 8, 10, 11, 12, 22], L157716 = [2, 4, 8, 10, 11, 16, 20], L157786 = [2, 4, 10, 11, 11, 12, 14], L157787 = [2, 4, 10, 11, 11, 12, 16], L157803 = [2, 4, 10, 11, 12, 14, 22], L157806 = [2, 4, 10, 11, 12, 16, 22], L157835 = [2, 4, 11, 11, 11, 16, 18], L157850 = [2, 4, 11, 11, 12, 14, 20], L157871 = [2, 4, 11, 11, 16, 18, 22], L157903 = [2, 4, 11, 12, 14, 20, 22], L157939 = [2, 4, 11, 16, 18, 22, 22], L157987 = [2, 6, 8, 11, 11, 11, 16], L157994 = [2, 6, 8, 11, 11, 16, 22], L158006 = [2, 6, 8, 11, 16, 22, 22], L158011 = [2, 6, 10, 11, 11, 11, 11], L158014 = [2, 6, 10, 11, 11, 11, 22], L158019 = [2, 6, 10, 11, 11, 22, 22], L158020 = [2, 6, 10, 11, 14, 18, 22], L158025 = [2, 6, 10, 11, 22, 22, 22], L158027 = [2, 6, 11, 11, 11, 11, 14], L158032 = [2, 6, 11, 11, 11, 14, 22], L158041 = [2, 6, 11, 11, 14, 22, 22], L158055 = [2, 6, 11, 14, 22, 22, 22], L158550 = [4, 8, 11, 11, 11, 11, 12], L158551 = [4, 8, 11, 11, 11, 11, 16], L158554 = [4, 8, 11, 11, 11, 12, 22], L158555 = [4, 8, 11, 11, 11, 16, 22], L158559 = [4, 8, 11, 11, 12, 22, 22], L158560 = [4, 8, 11, 11, 16, 22, 22], L158564 = [4, 8, 11, 12, 22, 22, 22], L158565 = [4, 8, 11, 16, 22, 22, 22].
APPENDIX
181
7. Computational results for dimension 15 q = 6 : L52 = [0, 0, 1, 1, 1, 2, 2, 3], L88 = [0, 1, 1, 2, 2, 2, 3, 3]. q = 7 : L28 = [0, 0, 1, 1, 2, 2, 3, 3], L40 = [0, 1, 1, 1, 2, 2, 3, 3]. q = 9 : L21 = [0, 0, 0, 0, 1, 2, 3, 4], L36 = [0, 0, 0, 1, 1, 2, 3, 4], L40 = [0, 0, 0, 1, 2, 3, 3, 4], L56 = [0, 0, 1, 1, 1, 2, 3, 4], L62 = [0, 0, 1, 1, 2, 2, 3, 4], L65 = [0, 0, 1, 1, 2, 3, 3, 4], L69 = [0, 0, 1, 2, 3, 3, 3, 4], L85 = [0, 1, 1, 1, 1, 2, 3, 4], L94 = [0, 1, 1, 1, 2, 2, 3, 4], L97 = [0, 1, 1, 1, 2, 3, 3, 4], L98 = [0, 1, 1, 1, 2, 3, 4, 4], L103 = [0, 1, 1, 2, 2, 3, 3, 4], L104 = [0, 1, 1, 2, 2, 3, 4, 4], L106 = [0, 1, 1, 2, 3, 3, 3, 4], L110 = [0, 1, 2, 3, 3, 3, 3, 4]. q = 10 : L167 = [0, 0, 1, 1, 2, 3, 4, 5], L351 = [0, 1, 2, 2, 3, 4, 5, 5]. q = 11 : L9 = [0, 0, 0, 0, 0, 1, 2, 3], L10 = [0, 0, 0, 0, 0, 1, 2, 4], L50 = [0, 0, 0, 1, 2, 3, 4, 5], L91 = [0, 0, 1, 1, 2, 3, 4, 5], L141 = [0, 1, 1, 1, 2, 3, 4, 5], L153 = [0, 1, 1, 2, 2, 3, 3, 4], L154 = [0, 1, 1, 2, 2, 3, 3, 5], L155 = [0, 1, 1, 2, 2, 3, 4, 4], L156 = [0, 1, 1, 2, 2, 3, 4, 5], L158 = [0, 1, 1, 2, 3, 3, 4, 5], L256 = [1, 1, 2, 2, 3, 3, 4, 5], L257 = [1, 1, 2, 2, 3, 4, 4, 5]. q = 12 : L657 = [0, 1, 1, 2, 2, 4, 4, 6], L671 = [0, 1, 1, 2, 3, 3, 5, 5], L790 = [0, 1, 2, 2, 4, 4, 5, 6], L1056 = [1, 1, 1, 1, 3, 3, 5, 5], L1169 = [1, 1, 1, 3, 3, 5, 5, 5], L1341 = [1, 1, 3, 3, 4, 5, 5, 6]. q = 13 : L11 = [0, 0, 0, 0, 0, 1, 2, 3], L12 = [0, 0, 0, 0, 0, 1, 2, 4], L13 = [0, 0, 0, 0, 0, 1, 2, 5], L14 = [0, 0, 0, 0, 0, 1, 3, 4], L34 = [0, 0, 0, 0, 1, 2, 3, 4], L35 = [0, 0, 0, 0, 1, 2, 3, 5], L36 = [0, 0, 0, 0, 1, 2, 3, 6], L158 = [0, 0, 1, 2, 3, 4, 5, 6], L271 = [0, 1, 1, 2, 2, 3, 3, 5], L273 = [0, 1, 1, 2, 2, 3, 4, 4], L289 = [0, 1, 1, 2, 3, 4, 5, 6], L492 = [1, 1, 2, 2, 3, 3, 4, 4], L493 = [1, 1, 2, 2, 3, 3, 4, 5], L494 = [1, 1, 2, 2, 3, 3, 4, 6], L495 = [1, 1, 2, 2, 3, 3, 5, 5], L496 = [1, 1, 2, 2, 3, 3, 5, 6], L502 = [1, 1, 2, 2, 3, 4, 6, 6], L503 = [1, 1, 2, 2, 3, 5, 5, 6], L505 = [1, 1, 2, 3, 3, 4, 4, 5]. q = 14 : L66 = [0, 0, 0, 0, 1, 2, 3, 4], L68 = [0, 0, 0, 0, 1, 2, 3, 6], L198 = [0, 0, 0, 1, 2, 3, 4, 7], L200 = [0, 0, 0, 1, 2, 3, 6, 7], L477 = [0, 0, 1, 2, 3, 4, 5, 7], L479 = [0, 0, 1, 2, 3, 4, 7, 7], L481 = [0, 0, 1, 2, 3, 6, 7, 7], L806 = [0, 1, 1, 2, 3, 3, 4, 5], L810 = [0, 1, 1, 2, 3, 3, 5, 6], L865 = [0, 1, 1, 3, 3, 5, 5, 7], L975 = [0, 1, 2, 2, 3, 4, 4, 6], L979 = [0, 1, 2, 2, 3, 4, 6, 6], L990 = [0, 1, 2, 2, 4, 4, 6, 6], L1016 = [0, 1, 2, 3, 4, 6, 7, 7], L1017 = [0, 1, 2, 3, 4, 7, 7, 7], L1019 = [0, 1, 2, 3, 6, 7, 7, 7], L1101 = [0, 2, 2, 4, 4, 6, 6, 7], L1460 = [1, 1, 1, 3, 3, 5, 5, 7], L1621 = [1, 1, 2, 2, 3, 5, 6, 6], L1660 = [1, 1, 2, 3, 3, 4, 4, 6], L1664 = [1, 1, 2, 3, 3, 4, 5, 7], L1667 = [1, 1, 2, 3, 3, 5, 5, 7], L1668 = [1, 1, 2, 3, 3, 5, 6, 7], L1747 = [1, 1, 3, 3, 5, 5, 7, 7], L1925 = [1, 2, 2, 3, 4, 4, 6, 7], L1929 = [1, 2, 2, 3, 4, 6, 6, 7], L1977 = [1, 2, 3, 4, 7, 7, 7, 7], L1979 = [1, 2, 3, 6, 7, 7, 7, 7].
Table 6. m = 8 q 6 7 9 10 11 12 13
14
I {4, 5} {2, 3, 4, 5, 6} {7}
indexes of I-isospectral families {52, 88} {28, 40} {21, 40, 69, 110}, {36, 65, 106}, {56, 62, 97, 103}, {85, 94, 98, 104} {6, 7} {167, 351} {0} {9, 10}, {153, 154, 155}, {256, 257} {5, 6, 7} {50, 91, 141, 156, 158} {4, 5} {657, 790}, {671, 1341}, {1056, 1169} {0} {11, 12}, {13, 14}, {34, 35, 36}, {271, 273}, {492, 495}, {493, 494}, {496, 502}, {503, 505} {0, 1} {34, 35} {3, 4, 5, 6, 7} {158, 289} {0} {66, 68}, {198, 200}, {479, 481}, {806, 810}, {975, 979}, {1017, 1019}, {1621, 1660}, {1664, 1668}, {1925, 1929}, {1977, 1979} {3, 4, 5} {477, 1016} {2, 3, 4, 5, 6} {865, 1667}, {990, 1101}, {1460, 1747}
182
EMILIO A. LAURET
Table 6. (continued) m = 8 q 15
I {0}
indexes of I-isospectral families {18, 20}, {66, 72}, {175, 187}, {179, 191}, {408, 427}, {413, 433}, {686, 710}, {846, 874}, {852, 882}, {1609, 1649}, {1618, 1657}, {1625, 1667} {0, 5} {838, 868}, {1384, 1427} 16 {0} {78, 80}, {180, 181}, {233, 235}, {250, 252}, {256, 258}, {512, 513}, {517, 518}, {604, 606}, {621, 623}, {625, 629}, {627, 631}, {655, 657}, {661, 663}, {668, 670}, {1155, 1158}, {1248, 1249}, {1253, 1254}, {1259, 1260}, {1391, 1393}, {1408, 1410}, {1412, 1416}, {1414, 1418}, {1443, 1445}, {1447, 1451}, {1449, 1453}, {1459, 1463}, {1498, 1500}, {1504, 1506}, {1511, 1513}, {1518, 1520}, {2560, 2563}, {2572, 2576}, {2715, 2716}, {2720, 2721}, {2726, 2727}, {2733, 2734}, {2921, 2923}, {2938, 2940}, {2942, 2946}, {2944, 2948}, {2973, 2975}, {2977, 2981}, {2979, 2983}, {2985, 2991}, {2987, 2993}, {2989, 2995}, {3032, 3034}, {3036, 3040}, {3038, 3042}, {3046, 3050}, {3048, 3052}, {3057, 3061}, {3059, 3063}, {3111, 3113}, {3117, 3119}, {3124, 3126}, {3131, 3133}, {3138, 3140} {0, 7} {1457, 1461}, {2569, 2573} q = 15 : L18 = [0, 0, 0, 0, 0, 1, 2, 6], L20 = [0, 0, 0, 0, 0, 1, 3, 4], L66 = [0, 0, 0, 0, 1, 2, 5, 6], L72 = [0, 0, 0, 0, 1, 3, 4, 5], L175 = [0, 0, 0, 1, 2, 3, 6, 6], L179 = [0, 0, 0, 1, 2, 5, 5, 6], L187 = [0, 0, 0, 1, 3, 3, 4, 6], L191 = [0, 0, 0, 1, 3, 4, 5, 5], L408 = [0, 0, 1, 2, 3, 5, 6, 6], L413 = [0, 0, 1, 2, 5, 5, 5, 6], L427 = [0, 0, 1, 3, 3, 4, 5, 6], L433 = [0, 0, 1, 3, 4, 5, 5, 5], L686 = [0, 1, 1, 2, 2, 4, 6, 7], L710 = [0, 1, 1, 2, 3, 4, 4, 7], L838 = [0, 1, 2, 3, 3, 6, 6, 6], L846 = [0, 1, 2, 3, 5, 5, 6, 6], L852 = [0, 1, 2, 5, 5, 5, 5, 6], L868 = [0, 1, 3, 3, 3, 4, 6, 6], L874 = [0, 1, 3, 3, 4, 5, 5, 6], L882 = [0, 1, 3, 4, 5, 5, 5, 5], L1384 = [1, 1, 2, 2, 4, 5, 6, 7], L1427 = [1, 1, 2, 3, 4, 4, 5, 7], L1609 = [1, 2, 3, 3, 5, 6, 6, 6], L1618 = [1, 2, 3, 5, 5, 5, 6, 6], L1625 = [1, 2, 5, 5, 5, 5, 5, 6], L1649 = [1, 3, 3, 3, 4, 5, 6, 6], L1657 = [1, 3, 3, 4, 5, 5, 5, 6], L1667 = [1, 3, 4, 5, 5, 5, 5, 5]. q = 16 : L78 = [0, 0, 0, 0, 1, 2, 3, 5], L80 = [0, 0, 0, 0, 1, 2, 3, 7], L180 = [0, 0, 0, 1, 1, 3, 3, 5], L181 = [0, 0, 0, 1, 1, 3, 3, 7], L233 = [0, 0, 0, 1, 2, 2, 3, 5], L235 = [0, 0, 0, 1, 2, 2, 3, 7], L250 = [0, 0, 0, 1, 2, 3, 4, 5], L252 = [0, 0, 0, 1, 2, 3, 4, 7], L256 = [0, 0, 0, 1, 2, 3, 5, 8], L258 = [0, 0, 0, 1, 2, 3, 7, 8], L512 = [0, 0, 1, 1, 3, 3, 4, 5], L513 = [0, 0, 1, 1, 3, 3, 4, 7], L517 = [0, 0, 1, 1, 3, 3, 5, 8], L518 = [0, 0, 1, 1, 3, 3, 7, 8], L604 = [0, 0, 1, 2, 2, 2, 3, 5], L606 = [0, 0, 1, 2, 2, 2, 3, 7], L621 = [0, 0, 1, 2, 2, 3, 4, 5], L623 = [0, 0, 1, 2, 2, 3, 4, 7], L625 = [0, 0, 1, 2, 2, 3, 5, 6], L627 = [0, 0, 1, 2, 2, 3, 5, 8], L629 = [0, 0, 1, 2, 2, 3, 6, 7], L631 = [0, 0, 1, 2, 2, 3, 7, 8], L655 = [0, 0, 1, 2, 3, 4, 4, 5], L657 = [0, 0, 1, 2, 3, 4, 4, 7], L661 = [0, 0, 1, 2, 3, 4, 5, 8], L663 = [0, 0, 1, 2, 3, 4, 7, 8], L668 = [0, 0, 1, 2, 3, 5, 8, 8], L670 = [0, 0, 1, 2, 3, 7, 8, 8], L1155 = [0, 1, 1, 2, 3, 3, 5, 6], L1158 = [0, 1, 1, 2, 3, 3, 6, 7], L1248 = [0, 1, 1, 3, 3, 4, 4, 5], L1249 = [0, 1, 1, 3, 3, 4, 4, 7], L1253 = [0, 1, 1, 3, 3, 4, 5, 8], L1254 = [0, 1, 1, 3, 3, 4, 7, 8], L1259 = [0, 1, 1, 3, 3, 5, 8, 8], L1260 = [0, 1, 1, 3, 3, 7, 8, 8], L1391 = [0, 1, 2, 2, 2, 2, 3, 5], L1393 = [0, 1, 2, 2, 2, 2, 3, 7], L1408 = [0, 1, 2, 2, 2, 3, 4, 5], L1410 = [0, 1, 2, 2, 2, 3, 4, 7], L1412 = [0, 1, 2, 2, 2, 3, 5, 6], L1414 = [0, 1, 2, 2, 2, 3, 5, 8], L1416 = [0, 1, 2, 2, 2, 3, 6, 7], L1418 = [0, 1, 2, 2, 2, 3, 7, 8], L1443 = [0, 1, 2, 2, 3, 4, 4, 5], L1445 = [0, 1, 2, 2, 3, 4, 4, 7], L1447 = [0, 1, 2, 2, 3, 4, 5, 6], L1449 = [0, 1, 2, 2, 3, 4, 5, 8], L1451 = [0, 1, 2, 2, 3, 4, 6, 7], L1453 = [0, 1, 2, 2, 3, 4, 7, 8], L1457 = [0, 1, 2, 2, 3, 5, 6, 8], L1459 = [0, 1, 2, 2, 3, 5, 8, 8], L1461 = [0, 1, 2, 2, 3, 6, 7, 8], L1463 = [0, 1, 2, 2, 3, 7, 8, 8], L1498 = [0, 1, 2, 3, 4, 4, 4, 5], L1500 = [0, 1, 2, 3, 4, 4, 4, 7], L1504 = [0, 1, 2, 3, 4, 4, 5, 8], L1506 = [0, 1, 2, 3, 4, 4, 7, 8], L1511 = [0, 1, 2, 3, 4, 5, 8, 8], L1513 = [0, 1, 2, 3, 4, 7, 8, 8], L1518 = [0, 1, 2, 3, 5, 8, 8, 8], L1520 = [0, 1, 2, 3, 7, 8, 8, 8], L2560 = [1, 1, 2, 3, 3, 4, 5, 6], L2563 = [1, 1, 2, 3, 3, 4, 6, 7], L2569 = [1, 1, 2, 3, 3, 5, 5, 7], L2572 = [1, 1, 2, 3, 3, 5, 6, 8], L2573 = [1, 1, 2, 3, 3, 5, 7, 7], L2576 = [1, 1, 2, 3, 3, 6, 7, 8], L2715 = [1, 1, 3, 3, 4, 4, 4, 5], L2716 = [1, 1, 3, 3, 4, 4, 4, 7], L2720 = [1, 1, 3, 3, 4, 4, 5, 8], L2721 = [1, 1, 3, 3, 4, 4, 7, 8], L2726 =
APPENDIX
183
Table 6. (continued) m = 8 q 17
I {0}
indexes of I-isospectral families {16, 17}, {18, 19}, {55, 56, 58}, {62, 63}, {156, 157, 158, 159, 160}, {161, 162}, {376, 377, 378, 379} {0, 1} {57, 59}, {157, 158}, {376, 377, 378} {0, 1, 2} {377, 378}
[1, 1, 3, 3, 4, 5, 8, 8], L2727 = [1, 1, 3, 3, 4, 7, 8, 8], L2733 = [1, 1, 3, 3, 5, 8, 8, 8], L2734 = [1, 1, 3, 3, 7, 8, 8, 8], L2921 = [1, 2, 2, 2, 2, 2, 3, 5], L2923 = [1, 2, 2, 2, 2, 2, 3, 7], L2938 = [1, 2, 2, 2, 2, 3, 4, 5], L2940 = [1, 2, 2, 2, 2, 3, 4, 7], L2942 = [1, 2, 2, 2, 2, 3, 5, 6], L2944 = [1, 2, 2, 2, 2, 3, 5, 8], L2946 = [1, 2, 2, 2, 2, 3, 6, 7], L2948 = [1, 2, 2, 2, 2, 3, 7, 8], L2973 = [1, 2, 2, 2, 3, 4, 4, 5], L2975 = [1, 2, 2, 2, 3, 4, 4, 7], L2977 = [1, 2, 2, 2, 3, 4, 5, 6], L2979 = [1, 2, 2, 2, 3, 4, 5, 8], L2981 = [1, 2, 2, 2, 3, 4, 6, 7], L2983 = [1, 2, 2, 2, 3, 4, 7, 8], L2985 = [1, 2, 2, 2, 3, 5, 6, 6], L2987 = [1, 2, 2, 2, 3, 5, 6, 8], L2989 = [1, 2, 2, 2, 3, 5, 8, 8], L2991 = [1, 2, 2, 2, 3, 6, 6, 7], L2993 = [1, 2, 2, 2, 3, 6, 7, 8], L2995 = [1, 2, 2, 2, 3, 7, 8, 8], L3032 = [1, 2, 2, 3, 4, 4, 4, 5], L3034 = [1, 2, 2, 3, 4, 4, 4, 7], L3036 = [1, 2, 2, 3, 4, 4, 5, 6], L3038 = [1, 2, 2, 3, 4, 4, 5, 8], L3040 = [1, 2, 2, 3, 4, 4, 6, 7], L3042 = [1, 2, 2, 3, 4, 4, 7, 8], L3046 = [1, 2, 2, 3, 4, 5, 6, 8], L3048 = [1, 2, 2, 3, 4, 5, 8, 8], L3050 = [1, 2, 2, 3, 4, 6, 7, 8], L3052 = [1, 2, 2, 3, 4, 7, 8, 8], L3057 = [1, 2, 2, 3, 5, 6, 8, 8], L3059 = [1, 2, 2, 3, 5, 8, 8, 8], L3061 = [1, 2, 2, 3, 6, 7, 8, 8], L3063 = [1, 2, 2, 3, 7, 8, 8, 8], L3111 = [1, 2, 3, 4, 4, 4, 4, 5], L3113 = [1, 2, 3, 4, 4, 4, 4, 7], L3117 = [1, 2, 3, 4, 4, 4, 5, 8], L3119 = [1, 2, 3, 4, 4, 4, 7, 8], L3124 = [1, 2, 3, 4, 4, 5, 8, 8], L3126 = [1, 2, 3, 4, 4, 7, 8, 8], L3131 = [1, 2, 3, 4, 5, 8, 8, 8], L3133 = [1, 2, 3, 4, 7, 8, 8, 8], L3138 = [1, 2, 3, 5, 8, 8, 8, 8], L3140 = [1, 2, 3, 7, 8, 8, 8, 8]. q = 17 : L16 = [0, 0, 0, 0, 0, 1, 2, 5], L17 = [0, 0, 0, 0, 0, 1, 2, 6], L18 = [0, 0, 0, 0, 0, 1, 2, 7], L19 = [0, 0, 0, 0, 0, 1, 3, 4], L55 = [0, 0, 0, 0, 1, 2, 3, 5], L56 = [0, 0, 0, 0, 1, 2, 3, 6], L57 = [0, 0, 0, 0, 1, 2, 3, 7], L58 = [0, 0, 0, 0, 1, 2, 3, 8], L59 = [0, 0, 0, 0, 1, 2, 4, 5], L62 = [0, 0, 0, 0, 1, 2, 6, 7], L63 = [0, 0, 0, 0, 1, 3, 4, 5], L156 = [0, 0, 0, 1, 2, 3, 4, 5], L157 = [0, 0, 0, 1, 2, 3, 4, 6], L158 = [0, 0, 0, 1, 2, 3, 4, 7], L159 = [0, 0, 0, 1, 2, 3, 4, 8], L160 = [0, 0, 0, 1, 2, 3, 5, 6], L161 = [0, 0, 0, 1, 2, 3, 5, 8], L162 = [0, 0, 0, 1, 2, 3, 6, 7], L376 = [0, 0, 1, 2, 3, 4, 5, 6], L377 = [0, 0, 1, 2, 3, 4, 5, 7], L378 = [0, 0, 1, 2, 3, 4, 5, 8], L379 = [0, 0, 1, 2, 3, 4, 6, 8]. q = 18 : L117 = [0, 0, 0, 0, 1, 2, 4, 5], L119 = [0, 0, 0, 0, 1, 2, 4, 7], L407 = [0, 0, 0, 1, 2, 3, 4, 5], L409 = [0, 0, 0, 1, 2, 3, 4, 7], L429 = [0, 0, 0, 1, 2, 4, 5, 6], L432 = [0, 0, 0, 1, 2, 4, 5, 9], L434 = [0, 0, 0, 1, 2, 4, 6, 7], L435 = [0, 0, 0, 1, 2, 4, 6, 8], L437 = [0, 0, 0, 1, 2, 4, 7, 9], L498 = [0, 0, 0, 1, 3, 5, 7, 9], L603 = [0, 0, 0, 2, 3, 4, 6, 8], L612 = [0, 0, 0, 2, 4, 6, 8, 9], L861 = [0, 0, 1, 1, 2, 4, 6, 8], L956 = [0, 0, 1, 1, 3, 5, 7, 9], L1143 = [0, 0, 1, 2, 2, 4, 6, 8], L1182 = [0, 0, 1, 2, 3, 3, 4, 5], L1184 = [0, 0, 1, 2, 3, 3, 4, 7], L1204 = [0, 0, 1, 2, 3, 4, 5, 6], L1207 = [0, 0, 1, 2, 3, 4, 5, 9], L1209 = [0, 0, 1, 2, 3, 4, 6, 7], L1210 = [0, 0, 1, 2, 3, 4, 6, 8], L1212 = [0, 0, 1, 2, 3, 4, 7, 9], L1219 = [0, 0, 1, 2, 3, 5, 7, 9], L1246 = [0, 0, 1, 2, 4, 4, 6, 8], L1251 = [0, 0, 1, 2, 4, 5, 6, 6], L1253 = [0, 0, 1, 2, 4, 5, 6, 8], L1254 = [0, 0, 1, 2, 4, 5, 6, 9], L1256 = [0, 0, 1, 2, 4, 5, 7, 9], L1258 = [0, 0, 1, 2, 4, 5, 9, 9], L1260 = [0, 0, 1, 2, 4, 6, 6, 7], L1261 = [0, 0, 1, 2, 4, 6, 6, 8], L1263 = [0, 0, 1, 2, 4, 6, 7, 9], L1264 = [0, 0, 1, 2, 4, 6, 8, 8], L1265 = [0, 0, 1, 2, 4, 6, 8, 9], L1267 = [0, 0, 1, 2, 4, 7, 9, 9], L1340 = [0, 0, 1, 3, 3, 5, 7, 9], L1381 = [0, 0, 1, 3, 5, 6, 7, 9], L1383 = [0, 0, 1, 3, 5, 7, 9, 9], L1529 = [0, 0, 2, 2, 3, 4, 6, 8], L1544 = [0, 0, 2, 2, 4, 6, 8, 9], L1566 = [0, 0, 2, 3, 3, 4, 6, 8], L1575 = [0, 0, 2, 3, 4, 6, 6, 8], L1577 = [0, 0, 2, 3, 4, 6, 8, 9], L1587 = [0, 0, 2, 4, 6, 6, 8, 9], L1589 = [0, 0, 2, 4, 6, 8, 9, 9], L1840 = [0, 1, 1, 1, 2, 4, 6, 8], L1943 = [0, 1, 1, 1, 3, 5, 7, 9], L2161 = [0, 1, 1, 2, 2, 4, 6, 8], L2243 = [0, 1, 1, 2, 3, 4, 6, 8], L2260 = [0, 1, 1, 2, 3, 5, 7, 9], L2296 = [0, 1, 1, 2, 4, 4, 6, 8], L2304 = [0, 1, 1, 2, 4, 5, 5, 7], L2309 = [0, 1, 1, 2, 4, 5, 6, 8], L2311 = [0, 1, 1, 2, 4, 5, 7, 7], L2319 = [0, 1, 1, 2, 4, 6, 6, 8], L2322 = [0, 1, 1, 2, 4, 6, 7, 8], L2324 = [0, 1, 1, 2, 4, 6, 8, 8], L2325 = [0, 1, 1, 2, 4, 6, 8, 9], L2446 = [0, 1, 1, 3, 3, 5, 7, 9], L2494 = [0, 1, 1, 3, 4, 5, 7, 9], L2518 = [0, 1, 1, 3, 5, 5, 7, 9], L2525 = [0, 1, 1, 3, 5, 6, 7, 9], L2530 = [0, 1, 1, 3, 5, 7, 8, 9], L2531 = [0, 1, 1, 3, 5, 7, 9, 9], L2797 = [0, 1, 2, 2, 2, 4, 6, 8], L2867 = [0, 1, 2, 2, 3, 4, 6, 8], L2879 = [0, 1, 2, 2, 3, 5, 7, 9], L2905 = [0, 1, 2, 2, 4, 4, 5, 8], L2909 = [0, 1, 2, 2, 4, 4, 6, 8], L2911 = [0, 1, 2, 2, 4, 4, 7, 8], L2918 = [0, 1, 2, 2, 4, 5, 6, 8], L2926 = [0, 1, 2, 2, 4, 6, 6, 8], L2928 = [0, 1, 2, 2, 4, 6, 7, 8], L2930 = [0, 1, 2, 2, 4, 6, 8, 8], L2931 =
184
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 18 {0} {117, 119}, {407, 409}, {429, 434}, {432, 437}, {1182, 1184}, {1204, 1209}, {1207, 1212}, {1251, 1260}, {1254, 1263}, {1258, 1267}, {2304, 2311}, {2905, 2911}, {2985, 2987}, {3007, 3012}, {3010, 3015}, {3054, 3063}, {3057, 3066}, {3061, 3070}, {3136, 3149}, {3139, 3152}, {3143, 3156}, {3147, 3161}, {5233, 5482}, {5373, 5380}, {5510, 5522}, {5515, 5528}, {6577, 6583}, {6665, 6676}, {6670, 6681}, {6784, 6786}, {6806, 6811}, {6809, 6814}, {6853, 6862}, {6856, 6865}, {6860, 6869}, {6935, 6948}, {6938, 6951}, {6942, 6955}, {6946, 6960}, {7062, 7079}, {7065, 7082}, {7069, 7086}, {7073, 7091}, {7077, 7097} [0, 1, 2, 2, 4, 6, 8, 9], L2985 = [0, 1, 2, 3, 3, 3, 4, 5], L2987 = [0, 1, 2, 3, 3, 3, 4, 7], L3007 = [0, 1, 2, 3, 3, 4, 5, 6], L3010 = [0, 1, 2, 3, 3, 4, 5, 9], L3012 = [0, 1, 2, 3, 3, 4, 6, 7], L3013 = [0, 1, 2, 3, 3, 4, 6, 8], L3015 = [0, 1, 2, 3, 3, 4, 7, 9], L3022 = [0, 1, 2, 3, 3, 5, 7, 9], L3027 = [0, 1, 2, 3, 3, 6, 6, 9], L3049 = [0, 1, 2, 3, 4, 4, 6, 8], L3054 = [0, 1, 2, 3, 4, 5, 6, 6], L3056 = [0, 1, 2, 3, 4, 5, 6, 8], L3057 = [0, 1, 2, 3, 4, 5, 6, 9], L3058 = [0, 1, 2, 3, 4, 5, 7, 8], L3059 = [0, 1, 2, 3, 4, 5, 7, 9], L3060 = [0, 1, 2, 3, 4, 5, 8, 9], L3061 = [0, 1, 2, 3, 4, 5, 9, 9], L3063 = [0, 1, 2, 3, 4, 6, 6, 7], L3064 = [0, 1, 2, 3, 4, 6, 6, 8], L3066 = [0, 1, 2, 3, 4, 6, 7, 9], L3067 = [0, 1, 2, 3, 4, 6, 8, 8], L3068 = [0, 1, 2, 3, 4, 6, 8, 9], L3070 = [0, 1, 2, 3, 4, 7, 9, 9], L3078 = [0, 1, 2, 3, 5, 6, 7, 9], L3080 = [0, 1, 2, 3, 5, 7, 9, 9], L3116 = [0, 1, 2, 4, 4, 4, 6, 8], L3122 = [0, 1, 2, 4, 4, 5, 6, 8], L3127 = [0, 1, 2, 4, 4, 6, 6, 8], L3129 = [0, 1, 2, 4, 4, 6, 8, 8], L3130 = [0, 1, 2, 4, 4, 6, 8, 9], L3136 = [0, 1, 2, 4, 5, 6, 6, 6], L3138 = [0, 1, 2, 4, 5, 6, 6, 8], L3139 = [0, 1, 2, 4, 5, 6, 6, 9], L3140 = [0, 1, 2, 4, 5, 6, 7, 8], L3141 = [0, 1, 2, 4, 5, 6, 7, 9], L3142 = [0, 1, 2, 4, 5, 6, 8, 9], L3143 = [0, 1, 2, 4, 5, 6, 9, 9], L3146 = [0, 1, 2, 4, 5, 8, 9, 9], L3147 = [0, 1, 2, 4, 5, 9, 9, 9], L3149 = [0, 1, 2, 4, 6, 6, 6, 7], L3150 = [0, 1, 2, 4, 6, 6, 6, 8], L3152 = [0, 1, 2, 4, 6, 6, 7, 9], L3153 = [0, 1, 2, 4, 6, 6, 8, 8], L3154 = [0, 1, 2, 4, 6, 6, 8, 9], L3156 = [0, 1, 2, 4, 6, 7, 9, 9], L3157 = [0, 1, 2, 4, 6, 8, 8, 8], L3158 = [0, 1, 2, 4, 6, 8, 8, 9], L3159 = [0, 1, 2, 4, 6, 8, 9, 9], L3161 = [0, 1, 2, 4, 7, 9, 9, 9], L3248 = [0, 1, 3, 3, 3, 5, 7, 9], L3278 = [0, 1, 3, 3, 4, 6, 6, 9], L3289 = [0, 1, 3, 3, 5, 6, 7, 9], L3291 = [0, 1, 3, 3, 5, 7, 9, 9], L3356 = [0, 1, 3, 5, 6, 6, 7, 9], L3358 = [0, 1, 3, 5, 6, 7, 9, 9], L3360 = [0, 1, 3, 5, 7, 9, 9, 9], L3549 = [0, 2, 2, 2, 3, 4, 6, 8], L3568 = [0, 2, 2, 2, 4, 6, 8, 9], L3600 = [0, 2, 2, 3, 3, 4, 6, 8], L3612 = [0, 2, 2, 3, 4, 4, 6, 8], L3618 = [0, 2, 2, 3, 4, 6, 6, 8], L3620 = [0, 2, 2, 3, 4, 6, 8, 9], L3634 = [0, 2, 2, 4, 4, 6, 8, 9], L3640 = [0, 2, 2, 4, 6, 6, 8, 9], L3642 = [0, 2, 2, 4, 6, 8, 9, 9], L3666 = [0, 2, 3, 3, 3, 4, 6, 8], L3675 = [0, 2, 3, 3, 4, 6, 6, 8], L3677 = [0, 2, 3, 3, 4, 6, 8, 9], L3687 = [0, 2, 3, 4, 6, 6, 6, 8], L3689 = [0, 2, 3, 4, 6, 6, 8, 9], L3691 = [0, 2, 3, 4, 6, 8, 9, 9], L3702 = [0, 2, 4, 6, 6, 6, 8, 9], L3704 = [0, 2, 4, 6, 6, 8, 9, 9], L3706 = [0, 2, 4, 6, 8, 9, 9, 9], L4061 = [1, 1, 1, 1, 3, 5, 7, 9], L4390 = [1, 1, 1, 2, 3, 5, 7, 9], L4597 = [1, 1, 1, 3, 3, 5, 7, 9], L4652 = [1, 1, 1, 3, 4, 5, 7, 9], L4684 = [1, 1, 1, 3, 5, 5, 7, 9], L4694 = [1, 1, 1, 3, 5, 6, 7, 9], L4699 = [1, 1, 1, 3, 5, 7, 7, 9], L4701 = [1, 1, 1, 3, 5, 7, 8, 9], L4702 = [1, 1, 1, 3, 5, 7, 9, 9], L5135 = [1, 1, 2, 2, 3, 5, 7, 9], L5188 = [1, 1, 2, 2, 4, 5, 7, 8], L5233 = [1, 1, 2, 2, 5, 7, 8, 8], L5329 = [1, 1, 2, 3, 3, 5, 7, 9], L5373 = [1, 1, 2, 3, 4, 5, 5, 7], L5380 = [1, 1, 2, 3, 4, 5, 7, 7], L5382 = [1, 1, 2, 3, 4, 5, 7, 9], L5408 = [1, 1, 2, 3, 5, 5, 7, 9], L5416 = [1, 1, 2, 3, 5, 6, 7, 9], L5421 = [1, 1, 2, 3, 5, 7, 7, 9], L5423 = [1, 1, 2, 3, 5, 7, 8, 9], L5424 = [1, 1, 2, 3, 5, 7, 9, 9], L5482 = [1, 1, 2, 4, 4, 5, 5, 8], L5488 = [1, 1, 2, 4, 4, 5, 7, 8], L5510 = [1, 1, 2, 4, 5, 5, 6, 7], L5515 = [1, 1, 2, 4, 5, 5, 7, 9], L5522 = [1, 1, 2, 4, 5, 6, 7, 7], L5528 = [1, 1, 2, 4, 5, 7, 7, 9], L5705 = [1, 1, 3, 3, 3, 5, 7, 9], L5753 = [1, 1, 3, 3, 4, 5, 7, 9], L5777 = [1, 1, 3, 3, 5, 5, 7, 9], L5784 = [1, 1, 3, 3, 5, 6, 7, 9], L5789 = [1, 1, 3, 3, 5, 7, 8, 9], L5790 = [1, 1, 3, 3, 5, 7, 9, 9], L5848 = [1, 1, 3, 4, 4, 5, 7, 9], L5871 = [1, 1, 3, 4, 5, 5, 7, 9], L5878 = [1, 1, 3, 4, 5, 6, 7, 9], L5883 = [1, 1, 3, 4, 5, 7, 8, 9], L5884 = [1, 1, 3, 4, 5, 7, 9, 9], L5918 = [1, 1, 3, 5, 5, 6, 7, 9], L5920 = [1, 1, 3, 5, 5, 7, 7, 9], L5921 = [1, 1, 3, 5, 5, 7, 9, 9], L5928 = [1, 1, 3, 5, 6, 6, 7, 9], L5933 = [1, 1, 3, 5, 6, 7, 8, 9], L5934 = [1, 1, 3, 5, 6, 7, 9, 9], L5940 = [1, 1, 3, 5, 7, 8, 8, 9], L5941 = [1, 1, 3, 5, 7, 8, 9, 9], L5942 = [1, 1, 3, 5, 7, 9, 9, 9], L6397 = [1, 2, 2, 2, 3, 5, 7, 9], L6551 = [1, 2, 2, 3, 3, 5, 7, 9], L6577 = [1, 2, 2, 3, 4, 4, 5, 8], L6583 = [1, 2, 2, 3, 4, 4, 7, 8], L6593 =
APPENDIX
185
Table 6. (continued) m = 8 q 18 (cont.)
I {4} {5} {4, 5} {7}
indexes of I-isospectral families {1256, 3146} {3060, 3141} {3027, 3278}, {3058, 7070}, {5188, 5488} {435, 1261, 3150}, {498, 1381, 3356, 7409}, {603, 612, 1575, 1587, 3687, 3702}, {861, 1253, 2319, 3138}, {956, 2525, 5928}, {1143, 1246, 1264, 2926, 3127, 3153}, {1210, 1265, 3064, 3154}, {1219, 3078, 6969}, {1340, 1383, 3289, 3358, 7308, 7411}, {1529, 1544, 3618, 3640}, {1566, 1577, 1589, 3675, 3689, 3704}, {1840, 2309, 2322, 3140}, {1943, 2518, 4694, 5918}, {2161, 2296, 2324, 2918, 2928, 3122}, {2243, 2325, 3056, 3142}, {2260, 2494, 2530, 5416, 5878, 5933}, {2446, 2531, 5784, 5934}, {2797, 2909, 2930, 3116, 3129, 3157}, {2867, 2931, 3049, 3067, 3130, 3158}, {2879, 3059, 6617, 6940}, {3013, 3068, 3159}, {3022, 3080, 6877, 6971}, {3248, 3291, 3360, 7241, 7310, 7413}, {3549, 3568, 3612, 3634}, {3600, 3620, 3642}, {3666, 3677, 3691, 3706}, {4061, 4684, 4699, 5920}, {4390, 4652, 4701, 5408, 5421, 5871}, {4597, 4702, 5777, 5921}, {5135, 5382, 5423, 5848, 5883, 5940}, {5329, 5424, 5753, 5789, 5884, 5941}, {5705, 5790, 5942}, {6397, 6593, 6620, 6943}, {6551, 6621, 6858, 6944}, {6821, 6879, 6973}, {7200, 7243, 7312, 7415}
[1, 2, 2, 3, 4, 5, 7, 9], L6617 = [1, 2, 2, 3, 5, 6, 7, 9], L6620 = [1, 2, 2, 3, 5, 7, 8, 9], L6621 = [1, 2, 2, 3, 5, 7, 9, 9], L6665 = [1, 2, 2, 4, 4, 5, 6, 8], L6670 = [1, 2, 2, 4, 4, 5, 8, 9], L6676 = [1, 2, 2, 4, 4, 6, 7, 8], L6681 = [1, 2, 2, 4, 4, 7, 8, 9], L6784 = [1, 2, 3, 3, 3, 3, 4, 5], L6786 = [1, 2, 3, 3, 3, 3, 4, 7], L6806 = [1, 2, 3, 3, 3, 4, 5, 6], L6809 = [1, 2, 3, 3, 3, 4, 5, 9], L6811 = [1, 2, 3, 3, 3, 4, 6, 7], L6814 = [1, 2, 3, 3, 3, 4, 7, 9], L6821 = [1, 2, 3, 3, 3, 5, 7, 9], L6853 = [1, 2, 3, 3, 4, 5, 6, 6], L6856 = [1, 2, 3, 3, 4, 5, 6, 9], L6858 = [1, 2, 3, 3, 4, 5, 7, 9], L6860 = [1, 2, 3, 3, 4, 5, 9, 9], L6862 = [1, 2, 3, 3, 4, 6, 6, 7], L6865 = [1, 2, 3, 3, 4, 6, 7, 9], L6869 = [1, 2, 3, 3, 4, 7, 9, 9], L6877 = [1, 2, 3, 3, 5, 6, 7, 9], L6879 = [1, 2, 3, 3, 5, 7, 9, 9], L6935 = [1, 2, 3, 4, 5, 6, 6, 6], L6938 = [1, 2, 3, 4, 5, 6, 6, 9], L6940 = [1, 2, 3, 4, 5, 6, 7, 9], L6942 = [1, 2, 3, 4, 5, 6, 9, 9], L6943 = [1, 2, 3, 4, 5, 7, 8, 9], L6944 = [1, 2, 3, 4, 5, 7, 9, 9], L6946 = [1, 2, 3, 4, 5, 9, 9, 9], L6948 = [1, 2, 3, 4, 6, 6, 6, 7], L6951 = [1, 2, 3, 4, 6, 6, 7, 9], L6955 = [1, 2, 3, 4, 6, 7, 9, 9], L6960 = [1, 2, 3, 4, 7, 9, 9, 9], L6969 = [1, 2, 3, 5, 6, 6, 7, 9], L6971 = [1, 2, 3, 5, 6, 7, 9, 9], L6973 = [1, 2, 3, 5, 7, 9, 9, 9], L7062 = [1, 2, 4, 5, 6, 6, 6, 6], L7065 = [1, 2, 4, 5, 6, 6, 6, 9], L7069 = [1, 2, 4, 5, 6, 6, 9, 9], L7070 = [1, 2, 4, 5, 6, 7, 8, 9], L7073 = [1, 2, 4, 5, 6, 9, 9, 9], L7077 = [1, 2, 4, 5, 9, 9, 9, 9], L7079 = [1, 2, 4, 6, 6, 6, 6, 7], L7082 = [1, 2, 4, 6, 6, 6, 7, 9], L7086 = [1, 2, 4, 6, 6, 7, 9, 9], L7091 = [1, 2, 4, 6, 7, 9, 9, 9], L7097 = [1, 2, 4, 7, 9, 9, 9, 9], L7200 = [1, 3, 3, 3, 3, 5, 7, 9], L7241 = [1, 3, 3, 3, 5, 6, 7, 9], L7243 = [1, 3, 3, 3, 5, 7, 9, 9], L7308 = [1, 3, 3, 5, 6, 6, 7, 9], L7310 = [1, 3, 3, 5, 6, 7, 9, 9], L7312 = [1, 3, 3, 5, 7, 9, 9, 9], L7409 = [1, 3, 5, 6, 6, 6, 7, 9], L7411 = [1, 3, 5, 6, 6, 7, 9, 9], L7413 = [1, 3, 5, 6, 7, 9, 9, 9], L7415 = [1, 3, 5, 7, 9, 9, 9, 9]. q = 19 : L19 = [0, 0, 0, 0, 0, 1, 2, 7], L21 = [0, 0, 0, 0, 0, 1, 3, 4], L67 = [0, 0, 0, 0, 1, 2, 3, 5], L68 = [0, 0, 0, 0, 1, 2, 3, 6], L70 = [0, 0, 0, 0, 1, 2, 3, 8], L71 = [0, 0, 0, 0, 1, 2, 3, 9], L72 = [0, 0, 0, 0, 1, 2, 4, 5], L74 = [0, 0, 0, 0, 1, 2, 4, 8], L77 = [0, 0, 0, 0, 1, 2, 6, 8], L79 = [0, 0, 0, 0, 1, 3, 4, 5], L209 = [0, 0, 0, 1, 2, 3, 4, 5], L210 = [0, 0, 0, 1, 2, 3, 4, 6], L211 = [0, 0, 0, 1, 2, 3, 4, 7], L213 = [0, 0, 0, 1, 2, 3, 4, 9], L214 = [0, 0, 0, 1, 2, 3, 5, 6], L215 = [0, 0, 0, 1, 2, 3, 5, 7], L216 = [0, 0, 0, 1, 2, 3, 5, 9], L217 = [0, 0, 0, 1, 2, 3, 6, 7], L218 = [0, 0, 0, 1, 2, 3, 6, 8],
186
EMILIO A. LAURET
Table 6. (continued) m = 8 q 19
I {0}
indexes of I-isospectral families {19, 21}, {67, 68, 71}, {70, 72, 74}, {77, 79}, {209, 210}, {211, 213, 215, 217}, {214, 216, 218, 220}, {219, 222}, {548, 549, 550, 551, 552, 553, 554}, {555, 556, 557}, {1269, 1270, 1271, 1272} {0, 1} {216, 218}, {550, 551}, {552, 554}, {555, 557}, {1269, 1270, 1271} {0, 1, 2, 3} {1270, 1271}
L219 = [0, 0, 0, 1, 2, 3, 7, 8], L220 = [0, 0, 0, 1, 2, 3, 7, 9], L222 = [0, 0, 0, 1, 2, 5, 6, 8], L548 = [0, 0, 1, 2, 3, 4, 5, 6], L549 = [0, 0, 1, 2, 3, 4, 5, 7], L550 = [0, 0, 1, 2, 3, 4, 5, 8], L551 = [0, 0, 1, 2, 3, 4, 5, 9], L552 = [0, 0, 1, 2, 3, 4, 6, 7], L553 = [0, 0, 1, 2, 3, 4, 6, 8], L554 = [0, 0, 1, 2, 3, 4, 6, 9], L555 = [0, 0, 1, 2, 3, 4, 7, 9], L556 = [0, 0, 1, 2, 3, 5, 6, 9], L557 = [0, 0, 1, 2, 3, 5, 7, 8], L1269 = [0, 1, 2, 3, 4, 5, 6, 7], L1270 = [0, 1, 2, 3, 4, 5, 6, 8], L1271 = [0, 1, 2, 3, 4, 5, 6, 9], L1272 = [0, 1, 2, 3, 4, 5, 8, 9]. q = 20 : L355 = [0, 0, 0, 1, 1, 3, 3, 7], L357 = [0, 0, 0, 1, 1, 3, 3, 9], L505 = [0, 0, 0, 1, 2, 3, 4, 7], L507 = [0, 0, 0, 1, 2, 3, 4, 9], L1175 = [0, 0, 1, 1, 3, 3, 5, 7], L1177 = [0, 0, 1, 1, 3, 3, 5, 9], L1182 = [0, 0, 1, 1, 3, 3, 7, 10], L1186 = [0, 0, 1, 1, 3, 3, 9, 10], L1574 = [0, 0, 1, 2, 3, 4, 5, 7], L1576 = [0, 0, 1, 2, 3, 4, 5, 9], L1584 = [0, 0, 1, 2, 3, 4, 7, 10], L1588 = [0, 0, 1, 2, 3, 4, 9, 10], L1600 = [0, 0, 1, 2, 3, 5, 7, 9], L2597 = [0, 1, 1, 1, 3, 5, 7, 9], L3014 = [0, 1, 1, 2, 3, 3, 6, 7], L3016 = [0, 1, 1, 2, 3, 3, 6, 9], L3069 = [0, 1, 1, 2, 3, 5, 7, 9], L3168 = [0, 1, 1, 2, 4, 6, 8, 10], L3305 = [0, 1, 1, 3, 3, 4, 7, 8], L3309 = [0, 1, 1, 3, 3, 4, 8, 9], L3315 = [0, 1, 1, 3, 3, 5, 5, 7], L3317 = [0, 1, 1, 3, 3, 5, 5, 9], L3322 = [0, 1, 1, 3, 3, 5, 7, 10], L3326 = [0, 1, 1, 3, 3, 5, 9, 10], L3334 = [0, 1, 1, 3, 3, 7, 10, 10], L3340 = [0, 1, 1, 3, 3, 9, 10, 10], L3444 = [0, 1, 1, 3, 5, 6, 7, 9], L3455 = [0, 1, 1, 3, 5, 7, 9, 9], L3988 = [0, 1, 2, 2, 3, 4, 4, 7], L3990 = [0, 1, 2, 2, 3, 4, 4, 9], L3999 = [0, 1, 2, 2, 3, 4, 6, 7], L4001 = [0, 1, 2, 2, 3, 4, 6, 9], L4023 = [0, 1, 2, 2, 3, 5, 7, 9], L4205 = [0, 1, 2, 3, 4, 4, 7, 8], L4209 = [0, 1, 2, 3, 4, 4, 8, 9], L4215 = [0, 1, 2, 3, 4, 5, 5, 7], L4217 = [0, 1, 2, 3, 4, 5, 5, 9], L4224 = [0, 1, 2, 3, 4, 5, 7, 9], L4225 = [0, 1, 2, 3, 4, 5, 7, 10], L4229 = [0, 1, 2, 3, 4, 5, 9, 10], L4232 = [0, 1, 2, 3, 4, 6, 7, 9], L4242 = [0, 1, 2, 3, 4, 7, 10, 10], L4248 = [0, 1, 2, 3, 4, 9, 10, 10], L4260 = [0, 1, 2, 3, 5, 5, 7, 9], L4267 = [0, 1, 2, 3, 5, 6, 7, 9], L4273 = [0, 1, 2, 3, 5, 7, 8, 9], L4275 = [0, 1, 2, 3, 5, 7, 9, 10], L4414 = [0, 1, 2, 4, 6, 8, 9, 10], L4594 = [0, 1, 3, 4, 5, 7, 9, 10], L5678 = [1, 1, 1, 1, 3, 5, 7, 9], L6171 = [1, 1, 1, 2, 3, 5, 7, 9], L6482 = [1, 1, 1, 3, 3, 5, 7, 9], L6565 = [1, 1, 1, 3, 4, 5, 7, 9], L6620 = [1, 1, 1, 3, 5, 5, 7, 9], L6635 = [1, 1, 1, 3, 5, 6, 7, 9], L6644 = [1, 1, 1, 3, 5, 7, 7, 9], L6647 = [1, 1, 1, 3, 5, 7, 8, 9], L6649 = [1, 1, 1, 3, 5, 7, 9, 9], L6650 = [1, 1, 1, 3, 5, 7, 9, 10], L7640 = [1, 1, 2, 3, 3, 5, 6, 7], L7642 = [1, 1, 2, 3, 3, 5, 6, 9], L7646 = [1, 1, 2, 3, 3, 5, 7, 9], L7657 = [1, 1, 2, 3, 3, 6, 7, 10], L7661 = [1, 1, 2, 3, 3, 6, 9, 10], L7722 = [1, 1, 2, 3, 4, 5, 7, 9], L7798 = [1, 1, 2, 3, 5, 7, 7, 9], L7803 = [1, 1, 2, 3, 5, 7, 9, 9], L8263 = [1, 1, 3, 3, 4, 5, 7, 8], L8264 = [1, 1, 3, 3, 4, 5, 7, 9], L8267 = [1, 1, 3, 3, 4, 5, 8, 9], L8277 = [1, 1, 3, 3, 4, 7, 8, 10], L8284 = [1, 1, 3, 3, 4, 8, 9, 10], L8290 = [1, 1, 3, 3, 5, 5, 5, 7], L8292 = [1, 1, 3, 3, 5, 5, 5, 9], L8297 = [1, 1, 3, 3, 5, 5, 7, 10], L8301 = [1, 1, 3, 3, 5, 5, 9, 10], L8303 = [1, 1, 3, 3, 5, 7, 7, 9], L8306 = [1, 1, 3, 3, 5, 7, 8, 9], L8309 = [1, 1, 3, 3, 5, 7, 10, 10], L8315 = [1, 1, 3, 3, 5, 9, 10, 10], L8326 = [1, 1, 3, 3, 7, 10, 10, 10], L8334 = [1, 1, 3, 3, 9, 10, 10, 10], L8449 = [1, 1, 3, 4, 5, 7, 9, 9], L8450 = [1, 1, 3, 4, 5, 7, 9, 10], L8548 = [1, 1, 3, 5, 5, 7, 9, 9], L8575 = [1, 1, 3, 5, 6, 7, 8, 9], L8577 = [1, 1, 3, 5, 6, 7, 9, 9], L8592 = [1, 1, 3, 5, 7, 8, 9, 9], L8593 = [1, 1, 3, 5, 7, 8, 9, 10], L8595 = [1, 1, 3, 5, 7, 9, 9, 10], L9639 = [1, 2, 2, 3, 4, 4, 5, 7], L9641 = [1, 2, 2, 3, 4, 4, 5, 9], L9650 = [1, 2, 2, 3, 4, 4, 7, 10], L9654 = [1, 2, 2, 3, 4, 4, 9, 10], L9663 = [1, 2, 2, 3, 4, 5, 6, 7], L9665 = [1, 2, 2, 3, 4, 5, 6, 9], L9668 = [1, 2, 2, 3, 4, 5, 7, 9], L9681 = [1, 2, 2, 3, 4, 6, 7, 10], L9685 = [1, 2, 2, 3, 4, 6, 9, 10], L10060 = [1, 2, 3, 4, 4, 5, 7, 8], L10061 = [1, 2, 3, 4, 4, 5, 7, 9], L10064 = [1, 2, 3, 4, 4, 5, 8, 9], L10078 = [1, 2, 3, 4, 4, 7, 8, 10], L10084 = [1, 2, 3, 4, 4, 8, 9, 10], L10090 = [1, 2, 3, 4, 5, 5, 5, 7], L10092 = [1, 2, 3, 4, 5, 5, 5, 9], L10100 = [1, 2, 3, 4, 5, 5, 7, 10], L10104 = [1, 2, 3, 4, 5, 5, 9, 10], L10107 = [1, 2, 3, 4, 5, 6, 7, 9], L10114 = [1, 2, 3, 4, 5, 7, 8, 9], L10116 = [1, 2, 3, 4, 5, 7, 9, 10], L10117 = [1, 2, 3, 4, 5, 7, 10, 10], L10123 = [1, 2, 3, 4, 5, 9, 10, 10], L10137 = [1, 2, 3, 4, 7, 8, 9, 10], L10140 = [1, 2, 3, 4, 7, 10, 10, 10], L10148 = [1, 2, 3, 4, 9, 10, 10, 10], L10193 = [1, 2, 3, 5, 7, 8, 9, 10], L10685 =
APPENDIX
187
Table 6. (continued) m = 8 q 20
I {0}
indexes of I-isospectral families {355, 357}, {505, 507}, {1175, 1177}, {1182, 1186}, {1574, 1576}, {1584, 1588}, {3014, 3016}, {3305, 3309}, {3315, 3317}, {3322, 3326}, {3334, 3340}, {3988, 3990}, {3999, 4001}, {4205, 4209}, {4215, 4217}, {4225, 4229}, {4242, 4248}, {7640, 7642}, {7657, 7661}, {8263, 8267}, {8277, 8284}, {8290, 8292}, {8297, 8301}, {8309, 8315}, {8326, 8334}, {9639, 9641}, {9650, 9654}, {9663, 9665}, {9681, 9685}, {10060, 10064}, {10078, 10084}, {10090, 10092}, {10100, 10104}, {10117, 10123}, {10140, 10148} {6, 7} {1600, 4594}, {2597, 3455}, {3069, 8593}, {3168, 4414}, {3444, 8450}, {4023, 10193}, {4224, 10727}, {4232, 10137}, {4260, 10720}, {4267, 10116}, {4273, 10685}, {4275, 10729}, {5678, 6649}, {6171, 7803}, {6482, 6644, 8303}, {6565, 8449}, {6620, 8548}, {6635, 8577}, {6647, 8592}, {6650, 8595}, {7646, 7798}, {7722, 8575}, {8264, 8306}, {9668, 10107}, {10061, 10114}
[1, 3, 4, 4, 5, 7, 9, 10], L10720 = [1, 3, 4, 5, 5, 7, 9, 10], L10727 = [1, 3, 4, 5, 7, 8, 9, 10], L10729 = [1, 3, 4, 5, 7, 9, 10, 10]. q = 21 : L110 = [0, 0, 0, 0, 1, 2, 4, 5], L112 = [0, 0, 0, 0, 1, 2, 4, 8], L121 = [0, 0, 0, 0, 1, 2, 6, 9], L135 = [0, 0, 0, 0, 1, 3, 4, 6], L384 = [0, 0, 0, 1, 2, 3, 4, 8], L385 = [0, 0, 0, 1, 2, 3, 4, 9], L387 = [0, 0, 0, 1, 2, 3, 5, 6], L389 = [0, 0, 0, 1, 2, 3, 5, 8], L390 = [0, 0, 0, 1, 2, 3, 5, 9], L391 = [0, 0, 0, 1, 2, 3, 5, 10], L394 = [0, 0, 0, 1, 2, 3, 6, 8], L401 = [0, 0, 0, 1, 2, 3, 8, 9], L402 = [0, 0, 0, 1, 2, 3, 8, 10], L404 = [0, 0, 0, 1, 2, 4, 5, 7], L408 = [0, 0, 0, 1, 2, 4, 7, 8], L426 = [0, 0, 0, 1, 2, 6, 7, 9], L459 = [0, 0, 0, 1, 3, 4, 5, 6], L462 = [0, 0, 0, 1, 3, 4, 6, 7], L1150 = [0, 0, 1, 2, 3, 4, 5, 9], L1155 = [0, 0, 1, 2, 3, 4, 6, 10], L1157 = [0, 0, 1, 2, 3, 4, 7, 8], L1158 = [0, 0, 1, 2, 3, 4, 7, 9], L1164 = [0, 0, 1, 2, 3, 5, 6, 7], L1165 = [0, 0, 1, 2, 3, 5, 6, 8], L1168 = [0, 0, 1, 2, 3, 5, 7, 8], L1169 = [0, 0, 1, 2, 3, 5, 7, 9], L1170 = [0, 0, 1, 2, 3, 5, 7, 10], L1171 = [0, 0, 1, 2, 3, 5, 8, 9], L1179 = [0, 0, 1, 2, 3, 6, 7, 8], L1183 = [0, 0, 1, 2, 3, 6, 8, 10], L1189 = [0, 0, 1, 2, 3, 7, 8, 9], L1190 = [0, 0, 1, 2, 3, 7, 8, 10], L1194 = [0, 0, 1, 2, 4, 5, 7, 7], L1200 = [0, 0, 1, 2, 4, 7, 7, 8], L1231 = [0, 0, 1, 2, 6, 7, 7, 9], L1298 = [0, 0, 1, 3, 4, 5, 6, 7], L1304 = [0, 0, 1, 3, 4, 6, 7, 7], L2946 = [0, 1, 2, 3, 3, 4, 8, 9], L2959 = [0, 1, 2, 3, 3, 5, 8, 9], L2987 = [0, 1, 2, 3, 4, 5, 6, 8], L2988 = [0, 1, 2, 3, 4, 5, 6, 9], L2989 = [0, 1, 2, 3, 4, 5, 6, 10], L2992 = [0, 1, 2, 3, 4, 5, 7, 9], L3000 = [0, 1, 2, 3, 4, 6, 7, 10], L3001 = [0, 1, 2, 3, 4, 6, 8, 9], L3004 = [0, 1, 2, 3, 4, 7, 7, 8], L3005 = [0, 1, 2, 3, 4, 7, 7, 9], L3015 = [0, 1, 2, 3, 5, 6, 7, 7], L3016 = [0, 1, 2, 3, 5, 6, 7, 8], L3021 = [0, 1, 2, 3, 5, 7, 7, 8], L3022 = [0, 1, 2, 3, 5, 7, 7, 9], L3023 = [0, 1, 2, 3, 5, 7, 7, 10], L3024 = [0, 1, 2, 3, 5, 7, 8, 9], L3039 = [0, 1, 2, 3, 6, 6, 9, 9], L3041 = [0, 1, 2, 3, 6, 7, 7, 8], L3045 = [0, 1, 2, 3, 6, 7, 8, 10], L3053 = [0, 1, 2, 3, 7, 7, 8, 9], L3054 = [0, 1, 2, 3, 7, 7, 8, 10], L3060 = [0, 1, 2, 4, 5, 7, 7, 7], L3063 = [0, 1, 2, 4, 5, 7, 8, 10], L3067 = [0, 1, 2, 4, 7, 7, 7, 8], L3115 = [0, 1, 2, 6, 7, 7, 7, 9], L3194 = [0, 1, 3, 3, 4, 6, 6, 9], L3216 = [0, 1, 3, 3, 6, 6, 9, 9], L3233 = [0, 1, 3, 4, 5, 6, 7, 7], L3241 = [0, 1, 3, 4, 6, 7, 7, 7], L3363 = [0, 3, 3, 6, 6, 7, 9, 9], L5844 = [1, 1, 2, 4, 5, 7, 8, 10], L6913 = [1, 2, 3, 3, 4, 6, 8, 9], L6915 = [1, 2, 3, 3, 4, 6, 9, 9], L6921 = [1, 2, 3, 3, 4, 7, 8, 9], L6931 = [1, 2, 3, 3, 5, 6, 6, 9], L6936 = [1, 2, 3, 3, 5, 6, 8, 9], L6937 = [1, 2, 3, 3, 5, 6, 9, 9], L6938 = [1, 2, 3, 3, 5, 6, 9, 10], L6943 = [1, 2, 3, 3, 5, 7, 8, 9], L6957 = [1, 2, 3, 3, 6, 6, 8, 9], L6969 = [1, 2, 3, 3, 6, 8, 9, 9], L6970 = [1, 2, 3, 3, 6, 8, 9, 10], L6986 = [1, 2, 3, 4, 5, 6, 7, 8], L6987 = [1, 2, 3, 4, 5, 6, 7, 9], L6988 = [1, 2, 3, 4, 5, 6, 7, 10], L6994 = [1, 2, 3, 4, 5, 7, 7, 9], L6996 = [1, 2, 3, 4, 5, 7, 8, 10], L7003 = [1, 2, 3, 4, 6, 7, 7, 10], L7004 = [1, 2, 3, 4, 6, 7, 8, 9], L7008 = [1, 2, 3, 4, 7, 7, 7, 8], L7009 = [1, 2, 3, 4, 7, 7, 7, 9], L7025 = [1, 2, 3, 5, 6, 7, 7, 7], L7026 = [1, 2, 3, 5, 6, 7, 7, 8], L7033 = [1, 2, 3, 5, 7, 7, 7, 8], L7034 = [1, 2, 3, 5, 7, 7, 7, 9], L7035 = [1, 2, 3, 5, 7, 7, 7, 10], L7036 = [1, 2, 3, 5, 7, 7, 8, 9], L7060 = [1, 2, 3, 6, 6, 7, 9, 9], L7064 = [1, 2, 3, 6, 7, 7, 7, 8], L7068 = [1, 2, 3, 6, 7, 7, 8, 10], L7078 = [1, 2, 3, 7, 7, 7, 8, 9], L7079 = [1, 2, 3, 7, 7, 7, 8, 10], L7087 = [1, 2, 4, 5, 7, 7, 7, 7], L7090 = [1, 2, 4, 5, 7, 7, 8, 10], L7095 = [1, 2, 4, 7, 7, 7, 7, 8], L7164 = [1, 2, 6, 7, 7, 7, 7, 9],
188
EMILIO A. LAURET
Table 6. (continued) m = 8 q 21
I {0}
indexes of I-isospectral families {110, 112}, {121, 135}, {384, 389}, {385, 387}, {390, 394}, {391, 402}, {401, 459}, {404, 408}, {426, 462}, {1150, 1155, 1165}, {1157, 1168}, {1158, 1164}, {1169, 1179}, {1170, 1190}, {1189, 1298}, {1194, 1200}, {1231, 1304}, {2946, 2959}, {2988, 3001}, {2992, 3000, 3016}, {3004, 3021}, {3005, 3015}, {3022, 3041}, {3023, 3054}, {3039, 3194}, {3053, 3233}, {3060, 3067}, {3115, 3241}, {6913, 6936}, {6915, 6931}, {6921, 6943}, {6937, 6957}, {6938, 6970}, {6969, 7291}, {6987, 7004}, {6994, 7003, 7026}, {7008, 7033}, {7009, 7025}, {7034, 7064}, {7035, 7079}, {7060, 7300}, {7078, 7353}, {7087, 7095}, {7164, 7363} {0, 1} {1171, 1183}, {2987, 2989}, {3024, 3045}, {6986, 6988}, {7036, 7068} {2, 3, 4, 5, 6} {3063, 6996}, {3216, 3363}, {5844, 7090}
L7291 = [1, 3, 3, 4, 5, 6, 6, 9], L7300 = [1, 3, 3, 4, 6, 6, 7, 9], L7353 = [1, 3, 4, 5, 6, 7, 7, 7], L7363 = [1, 3, 4, 6, 7, 7, 7, 7]. q = 22 : L33 = [0, 0, 0, 0, 0, 1, 3, 5], L34 = [0, 0, 0, 0, 0, 1, 3, 7], L166 = [0, 0, 0, 0, 1, 2, 8, 9], L177 = [0, 0, 0, 0, 1, 3, 4, 8], L182 = [0, 0, 0, 0, 1, 3, 5, 11], L184 = [0, 0, 0, 0, 1, 3, 7, 11], L242 = [0, 0, 0, 0, 2, 4, 6, 11], L243 = [0, 0, 0, 0, 2, 4, 8, 11], L567 = [0, 0, 0, 1, 2, 3, 4, 9], L570 = [0, 0, 0, 1, 2, 3, 5, 6], L577 = [0, 0, 0, 1, 2, 3, 6, 8], L582 = [0, 0, 0, 1, 2, 3, 7, 10], L600 = [0, 0, 0, 1, 2, 4, 5, 6], L623 = [0, 0, 0, 1, 2, 5, 6, 7], L624 = [0, 0, 0, 1, 2, 5, 6, 8], L641 = [0, 0, 0, 1, 2, 6, 7, 10], L662 = [0, 0, 0, 1, 2, 8, 9, 11], L686 = [0, 0, 0, 1, 3, 4, 8, 11], L694 = [0, 0, 0, 1, 3, 5, 11, 11], L697 = [0, 0, 0, 1, 3, 7, 11, 11], L818 = [0, 0, 0, 2, 4, 6, 11, 11], L819 = [0, 0, 0, 2, 4, 8, 11, 11], L1880 = [0, 0, 1, 2, 3, 4, 5, 7], L1881 = [0, 0, 1, 2, 3, 4, 5, 8], L1882 = [0, 0, 1, 2, 3, 4, 5, 9], L1883 = [0, 0, 1, 2, 3, 4, 5, 10], L1885 = [0, 0, 1, 2, 3, 4, 6, 7], L1886 = [0, 0, 1, 2, 3, 4, 6, 8], L1887 = [0, 0, 1, 2, 3, 4, 6, 9], L1888 = [0, 0, 1, 2, 3, 4, 6, 10], L1892 = [0, 0, 1, 2, 3, 4, 7, 10], L1898 = [0, 0, 1, 2, 3, 4, 9, 10], L1899 = [0, 0, 1, 2, 3, 4, 9, 11], L1903 = [0, 0, 1, 2, 3, 5, 6, 7], L1904 = [0, 0, 1, 2, 3, 5, 6, 8], L1907 = [0, 0, 1, 2, 3, 5, 6, 11], L1908 = [0, 0, 1, 2, 3, 5, 7, 8], L1913 = [0, 0, 1, 2, 3, 5, 8, 10], L1922 = [0, 0, 1, 2, 3, 6, 8, 9], L1924 = [0, 0, 1, 2, 3, 6, 8, 11], L1932 = [0, 0, 1, 2, 3, 7, 10, 11], L1976 = [0, 0, 1, 2, 4, 5, 6, 7], L1977 = [0, 0, 1, 2, 4, 5, 6, 8], L1979 = [0, 0, 1, 2, 4, 5, 6, 11], L1982 = [0, 0, 1, 2, 4, 5, 8, 10], L1996 = [0, 0, 1, 2, 4, 6, 8, 10], L2027 = [0, 0, 1, 2, 5, 6, 7, 11], L2030 = [0, 0, 1, 2, 5, 6, 8, 11], L2063 = [0, 0, 1, 2, 6, 7, 10, 11], L2099 = [0, 0, 1, 2, 8, 9, 11, 11], L2142 = [0, 0, 1, 3, 4, 8, 11, 11], L2147 = [0, 0, 1, 3, 5, 7, 9, 11], L2152 = [0, 0, 1, 3, 5, 11, 11, 11], L2156 = [0, 0, 1, 3, 7, 11, 11, 11], L2377 = [0, 0, 2, 4, 6, 8, 10, 11], L2379 = [0, 0, 2, 4, 6, 11, 11, 11], L2380 = [0, 0, 2, 4, 8, 11, 11, 11], L3804 = [0, 1, 1, 2, 4, 6, 8, 10], L4049 = [0, 1, 1, 3, 3, 5, 5, 9], L4051 = [0, 1, 1, 3, 3, 5, 7, 7], L4060 = [0, 1, 1, 3, 3, 5, 9, 9], L4232 = [0, 1, 1, 3, 5, 7, 9, 11], L5172 = [0, 1, 2, 2, 4, 6, 8, 10], L5345 = [0, 1, 2, 3, 4, 5, 6, 7], L5346 = [0, 1, 2, 3, 4, 5, 6, 8], L5347 = [0, 1, 2, 3, 4, 5, 6, 9], L5348 = [0, 1, 2, 3, 4, 5, 6, 10], L5350 = [0, 1, 2, 3, 4, 5, 7, 8], L5352 = [0, 1, 2, 3, 4, 5, 7, 10], L5353 = [0, 1, 2, 3, 4, 5, 7, 11], L5355 = [0, 1, 2, 3, 4, 5, 8, 10], L5356 = [0, 1, 2, 3, 4, 5, 8, 11], L5357 = [0, 1, 2, 3, 4, 5, 9, 10], L5358 = [0, 1, 2, 3, 4, 5, 9, 11], L5359 = [0, 1, 2, 3, 4, 5, 10, 11], L5361 = [0, 1, 2, 3, 4, 6, 7, 8], L5362 = [0, 1, 2, 3, 4, 6, 7, 9], L5363 = [0, 1, 2, 3, 4, 6, 7, 10], L5364 = [0, 1, 2, 3, 4, 6, 7, 11], L5366 = [0, 1, 2, 3, 4, 6, 8, 9], L5367 = [0, 1, 2, 3, 4, 6, 8, 10], L5368 = [0, 1, 2, 3, 4, 6, 8, 11], L5369 = [0, 1, 2, 3, 4, 6, 9, 11], L5371 = [0, 1, 2, 3, 4, 6, 10, 11], L5374 = [0, 1, 2, 3, 4, 7, 8, 10], L5376 = [0, 1, 2, 3, 4, 7, 9, 10], L5379 = [0, 1, 2, 3, 4, 7, 10, 11], L5385 = [0, 1, 2, 3, 4, 8, 9, 10], L5391 = [0, 1, 2, 3, 4, 9, 10, 11], L5392 = [0, 1, 2, 3, 4, 9, 11, 11], L5398 = [0, 1, 2, 3, 5, 6, 7, 11], L5400 = [0, 1, 2, 3, 5, 6, 8, 9], L5401 = [0, 1, 2, 3, 5, 6, 8, 10], L5402 = [0, 1, 2, 3, 5, 6, 8, 11], L5405 = [0, 1, 2, 3, 5, 6, 11, 11], L5406 = [0, 1, 2, 3, 5, 7, 8, 11], L5407 = [0, 1, 2, 3, 5, 7, 9, 11], L5413 = [0, 1, 2, 3, 5, 8, 9, 10], L5415 = [0, 1, 2, 3, 5, 8, 10, 11], L5428 = [0, 1, 2, 3, 6, 8, 9, 11], L5431 = [0, 1, 2, 3, 6, 8, 11, 11], L5442 = [0, 1, 2, 3, 7, 10, 11, 11], L5513 = [0, 1, 2, 4, 4, 6, 8, 10 L5536 = [0, 1, 2, 4, 5, 6, 7, 11], L5538 = [0, 1, 2, 4, 5, 6, 8, 10], L5539 = [0, 1, 2, 4, 5, 6, 8, 11], L5541 = [0, 1, 2, 4, 5, 6, 11, 11], L5546 = [0, 1, 2, 4, 5, 8, 10, 11], L5560 = [0, 1, 2, 4, 6, 6, 8, 10], L5573 = [0, 1, 2, 4, 6, 8, 8, 10],
APPENDIX
189
Table 6. (continued) m = 8 q I indexes of I-isospectral families 22 {0} {33, 34}, {166, 177}, {182, 184}, {242, 243}, {567, 570}, {577, 600}, {582, 623}, {624, 641}, {662, 686}, {694, 697}, {818, 819}, {1880, 1882}, {1881, 1883, 1885, 1887}, {1886, 1888}, {1892, 1913}, {1898, 1904}, {1899, 1907}, {1903, 1908}, {1922, 1976}, {1924, 1979}, {1932, 2027}, {1977, 1982}, {2030, 2063}, {2099, 2142}, {2152, 2156}, {2379, 2380}, {4049, 4051, 4060}, {5345, 5347, 5352}, {5346, 5348, 5361}, {5350, 5357, 5362}, {5353, 5358}, {5355, 5363, 5366}, {5356, 5359, 5364, 5369}, {5368, 5371}, {5374, 5385, 5401}, {5376, 5400, 5413}, {5379, 5415}, {5391, 5402}, {5392, 5405}, {5398, 5406}, {5428, 5536}, {5431, 5541}, {5442, 5624}, {5539, 5546}, {5629, 5687}, {5742, 5811}, {5823, 5828}, {6204, 6205}, {10847, 10854}, {10852, 10856, 10876}, {13505, 13507, 13510, 13513}, {13506, 13517}, {13508, 13514, 13520}, {13511, 13531}, {13512, 13515, 13532}, {13518, 13527, 13533}, {13521, 13528}, {13525, 13535, 13541}, {13526, 13529, 13536, 13545}, {13544, 13548}, {13553, 13572, 13594}, {13556, 13593, 13610}, {13560, 13612}, {13580, 13595}, {13581, 13598}, {13588, 13599}, {13630, 13823}, {13634, 13830}, {13648, 13959}, {13828, 13837}, {13966, 14060}, {14138, 14241}, {14255, 14261}, {14818, 14819, 14821}, {14858, 14859}
L5575 = [0, 1, 2, 4, 6, 8, 10, 10], L5576 = [0, 1, 2, 4, 6, 8, 10, 11], L5624 = [0, 1, 2, 5, 6, 7, 11, 11], L5629 = [0, 1, 2, 5, 6, 8, 11, 11], L5687 = [0, 1, 2, 6, 7, 10, 11, 11], L5742 = [0, 1, 2, 8, 9, 11, 11, 11], L5811 = [0, 1, 3, 4, 8, 11, 11, 11], L5817 = [0, 1, 3, 5, 7, 9, 11, 11], L5823 = [0, 1, 3, 5, 11, 11, 11, 11], L5828 = [0, 1, 3, 7, 11, 11, 11, 11], L6182 = [0, 2, 2, 4, 6, 8, 10, 11], L6202 = [0, 2, 4, 6, 8, 10, 11, 11], L6204 = [0, 2, 4, 6, 11, 11, 11, 11], L6205 = [0, 2, 4, 8, 11, 11, 11, 11], L8239 = [1, 1, 1, 3, 5, 7, 9, 11], L10025 = [1, 1, 2, 3, 5, 7, 9, 11], L10847 = [1, 1, 3, 3, 5, 5, 7, 9], L10852 = [1, 1, 3, 3, 5, 5, 9, 11], L10854 = [1, 1, 3, 3, 5, 7, 7, 9], L10856 = [1, 1, 3, 3, 5, 7, 7, 11], L10862 = [1, 1, 3, 3, 5, 7, 9, 11], L10876 = [1, 1, 3, 3, 5, 9, 9, 11], L11067 = [1, 1, 3, 4, 5, 7, 9, 11], L11188 = [1, 1, 3, 5, 5, 7, 9, 11], L11221 = [1, 1, 3, 5, 6, 7, 9, 11], L11246 = [1, 1, 3, 5, 7, 8, 9, 11], L11251 = [1, 1, 3, 5, 7, 9, 10, 11], L11252 = [1, 1, 3, 5, 7, 9, 11, 11], L12962 = [1, 2, 2, 3, 5, 7, 9, 11], L13505 = [1, 2, 3, 4, 5, 6, 7, 8], L13506 = [1, 2, 3, 4, 5, 6, 7, 9], L13507 = [1, 2, 3, 4, 5, 6, 7, 10], L13508 = [1, 2, 3, 4, 5, 6, 7, 11], L13510 = [1, 2, 3, 4, 5, 6, 8, 9], L13511 = [1, 2, 3, 4, 5, 6, 8, 10], L13512 = [1, 2, 3, 4, 5, 6, 8, 11], L13513 = [1, 2, 3, 4, 5, 6, 9, 10], L13514 = [1, 2, 3, 4, 5, 6, 9, 11], L13515 = [1, 2, 3, 4, 5, 6, 10, 11], L13517 = [1, 2, 3, 4, 5, 7, 8, 9], L13518 = [1, 2, 3, 4, 5, 7, 8, 11], L13519 = [1, 2, 3, 4, 5, 7, 9, 11], L13520 = [1, 2, 3, 4, 5, 7, 10, 11], L13521 = [1, 2, 3, 4, 5, 7, 11, 11], L13525 = [1, 2, 3, 4, 5, 8, 10, 11], L13526 = [1, 2, 3, 4, 5, 8, 11, 11], L13527 = [1, 2, 3, 4, 5, 9, 10, 11], L13528 = [1, 2, 3, 4, 5, 9, 11, 11], L13529 = [1, 2, 3, 4, 5, 10, 11, 11], L13531 = [1, 2, 3, 4, 6, 7, 8, 10], L13532 = [1, 2, 3, 4, 6, 7, 8, 11], L13533 = [1, 2, 3, 4, 6, 7, 9, 11], L13535 = [1, 2, 3, 4, 6, 7, 10, 11], L13536 = [1, 2, 3, 4, 6, 7, 11, 11], L13541 = [1, 2, 3, 4, 6, 8, 9, 11], L13544 = [1, 2, 3, 4, 6, 8, 11, 11], L13545 = [1, 2, 3, 4, 6, 9, 11, 11], L13548 = [1, 2, 3, 4, 6, 10, 11, 11], L13553 = [1, 2, 3, 4, 7, 8, 10, 11], L13556 = [1, 2, 3, 4, 7, 9, 10, 11], L13560 = [1, 2, 3, 4, 7, 10, 11, 11], L13572 = [1, 2, 3, 4, 8, 9, 10, 11], L13580 = [1, 2, 3, 4, 9, 10, 11, 11], L13581 = [1, 2, 3, 4, 9, 11, 11, 11], L13587 = [1, 2, 3, 5, 6, 7, 9, 11], L13588 = [1, 2, 3, 5, 6, 7, 11, 11], L13593 = [1, 2, 3, 5, 6, 8, 9, 11], L13594 = [1, 2, 3, 5, 6, 8, 10, 1 L13595 = [1, 2, 3, 5, 6, 8, 11, 11], L13598 = [1, 2, 3, 5, 6, 11, 11, 11], L13599 = [1, 2, 3, 5, 7, 8, 11, 11], L13600 = [1, 2, 3, 5, 7, 9, 11, 11], L13610 = [1, 2, 3, 5, 8, 9, 10, 11], L13612 = [1, 2, 3, 5, 8, 10, 11, 11], L13630 = [1, 2, 3, 6, 8, 9, 11, 11], L13634 = [1, 2, 3, 6, 8, 11, 11, 11], L13648 = [1, 2, 3, 7, 10, 11, 11, 11], L13823 = [1, 2, 4, 5, 6, 7, 11, 11], L13828 = [1, 2, 4, 5, 6, 8, 11, 11], L13830 = [1, 2, 4, 5, 6, 11, 11, 11], L13837 = [1, 2, 4, 5, 8, 10, 11, 11], L13959 = [1, 2, 5, 6, 7, 11, 11, 11], L13966 = [1, 2, 5, 6, 8, 11, 11, 11],
190
EMILIO A. LAURET
Table 6. (continued) m = 8 q 22 (cont.)
I {0, 1} {0, 1, 2, 3, 4} {5, 6, 7}
indexes of I-isospectral families {5347, 5352}, {5355, 5363}, {13514, 13520}, {13525, 13535} {13507, 13510} {1996, 2377, 5172, 5513, 5560, 5573, 5575, 6182}, {2147, 5407, 12962, 13519, 13587}, {3804, 5367, 5538, 5576, 6202}, {4232, 5817, 10025, 11067, 11221, 11246, 11251, 13600}, {8239, 10862, 11188, 11252, 14248}
L14060 = [1, 2, 6, 7, 10, 11, 11, 11], L14138 = [1, 2, 8, 9, 11, 11, 11, 11], L14241 = [1, 3, 4, 8, 11, 11, 11, 11], L14248 = [1, 3, 5, 7, 9, 11, 11, 11], L14255 = [1, 3, 5, 11, 11, 11, 11, 11], L14261 = [1, 3, 7, 11, 11, 11, 11, 11], L14818 = [2, 2, 4, 4, 6, 6, 8, 11], L14819 = [2, 2, 4, 4, 6, 6, 10, 11], L14821 = [2, 2, 4, 4, 6, 8, 8, 11], L14858 = [2, 4, 6, 11, 11, 11, 11, 11], L14859 = [2, 4, 8, 11, 11, 11, 11, 11]. q = 23 : L102 = [0, 0, 0, 0, 1, 2, 4, 5], L104 = [0, 0, 0, 0, 1, 2, 4, 8], L108 = [0, 0, 0, 0, 1, 2, 5, 7], L110 = [0, 0, 0, 0, 1, 2, 5, 9], L114 = [0, 0, 0, 0, 1, 2, 6, 10], L121 = [0, 0, 0, 0, 1, 3, 4, 9], L357 = [0, 0, 0, 1, 2, 3, 4, 7], L358 = [0, 0, 0, 1, 2, 3, 4, 8], L361 = [0, 0, 0, 1, 2, 3, 4, 11], L362 = [0, 0, 0, 1, 2, 3, 5, 6], L365 = [0, 0, 0, 1, 2, 3, 5, 9], L368 = [0, 0, 0, 1, 2, 3, 6, 7], L369 = [0, 0, 0, 1, 2, 3, 6, 8], L371 = [0, 0, 0, 1, 2, 3, 6, 10], L373 = [0, 0, 0, 1, 2, 3, 7, 9], L376 = [0, 0, 0, 1, 2, 3, 8, 10], L378 = [0, 0, 0, 1, 2, 3, 9, 10], L383 = [0, 0, 0, 1, 2, 4, 5, 11], L385 = [0, 0, 0, 1, 2, 4, 7, 11], L386 = [0, 0, 0, 1, 2, 4, 9, 10], L388 = [0, 0, 0, 1, 2, 5, 6, 8], L390 = [0, 0, 0, 1, 2, 5, 6, 10], L391 = [0, 0, 0, 1, 2, 6, 7, 10], L392 = [0, 0, 0, 1, 2, 6, 8, 9], L396 = [0, 0, 0, 1, 3, 4, 5, 7], L1085 = [0, 0, 1, 2, 3, 4, 5, 8], L1086 = [0, 0, 1, 2, 3, 4, 5, 9], L1087 = [0, 0, 1, 2, 3, 4, 5, 10], L1088 = [0, 0, 1, 2, 3, 4, 5, 11], L1089 = [0, 0, 1, 2, 3, 4, 6, 7], L1090 = [0, 0, 1, 2, 3, 4, 6, 8], L1091 = [0, 0, 1, 2, 3, 4, 6, 9], L1092 = [0, 0, 1, 2, 3, 4, 6, 10], L1093 = [0, 0, 1, 2, 3, 4, 6, 11], L1094 = [0, 0, 1, 2, 3, 4, 7, 8], L1095 = [0, 0, 1, 2, 3, 4, 7, 9], L1097 = [0, 0, 1, 2, 3, 4, 7, 11], L1099 = [0, 0, 1, 2, 3, 4, 8, 10], L1100 = [0, 0, 1, 2, 3, 4, 8, 11], L1101 = [0, 0, 1, 2, 3, 4, 9, 10], L1102 = [0, 0, 1, 2, 3, 4, 9, 11], L1103 = [0, 0, 1, 2, 3, 5, 6, 7], L1104 = [0, 0, 1, 2, 3, 5, 6, 8], L1105 = [0, 0, 1, 2, 3, 5, 6, 9], L1106 = [0, 0, 1, 2, 3, 5, 6, 10], L1107 = [0, 0, 1, 2, 3, 5, 7, 8], L1108 = [0, 0, 1, 2, 3, 5, 7, 10], L1109 = [0, 0, 1, 2, 3, 5, 7, 11], L1110 = [0, 0, 1, 2, 3, 5, 8, 9], L1111 = [0, 0, 1, 2, 3, 5, 8, 11], L1112 = [0, 0, 1, 2, 3, 5, 9, 10], L1113 = [0, 0, 1, 2, 3, 5, 9, 11], L1114 = [0, 0, 1, 2, 3, 6, 7, 9], L1117 = [0, 0, 1, 2, 3, 6, 8, 11], L1118 = [0, 0, 1, 2, 3, 6, 9, 10], L1119 = [0, 0, 1, 2, 3, 8, 9, 10], L1120 = [0, 0, 1, 2, 3, 8, 9, 11], L1124 = [0, 0, 1, 2, 6, 8, 9, 10], L2863 = [0, 1, 2, 3, 4, 5, 6, 7], L2864 = [0, 1, 2, 3, 4, 5, 6, 8], L2865 = [0, 1, 2, 3, 4, 5, 6, 9], L2866 = [0, 1, 2, 3, 4, 5, 6, 10], L2867 = [0, 1, 2, 3, 4, 5, 6, 11], L2868 = [0, 1, 2, 3, 4, 5, 7, 8], L2869 = [0, 1, 2, 3, 4, 5, 7, 9], L2870 = [0, 1, 2, 3, 4, 5, 7, 10], L2871 = [0, 1, 2, 3, 4, 5, 7, 11], L2872 = [0, 1, 2, 3, 4, 5, 8, 9], L2873 = [0, 1, 2, 3, 4, 5, 8, 10], L2874 = [0, 1, 2, 3, 4, 5, 8, 11], L2875 = [0, 1, 2, 3, 4, 5, 9, 11], L2876 = [0, 1, 2, 3, 4, 5, 10, 11], L2877 = [0, 1, 2, 3, 4, 6, 7, 8], L2878 = [0, 1, 2, 3, 4, 6, 7, 9], L2879 = [0, 1, 2, 3, 4, 6, 7, 11], L2880 = [0, 1, 2, 3, 4, 6, 8, 9], L2881 = [0, 1, 2, 3, 4, 6, 8, 11], L2882 = [0, 1, 2, 3, 4, 6, 9, 10], L2883 = [0, 1, 2, 3, 4, 6, 9, 11], L2884 = [0, 1, 2, 3, 4, 7, 8, 10], L2885 = [0, 1, 2, 3, 4, 7, 9, 10], L2886 = [0, 1, 2, 3, 4, 7, 9, 11], L2887 = [0, 1, 2, 3, 4, 8, 9, 10], L2888 = [0, 1, 2, 3, 4, 8, 9, 11], L2889 = [0, 1, 2, 3, 5, 6, 7, 8], L2891 = [0, 1, 2, 3, 5, 7, 8, 11], L2892 = [0, 1, 2, 3, 5, 8, 9, 11], L6856 = [1, 2, 3, 4, 5, 6, 7, 8], L6857 = [1, 2, 3, 4, 5, 6, 7, 9], L6858 = [1, 2, 3, 4, 5, 6, 7, 10], L6859 = [1, 2, 3, 4, 5, 6, 7, 11], L6860 = [1, 2, 3, 4, 5, 6, 8, 9], L6861 = [1, 2, 3, 4, 5, 6, 8, 10], L6862 = [1, 2, 3, 4, 5, 6, 8, 11], L6863 = [1, 2, 3, 4, 5, 6, 9, 10], L6864 = [1, 2, 3, 4, 5, 6, 9, 11], L6865 = [1, 2, 3, 4, 5, 6, 10, 11], L6866 = [1, 2, 3, 4, 5, 7, 8, 9], L6867 = [1, 2, 3, 4, 5, 7, 9, 10], L6868 = [1, 2, 3, 4, 5, 7, 10, 11], L6869 = [1, 2, 3, 4, 5, 8, 9, 11], L6870 = [1, 2, 3, 4, 6, 7, 9, 11]. q = 24 : L41 = [0, 0, 0, 0, 0, 1, 3, 5], L43 = [0, 0, 0, 0, 0, 1, 3, 7], L213 = [0, 0, 0, 0, 1, 2, 5, 7], L217 = [0, 0, 0, 0, 1, 2, 5, 11], L254 = [0, 0, 0, 0, 1, 3, 4, 5], L256 = [0, 0, 0, 0, 1, 3, 4, 7], L262 = [0, 0, 0, 0, 1, 3, 5, 6], L264 = [0, 0, 0, 0, 1, 3, 5, 8], L267 = [0, 0, 0, 0, 1, 3, 5, 12], L269 = [0, 0, 0, 0, 1, 3, 6, 7], L275 = [0, 0, 0, 0, 1, 3, 7, 8], L277 = [0, 0, 0, 0, 1, 3, 7, 12], L846 = [0, 0, 0, 1, 2, 2, 5, 7], L850 = [0, 0, 0, 1, 2, 2, 5, 11], L899 = [0, 0, 0, 1, 2, 3, 5, 10], L911 = [0, 0, 0, 1, 2, 3, 7, 10], L938 = [0, 0, 0, 1, 2, 4, 5, 7], L942 = [0, 0, 0, 1, 2, 4, 5, 11], L969 = [0, 0, 0, 1, 2, 5, 6, 7], L973 = [0, 0, 0, 1, 2, 5, 6, 11], L975 = [0, 0, 0, 1, 2, 5, 7, 8], L979 = [0, 0, 0, 1, 2, 5, 7, 12],
APPENDIX
191
Table 6. (continued) m = 8 q 23
I {0}
indexes of I-isospectral families {102, 104}, {108, 110}, {114, 121}, {357, 358}, {361, 362}, {365, 369}, {368, 371, 373}, {376, 378, 386, 392}, {383, 385}, {388, 390}, {391, 396}, {1085, 1086, 1090}, {1087, 1089, 1092, 1093, 1094, 1100}, {1088, 1091}, {1095, 1105}, {1097, 1102, 1103, 1104, 1106, 1107, 1108}, {1099, 1117}, {1101, 1112, 1113, 1114, 1120}, {1109, 1110, 1111, 1118}, {1119, 1124}, {2863, 2864, 2865, 2867, 2869}, {2866, 2868, 2873, 2877, 2881}, {2870, 2872, 2874, 2876, 2880, 2883}, {2871, 2875, 2878, 2879, 2882, 2884, 2885, 2886, 2888, 2889}, {6856, 6857, 6858, 6859, 6860, 6861, 6862, 6863, 6864, 6865, 6866, 6867}, {2887, 2891, 2892}, {6868, 6869, 6870} {0, 1} {1092, 1094}, {1102, 1108}, {2875, 2885, 2886}, {2882, 2888}, {6857, 6858, 6859}, {6861, 6863}, {6862, 6864, 6866, 6867}, {6868, 6869} {0, 1, 2} {6858, 6859}, {6862, 6864, 6866} {0, 1, 2, 3, 4} {6862, 6864}
L983 = [0, 0, 0, 1, 2, 5, 8, 11], L988 = [0, 0, 0, 1, 2, 5, 11, 12], L1071 = [0, 0, 0, 1, 3, 3, 5, 9], L1082 = [0, 0, 0, 1, 3, 3, 7, 9], L1099 = [0, 0, 0, 1, 3, 4, 4, 5], L1101 = [0, 0, 0, 1, 3, 4, 4, 7], L1107 = [0, 0, 0, 1, 3, 4, 5, 6], L1109 = [0, 0, 0, 1, 3, 4, 5, 8], L1112 = [0, 0, 0, 1, 3, 4, 5, 12], L1114 = [0, 0, 0, 1, 3, 4, 6, 7], L1120 = [0, 0, 0, 1, 3, 4, 7, 8], L1122 = [0, 0, 0, 1, 3, 4, 7, 12], L1137 = [0, 0, 0, 1, 3, 5, 6, 6], L1139 = [0, 0, 0, 1, 3, 5, 6, 8], L1142 = [0, 0, 0, 1, 3, 5, 6, 12], L1147 = [0, 0, 0, 1, 3, 5, 8, 8], L1150 = [0, 0, 0, 1, 3, 5, 8, 12], L1153 = [0, 0, 0, 1, 3, 5, 12, 12], L1155 = [0, 0, 0, 1, 3, 6, 6, 7], L1161 = [0, 0, 0, 1, 3, 6, 7, 8], L1163 = [0, 0, 0, 1, 3, 6, 7, 12], L1178 = [0, 0, 0, 1, 3, 7, 8, 8], L1180 = [0, 0, 0, 1, 3, 7, 8, 12], L1183 = [0, 0, 0, 1, 3, 7, 12, 12], L2380 = [0, 0, 1, 1, 3, 5, 5, 11], L2389 = [0, 0, 1, 1, 3, 5, 7, 7], L2942 = [0, 0, 1, 2, 2, 2, 5, 7], L2946 = [0, 0, 1, 2, 2, 2, 5, 11], L3034 = [0, 0, 1, 2, 2, 4, 5, 7], L3038 = [0, 0, 1, 2, 2, 4, 5, 11], L3065 = [0, 0, 1, 2, 2, 5, 6, 7], L3069 = [0, 0, 1, 2, 2, 5, 6, 11], L3071 = [0, 0, 1, 2, 2, 5, 7, 8], L3073 = [0, 0, 1, 2, 2, 5, 7, 10], L3075 = [0, 0, 1, 2, 2, 5, 7, 12], L3079 = [0, 0, 1, 2, 2, 5, 8, 11], L3085 = [0, 0, 1, 2, 2, 5, 10, 11], L3087 = [0, 0, 1, 2, 2, 5, 11, 12], L3214 = [0, 0, 1, 2, 3, 4, 5, 10], L3226 = [0, 0, 1, 2, 3, 4, 7, 10], L3247 = [0, 0, 1, 2, 3, 5, 6, 10], L3251 = [0, 0, 1, 2, 3, 5, 7, 9], L3257 = [0, 0, 1, 2, 3, 5, 8, 10], L3262 = [0, 0, 1, 2, 3, 5, 9, 11], L3265 = [0, 0, 1, 2, 3, 5, 10, 12], L3277 = [0, 0, 1, 2, 3, 6, 7, 10], L3296 = [0, 0, 1, 2, 3, 7, 8, 10], L3302 = [0, 0, 1, 2, 3, 7, 10, 12], L3344 = [0, 0, 1, 2, 4, 4, 5, 7], L3348 = [0, 0, 1, 2, 4, 4, 5, 11], L3375 = [0, 0, 1, 2, 4, 5, 6, 7], L3379 = [0, 0, 1, 2, 4, 5, 6, 11], L3381 = [0, 0, 1, 2, 4, 5, 7, 8], L3385 = [0, 0, 1, 2, 4, 5, 7, 12], L3389 = [0, 0, 1, 2, 4, 5, 8, 11], L3394 = [0, 0, 1, 2, 4, 5, 11, 12], L3456 = [0, 0, 1, 2, 5, 6, 6, 7], L3460 = [0, 0, 1, 2, 5, 6, 6, 11], L3462 = [0, 0, 1, 2, 5, 6, 7, 8], L3466 = [0, 0, 1, 2, 5, 6, 7, 12], L3470 = [0, 0, 1, 2, 5, 6, 8, 11], L3475 = [0, 0, 1, 2, 5, 6, 11, 12], L3477 = [0, 0, 1, 2, 5, 7, 8, 8], L3481 = [0, 0, 1, 2, 5, 7, 8, 12], L3487 = [0, 0, 1, 2, 5, 7, 12, 12], L3491 = [0, 0, 1, 2, 5, 8, 8, 11], L3496 = [0, 0, 1, 2, 5, 8, 11, 12], L3502 = [0, 0, 1, 2, 5, 11, 12, 12], L3685 = [0, 0, 1, 3, 3, 4, 5, 9], L3696 = [0, 0, 1, 3, 3, 4, 7, 9], L3715 = [0, 0, 1, 3, 3, 5, 6, 9], L3723 = [0, 0, 1, 3, 3, 5, 8, 9], L3728 = [0, 0, 1, 3, 3, 5, 9, 12], L3739 = [0, 0, 1, 3, 3, 6, 7, 9], L3756 = [0, 0, 1, 3, 3, 7, 8, 9], L3759 = [0, 0, 1, 3, 3, 7, 9, 12], L3792 = [0, 0, 1, 3, 4, 4, 4, 5], L3794 = [0, 0, 1, 3, 4, 4, 4, 7], L3800 = [0, 0, 1, 3, 4, 4, 5, 6], L3802 = [0, 0, 1, 3, 4, 4, 5, 8], L3805 = [0, 0, 1, 3, 4, 4, 5, 12], L3807 = [0, 0, 1, 3, 4, 4, 6, 7], L3813 = [0, 0, 1, 3, 4, 4, 7, 8], L3815 = [0, 0, 1, 3, 4, 4, 7, 12], L3830 = [0, 0, 1, 3, 4, 5, 6, 6], L3832 = [0, 0, 1, 3, 4, 5, 6, 8], L3835 = [0, 0, 1, 3, 4, 5, 6, 12], L3840 = [0, 0, 1, 3, 4, 5, 8, 8], L3843 = [0, 0, 1, 3, 4, 5, 8, 12], L3846 = [0, 0, 1, 3, 4, 5, 12, 12], L3848 = [0, 0, 1, 3, 4, 6, 6, 7], L3854 = [0, 0, 1, 3, 4, 6, 7, 8], L3856 = [0, 0, 1, 3, 4, 6, 7, 12], L3871 = [0, 0, 1, 3, 4, 7, 8, 8], L3873 = [0, 0, 1, 3, 4, 7, 8, 12], L3876 = [0, 0, 1, 3, 4, 7, 12, 12], L3906 = [0, 0, 1, 3, 5, 6, 6, 6], L3908 = [0, 0, 1, 3, 5, 6, 6, 8],
192
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 24 {0} {41, 43}, {213, 217}, {254, 256}, {262, 269}, {264, 275}, {267, 277}, {846, 850}, {899, 911}, {938, 942}, {969, 973}, {975, 983}, {979, 988}, {1071, 1082}, {1099, 1101}, {1107, 1114}, {1109, 1120}, {1112, 1122}, {1137, 1155}, {1139, 1161}, {1142, 1163}, {1147, 1178}, {1150, 1180}, {1153, 1183}, {2942, 2946}, {3034, 3038}, {3065, 3069}, {3071, 3079}, {3073, 3085}, {3075, 3087}, {3214, 3226}, {3247, 3277}, {3251, 3262}, {3257, 3296}, {3265, 3302}, {3344, 3348}, {3375, 3379}, {3381, 3389}, {3385, 3394}, {3456, 3460}, {3462, 3470}, {3466, 3475}, {3477, 3491}, {3481, 3496}, {3487, 3502}, {3685, 3696},
L3911 = [0, 0, 1, 3, 5, 6, 6, 12], L3916 = [0, 0, 1, 3, 5, 6, 8, 8], L3919 = [0, 0, 1, 3, 5, 6, 8, 12], L3922 = [0, 0, 1, 3, 5, 6, 12, 12], L3931 = [0, 0, 1, 3, 5, 8, 8, 8], L3934 = [0, 0, 1, 3, 5, 8, 8, 12], L3937 = [0, 0, 1, 3, 5, 8, 12, 12], L3940 = [0, 0, 1, 3, 5, 12, 12, 12], L3942 = [0, 0, 1, 3, 6, 6, 6, 7], L3948 = [0, 0, 1, 3, 6, 6, 7, 8], L3950 = [0, 0, 1, 3, 6, 6, 7, 12], L3965 = [0, 0, 1, 3, 6, 7, 8, 8], L3967 = [0, 0, 1, 3, 6, 7, 8, 12], L3970 = [0, 0, 1, 3, 6, 7, 12, 12], L4000 = [0, 0, 1, 3, 7, 8, 8, 8], L4002 = [0, 0, 1, 3, 7, 8, 8, 12], L4005 = [0, 0, 1, 3, 7, 8, 12, 12], L4009 = [0, 0, 1, 3, 7, 12, 12, 12], L7525 = [0, 1, 1, 3, 4, 5, 5, 11], L7534 = [0, 1, 1, 3, 4, 5, 7, 7], L7639 = [0, 1, 1, 3, 5, 5, 6, 11], L7644 = [0, 1, 1, 3, 5, 5, 7, 11], L7648 = [0, 1, 1, 3, 5, 5, 8, 11], L7652 = [0, 1, 1, 3, 5, 5, 11, 12], L7661 = [0, 1, 1, 3, 5, 6, 7, 7], L7682 = [0, 1, 1, 3, 5, 7, 7, 8], L7684 = [0, 1, 1, 3, 5, 7, 7, 11], L7685 = [0, 1, 1, 3, 5, 7, 7, 12], L8917 = [0, 1, 2, 2, 2, 2, 5, 7], L8921 = [0, 1, 2, 2, 2, 2, 5, 11], L9009 = [0, 1, 2, 2, 2, 4, 5, 7], L9013 = [0, 1, 2, 2, 2, 4, 5, 11], L9040 = [0, 1, 2, 2, 2, 5, 6, 7], L9044 = [0, 1, 2, 2, 2, 5, 6, 11], L9046 = [0, 1, 2, 2, 2, 5, 7, 8], L9048 = [0, 1, 2, 2, 2, 5, 7, 10], L9050 = [0, 1, 2, 2, 2, 5, 7, 12], L9054 = [0, 1, 2, 2, 2, 5, 8, 11], L9060 = [0, 1, 2, 2, 2, 5, 10, 11], L9062 = [0, 1, 2, 2, 2, 5, 11, 12], L9226 = [0, 1, 2, 2, 3, 5, 7, 9], L9237 = [0, 1, 2, 2, 3, 5, 9, 11], L9239 = [0, 1, 2, 2, 3, 5, 10, 10], L9278 = [0, 1, 2, 2, 3, 7, 10, 10], L9322 = [0, 1, 2, 2, 4, 4, 5, 7], L9326 = [0, 1, 2, 2, 4, 4, 5, 11], L9353 = [0, 1, 2, 2, 4, 5, 6, 7], L9357 = [0, 1, 2, 2, 4, 5, 6, 11], L9359 = [0, 1, 2, 2, 4, 5, 7, 8], L9361 = [0, 1, 2, 2, 4, 5, 7, 10], L9363 = [0, 1, 2, 2, 4, 5, 7, 12], L9367 = [0, 1, 2, 2, 4, 5, 8, 11], L9373 = [0, 1, 2, 2, 4, 5, 10, 11], L9375 = [0, 1, 2, 2, 4, 5, 11, 12], L9438 = [0, 1, 2, 2, 5, 6, 6, 7], L9442 = [0, 1, 2, 2, 5, 6, 6, 11], L9444 = [0, 1, 2, 2, 5, 6, 7, 8], L9446 = [0, 1, 2, 2, 5, 6, 7, 10], L9448 = [0, 1, 2, 2, 5, 6, 7, 12], L9452 = [0, 1, 2, 2, 5, 6, 8, 11], L9458 = [0, 1, 2, 2, 5, 6, 10, 11], L9460 = [0, 1, 2, 2, 5, 6, 11, 12], L9462 = [0, 1, 2, 2, 5, 7, 8, 8], L9464 = [0, 1, 2, 2, 5, 7, 8, 10], L9466 = [0, 1, 2, 2, 5, 7, 8, 12], L9472 = [0, 1, 2, 2, 5, 7, 10, 12], L9474 = [0, 1, 2, 2, 5, 7, 12, 12], L9478 = [0, 1, 2, 2, 5, 8, 8, 11], L9484 = [0, 1, 2, 2, 5, 8, 10, 11], L9486 = [0, 1, 2, 2, 5, 8, 11, 12 L9494 = [0, 1, 2, 2, 5, 10, 11, 12], L9496 = [0, 1, 2, 2, 5, 11, 12, 12], L9734 = [0, 1, 2, 3, 3, 5, 9, 10], L9773 = [0, 1, 2, 3, 3, 7, 9, 10], L9822 = [0, 1, 2, 3, 4, 4, 5, 10], L9834 = [0, 1, 2, 3, 4, 4, 7, 10], L9855 = [0, 1, 2, 3, 4, 5, 6, 10], L9859 = [0, 1, 2, 3, 4, 5, 7, 9], L9865 = [0, 1, 2, 3, 4, 5, 8, 10], L9870 = [0, 1, 2, 3, 4, 5, 9, 11], L9873 = [0, 1, 2, 3, 4, 5, 10, 12], L9885 = [0, 1, 2, 3, 4, 6, 7, 10], L9904 = [0, 1, 2, 3, 4, 7, 8, 10], L9910 = [0, 1, 2, 3, 4, 7, 10, 12], L9946 = [0, 1, 2, 3, 5, 6, 6, 10], L9950 = [0, 1, 2, 3, 5, 6, 7, 9], L9956 = [0, 1, 2, 3, 5, 6, 8, 10], L9961 = [0, 1, 2, 3, 5, 6, 9, 11], L9964 = [0, 1, 2, 3, 5, 6, 10, 12], L9968 = [0, 1, 2, 3, 5, 7, 8, 9], L9974 = [0, 1, 2, 3, 5, 7, 9, 11], L9975 = [0, 1, 2, 3, 5, 7, 9, 12], L9982 = [0, 1, 2, 3, 5, 8, 8, 10], L9987 = [0, 1, 2, 3, 5, 8, 9, 11], L9990 = [0, 1, 2, 3, 5, 8, 10, 12], L9996 = [0, 1, 2, 3, 5, 9, 11, 12], L9999 = [0, 1, 2, 3, 5, 10, 12, 12], L10011 = [0, 1, 2, 3, 6, 6, 7, 10], L10030 = [0, 1, 2, 3, 6, 7, 8, 10], L10036 = [0, 1, 2, 3, 6, 7, 10, 12], L10070 = [0, 1, 2, 3, 7, 8, 8, 10], L10076 = [0, 1, 2, 3, 7, 8, 10, 12], L10084 = [0, 1, 2, 3, 7, 10, 12, 12], L10148 = [0, 1, 2, 4, 4, 4, 5, 7], L10152 = [0, 1, 2, 4, 4, 4, 5, 11], L10179 = [0, 1, 2, 4, 4, 5, 6, 7], L10183 = [0, 1, 2, 4, 4, 5, 6, 11], L10185 = [0, 1, 2, 4, 4, 5, 7, 8], L10189 = [0, 1, 2, 4, 4, 5, 7, 12], L10193 = [0, 1, 2, 4, 4, 5, 8, 11], L10198 = [0, 1, 2, 4, 4, 5, 11, 12], L10237 = [0, 1, 2, 4, 4, 8, 8, 12], L10260 = [0, 1, 2, 4, 5, 6, 6, 7], L10264 = [0, 1, 2, 4, 5, 6, 6, 11], L10266 = [0, 1, 2, 4, 5, 6, 7, 8], L10270 = [0, 1, 2, 4, 5, 6, 7, 12], L10274 = [0, 1, 2, 4, 5, 6, 8, 11], L10279 = [0, 1, 2, 4, 5, 6, 11, 12], L10281 = [0, 1, 2, 4, 5, 7, 8, 8], L10285 = [0, 1, 2, 4, 5, 7, 8, 12], L10291 = [0, 1, 2, 4, 5, 7, 12, 12 L10295 = [0, 1, 2, 4, 5, 8, 8, 11], L10300 = [0, 1, 2, 4, 5, 8, 11, 12], L10306 = [0, 1, 2, 4, 5, 11, 12, 12],
APPENDIX
193
Table 6. (continued) m = 8 q I indexes of I-isospectral families 24 {0} {3715, 3739}, {3723, 3756}, {3728, 3759}, {3792, 3794}, {3800, 3807}, (cont.) {3802, 3813}, {3805, 3815}, {3830, 3848}, {3832, 3854}, {3835, 3856}, {3840, 3871}, {3843, 3873}, {3846, 3876}, {3906, 3942}, {3908, 3948}, {3911, 3950}, {3916, 3965}, {3919, 3967}, {3922, 3970}, {3931, 4000}, {3934, 4002}, {3937, 4005}, {3940, 4009}, {7644, 7684}, {8917, 8921}, {9009, 9013}, {9040, 9044}, {9046, 9054}, {9048, 9060}, {9050, 9062}, {9226, 9237}, {9239, 9278}, {9322, 9326}, {9353, 9357}, {9359, 9367}, {9361, 9373}, {9363, 9375}, {9438, 9442}, {9444, 9452}, {9446, 9458}, {9448, 9460}, {9462, 9478}, {9464, 9484}, {9466, 9486}, {9472, 9494}, {9474, 9496}, {9734, 9773}, {9822, 9834}, {9855, 9885}, {9859, 9870}, {9865, 9904}, {9873, 9910}, {9946, 10011}, {9950, 9961}, {9956, 10030}, {9964, 10036}, {9968, 9987}, {9982, 10070}, {9990, 10076}, {9999, 10084}, {10148, 10152}, {10179, 10183}, {10185, 10193}, {10189, 10198}, {10260, 10264},
L10352 = [0, 1, 2, 4, 6, 8, 11, 12], L10429 = [0, 1, 2, 5, 6, 6, 6, 7], L10433 = [0, 1, 2, 5, 6, 6, 6, 11], L10435 = [0, 1, 2, 5, 6, 6, 7, 8], L10439 = [0, 1, 2, 5, 6, 6, 7, 12], L10443 = [0, 1, 2, 5, 6, 6, 8, 11], L10448 = [0, 1, 2, 5, 6, 6, 11, 12], L10450 = [0, 1, 2, 5, 6, 7, 8, 8], L10454 = [0, 1, 2, 5, 6, 7, 8, 12], L10460 = [0, 1, 2, 5, 6, 7, 12, 12], L10464 = [0, 1, 2, 5, 6, 8, 8, 11], L10469 = [0, 1, 2, 5, 6, 8, 11, 12], L10475 = [0, 1, 2, 5, 6, 11, 12, 12], L10477 = [0, 1, 2, 5, 7, 8, 8, 8], L10481 = [0, 1, 2, 5, 7, 8, 8, 12], L10487 = [0, 1, 2, 5, 7, 8, 12, 12], L10494 = [0, 1, 2, 5, 7, 12, 12, 1 L10498 = [0, 1, 2, 5, 8, 8, 8, 11], L10503 = [0, 1, 2, 5, 8, 8, 11, 12], L10509 = [0, 1, 2, 5, 8, 11, 12, 12], L10516 = [0, 1, 2, 5, 11, 12, 12, 12], L10836 = [0, 1, 3, 3, 3, 5, 9, 9], L10868 = [0, 1, 3, 3, 3, 7, 9, 9], L10913 = [0, 1, 3, 3, 4, 4, 5, 9], L10924 = [0, 1, 3, 3, 4, 4, 7, 9], L10943 = [0, 1, 3, 3, 4, 5, 6, 9], L10951 = [0, 1, 3, 3, 4, 5, 8, 9], L10956 = [0, 1, 3, 3, 4, 5, 9, 12], L10967 = [0, 1, 3, 3, 4, 6, 7, 9], L10984 = [0, 1, 3, 3, 4, 7, 8, 9], L10987 = [0, 1, 3, 3, 4, 7, 9, 12], L11022 = [0, 1, 3, 3, 5, 6, 6, 9], L11030 = [0, 1, 3, 3, 5, 6, 8, 9], L11035 = [0, 1, 3, 3, 5, 6, 9, 12], L11048 = [0, 1, 3, 3, 5, 8, 8, 9], L11053 = [0, 1, 3, 3, 5, 8, 9, 12], L11058 = [0, 1, 3, 3, 5, 9, 12, 12], L11069 = [0, 1, 3, 3, 6, 6, 7, 9], L11086 = [0, 1, 3, 3, 6, 7, 8, 9], L11089 = [0, 1, 3, 3, 6, 7, 9, 12], L11122 = [0, 1, 3, 3, 7, 8, 8, 9], L11125 = [0, 1, 3, 3, 7, 8, 9, 12], L11129 = [0, 1, 3, 3, 7, 9, 12, 12], L11186 = [0, 1, 3, 4, 4, 4, 4, 5], L11188 = [0, 1, 3, 4, 4, 4, 4, 7], L11194 = [0, 1, 3, 4, 4, 4, 5, 6], L11196 = [0, 1, 3, 4, 4, 4, 5, 8], L11199 = [0, 1, 3, 4, 4, 4, 5, 12], L11201 = [0, 1, 3, 4, 4, 4, 6, 7], L11207 = [0, 1, 3, 4, 4, 4, 7, 8], L11209 = [0, 1, 3, 4, 4, 4, 7, 12], L11224 = [0, 1, 3, 4, 4, 5, 6, 6], L11226 = [0, 1, 3, 4, 4, 5, 6, 8], L11229 = [0, 1, 3, 4, 4, 5, 6, 12], L11234 = [0, 1, 3, 4, 4, 5, 8, 8], L11237 = [0, 1, 3, 4, 4, 5, 8, 12], L11240 = [0, 1, 3, 4, 4, 5, 12, 12], L11242 = [0, 1, 3, 4, 4, 6, 6, 7], L11248 = [0, 1, 3, 4, 4, 6, 7, 8], L11250 = [0, 1, 3, 4, 4, 6, 7, 12], L11265 = [0, 1, 3, 4, 4, 7, 8, 8], L11267 = [0, 1, 3, 4, 4, 7, 8, 12], L11270 = [0, 1, 3, 4, 4, 7, 12, 12], L11300 = [0, 1, 3, 4, 5, 6, 6, 6], L11302 = [0, 1, 3, 4, 5, 6, 6, 8], L11305 = [0, 1, 3, 4, 5, 6, 6, 12], L11310 = [0, 1, 3, 4, 5, 6, 8, 8], L11313 = [0, 1, 3, 4, 5, 6, 8, 12], L11316 = [0, 1, 3, 4, 5, 6, 12, 12], L11321 = [0, 1, 3, 4, 5, 7, 9, 11], L11325 = [0, 1, 3, 4, 5, 8, 8, 8], L11328 = [0, 1, 3, 4, 5, 8, 8, 12], L11331 = [0, 1, 3, 4, 5, 8, 12, 12], L11334 = [0, 1, 3, 4, 5, 12, 12, 12], L11336 = [0, 1, 3, 4, 6, 6, 6, 7], L11342 = [0, 1, 3, 4, 6, 6, 7, 8], L11344 = [0, 1, 3, 4, 6, 6, 7, 12], L11359 = [0, 1, 3, 4, 6, 7, 8, 8], L11361 = [0, 1, 3, 4, 6, 7, 8, 12], L11364 = [0, 1, 3, 4, 6, 7, 12, 12], L11394 = [0, 1, 3, 4, 7, 8, 8, 8], L11396 = [0, 1, 3, 4, 7, 8, 8, 12], L11399 = [0, 1, 3, 4, 7, 8, 12, 12], L11403 = [0, 1, 3, 4, 7, 12, 12, 12], L11455 = [0, 1, 3, 5, 6, 6, 6, 6], L11457 = [0, 1, 3, 5, 6, 6, 6, 8], L11460 = [0, 1, 3, 5, 6, 6, 6, 12], L11465 = [0, 1, 3, 5, 6, 6, 8, 8], L11468 = [0, 1, 3, 5, 6, 6, 8, 12], L11471 = [0, 1, 3, 5, 6, 6, 12, 12], L11480 = [0, 1, 3, 5, 6, 8, 8, 8], L11483 = [0, 1, 3, 5, 6, 8, 8, 12], L11486 = [0, 1, 3, 5, 6, 8, 12, 12], L11489 = [0, 1, 3, 5, 6, 12, 12, 12], L11502 = [0, 1, 3, 5, 8, 8, 8, 8], L11505 = [0, 1, 3, 5, 8, 8, 8, 12], L11508 = [0, 1, 3, 5, 8, 8, 12, 12], L11511 = [0, 1, 3, 5, 8, 12, 12, 12], L11514 = [0, 1, 3, 5, 12, 12, 12, 12], L11516 = [0, 1, 3, 6, 6, 6, 6, 7], L11522 = [0, 1, 3, 6, 6, 6, 7, 8], L11524 = [0, 1, 3, 6, 6, 6, 7, 12 L11539 = [0, 1, 3, 6, 6, 7, 8, 8], L11541 = [0, 1, 3, 6, 6, 7, 8, 12], L11544 = [0, 1, 3, 6, 6, 7, 12, 12], L11574 =
194
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 24 {0} {10266, 10274}, {10270, 10279}, {10281, 10295}, {10285, 10300}, {10291, 10306}, (cont.) {10429, 10433}, {10435, 10443}, {10439, 10448}, {10450, 10464}, {10454, 10469}, {10460, 10475}, {10477, 10498}, {10481, 10503}, {10487, 10509}, {10494, 10516}, {10836, 10868}, {10913, 10924}, {10943, 10967}, {10951, 10984}, {10956, 10987}, {11022, 11069}, {11030, 11086}, {11048, 11122}, {11053, 11125}, {11058, 11129}, {11186, 11188}, {11194, 11201}, {11196, 11207}, {11199, 11209}, {11224, 11242}, {11226, 11248}, {11229, 11250}, {11234, 11265}, {11237, 11267}, {11240, 11270}, {11300, 11336}, {11302, 11342}, {11305, 11344}, {11310, 11359}, {11313, 11361}, {11316, 11364}, {11325, 11394}, {11328, 11396}, {11331, 11399}, {11334, 11403}, {11455, 11516}, {11457, 11522}, {11460, 11524}, {11465, 11539}, {11468, 11541}, {11471, 11544}, {11480, 11574}, {11483, 11576}, {11486, 11579}, {11489, 11583}, {11502, 11635}, {11505, 11637}, {11508, 11640}, {11511, 11644}, {11514, 11649}, {19877, 19889}, {21290, 21330}, {21573, 21638}, {21589, 21691}, {21594, 21696}, {24160, 24164}, {24252, 24256}, {24283, 24287}, {24289, 24297}, {24291, 24303}, {24293, 24305}, {24469, 24480}, {24565, 24569}, {24596, 24600}, {24602, 24610},
[0, 1, 3, 6, 7, 8, 8, 8], L11576 = [0, 1, 3, 6, 7, 8, 8, 12], L11579 = [0, 1, 3, 6, 7, 8, 12, 12], L11583 = [0, 1, 3, 6, 7, 12, 12, 1 L11635 = [0, 1, 3, 7, 8, 8, 8, 8], L11637 = [0, 1, 3, 7, 8, 8, 8, 12], L11640 = [0, 1, 3, 7, 8, 8, 12, 12], L11644 = [0, 1, 3, 7, 8, 12, 12, 12], L11649 = [0, 1, 3, 7, 12, 12, 12, 12], L11926 = [0, 1, 4, 4, 8, 8, 10, 12], L12079 = [0, 1, 4, 6, 8, 10, 11, 12], L16307 = [1, 1, 1, 3, 5, 7, 9, 11], L19121 = [1, 1, 2, 3, 5, 5, 10, 11], L19156 = [1, 1, 2, 3, 5, 7, 7, 10], L19166 = [1, 1, 2, 3, 5, 7, 9, 11], L19877 = [1, 1, 2, 5, 5, 7, 7, 11], L19889 = [1, 1, 2, 5, 5, 7, 11, 11 L20851 = [1, 1, 3, 3, 5, 5, 9, 11], L20885 = [1, 1, 3, 3, 5, 7, 7, 9], L20900 = [1, 1, 3, 3, 5, 7, 11, 11], L21171 = [1, 1, 3, 4, 4, 5, 5, 11], L21180 = [1, 1, 3, 4, 4, 5, 7, 7], L21285 = [1, 1, 3, 4, 5, 5, 6, 11], L21290 = [1, 1, 3, 4, 5, 5, 7, 11], L21294 = [1, 1, 3, 4, 5, 5, 8, 11], L21298 = [1, 1, 3, 4, 5, 5, 11, 12], L21307 = [1, 1, 3, 4, 5, 6, 7, 7], L21328 = [1, 1, 3, 4, 5, 7, 7, 8], L21330 = [1, 1, 3, 4, 5, 7, 7, 11], L21331 = [1, 1, 3, 4, 5, 7, 7, 12], L21568 = [1, 1, 3, 5, 5, 6, 6, 11], L21573 = [1, 1, 3, 5, 5, 6, 7, 11], L21577 = [1, 1, 3, 5, 5, 6, 8, 11], L21581 = [1, 1, 3, 5, 5, 6, 11, 12], L21584 = [1, 1, 3, 5, 5, 7, 7, 9], L21589 = [1, 1, 3, 5, 5, 7, 8, 11], L21591 = [1, 1, 3, 5, 5, 7, 9, 11], L21594 = [1, 1, 3, 5, 5, 7, 11, 12], L21598 = [1, 1, 3, 5, 5, 8, 8, 11], L21602 = [1, 1, 3, 5, 5, 8, 11, 12], L21606 = [1, 1, 3, 5, 5, 11, 12, 12], L21615 = [1, 1, 3, 5, 6, 6, 7, 7], L21636 = [1, 1, 3, 5, 6, 7, 7, 8], L21638 = [1, 1, 3, 5, 6, 7, 7, 11], L21639 = [1, 1, 3, 5, 6, 7, 7, 12], L21689 = [1, 1, 3, 5, 7, 7, 8, 8], L21691 = [1, 1, 3, 5, 7, 7, 8, 11], L21692 = [1, 1, 3, 5, 7, 7, 8, 12], L21694 = [1, 1, 3, 5, 7, 7, 9, 11], L21696 = [1, 1, 3, 5, 7, 7, 11, 12], L21697 = [1, 1, 3, 5, 7, 7, 12, 12], L21718 = [1, 1, 3, 5, 7, 9, 10, 11], L21720 = [1, 1, 3, 5, 7, 9, 11, 11], L24160 = [1, 2, 2, 2, 2, 2, 5, 7], L24164 = [1, 2, 2, 2, 2, 2, 5, 11], L24252 = [1, 2, 2, 2, 2, 4, 5, 7], L24256 = [1, 2, 2, 2, 2, 4, 5, 11], L24283 = [1, 2, 2, 2, 2, 5, 6, 7], L24287 = [1, 2, 2, 2, 2, 5, 6, 11], L24289 = [1, 2, 2, 2, 2, 5, 7, 8], L24291 = [1, 2, 2, 2, 2, 5, 7, 10], L24293 = [1, 2, 2, 2, 2, 5, 7, 12], L24297 = [1, 2, 2, 2, 2, 5, 8, 11], L24303 = [1, 2, 2, 2, 2, 5, 10, 11], L24305 = [1, 2, 2, 2, 2, 5, 11, 1 L24469 = [1, 2, 2, 2, 3, 5, 7, 9], L24480 = [1, 2, 2, 2, 3, 5, 9, 11], L24565 = [1, 2, 2, 2, 4, 4, 5, 7], L24569 = [1, 2, 2, 2, 4, 4, 5, 11], L24596 = [1, 2, 2, 2, 4, 5, 6, 7], L24600 = [1, 2, 2, 2, 4, 5, 6, 11], L24602 = [1, 2, 2, 2, 4, 5, 7, 8], L24604 = [1, 2, 2, 2, 4, 5, 7, 10], L24606 = [1, 2, 2, 2, 4, 5, 7, 12], L24610 = [1, 2, 2, 2, 4, 5, 8, 11], L24616 = [1, 2, 2, 2, 4, 5, 10, 11], L24618 = [1, 2, 2, 2, 4, 5, 11, 12], L24681 = [1, 2, 2, 2, 5, 6, 6, 7], L24685 = [1, 2, 2, 2, 5, 6, 6, 11 L24687 = [1, 2, 2, 2, 5, 6, 7, 8], L24689 = [1, 2, 2, 2, 5, 6, 7, 10], L24691 = [1, 2, 2, 2, 5, 6, 7, 12], L24695 = [1, 2, 2, 2, 5, 6, 8, 11], L24701 = [1, 2, 2, 2, 5, 6, 10, 11], L24703 = [1, 2, 2, 2, 5, 6, 11, 12], L24705 = [1, 2, 2, 2, 5, 7, 8, 8], L24707 = [1, 2, 2, 2, 5, 7, 8, 10], L24709 = [1, 2, 2, 2, 5, 7, 8, 12], L24713 = [1, 2, 2, 2, 5, 7, 10, 10], L24715 = [1, 2, 2, 2, 5, 7, 10, 12], L24717 = [1, 2, 2, 2, 5, 7, 12, 12], L24721 = [1, 2, 2, 2, 5, 8, 8, 11], L24727 = [1, 2, 2, 2, 5, 8, 10, 11], L24729 = [1, 2, 2, 2, 5, 8, 11, 12], L24738 = [1, 2, 2, 2, 5, 10, 10, 11], L24740 = [1, 2, 2, 2, 5, 10, 11, 12], L24742 = [1, 2, 2, 2, 5, 11, 12, 12], L24763 = [1, 2, 2, 2, 6, 6, 10, 10], L25109 = [1, 2, 2, 3, 4, 5, 7, 9], L25120 = [1, 2, 2, 3, 4, 5, 9, 11], L25122 = [1, 2, 2, 3, 4, 5, 10, 10], L25161 =
APPENDIX
195
Table 6. (continued) m = 8 q I indexes of I-isospectral families 24 {0} {24604, 24616}, {24606, 24618}, {24681, 24685}, {24687, 24695}, {24689, 24701}, (cont.) {24691, 24703}, {24705, 24721}, {24707, 24727}, {24709, 24729}, {24713, 24738}, {24715, 24740}, {24717, 24742}, {25109, 25120}, {25122, 25161}, {25203, 25214}, {25216, 25297}, {25222, 25242}, {25227, 25253}, {25229, 25255}, {25244, 25339}, {25258, 25350}, {25416, 25420}, {25447, 25451}, {25453, 25461}, {25455, 25467}, {25457, 25469}, {25532, 25536}, {25538, 25546}, {25540, 25552}, {25542, 25554}, {25556, 25572}, {25558, 25578}, {25560, 25580}, {25566, 25588}, {25568, 25590}, {25717, 25721}, {25723, 25731}, {25725, 25737}, {25727, 25739}, {25741, 25757}, {25743, 25763}, {25745, 25765}, {25751, 25773}, {25753, 25775}, {25777, 25804}, {25779, 25810}, {25781, 25812}, {25787, 25820}, {25789, 25822}, {25798, 25832}, {25800, 25834}, {26309, 26348}, {26402, 26479}, {26414, 26437}, {26428, 26521}, {26440, 26530}, {26603, 26615}, {26636, 26666}, {26640, 26651}, {26646, 26685}, {26654, 26691}, {26727, 26792}, {26731, 26742}, {26737, 26811}, {26745, 26817}, {26749, 26768}, {26756, 26777}, {26763, 26851}, {26771, 26857}, {26780, 26865}, {26923, 27043}, {26927, 26938}, {26933, 27062}, {26941, 27068}, {26945, 26964}, {26952, 26973}, {26959, 27102}, {26967, 27108}, {26976, 27116}, {26980, 27009}, {26987, 27018}, {26997, 27028}, {27004, 27172}, {27012, 27178}, {27021, 27186}, {27031, 27196}, {27290, 27294}, {27321, 27325}, {27327, 27335}, {27331, 27340}, {27402, 27406}, {27408, 27416}, {27412, 27421}, {27423, 27437}, {27427, 27442}, {27433, 27448}, {27571, 27575}, {27577, 27585}, {27581, 27590}, {27592, 27606},
[1, 2, 2, 3, 4, 7, 10, 10], L25203 = [1, 2, 2, 3, 5, 6, 7, 9], L25214 = [1, 2, 2, 3, 5, 6, 9, 11], L25216 = [1, 2, 2, 3, 5, 6, 10, 10 L25222 = [1, 2, 2, 3, 5, 7, 8, 9], L25227 = [1, 2, 2, 3, 5, 7, 9, 10], L25228 = [1, 2, 2, 3, 5, 7, 9, 11], L25229 = [1, 2, 2, 3, 5, 7, 9, 12], L25242 = [1, 2, 2, 3, 5, 8, 9, 11], L25244 = [1, 2, 2, 3, 5, 8, 10, 10], L25253 = [1, 2, 2, 3, 5, 9, 10, 1 L25255 = [1, 2, 2, 3, 5, 9, 11, 12], L25258 = [1, 2, 2, 3, 5, 10, 10, 12], L25297 = [1, 2, 2, 3, 6, 7, 10, 10], L25339 = [1, 2, 2, 3, 7, 8, 10, 10], L25350 = [1, 2, 2, 3, 7, 10, 10, 12], L25416 = [1, 2, 2, 4, 4, 4, 5, 7], L25420 = [1, 2, 2, 4, 4, 4, 5, 11], L25447 = [1, 2, 2, 4, 4, 5, 6, 7], L25451 = [1, 2, 2, 4, 4, 5, 6, 11], L25453 = [1, 2, 2, 4, 4, 5, 7, 8], L25455 = [1, 2, 2, 4, 4, 5, 7, 10], L25457 = [1, 2, 2, 4, 4, 5, 7, 12], L25461 = [1, 2, 2, 4, 4, 5, 8, 11], L25467 = [1, 2, 2, 4, 4, 5, 10, 11], L25469 = [1, 2, 2, 4, 4, 5, 11, 12], L25532 = [1, 2, 2, 4, 5, 6, 6, 7], L25536 = [1, 2, 2, 4, 5, 6, 6, 11], L25538 = [1, 2, 2, 4, 5, 6, 7, 8], L25540 = [1, 2, 2, 4, 5, 6, 7, 10], L25542 = [1, 2, 2, 4, 5, 6, 7, 12], L25546 = [1, 2, 2, 4, 5, 6, 8, 11], L25552 = [1, 2, 2, 4, 5, 6, 10, 11], L25554 = [1, 2, 2, 4, 5, 6, 11, 12], L25556 = [1, 2, 2, 4, 5, 7, 8, 8], L25558 = [1, 2, 2, 4, 5, 7, 8, 10], L25560 = [1, 2, 2, 4, 5, 7, 8, 12], L25566 = [1, 2, 2, 4, 5, 7, 10, 12], L25568 = [1, 2, 2, 4, 5, 7, 12, 12], L25572 = [1, 2, 2, 4, 5, 8, 8, 11], L25578 = [1, 2, 2, 4, 5, 8, 10, 11], L25580 = [1, 2, 2, 4, 5, 8, 11, 12], L25588 = [1, 2, 2, 4, 5, 10, 11, 12], L25590 = [1, 2, 2, 4, 5, 11, 12, 12], L25717 = [1, 2, 2, 5, 6, 6, 6, 7], L25721 = [1, 2, 2, 5, 6, 6, 6, 11], L25723 = [1, 2, 2, 5, 6, 6, 7, 8], L25725 = [1, 2, 2, 5, 6, 6, 7, 10], L25727 = [1, 2, 2, 5, 6, 6, 7, 12], L25731 = [1, 2, 2, 5, 6, 6, 8, 11], L25737 = [1, 2, 2, 5, 6, 6, 10, 11], L25739 = [1, 2, 2, 5, 6, 6, 11, 12], L25741 = [1, 2, 2, 5, 6, 7, 8, 8], L25743 = [1, 2, 2, 5, 6, 7, 8, 10 L25745 = [1, 2, 2, 5, 6, 7, 8, 12], L25751 = [1, 2, 2, 5, 6, 7, 10, 12], L25753 = [1, 2, 2, 5, 6, 7, 12, 12], L25757 = [1, 2, 2, 5, 6, 8, 8, 11], L25763 = [1, 2, 2, 5, 6, 8, 10, 11], L25765 = [1, 2, 2, 5, 6, 8, 11, 12], L25773 = [1, 2, 2, 5, 6, 10, 11, 12], L25775 = [1, 2, 2, 5, 6, 11, 12, 12], L25777 = [1, 2, 2, 5, 7, 8, 8, 8], L25779 = [1, 2, 2, 5, 7, 8, 8, 10], L25781 = [1, 2, 2, 5, 7, 8, 8, 12], L25787 = [1, 2, 2, 5, 7, 8, 10, 12], L25789 = [1, 2, 2, 5, 7, 8, 12, 12], L25798 = [1, 2, 2, 5, 7, 10, 12, 12], L25800 = [1, 2, 2, 5, 7, 12, 12, 12], L25804 = [1, 2, 2, 5, 8, 8, 8, 11], L25810 = [1, 2, 2, 5, 8, 8, 10, 11], L25812 = [1, 2, 2, 5, 8, 8, 11, 12], L25820 = [1, 2, 2, 5, 8, 10, 11, 12], L25822 = [1, 2, 2, 5, 8, 11, 12, 12], L25832 = [1, 2, 2, 5, 10, 11, 12, 12], L25834 = [1, 2, 2, 5, 11, 12, 12, 12], L25889 = [1, 2, 2, 6, 6, 10, 10, 10], L26309 = [1, 2, 3, 3, 4, 5, 9, 10], L26348 = [1, 2, 3, 3, 4, 7, 9, 10], L26402 = [1, 2, 3, 3, 5, 6, 9, 10], L26414 = [1, 2, 3, 3, 5, 7, 9, 9], L26428 = [1, 2, 3, 3, 5, 8, 9, 10],
196
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 24 {0} {27596, 27611}, {27602, 27617}, {27619, 27640}, {27623, 27645}, {27629, 27651}, (cont.) {27636, 27658}, {27877, 27881}, {27883, 27891}, {27887, 27896}, {27898, 27912}, {27902, 27917}, {27908, 27923}, {27925, 27946}, {27929, 27951}, {27935, 27957}, {27942, 27964}, {27966, 27995}, {27970, 28000}, {27976, 28006}, {27983, 28013}, {27991, 28021}, {28600, 28632}, {28679, 28736}, {28697, 28772}, {28704, 28776}, {28846, 28857}, {28876, 28900}, {28884, 28917}, {28889, 28920}, {28955, 29002}, {28963, 29019}, {28968, 29022}, {28981, 29055}, {28986, 29058}, {28991, 29062}, {29121, 29202}, {29129, 29219}, {29134, 29222}, {29147, 29255}, {29152, 29258}, {29157, 29262}, {29176, 29319}, {29181, 29322}, {29186, 29326}, {29191, 29331}, {29421, 29423}, {29429, 29436}, {29431, 29442}, {29434, 29444}, {29459, 29477}, {29461, 29483}, {29464, 29485}, {29469, 29500}, {29472, 29502}, {29475, 29505}, {29535, 29571}, {29537, 29577}, {29540, 29579}, {29545, 29594}, {29548, 29596}, {29551, 29599}, {29560, 29629}, {29563, 29631}, {29566, 29634}, {29569, 29638}, {29690, 29751}, {29692, 29757}, {29695, 29759}, {29700, 29774}, {29703, 29776}, {29706, 29779}, {29715, 29809}, {29718, 29811}, {29721, 29814}, {29724, 29818}, {29737, 29870}, {29740, 29872}, {29743, 29875}, {29746, 29879}, {29749, 29884}, {29966, 30059}, {29968, 30065}, {29971, 30067}, {29976, 30082}, {29979, 30084}, {29982, 30087}, {29991, 30117}, {29994, 30119}, {29997, 30122}, {30000, 30126}, {30013, 30178}, {30016, 30180}, {30019, 30183}, {30022, 30187}, {30025, 30192}, {30042, 30274}, {30045, 30276}, {30048, 30279}, {30051, 30283}, {30054, 30288}, {30057, 30294}
L26437 = [1, 2, 3, 3, 5, 9, 9, 11], L26440 = [1, 2, 3, 3, 5, 9, 10, 12], L26479 = [1, 2, 3, 3, 6, 7, 9, 10], L26521 = [1, 2, 3, 3, 7, 8, 9, 10], L26530 = [1, 2, 3, 3, 7, 9, 10, 12], L26603 = [1, 2, 3, 4, 4, 4, 5, 10], L26615 = [1, 2, 3, 4, 4, 4, 7, 10 L26636 = [1, 2, 3, 4, 4, 5, 6, 10], L26640 = [1, 2, 3, 4, 4, 5, 7, 9], L26646 = [1, 2, 3, 4, 4, 5, 8, 10], L26651 = [1, 2, 3, 4, 4, 5, 9, 11], L26654 = [1, 2, 3, 4, 4, 5, 10, 12], L26666 = [1, 2, 3, 4, 4, 6, 7, 10], L26685 = [1, 2, 3, 4, 4, 7, 8, 10 L26691 = [1, 2, 3, 4, 4, 7, 10, 12], L26727 = [1, 2, 3, 4, 5, 6, 6, 10], L26731 = [1, 2, 3, 4, 5, 6, 7, 9], L26737 = [1, 2, 3, 4, 5, 6, 8, 10], L26742 = [1, 2, 3, 4, 5, 6, 9, 11], L26745 = [1, 2, 3, 4, 5, 6, 10, 12], L26749 = [1, 2, 3, 4, 5, 7, 8, 9], L26756 = [1, 2, 3, 4, 5, 7, 9, 12], L26763 = [1, 2, 3, 4, 5, 8, 8, 10], L26768 = [1, 2, 3, 4, 5, 8, 9, 11], L26771 = [1, 2, 3, 4, 5, 8, 10, 12], L26777 = [1, 2, 3, 4, 5, 9, 11, 12], L26780 = [1, 2, 3, 4, 5, 10, 12, 12], L26792 = [1, 2, 3, 4, 6, 6, 7, 10], L26811 = [1, 2, 3, 4, 6, 7, 8, 10], L26817 = [1, 2, 3, 4, 6, 7, 10, 12], L26851 = [1, 2, 3, 4, 7, 8, 8, 10 L26857 = [1, 2, 3, 4, 7, 8, 10, 12], L26865 = [1, 2, 3, 4, 7, 10, 12, 12], L26923 = [1, 2, 3, 5, 6, 6, 6, 10], L26927 = [1, 2, 3, 5, 6, 6, 7, 9], L26933 = [1, 2, 3, 5, 6, 6, 8, 10], L26938 = [1, 2, 3, 5, 6, 6, 9, 11], L26941 = [1, 2, 3, 5, 6, 6, 10, 12], L26945 = [1, 2, 3, 5, 6, 7, 8, 9], L26952 = [1, 2, 3, 5, 6, 7, 9, 12], L26959 = [1, 2, 3, 5, 6, 8, 8, 10], L26964 = [1, 2, 3, 5, 6, 8, 9, 11], L26967 = [1, 2, 3, 5, 6, 8, 10, 12], L26973 = [1, 2, 3, 5, 6, 9, 11, 12], L26976 = [1, 2, 3, 5, 6, 10, 12, 12], L26980 = [1, 2, 3, 5, 7, 8, 8, 9], L26987 = [1, 2, 3, 5, 7, 8, 9, 12], L26994 = [1, 2, 3, 5, 7, 9, 10, 11], L26996 = [1, 2, 3, 5, 7, 9, 11, 12], L26997 = [1, 2, 3, 5, 7, 9, 12, 12], L27004 = [1, 2, 3, 5, 8, 8, 8, 10], L27009 = [1, 2, 3, 5, 8, 8, 9, 11], L27012 = [1, 2, 3, 5, 8, 8, 10, 12], L27018 = [1, 2, 3, 5, 8, 9, 11, 1 L27021 = [1, 2, 3, 5, 8, 10, 12, 12], L27028 = [1, 2, 3, 5, 9, 11, 12, 12], L27031 = [1, 2, 3, 5, 10, 12, 12, 12], L27043 = [1, 2, 3, 6, 6, 6, 7, 10], L27062 = [1, 2, 3, 6, 6, 7, 8, 10], L27068 = [1, 2, 3, 6, 6, 7, 10, 12], L27102 = [1, 2, 3, 6, 7, 8, 8, 10], L27108 = [1, 2, 3, 6, 7, 8, 10, 12], L27116 = [1, 2, 3, 6, 7, 10, 12, 12], L27172 = [1, 2, 3, 7, 8, 8, 8, 10], L27178 = [1, 2, 3, 7, 8, 8, 10, 12], L27186 = [1, 2, 3, 7, 8, 10, 12, 12], L27196 = [1, 2, 3, 7, 10, 12, 12, 12], L27290 = [1, 2, 4, 4, 4, 4, 5, 7], L27294 = [1, 2, 4, 4, 4, 4, 5, 11], L27321 = [1, 2, 4, 4, 4, 5, 6, 7], L27325 = [1, 2, 4, 4, 4, 5, 6, 11], L27327 = [1, 2, 4, 4, 4, 5, 7, 8], L27331 = [1, 2, 4, 4, 4, 5, 7, 12], L27335 = [1, 2, 4, 4, 4, 5, 8, 11], L27340 = [1, 2, 4, 4, 4, 5, 11, 12], L27402 = [1, 2, 4, 4, 5, 6, 6, 7], L27406 = [1, 2, 4, 4, 5, 6, 6, 11], L27408 = [1, 2, 4, 4, 5, 6, 7, 8], L27412 = [1, 2, 4, 4, 5, 6, 7, 12], L27416 = [1, 2, 4, 4, 5, 6, 8, 11],
APPENDIX
197
Table 6. (continued) m = 8 q 24 (cont.)
I {0, 1}
indexes of I-isospectral families {2380, 2389}, {7525, 7534}, {7639, 7661}, {7648, 7682}, {7652, 7685}, {19121, 19156}, {20851, 20885}, {20900, 21584}, {21171, 21180}, {21285, 21307}, {21294, 21328}, {21298, 21331}, {21568, 21615}, {21577, 21636}, {21581, 21639}, {21598, 21689}, {21602, 21692}, {21606, 21697} {4, 5} {9974, 30005}, {10237, 11926}, {10352, 12079}, {16307, 21694}, {21591, 21720}, {24763, 25889}, {26996, 29711} {0, 7} {9975, 9996}, {11035, 11089} {4, 5, 6, 7} {11321, 30034}, {19166, 21718}, {25228, 26994}
L27421 = [1, 2, 4, 4, 5, 6, 11, 12], L27423 = [1, 2, 4, 4, 5, 7, 8, 8], L27427 = [1, 2, 4, 4, 5, 7, 8, 12], L27433 = [1, 2, 4, 4, 5, 7, 12, 12], L27437 = [1, 2, 4, 4, 5, 8, 8, 11], L27442 = [1, 2, 4, 4, 5, 8, 11, 12], L27448 = [1, 2, 4, 4, 5, 11, 12, 12], L27571 = [1, 2, 4, 5, 6, 6, 6, 7], L27575 = [1, 2, 4, 5, 6, 6, 6, 11], L27577 = [1, 2, 4, 5, 6, 6, 7, 8], L27581 = [1, 2, 4, 5, 6, 6, 7, 12], L27585 = [1, 2, 4, 5, 6, 6, 8, 11], L27590 = [1, 2, 4, 5, 6, 6, 11, 12], L27592 = [1, 2, 4, 5, 6, 7, 8, 8], L27596 = [1, 2, 4, 5, 6, 7, 8, 12], L27602 = [1, 2, 4, 5, 6, 7, 12, 12], L27606 = [1, 2, 4, 5, 6, 8, 8, 11], L27611 = [1, 2, 4, 5, 6, 8, 11, 12], L27617 = [1, 2, 4, 5, 6, 11, 12, 12], L27619 = [1, 2, 4, 5, 7, 8, 8, 8], L27623 = [1, 2, 4, 5, 7, 8, 8, 12], L27629 = [1, 2, 4, 5, 7, 8, 12, 12], L27636 = [1, 2, 4, 5, 7, 12, 12, 12], L27640 = [1, 2, 4, 5, 8, 8, 8, 11], L27645 = [1, 2, 4, 5, 8, 8, 11, 12], L27651 = [1, 2, 4, 5, 8, 11, 12, 12], L27658 = [1, 2, 4, 5, 11, 12, 12, 12], L27877 = [1, 2, 5, 6, 6, 6, 6, 7], L27881 = [1, 2, 5, 6, 6, 6, 6, 11], L27883 = [1, 2, 5, 6, 6, 6, 7, 8], L27887 = [1, 2, 5, 6, 6, 6, 7, 12], L27891 = [1, 2, 5, 6, 6, 6, 8, 11], L27896 = [1, 2, 5, 6, 6, 6, 11, 12], L27898 = [1, 2, 5, 6, 6, 7, 8, 8], L27902 = [1, 2, 5, 6, 6, 7, 8, 12], L27908 = [1, 2, 5, 6, 6, 7, 12, 12 L27912 = [1, 2, 5, 6, 6, 8, 8, 11], L27917 = [1, 2, 5, 6, 6, 8, 11, 12], L27923 = [1, 2, 5, 6, 6, 11, 12, 12], L27925 = [1, 2, 5, 6, 7, 8, 8, 8], L27929 = [1, 2, 5, 6, 7, 8, 8, 12], L27935 = [1, 2, 5, 6, 7, 8, 12, 12], L27942 = [1, 2, 5, 6, 7, 12, 12, 12], L27946 = [1, 2, 5, 6, 8, 8, 8, 11], L27951 = [1, 2, 5, 6, 8, 8, 11, 12], L27957 = [1, 2, 5, 6, 8, 11, 12, 12], L27964 = [1, 2, 5, 6, 11, 12, 12, 12], L27966 = [1, 2, 5, 7, 8, 8, 8, 8], L27970 = [1, 2, 5, 7, 8, 8, 8, 12], L27976 = [1, 2, 5, 7, 8, 8, 12, 12], L27983 = [1, 2, 5, 7, 8, 12, 12, 12], L27991 = [1, 2, 5, 7, 12, 12, 12, 12], L27995 = [1, 2, 5, 8, 8, 8, 8, 11], L28000 = [1, 2, 5, 8, 8, 8, 11, 12], L28006 = [1, 2, 5, 8, 8, 11, 12, 12], L28013 = [1, 2, 5, 8, 11, 12, 12, 12], L28021 = [1, 2, 5, 11, 12, 12, 12, 12], L28600 = [1, 3, 3, 3, 4, 5, 9, 9], L28632 = [1, 3, 3, 3, 4, 7, 9, 9], L28679 = [1, 3, 3, 3, 5, 6, 9, 9], L28697 = [1, 3, 3, 3, 5, 8, 9, 9], L28704 = [1, 3, 3, 3, 5, 9, 9, 12], L28736 = [1, 3, 3, 3, 6, 7, 9, 9], L28772 = [1, 3, 3, 3, 7, 8, 9, 9], L28776 = [1, 3, 3, 3, 7, 9, 9, 12], L28846 = [1, 3, 3, 4, 4, 4, 5, 9], L28857 = [1, 3, 3, 4, 4, 4, 7, 9], L28876 = [1, 3, 3, 4, 4, 5, 6, 9], L28884 = [1, 3, 3, 4, 4, 5, 8, 9], L28889 = [1, 3, 3, 4, 4, 5, 9, 12], L28900 = [1, 3, 3, 4, 4, 6, 7, 9], L28917 = [1, 3, 3, 4, 4, 7, 8, 9], L28920 = [1, 3, 3, 4, 4, 7, 9, 12], L28955 = [1, 3, 3, 4, 5, 6, 6, 9], L28963 = [1, 3, 3, 4, 5, 6, 8, 9], L28968 = [1, 3, 3, 4, 5, 6, 9, 12], L28981 = [1, 3, 3, 4, 5, 8, 8, 9], L28986 = [1, 3, 3, 4, 5, 8, 9, 12], L28991 = [1, 3, 3, 4, 5, 9, 12, 12], L29002 = [1, 3, 3, 4, 6, 6, 7, 9], L29019 = [1, 3, 3, 4, 6, 7, 8, 9], L29022 = [1, 3, 3, 4, 6, 7, 9, 12], L29055 = [1, 3, 3, 4, 7, 8, 8, 9], L29058 = [1, 3, 3, 4, 7, 8, 9, 12], L29062 = [1, 3, 3, 4, 7, 9, 12, 12], L29121 = [1, 3, 3, 5, 6, 6, 6, 9], L29129 = [1, 3, 3, 5, 6, 6, 8, 9], L29134 = [1, 3, 3, 5, 6, 6, 9, 12], L29147 = [1, 3, 3, 5, 6, 8, 8, 9], L29152 = [1, 3, 3, 5, 6, 8, 9, 12], L29157 = [1, 3, 3, 5, 6, 9, 12, 12], L29176 = [1, 3, 3, 5, 8, 8, 8, 9], L29181 = [1, 3, 3, 5, 8, 8, 9, 12], L29186 = [1, 3, 3, 5, 8, 9, 12, 12], L29191 = [1, 3, 3, 5, 9, 12, 12, 12], L29202 = [1, 3, 3, 6, 6, 6, 7, 9], L29219 = [1, 3, 3, 6, 6, 7, 8, 9], L29222 = [1, 3, 3, 6, 6, 7, 9, 12], L29255 = [1, 3, 3, 6, 7, 8, 8, 9], L29258 = [1, 3, 3, 6, 7, 8, 9, 12], L29262 = [1, 3, 3, 6, 7, 9, 12, 12], L29319 = [1, 3, 3, 7, 8, 8, 8, 9], L29322 = [1, 3, 3, 7, 8, 8, 9, 12], L29326 = [1, 3, 3, 7, 8, 9, 12, 12], L29331 = [1, 3, 3, 7, 9, 12, 12, 12], L29421 = [1, 3, 4, 4, 4, 4, 4, 5], L29423 = [1, 3, 4, 4, 4, 4, 4, 7], L29429 = [1, 3, 4, 4, 4, 4, 5, 6], L29431 = [1, 3, 4, 4, 4, 4, 5, 8], L29434 = [1, 3, 4, 4, 4, 4, 5, 12], L29436 = [1, 3, 4, 4, 4, 4, 6, 7], L29442 = [1, 3, 4, 4, 4, 4, 7, 8], L29444 = [1, 3, 4, 4, 4, 4, 7, 12], L29459 = [1, 3, 4, 4, 4, 5, 6, 6], L29461 = [1, 3, 4, 4, 4, 5, 6, 8], L29464 = [1, 3, 4, 4, 4, 5, 6, 12], L29469 = [1, 3, 4, 4, 4, 5, 8, 8], L29472 = [1, 3, 4, 4, 4, 5, 8, 12], L29475 = [1, 3, 4, 4, 4, 5, 12, 12], L29477 =
198
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 25 {0} {133, 146}, {141, 142}, {143, 145, 157}, {499, 514}, {504, 508}, {509, 511}, {510, 513, 516, 524}, {515, 519, 521}, {523, 563}, {529, 534}, {538, 554}, {565, 567}, {1406, 1411}, {1456, 1463}, {1655, 1660}, {1657, 1658}, {1661, 1663, 1671}, {1662, 1666}, {1664, 1668}, {1665, 1688}, {1670, 1674, 1707}, {1673, 1706, 1711, 1712, 1717}, {1677, 1691}, {1687, 1715}, {1696, 1724}, {1699, 1722}, {1719, 1740, 1774}, {1747, 1783}, {1775, 1777}, {1779, 1782, 1815}, {4321, 4326}, {4339, 4347}, {4393, 4400}, {4455, 4465}, {4750, 4752}, {4751, 4753}, {4756, 4776}, {4762, 4792}, {4765, 4838}, {4768, 4769, 4771, 4772, 4773, 4774, 4775, 4778}, {4780, 4782, 4827, 4835}, {4785, 4789}, {4787, 4840}, {4795, 4830, 4831}, {4817, 4871}, {4819, 4826}, {4820, 4869}, {4829, 4834},
[1, 3, 4, 4, 4, 6, 6, 7], L29483 = [1, 3, 4, 4, 4, 6, 7, 8], L29485 = [1, 3, 4, 4, 4, 6, 7, 12], L29500 = [1, 3, 4, 4, 4, 7, 8, 8], L29502 = [1, 3, 4, 4, 4, 7, 8, 12], L29505 = [1, 3, 4, 4, 4, 7, 12, 12], L29535 = [1, 3, 4, 4, 5, 6, 6, 6], L29537 = [1, 3, 4, 4, 5, 6, 6, 8], L29540 = [1, 3, 4, 4, 5, 6, 6, 12], L29545 = [1, 3, 4, 4, 5, 6, 8, 8], L29548 = [1, 3, 4, 4, 5, 6, 8, 12], L29551 = [1, 3, 4, 4, 5, 6, 12, 12], L29560 = [1, 3, 4, 4, 5, 8, 8, 8], L29563 = [1, 3, 4, 4, 5, 8, 8, 12], L29566 = [1, 3, 4, 4, 5, 8, 12, 12], L29569 = [1, 3, 4, 4, 5, 12, 12, 12], L29571 = [1, 3, 4, 4, 6, 6, 6, 7], L29577 = [1, 3, 4, 4, 6, 6, 7, 8], L29579 = [1, 3, 4, 4, 6, 6, 7, 12], L29594 = [1, 3, 4, 4, 6, 7, 8, 8], L29596 = [1, 3, 4, 4, 6, 7, 8, 12], L29599 = [1, 3, 4, 4, 6, 7, 12, 12], L29629 = [1, 3, 4, 4, 7, 8, 8, 8], L29631 = [1, 3, 4, 4, 7, 8, 8, 12], L29634 = [1, 3, 4, 4, 7, 8, 12, 12], L29638 = [1, 3, 4, 4, 7, 12, 12, 12], L29690 = [1, 3, 4, 5, 6, 6, 6, 6], L29692 = [1, 3, 4, 5, 6, 6, 6, 8], L29695 = [1, 3, 4, 5, 6, 6, 6, 12], L29700 = [1, 3, 4, 5, 6, 6, 8, 8], L29703 = [1, 3, 4, 5, 6, 6, 8, 12], L29706 = [1, 3, 4, 5, 6, 6, 12, 12], L29711 = [1, 3, 4, 5, 6, 7, 9, 11], L29715 = [1, 3, 4, 5, 6, 8, 8, 8], L29718 = [1, 3, 4, 5, 6, 8, 8, 12], L29721 = [1, 3, 4, 5, 6, 8, 12, 12], L29724 = [1, 3, 4, 5, 6, 12, 12, 12], L29737 = [1, 3, 4, 5, 8, 8, 8, 8], L29740 = [1, 3, 4, 5, 8, 8, 8, 12], L29743 = [1, 3, 4, 5, 8, 8, 12, 12], L29746 = [1, 3, 4, 5, 8, 12, 12, 1 L29749 = [1, 3, 4, 5, 12, 12, 12, 12], L29751 = [1, 3, 4, 6, 6, 6, 6, 7], L29757 = [1, 3, 4, 6, 6, 6, 7, 8], L29759 = [1, 3, 4, 6, 6, 6, 7, 12], L29774 = [1, 3, 4, 6, 6, 7, 8, 8], L29776 = [1, 3, 4, 6, 6, 7, 8, 12], L29779 = [1, 3, 4, 6, 6, 7, 12, 12], L29809 = [1, 3, 4, 6, 7, 8, 8, 8], L29811 = [1, 3, 4, 6, 7, 8, 8, 12], L29814 = [1, 3, 4, 6, 7, 8, 12, 12], L29818 = [1, 3, 4, 6, 7, 12, 12, 12], L29870 = [1, 3, 4, 7, 8, 8, 8, 8], L29872 = [1, 3, 4, 7, 8, 8, 8, 12], L29875 = [1, 3, 4, 7, 8, 8, 12, 1 L29879 = [1, 3, 4, 7, 8, 12, 12, 12], L29884 = [1, 3, 4, 7, 12, 12, 12, 12], L29966 = [1, 3, 5, 6, 6, 6, 6, 6], L29968 = [1, 3, 5, 6, 6, 6, 6, 8], L29971 = [1, 3, 5, 6, 6, 6, 6, 12], L29976 = [1, 3, 5, 6, 6, 6, 8, 8], L29979 = [1, 3, 5, 6, 6, 6, 8, 12], L29982 = [1, 3, 5, 6, 6, 6, 12, 12], L29991 = [1, 3, 5, 6, 6, 8, 8, 8], L29994 = [1, 3, 5, 6, 6, 8, 8, 12], L29997 = [1, 3, 5, 6, 6, 8, 12, 12], L30000 = [1, 3, 5, 6, 6, 12, 12, 12], L30005 = [1, 3, 5, 6, 7, 8, 9, 11], L30013 = [1, 3, 5, 6, 8, 8, 8, 8], L30016 = [1, 3, 5, 6, 8, 8, 8, 12], L30019 = [1, 3, 5, 6, 8, 8, 12, 12], L30022 = [1, 3, 5, 6, 8, 12, 12, 12], L30025 = [1, 3, 5, 6, 12, 12, 12, 12], L30034 = [1, 3, 5, 7, 8, 9, 11, 12], L30042 = [1, 3, 5, 8, 8, 8, 8, 8], L30045 = [1, 3, 5, 8, 8, 8, 8, 12], L30048 = [1, 3, 5, 8, 8, 8, 12, 12], L30051 = [1, 3, 5, 8, 8, 12, 12, 1 L30054 = [1, 3, 5, 8, 12, 12, 12, 12], L30057 = [1, 3, 5, 12, 12, 12, 12, 12], L30059 = [1, 3, 6, 6, 6, 6, 6, 7], L30065 = [1, 3, 6, 6, 6, 6, 7, 8], L30067 = [1, 3, 6, 6, 6, 6, 7, 12], L30082 = [1, 3, 6, 6, 6, 7, 8, 8], L30084 = [1, 3, 6, 6, 6, 7, 8, 12], L30087 = [1, 3, 6, 6, 6, 7, 12, 12], L30117 = [1, 3, 6, 6, 7, 8, 8, 8], L30119 = [1, 3, 6, 6, 7, 8, 8, 12], L30122 = [1, 3, 6, 6, 7, 8, 12, 12], L30126 = [1, 3, 6, 6, 7, 12, 12, 12], L30178 = [1, 3, 6, 7, 8, 8, 8, 8], L30180 = [1, 3, 6, 7, 8, 8, 8, 12], L30183 = [1, 3, 6, 7, 8, 8, 12, 12], L30187 = [1, 3, 6, 7, 8, 12, 12, 12], L30192 = [1, 3, 6, 7, 12, 12, 12, 12], L30274 = [1, 3, 7, 8, 8, 8, 8, 8], L30276 = [1, 3, 7, 8, 8, 8, 8, 12], L30279 = [1, 3, 7, 8, 8, 8, 12, 12], L30283 = [1, 3, 7, 8, 8, 12, 12, 12], L30288 = [1, 3, 7, 8, 12, 12, 12, 12], L30294 = [1, 3, 7, 12, 12, 12, 12, 12]. q = 25 : L133 = [0, 0, 0, 0, 1, 2, 4, 11], L141 = [0, 0, 0, 0, 1, 2, 6, 7], L142 = [0, 0, 0, 0, 1, 2, 6, 8], L143 = [0, 0, 0, 0, 1, 2, 6, 9], L145 = [0, 0, 0, 0, 1, 2, 6, 11], L146 = [0, 0, 0, 0, 1, 2, 7, 8], L157 = [0, 0, 0, 0, 1, 3, 4, 9], L499 = [0, 0, 0, 1, 2, 3, 4, 11], L504 = [0, 0, 0, 1, 2, 3, 5, 8], L508 = [0, 0, 0, 1, 2, 3, 5, 12], L509 =
APPENDIX
199
Table 6. (continued) m = 8 q I indexes of I-isospectral families 25 {0} {4832, 4837, 4842, 4851}, {4839, 4845, 4848}, {4841, 4865}, {4846, 4855}, (cont.) {4850, 4948}, {4886, 4895}, {4899, 4938}, {4951, 4953}, {11593, 11598}, {11611, 11619}, {11638, 11647}, {11693, 11700}, {11755, 11765}, {11839, 11849}, {12218, 12220}, {12233, 12248}, {12236, 12237, 12240, 12243}, {12238, 12242}, {12239, 12241, 12244, 12252}, {12247, 12251, 12254, 12267}, {12249, 12253, 12266}, {12250, 12259}, {12256, 12262}, {12257, 12261, 12263, 12271, 12278, 12281}, {12258, 12340}, {12265, 12270, 12363}, {12269, 12362, 12367, 12368, 12373}, {12274, 12344}, {12275, 12276, 12282}, {12286, 12288}, {12291, 12295}, {12323, 12403}, {12326, 12401}, {12333, 12341}, {12338, 12371}, {12347, 12397}, {12351, 12380}, {12353, 12387}, {12355, 12378}, {12375, 12430, 12488}, {12437, 12498}, {12490, 12492}, {12494, 12497, 12549}
[0, 0, 0, 1, 2, 3, 6, 7], L510 = [0, 0, 0, 1, 2, 3, 6, 8], L511 = [0, 0, 0, 1, 2, 3, 6, 9], L513 = [0, 0, 0, 1, 2, 3, 6, 11], L514 = [0, 0, 0, 1, 2, 3, 6, 12], L515 = [0, 0, 0, 1, 2, 3, 7, 8], L516 = [0, 0, 0, 1, 2, 3, 7, 9], L518 = [0, 0, 0, 1, 2, 3, 7, 11], L519 = [0, 0, 0, 1, 2, 3, 7, 12], L521 = [0, 0, 0, 1, 2, 3, 8, 12], L523 = [0, 0, 0, 1, 2, 3, 9, 11], L524 = [0, 0, 0, 1, 2, 3, 9, 12], L529 = [0, 0, 0, 1, 2, 4, 5, 7], L534 = [0, 0, 0, 1, 2, 4, 5, 12], L535 = [0, 0, 0, 1, 2, 4, 7, 8], L538 = [0, 0, 0, 1, 2, 4, 9, 10], L554 = [0, 0, 0, 1, 2, 5, 7, 8], L563 = [0, 0, 0, 1, 2, 6, 7, 8], L565 = [0, 0, 0, 1, 2, 6, 7, 11], L567 = [0, 0, 0, 1, 2, 6, 8, 11], L1406 = [0, 0, 1, 1, 4, 4, 6, 11], L1411 = [0, 0, 1, 1, 4, 4, 9, 11], L1456 = [0, 0, 1, 1, 4, 6, 9, 9], L1463 = [0, 0, 1, 1, 4, 6, 11, 11], L1655 = [0, 0, 1, 2, 3, 4, 5, 11], L1657 = [0, 0, 1, 2, 3, 4, 6, 7], L1658 = [0, 0, 1, 2, 3, 4, 6, 8], L1660 = [0, 0, 1, 2, 3, 4, 6, 10], L1661 = [0, 0, 1, 2, 3, 4, 6, 11], L1662 = [0, 0, 1, 2, 3, 4, 6, 12], L1663 = [0, 0, 1, 2, 3, 4, 7, 8], L1664 = [0, 0, 1, 2, 3, 4, 7, 9], L1665 = [0, 0, 1, 2, 3, 4, 7, 10], L1666 = [0, 0, 1, 2, 3, 4, 7, 11], L1668 = [0, 0, 1, 2, 3, 4, 8, 9], L1670 = [0, 0, 1, 2, 3, 4, 8, 11], L1671 = [0, 0, 1, 2, 3, 4, 8, 12], L1673 = [0, 0, 1, 2, 3, 4, 9, 11], L1674 = [0, 0, 1, 2, 3, 4, 9, 12], L1677 = [0, 0, 1, 2, 3, 4, 10, 12], L1687 = [0, 0, 1, 2, 3, 5, 6, 8], L1688 = [0, 0, 1, 2, 3, 5, 6, 9], L1691 = [0, 0, 1, 2, 3, 5, 6, 12], L1696 = [0, 0, 1, 2, 3, 5, 7, 12], L1699 = [0, 0, 1, 2, 3, 5, 8, 12], L1706 = [0, 0, 1, 2, 3, 6, 7, 8], L1707 = [0, 0, 1, 2, 3, 6, 7, 9], L1711 = [0, 0, 1, 2, 3, 6, 8, 12], L1712 = [0, 0, 1, 2, 3, 6, 9, 11], L1715 = [0, 0, 1, 2, 3, 6, 10, 12], L1717 = [0, 0, 1, 2, 3, 7, 8, 11], L1719 = [0, 0, 1, 2, 3, 7, 9, 10], L1722 = [0, 0, 1, 2, 3, 7, 10, 12], L1724 = [0, 0, 1, 2, 3, 8, 10, 12], L1740 = [0, 0, 1, 2, 4, 5, 7, 12], L1747 = [0, 0, 1, 2, 4, 5, 10, 11], L1774 = [0, 0, 1, 2, 5, 6, 7, 8], L1775 = [0, 0, 1, 2, 5, 6, 7, 10], L1777 = [0, 0, 1, 2, 5, 6, 8, 10], L1779 = [0, 0, 1, 2, 5, 6, 9, 10], L1782 = [0, 0, 1, 2, 5, 6, 10, 11], L1783 = [0, 0, 1, 2, 5, 7, 8, 10], L1815 = [0, 0, 1, 3, 4, 5, 9, 10], L4321 = [0, 1, 1, 4, 4, 5, 6, 11], L4326 = [0, 1, 1, 4, 4, 5, 9, 11], L4330 = [0, 1, 1, 4, 4, 6, 6, 9], L4332 = [0, 1, 1, 4, 4, 6, 6, 11], L4339 = [0, 1, 1, 4, 4, 6, 10, 11], L4340 = [0, 1, 1, 4, 4, 6, 11, 11], L4347 = [0, 1, 1, 4, 4, 9, 10, 11], L4348 = [0, 1, 1, 4, 4, 9, 11, 11], L4393 = [0, 1, 1, 4, 5, 6, 9, 9], L4400 = [0, 1, 1, 4, 5, 6, 11, 11], L4455 = [0, 1, 1, 4, 6, 9, 9, 10], L4465 = [0, 1, 1, 4, 6, 10, 11, 11], L4750 = [0, 1, 2, 3, 4, 5, 6, 11], L4751 = [0, 1, 2, 3, 4, 5, 6, 12], L4752 = [0, 1, 2, 3, 4, 5, 7, 8], L4753 = [0, 1, 2, 3, 4, 5, 7, 9], L4755 = [0, 1, 2, 3, 4, 5, 7, 11], L4756 = [0, 1, 2, 3, 4, 5, 7, 12], L4757 = [0, 1, 2, 3, 4, 5, 8, 9], L4762 = [0, 1, 2, 3, 4, 5, 9, 11], L4763 = [0, 1, 2, 3, 4, 5, 9, 12], L4765 = [0, 1, 2, 3, 4, 5, 10, 11], L4768 = [0, 1, 2, 3, 4, 6, 7, 8], L4769 = [0, 1, 2, 3, 4, 6, 7, 9], L4771 = [0, 1, 2, 3, 4, 6, 7, 11], L4772 = [0, 1, 2, 3, 4, 6, 7, 12], L4773 = [0, 1, 2, 3, 4, 6, 8, 9], L4774 = [0, 1, 2, 3, 4, 6, 8, 11], L4775 = [0, 1, 2, 3, 4, 6, 8, 12], L4776 = [0, 1, 2, 3, 4, 6, 9, 10], L4777 = [0, 1, 2, 3, 4, 6, 9, 11], L4778 = [0, 1, 2, 3, 4, 6, 9, 12], L4780 = [0, 1, 2, 3, 4, 6, 10, 11], L4782 = [0, 1, 2, 3, 4, 7, 8, 10], L4783 = [0, 1, 2, 3, 4, 7, 8, 12], L4785 = [0, 1, 2, 3, 4, 7, 9, 12], L4787 = [0, 1, 2, 3, 4, 7, 10, 12], L4789 = [0, 1, 2, 3, 4, 8, 9, 11], L4792 = [0, 1, 2, 3, 4, 8, 10, 12], L4795 = [0, 1, 2, 3, 4, 9, 10, 12 L4817 = [0, 1, 2, 3, 5, 5, 7, 12], L4819 = [0, 1, 2, 3, 5, 5, 8, 10], L4820 = [0, 1, 2, 3, 5, 5, 8, 12], L4826 = [0, 1, 2, 3, 5, 5, 10, 12], L4827 = [0, 1, 2, 3, 5, 6, 7, 8], L4828 = [0, 1, 2, 3, 5, 6, 7, 9], L4829 = [0, 1, 2, 3, 5, 6, 7, 10], L4830 = [0, 1, 2, 3, 5, 6, 7, 11], L4831 = [0, 1, 2, 3, 5, 6, 8, 9], L4832 = [0, 1, 2, 3, 5, 6, 8, 10], L4834 =
200
EMILIO A. LAURET
Table 6. (continued) m = 8 q 25 (cont.)
I {0, 1}
indexes of I-isospectral families {518, 535}, {519, 521}, {1674, 1707}, {1712, 1717}, {4330, 4332}, {4340, 4348}, {4755, 4757}, {4763, 4828}, {4772, 4773, 4774, 4778}, {4782, 4835}, {4795, 4831}, {4844, 4896}, {4845, 4848}, {11602, 11604}, {11612, 11620}, {11625, 11628}, {11639, 11648}, {12231, 12334}, {12270, 12363}, {12271, 12278}, {12275, 12276}, {12301, 12337}, {12368, 12373} {0, 1, 2} {4772, 4778} {0, 1, 4} {12246, 12255}, {12284, 12289} {0, 1, 2, 3, 4} {4777, 4783}, {12277, 12279}
[0, 1, 2, 3, 5, 6, 9, 10], L4835 = [0, 1, 2, 3, 5, 6, 9, 11], L4837 = [0, 1, 2, 3, 5, 6, 10, 11], L4838 = [0, 1, 2, 3, 5, 6, 10, 12], L4839 = [0, 1, 2, 3, 5, 7, 8, 10], L4840 = [0, 1, 2, 3, 5, 7, 8, 11], L4841 = [0, 1, 2, 3, 5, 7, 8, 12], L4842 = [0, 1, 2, 3, 5, 7, 9, 10], L4844 = [0, 1, 2, 3, 5, 7, 10, 11], L4845 = [0, 1, 2, 3, 5, 7, 10, 12], L4846 = [0, 1, 2, 3, 5, 8, 9, 12], L4848 = [0, 1, 2, 3, 5, 8, 10, 12], L4850 = [0, 1, 2, 3, 5, 9, 10, 11], L4851 = [0, 1, 2, 3, 5, 9, 10, 12], L4855 = [0, 1, 2, 3, 6, 7, 8, 10], L4865 = [0, 1, 2, 3, 7, 8, 10, 12], L4869 = [0, 1, 2, 3, 7, 10, 10, 12], L4871 = [0, 1, 2, 3, 8, 10, 10, L4886 = [0, 1, 2, 4, 5, 5, 7, 10], L4895 = [0, 1, 2, 4, 5, 5, 10, 12], L4896 = [0, 1, 2, 4, 5, 7, 8, 10], L4899 = [0, 1, 2, 4, 5, 9, 10, 10], L4938 = [0, 1, 2, 5, 5, 7, 8, 10], L4948 = [0, 1, 2, 5, 6, 7, 8, 10], L4951 = [0, 1, 2, 5, 6, 7, 10, 11], L4953 = [0, 1, 2, 5, 6, 8, 10, 11], L11593 = [1, 1, 4, 4, 5, 5, 6, 11], L11598 = [1, 1, 4, 4, 5, 5, 9, 11], L11602 = [1, 1, 4, 4, 5, 6, 6, 9], L11604 = [1, 1, 4, 4, 5, 6, 6, 11], L11611 = [1, 1, 4, 4, 5, 6, 10, 11], L11612 = [1, 1, 4, 4, 5, 6, 11, 11 L11619 = [1, 1, 4, 4, 5, 9, 10, 11], L11620 = [1, 1, 4, 4, 5, 9, 11, 11], L11625 = [1, 1, 4, 4, 6, 6, 9, 10], L11628 = [1, 1, 4, 4, 6, 6, 10, 11], L11638 = [1, 1, 4, 4, 6, 10, 10, 11], L11639 = [1, 1, 4, 4, 6, 10, 11, 11], L11647 = [1, 1, 4, 4, 9, 10, 10, 11], L11648 = [1, 1, 4, 4, 9, 10, 11, 11], L11693 = [1, 1, 4, 5, 5, 6, 9, 9], L11700 = [1, 1, 4, 5, 5, 6, 11, 11], L11755 = [1, 1, 4, 5, 6, 9, 9, 10], L11765 = [1, 1, 4, 5, 6, 10, 11, 11], L11839 = [1, 1, 4, 6, 9, 9, 10, 10], L11849 = [1, 1, 4, 6, 10, 10, 11, 11], L12218 = [1, 2, 3, 4, 5, 5, 6, 11], L12220 = [1, 2, 3, 4, 5, 5, 7, 8], L12231 = [1, 2, 3, 4, 5, 5, 9, 12], L12233 = [1, 2, 3, 4, 5, 5, 10, 11], L12236 = [1, 2, 3, 4, 5, 6, 7, 8], L12237 = [1, 2, 3, 4, 5, 6, 7, 9], L12238 = [1, 2, 3, 4, 5, 6, 7, 10], L12239 = [1, 2, 3, 4, 5, 6, 7, 11], L12240 = [1, 2, 3, 4, 5, 6, 7, 12], L12241 = [1, 2, 3, 4, 5, 6, 8, 9], L12242 = [1, 2, 3, 4, 5, 6, 8, 10], L12243 = [1, 2, 3, 4, 5, 6, 8, 11], L12244 = [1, 2, 3, 4, 5, 6, 8, 12], L12246 = [1, 2, 3, 4, 5, 6, 9, 11], L12247 = [1, 2, 3, 4, 5, 6, 9, 12], L12248 = [1, 2, 3, 4, 5, 6, 10, 10], L12249 = [1, 2, 3, 4, 5, 6, 10, 11], L12250 = [1, 2, 3, 4, 5, 6, 10, 12], L12251 = [1, 2, 3, 4, 5, 6, 11, 12], L12252 = [1, 2, 3, 4, 5, 7, 8, 9], L12253 = [1, 2, 3, 4, 5, 7, 8, 10], L12254 = [1, 2, 3, 4, 5, 7, 8, 11], L12255 = [1, 2, 3, 4, 5, 7, 8, 12], L12256 = [1, 2, 3, 4, 5, 7, 9, 10], L12257 = [1, 2, 3, 4, 5, 7, 9, 12], L12258 = [1, 2, 3, 4, 5, 7, 10, 10], L12259 = [1, 2, 3, 4, 5, 7, 10, 11], L12261 = [1, 2, 3, 4, 5, 7, 11, 12], L12262 = [1, 2, 3, 4, 5, 8, 9, 10], L12263 = [1, 2, 3, 4, 5, 8, 9, 11], L12265 = [1, 2, 3, 4, 5, 8, 10, 11], L12266 = [1, 2, 3, 4, 5, 8, 10, 12], L12267 = [1, 2, 3, 4, 5, 8, 11, 12], L12269 = [1, 2, 3, 4, 5, 9, 10, 11], L12270 = [1, 2, 3, 4, 5, 9, 10, 12], L12271 = [1, 2, 3, 4, 5, 9, 11, 12], L12274 = [1, 2, 3, 4, 5, 10, 10, 12], L12275 = [1, 2, 3, 4, 6, 7, 8, 9], L12276 = [1, 2, 3, 4, 6, 7, 8, 11], L12277 = [1, 2, 3, 4, 6, 7, 8, 12], L12278 = [1, 2, 3, 4, 6, 7, 9, 10], L12279 = [1, 2, 3, 4, 6, 7, 9, 11], L12281 = [1, 2, 3, 4, 6, 7, 10, 12], L12282 = [1, 2, 3, 4, 6, 7, 11, 12], L12284 = [1, 2, 3, 4, 6, 9, 10, 11], L12286 = [1, 2, 3, 4, 6, 10, 10, 11], L12288 = [1, 2, 3, 4, 7, 8, 10, 10], L12289 = [1, 2, 3, 4, 7, 8, 10, 12], L12291 = [1, 2, 3, 4, 7, 9, 10, 12], L12295 = [1, 2, 3, 4, 8, 9, 10, 11], L12301 = [1, 2, 3, 4, 9, 10, 10, 12], L12323 = [1, 2, 3, 5, 5, 5, 7, 12], L12326 = [1, 2, 3, 5, 5, 5, 8, 12], L12333 = [1, 2, 3, 5, 5, 6, 7, 8], L12334 = [1, 2, 3, 5, 5, 6, 7, 9], L12337 = [1, 2, 3, 5, 5, 6, 8, 9], L12338 = [1, 2, 3, 5, 5, 6, 8, 10], L12340 = [1, 2, 3, 5, 5, 6, 9, 10], L12341 = [1, 2, 3, 5, 5, 6, 9, 11], L12344 = [1, 2, 3, 5, 5, 6, 10, 12 L12347 = [1, 2, 3, 5, 5, 7, 8, 12], L12351 = [1, 2, 3, 5, 5, 7, 10, 12], L12353 = [1, 2, 3, 5, 5, 8, 9, 12], L12355 = [1, 2, 3, 5, 5, 8, 10, 12], L12362 = [1, 2, 3, 5, 6, 7, 8, 10], L12363 = [1, 2, 3, 5, 6, 7, 9, 10], L12367 = [1, 2, 3, 5, 6, 8, 10, 1 L12368 = [1, 2, 3, 5, 6, 9, 10, 11], L12371 = [1, 2, 3, 5, 6, 10, 10, 12], L12373 = [1, 2, 3, 5, 7, 8, 10, 11], L12375 = [1, 2, 3, 5, 7, 9, 10, 10], L12378 = [1, 2, 3, 5, 7, 10, 10, 12], L12380 = [1, 2, 3, 5, 8, 10, 10, 12],
APPENDIX
201
Table 6. (continued) m = 8 q I indexes of I-isospectral families 26 {0} {39, 42}, {40, 44}, {218, 244}, {233, 282}, {246, 247}, {249, 251, 252}, {254, 263}, {257, 269}, {360, 361}, {362, 364}, {902, 961}, {952, 965}, {994, 1045}, {1020, 1088}, {1044, 1077}, {1057, 1181}, {1093, 1095}, {1099, 1104, 1105}, {1108, 1129}, {1114, 1141}, {1352, 1353, 1354}, {1355, 1356}, {1357, 1359}, {3289, 3351}, {3298, 3317}, {3323, 3345}, {3334, 3372}, {3352, 3470}, {3359, 3501}, {3368, 3661}, {3400, 3575}, {3405, 3578}, {3485, 3500}, {3544, 3586}, {3557, 3589}, {3660, 3766}, {3716, 3857}, {3764, 3835}, {3786, 4052}, {3866, 3869}, {3875, 3885, 3886}, {3890, 3931}, {3900, 3951}, {4385, 4386, 4387}, {4388, 4389}, {4390, 4392}, {7493, 7495}, {7534, 7541}, {10497, 10500, 10504}, {10501, 10503}, {10509, 10527}, {10514, 10608}, {10516, 10525}, {10524, 10531}, {10532, 10534}, {10541, 10617},
L12387 = [1, 2, 3, 6, 7, 8, 10, 10], L12397 = [1, 2, 3, 7, 8, 10, 10, 12], L12401 = [1, 2, 3, 7, 10, 10, 10, 12], L12403 = [1, 2, 3, 8, 10, 10, 10, 12], L12430 = [1, 2, 4, 5, 5, 7, 10, 12], L12437 = [1, 2, 4, 5, 5, 10, 10, 11], L12488 = [1, 2, 5, 5, 6, 7, 8, 10], L12490 = [1, 2, 5, 5, 6, 7, 10, 10], L12492 = [1, 2, 5, 5, 6, 8, 10, 10], L12494 = [1, 2, 5, 5, 6, 9, 10, 10], L12497 = [1, 2, 5, 5, 6, 10, 10, 11], L12498 = [1, 2, 5, 5, 7, 8, 10, 10], L12549 = [1, 3, 4, 5, 5, 9, 10, 10]. q = 26 : L39 = [0, 0, 0, 0, 0, 1, 3, 5], L40 = [0, 0, 0, 0, 0, 1, 3, 7], L42 = [0, 0, 0, 0, 0, 1, 3, 9], L44 = [0, 0, 0, 0, 0, 1, 3, 11], L218 = [0, 0, 0, 0, 1, 2, 7, 8], L233 = [0, 0, 0, 0, 1, 2, 10, 11], L244 = [0, 0, 0, 0, 1, 3, 4, 8], L246 = [0, 0, 0, 0, 1, 3, 4, 10], L247 = [0, 0, 0, 0, 1, 3, 4, 12], L249 = [0, 0, 0, 0, 1, 3, 5, 7], L251 = [0, 0, 0, 0, 1, 3, 5, 9], L252 = [0, 0, 0, 0, 1, 3, 5, 11], L254 = [0, 0, 0, 0, 1, 3, 5, 13], L257 = [0, 0, 0, 0, 1, 3, 7, 13], L263 = [0, 0, 0, 0, 1, 3, 9, 13], L269 = [0, 0, 0, 0, 1, 3, 11, 13], L282 = [0, 0, 0, 0, 1, 4, 5, 8], L360 = [0, 0, 0, 0, 2, 4, 6, 13], L361 = [0, 0, 0, 0, 2, 4, 8, 13], L362 = [0, 0, 0, 0, 2, 4, 10, 13], L364 = [0, 0, 0, 0, 2, 6, 8, 13], L902 = [0, 0, 0, 1, 2, 3, 9, 12], L952 = [0, 0, 0, 1, 2, 4, 10, 11], L961 = [0, 0, 0, 1, 2, 5, 6, 7], L965 = [0, 0, 0, 1, 2, 5, 6, 12], L994 = [0, 0, 0, 1, 2, 6, 7, 8], L1020 = [0, 0, 0, 1, 2, 7, 8, 13], L1044 = [0, 0, 0, 1, 2, 9, 10, 11], L1045 = [0, 0, 0, 1, 2, 9, 10, 12], L1057 = [0, 0, 0, 1, 2, 10, 11, 13], L1077 = [0, 0, 0, 1, 3, 4, 5, 8], L1088 = [0, 0, 0, 1, 3, 4, 8, 13], L1093 = [0, 0, 0, 1, 3, 4, 10, 13], L1095 = [0, 0, 0, 1, 3, 4, 12, 13], L1099 = [0, 0, 0, 1, 3, 5, 7, 13], L1104 = [0, 0, 0, 1, 3, 5, 9, 13], L1105 = [0, 0, 0, 1, 3, 5, 11, 13], L1108 = [0, 0, 0, 1, 3, 5, 13, 13], L1114 = [0, 0, 0, 1, 3, 7, 13, 13], L1129 = [0, 0, 0, 1, 3, 9, 13, 13], L1141 = [0, 0, 0, 1, 3, 11, 13, L1181 = [0, 0, 0, 1, 4, 5, 8, 13], L1352 = [0, 0, 0, 2, 4, 6, 8, 13], L1353 = [0, 0, 0, 2, 4, 6, 10, 13], L1354 = [0, 0, 0, 2, 4, 6, 12, 13], L1355 = [0, 0, 0, 2, 4, 6, 13, 13], L1356 = [0, 0, 0, 2, 4, 8, 13, 13], L1357 = [0, 0, 0, 2, 4, 10, 13, L1359 = [0, 0, 0, 2, 6, 8, 13, 13], L3289 = [0, 0, 1, 2, 3, 4, 7, 8], L3298 = [0, 0, 1, 2, 3, 4, 8, 11], L3317 = [0, 0, 1, 2, 3, 5, 6, 10], L3323 = [0, 0, 1, 2, 3, 5, 7, 10], L3334 = [0, 0, 1, 2, 3, 5, 9, 12], L3345 = [0, 0, 1, 2, 3, 6, 7, 9], L3351 = [0, 0, 1, 2, 3, 6, 8, 9], L3352 = [0, 0, 1, 2, 3, 6, 8, 10], L3359 = [0, 0, 1, 2, 3, 6, 10, 11], L3368 = [0, 0, 1, 2, 3, 7, 8, 10], L3372 = [0, 0, 1, 2, 3, 7, 9, 10], L3400 = [0, 0, 1, 2, 3, 9, 10, 12], L3405 = [0, 0, 1, 2, 3, 9, 12, 13], L3470 = [0, 0, 1, 2, 4, 5, 6, 12], L3485 = [0, 0, 1, 2, 4, 5, 10, 12], L3500 = [0, 0, 1, 2, 4, 6, 7, 8], L3501 = [0, 0, 1, 2, 4, 6, 7, 9], L3544 = [0, 0, 1, 2, 4, 9, 10, 11], L3557 = [0, 0, 1, 2, 4, 10, 11, 13], L3575 = [0, 0, 1, 2, 5, 6, 7, 8], L3578 = [0, 0, 1, 2, 5, 6, 7, 13], L3586 = [0, 0, 1, 2, 5, 6, 11, 12], L3589 = [0, 0, 1, 2, 5, 6, 12, 13], L3660 = [0, 0, 1, 2, 6, 7, 8, 13], L3661 = [0, 0, 1, 2, 6, 7, 9, 10], L3716 = [0, 0, 1, 2, 7, 8, 13, 13], L3764 = [0, 0, 1, 2, 9, 10, 11, 13 L3766 = [0, 0, 1, 2, 9, 10, 12, 13], L3786 = [0, 0, 1, 2, 10, 11, 13, 13], L3835 = [0, 0, 1, 3, 4, 5, 8, 13], L3857 = [0, 0, 1, 3, 4, 8, 13, 13], L3866 = [0, 0, 1, 3, 4, 10, 13, 13], L3869 = [0, 0, 1, 3, 4, 12, 13, 13], L3875 = [0, 0, 1, 3, 5, 7, 13, 13], L3885 = [0, 0, 1, 3, 5, 9, 13, 13], L3886 = [0, 0, 1, 3, 5, 11, 13, 13], L3890 = [0, 0, 1, 3, 5, 13, 13, 13], L3900 = [0, 0, 1, 3, 7, 13, 13, 13], L3931 = [0, 0, 1, 3, 9, 13, 13, 13], L3951 = [0, 0, 1, 3, 11, 13, 13, 13], L4052 = [0, 0, 1, 4, 5, 8, 13, 13], L4385 = [0, 0, 2, 4, 6, 8, 13, 13],
202
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 26 {0} {10550, 10614}, {10551, 10552, 10963}, {10553, 10694}, {10560, 10572}, (cont.) {10571, 10610}, {10578, 10615}, {10579, 10623}, {10587, 10648}, {10609, 10620}, {10630, 10679}, {10637, 10680}, {10646, 10962}, {10661, 10739}, {10675, 10974}, {10696, 11049}, {10698, 10977}, {10712, 11050}, {10730, 10971}, {10731, 11365}, {10774, 11133}, {10793, 11195}, {10800, 11199}, {11005, 11048}, {11046, 11061}, {11134, 11215}, {11156, 11219}, {11362, 11547}, {11461, 11714}, {11544, 11677}, {11577, 12077}, {11659, 11661}, {11727, 11731}, {11738, 11754, 11755}, {11760, 11831}, {11775, 11861}, {12670, 12671, 12672}, {12673, 12674}, {12675, 12677}, {22588, 22592}, {22621, 22625}, {22622, 22642}, {22634, 22651}, {22682, 22744}, {22699, 22714}, {29654, 29656, 29659}, {29655, 29679},
L4386 = [0, 0, 2, 4, 6, 10, 13, 13], L4387 = [0, 0, 2, 4, 6, 12, 13, 13], L4388 = [0, 0, 2, 4, 6, 13, 13, 13], L4389 = [0, 0, 2, 4, 8, 13, 13, 13], L4390 = [0, 0, 2, 4, 10, 13, 13, 13], L4392 = [0, 0, 2, 6, 8, 13, 13, 13], L7493 = [0, 1, 1, 3, 3, 4, 9, 10], L7495 = [0, 1, 1, 3, 3, 4, 9, 12], L7534 = [0, 1, 1, 3, 3, 5, 11, 11], L7541 = [0, 1, 1, 3, 3, 7, 7, 9], L10497 = [0, 1, 2, 3, 4, 5, 6, 11], L10500 = [0, 1, 2, 3, 4, 5, 7, 8], L10501 = [0, 1, 2, 3, 4, 5, 7, 9], L10503 = [0, 1, 2, 3, 4, 5, 7, 11], L10504 = [0, 1, 2, 3, 4, 5, 7, 12], L10509 = [0, 1, 2, 3, 4, 5, 8, 11], L10514 = [0, 1, 2, 3, 4, 5, 9, 12], L10516 = [0, 1, 2, 3, 4, 5, 10, 11], L10517 = [0, 1, 2, 3, 4, 5, 10, 12], L10524 = [0, 1, 2, 3, 4, 6, 7, 8], L10525 = [0, 1, 2, 3, 4, 6, 7, 9], L10527 = [0, 1, 2, 3, 4, 6, 7, 11], L10531 = [0, 1, 2, 3, 4, 6, 8, 9], L10532 = [0, 1, 2, 3, 4, 6, 8, 10], L10534 = [0, 1, 2, 3, 4, 6, 8, 12], L10536 = [0, 1, 2, 3, 4, 6, 9, 10], L10541 = [0, 1, 2, 3, 4, 6, 10, 11], L10550 = [0, 1, 2, 3, 4, 7, 8, 9], L10551 = [0, 1, 2, 3, 4, 7, 8, 10], L10552 = [0, 1, 2, 3, 4, 7, 8, 12], L10553 = [0, 1, 2, 3, 4, 7, 8, 13], L10554 = [0, 1, 2, 3, 4, 7, 9, 10], L10560 = [0, 1, 2, 3, 4, 7, 10, 12], L10571 = [0, 1, 2, 3, 4, 8, 9, 11], L10572 = [0, 1, 2, 3, 4, 8, 9, 12], L10578 = [0, 1, 2, 3, 4, 8, 11, 12], L10579 = [0, 1, 2, 3, 4, 8, 11, 1 L10587 = [0, 1, 2, 3, 4, 9, 11, 12], L10608 = [0, 1, 2, 3, 5, 6, 7, 8], L10609 = [0, 1, 2, 3, 5, 6, 7, 9], L10610 = [0, 1, 2, 3, 5, 6, 7, 10], L10614 = [0, 1, 2, 3, 5, 6, 8, 9], L10615 = [0, 1, 2, 3, 5, 6, 8, 10], L10616 = [0, 1, 2, 3, 5, 6, 8, 11], L10617 = [0, 1, 2, 3, 5, 6, 8, 12], L10620 = [0, 1, 2, 3, 5, 6, 9, 11], L10623 = [0, 1, 2, 3, 5, 6, 10, 13], L10630 = [0, 1, 2, 3, 5, 7, 8, 10], L10637 = [0, 1, 2, 3, 5, 7, 10, 13], L10646 = [0, 1, 2, 3, 5, 8, 9, 12], L10648 = [0, 1, 2, 3, 5, 8, 10, 1 L10661 = [0, 1, 2, 3, 5, 9, 12, 13], L10675 = [0, 1, 2, 3, 6, 7, 8, 10], L10679 = [0, 1, 2, 3, 6, 7, 9, 10], L10680 = [0, 1, 2, 3, 6, 7, 9, 13], L10694 = [0, 1, 2, 3, 6, 8, 9, 13], L10696 = [0, 1, 2, 3, 6, 8, 10, 11], L10698 = [0, 1, 2, 3, 6, 8, 10, 1 L10712 = [0, 1, 2, 3, 6, 10, 11, 13], L10730 = [0, 1, 2, 3, 7, 8, 10, 12], L10731 = [0, 1, 2, 3, 7, 8, 10, 13], L10739 = [0, 1, 2, 3, 7, 9, 10, 13], L10774 = [0, 1, 2, 3, 8, 10, 11, 12], L10793 = [0, 1, 2, 3, 9, 10, 12, 13], L10800 = [0, 1, 2, 3, 9, 12, 13, 13], L10962 = [0, 1, 2, 4, 5, 6, 7, 9], L10963 = [0, 1, 2, 4, 5, 6, 7, 10], L10971 = [0, 1, 2, 4, 5, 6, 9, 12], L10974 = [0, 1, 2, 4, 5, 6, 11, 12], L10977 = [0, 1, 2, 4, 5, 6, 12, 13], L11005 = [0, 1, 2, 4, 5, 10, 12, 13], L11046 = [0, 1, 2, 4, 6, 7, 8, 10], L11048 = [0, 1, 2, 4, 6, 7, 8, 13], L11049 = [0, 1, 2, 4, 6, 7, 9, 10], L11050 = [0, 1, 2, 4, 6, 7, 9, 13], L11061 = [0, 1, 2, 4, 6, 8, 10, 11], L11062 = [0, 1, 2, 4, 6, 8, 10, 1 L11133 = [0, 1, 2, 4, 9, 10, 11, 12], L11134 = [0, 1, 2, 4, 9, 10, 11, 13], L11156 = [0, 1, 2, 4, 10, 11, 13, 13], L11195 = [0, 1, 2, 5, 6, 7, 8, 13], L11199 = [0, 1, 2, 5, 6, 7, 13, 13], L11215 = [0, 1, 2, 5, 6, 11, 12, 13], L11219 = [0, 1, 2, 5, 6, 12, 13, 13], L11362 = [0, 1, 2, 6, 7, 8, 13, 13], L11365 = [0, 1, 2, 6, 7, 9, 10, 13], L11461 = [0, 1, 2, 7, 8, 13, 13, 13], L11544 = [0, 1, 2, 9, 10, 11, 13, 13], L11547 = [0, 1, 2, 9, 10, 12, 13, 13], L11577 = [0, 1, 2, 10, 11, 13, 13, 13], L11659 = [0, 1, 3, 4, 4, 10, 10, 12], L11661 = [0, 1, 3, 4, 4, 10, 12, 12], L11677 = [0, 1, 3, 4, 5, 8, 13, 13], L11714 = [0, 1, 3, 4, 8, 13, 13, 13], L11727 = [0, 1, 3, 4, 10, 13, 13, 13], L11731 = [0, 1, 3, 4, 12, 13, 13, 13], L11736 = [0, 1, 3, 5, 7, 9, 11, 13], L11738 = [0, 1, 3, 5, 7, 13, 13, 13], L11754 = [0, 1, 3, 5, 9, 13, 13, 13], L11755 = [0, 1, 3, 5, 11, 13, 13, 13], L11760 = [0, 1, 3, 5, 13, 13, 13, 13], L11775 = [0, 1, 3, 7, 13, 13, 13, 13], L11831 = [0, 1, 3, 9, 13, 13, 13, 13], L11861 = [0, 1, 3, 11, 13, 13, 13, 13], L12077 = [0, 1, 4, 5, 8, 13, 13, 13], L12668 = [0, 2, 4, 6, 8, 10, 12, 13], L12670 = [0, 2, 4, 6, 8, 13, 13, 13],
APPENDIX
203
Table 6. (continued) m = 8 q I indexes of I-isospectral families 26 {0} {29661, 29664, 29666, 29686}, {29665, 29677, 29688}, {29669, 29751}, (cont.) {29671, 29678, 29752}, {29672, 29681, 29690}, {29682, 29894}, {29684, 29689}, {29698, 29735}, {29699, 29717, 29734, 29809}, {29701, 29742}, {29702, 29765}, {29705, 29743}, {29710, 29764, 29799, 29912}, {29715, 29897}, {29718, 29737}, {29731, 29732, 29758}, {29733, 29753}, {29757, 29761}, {29774, 29840}, {29775, 29915}, {29791, 29909}, {29793, 30587}, {29794, 29795, 30591}, {29796, 30042}, {29798, 29896}, {29811, 29834}, {29831, 29895}, {29832, 29901}, {29846, 29911}, {29847, 29922}, {29856, 29964}, {29862, 29965}, {29900, 29918}, {29934, 30117}, {29935, 30014}, {29943, 30015}, {29962, 30590}, {29984, 30120}, {30007, 30047}, {30008, 30611}, {30048, 30758}, {30051, 30615}, {30074, 30759}, {30105, 30604}, {30107, 30607}, {30108, 31305}, {30181, 30898}, {30210, 31004}, {30219, 31008}, {30657, 30756}, {30754, 30780}, {30899, 31034}, {30932, 31039}, {31300, 31592}, {31457, 31871}, {31588, 31813}, {31634, 32505}, {31788, 31791}, {31889, 31894}, {31902, 31926, 31927}, {31933, 32046}, {31954, 32088}, {33402, 33405}, {33488, 33489, 33490}, {33491, 33492}, {33493, 33495}
L12671 = [0, 2, 4, 6, 10, 13, 13, 13], L12672 = [0, 2, 4, 6, 12, 13, 13, 13], L12673 = [0, 2, 4, 6, 13, 13, 13, 13], L12674 = [0, 2, 4, 8, 13, 13, 13, 13], L12675 = [0, 2, 4, 10, 13, 13, 13, 13], L12677 = [0, 2, 6, 8, 13, 13, 13, 13], L22588 = [1, 1, 3, 3, 4, 9, 10, 13], L22592 = [1, 1, 3, 3, 4, 9, 12, 13], L22621 = [1, 1, 3, 3, 5, 5, 9, 9], L22622 = [1, 1, 3, 3, 5, 5, 9, 11], L22625 = [1, 1, 3, 3, 5, 5, 11, 11], L22634 = [1, 1, 3, 3, 5, 7, 7, 11], L22642 = [1, 1, 3, 3, 5, 7, 9, 9], L22651 = [1, 1, 3, 3, 5, 7, 11, 11], L22682 = [1, 1, 3, 3, 5, 9, 11, 11], L22699 = [1, 1, 3, 3, 5, 11, 11, 13], L22714 = [1, 1, 3, 3, 7, 7, 9, 13], L22744 = [1, 1, 3, 3, 7, 9, 11, 11], L23633 = [1, 1, 3, 5, 7, 9, 11, 13], L29654 = [1, 2, 3, 4, 5, 6, 7, 10], L29655 = [1, 2, 3, 4, 5, 6, 7, 11], L29656 = [1, 2, 3, 4, 5, 6, 7, 12], L29659 = [1, 2, 3, 4, 5, 6, 8, 9], L29661 = [1, 2, 3, 4, 5, 6, 8, 11], L29664 = [1, 2, 3, 4, 5, 6, 9, 10], L29665 = [1, 2, 3, 4, 5, 6, 9, 11], L29666 = [1, 2, 3, 4, 5, 6, 9, 12], L29669 = [1, 2, 3, 4, 5, 6, 10, 12], L29671 = [1, 2, 3, 4, 5, 6, 11, 12], L29672 = [1, 2, 3, 4, 5, 6, 11, 13], L29677 = [1, 2, 3, 4, 5, 7, 8, 9], L29678 = [1, 2, 3, 4, 5, 7, 8, 10], L29679 = [1, 2, 3, 4, 5, 7, 8, 11], L29680 = [1, 2, 3, 4, 5, 7, 8, 12], L29681 = [1, 2, 3, 4, 5, 7, 8, 13], L29682 = [1, 2, 3, 4, 5, 7, 9, 10], L29684 = [1, 2, 3, 4, 5, 7, 9, 13], L29686 = [1, 2, 3, 4, 5, 7, 10, 12], L29688 = [1, 2, 3, 4, 5, 7, 11, 12], L29689 = [1, 2, 3, 4, 5, 7, 11, 13], L29690 = [1, 2, 3, 4, 5, 7, 12, 13], L29698 = [1, 2, 3, 4, 5, 8, 9, 11], L29699 = [1, 2, 3, 4, 5, 8, 9, 12], L29701 = [1, 2, 3, 4, 5, 8, 10, 11], L29702 = [1, 2, 3, 4, 5, 8, 10, 12], L29704 = [1, 2, 3, 4, 5, 8, 11, 12], L29705 = [1, 2, 3, 4, 5, 8, 11, 13], L29710 = [1, 2, 3, 4, 5, 9, 10, 12], L29715 = [1, 2, 3, 4, 5, 9, 12, 13], L29717 = [1, 2, 3, 4, 5, 10, 11, 12], L29718 = [1, 2, 3, 4, 5, 10, 11, 13], L29720 = [1, 2, 3, 4, 5, 10, 12, 13], L29730 = [1, 2, 3, 4, 6, 7, 8, 9], L29731 = [1, 2, 3, 4, 6, 7, 8, 10], L29732 = [1, 2, 3, 4, 6, 7, 8, 12], L29733 = [1, 2, 3, 4, 6, 7, 8, 13], L29734 = [1, 2, 3, 4, 6, 7, 9, 10], L29735 = [1, 2, 3, 4, 6, 7, 9, 11], L29737 = [1, 2, 3, 4, 6, 7, 9, 13], L29739 = [1, 2, 3, 4, 6, 7, 10, 11], L29742 = [1, 2, 3, 4, 6, 7, 11, 12], L29743 = [1, 2, 3, 4, 6, 7, 11, 13], L29751 = [1, 2, 3, 4, 6, 8, 9, 10], L29752 = [1, 2, 3, 4, 6, 8, 9, 11], L29753 = [1, 2, 3, 4, 6, 8, 9, 13], L29757 = [1, 2, 3, 4, 6, 8, 10, 13], L29758 = [1, 2, 3, 4, 6, 8, 11, 12], L29761 = [1, 2, 3, 4, 6, 8, 12, 13], L29764 = [1, 2, 3, 4, 6, 9, 10, 11], L29765 = [1, 2, 3, 4, 6, 9, 10, 12], L29766 = [1, 2, 3, 4, 6, 9, 10, 13], L29774 = [1, 2, 3, 4, 6, 10, 11, 12], L29775 = [1, 2, 3, 4, 6, 10, 11, 13], L29791 = [1, 2, 3, 4, 7, 8, 9, 13], L29793 = [1, 2, 3, 4, 7, 8, 10, 12], L29794 = [1, 2, 3, 4, 7, 8, 10, 13], L29795 = [1, 2, 3, 4, 7, 8, 12, 13], L29796 = [1, 2, 3, 4, 7, 8, 13, 13], L29798 = [1, 2, 3, 4, 7, 9, 10, 11], L29799 = [1, 2, 3, 4, 7, 9, 10, 12], L29800 = [1, 2, 3, 4, 7, 9, 10, 13], L29809 = [1, 2, 3, 4, 7, 10, 11, 12], L29811 = [1, 2, 3, 4, 7, 10, 12, 13], L29831 = [1, 2, 3, 4, 8, 9, 11, 12], L29832 = [1, 2, 3, 4, 8, 9, 11, 13], L29834 =
204
EMILIO A. LAURET
Table 6. (continued) m = 8 q 26 (cont.)
I {0, 1}
indexes of I-isospectral families {251, 252}, {1104, 1105}, {1352, 1353}, {3885, 3886}, {4385, 4386}, {10517, 10536}, {10554, 10616}, {11754, 11755}, {12670, 12671}, {29680, 29730}, {29704, 29739}, {29710, 29799}, {29720, 29766}, {29800, 29913}, {31926, 31927}, {33488, 33489} {3, 4, 5, 6, 7} {11062, 12668}, {11736, 29940}, {23633, 31900}
[1, 2, 3, 4, 8, 9, 12, 13], L29840 = [1, 2, 3, 4, 8, 10, 11, 12], L29846 = [1, 2, 3, 4, 8, 11, 12, 13], L29847 = [1, 2, 3, 4, 8, 11, 13, 13], L29856 = [1, 2, 3, 4, 9, 10, 11, 12], L29862 = [1, 2, 3, 4, 9, 11, 12, 13], L29894 = [1, 2, 3, 5, 6, 7, 8, 9], L29895 = [1, 2, 3, 5, 6, 7, 8, 10], L29896 = [1, 2, 3, 5, 6, 7, 8, 11], L29897 = [1, 2, 3, 5, 6, 7, 8, 13], L29900 = [1, 2, 3, 5, 6, 7, 9, 13], L29901 = [1, 2, 3, 5, 6, 7, 10, 13], L29909 = [1, 2, 3, 5, 6, 8, 9, 13], L29911 = [1, 2, 3, 5, 6, 8, 10, 13], L29912 = [1, 2, 3, 5, 6, 8, 11, 12], L29913 = [1, 2, 3, 5, 6, 8, 11, 13], L29915 = [1, 2, 3, 5, 6, 8, 12, 13], L29918 = [1, 2, 3, 5, 6, 9, 11, 13], L29922 = [1, 2, 3, 5, 6, 10, 13, 13], L29934 = [1, 2, 3, 5, 7, 8, 10, 11], L29935 = [1, 2, 3, 5, 7, 8, 10, 13], L29940 = [1, 2, 3, 5, 7, 9, 11, 13], L29943 = [1, 2, 3, 5, 7, 10, 13, 13], L29962 = [1, 2, 3, 5, 8, 9, 12, 13], L29964 = [1, 2, 3, 5, 8, 10, 11, 12], L29965 = [1, 2, 3, 5, 8, 10, 11, 13], L29984 = [1, 2, 3, 5, 9, 12, 13, 13], L30007 = [1, 2, 3, 6, 7, 8, 10, 12], L30008 = [1, 2, 3, 6, 7, 8, 10, 13], L30014 = [1, 2, 3, 6, 7, 9, 10, 13], L30015 = [1, 2, 3, 6, 7, 9, 13, 13], L30042 = [1, 2, 3, 6, 8, 9, 13, 13], L30047 = [1, 2, 3, 6, 8, 10, 11, 12], L30048 = [1, 2, 3, 6, 8, 10, 11, 13], L30051 = [1, 2, 3, 6, 8, 10, 13, 13], L30074 = [1, 2, 3, 6, 10, 11, 13, 13], L30105 = [1, 2, 3, 7, 8, 10, 11, 12], L30107 = [1, 2, 3, 7, 8, 10, 12, 13], L30108 = [1, 2, 3, 7, 8, 10, 13, 13], L30117 = [1, 2, 3, 7, 9, 10, 11, 12], L30120 = [1, 2, 3, 7, 9, 10, 13, 13], L30181 = [1, 2, 3, 8, 10, 11, 12, 13], L30210 = [1, 2, 3, 9, 10, 12, 13, 13], L30219 = [1, 2, 3, 9, 12, 13, 13, 13], L30587 = [1, 2, 4, 5, 6, 7, 8, 10], L30590 = [1, 2, 4, 5, 6, 7, 9, 13], L30591 = [1, 2, 4, 5, 6, 7, 10, 13], L30604 = [1, 2, 4, 5, 6, 9, 11, 12], L30607 = [1, 2, 4, 5, 6, 9, 12, 13], L30611 = [1, 2, 4, 5, 6, 11, 12, 13], L30615 = [1, 2, 4, 5, 6, 12, 13, 13], L30657 = [1, 2, 4, 5, 10, 12, 13, 13], L30754 = [1, 2, 4, 6, 7, 8, 10, 13], L30756 = [1, 2, 4, 6, 7, 8, 13, 13], L30758 = [1, 2, 4, 6, 7, 9, 10, 13], L30759 = [1, 2, 4, 6, 7, 9, 13, 13], L30780 = [1, 2, 4, 6, 8, 10, 11, 13], L30898 = [1, 2, 4, 9, 10, 11, 12, 13], L30899 = [1, 2, 4, 9, 10, 11, 13, 13], L30932 = [1, 2, 4, 10, 11, 13, 13, 13], L31004 = [1, 2, 5, 6, 7, 8, 13, 13], L31008 = [1, 2, 5, 6, 7, 13, 13, 13], L31034 = [1, 2, 5, 6, 11, 12, 13, 13], L31039 = [1, 2, 5, 6, 12, 13, 13, 13], L31300 = [1, 2, 6, 7, 8, 13, 13, 13], L31305 = [1, 2, 6, 7, 9, 10, 13, 13], L31457 = [1, 2, 7, 8, 13, 13, 13, 13], L31588 = [1, 2, 9, 10, 11, 13, 13, 13], L31592 = [1, 2, 9, 10, 12, 13, 13, 13], L31634 = [1, 2, 10, 11, 13, 13, 13, 13], L31788 = [1, 3, 4, 4, 10, 10, 12, 13], L31791 = [1, 3, 4, 4, 10, 12, 12, 13], L31813 = [1, 3, 4, 5, 8, 13, 13, 13], L31871 = [1, 3, 4, 8, 13, 13, 13, 13], L31889 = [1, 3, 4, 10, 13, 13, 13, 13], L31894 = [1, 3, 4, 12, 13, 13, 13, 13], L31900 = [1, 3, 5, 7, 9, 11, 13, 13], L31902 = [1, 3, 5, 7, 13, 13, 13, 13], L31926 = [1, 3, 5, 9, 13, 13, 13, 13], L31927 = [1, 3, 5, 11, 13, 13, 13, 13], L31933 = [1, 3, 5, 13, 13, 13, 13, 13], L31954 = [1, 3, 7, 13, 13, 13, 13, 13], L32046 = [1, 3, 9, 13, 13, 13, 13, 13], L32088 = [1, 3, 11, 13, 13, 13, 13, 13], L32505 = [1, 4, 5, 8, 13, 13, 13, 13], L33402 = [2, 2, 4, 4, 6, 6, 10, 13], L33405 = [2, 2, 4, 4, 6, 8, 8, 13], L33488 = [2, 4, 6, 8, 13, 13, 13, 13], L33489 = [2, 4, 6, 10, 13, 13, 13, 13], L33490 = [2, 4, 6, 12, 13, 13, 13, 13], L33491 = [2, 4, 6, 13, 13, 13, 13, 13], L33492 = [2, 4, 8, 13, 13, 13, 13, 13], L33493 = [2, 4, 10, 13, 13, 13, 13, 13], L33495 = [2, 6, 8, 13, 13, 13, 13, 13]. q = 27 : L162 = [0, 0, 0, 0, 1, 2, 4, 11], L165 = [0, 0, 0, 0, 1, 2, 5, 7], L168 = [0, 0, 0, 0, 1, 2, 5, 10], L177 = [0, 0, 0, 0, 1, 2, 7, 8], L179 = [0, 0, 0, 0, 1, 2, 7, 10], L687 = [0, 0, 0, 1, 2, 3, 5, 10], L690 = [0, 0, 0, 1, 2, 3, 5, 13], L704 = [0, 0, 0, 1, 2, 3, 7, 13], L716 = [0, 0, 0, 1, 2, 3, 10, 13], L720 = [0, 0, 0, 1, 2, 4, 5, 7], L721 = [0, 0, 0, 1, 2, 4, 5, 8], L723 = [0, 0, 0, 1, 2, 4, 5, 10], L724 = [0, 0, 0, 1, 2, 4, 5, 11], L727 = [0, 0, 0, 1, 2, 4, 7, 8], L730 = [0, 0, 0, 1, 2, 4, 7, 11], L732 = [0, 0, 0, 1, 2, 4, 7, 13], L736 = [0, 0, 0, 1, 2, 4, 9, 11], L738 = [0, 0, 0, 1, 2, 4, 10, 11], L739 = [0, 0, 0, 1, 2, 4, 10, 12], L748 = [0, 0, 0, 1, 2, 5, 7, 8], L749 = [0, 0, 0, 1, 2, 5, 7, 9], L750 = [0, 0, 0, 1, 2, 5, 7, 11], L751 = [0, 0, 0, 1, 2, 5, 7, 12], L755 = [0, 0, 0, 1, 2, 5, 9, 10], L781 = [0, 0, 0, 1, 2, 7, 8, 9], L786 = [0, 0, 0, 1, 2, 7, 9, 10], L880 = [0, 0, 0, 1, 3, 6, 9, 12], L1909 = [0, 0, 1, 1, 3, 6, 9, 12], L2478 = [0, 0, 1, 2, 3, 4, 5, 12], L2480 = [0, 0, 1, 2, 3, 4, 6, 7], L2481 = [0, 0, 1, 2, 3, 4, 6, 8],
APPENDIX
205
Table 6. (continued) m = 8 q I indexes of I-isospectral families 27 {0} {162, 165, 168}, {177, 179}, {687, 690}, {704, 716}, {720, 721}, {723, 724, 727, 732}, {736, 749, 755}, {738, 748}, {739, 751}, {781, 786}, {2478, 2483}, {2480, 2481}, {2487, 2489}, {2492, 2507}, {2496, 2511}, {2504, 2563}, {2525, 2561}, {2528, 2531}, {2574, 2593}, {2575, 2699}, {2576, 2705}, {2583, 2710}, {2602, 2604, 2610}, {2603, 2608}, {2605, 2611, 2617}, {2613, 2614, 2620, 2625}, {2618, 2649}, {2633, 2661, 2669}, {2635, 2659}, {2636, 2663}, {2724, 2733}, {7662, 7800}, {7710, 7711}, {7718, 7723, 7744}, {7728, 7748}, {7731, 7746, 7761}, {7737, 7739}, {7738, 7743}, {7752, 7756}, {7754, 7805, 7807}, {7755, 7809, 7819}, {7758, 7764}, {7767, 7791}, {7776, 7810}, {7779, 7811}, {7788, 7910}, {7793, 8041}, {7813, 7821}, {7825, 7913}, {7833, 7899}, {7838, 7908}, {7843, 7846}, {7886, 7891}, {7923, 8128}, {7924, 8129}, {7930, 7954},
L2483 = [0, 0, 1, 2, 3, 4, 6, 10], L2487 = [0, 0, 1, 2, 3, 4, 7, 8], L2489 = [0, 0, 1, 2, 3, 4, 7, 10], L2492 = [0, 0, 1, 2, 3, 4, 7, 13], L2496 = [0, 0, 1, 2, 3, 4, 8, 12], L2504 = [0, 0, 1, 2, 3, 4, 10, 12], L2507 = [0, 0, 1, 2, 3, 4, 11, 13], L2511 = [0, 0, 1, 2, 3, 5, 6, 8], L2525 = [0, 0, 1, 2, 3, 5, 8, 12], L2528 = [0, 0, 1, 2, 3, 5, 9, 10], L2531 = [0, 0, 1, 2, 3, 5, 9, 13], L2557 = [0, 0, 1, 2, 3, 6, 9, 12], L2561 = [0, 0, 1, 2, 3, 6, 10, 13], L2563 = [0, 0, 1, 2, 3, 6, 11, 13], L2574 = [0, 0, 1, 2, 3, 7, 9, 13], L2575 = [0, 0, 1, 2, 3, 7, 10, 12], L2576 = [0, 0, 1, 2, 3, 7, 11, 12], L2583 = [0, 0, 1, 2, 3, 8, 10, 12], L2593 = [0, 0, 1, 2, 3, 9, 10, 13], L2602 = [0, 0, 1, 2, 4, 5, 7, 8], L2603 = [0, 0, 1, 2, 4, 5, 7, 9], L2604 = [0, 0, 1, 2, 4, 5, 7, 10], L2605 = [0, 0, 1, 2, 4, 5, 7, 11], L2607 = [0, 0, 1, 2, 4, 5, 7, 13], L2608 = [0, 0, 1, 2, 4, 5, 8, 9], L2609 = [0, 0, 1, 2, 4, 5, 8, 10], L2610 = [0, 0, 1, 2, 4, 5, 8, 11], L2611 = [0, 0, 1, 2, 4, 5, 8, 13], L2613 = [0, 0, 1, 2, 4, 5, 9, 10], L2614 = [0, 0, 1, 2, 4, 5, 9, 11], L2617 = [0, 0, 1, 2, 4, 5, 10, 13], L2618 = [0, 0, 1, 2, 4, 5, 11, 12], L2620 = [0, 0, 1, 2, 4, 7, 8, 9], L2623 = [0, 0, 1, 2, 4, 7, 9, 11], L2625 = [0, 0, 1, 2, 4, 7, 9, 13], L2633 = [0, 0, 1, 2, 4, 9, 9, 11], L2635 = [0, 0, 1, 2, 4, 9, 10, 11], L2636 = [0, 0, 1, 2, 4, 9, 10, 12], L2649 = [0, 0, 1, 2, 5, 6, 7, 8], L2659 = [0, 0, 1, 2, 5, 7, 8, 9], L2661 = [0, 0, 1, 2, 5, 7, 9, 9], L2662 = [0, 0, 1, 2, 5, 7, 9, 11], L2663 = [0, 0, 1, 2, 5, 7, 9, 12], L2669 = [0, 0, 1, 2, 5, 9, 9, 10], L2699 = [0, 0, 1, 2, 6, 7, 8, 12], L2705 = [0, 0, 1, 2, 6, 7, 11, 12], L2710 = [0, 0, 1, 2, 6, 8, 10, 12], L2724 = [0, 0, 1, 2, 7, 8, 9, 9], L2733 = [0, 0, 1, 2, 7, 9, 9, 10], L2846 = [0, 0, 1, 3, 3, 6, 9, 12], L2886 = [0, 0, 1, 3, 4, 6, 9, 12], L2901 = [0, 0, 1, 3, 5, 6, 9, 12], L2913 = [0, 0, 1, 3, 6, 6, 9, 12], L2917 = [0, 0, 1, 3, 6, 8, 9, 12], L2921 = [0, 0, 1, 3, 6, 9, 9, 12], L2922 = [0, 0, 1, 3, 6, 9, 12, 12], L4023 = [0, 1, 1, 1, 3, 6, 9, 12], L5238 = [0, 1, 1, 2, 3, 6, 9, 12], L6070 = [0, 1, 1, 3, 3, 6, 9, 12], L6242 = [0, 1, 1, 3, 4, 6, 9, 12], L6367 = [0, 1, 1, 3, 5, 6, 9, 12], L6458 = [0, 1, 1, 3, 6, 6, 9, 12], L6476 = [0, 1, 1, 3, 6, 7, 9, 12], L6491 = [0, 1, 1, 3, 6, 8, 9, 12], L6503 = [0, 1, 1, 3, 6, 9, 9, 12], L6506 = [0, 1, 1, 3, 6, 9, 10, 12], L6508 = [0, 1, 1, 3, 6, 9, 11, 12], L6510 = [0, 1, 1, 3, 6, 9, 12, 12], L6511 = [0, 1, 1, 3, 6, 9, 12, 13], L7656 = [0, 1, 2, 3, 3, 6, 9, 12 L7662 = [0, 1, 2, 3, 3, 6, 11, 13], L7710 = [0, 1, 2, 3, 4, 5, 6, 10], L7711 = [0, 1, 2, 3, 4, 5, 6, 11], L7718 = [0, 1, 2, 3, 4, 5, 7, 12], L7719 = [0, 1, 2, 3, 4, 5, 7, 13], L7721 = [0, 1, 2, 3, 4, 5, 8, 10], L7723 = [0, 1, 2, 3, 4, 5, 8, 12], L7728 = [0, 1, 2, 3, 4, 5, 9, 12], L7731 = [0, 1, 2, 3, 4, 5, 10, 12], L7732 = [0, 1, 2, 3, 4, 5, 10, 13], L7734 = [0, 1, 2, 3, 4, 5, 11, 13], L7737 = [0, 1, 2, 3, 4, 6, 7, 8], L7738 = [0, 1, 2, 3, 4, 6, 7, 9], L7739 = [0, 1, 2, 3, 4, 6, 7, 10], L7743 = [0, 1, 2, 3, 4, 6, 8, 9], L7744 = [0, 1, 2, 3, 4, 6, 8, 11], L7746 = [0, 1, 2, 3, 4, 6, 8, 13], L7748 = [0, 1, 2, 3, 4, 6, 9, 10], L7750 = [0, 1, 2, 3, 4, 6, 9, 12], L7752 = [0, 1, 2, 3, 4, 6, 10, 11], L7754 = [0, 1, 2, 3, 4, 6, 10, 13], L7755 = [0, 1, 2, 3, 4, 6, 11, 12], L7756 = [0, 1, 2, 3, 4, 6, 11, 13], L7758 = [0, 1, 2, 3, 4, 7, 8, 9], L7759 = [0, 1, 2, 3, 4, 7, 8, 10], L7760 = [0, 1, 2, 3, 4, 7, 8, 11], L7761 = [0, 1, 2, 3, 4, 7, 8, 12], L7764 = [0, 1, 2, 3, 4, 7, 9, 10], L7767 = [0, 1, 2, 3, 4, 7, 9, 13], L7776 = [0, 1, 2, 3, 4, 8, 9, 12], L7779 = [0, 1, 2, 3, 4, 8, 10, 12], L7780 = [0, 1, 2, 3, 4, 8, 10, 13], L7788 = [0, 1, 2, 3, 4, 9, 10, 12], L7791 = [0, 1, 2, 3, 4, 9, 11, 13], L7793 = [0, 1, 2, 3, 4, 10, 11, L7800 = [0, 1, 2, 3, 5, 6, 6, 8], L7805 = [0, 1, 2, 3, 5, 6, 7, 8], L7807 = [0, 1, 2, 3, 5, 6, 7, 10], L7809 = [0, 1, 2, 3, 5, 6, 7, 12], L7810 = [0, 1, 2, 3, 5, 6, 8, 9], L7811 = [0, 1, 2, 3, 5, 6, 8, 10], L7813 = [0, 1, 2, 3, 5, 6, 8, 13],
206
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 27 {0} {7931, 8126}, {7932, 8136}, {7942, 8144}, {7967, 7971, 7981}, {7968, 7969, 7975}, (cont.) {7970, 7979}, {7972, 7982, 7988}, {7984, 7985, 7993, 7998}, {7989, 8040}, {8010, 8057, 8067}, {8012, 8054}, {8013, 8059}, {8164, 8177}, {21088, 21093}, {21178, 21202}, {21196, 21429}, {21267, 21273}, {21269, 21274}, {21275, 21328}, {21277, 21278}, {21282, 21284, 21333, 21344}, {21283, 21313}, {21285, 21303, 21310, 21332, 21339}, {21289, 21290, 21299}, {21291, 21312}, {21292, 21298, 21309}, {21296, 21307, 21346}, {21300, 21342, 21372, 21441}, {21301, 21311, 21371}, {21317, 21351}, {21320, 21348, 21369}, {21326, 21362}, {21327, 21373, 21397}, {21331, 21335}, {21334, 21345}, {21355, 21359}, {21357, 21440, 21444}, {21358, 21446, 21460}, {21361, 21442}, {21363, 21448}, {21366, 21375}, {21378, 21407}, {21384, 21453}, {21391, 21449}, {21394, 21450}, {21404, 21601}, {21409, 21776}, {21452, 21462}, {21467, 21604}, {21476, 21588}, {21483, 21599}, {21489, 21492}, {21568, 21577}, {21618, 21912}, {21619, 21913}, {21621, 21915}, {21629, 21658}, {21630, 21910}, {21631, 21924}, {21644, 21935}, {21675, 21680, 21692}, {21676, 21677, 21684}, {21679, 21690}, {21681, 21693, 21699}, {21695, 21696, 21706, 21711}, {21700, 21775}, {21727, 21797, 21809}, {21729, 21793}, {21730, 21799}, {21961, 21978}
L7817 = [0, 1, 2, 3, 5, 6, 9, 12], L7819 = [0, 1, 2, 3, 5, 6, 10, 12], L7821 = [0, 1, 2, 3, 5, 6, 11, 13], L7825 = [0, 1, 2, 3, 5, 7, 8, 12], L7832 = [0, 1, 2, 3, 5, 7, 10, 11], L7833 = [0, 1, 2, 3, 5, 7, 11, 12], L7838 = [0, 1, 2, 3, 5, 8, 9, 12], L7843 = [0, 1, 2, 3, 5, 9, 9, 10], L7846 = [0, 1, 2, 3, 5, 9, 9, 13], L7875 = [0, 1, 2, 3, 6, 6, 9, 12], L7886 = [0, 1, 2, 3, 6, 7, 8, 12], L7890 = [0, 1, 2, 3, 6, 7, 9, 12], L7891 = [0, 1, 2, 3, 6, 7, 10, 12], L7896 = [0, 1, 2, 3, 6, 8, 9, 12], L7899 = [0, 1, 2, 3, 6, 8, 10, 13], L7904 = [0, 1, 2, 3, 6, 9, 9, 12], L7907 = [0, 1, 2, 3, 6, 9, 10, 12], L7908 = [0, 1, 2, 3, 6, 9, 10, 13], L7909 = [0, 1, 2, 3, 6, 9, 11, 12], L7910 = [0, 1, 2, 3, 6, 9, 11, 13], L7911 = [0, 1, 2, 3, 6, 9, 12, 1 L7913 = [0, 1, 2, 3, 6, 10, 11, 13], L7923 = [0, 1, 2, 3, 7, 8, 10, 12], L7924 = [0, 1, 2, 3, 7, 8, 11, 12], L7930 = [0, 1, 2, 3, 7, 9, 9, 13], L7931 = [0, 1, 2, 3, 7, 9, 10, 12], L7932 = [0, 1, 2, 3, 7, 9, 11, 12], L7942 = [0, 1, 2, 3, 8, 9, 10, 12], L7954 = [0, 1, 2, 3, 9, 9, 10, 13], L7967 = [0, 1, 2, 4, 5, 7, 8, 9], L7968 = [0, 1, 2, 4, 5, 7, 8, 10], L7969 = [0, 1, 2, 4, 5, 7, 8, 11], L7970 = [0, 1, 2, 4, 5, 7, 9, 9], L7971 = [0, 1, 2, 4, 5, 7, 9, 10], L7972 = [0, 1, 2, 4, 5, 7, 9, 11], L7974 = [0, 1, 2, 4, 5, 7, 9, 13], L7975 = [0, 1, 2, 4, 5, 7, 10, 13], L7979 = [0, 1, 2, 4, 5, 8, 9, 9], L7980 = [0, 1, 2, 4, 5, 8, 9, 10], L7981 = [0, 1, 2, 4, 5, 8, 9, 11], L7982 = [0, 1, 2, 4, 5, 8, 9, 13], L7984 = [0, 1, 2, 4, 5, 9, 9, 10], L7985 = [0, 1, 2, 4, 5, 9, 9, 11], L7988 = [0, 1, 2, 4, 5, 9, 10, 13], L7989 = [0, 1, 2, 4, 5, 9, 11, 12], L7993 = [0, 1, 2, 4, 7, 8, 9, 9], L7996 = [0, 1, 2, 4, 7, 9, 9, 11], L7998 = [0, 1, 2, 4, 7, 9, 9, 13], L8010 = [0, 1, 2, 4, 9, 9, 9, 11], L8012 = [0, 1, 2, 4, 9, 9, 10, 11], L8013 = [0, 1, 2, 4, 9, 9, 10, 12], L8040 = [0, 1, 2, 5, 6, 7, 8, 9], L8041 = [0, 1, 2, 5, 6, 7, 8, 12], L8054 = [0, 1, 2, 5, 7, 8, 9, 9], L8057 = [0, 1, 2, 5, 7, 9, 9, 9], L8058 = [0, 1, 2, 5, 7, 9, 9, 11], L8059 = [0, 1, 2, 5, 7, 9, 9, 12], L8067 = [0, 1, 2, 5, 9, 9, 9, 10], L8126 = [0, 1, 2, 6, 7, 8, 9, 12], L8128 = [0, 1, 2, 6, 7, 8, 10, 12], L8129 = [0, 1, 2, 6, 7, 8, 11, 12], L8136 = [0, 1, 2, 6, 7, 9, 11, 12], L8144 = [0, 1, 2, 6, 8, 9, 10, 12], L8164 = [0, 1, 2, 7, 8, 9, 9, 9], L8177 = [0, 1, 2, 7, 9, 9, 9, 10], L8301 = [0, 1, 3, 3, 3, 6, 9, 12], L8344 = [0, 1, 3, 3, 4, 6, 9, 12], L8370 = [0, 1, 3, 3, 5, 6, 9, 12], L8385 = [0, 1, 3, 3, 6, 6, 9, 12], L8391 = [0, 1, 3, 3, 6, 7, 9, 12], L8396 = [0, 1, 3, 3, 6, 8, 9, 12], L8401 = [0, 1, 3, 3, 6, 9, 9, 12], L8402 = [0, 1, 3, 3, 6, 9, 11, 12], L8403 = [0, 1, 3, 3, 6, 9, 12, 12], L8438 = [0, 1, 3, 4, 5, 6, 9, 12], L8449 = [0, 1, 3, 4, 6, 6, 9, 12], L8453 = [0, 1, 3, 4, 6, 7, 9, 12], L8457 = [0, 1, 3, 4, 6, 9, 9, 12], L8458 = [0, 1, 3, 4, 6, 9, 10, 12], L8472 = [0, 1, 3, 5, 6, 6, 9, 12], L8474 = [0, 1, 3, 5, 6, 9, 9, 12], L8486 = [0, 1, 3, 6, 6, 6, 9, 12], L8490 = [0, 1, 3, 6, 6, 8, 9, 12], L8494 = [0, 1, 3, 6, 6, 9, 9, 12], L8495 = [0, 1, 3, 6, 6, 9, 12, 12], L8499 = [0, 1, 3, 6, 8, 9, 9, 12], L8500 = [0, 1, 3, 6, 8, 9, 10, 12], L8501 = [0, 1, 3, 6, 8, 9, 12, 12], L8505 = [0, 1, 3, 6, 9, 9, 9, 12], L8506 = [0, 1, 3, 6, 9, 9, 12, 12], L8507 = [0, 1, 3, 6, 9, 12, 12, 12], L20969 = [1, 2, 3, 3, 4, 5, 7, 13], L20971 = [1, 2, 3, 3, 4, 5, 8, 10], L20984 = [1, 2, 3, 3, 4, 5, 11, 13], L21019 = [1, 2, 3, 3, 4, 7, 8, 11], L21040 = [1, 2, 3, 3, 4, 8, 10, 13], L21088 =
APPENDIX
207
Table 6. (continued) m = 8 q 27 (cont.)
I {0, 1}
indexes of I-isospectral families {723, 724}, {2613, 2614}, {7719, 7721}, {7732, 7759}, {7734, 7760}, {7780, 7832}, {7984, 7985}, {20969, 20971}, {20984, 21019}, {21040, 21103}, {21270, 21272}, {21282, 21284}, {21285, 21332}, {21297, 21305}, {21300, 21441}, {21303, 21310}, {21321, 21367}, {21323, 21368}, {21395, 21475}, {21695, 21696} {0, 1, 2} {730, 750}, {2607, 2609}, {2611, 2617}, {2623, 2662}, {7968, 7969}, {7974, 7980}, {7982, 7988}, {7996, 8058}, {21341, 21447}, {21676, 21677}, {21683, 21691}, {21693, 21699}, {21709, 21798} {7} {880, 2921, 8505}, {1909, 2917, 6503, 8499}, {2557, 2886, 2901, 7904, 8457, 8474}, {2846, 2913, 2922, 8401, 8494, 8506}, {4023, 6491, 6506, 8500}, {5238, 6476, 6508, 7896, 7907, 8438}, {6070, 6458, 6510, 8396, 8490, 8501}, {6242, 6367, 6511, 7890, 7909, 8458}, {7656, 7875, 7911, 8344, 8370, 8391, 8402, 8449, 8472}, {7750, 7817, 8453}, {8301, 8385, 8403, 8486, 8495, 8507}
[1, 2, 3, 3, 5, 6, 10, 12], L21093 = [1, 2, 3, 3, 5, 6, 12, 13], L21103 = [1, 2, 3, 3, 5, 7, 10, 11], L21178 = [1, 2, 3, 3, 6, 7, 12, 13], L21196 = [1, 2, 3, 3, 6, 9, 11, 13], L21202 = [1, 2, 3, 3, 6, 10, 12, 13], L21267 = [1, 2, 3, 4, 5, 6, 7, 10], L21269 = [1, 2, 3, 4, 5, 6, 7, 12], L21270 = [1, 2, 3, 4, 5, 6, 7, 13], L21272 = [1, 2, 3, 4, 5, 6, 8, 10], L21273 = [1, 2, 3, 4, 5, 6, 8, 11], L21274 = [1, 2, 3, 4, 5, 6, 8, 12], L21275 = [1, 2, 3, 4, 5, 6, 8, 13], L21277 = [1, 2, 3, 4, 5, 6, 9, 10], L21278 = [1, 2, 3, 4, 5, 6, 9, 11], L21282 = [1, 2, 3, 4, 5, 6, 10, 12], L21283 = [1, 2, 3, 4, 5, 6, 10, 1 L21284 = [1, 2, 3, 4, 5, 6, 11, 12], L21285 = [1, 2, 3, 4, 5, 6, 11, 13], L21289 = [1, 2, 3, 4, 5, 7, 8, 10], L21290 = [1, 2, 3, 4, 5, 7, 8, 11], L21291 = [1, 2, 3, 4, 5, 7, 8, 12], L21292 = [1, 2, 3, 4, 5, 7, 8, 13], L21296 = [1, 2, 3, 4, 5, 7, 9, 12], L21297 = [1, 2, 3, 4, 5, 7, 9, 13], L21298 = [1, 2, 3, 4, 5, 7, 10, 11], L21299 = [1, 2, 3, 4, 5, 7, 10, 1 L21300 = [1, 2, 3, 4, 5, 7, 11, 12], L21301 = [1, 2, 3, 4, 5, 7, 11, 13], L21303 = [1, 2, 3, 4, 5, 7, 12, 13], L21305 = [1, 2, 3, 4, 5, 8, 9, 10], L21307 = [1, 2, 3, 4, 5, 8, 9, 12], L21309 = [1, 2, 3, 4, 5, 8, 10, 11], L21310 = [1, 2, 3, 4, 5, 8, 10, 12], L21311 = [1, 2, 3, 4, 5, 8, 10, 13], L21312 = [1, 2, 3, 4, 5, 8, 11, 12], L21313 = [1, 2, 3, 4, 5, 8, 12, 13], L21317 = [1, 2, 3, 4, 5, 9, 9, 12], L21320 = [1, 2, 3, 4, 5, 9, 10, 12], L21321 = [1, 2, 3, 4, 5, 9, 10, 13], L21323 = [1, 2, 3, 4, 5, 9, 11, 13], L21326 = [1, 2, 3, 4, 5, 10, 11, 12], L21327 = [1, 2, 3, 4, 5, 10, 11, 13], L21328 = [1, 2, 3, 4, 5, 10, 12, 13], L21331 = [1, 2, 3, 4, 6, 7, 8, 9], L21332 = [1, 2, 3, 4, 6, 7, 8, 11], L21333 = [1, 2, 3, 4, 6, 7, 8, 12], L21334 = [1, 2, 3, 4, 6, 7, 9, 9], L21335 = [1, 2, 3, 4, 6, 7, 9, 10], L21339 = [1, 2, 3, 4, 6, 7, 10, 11], L21341 = [1, 2, 3, 4, 6, 7, 11, 12], L21342 = [1, 2, 3, 4, 6, 7, 11, 13], L21344 = [1, 2, 3, 4, 6, 7, 12, 13], L21345 = [1, 2, 3, 4, 6, 8, 9, 9], L21346 = [1, 2, 3, 4, 6, 8, 9, 11], L21348 = [1, 2, 3, 4, 6, 8, 9, 13], L21351 = [1, 2, 3, 4, 6, 9, 9, 10], L21355 = [1, 2, 3, 4, 6, 9, 10, 11], L21357 = [1, 2, 3, 4, 6, 9, 10, 1 L21358 = [1, 2, 3, 4, 6, 9, 11, 12], L21359 = [1, 2, 3, 4, 6, 9, 11, 13], L21361 = [1, 2, 3, 4, 6, 10, 11, 12], L21362 = [1, 2, 3, 4, 6, 10, 11, 13], L21363 = [1, 2, 3, 4, 6, 10, 12, 12], L21366 = [1, 2, 3, 4, 7, 8, 9, 9], L21367 = [1, 2, 3, 4, 7, 8, 9, 10], L21368 = [1, 2, 3, 4, 7, 8, 9, 11], L21369 = [1, 2, 3, 4, 7, 8, 9, 12], L21371 = [1, 2, 3, 4, 7, 8, 10, 11], L21372 = [1, 2, 3, 4, 7, 8, 10, 12], L21373 = [1, 2, 3, 4, 7, 8, 11, 13], L21375 = [1, 2, 3, 4, 7, 9, 9, 10], L21378 = [1, 2, 3, 4, 7, 9, 9, 13], L21384 = [1, 2, 3, 4, 7, 10, 11, 12], L21391 = [1, 2, 3, 4, 8, 9, 9, 12], L21394 = [1, 2, 3, 4, 8, 9, 10, 12], L21395 = [1, 2, 3, 4, 8, 9, 10, 13], L21397 = [1, 2, 3, 4, 8, 10, 11, 13], L21404 = [1, 2, 3, 4, 9, 9, 10, 12], L21407 = [1, 2, 3, 4, 9, 9, 11, 13], L21409 = [1, 2, 3, 4, 9, 10, 11, 12], L21429 = [1, 2, 3, 5, 6, 6, 8, 9], L21440 = [1, 2, 3, 5, 6, 7, 8, 9], L21441 = [1, 2, 3, 5, 6, 7, 8, 10], L21442 = [1, 2, 3, 5, 6, 7, 8, 12], L21444 = [1, 2, 3, 5, 6, 7, 9, 10], L21446 = [1, 2, 3, 5, 6, 7, 9, 12], L21447 = [1, 2, 3, 5, 6, 7, 11, 12], L21448 = [1, 2, 3, 5, 6, 7, 12, 12], L21449 = [1, 2, 3, 5, 6, 8, 9, 9], L21450 = [1, 2, 3, 5, 6, 8, 9, 10 L21452 = [1, 2, 3, 5, 6, 8, 9, 13], L21453 = [1, 2, 3, 5, 6, 8, 10, 13], L21460 = [1, 2, 3, 5, 6, 9, 10, 12], L21462 = [1, 2, 3, 5, 6, 9, 11, 13], L21467 = [1, 2, 3, 5, 7, 8, 9, 12], L21475 = [1, 2, 3, 5, 7, 9, 10, 11], L21476 = [1, 2, 3, 5, 7, 9, 11, 12], L21483 = [1, 2, 3, 5, 8, 9, 9, 12], L21489 = [1, 2, 3, 5, 9, 9, 9, 10], L21492 = [1, 2, 3, 5, 9, 9, 9, 13], L21568 = [1, 2, 3, 6, 7, 8, 9, 12], L21577 = [1, 2, 3, 6, 7, 9, 10, 12], L21588 = [1, 2, 3, 6, 8, 9, 10, 1
208
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 28 {0} {43, 46}, {299, 307}, {304, 319}, {1134, 1141}, {1399, 1411}, {1433, 1451}, {1438, 1463}, {1448, 1496}, {1915, 1917}, {3023, 3113}, {4538, 4572}, {4558, 4609}, {4561, 4578}, {4566, 4596}, {4585, 4611}, {5337, 5366}, {5342, 5347}, {5343, 5394}, {5354, 5396}, {5438, 5472}, {5443, 5484}, {5453, 5517}, {5469, 5587}, {6566, 6568}, {6573, 6575}, {10811, 10813}, {10832, 10834}, {10848, 10927}, {10868, 11246}, {10922, 11255}, {10923, 11263}, {11253, 11258}, {15331, 15338}, {15354, 15362}, {15394, 15509}, {15425, 16085}, {15436, 15483}, {15440, 15541}, {15474, 15595}, {15477, 15515}, {15487, 15493}, {15492, 15633}, {15498, 15554}, {15503, 15582}, {15522, 15597}, {15538, 15546}, {15567, 15635}, {17360, 17418}, {17365, 17370}, {17366, 17446}, {17377, 17448}, {17384, 17386}, {17390, 17397}, {17392, 17509}, {17406, 17511}, {17581, 17637}, {17586, 17649}, {17596, 17682}, {17612, 17752}, {17634, 17879}, {19944, 19946}, {19951, 19953}, {19961, 19963}, {34164, 34166}, {34174, 34179}, {34175, 34177}, {34181, 34251}, {34182, 34186}, {34205, 34207}, {34221, 34377}, {34261, 34266}, {34298, 34519}, {34318, 35496}, {34372, 35505}, {34373, 35513}, {34511, 35534}, {34512, 35546}, {35503, 35508}, {35530, 35539}, {43460, 43582}, {45738, 45742}, {45741, 45743, 45750}, {45746, 45884},
L21599 = [1, 2, 3, 6, 9, 9, 10, 13], L21601 = [1, 2, 3, 6, 9, 9, 11, 13], L21604 = [1, 2, 3, 6, 9, 10, 11, 13], L21618 = [1, 2, 3, 7, 8, 9, 10, 12], L21619 = [1, 2, 3, 7, 8, 9, 11, 12], L21621 = [1, 2, 3, 7, 8, 10, 11, 12], L21629 = [1, 2, 3, 7, 9, 9, 9, 13], L21630 = [1, 2, 3, 7, 9, 9, 10, 12], L21631 = [1, 2, 3, 7, 9, 9, 11, 12], L21644 = [1, 2, 3, 8, 9, 9, 10, 12], L21658 = [1, 2, 3, 9, 9, 9, 10, 13], L21675 = [1, 2, 4, 5, 7, 8, 9, 9], L21676 = [1, 2, 4, 5, 7, 8, 9, 10], L21677 = [1, 2, 4, 5, 7, 8, 9, 11], L21679 = [1, 2, 4, 5, 7, 9, 9, 9], L21680 = [1, 2, 4, 5, 7, 9, 9, 10], L21681 = [1, 2, 4, 5, 7, 9, 9, 11], L21683 = [1, 2, 4, 5, 7, 9, 9, 13], L21684 = [1, 2, 4, 5, 7, 9, 10, 13], L21690 = [1, 2, 4, 5, 8, 9, 9, 9], L21691 = [1, 2, 4, 5, 8, 9, 9, 10], L21692 = [1, 2, 4, 5, 8, 9, 9, 11], L21693 = [1, 2, 4, 5, 8, 9, 9, 13], L21695 = [1, 2, 4, 5, 9, 9, 9, 10], L21696 = [1, 2, 4, 5, 9, 9, 9, 11], L21699 = [1, 2, 4, 5, 9, 9, 10, 13], L21700 = [1, 2, 4, 5, 9, 9, 11, 12], L21706 = [1, 2, 4, 7, 8, 9, 9, 9], L21709 = [1, 2, 4, 7, 9, 9, 9, 11], L21711 = [1, 2, 4, 7, 9, 9, 9, 13], L21727 = [1, 2, 4, 9, 9, 9, 9, 11], L21729 = [1, 2, 4, 9, 9, 9, 10, 11], L21730 = [1, 2, 4, 9, 9, 9, 10, 12], L21775 = [1, 2, 5, 6, 7, 8, 9, 9], L21776 = [1, 2, 5, 6, 7, 8, 9, 12], L21793 = [1, 2, 5, 7, 8, 9, 9, 9], L21797 = [1, 2, 5, 7, 9, 9, 9, 9], L21798 = [1, 2, 5, 7, 9, 9, 9, 11], L21799 = [1, 2, 5, 7, 9, 9, 9, 12], L21809 = [1, 2, 5, 9, 9, 9, 9, 10], L21910 = [1, 2, 6, 7, 8, 9, 9, 12], L21912 = [1, 2, 6, 7, 8, 9, 10, 12], L21913 = [1, 2, 6, 7, 8, 9, 11, 12], L21915 = [1, 2, 6, 7, 8, 10, 11, 12], L21924 = [1, 2, 6, 7, 9, 9, 11, 12], L21935 = [1, 2, 6, 8, 9, 9, 10, 12], L21961 = [1, 2, 7, 8, 9, 9, 9, 9], L21978 = [1, 2, 7, 9, 9, 9, 9, 10]. q = 28 : L43 = [0, 0, 0, 0, 0, 1, 3, 5], L46 = [0, 0, 0, 0, 0, 1, 3, 9], L299 = [0, 0, 0, 0, 1, 3, 5, 7], L301 = [0, 0, 0, 0, 1, 3, 5, 9], L302 = [0, 0, 0, 0, 1, 3, 5, 11], L304 = [0, 0, 0, 0, 1, 3, 5, 14], L307 = [0, 0, 0, 0, 1, 3, 7, 9], L319 = [0, 0, 0, 0, 1, 3, 9, 14], L1134 = [0, 0, 0, 1, 2, 3, 5, 10], L1141 = [0, 0, 0, 1, 2, 3, 6, 9], L1399 = [0, 0, 0, 1, 3, 4, 5, 12], L1411 = [0, 0, 0, 1, 3, 4, 8, 9], L1433 = [0, 0, 0, 1, 3, 5, 7, 7], L1435 = [0, 0, 0, 1, 3, 5, 7, 9], L1436 = [0, 0, 0, 1, 3, 5, 7, 11], L1438 = [0, 0, 0, 1, 3, 5, 7, 14], L1444 = [0, 0, 0, 1, 3, 5, 9, 14], L1445 = [0, 0, 0, 1, 3, 5, 11, 14], L1448 = [0, 0, 0, 1, 3, 5, 14, 14], L1451 = [0, 0, 0, 1, 3, 7, 7, 9], L1463 = [0, 0, 0, 1, 3, 7, 9, 14], L1496 = [0, 0, 0, 1, 3, 9, 14, 14], L1915 = [0, 0, 0, 2, 4, 6, 7, 8], L1917 = [0, 0, 0, 2, 4, 6, 7, 12], L3023 = [0, 0, 1, 1, 3, 3, 9, 11], L3113 = [0, 0, 1, 1, 3, 5, 5, 13], L4538 = [0, 0, 1, 2, 3, 4, 9, 11], L4558 = [0, 0, 1, 2, 3, 5, 6, 10], L4561 = [0, 0, 1, 2, 3, 5, 6, 13], L4566 = [0, 0, 1, 2, 3, 5, 7, 10], L4572 = [0, 0, 1, 2, 3, 5, 8, 9], L4578 = [0, 0, 1, 2, 3, 5, 9, 10], L4585 = [0, 0, 1, 2, 3, 5, 10, 14], L4596 = [0, 0, 1, 2, 3, 6, 7, 9], L4609 = [0, 0, 1, 2, 3, 6, 9, 10], L4611 = [0, 0, 1, 2, 3, 6, 9, 14], L4942 = [0, 0, 1, 2, 5, 6, 8, 12], L5084 = [0, 0, 1, 2, 6, 8, 9, 12], L5337 = [0, 0, 1, 3, 4, 5, 7, 12], L5342 = [0, 0, 1, 3, 4, 5, 8, 11], L5343 = [0, 0, 1, 3, 4, 5, 8, 12], L5347 = [0, 0, 1, 3, 4, 5, 9, 12], L5354 = [0, 0, 1, 3, 4, 5, 12, 14], L5366 = [0, 0, 1, 3, 4, 7, 8, 9], L5394 = [0, 0, 1, 3, 4, 8, 9, 12],
APPENDIX
209
Table 6. (continued) m = 8 q I indexes of I-isospectral families 28 {0} {45775, 45782}, {45797, 45799, 45805}, {45801, 45887}, {45802, 45886}, (cont.) {45822, 45835}, {45853, 45861}, {45888, 45907}, {45951, 46219}, {45982, 47560}, {45993, 46154}, {45997, 46251}, {46065, 46187, 47581}, {46070, 47582}, {46088, 46188}, {46093, 46319}, {46145, 46390}, {46148, 46225}, {46158, 46164}, {46163, 46428}, {46169, 46264}, {46194, 46201}, {46200, 46505}, {46208, 46339}, {46213, 46377}, {46232, 46392}, {46248, 46256}, {46277, 46430}, {46314, 46328}, {46358, 46507}, {49911, 50028}, {50126, 50223}, {50131, 50136}, {50132, 50251}, {50143, 50253}, {50150, 50152}, {50156, 50163}, {50158, 50314}, {50172, 50316}, {50186, 50188}, {50192, 50200}, {50195, 50430}, {50211, 50432}, {50538, 50623}, {50543, 50635}, {50553, 50668}, {50569, 50738}, {50591, 50865}, {50620, 51073}, {54671, 54675}, {55023, 55027}, {55087, 55089}, {55094, 55096}, {55104, 55106}, {55116, 55118}
L5396 = [0, 0, 1, 3, 4, 8, 9, 14], L5438 = [0, 0, 1, 3, 5, 7, 7, 7], L5440 = [0, 0, 1, 3, 5, 7, 7, 9], L5441 = [0, 0, 1, 3, 5, 7, 7, 11], L5443 = [0, 0, 1, 3, 5, 7, 7, 14], L5449 = [0, 0, 1, 3, 5, 7, 9, 14], L5450 = [0, 0, 1, 3, 5, 7, 11, 14], L5453 = [0, 0, 1, 3, 5, 7, 14, 14], L5464 = [0, 0, 1, 3, 5, 9, 14, 14], L5465 = [0, 0, 1, 3, 5, 11, 14, 14], L5469 = [0, 0, 1, 3, 5, 14, 14, 14], L5472 = [0, 0, 1, 3, 7, 7, 7, 9], L5484 = [0, 0, 1, 3, 7, 7, 9, 14], L5517 = [0, 0, 1, 3, 7, 9, 14, 14], L5587 = [0, 0, 1, 3, 9, 14, 14, 14], L6566 = [0, 0, 2, 4, 6, 7, 7, 8], L6568 = [0, 0, 2, 4, 6, 7, 7, 12], L6573 = [0, 0, 2, 4, 6, 7, 8, 14], L6575 = [0, 0, 2, 4, 6, 7, 12, 14], L10811 = [0, 1, 1, 3, 3, 5, 5, 11], L10813 = [0, 1, 1, 3, 3, 5, 5, 13], L10832 = [0, 1, 1, 3, 3, 5, 9, 11], L10834 = [0, 1, 1, 3, 3, 5, 9, 13], L10848 = [0, 1, 1, 3, 3, 5, 13, 13 L10868 = [0, 1, 1, 3, 3, 7, 9, 11], L10922 = [0, 1, 1, 3, 3, 9, 11, 13], L10923 = [0, 1, 1, 3, 3, 9, 11, 14], L10927 = [0, 1, 1, 3, 3, 9, 13, 13], L11246 = [0, 1, 1, 3, 5, 5, 7, 13], L11253 = [0, 1, 1, 3, 5, 5, 9, 11], L11255 = [0, 1, 1, 3, 5, 5, 9, 13], L11258 = [0, 1, 1, 3, 5, 5, 11, 13], L11263 = [0, 1, 1, 3, 5, 5, 13, 14], L15331 = [0, 1, 2, 3, 4, 5, 9, 13], L15338 = [0, 1, 2, 3, 4, 5, 11, 13], L15354 = [0, 1, 2, 3, 4, 6, 8, 9], L15362 = [0, 1, 2, 3, 4, 6, 9, 12], L15394 = [0, 1, 2, 3, 4, 7, 9, 11], L15423 = [0, 1, 2, 3, 4, 8, 10, 11], L15425 = [0, 1, 2, 3, 4, 8, 10, 13], L15436 = [0, 1, 2, 3, 4, 9, 10, 12], L15440 = [0, 1, 2, 3, 4, 9, 11, 14], L15474 = [0, 1, 2, 3, 5, 6, 7, 10], L15477 = [0, 1, 2, 3, 5, 6, 7, 13], L15483 = [0, 1, 2, 3, 5, 6, 8, 12], L15486 = [0, 1, 2, 3, 5, 6, 9, 10], L15487 = [0, 1, 2, 3, 5, 6, 9, 11], L15490 = [0, 1, 2, 3, 5, 6, 10, 11], L15492 = [0, 1, 2, 3, 5, 6, 10, 14], L15493 = [0, 1, 2, 3, 5, 6, 11, 13], L15498 = [0, 1, 2, 3, 5, 6, 13, 14], L15503 = [0, 1, 2, 3, 5, 7, 7, 10], L15509 = [0, 1, 2, 3, 5, 7, 8, 9], L15515 = [0, 1, 2, 3, 5, 7, 9, 10], L15522 = [0, 1, 2, 3, 5, 7, 10, 14], L15538 = [0, 1, 2, 3, 5, 8, 9, 11], L15541 = [0, 1, 2, 3, 5, 8, 9, 14], L15546 = [0, 1, 2, 3, 5, 8, 11, 13], L15554 = [0, 1, 2, 3, 5, 9, 10, 14], L15567 = [0, 1, 2, 3, 5, 10, 14, 14], L15582 = [0, 1, 2, 3, 6, 7, 7, 9], L15595 = [0, 1, 2, 3, 6, 7, 9, 10], L15597 = [0, 1, 2, 3, 6, 7, 9, 14], L15633 = [0, 1, 2, 3, 6, 9, 10, 14], L15635 = [0, 1, 2, 3, 6, 9, 14, 14], L16085 = [0, 1, 2, 4, 5, 6, 8, 9], L16088 = [0, 1, 2, 4, 5, 6, 8, 13], L16485 = [0, 1, 2, 5, 6, 7, 8, 12], L16508 = [0, 1, 2, 5, 6, 8, 12, 14], L16779 = [0, 1, 2, 6, 7, 8, 9, 12], L16827 = [0, 1, 2, 6, 8, 9, 12, 14], L17360 = [0, 1, 3, 4, 5, 7, 7, 12], L17365 = [0, 1, 3, 4, 5, 7, 8, 11], L17366 = [0, 1, 3, 4, 5, 7, 8, 12], L17370 = [0, 1, 3, 4, 5, 7, 9, 12], L17377 = [0, 1, 3, 4, 5, 7, 12, 14 L17384 = [0, 1, 3, 4, 5, 8, 9, 11], L17385 = [0, 1, 3, 4, 5, 8, 9, 12], L17386 = [0, 1, 3, 4, 5, 8, 9, 13], L17388 = [0, 1, 3, 4, 5, 8, 11, 12], L17390 = [0, 1, 3, 4, 5, 8, 11, 14], L17392 = [0, 1, 3, 4, 5, 8, 12, 14], L17397 = [0, 1, 3, 4, 5, 9, 12, 14], L17406 = [0, 1, 3, 4, 5, 12, 14, 14], L17418 = [0, 1, 3, 4, 7, 7, 8, 9], L17446 = [0, 1, 3, 4, 7, 8, 9, 12], L17448 = [0, 1, 3, 4, 7, 8, 9, 14], L17509 = [0, 1, 3, 4, 8, 9, 12, 14], L17511 = [0, 1, 3, 4, 8, 9, 14, 1 L17581 = [0, 1, 3, 5, 7, 7, 7, 7], L17583 = [0, 1, 3, 5, 7, 7, 7, 9], L17584 = [0, 1, 3, 5, 7, 7, 7, 11], L17586 = [0, 1, 3, 5, 7, 7, 7, 14], L17592 = [0, 1, 3, 5, 7, 7, 9, 14], L17593 = [0, 1, 3, 5, 7, 7, 11, 14], L17596 = [0, 1, 3, 5, 7, 7, 14, 1 L17605 = [0, 1, 3, 5, 7, 9, 11, 13], L17607 = [0, 1, 3, 5, 7, 9, 14, 14], L17608 = [0, 1, 3, 5, 7, 11, 14, 14], L17612 = [0, 1, 3, 5, 7, 14, 14, 14], L17628 = [0, 1, 3, 5, 9, 14, 14, 14], L17629 = [0, 1, 3, 5, 11, 14, 14, 14], L17634 = [0, 1, 3, 5, 14, 14, 14, 14], L17637 = [0, 1, 3, 7, 7, 7, 7, 9], L17649 = [0, 1, 3, 7, 7, 7, 9, 14], L17682 = [0, 1, 3, 7, 7, 9, 14, 14], L17752 = [0, 1, 3, 7, 9, 14, 14, 14], L17879 = [0, 1, 3, 9, 14, 14, 14, 14],
210
EMILIO A. LAURET
Table 6. (continued) m = 8 q 28 (cont.)
I {0, 1}
indexes of I-isospectral families {301, 302}, {1435, 1436}, {1444, 1445}, {4942, 5084}, {5440, 5441}, {5449, 5450}, {5464, 5465}, {15423, 16088}, {15486, 15490}, {16485, 16779}, {16508, 16827}, {17583, 17584}, {17592, 17593}, {17607, 17608}, {17628, 17629}, {34258, 34265}, {34289, 34510}, {45824, 46084}, {45980, 47563}, {46066, 47588}, {46157, 46161}, {48398, 48957}, {48421, 49005}, {48461, 49090}, {50151, 50154}, {50187, 50190}, {50540, 50541}, {50549, 50550}, {50564, 50565}, {50585, 50586}, {50613, 50614} {2, 3, 4, 5, 6} {17605, 50161}, {18283, 20134}, {35760, 50562}, {44949, 54788}, {46266, 50583} {0, 1, 7} {17385, 17388}, {46192, 46197}
L18283 = [0, 1, 4, 4, 8, 8, 12, 12], L19944 = [0, 2, 4, 6, 7, 7, 7, 8], L19946 = [0, 2, 4, 6, 7, 7, 7, 12], L19951 = [0, 2, 4, 6, 7, 7, 8, 14], L19953 = [0, 2, 4, 6, 7, 7, 12, 14], L19961 = [0, 2, 4, 6, 7, 8, 14, 14], L19963 = [0, 2, 4, 6, 7, 12, 14, 14], L20134 = [0, 4, 4, 7, 8, 8, 12, 12], L34164 = [1, 1, 3, 3, 5, 5, 7, 11], L34166 = [1, 1, 3, 3, 5, 5, 7, 13], L34174 = [1, 1, 3, 3, 5, 5, 9, 9], L34175 = [1, 1, 3, 3, 5, 5, 9, 11], L34177 = [1, 1, 3, 3, 5, 5, 9, 13], L34179 = [1, 1, 3, 3, 5, 5, 11, 11], L34181 = [1, 1, 3, 3, 5, 5, 11, 13], L34182 = [1, 1, 3, 3, 5, 5, 11, 14], L34186 = [1, 1, 3, 3, 5, 5, 13, 14], L34205 = [1, 1, 3, 3, 5, 7, 9, 11], L34207 = [1, 1, 3, 3, 5, 7, 9, 13], L34221 = [1, 1, 3, 3, 5, 7, 13, 13], L34251 = [1, 1, 3, 3, 5, 9, 9, 11], L34258 = [1, 1, 3, 3, 5, 9, 11, 11], L34261 = [1, 1, 3, 3, 5, 9, 11, 14], L34265 = [1, 1, 3, 3, 5, 9, 13, 13], L34266 = [1, 1, 3, 3, 5, 9, 13, 14], L34289 = [1, 1, 3, 3, 5, 11, 13, 13], L34298 = [1, 1, 3, 3, 5, 13, 13, 14], L34318 = [1, 1, 3, 3, 7, 7, 9, 11], L34372 = [1, 1, 3, 3, 7, 9, 11, 13], L34373 = [1, 1, 3, 3, 7, 9, 11, 14], L34377 = [1, 1, 3, 3, 7, 9, 13, 13], L34510 = [1, 1, 3, 3, 9, 11, 13, 13], L34511 = [1, 1, 3, 3, 9, 11, 13, 14], L34512 = [1, 1, 3, 3, 9, 11, 14, 14], L34519 = [1, 1, 3, 3, 9, 13, 13, 14], L35496 = [1, 1, 3, 5, 5, 7, 7, 13], L35503 = [1, 1, 3, 5, 5, 7, 9, 11], L35505 = [1, 1, 3, 5, 5, 7, 9, 13], L35508 = [1, 1, 3, 5, 5, 7, 11, 13], L35513 = [1, 1, 3, 5, 5, 7, 13, 14], L35530 = [1, 1, 3, 5, 5, 9, 11, 14], L35534 = [1, 1, 3, 5, 5, 9, 13, 14], L35539 = [1, 1, 3, 5, 5, 11, 13, 14], L35546 = [1, 1, 3, 5, 5, 13, 14, 14], L35760 = [1, 1, 3, 5, 7, 9, 11, 13], L43460 = [1, 2, 2, 3, 5, 6, 10, 10], L43582 = [1, 2, 2, 3, 6, 6, 9, 10], L44949 = [1, 2, 2, 6, 6, 10, 10, 14], L45738 = [1, 2, 3, 4, 5, 6, 8, 13], L45741 = [1, 2, 3, 4, 5, 6, 9, 11], L45742 = [1, 2, 3, 4, 5, 6, 9, 12], L45743 = [1, 2, 3, 4, 5, 6, 9, 13], L45746 = [1, 2, 3, 4, 5, 6, 10, 12 L45750 = [1, 2, 3, 4, 5, 6, 11, 13], L45775 = [1, 2, 3, 4, 5, 7, 9, 13], L45782 = [1, 2, 3, 4, 5, 7, 11, 13], L45797 = [1, 2, 3, 4, 5, 8, 9, 11], L45799 = [1, 2, 3, 4, 5, 8, 9, 13], L45801 = [1, 2, 3, 4, 5, 8, 10, 11], L45802 = [1, 2, 3, 4, 5, 8, 10, 12], L45805 = [1, 2, 3, 4, 5, 8, 11, 13], L45822 = [1, 2, 3, 4, 5, 9, 13, 14], L45824 = [1, 2, 3, 4, 5, 10, 11, 12], L45835 = [1, 2, 3, 4, 5, 11, 13, 14], L45853 = [1, 2, 3, 4, 6, 7, 8, 9], L45861 = [1, 2, 3, 4, 6, 7, 9, 12], L45884 = [1, 2, 3, 4, 6, 8, 9, 10], L45886 = [1, 2, 3, 4, 6, 8, 9, 12], L45887 = [1, 2, 3, 4, 6, 8, 9, 13], L45888 = [1, 2, 3, 4, 6, 8, 9, 14], L45907 = [1, 2, 3, 4, 6, 9, 12, 14], L45951 = [1, 2, 3, 4, 7, 7, 9, 11], L45980 = [1, 2, 3, 4, 7, 8, 10, 11], L45982 = [1, 2, 3, 4, 7, 8, 10, 13], L45993 = [1, 2, 3, 4, 7, 9, 10, 12], L45997 = [1, 2, 3, 4, 7, 9, 11, 14], L46065 = [1, 2, 3, 4, 8, 10, 11, 13], L46066 = [1, 2, 3, 4, 8, 10, 11, 14], L46070 = [1, 2, 3, 4, 8, 10, 13, 14], L46084 = [1, 2, 3, 4, 9, 10, 11, 12], L46088 = [1, 2, 3, 4, 9, 10, 12, 14], L46093 = [1, 2, 3, 4, 9, 11, 14, 14], L46145 = [1, 2, 3, 5, 6, 7, 7, 10], L46148 = [1, 2, 3, 5, 6, 7, 7, 13], L46154 = [1, 2, 3, 5, 6, 7, 8, 12], L46157 = [1, 2, 3, 5, 6, 7, 9, 10], L46158 = [1, 2, 3, 5, 6, 7, 9, 11], L46161 = [1, 2, 3, 5, 6, 7, 10, 11 L46163 = [1, 2, 3, 5, 6, 7, 10, 14], L46164 = [1, 2, 3, 5, 6, 7, 11, 13], L46169 = [1, 2, 3, 5, 6, 7, 13, 14], L46187 = [1, 2, 3, 5, 6, 8, 12, 13], L46188 = [1, 2, 3, 5, 6, 8, 12, 14], L46192 = [1, 2, 3, 5, 6, 9, 10, 14], L46194 = [1, 2, 3, 5, 6, 9, 11, 14], L46197 = [1, 2, 3, 5, 6, 10, 11, 14], L46200 = [1, 2, 3, 5, 6, 10, 14, 14], L46201 = [1, 2, 3, 5, 6, 11, 13, 14], L46208 = [1, 2, 3, 5, 6, 13, 14, 14], L46213 = [1, 2, 3, 5, 7, 7, 7, 10], L46219 = [1, 2, 3, 5, 7, 7, 8, 9], L46225 = [1, 2, 3, 5, 7, 7, 9, 10], L46232 = [1, 2, 3, 5, 7, 7, 10, 14], L46248 = [1, 2, 3, 5, 7, 8, 9, 11], L46251 = [1, 2, 3, 5, 7, 8, 9, 14], L46256 = [1, 2, 3, 5, 7, 8, 11, 13], L46264 = [1, 2, 3, 5, 7, 9, 10, 1
APPENDIX
211
L46266 = [1, 2, 3, 5, 7, 9, 11, 13], L46277 = [1, 2, 3, 5, 7, 10, 14, 14], L46314 = [1, 2, 3, 5, 8, 9, 11, 14], L46319 = [1, 2, 3, 5, 8, 9, 14, 14], L46328 = [1, 2, 3, 5, 8, 11, 13, 14], L46339 = [1, 2, 3, 5, 9, 10, 14, 14], L46358 = [1, 2, 3, 5, 10, 14, 14, 14], L46377 = [1, 2, 3, 6, 7, 7, 7, 9], L46390 = [1, 2, 3, 6, 7, 7, 9, 10], L46392 = [1, 2, 3, 6, 7, 7, 9, 14], L46428 = [1, 2, 3, 6, 7, 9, 10, 14], L46430 = [1, 2, 3, 6, 7, 9, 14, 14], L46505 = [1, 2, 3, 6, 9, 10, 14, 14], L46507 = [1, 2, 3, 6, 9, 14, 14, 14], L47560 = [1, 2, 4, 5, 6, 7, 8, 9], L47563 = [1, 2, 4, 5, 6, 7, 8, 13], L47581 = [1, 2, 4, 5, 6, 8, 9, 13], L47582 = [1, 2, 4, 5, 6, 8, 9, 14], L47588 = [1, 2, 4, 5, 6, 8, 13, 14], L48398 = [1, 2, 5, 6, 7, 7, 8, 12], L48421 = [1, 2, 5, 6, 7, 8, 12, 14], L48461 = [1, 2, 5, 6, 8, 12, 14, 14], L48957 = [1, 2, 6, 7, 7, 8, 9, 12], L49005 = [1, 2, 6, 7, 8, 9, 12, 14], L49090 = [1, 2, 6, 8, 9, 12, 14, 14], L49911 = [1, 3, 4, 4, 5, 8, 12, 12], L50028 = [1, 3, 4, 4, 8, 8, 9, 12], L50126 = [1, 3, 4, 5, 7, 7, 7, 12], L50131 = [1, 3, 4, 5, 7, 7, 8, 11], L50132 = [1, 3, 4, 5, 7, 7, 8, 12], L50136 = [1, 3, 4, 5, 7, 7, 9, 12], L50143 = [1, 3, 4, 5, 7, 7, 12, 14], L50150 = [1, 3, 4, 5, 7, 8, 9, 11], L50151 = [1, 3, 4, 5, 7, 8, 9, 12], L50152 = [1, 3, 4, 5, 7, 8, 9, 13], L50154 = [1, 3, 4, 5, 7, 8, 11, 12], L50156 = [1, 3, 4, 5, 7, 8, 11, 14], L50158 = [1, 3, 4, 5, 7, 8, 12, 14], L50161 = [1, 3, 4, 5, 7, 9, 11, 13], L50163 = [1, 3, 4, 5, 7, 9, 12, 14], L50172 = [1, 3, 4, 5, 7, 12, 14, 14], L50186 = [1, 3, 4, 5, 8, 9, 11, 14], L50187 = [1, 3, 4, 5, 8, 9, 12, 14], L50188 = [1, 3, 4, 5, 8, 9, 13, 14], L50190 = [1, 3, 4, 5, 8, 11, 12, 14], L50192 = [1, 3, 4, 5, 8, 11, 14, 14], L50195 = [1, 3, 4, 5, 8, 12, 14, 14], L50200 = [1, 3, 4, 5, 9, 12, 14, 14], L50211 = [1, 3, 4, 5, 12, 14, 14, 14], L50223 = [1, 3, 4, 7, 7, 7, 8, 9], L50251 = [1, 3, 4, 7, 7, 8, 9, 12], L50253 = [1, 3, 4, 7, 7, 8, 9, 14], L50314 = [1, 3, 4, 7, 8, 9, 12, 14], L50316 = [1, 3, 4, 7, 8, 9, 14, 14], L50430 = [1, 3, 4, 8, 9, 12, 14, 14], L50432 = [1, 3, 4, 8, 9, 14, 14, 14], L50538 = [1, 3, 5, 7, 7, 7, 7, 7], L50540 = [1, 3, 5, 7, 7, 7, 7, 9], L50541 = [1, 3, 5, 7, 7, 7, 7, 11], L50543 = [1, 3, 5, 7, 7, 7, 7, 14], L50549 = [1, 3, 5, 7, 7, 7, 9, 14], L50550 = [1, 3, 5, 7, 7, 7, 11, 14], L50553 = [1, 3, 5, 7, 7, 7, 14, 1 L50562 = [1, 3, 5, 7, 7, 9, 11, 13], L50564 = [1, 3, 5, 7, 7, 9, 14, 14], L50565 = [1, 3, 5, 7, 7, 11, 14, 14], L50569 = [1, 3, 5, 7, 7, 14, 14, 14], L50583 = [1, 3, 5, 7, 9, 11, 13, 14], L50585 = [1, 3, 5, 7, 9, 14, 14, 14], L50586 = [1, 3, 5, 7, 11, 14, 14, 14], L50591 = [1, 3, 5, 7, 14, 14, 14, 14], L50613 = [1, 3, 5, 9, 14, 14, 14, 14], L50614 = [1, 3, 5, 11, 14, 14, 14, 14], L50620 = [1, 3, 5, 14, 14, 14, 14, 14], L50623 = [1, 3, 7, 7, 7, 7, 7, 9], L50635 = [1, 3, 7, 7, 7, 7, 9, 14], L50668 = [1, 3, 7, 7, 7, 9, 14, 14], L50738 = [1, 3, 7, 7, 9, 14, 14, 14], L50865 = [1, 3, 7, 9, 14, 14, 14, 14], L51073 = [1, 3, 9, 14, 14, 14, 14, 14], L54671 = [2, 2, 4, 6, 6, 7, 8, 10], L54675 = [2, 2, 4, 6, 6, 7, 10, 12], L54788 = [2, 2, 6, 6, 7, 10, 10, 14], L55023 = [2, 4, 4, 6, 7, 8, 8, 12], L55027 = [2, 4, 4, 6, 7, 8, 12, 12], L55087 = [2, 4, 6, 7, 7, 7, 7, 8], L55089 = [2, 4, 6, 7, 7, 7, 7, 12], L55094 = [2, 4, 6, 7, 7, 7, 8, 14], L55096 = [2, 4, 6, 7, 7, 7, 12, 14], L55104 = [2, 4, 6, 7, 7, 8, 14, 14], L55106 = [2, 4, 6, 7, 7, 12, 14, 14], L55116 = [2, 4, 6, 7, 8, 14, 14, 14], L55118 = [2, 4, 6, 7, 12, 14, 14, 14]. q = 29 : L164 = [0, 0, 0, 0, 1, 2, 4, 11], L171 = [0, 0, 0, 0, 1, 2, 5, 10], L215 = [0, 0, 0, 0, 1, 4, 5, 7], L216 = [0, 0, 0, 0, 1, 4, 5, 13], L728 = [0, 0, 0, 1, 2, 3, 8, 13], L750 = [0, 0, 0, 1, 2, 4, 7, 8], L755 = [0, 0, 0, 1, 2, 4, 7, 14], L799 = [0, 0, 0, 1, 2, 7, 8, 9], L815 = [0, 0, 0, 1, 2, 10, 11, 12], L2582 = [0, 0, 1, 2, 3, 4, 7, 13], L2589 = [0, 0, 1, 2, 3, 4, 8, 14], L2591 = [0, 0, 1, 2, 3, 4, 9, 11], L2593 = [0, 0, 1, 2, 3, 4, 9, 13], L2597 = [0, 0, 1, 2, 3, 4, 10, 13], L2601 = [0, 0, 1, 2, 3, 4, 11, 14], L2608 = [0, 0, 1, 2, 3, 5, 6, 11], L2610 = [0, 0, 1, 2, 3, 5, 6, 13], L2611 = [0, 0, 1, 2, 3, 5, 6, 14], L2617 = [0, 0, 1, 2, 3, 5, 7, 13], L2622 = [0, 0, 1, 2, 3, 5, 8, 12], L2628 = [0, 0, 1, 2, 3, 5, 9, 14], L2630 = [0, 0, 1, 2, 3, 5, 10, 12], L2632 = [0, 0, 1, 2, 3, 5, 10, 14], L2635 = [0, 0, 1, 2, 3, 5, 11, 14 L2637 = [0, 0, 1, 2, 3, 5, 12, 14], L2638 = [0, 0, 1, 2, 3, 6, 7, 8], L2639 = [0, 0, 1, 2, 3, 6, 7, 9], L2644 = [0, 0, 1, 2, 3, 6, 7, 14], L2645 = [0, 0, 1, 2, 3, 6, 8, 9], L2650 = [0, 0, 1, 2, 3, 6, 8, 14], L2672 = [0, 0, 1, 2, 3, 7, 11, 13], L2677 = [0, 0, 1, 2, 3, 8, 9, 12], L2678 = [0, 0, 1, 2, 3, 8, 9, 13], L2692 = [0, 0, 1, 2, 3, 10, 11, 12], L2698 = [0, 0, 1, 2, 4, 5, 7, 9], L2712 = [0, 0, 1, 2, 4, 5, 11, 12], L2713 = [0, 0, 1, 2, 4, 5, 11, 13], L2723 = [0, 0, 1, 2, 4, 7, 12, 13], L2725 = [0, 0, 1, 2, 4, 10, 11, 12], L2726 = [0, 0, 1, 2, 4, 10, 11, 13], L2727 = [0, 0, 1, 2, 4, 10, 12, 13], L2728 = [0, 0, 1, 2, 4, 11, 12, 13], L2735 = [0, 0, 1, 2, 5, 6, 8, 10], L2740 = [0, 0, 1, 2, 5, 6, 11, 13], L2745 = [0, 0, 1, 2, 5, 7, 10, 11], L2755 = [0, 0, 1, 2, 6, 7, 8, 11], L2767 = [0, 0, 1, 2, 7, 8, 12, 13], L2769 = [0, 0, 1, 2, 7, 10, 12, 1 L2772 = [0, 0, 1, 2, 10, 11, 12, 13], L8080 = [0, 1, 2, 3, 4, 5, 7, 11], L8081 = [0, 1, 2, 3, 4, 5, 7, 12], L8087 = [0, 1, 2, 3, 4, 5, 8, 12], L8090 = [0, 1, 2, 3, 4, 5, 9, 10], L8094 = [0, 1, 2, 3, 4, 5, 9, 14], L8097 = [0, 1, 2, 3, 4, 5, 10, 13], L8100 = [0, 1, 2, 3, 4, 5, 11, 13], L8101 = [0, 1, 2, 3, 4, 5, 11, 14], L8102 = [0, 1, 2, 3, 4, 5, 12, 13], L8106 = [0, 1, 2, 3, 4, 6, 7, 9], L8107 = [0, 1, 2, 3, 4, 6, 7, 10], L8109 = [0, 1, 2, 3, 4, 6, 7, 12], L8110 = [0, 1, 2, 3, 4, 6, 7, 13], L8112 = [0, 1, 2, 3, 4, 6, 8, 9], L8113 = [0, 1, 2, 3, 4, 6, 8, 11], L8115 = [0, 1, 2, 3, 4, 6, 8, 13], L8116 =
212
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 29 {0} {164, 171}, {215, 216}, {728, 750, 755}, {799, 815}, {2582, 2589}, {2591, 2608, 2611}, {2593, 2630}, {2597, 2644}, {2601, 2637}, {2610, 2638}, {2617, 2628}, {2622, 2635}, {2632, 2639, 2645}, {2650, 2698}, {2672, 2712}, {2677, 2692}, {2678, 2735}, {2713, 2745}, {2723, 2726}, {2725, 2755}, {2727, 2740}, {2728, 2772}, {2767, 2769}, {8080, 8081}, {8087, 8106}, {8090, 8112}, {8094, 8118}, {8097, 8101, 8123, 8131}, {8100, 8163, 8182}, {8102, 8129}, {8107, 8124}, {8109, 8113}, {8110, 8115, 8116, 8133}, {8120, 8141, 8184}, {8128, 8183, 8189, 8190, 8192}, {8132, 8137}, {8139, 8166, 8174}, {8142, 8197}, {8144, 8159}, {8146, 8160, 8234}, {8147, 8208}, {8150, 8188}, {8152, 8156, 8194, 8222}, {8154, 8248}, {8155, 8195}, {8161, 8187}, {8172, 8201, 8227, 8240}, {8179, 8180}, {8198, 8239, 8256}, {8206, 8217}, {8209, 8270}, {8210, 8223}, {8211, 8274, 8299, 8301, 8306}, {8214, 8254}, {8218, 8225}, {8224, 8245}, {8229, 8305}, {8235, 8241}, {8243, 8250}, {8260, 8279}, {8261, 8287}, {8268, 8300}, {8275, 8298}, {8277, 8303, 8311}, {22650, 22655}, {22651, 22652, 22656}, {22658, 22659}, {22660, 22662, 22663, 22670, 22676}, {22664, 22666}, {22667, 22668, 22677, 22680}, {22669, 22678, 22679}, {22671, 22685, 22686, 22691, 22698, 22703, 22719, 22741, 22754},
[0, 1, 2, 3, 4, 6, 8, 14], L8118 = [0, 1, 2, 3, 4, 6, 9, 11], L8120 = [0, 1, 2, 3, 4, 6, 9, 13], L8123 = [0, 1, 2, 3, 4, 6, 10, 12], L8124 = [0, 1, 2, 3, 4, 6, 10, 13], L8128 = [0, 1, 2, 3, 4, 6, 11, 14], L8129 = [0, 1, 2, 3, 4, 6, 12, 13], L8131 = [0, 1, 2, 3, 4, 7, 8, 9], L8132 = [0, 1, 2, 3, 4, 7, 8, 10], L8133 = [0, 1, 2, 3, 4, 7, 8, 11], L8137 = [0, 1, 2, 3, 4, 7, 9, 10], L8139 = [0, 1, 2, 3, 4, 7, 9, 13], L8141 = [0, 1, 2, 3, 4, 7, 10, 11], L8142 = [0, 1, 2, 3, 4, 7, 10, 12], L8144 = [0, 1, 2, 3, 4, 7, 10, 14], L8146 = [0, 1, 2, 3, 4, 7, 11, 13], L8147 = [0, 1, 2, 3, 4, 7, 12, 13], L8150 = [0, 1, 2, 3, 4, 8, 9, 11 L8152 = [0, 1, 2, 3, 4, 8, 9, 13], L8154 = [0, 1, 2, 3, 4, 8, 10, 11], L8155 = [0, 1, 2, 3, 4, 8, 10, 12], L8156 = [0, 1, 2, 3, 4, 8, 10, 13], L8159 = [0, 1, 2, 3, 4, 8, 11, 13], L8160 = [0, 1, 2, 3, 4, 8, 11, 14], L8161 = [0, 1, 2, 3, 4, 8, 12, 1 L8163 = [0, 1, 2, 3, 4, 9, 10, 13], L8166 = [0, 1, 2, 3, 4, 9, 11, 13], L8172 = [0, 1, 2, 3, 4, 10, 11, 14], L8174 = [0, 1, 2, 3, 4, 10, 12, 14], L8179 = [0, 1, 2, 3, 5, 6, 7, 10], L8180 = [0, 1, 2, 3, 5, 6, 7, 11], L8182 = [0, 1, 2, 3, 5, 6, 7, 13], L8183 = [0, 1, 2, 3, 5, 6, 7, 14], L8184 = [0, 1, 2, 3, 5, 6, 8, 9], L8187 = [0, 1, 2, 3, 5, 6, 8, 12], L8188 = [0, 1, 2, 3, 5, 6, 8, 14], L8189 = [0, 1, 2, 3, 5, 6, 9, 10], L8190 = [0, 1, 2, 3, 5, 6, 9, 11], L8192 = [0, 1, 2, 3, 5, 6, 9, 14], L8194 = [0, 1, 2, 3, 5, 6, 10, 12], L8195 = [0, 1, 2, 3, 5, 6, 10, 14], L8197 = [0, 1, 2, 3, 5, 6, 11, 14 L8198 = [0, 1, 2, 3, 5, 6, 12, 13], L8201 = [0, 1, 2, 3, 5, 7, 8, 10], L8206 = [0, 1, 2, 3, 5, 7, 9, 14], L8208 = [0, 1, 2, 3, 5, 7, 10, 13], L8209 = [0, 1, 2, 3, 5, 7, 10, 14], L8210 = [0, 1, 2, 3, 5, 7, 11, 12], L8211 = [0, 1, 2, 3, 5, 7, 11, 1 L8214 = [0, 1, 2, 3, 5, 8, 9, 12], L8217 = [0, 1, 2, 3, 5, 8, 10, 12], L8218 = [0, 1, 2, 3, 5, 8, 10, 14], L8222 = [0, 1, 2, 3, 5, 9, 10, 12], L8223 = [0, 1, 2, 3, 5, 9, 10, 13], L8224 = [0, 1, 2, 3, 5, 9, 11, 12], L8225 = [0, 1, 2, 3, 5, 9, 11, 1 L8227 = [0, 1, 2, 3, 5, 9, 12, 14], L8229 = [0, 1, 2, 3, 5, 10, 11, 13], L8234 = [0, 1, 2, 3, 5, 11, 12, 14], L8235 = [0, 1, 2, 3, 6, 7, 8, 9], L8239 = [0, 1, 2, 3, 6, 7, 8, 13], L8240 = [0, 1, 2, 3, 6, 7, 9, 10], L8241 = [0, 1, 2, 3, 6, 7, 9, 13], L8243 = [0, 1, 2, 3, 6, 7, 10, 12], L8245 = [0, 1, 2, 3, 6, 7, 11, 13], L8248 = [0, 1, 2, 3, 6, 7, 12, 14 L8250 = [0, 1, 2, 3, 6, 8, 10, 11], L8254 = [0, 1, 2, 3, 6, 8, 11, 14], L8256 = [0, 1, 2, 3, 6, 8, 12, 14], L8260 = [0, 1, 2, 3, 7, 8, 9, 13], L8261 = [0, 1, 2, 3, 7, 8, 10, 11], L8268 = [0, 1, 2, 3, 7, 10, 11, 12], L8270 = [0, 1, 2, 3, 7, 10, 12, L8274 = [0, 1, 2, 3, 8, 9, 11, 14], L8275 = [0, 1, 2, 3, 8, 9, 12, 13], L8277 = [0, 1, 2, 3, 8, 10, 11, 12], L8279 = [0, 1, 2, 3, 8, 10, 11, 14], L8287 = [0, 1, 2, 4, 5, 7, 9, 14], L8298 = [0, 1, 2, 4, 10, 11, 12, 13], L8299 = [0, 1, 2, 5, 6, 7, 8, 9], L8300 = [0, 1, 2, 5, 6, 7, 8, 10], L8301 = [0, 1, 2, 5, 6, 7, 8, 11], L8303 = [0, 1, 2, 5, 6, 7, 10, 11], L8305 = [0, 1, 2, 5, 6, 7, 11, 13], L8306 = [0, 1, 2, 5, 6, 8, 10, 11], L8311 = [0, 1, 2, 6, 7, 8, 10, 1 L22650 = [1, 2, 3, 4, 5, 6, 7, 10], L22651 = [1, 2, 3, 4, 5, 6, 7, 11], L22652 = [1, 2, 3, 4, 5, 6, 7, 12], L22655 =
APPENDIX
213
Table 6. (continued) m = 8 q 29 (cont.)
I {0}
indexes of I-isospectral families {22672, 22687, 22696}, {22673, 22732, 22745, 22753}, {22681, 22682, 22697, 22699, 22704, 22710, 22725, 22728, 22729, 22730, 22734, 22747}, {22690, 22724, 22733, 22736, 22763, 22771}, {22692, 22716, 22739, 22744, 22752, 22764, 22789, 22819}, {22694, 22713, 22715, 22722, 22755, 22758}, {22695, 22700}, {22702, 22779}, {22705, 22750}, {22707, 22757, 22770}, {22709, 22712, 22737, 22748, 22767}, {22711, 22731}, {22717, 22765, 22803, 22805}, {22718, 22740, 22742, 22743, 22812}, {22721, 22801, 22813, 22824}, {22723, 22774, 22792, 22799, 22826, 22846}, {22726, 22802}, {22738, 22746, 22788}, {22756, 22759, 22777, 22807, 22808, 22810, 22817, 22820, 22821, 22829}, {22760, 22761, 22768}, {22762, 22784, 22794, 22811}, {22772, 22778, 22783, 22798, 22830}, {22781, 22840, 22853}, {22785, 22814, 22827, 22841}, {22786, 22797, 22844, 22847, 22859}, {22787, 22839}, {22791, 22796, 22800}, {22793, 22795, 22825, 22843}, {22804, 22835}, {22806, 22809}, {22815, 22831}, {22833, 22836, 22863}, {22834, 22850}, {22837, 22849}, {22838, 22848, 22861}, {22851, 22855} {0, 1} {22694, 22715}, {22717, 22803}, {22772, 22783}, {22820, 22821}
[1, 2, 3, 4, 5, 6, 8, 9], L22656 = [1, 2, 3, 4, 5, 6, 8, 10], L22658 = [1, 2, 3, 4, 5, 6, 8, 12], L22659 = [1, 2, 3, 4, 5, 6, 8, 13], L22660 = [1, 2, 3, 4, 5, 6, 8, 14], L22662 = [1, 2, 3, 4, 5, 6, 9, 11], L22663 = [1, 2, 3, 4, 5, 6, 9, 12], L22664 = [1, 2, 3, 4, 5, 6, 9, 13], L22666 = [1, 2, 3, 4, 5, 6, 10, 11], L22667 = [1, 2, 3, 4, 5, 6, 10, 12], L22668 = [1, 2, 3, 4, 5, 6, 10, 13], L22669 = [1, 2, 3, 4, 5, 6, 10, 14], L22670 = [1, 2, 3, 4, 5, 6, 11, 12], L22671 = [1, 2, 3, 4, 5, 6, 11, 13], L22672 = [1, 2, 3, 4, 5, 6, 11, 14], L22673 = [1, 2, 3, 4, 5, 6, 12, 13], L22676 = [1, 2, 3, 4, 5, 7, 8, 9], L22677 = [1, 2, 3, 4, 5, 7, 8, 10], L22678 = [1, 2, 3, 4, 5, 7, 8, 11], L22679 = [1, 2, 3, 4, 5, 7, 8, 12], L22680 = [1, 2, 3, 4, 5, 7, 8, 13], L22681 = [1, 2, 3, 4, 5, 7, 8, 14], L22682 = [1, 2, 3, 4, 5, 7, 9, 10], L22685 = [1, 2, 3, 4, 5, 7, 9, 13], L22686 = [1, 2, 3, 4, 5, 7, 9, 14], L22687 = [1, 2, 3, 4, 5, 7, 10, 11], L22690 = [1, 2, 3, 4, 5, 7, 10, 1 L22691 = [1, 2, 3, 4, 5, 7, 11, 12], L22692 = [1, 2, 3, 4, 5, 7, 11, 13], L22694 = [1, 2, 3, 4, 5, 7, 12, 13], L22695 = [1, 2, 3, 4, 5, 7, 12, 14], L22696 = [1, 2, 3, 4, 5, 7, 13, 14], L22697 = [1, 2, 3, 4, 5, 8, 9, 10], L22698 = [1, 2, 3, 4, 5, 8, 9, 11], L22699 = [1, 2, 3, 4, 5, 8, 9, 12], L22700 = [1, 2, 3, 4, 5, 8, 9, 13], L22702 = [1, 2, 3, 4, 5, 8, 10, 11], L22703 = [1, 2, 3, 4, 5, 8, 10, 12], L22704 = [1, 2, 3, 4, 5, 8, 10, 13], L22705 = [1, 2, 3, 4, 5, 8, 10, 14], L22707 = [1, 2, 3, 4, 5, 8, 11, 14], L22709 = [1, 2, 3, 4, 5, 8, 12, 14], L22710 = [1, 2, 3, 4, 5, 8, 13, 14], L22711 = [1, 2, 3, 4, 5, 9, 10, 11], L22712 = [1, 2, 3, 4, 5, 9, 10, 12], L22713 = [1, 2, 3, 4, 5, 9, 10, 13], L22715 = [1, 2, 3, 4, 5, 9, 11, 13], L22716 = [1, 2, 3, 4, 5, 9, 11, 14], L22717 = [1, 2, 3, 4, 5, 9, 12, 13], L22718 = [1, 2, 3, 4, 5, 9, 12, 14], L22719 = [1, 2, 3, 4, 5, 9, 13, 14], L22721 = [1, 2, 3, 4, 5, 10, 11, 13], L22722 = [1, 2, 3, 4, 5, 10, 11, 14], L22723 = [1, 2, 3, 4, 5, 10, 12, 13], L22724 = [1, 2, 3, 4, 5, 10, 12, 14], L22725 = [1, 2, 3, 4, 5, 10, 13, 14], L22726 = [1, 2, 3, 4, 5, 11, 12, 13], L22728 = [1, 2, 3, 4, 5, 11, 13, 14], L22729 = [1, 2, 3, 4, 6, 7, 8, 9], L22730 = [1, 2, 3, 4, 6, 7, 8, 11], L22731 = [1, 2, 3, 4, 6, 7, 8, 12 L22732 = [1, 2, 3, 4, 6, 7, 8, 13], L22733 = [1, 2, 3, 4, 6, 7, 9, 10], L22734 = [1, 2, 3, 4, 6, 7, 9, 11], L22736 = [1, 2, 3, 4, 6, 7, 9, 13], L22737 = [1, 2, 3, 4, 6, 7, 9, 14], L22738 = [1, 2, 3, 4, 6, 7, 10, 11], L22739 = [1, 2, 3, 4, 6, 7, 10, 1 L22740 = [1, 2, 3, 4, 6, 7, 10, 14], L22741 = [1, 2, 3, 4, 6, 7, 11, 12], L22742 = [1, 2, 3, 4, 6, 7, 11, 13], L22743 = [1, 2, 3, 4, 6, 7, 12, 13], L22744 = [1, 2, 3, 4, 6, 7, 12, 14], L22745 = [1, 2, 3, 4, 6, 7, 13, 14], L22746 = [1, 2, 3, 4, 6, 8, 9, 11], L22747 = [1, 2, 3, 4, 6, 8, 9, 12], L22748 = [1, 2, 3, 4, 6, 8, 9, 13], L22750 =
214
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 30 {0} {55, 59}, {423, 427}, {444, 463}, {448, 469}, {800, 815}, {805, 837}, {1814, 1820}, {1817, 1819}, {2140, 2155}, {2241, 2245}, {2262, 2281}, {2266, 2287}, {2311, 2334}, {2354, 2413}, {2358, 2419}, {2366, 2431}, {3413, 3463}, {3520, 3560}, {3532, 3586}, {3535, 3588}, {3547, 3644}, {3550, 3646}, {7672, 8282}, {7780, 7786}, {7783, 7785}, {7873, 7888}, {7874, 7896}, {7878, 7898}, {7885, 7887}, {7892, 7897}, {8886, 8901}, {8978, 9030}, {8982, 9036}, {9326, 9330}, {9347, 9366}, {9351, 9372}, {9396, 9419}, {9439, 9498}, {9443, 9504}, {9451, 9516}, {9594, 9659}, {9602, 9671}, {9712, 9854}, {9716, 9860}, {9724, 9872},
[1, 2, 3, 4, 6, 8, 11, 12], L22752 = [1, 2, 3, 4, 6, 8, 11, 14], L22753 = [1, 2, 3, 4, 6, 8, 12, 13], L22754 = [1, 2, 3, 4, 6, 9, 10, 11], L22755 = [1, 2, 3, 4, 6, 9, 10, 12], L22756 = [1, 2, 3, 4, 6, 9, 10, 14], L22757 = [1, 2, 3, 4, 6, 9, 11, 13], L22758 = [1, 2, 3, 4, 6, 9, 11, 14], L22759 = [1, 2, 3, 4, 6, 9, 12, 13], L22760 = [1, 2, 3, 4, 6, 10, 11, 12], L22761 = [1, 2, 3, 4, 6, 10, 11, 13], L22762 = [1, 2, 3, 4, 6, 10, 11, 14], L22763 = [1, 2, 3, 4, 6, 10, 12, 13], L22764 = [1, 2, 3, 4, 6, 10, 12, 14], L22765 = [1, 2, 3, 4, 6, 11, 12, 13], L22767 = [1, 2, 3, 4, 7, 8, 9, 10], L22768 = [1, 2, 3, 4, 7, 8, 9, 12], L22770 = [1, 2, 3, 4, 7, 8, 9, 14], L22771 = [1, 2, 3, 4, 7, 8, 10, 11 L22772 = [1, 2, 3, 4, 7, 8, 10, 12], L22774 = [1, 2, 3, 4, 7, 8, 10, 14], L22777 = [1, 2, 3, 4, 7, 8, 12, 14], L22778 = [1, 2, 3, 4, 7, 9, 10, 12], L22779 = [1, 2, 3, 4, 7, 9, 10, 13], L22781 = [1, 2, 3, 4, 7, 9, 12, 13], L22783 = [1, 2, 3, 4, 7, 10, 11, 12], L22784 = [1, 2, 3, 4, 7, 10, 11, 13], L22785 = [1, 2, 3, 4, 7, 10, 12, 13], L22786 = [1, 2, 3, 4, 7, 10, 12, 14], L22787 = [1, 2, 3, 4, 7, 11, 12, 13], L22788 = [1, 2, 3, 4, 8, 9, 10, 12], L22789 = [1, 2, 3, 4, 8, 9, 10, 13], L22791 = [1, 2, 3, 4, 8, 9, 11, 12], L22792 = [1, 2, 3, 4, 8, 9, 11, 13], L22793 = [1, 2, 3, 4, 8, 9, 11, 14], L22794 = [1, 2, 3, 4, 8, 9, 12, 14], L22795 = [1, 2, 3, 4, 8, 10, 11, 12], L22796 = [1, 2, 3, 4, 8, 10, 11, 13], L22797 = [1, 2, 3, 4, 8, 10, 11, 14], L22798 = [1, 2, 3, 4, 8, 10, 12, 14], L22799 = [1, 2, 3, 4, 8, 11, 12, 14], L22800 = [1, 2, 3, 4, 9, 10, 12, 13], L22801 = [1, 2, 3, 4, 9, 10, 12, 14], L22802 = [1, 2, 3, 4, 9, 11, 12, 13], L22803 = [1, 2, 3, 4, 9, 11, 12, 14], L22804 = [1, 2, 3, 4, 10, 11, 12, 13], L22805 = [1, 2, 3, 4, 10, 11, 12, 14], L22806 = [1, 2, 3, 5, 6, 7, 8, 9], L22807 = [1, 2, 3, 5, 6, 7, 8, 10], L22808 = [1, 2, 3, 5, 6, 7, 8, 11], L22809 = [1, 2, 3, 5, 6, 7, 8, 12], L22810 = [1, 2, 3, 5, 6, 7, 9, 10], L22811 = [1, 2, 3, 5, 6, 7, 9, 13], L22812 = [1, 2, 3, 5, 6, 7, 9, 14], L22813 = [1, 2, 3, 5, 6, 7, 10, 11], L22814 = [1, 2, 3, 5, 6, 7, 10, 1 L22815 = [1, 2, 3, 5, 6, 7, 11, 13], L22817 = [1, 2, 3, 5, 6, 7, 12, 13], L22819 = [1, 2, 3, 5, 6, 8, 9, 10], L22820 = [1, 2, 3, 5, 6, 8, 9, 11], L22821 = [1, 2, 3, 5, 6, 8, 9, 14], L22824 = [1, 2, 3, 5, 6, 8, 10, 14], L22825 = [1, 2, 3, 5, 6, 8, 11, 14], L22826 = [1, 2, 3, 5, 6, 8, 12, 14], L22827 = [1, 2, 3, 5, 6, 9, 11, 13], L22829 = [1, 2, 3, 5, 6, 10, 12, 14], L22830 = [1, 2, 3, 5, 7, 8, 9, 12], L22831 = [1, 2, 3, 5, 7, 8, 10, 11], L22833 = [1, 2, 3, 5, 7, 10, 11, 13], L22834 = [1, 2, 3, 5, 7, 10, 11, 14], L22835 = [1, 2, 3, 5, 7, 11, 12, 13], L22836 = [1, 2, 3, 5, 8, 9, 11, 12], L22837 = [1, 2, 3, 5, 8, 9, 11, 14], L22838 = [1, 2, 3, 5, 8, 9, 12, 14], L22839 = [1, 2, 3, 5, 8, 10, 11, 12], L22840 = [1, 2, 3, 5, 8, 10, 11, 14], L22841 = [1, 2, 3, 5, 8, 10, 12, 14], L22843 = [1, 2, 3, 5, 9, 10, 12, 13], L22844 = [1, 2, 3, 5, 9, 11, 12, 14], L22846 = [1, 2, 3, 5, 10, 11, 12, 14], L22847 = [1, 2, 3, 6, 7, 8, 9, 13], L22848 = [1, 2, 3, 6, 7, 8, 10, 11], L22849 = [1, 2, 3, 6, 7, 8, 10, 12], L22850 = [1, 2, 3, 6, 7, 8, 11, 13], L22851 = [1, 2, 3, 6, 7, 8, 12, 13], L22853 = [1, 2, 3, 6, 7, 10, 12, 14], L22855 = [1, 2, 3, 6, 8, 10, 12, 14], L22859 = [1, 2, 3, 7, 10, 11, 12, 14], L22861 = [1, 2, 3, 8, 10, 11, 12, 14], L22863 = [1, 2, 5, 6, 7, 8, 10, 11]. q = 30 : L55 = [0, 0, 0, 0, 0, 1, 3, 7], L59 = [0, 0, 0, 0, 0, 1, 3, 11], L423 = [0, 0, 0, 0, 1, 3, 5, 7], L427 = [0, 0, 0, 0, 1, 3, 5, 11], L444 = [0, 0, 0, 0, 1, 3, 7, 10], L448 = [0, 0, 0, 0, 1, 3, 7, 15], L463 = [0, 0, 0, 0, 1, 3, 10, 11], L469 = [0, 0, 0, 0, 1, 3, 11, 15], L800 = [0, 0, 0, 0, 2, 4, 5, 12], L805 = [0, 0, 0, 0, 2, 4, 12, 15], L815 = [0, 0, 0, 0, 2, 5, 6, 8], L837 = [0, 0, 0, 0, 2, 6, 8, 15], L1814 = [0, 0, 0, 1, 2, 4, 7, 8], L1817 = [0, 0, 0, 1, 2, 4, 7, 11], L1819 = [0, 0, 0, 1, 2, 4, 7, 13], L1820 = [0, 0, 0, 1, 2, 4, 7, 14], L2140 = [0, 0, 0, 1, 3, 3, 7, 9],
APPENDIX
215
Table 6. (continued) m = 8 q I indexes of I-isospectral families 30 {0} {9736, 9892}, {12669, 12778}, {12718, 12856}, {12721, 12858}, {12960, 13051}, (cont.) {12972, 13077}, {12975, 13079}, {12991, 13128}, {13001, 13144}, {13004, 13146}, {13008, 13149}, {13024, 13241}, {13034, 13269}, {13037, 13271}, {13041, 13274}, {20406, 20498}, {27061, 27073}, {27066, 27114}, {27070, 27072}, {27083, 27113}, {27419, 29191}, {27892, 29813}, {27922, 29817}, {28238, 28244}, {28241, 28243}, {28331, 28346}, {28332, 28354}, {28336, 28356}, {28343, 28345}, {28350, 28355}, {28502, 28504}, {28503, 28524}, {28518, 28523}, {28635, 28668}, {28636, 28676}, {28640, 28678}, {28649, 28692}, {28665, 28667}, {28672, 28677}, {28681, 29824}, {28684, 28691}, {31027, 31075}, {31398, 31413}, {31490, 31542}, {31494, 31548}, {31651, 31707}, {31777, 31911}, {31781, 31917}, {31789, 31929}, {32760, 32764}, {32781, 32800}, {32785, 32806}, {32830, 32853}, {32873, 32932}, {32877, 32938},
L2155 = [0, 0, 0, 1, 3, 3, 9, 11], L2241 = [0, 0, 0, 1, 3, 5, 5, 7], L2245 = [0, 0, 0, 1, 3, 5, 5, 11], L2262 = [0, 0, 0, 1, 3, 5, 7, 10], L2266 = [0, 0, 0, 1, 3, 5, 7, 15], L2281 = [0, 0, 0, 1, 3, 5, 10, 11], L2287 = [0, 0, 0, 1, 3, 5, 11, 15], L2311 = [0, 0, 0, 1, 3, 6, 7, 12], L2334 = [0, 0, 0, 1, 3, 6, 11, 12], L2354 = [0, 0, 0, 1, 3, 7, 10, 10], L2358 = [0, 0, 0, 1, 3, 7, 10, 15], L2366 = [0, 0, 0, 1, 3, 7, 15, 15], L2413 = [0, 0, 0, 1, 3, 10, 10, 11], L2419 = [0, 0, 0, 1, 3, 10, 11, 15], L2431 = [0, 0, 0, 1, 3, 11, 15, 15], L3413 = [0, 0, 0, 2, 3, 4, 9, 12], L3463 = [0, 0, 0, 2, 3, 6, 8, 9], L3520 = [0, 0, 0, 2, 4, 5, 5, 12], L3532 = [0, 0, 0, 2, 4, 5, 10, 12], L3535 = [0, 0, 0, 2, 4, 5, 12, 15], L3547 = [0, 0, 0, 2, 4, 10, 12, 15], L3550 = [0, 0, 0, 2, 4, 12, 15, 15], L3560 = [0, 0, 0, 2, 5, 5, 6, 8], L3586 = [0, 0, 0, 2, 5, 6, 8, 10], L3588 = [0, 0, 0, 2, 5, 6, 8, 15], L3644 = [0, 0, 0, 2, 6, 8, 10, 15], L3646 = [0, 0, 0, 2, 6, 8, 15, 15], L7411 = [0, 0, 1, 2, 3, 4, 7, 14], L7416 = [0, 0, 1, 2, 3, 4, 8, 11], L7672 = [0, 0, 1, 2, 3, 11, 12, 14], L7780 = [0, 0, 1, 2, 4, 5, 7, 8], L7783 = [0, 0, 1, 2, 4, 5, 7, 11], L7785 = [0, 0, 1, 2, 4, 5, 7, 13], L7786 = [0, 0, 1, 2, 4, 5, 7, 14], L7873 = [0, 0, 1, 2, 4, 7, 8, 10], L7874 = [0, 0, 1, 2, 4, 7, 8, 11], L7878 = [0, 0, 1, 2, 4, 7, 8, 15], L7885 = [0, 0, 1, 2, 4, 7, 10, 11], L7887 = [0, 0, 1, 2, 4, 7, 10, 13], L7888 = [0, 0, 1, 2, 4, 7, 10, 14], L7890 = [0, 0, 1, 2, 4, 7, 11, 1 L7892 = [0, 0, 1, 2, 4, 7, 11, 15], L7896 = [0, 0, 1, 2, 4, 7, 13, 14], L7897 = [0, 0, 1, 2, 4, 7, 13, 15], L7898 = [0, 0, 1, 2, 4, 7, 14, 15], L8282 = [0, 0, 1, 2, 6, 7, 8, 9], L8284 = [0, 0, 1, 2, 6, 7, 8, 11], L8886 = [0, 0, 1, 3, 3, 5, 7, 9], L8901 = [0, 0, 1, 3, 3, 5, 9, 11], L8978 = [0, 0, 1, 3, 3, 7, 9, 10], L8982 = [0, 0, 1, 3, 3, 7, 9, 15], L9030 = [0, 0, 1, 3, 3, 9, 10, 11], L9036 = [0, 0, 1, 3, 3, 9, 11, 15], L9326 = [0, 0, 1, 3, 5, 5, 5, 7], L9330 = [0, 0, 1, 3, 5, 5, 5, 11], L9347 = [0, 0, 1, 3, 5, 5, 7, 10], L9351 = [0, 0, 1, 3, 5, 5, 7, 15], L9366 = [0, 0, 1, 3, 5, 5, 10, 11], L9372 = [0, 0, 1, 3, 5, 5, 11, 15], L9396 = [0, 0, 1, 3, 5, 6, 7, 12], L9419 = [0, 0, 1, 3, 5, 6, 11, 12], L9439 = [0, 0, 1, 3, 5, 7, 10, 10 L9443 = [0, 0, 1, 3, 5, 7, 10, 15], L9451 = [0, 0, 1, 3, 5, 7, 15, 15], L9498 = [0, 0, 1, 3, 5, 10, 10, 11], L9504 = [0, 0, 1, 3, 5, 10, 11, 15], L9516 = [0, 0, 1, 3, 5, 11, 15, 15], L9594 = [0, 0, 1, 3, 6, 7, 10, 12], L9602 = [0, 0, 1, 3, 6, 7, 12, 15], L9659 = [0, 0, 1, 3, 6, 10, 11, 12], L9671 = [0, 0, 1, 3, 6, 11, 12, 15], L9712 = [0, 0, 1, 3, 7, 10, 10, 10], L9716 = [0, 0, 1, 3, 7, 10, 10, 15], L9724 = [0, 0, 1, 3, 7, 10, 15, 15], L9736 = [0, 0, 1, 3, 7, 15, 15, 15], L9854 = [0, 0, 1, 3, 10, 10, 10, 11], L9860 = [0, 0, 1, 3, 10, 10, 11, 15], L9872 = [0, 0, 1, 3, 10, 11, 15, 15], L9892 = [0, 0, 1, 3, 11, 15, 15, 15], L12669 = [0, 0, 2, 3, 4, 5, 9, 12], L12718 = [0, 0, 2, 3, 4, 9, 10, 12], L12721 = [0, 0, 2, 3, 4, 9, 12, 15], L12778 = [0, 0, 2, 3, 5, 6, 8, 9], L12856 = [0, 0, 2, 3, 6, 8, 9, 10], L12858 = [0, 0, 2, 3, 6, 8, 9, 15], L12960 = [0, 0, 2, 4, 5, 5, 5, 12], L12972 = [0, 0, 2, 4, 5, 5, 10, 12 L12975 = [0, 0, 2, 4, 5, 5, 12, 15], L12991 = [0, 0, 2, 4, 5, 6, 12, 12], L13001 = [0, 0, 2, 4, 5, 10, 10, 12], L13004 = [0, 0, 2, 4, 5, 10, 12, 15], L13008 = [0, 0, 2, 4, 5, 12, 15, 15], L13024 = [0, 0, 2, 4, 6, 12, 12, 15], L13034 = [0, 0, 2, 4, 10, 10, 12, 15], L13037 = [0, 0, 2, 4, 10, 12, 15, 15], L13041 = [0, 0, 2, 4, 12, 15, 15, 15], L13051 = [0, 0, 2, 5, 5, 5, 6, 8], L13077 = [0, 0, 2, 5, 5, 6, 8, 10], L13079 = [0, 0, 2, 5, 5, 6, 8, 15], L13128 = [0, 0, 2, 5, 6, 6, 8, 12], L13144 = [0, 0, 2, 5, 6, 8, 10, 10], L13146 = [0, 0, 2, 5, 6, 8, 10, 15], L13149 = [0, 0, 2, 5, 6, 8, 15, 15], L13241 = [0, 0, 2, 6, 6, 8, 12, 15], L13269 = [0, 0, 2, 6, 8, 10, 10, 15], L13271 = [0, 0, 2, 6, 8, 10, 15, 15], L13274 = [0, 0, 2, 6, 8, 15, 15, 15], L20406 = [0, 1, 1, 3, 7, 7, 11, 13], L20498 =
216
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 30 {0} {32885, 32950}, {33028, 33093}, {33036, 33105}, {33146, 33288}, {33150, 33294}, (cont.) {33158, 33306}, {33170, 33326}, {33540, 33691}, {33548, 33703}, {33560, 33723}, {33795, 34088}, {33799, 34094}, {33807, 34106}, {33819, 34126}, {33835, 34156}, {40902, 41051}, {41182, 41409}, {41231, 41487}, {41234, 41489}, {41294, 41613}, {41336, 41651}, {41339, 41653}, {41343, 41656}, {41822, 42004}, {41834, 42030}, {41837, 42032}, {41853, 42081}, {41863, 42097}, {41866, 42099}, {41870, 42102}, {41903, 42203}, {41908, 42206}, {41920, 42238}, {41923, 42240}, {41927, 42243}, {41932, 42247}, {41965, 42419}, {41970, 42422}, {41982, 42474}, {41985, 42476}, {41989, 42479}, {41994, 42483}, {67530, 67763}, {67545, 67797}, {86015, 88103}, {86501, 86513}, {86506, 86554}, {86510, 86512}, {86523, 86553}, {86829, 86862}, {86830, 86870}, {86834, 86872}, {86851, 86982}, {86859, 86861}, {86866, 86871}, {86882, 86965}, {86898, 86981}, {87374, 91944}, {87847, 92566}, {87877, 92570},
[0, 1, 1, 3, 7, 11, 11, 13], L26972 = [0, 1, 2, 3, 4, 5, 7, 14], L26977 = [0, 1, 2, 3, 4, 5, 8, 11], L27061 = [0, 1, 2, 3, 4, 7, 8, 9], L27066 = [0, 1, 2, 3, 4, 7, 8, 14], L27070 = [0, 1, 2, 3, 4, 7, 9, 11], L27072 = [0, 1, 2, 3, 4, 7, 9, 13], L27073 = [0, 1, 2, 3, 4, 7, 9, 14], L27079 = [0, 1, 2, 3, 4, 7, 10, 14], L27083 = [0, 1, 2, 3, 4, 7, 11, 14], L27091 = [0, 1, 2, 3, 4, 7, 14, 15], L27107 = [0, 1, 2, 3, 4, 8, 10, 11], L27113 = [0, 1, 2, 3, 4, 8, 11, 13], L27114 = [0, 1, 2, 3, 4, 8, 11, 14], L27115 = [0, 1, 2, 3, 4, 8, 11, 15], L27419 = [0, 1, 2, 3, 5, 11, 12, 14], L27577 = [0, 1, 2, 3, 6, 9, 12, 15], L27892 = [0, 1, 2, 3, 10, 11, 12, 14], L27922 = [0, 1, 2, 3, 11, 12, 14, 15], L28238 = [0, 1, 2, 4, 5, 5, 7, 8], L28241 = [0, 1, 2, 4, 5, 5, 7, 11], L28243 = [0, 1, 2, 4, 5, 5, 7, 13], L28244 = [0, 1, 2, 4, 5, 5, 7, 14], L28331 = [0, 1, 2, 4, 5, 7, 8, 10], L28332 = [0, 1, 2, 4, 5, 7, 8, 11], L28336 = [0, 1, 2, 4, 5, 7, 8, 15], L28343 = [0, 1, 2, 4, 5, 7, 10, 11], L28345 = [0, 1, 2, 4, 5, 7, 10, 13], L28346 = [0, 1, 2, 4, 5, 7, 10, 14], L28348 = [0, 1, 2, 4, 5, 7, 11, 12], L28350 = [0, 1, 2, 4, 5, 7, 11, 15], L28354 = [0, 1, 2, 4, 5, 7, 13, 14], L28355 = [0, 1, 2, 4, 5, 7, 13, 15], L28356 = [0, 1, 2, 4, 5, 7, 14, 15], L28502 = [0, 1, 2, 4, 6, 7, 8, 11], L28503 = [0, 1, 2, 4, 6, 7, 8, 12], L28504 = [0, 1, 2, 4, 6, 7, 8, 13], L28518 = [0, 1, 2, 4, 6, 7, 11, 12], L28523 = [0, 1, 2, 4, 6, 7, 12, 13], L28524 = [0, 1, 2, 4, 6, 7, 12, 14], L28635 = [0, 1, 2, 4, 7, 8, 10, 10], L28636 = [0, 1, 2, 4, 7, 8, 10, 11], L28640 = [0, 1, 2, 4, 7, 8, 10, 15], L28644 = [0, 1, 2, 4, 7, 8, 11, 15], L28649 = [0, 1, 2, 4, 7, 8, 15, 15], L28665 = [0, 1, 2, 4, 7, 10, 10, 11], L28667 = [0, 1, 2, 4, 7, 10, 10, 13], L28668 = [0, 1, 2, 4, 7, 10, 10, 14], L28670 = [0, 1, 2, 4, 7, 10, 11, 12], L28672 = [0, 1, 2, 4, 7, 10, 11, 15], L28676 = [0, 1, 2, 4, 7, 10, 13, 14], L28677 = [0, 1, 2, 4, 7, 10, 13, 15], L28678 = [0, 1, 2, 4, 7, 10, 14, 15], L28681 = [0, 1, 2, 4, 7, 11, 12, 13], L28682 = [0, 1, 2, 4, 7, 11, 12, 15], L28684 = [0, 1, 2, 4, 7, 11, 15, 15], L28690 = [0, 1, 2, 4, 7, 13, 14, 15], L28691 = [0, 1, 2, 4, 7, 13, 15, 15], L28692 = [0, 1, 2, 4, 7, 14, 15, 15], L29100 = [0, 1, 2, 5, 5, 10, 10, 15], L29191 = [0, 1, 2, 5, 6, 7, 8, 9], L29193 = [0, 1, 2, 5, 6, 7, 8, 11], L29425 = [0, 1, 2, 5, 8, 9, 10, 1 L29565 = [0, 1, 2, 5, 10, 11, 12, 15], L29813 = [0, 1, 2, 6, 7, 8, 9, 10], L29817 = [0, 1, 2, 6, 7, 8, 9, 15], L29819 = [0, 1, 2, 6, 7, 8, 10, 11], L29824 = [0, 1, 2, 6, 7, 8, 11, 13], L29825 = [0, 1, 2, 6, 7, 8, 11, 15], L31027 = [0, 1, 3, 3, 3, 7, 9, 9], L31075 = [0, 1, 3, 3, 3, 9, 9, 11], L31398 = [0, 1, 3, 3, 5, 5, 7, 9], L31413 = [0, 1, 3, 3, 5, 5, 9, 11], L31490 = [0, 1, 3, 3, 5, 7, 9, 10], L31494 = [0, 1, 3, 3, 5, 7, 9, 15], L31542 = [0, 1, 3, 3, 5, 9, 10, 11 L31548 = [0, 1, 3, 3, 5, 9, 11, 15], L31651 = [0, 1, 3, 3, 6, 7, 9, 12], L31707 = [0, 1, 3, 3, 6, 9, 11, 12], L31777 = [0, 1, 3, 3, 7, 9, 10, 10], L31781 = [0, 1, 3, 3, 7, 9, 10, 15], L31789 = [0, 1, 3, 3, 7, 9, 15, 15], L31911 = [0, 1, 3, 3, 9, 10, 10, 11], L31917 = [0, 1, 3, 3, 9, 10, 11, 15], L31929 = [0, 1, 3, 3, 9, 11, 15, 15], L32760 = [0, 1, 3, 5, 5, 5, 5, 7], L32764 = [0, 1, 3, 5, 5, 5, 5, 11], L32781 = [0, 1, 3, 5, 5, 5, 7, 10], L32785 = [0, 1, 3, 5, 5, 5, 7, 15], L32800 = [0, 1, 3, 5, 5, 5, 10, 11], L32806 = [0, 1, 3, 5, 5, 5, 11, 15], L32830 = [0, 1, 3, 5, 5, 6, 7, 12], L32853 = [0, 1, 3, 5, 5, 6, 11, 12], L32873 = [0, 1, 3, 5, 5, 7, 10, 10], L32877 = [0, 1, 3, 5, 5, 7, 10, 15], L32885 = [0, 1, 3, 5, 5, 7, 15, 15], L32932 = [0, 1, 3, 5, 5, 10, 10, 11], L32938 = [0, 1, 3, 5, 5, 10, 11, 15], L32950 = [0, 1, 3, 5, 5, 11, 15, 15], L33028 = [0, 1, 3, 5, 6, 7, 10, 12], L33036 =
APPENDIX
217
Table 6. (continued) m = 8 q I indexes of I-isospectral families 30 {0} {88386, 93709}, {88991, 94037}, {89021, 94041}, {89069, 94049}, {89978, 89984}, (cont.) {89981, 89983}, {90071, 90086}, {90072, 90094}, {90076, 90096}, {90083, 90085}, {90090, 90095}, {90242, 90244}, {90243, 90264}, {90258, 90263}, {90375, 90408}, {90376, 90416}, {90380, 90418}, {90384, 90430}, {90389, 90432}, {90405, 90407}, {90412, 90417}, {90424, 90431}, {90828, 90830}, {90829, 90871}, {90833, 90887}, {90836, 90842}, {90840, 90889}, {90865, 90870}, {90879, 90888}, {91140, 91201}, {91141, 91209}, {91145, 91211}, {91149, 91223}, {91154, 91225}, {91160, 91241}, {91166, 91243}, {91198, 91200}, {91205, 91210}, {91214, 94056}, {91217, 91224}, {91230, 94066}, {91233, 91242}, {96609, 96657}, {96896, 97023}, {97917, 97932}, {98009, 98061}, {98013, 98067}, {98170, 98226}, {98296, 98430}, {98300, 98436}, {98308, 98448}, {98717, 98857}, {98725, 98869}, {99005, 99293}, {99009, 99299}, {99017, 99311}, {99029, 99331}, {101424, 101428}, {101445, 101464}, {101449, 101470}, [0, 1, 3, 5, 6, 7, 12, 15], L33093 = [0, 1, 3, 5, 6, 10, 11, 12], L33105 = [0, 1, 3, 5, 6, 11, 12, 15], L33146 = [0, 1, 3, 5, 7, 10, 10, 10], L33150 = [0, 1, 3, 5, 7, 10, 10, 15], L33158 = [0, 1, 3, 5, 7, 10, 15, 15], L33170 = [0, 1, 3, 5, 7, 15, 15, 15], L33288 = [0, 1, 3, 5, 10, 10, 10, 11], L33294 = [0, 1, 3, 5, 10, 10, 11, 15], L33306 = [0, 1, 3, 5, 10, 11, 15, 15], L33326 = [0, 1, 3, 5, 11, 15, 15, 15], L33419 = [0, 1, 3, 6, 6, 7, 12, 12], L33490 = [0, 1, 3, 6, 6, 11, 12, 12], L33540 = [0, 1, 3, 6, 7, 10, 10, 12], L33548 = [0, 1, 3, 6, 7, 10, 12, 15], L33560 = [0, 1, 3, 6, 7, 12, 15, 15], L33600 = [0, 1, 3, 6, 8, 9, 12, 15], L33663 = [0, 1, 3, 6, 9, 10, 12, 15], L33691 = [0, 1, 3, 6, 10, 10, 11, 12], L33703 = [0, 1, 3, 6, 10, 11, 12, 15], L33723 = [0, 1, 3, 6, 11, 12, 15, 15], L33795 = [0, 1, 3, 7, 10, 10, 10, 10], L33799 = [0, 1, 3, 7, 10, 10, 10, 15], L33807 = [0, 1, 3, 7, 10, 10, 15, 15], L33819 = [0, 1, 3, 7, 10, 15, 15, 15], L33835 = [0, 1, 3, 7, 15, 15, 15, 15], L34088 = [0, 1, 3, 10, 10, 10, 10, 11], L34094 = [0, 1, 3, 10, 10, 10, 11, 15], L34106 = [0, 1, 3, 10, 10, 11, 15, 15], L34126 = [0, 1, 3, 10, 11, 15, 15, 15], L34156 = [0, 1, 3, 11, 15, 15, 15, 15], L35171 = [0, 1, 4, 5, 6, 9, 11, 14], L36320 = [0, 1, 5, 5, 6, 10, 10, 15], L36401 = [0, 1, 5, 5, 8, 10, 10, 15], L36472 = [0, 1, 5, 5, 10, 10, 12, 15], L40902 = [0, 2, 3, 3, 4, 9, 9, 12], L41051 = [0, 2, 3, 3, 6, 8, 9, 9], L41182 = [0, 2, 3, 4, 5, 5, 9, 12], L41231 = [0, 2, 3, 4, 5, 9, 10, 12], L41234 = [0, 2, 3, 4, 5, 9, 12, 15], L41294 = [0, 2, 3, 4, 6, 9, 12, 12], L41336 = [0, 2, 3, 4, 9, 10, 10, 12], L41339 = [0, 2, 3, 4, 9, 10, 12, 15], L41343 = [0, 2, 3, 4, 9, 12, 15, 15], L41409 = [0, 2, 3, 5, 5, 6, 8, 9], L41449 = [0, 2, 3, 5, 5, 10, 10, 15], L41487 = [0, 2, 3, 5, 6, 8, 9, 10], L41489 = [0, 2, 3, 5, 6, 8, 9, 15], L41504 = [0, 2, 3, 5, 6, 9, 12, 15], L41613 = [0, 2, 3, 6, 6, 8, 9, 12], L41651 = [0, 2, 3, 6, 8, 9, 10, 10], L41653 = [0, 2, 3, 6, 8, 9, 10, 15], L41656 = [0, 2, 3, 6, 8, 9, 15, 15], L41822 = [0, 2, 4, 5, 5, 5, 5, 12], L41834 = [0, 2, 4, 5, 5, 5, 10, 12], L41837 = [0, 2, 4, 5, 5, 5, 12, 15], L41853 = [0, 2, 4, 5, 5, 6, 12, 12], L41863 = [0, 2, 4, 5, 5, 10, 10, 12], L41866 = [0, 2, 4, 5, 5, 10, 12, 15], L41870 = [0, 2, 4, 5, 5, 12, 15, 15], L41903 = [0, 2, 4, 5, 6, 10, 12, 12], L41908 = [0, 2, 4, 5, 6, 12, 12, 15], L41920 = [0, 2, 4, 5, 10, 10, 10, 12], L41923 = [0, 2, 4, 5, 10, 10, 12, 15], L41927 = [0, 2, 4, 5, 10, 12, 15, 15], L41932 = [0, 2, 4, 5, 12, 15, 15, 15], L41965 = [0, 2, 4, 6, 10, 12, 12, 15], L41970 = [0, 2, 4, 6, 12, 12, 15, 15], L41982 = [0, 2, 4, 10, 10, 10, 12, 15], L41985 = [0, 2, 4, 10, 10, 12, 15, 15], L41989 = [0, 2, 4, 10, 12, 15, 15, 15], L41994 = [0, 2, 4, 12, 15, 15, 15, 15], L42004 = [0, 2, 5, 5, 5, 5, 6, 8], L42030 = [0, 2, 5, 5, 5, 6, 8, 10], L42032 = [0, 2, 5, 5, 5, 6, 8, 15], L42081 = [0, 2, 5, 5, 6, 6, 8, 12], L42097 = [0, 2, 5, 5, 6, 8, 10, 10], L42099 = [0, 2, 5, 5, 6, 8, 10, 15], L42102 = [0, 2, 5, 5, 6, 8, 15, 15], L42155 = [0, 2, 5, 5, 9, 10, 10, 15], L42203 = [0, 2, 5, 6, 6, 8, 10, 12], L42206 = [0, 2, 5, 6, 6, 8, 12, 15], L42238 = [0, 2, 5, 6, 8, 10, 10, 10], L42240 = [0, 2, 5, 6, 8, 10, 10, 15], L42243 = [0, 2, 5, 6, 8, 10, 15, 15], L42247 = [0, 2, 5, 6, 8, 15, 15, 15], L42419 = [0, 2, 6, 6, 8, 10, 12, 15], L42422 = [0, 2, 6, 6, 8, 12, 15, 15], L42474 = [0, 2, 6, 8, 10, 10, 10, 15], L42476 = [0, 2, 6, 8, 10, 10, 15, 15], L42479 = [0, 2, 6, 8, 10, 15, 15, 15], L42483 = [0, 2, 6, 8, 15, 15, 15, 15], L66428 = [1, 1, 3, 5, 7, 7, 11, 13], L66520 = [1, 1, 3, 5, 7, 11, 11, 13], L67530 = [1, 1, 3, 7, 7, 10, 11, 13], L67545 = [1, 1, 3, 7, 7, 11, 13, 15], L67763 =
218
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 30 {0} {101494, 101517}, {101537, 101596}, {101541, 101602}, {101549, 101614}, (cont.) {101692, 101757}, {101700, 101769}, {101810, 101952}, {101814, 101958}, {101822, 101970}, {101834, 101990}, {102083, 102154}, {102204, 102355}, {102212, 102367}, {102224, 102387}, {102459, 102752}, {102463, 102758}, {102471, 102770}, {102483, 102790}, {102499, 102820}, {103053, 103212}, {103065, 103232}, {103319, 103625}, {103327, 103637}, {103339, 103657}, {103355, 103687}, {103802, 104347}, {103806, 104353}, {103814, 104365}, {103826, 104385}, {103842, 104415}, {103862, 104457}, {117635, 117845}, {117684, 118044}, {119981, 120274}, {120106, 120449}, {120656, 121091},
[1, 1, 3, 7, 10, 11, 11, 13], L67797 = [1, 1, 3, 7, 11, 11, 13, 15], L70737 = [1, 1, 4, 6, 6, 9, 11, 14], L85230 = [1, 2, 3, 3, 4, 7, 9, 14], L85259 = [1, 2, 3, 3, 4, 8, 9, 11], L86015 = [1, 2, 3, 3, 9, 11, 12, 14], L86412 = [1, 2, 3, 4, 5, 5, 7, 14], L86417 = [1, 2, 3, 4, 5, 5, 8, 11], L86501 = [1, 2, 3, 4, 5, 7, 8, 9], L86506 = [1, 2, 3, 4, 5, 7, 8, 14], L86510 = [1, 2, 3, 4, 5, 7, 9, 11], L86512 = [1, 2, 3, 4, 5, 7, 9, 13], L86513 = [1, 2, 3, 4, 5, 7, 9, 14], L86519 = [1, 2, 3, 4, 5, 7, 10, 14], L86523 = [1, 2, 3, 4, 5, 7, 11, 14], L86531 = [1, 2, 3, 4, 5, 7, 14, 15], L86547 = [1, 2, 3, 4, 5, 8, 10, 11], L86553 = [1, 2, 3, 4, 5, 8, 11, 13], L86554 = [1, 2, 3, 4, 5, 8, 11, 14], L86555 = [1, 2, 3, 4, 5, 8, 11, 15], L86713 = [1, 2, 3, 4, 6, 7, 12, 14], L86739 = [1, 2, 3, 4, 6, 8, 11, 12], L86766 = [1, 2, 3, 4, 6, 9, 11, 14], L86829 = [1, 2, 3, 4, 7, 8, 9, 10], L86830 = [1, 2, 3, 4, 7, 8, 9, 11], L86834 = [1, 2, 3, 4, 7, 8, 9, 15 L86839 = [1, 2, 3, 4, 7, 8, 10, 14], L86851 = [1, 2, 3, 4, 7, 8, 14, 15], L86859 = [1, 2, 3, 4, 7, 9, 10, 11], L86861 = [1, 2, 3, 4, 7, 9, 10, 13], L86862 = [1, 2, 3, 4, 7, 9, 10, 14], L86864 = [1, 2, 3, 4, 7, 9, 11, 12], L86866 = [1, 2, 3, 4, 7, 9, 11, 15], L86870 = [1, 2, 3, 4, 7, 9, 13, 14], L86871 = [1, 2, 3, 4, 7, 9, 13, 15], L86872 = [1, 2, 3, 4, 7, 9, 14, 15], L86878 = [1, 2, 3, 4, 7, 10, 10, 14], L86882 = [1, 2, 3, 4, 7, 10, 11, 14], L86890 = [1, 2, 3, 4, 7, 10, 14, 15], L86898 = [1, 2, 3, 4, 7, 11, 14, 15], L86910 = [1, 2, 3, 4, 7, 14, 15, 15], L86959 = [1, 2, 3, 4, 8, 10, 10, 11], L86965 = [1, 2, 3, 4, 8, 10, 11, 13], L86966 = [1, 2, 3, 4, 8, 10, 11, 14], L86967 = [1, 2, 3, 4, 8, 10, 11, 15], L86981 = [1, 2, 3, 4, 8, 11, 13, 15], L86982 = [1, 2, 3, 4, 8, 11, 14, 15], L86983 = [1, 2, 3, 4, 8, 11, 15, 15], L87374 = [1, 2, 3, 5, 5, 11, 12, 14], L87847 = [1, 2, 3, 5, 10, 11, 12, 14], L87877 = [1, 2, 3, 5, 11, 12, 14, 15], L88103 = [1, 2, 3, 6, 7, 8, 9, 9], L88105 = [1, 2, 3, 6, 7, 8, 9, 11], L88119 = [1, 2, 3, 6, 7, 8, 12, 13], L88386 = [1, 2, 3, 6, 11, 12, 12, 14], L88991 = [1, 2, 3, 10, 10, 11, 12, 14], L89021 = [1, 2, 3, 10, 11, 12, 14, 15], L89069 = [1, 2, 3, 11, 12, 14, 15, 15], L89978 = [1, 2, 4, 5, 5, 5, 7, 8], L89981 = [1, 2, 4, 5, 5, 5, 7, 11], L89983 = [1, 2, 4, 5, 5, 5, 7, 13], L89984 = [1, 2, 4, 5, 5, 5, 7, 14], L90071 = [1, 2, 4, 5, 5, 7, 8, 10], L90072 = [1, 2, 4, 5, 5, 7, 8, 11], L90076 = [1, 2, 4, 5, 5, 7, 8, 15], L90083 = [1, 2, 4, 5, 5, 7, 10, 11 L90085 = [1, 2, 4, 5, 5, 7, 10, 13], L90086 = [1, 2, 4, 5, 5, 7, 10, 14], L90088 = [1, 2, 4, 5, 5, 7, 11, 12], L90090 = [1, 2, 4, 5, 5, 7, 11, 15], L90094 = [1, 2, 4, 5, 5, 7, 13, 14], L90095 = [1, 2, 4, 5, 5, 7, 13, 15], L90096 = [1, 2, 4, 5, 5, 7, 14, 15], L90242 = [1, 2, 4, 5, 6, 7, 8, 11], L90243 = [1, 2, 4, 5, 6, 7, 8, 12], L90244 = [1, 2, 4, 5, 6, 7, 8, 13], L90258 = [1, 2, 4, 5, 6, 7, 11, 12], L90263 = [1, 2, 4, 5, 6, 7, 12, 13], L90264 = [1, 2, 4, 5, 6, 7, 12, 14], L90375 = [1, 2, 4, 5, 7, 8, 10, 10], L90376 = [1, 2, 4, 5, 7, 8, 10, 11], L90380 = [1, 2, 4, 5, 7, 8, 10, 15], L90384 = [1, 2, 4, 5, 7, 8, 11, 15], L90389 = [1, 2, 4, 5, 7, 8, 15, 15], L90405 = [1, 2, 4, 5, 7, 10, 10, 11], L90407 = [1, 2, 4, 5, 7, 10, 10, 13], L90408 = [1, 2, 4, 5, 7, 10, 10, 14], L90410 = [1, 2, 4, 5, 7, 10, 11, 12], L90412 = [1, 2, 4, 5, 7, 10, 11, 15], L90416 = [1, 2, 4, 5, 7, 10, 13, 14], L90417 = [1, 2, 4, 5, 7, 10, 13, 15], L90418 = [1, 2, 4, 5, 7, 10, 14, 15], L90421 = [1, 2, 4, 5, 7, 11, 12, 13], L90422 = [1, 2, 4, 5, 7, 11, 12, 15], L90424 = [1, 2, 4, 5, 7, 11, 15, 15], L90430 = [1, 2, 4, 5, 7, 13, 14, 15], L90431 = [1, 2, 4, 5, 7, 13, 15, 15], L90432 = [1, 2, 4, 5, 7, 14, 15, 15], L90828 = [1, 2, 4, 6, 7, 8, 10, 11], L90829 = [1, 2, 4, 6, 7, 8, 10, 12], L90830 = [1, 2, 4, 6, 7, 8, 10, 13], L90833 = [1, 2, 4, 6, 7, 8, 11, 12], L90836 = [1, 2, 4, 6, 7, 8, 11, 15], L90840 = [1, 2, 4, 6, 7, 8, 12, 15], L90842 = [1, 2, 4, 6, 7, 8, 13, 15], L90865 = [1, 2, 4, 6, 7, 10, 11, 12], L90870 = [1, 2, 4, 6, 7, 10, 12, 13], L90871 = [1, 2, 4, 6, 7, 10, 12, 14], L90877 =
APPENDIX
219
Table 6. (continued) m = 8 q I indexes of I-isospectral families 30 {0} {120705, 121169}, {120708, 121171}, {120768, 121295}, {120810, 121333}, (cont.) {120813, 121335}, {120817, 121338}, {120935, 121565}, {120940, 121568}, {121002, 121635}, {121005, 121637}, {121009, 121640}, {121014, 121644}, {121896, 122224}, {121908, 122250}, {121911, 122252}, {121927, 122301}, {121937, 122317}, {121940, 122319}, {121944, 122322}, {121977, 122423}, {121982, 122426}, {121994, 122458}, {121997, 122460}, {122001, 122463}, {122006, 122467}, {122045, 122621}, {122067, 122655}, {122072, 122658}, {122078, 122662}, {122092, 122719}, {122095, 122721}, {122099, 122724}, {122104, 122728}, {122110, 122733}, {122149, 122977}, {122171, 123031}, {122176, 123034}, {122182, 123038}, {122196, 123125}, {122199, 123127}, {122203, 123130}, {122208, 123134}, {122214, 123139}
[1, 2, 4, 6, 7, 11, 12, 12], L90879 = [1, 2, 4, 6, 7, 11, 12, 15], L90887 = [1, 2, 4, 6, 7, 12, 13, 14], L90888 = [1, 2, 4, 6, 7, 12, 13, 15], L90889 = [1, 2, 4, 6, 7, 12, 14, 15], L91140 = [1, 2, 4, 7, 8, 10, 10, 10], L91141 = [1, 2, 4, 7, 8, 10, 10, 11], L91145 = [1, 2, 4, 7, 8, 10, 10, 15], L91149 = [1, 2, 4, 7, 8, 10, 11, 15], L91154 = [1, 2, 4, 7, 8, 10, 15, 15], L91160 = [1, 2, 4, 7, 8, 11, 15, 15], L91166 = [1, 2, 4, 7, 8, 15, 15, 15], L91198 = [1, 2, 4, 7, 10, 10, 10, 11], L91200 = [1, 2, 4, 7, 10, 10, 10, 13], L91201 = [1, 2, 4, 7, 10, 10, 10, 14], L91203 = [1, 2, 4, 7, 10, 10, 11, 12], L91205 = [1, 2, 4, 7, 10, 10, 11, 15], L91209 = [1, 2, 4, 7, 10, 10, 13, 14], L91210 = [1, 2, 4, 7, 10, 10, 13, 15], L91211 = [1, 2, 4, 7, 10, 10, 14, 15], L91214 = [1, 2, 4, 7, 10, 11, 12, 13], L91215 = [1, 2, 4, 7, 10, 11, 12, 15], L91217 = [1, 2, 4, 7, 10, 11, 15, 15], L91223 = [1, 2, 4, 7, 10, 13, 14, 15], L91224 = [1, 2, 4, 7, 10, 13, 15, 15], L91225 = [1, 2, 4, 7, 10, 14, 15, 15], L91230 = [1, 2, 4, 7, 11, 12, 13, 15], L91231 = [1, 2, 4, 7, 11, 12, 15, 15], L91233 = [1, 2, 4, 7, 11, 15, 15, 15], L91241 = [1, 2, 4, 7, 13, 14, 15, 15], L91242 = [1, 2, 4, 7, 13, 15, 15, 15], L91243 = [1, 2, 4, 7, 14, 15, 15, 15], L91944 = [1, 2, 5, 5, 6, 7, 8, 9], L91946 = [1, 2, 5, 5, 6, 7, 8, 11], L92566 = [1, 2, 5, 6, 7, 8, 9, 10], L92570 = [1, 2, 5, 6, 7, 8, 9, 15], L92572 = [1, 2, 5, 6, 7, 8, 10, 11 L92577 = [1, 2, 5, 6, 7, 8, 11, 13], L92578 = [1, 2, 5, 6, 7, 8, 11, 15], L93709 = [1, 2, 6, 6, 7, 8, 9, 12], L93717 = [1, 2, 6, 6, 7, 8, 11, 12], L94037 = [1, 2, 6, 7, 8, 9, 10, 10], L94041 = [1, 2, 6, 7, 8, 9, 10, 15], L94049 = [1, 2, 6, 7, 8, 9, 15, 15], L94051 = [1, 2, 6, 7, 8, 10, 10, 11], L94056 = [1, 2, 6, 7, 8, 10, 11, 13], L94057 = [1, 2, 6, 7, 8, 10, 11, 15], L94066 = [1, 2, 6, 7, 8, 11, 13, 15], L94067 = [1, 2, 6, 7, 8, 11, 15, 15], L96609 = [1, 3, 3, 3, 5, 7, 9, 9], L96657 = [1, 3, 3, 3, 5, 9, 9, 11], L96896 = [1, 3, 3, 3, 7, 9, 9, 10], L96900 = [1, 3, 3, 3, 7, 9, 9, 15], L97023 = [1, 3, 3, 3, 9, 9, 10, 11], L97029 = [1, 3, 3, 3, 9, 9, 11, 15], L97917 = [1, 3, 3, 5, 5, 5, 7, 9], L97932 = [1, 3, 3, 5, 5, 5, 9, 11], L98009 = [1, 3, 3, 5, 5, 7, 9, 10], L98013 = [1, 3, 3, 5, 5, 7, 9, 15], L98061 = [1, 3, 3, 5, 5, 9, 10, 11], L98067 = [1, 3, 3, 5, 5, 9, 11, 15], L98170 = [1, 3, 3, 5, 6, 7, 9, 12], L98226 = [1, 3, 3, 5, 6, 9, 11, 12], L98296 = [1, 3, 3, 5, 7, 9, 10, 10], L98300 = [1, 3, 3, 5, 7, 9, 10, 15], L98308 = [1, 3, 3, 5, 7, 9, 15, 15], L98430 = [1, 3, 3, 5, 9, 10, 10, 11], L98436 = [1, 3, 3, 5, 9, 10, 11, 15], L98448 = [1, 3, 3, 5, 9, 11, 15, 15], L98717 = [1, 3, 3, 6, 7, 9, 10, 12], L98725 = [1, 3, 3, 6, 7, 9, 12, 15], L98857 = [1, 3, 3, 6, 9, 10, 11, 12], L98869 = [1, 3, 3, 6, 9, 11, 12, 15], L99005 = [1, 3, 3, 7, 9, 10, 10, 10], L99009 = [1, 3, 3, 7, 9, 10, 10, 15], L99017 = [1, 3, 3, 7, 9, 10, 15, 15], L99029 = [1, 3, 3, 7, 9, 15, 15, 15], L99293 = [1, 3, 3, 9, 10, 10, 10, 11], L99299 = [1, 3, 3, 9, 10, 10, 11, 15], L99311 = [1, 3, 3, 9, 10, 11, 15, 15], L99331 = [1, 3, 3, 9, 11, 15, 15, 15], L101424 = [1, 3, 5, 5, 5, 5, 5, 7], L101428 = [1, 3, 5, 5, 5, 5, 5, 11], L101445 = [1, 3, 5, 5, 5, 5, 7, 10], L101449 = [1, 3, 5, 5, 5, 5, 7, 15], L101464 = [1, 3, 5, 5, 5, 5, 10, 11], L101470 = [1, 3, 5, 5, 5, 5, 11, 15], L101494 = [1, 3, 5, 5, 5, 6, 7, 12], L101517 = [1, 3, 5, 5, 5, 6, 11, 12], L101537 = [1, 3, 5, 5, 5, 7, 10, 10], L101541 = [1, 3, 5, 5, 5, 7, 10, 15], L101549 = [1, 3, 5, 5, 5, 7, 15, 15], L101596 = [1, 3, 5, 5, 5, 10, 10, 11], L101602 = [1, 3, 5, 5, 5, 10, 11, 15], L101614 = [1, 3, 5, 5, 5, 11, 15, 15], L101692 = [1, 3, 5, 5, 6, 7, 10, 12], L101700 = [1, 3, 5, 5, 6, 7, 12, 15], L101757 = [1, 3, 5, 5, 6, 10, 11, 12], L101769 = [1, 3, 5, 5, 6, 11, 12, 15], L101810 = [1, 3, 5, 5, 7, 10, 10, 10], L101814 = [1, 3, 5, 5, 7, 10, 10, 15], L101822 = [1, 3, 5, 5, 7, 10, 15, 15], L101834 = [1, 3, 5, 5, 7, 15, 15, 15], L101952 = [1, 3, 5, 5, 10, 10, 10, 11],
220
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 30 {0, 1} {7411, 7416}, {7890, 8284}, {26972, 26977}, {27079, 27107}, (cont.) {27091, 27115}, {28348, 29193}, {28670, 29819}, {28682, 29825}, {85230, 85259}, {86412, 86417}, {86519, 86547}, {86531, 86555}, {86713, 86739}, {86864, 88105}, {86878, 86959}, {86890, 86967}, {86910, 86983}, {90088, 91946}, {90410, 92572}, {90422, 92578}, {90877, 93717}, {91203, 94051}, {91215, 94057}, {91231, 94067} {0, 5} {33419, 33490}, {66428, 66520}, {86839, 86966}, {90421, 92577}, {96900, 97029}, {120109, 120451} {4, 5} {29100, 36401}, {29425, 29565}, {35171, 108060}, {36320, 41449}, {36472, 42155}, {70737, 105929}, {86766, 88119} {0, 7} {28644, 28690} {6, 7} {27577, 33600}, {33663, 41504}
L101958 = [1, 3, 5, 5, 10, 10, 11, 15], L101970 = [1, 3, 5, 5, 10, 11, 15, 15], L101990 = [1, 3, 5, 5, 11, 15, 15, 15], L102083 = [1, 3, 5, 6, 6, 7, 12, 12], L102154 = [1, 3, 5, 6, 6, 11, 12, 12], L102204 = [1, 3, 5, 6, 7, 10, 10, 12], L102212 = [1, 3, 5, 6, 7, 10, 12, 15], L102224 = [1, 3, 5, 6, 7, 12, 15, 15], L102355 = [1, 3, 5, 6, 10, 10, 11, 12], L102367 = [1, 3, 5, 6, 10, 11, 12, 15], L102387 = [1, 3, 5, 6, 11, 12, 15, 15], L102459 = [1, 3, 5, 7, 10, 10, 10, 10], L102463 = [1, 3, 5, 7, 10, 10, 10, 15], L102471 = [1, 3, 5, 7, 10, 10, 15, 15], L102483 = [1, 3, 5, 7, 10, 15, 15, 15], L102499 = [1, 3, 5, 7, 15, 15, 15, 15], L102752 = [1, 3, 5, 10, 10, 10, 10, 11], L102758 = [1, 3, 5, 10, 10, 10, 11, 15], L102770 = [1, 3, 5, 10, 10, 11, 15, 15], L102790 = [1, 3, 5, 10, 11, 15, 15, 15], L102820 = [1, 3, 5, 11, 15, 15, 15, 15], L103053 = [1, 3, 6, 6, 7, 10, 12, 12], L103065 = [1, 3, 6, 6, 7, 12, 12, 15], L103212 = [1, 3, 6, 6, 10, 11, 12, 12], L103232 = [1, 3, 6, 6, 11, 12, 12, 15], L103319 = [1, 3, 6, 7, 10, 10, 10, 12], L103327 = [1, 3, 6, 7, 10, 10, 12, 15], L103339 = [1, 3, 6, 7, 10, 12, 15, 15], L103355 = [1, 3, 6, 7, 12, 15, 15, 15], L103625 = [1, 3, 6, 10, 10, 10, 11, 12], L103637 = [1, 3, 6, 10, 10, 11, 12, 15], L103657 = [1, 3, 6, 10, 11, 12, 15, 15], L103687 = [1, 3, 6, 11, 12, 15, 15, 15], L103802 = [1, 3, 7, 10, 10, 10, 10, 10], L103806 = [1, 3, 7, 10, 10, 10, 10, 15], L103814 = [1, 3, 7, 10, 10, 10, 15, 15], L103826 = [1, 3, 7, 10, 10, 15, 15, 15], L103842 = [1, 3, 7, 10, 15, 15, 15, 15], L103862 = [1, 3, 7, 15, 15, 15, 15, 15], L104347 = [1, 3, 10, 10, 10, 10, 10, 11], L104353 = [1, 3, 10, 10, 10, 10, 11, 15], L104365 = [1, 3, 10, 10, 10, 11, 15, 15], L104385 = [1, 3, 10, 10, 11, 15, 15, 15], L104415 = [1, 3, 10, 11, 15, 15, 15, 15], L104457 = [1, 3, 11, 15, 15, 15, 15, 15], L105929 = [1, 4, 4, 6, 9, 9, 11, 14], L108060 = [1, 4, 6, 9, 10, 11, 14, 15], L117635 = [2, 2, 4, 4, 5, 8, 12, 14], L117684 = [2, 2, 4, 4, 8, 12, 14, 15], L117845 = [2, 2, 4, 5, 6, 8, 8, 14], L118044 = [2, 2, 4, 6, 8, 8, 14, 15], L119981 = [2, 3, 3, 4, 5, 9, 9, 12], L120106 = [2, 3, 3, 4, 9, 9, 10, 12], L120109 = [2, 3, 3, 4, 9, 9, 12, 15], L120274 = [2, 3, 3, 5, 6, 8, 9, 9], L120449 = [2, 3, 3, 6, 8, 9, 9, 10], L120451 = [2, 3, 3, 6, 8, 9, 9, 15], L120656 = [2, 3, 4, 5, 5, 5, 9, 12], L120705 = [2, 3, 4, 5, 5, 9, 10, 12], L120708 = [2, 3, 4, 5, 5, 9, 12, 15], L120768 = [2, 3, 4, 5, 6, 9, 12, 12], L120810 = [2, 3, 4, 5, 9, 10, 10, 12], L120813 = [2, 3, 4, 5, 9, 10, 12, 15], L120817 = [2, 3, 4, 5, 9, 12, 15, 15], L120935 = [2, 3, 4, 6, 9, 10, 12, 12], L120940 = [2, 3, 4, 6, 9, 12, 12, 15], L121002 = [2, 3, 4, 9, 10, 10, 10, 12], L121005 = [2, 3, 4, 9, 10, 10, 12, 15], L121009 = [2, 3, 4, 9, 10, 12, 15, 15], L121014 = [2, 3, 4, 9, 12, 15, 15, 15], L121091 = [2, 3, 5, 5, 5, 6, 8, 9], L121169 = [2, 3, 5, 5, 6, 8, 9, 10], L121171 = [2, 3, 5, 5, 6, 8, 9, 15], L121295 = [2, 3, 5, 6, 6, 8, 9, 12], L121333 = [2, 3, 5, 6, 8, 9, 10, 10], L121335 = [2, 3, 5, 6, 8, 9, 10, 15], L121338 = [2, 3, 5, 6, 8, 9, 15, 15], L121565 = [2, 3, 6, 6, 8, 9, 10, 12], L121568 = [2, 3, 6, 6, 8, 9, 12, 15], L121635 = [2, 3, 6, 8, 9, 10, 10, 10], L121637 = [2, 3, 6, 8, 9, 10, 10, 15], L121640 = [2, 3, 6, 8, 9, 10, 15, 15], L121644 = [2, 3, 6, 8, 9, 15, 15, 15], L121896 = [2, 4, 5, 5, 5, 5, 5, 12], L121908 = [2, 4, 5, 5, 5, 5, 10, 12], L121911 = [2, 4, 5, 5, 5, 5, 12, 15], L121927 = [2, 4, 5, 5, 5, 6, 12, 12], L121937 = [2, 4, 5, 5, 5, 10, 10, 12], L121940 = [2, 4, 5, 5, 5, 10, 12, 15], L121944 = [2, 4, 5, 5, 5, 12, 15, 15], L121977 = [2, 4, 5, 5, 6, 10, 12, 12], L121982 = [2, 4, 5, 5, 6, 12, 12, 15], L121994 = [2, 4, 5, 5, 10, 10, 10, 12], L121997 = [2, 4, 5, 5, 10, 10, 12, 15], L122001 = [2, 4, 5, 5, 10, 12, 15, 15], L122006 = [2, 4, 5, 5, 12, 15, 15, 15], L122045 = [2, 4, 5, 6, 6, 12, 12, 12], L122067 = [2, 4, 5, 6, 10, 10, 12, 12], L122072 = [2, 4, 5, 6, 10, 12, 12, 15], L122078 =
APPENDIX
221
Table 6. (continued) m = 8 q I indexes of I-isospectral families 31 {0} {874, 910}, {969, 983, 992}, {1014, 1017}, {3311, 3319}, {3323, 3384}, {3344, 3348}, {3364, 3380}, {3396, 3468}, {3409, 3496}, {3437, 3575}, {3460, 3550}, {3498, 3546}, {3544, 3596}, {10988, 10990}, {10995, 11001, 11002}, {11013, 11016, 11104}, {11024, 11031}, {11036, 11101}, {11041, 11069}, {11050, 11110}, {11057, 11195}, {11060, 11120}, {11062, 11074, 11117}, {11065, 11192}, {11068, 11123}, {11073, 11149}, {11075, 11197}, {11085, 11090}, {11086, 11121, 11190, 11196}, {11102, 11116}, {11107, 11115, 11131}, {11112, 11127}, {11124, 11289}, {11129, 11186}, {11140, 11168}, {11144, 11231}, {11148, 11171, 11308, 11317}, {11157, 11219}, {11169, 11191}, {11176, 11209}, {11182, 11334}, {11183, 11232}, {11184, 11200}, {11203, 11214}, {11217, 11297}, {11220, 11306}, {11244, 11263, 11341}, {11250, 11257}, {11262, 11332}, {11277, 11328}, {11282, 11365}, {11360, 11370},
[2, 4, 5, 6, 12, 12, 15, 15], L122092 = [2, 4, 5, 10, 10, 10, 10, 12], L122095 = [2, 4, 5, 10, 10, 10, 12, 15], L122099 = [2, 4, 5, 10, 10, 12, 15, 15], L122104 = [2, 4, 5, 10, 12, 15, 15, 15], L122110 = [2, 4, 5, 12, 15, 15, 15, 15], L122149 = [2, 4, 6, 6, 12, 12, 12, 15], L122171 = [2, 4, 6, 10, 10, 12, 12, 15], L122176 = [2, 4, 6, 10, 12, 12, 15, 15], L122182 = [2, 4, 6, 12, 12, 15, 15, 15], L122196 = [2, 4, 10, 10, 10, 10, 12, 15], L122199 = [2, 4, 10, 10, 10, 12, 15, 15], L122203 = [2, 4, 10, 10, 12, 15, 15, 15], L122208 = [2, 4, 10, 12, 15, 15, 15, 15], L122214 = [2, 4, 12, 15, 15, 15, 15, 15], L122224 = [2, 5, 5, 5, 5, 5, 6, 8], L122250 = [2, 5, 5, 5, 5, 6, 8, 10], L122252 = [2, 5, 5, 5, 5, 6, 8, 15], L122301 = [2, 5, 5, 5, 6, 6, 8, 12], L122317 = [2, 5, 5, 5, 6, 8, 10, 10], L122319 = [2, 5, 5, 5, 6, 8, 10, 15], L122322 = [2, 5, 5, 5, 6, 8, 15, 15], L122423 = [2, 5, 5, 6, 6, 8, 10, 12], L122426 = [2, 5, 5, 6, 6, 8, 12, 15], L122458 = [2, 5, 5, 6, 8, 10, 10, 10], L122460 = [2, 5, 5, 6, 8, 10, 10, 15], L122463 = [2, 5, 5, 6, 8, 10, 15, 15], L122467 = [2, 5, 5, 6, 8, 15, 15, 15], L122621 = [2, 5, 6, 6, 6, 8, 12, 12], L122655 = [2, 5, 6, 6, 8, 10, 10, 12], L122658 = [2, 5, 6, 6, 8, 10, 12, 15], L122662 = [2, 5, 6, 6, 8, 12, 15, 15], L122719 = [2, 5, 6, 8, 10, 10, 10, 10], L122721 = [2, 5, 6, 8, 10, 10, 10, 15], L122724 = [2, 5, 6, 8, 10, 10, 15, 15], L122728 = [2, 5, 6, 8, 10, 15, 15, 15], L122733 = [2, 5, 6, 8, 15, 15, 15, 15], L122977 = [2, 6, 6, 6, 8, 12, 12, 15], L123031 = [2, 6, 6, 8, 10, 10, 12, 15], L123034 = [2, 6, 6, 8, 10, 12, 15, 15], L123038 = [2, 6, 6, 8, 12, 15, 15, 15], L123125 = [2, 6, 8, 10, 10, 10, 10, 15], L123127 = [2, 6, 8, 10, 10, 10, 15, 15], L123130 = [2, 6, 8, 10, 10, 15, 15, 15], L123134 = [2, 6, 8, 10, 15, 15, 15, 15], L123139 = [2, 6, 8, 15, 15, 15, 15, 15]. q = 31 : L874 = [0, 0, 0, 1, 2, 3, 8, 11], L910 = [0, 0, 0, 1, 2, 4, 7, 12], L969 = [0, 0, 0, 1, 2, 6, 8, 14], L983 = [0, 0, 0, 1, 2, 7, 9, 10], L992 = [0, 0, 0, 1, 2, 8, 10, 13], L1014 = [0, 0, 0, 1, 3, 4, 7, 9], L1017 = [0, 0, 0, 1, 3, 4, 9, 10], L3311 = [0, 0, 1, 2, 3, 4, 7, 14], L3319 = [0, 0, 1, 2, 3, 4, 8, 15], L3323 = [0, 0, 1, 2, 3, 4, 9, 13], L3344 = [0, 0, 1, 2, 3, 5, 6, 11], L3348 = [0, 0, 1, 2, 3, 5, 6, 15], L3364 = [0, 0, 1, 2, 3, 5, 9, 11], L3380 = [0, 0, 1, 2, 3, 5, 12, 15], L3384 = [0, 0, 1, 2, 3, 6, 7, 9], L3396 = [0, 0, 1, 2, 3, 6, 8, 14], L3409 = [0, 0, 1, 2, 3, 6, 12, 14], L3437 = [0, 0, 1, 2, 3, 8, 9, 11], L3460 = [0, 0, 1, 2, 3, 9, 12, 14], L3468 = [0, 0, 1, 2, 3, 10, 13, 15], L3496 = [0, 0, 1, 2, 4, 5, 11, 15], L3498 = [0, 0, 1, 2, 4, 5, 12, 14], L3544 = [0, 0, 1, 2, 5, 6, 11, 14], L3546 = [0, 0, 1, 2, 5, 7, 8, 9], L3550 = [0, 0, 1, 2, 5, 7, 9, 10], L3575 = [0, 0, 1, 2, 6, 7, 8, 14], L3596 = [0, 0, 1, 2, 7, 8, 10, 13], L10988 = [0, 1, 2, 3, 4, 5, 14, 15], L10990 = [0, 1, 2, 3, 4, 6, 7, 9], L10995 = [0, 1, 2, 3, 4, 6, 7, 14], L11001 = [0, 1, 2, 3, 4, 6, 8, 14], L11002 = [0, 1, 2, 3, 4, 6, 8, 15], L11008 = [0, 1, 2, 3, 4, 6, 9, 15], L11010 = [0, 1, 2, 3, 4, 6, 10, 12], L11013 = [0, 1, 2, 3, 4, 6, 10, 15], L11016 = [0, 1, 2, 3, 4, 6, 11, 14], L11024 = [0, 1, 2, 3, 4, 7, 8, 10], L11031 = [0, 1, 2, 3, 4, 7, 9, 11], L11036 = [0, 1, 2, 3, 4, 7, 10, 11], L11041 = [0, 1, 2, 3, 4, 7, 11, 13], L11050 = [0, 1, 2, 3, 4, 8, 9, 11], L11057 = [0, 1, 2, 3, 4, 8, 10, 13], L11060 = [0, 1, 2, 3, 4, 8, 11, 12], L11062 = [0, 1, 2, 3, 4, 8, 11, 14], L11065 = [0, 1, 2, 3, 4, 8, 12, 14], L11068 = [0, 1, 2, 3, 4, 9, 10, 12], L11069 = [0, 1, 2, 3, 4, 9, 10, 13], L11073 = [0, 1, 2, 3, 4, 9, 11, 14], L11074 = [0, 1, 2, 3, 4, 9, 11, 15], L11075 = [0, 1, 2, 3, 4, 9, 12, 13], L11085 = [0, 1, 2, 3, 4, 10, 12, 14], L11086 = [0, 1, 2, 3, 4, 10, 12, 15], L11090 = [0, 1, 2, 3, 4, 11, 12, 14], L11101 = [0, 1, 2, 3, 5, 6, 7, 13], L11102 = [0, 1, 2, 3, 5, 6, 7, 14], L11104 =
222
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 31 {0} {32266, 32271}, {32282, 32284}, {32283, 32301}, (cont.) {32291, 32325, 32385, 32386}, {32293, 32327, 32345, 32363, 32369, 32405}, {32295, 32330, 32388, 32390, 32409, 32452}, {32304, 32321}, {32310, 32328}, {32320, 32324}, {32323, 32433, 32448}, {32326, 32346, 32352, 32375, 32380, 32387}, {32335, 32404}, {32336, 32359}, {32341, 32361, 32445}, {32347, 32353, 32354, 32418}, {32349, 32366, 32423, 32431}, {32350, 32360}, {32356, 32372, 32557}, {32362, 32435, 32437, 32540},
[0, 1, 2, 3, 5, 6, 8, 9], L11107 = [0, 1, 2, 3, 5, 6, 8, 12], L11110 = [0, 1, 2, 3, 5, 6, 8, 15], L11112 = [0, 1, 2, 3, 5, 6, 9, 11], L11115 = [0, 1, 2, 3, 5, 6, 9, 15], L11116 = [0, 1, 2, 3, 5, 6, 10, 11], L11117 = [0, 1, 2, 3, 5, 6, 10, 12], L11120 = [0, 1, 2, 3, 5, 6, 10, 15], L11121 = [0, 1, 2, 3, 5, 6, 11, 12], L11123 = [0, 1, 2, 3, 5, 6, 11, 15], L11124 = [0, 1, 2, 3, 5, 6, 12, 14], L11127 = [0, 1, 2, 3, 5, 6, 13, 15], L11129 = [0, 1, 2, 3, 5, 7, 8, 10], L11131 = [0, 1, 2, 3, 5, 7, 8, 12], L11140 = [0, 1, 2, 3, 5, 7, 10, 13], L11144 = [0, 1, 2, 3, 5, 7, 11, 14], L11148 = [0, 1, 2, 3, 5, 7, 13, 14], L11149 = [0, 1, 2, 3, 5, 7, 13, 15], L11157 = [0, 1, 2, 3, 5, 8, 10, 14], L11168 = [0, 1, 2, 3, 5, 9, 11, 14], L11169 = [0, 1, 2, 3, 5, 9, 11, 15], L11171 = [0, 1, 2, 3, 5, 9, 12, 14], L11176 = [0, 1, 2, 3, 5, 10, 11, 14], L11182 = [0, 1, 2, 3, 5, 11, 12, 13], L11183 = [0, 1, 2, 3, 5, 11, 12, 14], L11184 = [0, 1, 2, 3, 5, 11, 12, 15], L11186 = [0, 1, 2, 3, 5, 11, 13, 15], L11190 = [0, 1, 2, 3, 6, 7, 8, 10], L11191 = [0, 1, 2, 3, 6, 7, 8, 11], L11192 = [0, 1, 2, 3, 6, 7, 8, 12], L11195 = [0, 1, 2, 3, 6, 7, 9, 10], L11196 = [0, 1, 2, 3, 6, 7, 9, 13], L11197 = [0, 1, 2, 3, 6, 7, 9, 14], L11200 = [0, 1, 2, 3, 6, 7, 10, 13], L11203 = [0, 1, 2, 3, 6, 7, 11, 1 L11209 = [0, 1, 2, 3, 6, 8, 9, 10], L11214 = [0, 1, 2, 3, 6, 8, 10, 13], L11217 = [0, 1, 2, 3, 6, 8, 11, 12], L11219 = [0, 1, 2, 3, 6, 8, 11, 15], L11220 = [0, 1, 2, 3, 6, 8, 12, 14], L11231 = [0, 1, 2, 3, 6, 11, 13, 15], L11232 = [0, 1, 2, 3, 7, 8, 9, 10], L11244 = [0, 1, 2, 3, 7, 9, 10, 13], L11250 = [0, 1, 2, 3, 7, 9, 13, 15], L11257 = [0, 1, 2, 3, 7, 11, 13, 14], L11262 = [0, 1, 2, 3, 8, 9, 10, 13], L11263 = [0, 1, 2, 3, 8, 9, 10, 14], L11277 = [0, 1, 2, 3, 8, 11, 12, 15], L11282 = [0, 1, 2, 3, 9, 10, 12, 14], L11289 = [0, 1, 2, 3, 10, 12, 13, 15], L11297 = [0, 1, 2, 4, 5, 7, 9, 15], L11306 = [0, 1, 2, 4, 5, 8, 9, 15], L11308 = [0, 1, 2, 4, 5, 9, 10, 12], L11317 = [0, 1, 2, 4, 5, 11, 12, 15], L11328 = [0, 1, 2, 4, 7, 11, 13, 14], L11332 = [0, 1, 2, 5, 6, 7, 8, 9], L11334 = [0, 1, 2, 5, 6, 7, 8, 11], L11341 = [0, 1, 2, 5, 6, 8, 9, 10], L11360 = [0, 1, 2, 6, 7, 8, 9, 13], L11365 = [0, 1, 2, 6, 7, 8, 13, 14 L11370 = [0, 1, 2, 8, 9, 10, 12, 14], L32266 = [1, 2, 3, 4, 5, 6, 7, 12], L32271 = [1, 2, 3, 4, 5, 6, 8, 10], L32282 = [1, 2, 3, 4, 5, 6, 9, 15], L32283 = [1, 2, 3, 4, 5, 6, 10, 11], L32284 = [1, 2, 3, 4, 5, 6, 10, 12], L32291 = [1, 2, 3, 4, 5, 6, 11, 15], L32293 = [1, 2, 3, 4, 5, 6, 12, 14], L32295 = [1, 2, 3, 4, 5, 6, 13, 14], L32301 = [1, 2, 3, 4, 5, 7, 8, 12], L32304 = [1, 2, 3, 4, 5, 7, 8, 15], L32310 = [1, 2, 3, 4, 5, 7, 9, 15], L32320 = [1, 2, 3, 4, 5, 7, 12, 13], L32321 = [1, 2, 3, 4, 5, 7, 12, 14], L32323 = [1, 2, 3, 4, 5, 7, 13, 14], L32324 = [1, 2, 3, 4, 5, 7, 13, 15], L32325 = [1, 2, 3, 4, 5, 7, 14, 15], L32326 = [1, 2, 3, 4, 5, 8, 9, 10], L32327 = [1, 2, 3, 4, 5, 8, 9, 11], L32328 = [1, 2, 3, 4, 5, 8, 9, 12], L32330 = [1, 2, 3, 4, 5, 8, 9, 14], L32335 = [1, 2, 3, 4, 5, 8, 10, 15 L32336 = [1, 2, 3, 4, 5, 8, 11, 12], L32341 = [1, 2, 3, 4, 5, 8, 12, 14], L32345 = [1, 2, 3, 4, 5, 8, 14, 15], L32346 = [1, 2, 3, 4, 5, 9, 10, 11], L32347 = [1, 2, 3, 4, 5, 9, 10, 12], L32349 = [1, 2, 3, 4, 5, 9, 10, 14], L32350 = [1, 2, 3, 4, 5, 9, 10, 15], L32352 = [1, 2, 3, 4, 5, 9, 11, 13], L32353 = [1, 2, 3, 4, 5, 9, 11, 14], L32354 = [1, 2, 3, 4, 5, 9, 11, 15], L32356 = [1, 2, 3, 4, 5, 9, 12, 14], L32359 = [1, 2, 3, 4, 5, 9, 14, 15], L32360 = [1, 2, 3, 4, 5, 10, 11, 12], L32361 = [1, 2, 3, 4, 5, 10, 11, 13], L32362 = [1, 2, 3, 4, 5, 10, 11, 14], L32363 = [1, 2, 3, 4, 5, 10, 11, 15], L32365 = [1, 2, 3, 4, 5, 10, 12, 14], L32366 = [1, 2, 3, 4, 5, 10, 12, 15], L32369 = [1, 2, 3, 4, 5, 10, 14, 15], L32372 = [1, 2, 3, 4, 5, 11, 12, 15], L32373 = [1, 2, 3, 4, 5, 11, 13, 14], L32374 = [1, 2, 3, 4, 5, 11, 13, 15], L32375 = [1, 2, 3, 4, 5, 11, 14, 15], L32378 = [1, 2, 3, 4, 5, 12, 14, 15], L32379 = [1, 2, 3, 4, 6, 7, 8, 9], L32380 = [1, 2, 3, 4, 6, 7, 8, 11], L32381 = [1, 2, 3, 4, 6, 7, 8, 12], L32383 =
APPENDIX
223
Table 6. (continued) m = 8 q I indexes of I-isospectral families 31 {0} {32365, 32460, 32463, 32519, 32546, 32562}, {32373, 32470, 32511}, (cont.) {32374, 32401, 32531, 32550}, {32378, 32379}, {32381, 32384}, {32383, 32413}, {32392, 32408}, {32395, 32427}, {32396, 32449, 32459, 32465}, {32399, 32400}, {32406, 32412}, {32414, 32464, 32471, 32537}, {32421, 32528}, {32425, 32536, 32539}, {32426, 32538}, {32432, 32454}, {32434, 32479}, {32438, 32485, 32504}, {32439, 32518, 32574, 32575, 32621}, {32441, 32480, 32548, 32623}, {32447, 32547, 32567}, {32450, 32578},
[1, 2, 3, 4, 6, 7, 8, 14], L32384 = [1, 2, 3, 4, 6, 7, 8, 15], L32385 = [1, 2, 3, 4, 6, 7, 9, 10], L32386 = [1, 2, 3, 4, 6, 7, 9, 11], L32387 = [1, 2, 3, 4, 6, 7, 9, 12], L32388 = [1, 2, 3, 4, 6, 7, 9, 13], L32390 = [1, 2, 3, 4, 6, 7, 9, 15], L32392 = [1, 2, 3, 4, 6, 7, 10, 12], L32395 = [1, 2, 3, 4, 6, 7, 11, 12], L32396 = [1, 2, 3, 4, 6, 7, 11, 13], L32399 = [1, 2, 3, 4, 6, 7, 12, 14], L32400 = [1, 2, 3, 4, 6, 7, 12, 15], L32401 = [1, 2, 3, 4, 6, 7, 13, 14], L32404 = [1, 2, 3, 4, 6, 8, 9, 11], L32405 = [1, 2, 3, 4, 6, 8, 9, 12], L32406 = [1, 2, 3, 4, 6, 8, 9, 13], L32408 = [1, 2, 3, 4, 6, 8, 9, 15], L32409 = [1, 2, 3, 4, 6, 8, 11, 12], L32412 = [1, 2, 3, 4, 6, 8, 12, 13], L32413 = [1, 2, 3, 4, 6, 8, 12, 15], L32414 = [1, 2, 3, 4, 6, 8, 13, 14], L32418 = [1, 2, 3, 4, 6, 9, 10, 13], L32421 = [1, 2, 3, 4, 6, 9, 11, 12], L32423 = [1, 2, 3, 4, 6, 9, 11, 15], L32425 = [1, 2, 3, 4, 6, 9, 13, 14], L32426 = [1, 2, 3, 4, 6, 9, 13, 15], L32427 = [1, 2, 3, 4, 6, 10, 11, 12], L32431 = [1, 2, 3, 4, 6, 10, 12, 13], L32432 = [1, 2, 3, 4, 6, 10, 12, 14], L32433 = [1, 2, 3, 4, 6, 10, 12, 15], L32434 = [1, 2, 3, 4, 6, 10, 13, 14], L32435 = [1, 2, 3, 4, 6, 10, 13, 15], L32437 = [1, 2, 3, 4, 6, 11, 12, 14], L32438 = [1, 2, 3, 4, 6, 11, 12, 15], L32439 = [1, 2, 3, 4, 6, 11, 13, 14], L32441 = [1, 2, 3, 4, 6, 12, 13, 14], L32445 = [1, 2, 3, 4, 7, 8, 9, 12], L32447 = [1, 2, 3, 4, 7, 8, 9, 14], L32448 = [1, 2, 3, 4, 7, 8, 10, 11], L32449 = [1, 2, 3, 4, 7, 8, 10, 12], L32450 = [1, 2, 3, 4, 7, 8, 10, 13], L32452 = [1, 2, 3, 4, 7, 8, 11, 12], L32454 = [1, 2, 3, 4, 7, 8, 11, 14], L32458 = [1, 2, 3, 4, 7, 8, 13, 14], L32459 = [1, 2, 3, 4, 7, 8, 13, 15], L32460 = [1, 2, 3, 4, 7, 9, 10, 12], L32461 = [1, 2, 3, 4, 7, 9, 10, 13], L32463 = [1, 2, 3, 4, 7, 9, 11, 12], L32464 = [1, 2, 3, 4, 7, 9, 11, 14], L32465 = [1, 2, 3, 4, 7, 9, 11, 15], L32468 = [1, 2, 3, 4, 7, 9, 12, 15], L32469 = [1, 2, 3, 4, 7, 9, 13, 14], L32470 = [1, 2, 3, 4, 7, 9, 13, 15], L32471 = [1, 2, 3, 4, 7, 10, 11, 12], L32472 = [1, 2, 3, 4, 7, 10, 11, 13], L32475 = [1, 2, 3, 4, 7, 10, 12, 15], L32477 = [1, 2, 3, 4, 7, 11, 12, 13], L32478 = [1, 2, 3, 4, 7, 11, 12, 14], L32479 = [1, 2, 3, 4, 7, 11, 12, 15], L32480 = [1, 2, 3, 4, 7, 11, 13, 14], L32481 = [1, 2, 3, 4, 7, 11, 13, 15], L32483 = [1, 2, 3, 4, 7, 12, 13, 15], L32485 = [1, 2, 3, 4, 8, 9, 10, 13], L32488 = [1, 2, 3, 4, 8, 9, 11, 12], L32489 = [1, 2, 3, 4, 8, 9, 11, 14], L32490 = [1, 2, 3, 4, 8, 9, 11, 15], L32493 = [1, 2, 3, 4, 8, 9, 13, 14], L32494 = [1, 2, 3, 4, 8, 9, 13, 15], L32496 = [1, 2, 3, 4, 8, 10, 11, 13], L32497 = [1, 2, 3, 4, 8, 10, 11, 14], L32498 = [1, 2, 3, 4, 8, 10, 11, 15], L32501 = [1, 2, 3, 4, 8, 10, 13, 14], L32504 = [1, 2, 3, 4, 8, 11, 12, 14], L32506 = [1, 2, 3, 4, 8, 11, 13, 15], L32508 = [1, 2, 3, 4, 9, 10, 12, 13], L32509 = [1, 2, 3, 4, 9, 10, 12, 14], L32511 = [1, 2, 3, 4, 9, 10, 13, 14], L32512 = [1, 2, 3, 4, 9, 10, 13, 15], L32513 = [1, 2, 3, 4, 9, 11, 12, 14], L32514 = [1, 2, 3, 4, 9, 11, 12, 15], L32516 = [1, 2, 3, 4, 9, 12, 13, 15], L32518 = [1, 2, 3, 4, 10, 11, 12, 14], L32519 = [1, 2, 3, 4, 10, 11, 12, 15], L32523 = [1, 2, 3, 4, 10, 12, 13, 15], L32528 = [1, 2, 3, 5, 6, 7, 8, 11], L32531 = [1, 2, 3, 5, 6, 7, 8, 14], L32532 = [1, 2, 3, 5, 6, 7, 9, 10], L32534 = [1, 2, 3, 5, 6, 7, 9, 13], L32535 = [1, 2, 3, 5, 6, 7, 9, 14], L32536 = [1, 2, 3, 5, 6, 7, 9, 15], L32537 = [1, 2, 3, 5, 6, 7, 10, 11], L32538 = [1, 2, 3, 5, 6, 7, 10, 12], L32539 = [1, 2, 3, 5, 6, 7, 10, 13], L32540 = [1, 2, 3, 5, 6, 7, 10, 15], L32542 = [1, 2, 3, 5, 6, 7, 11, 13], L32543 = [1, 2, 3, 5, 6, 7, 11, 15], L32546 = [1, 2, 3, 5, 6, 7, 13, 15], L32547 = [1, 2, 3, 5, 6, 8, 9, 10], L32548 = [1, 2, 3, 5, 6, 8, 9, 11], L32550 = [1, 2, 3, 5, 6, 8, 9, 14], L32553 = [1, 2, 3, 5, 6, 8, 10, 12], L32555 = [1, 2, 3, 5, 6, 8, 10, 1 L32556 = [1, 2, 3, 5, 6, 8, 11, 12], L32557 = [1, 2, 3, 5, 6, 8, 11, 13], L32558 = [1, 2, 3, 5, 6, 8, 11, 15], L32559 = [1, 2, 3, 5, 6, 8, 12, 13], L32560 = [1, 2, 3, 5, 6, 8, 12, 14], L32561 = [1, 2, 3, 5, 6, 8, 12, 15], L32562 = [1, 2, 3, 5, 6, 8, 13, 14], L32565 = [1, 2, 3, 5, 6, 9, 11, 15], L32567 = [1, 2, 3, 5, 6, 9, 13, 15],
224
EMILIO A. LAURET
Table 6. (continued) m = 8 q 31 (cont.)
I {0}
indexes of I-isospectral families {32458, 32553, 32587}, {32461, 32576}, {32468, 32478}, {32469, 32481, 32565, 32580, 32620}, {32472, 32542}, {32475, 32561, 32624}, {32477, 32602}, {32483, 32506, 32523, 32560}, {32488, 32516, 32555}, {32489, 32535, 32569}, {32490, 32494, 32568}, {32493, 32534}, {32496, 32498}, {32497, 32596, 32611}, {32501, 32655}, {32508, 32556, 32558}, {32509, 32594}, {32512, 32584}, {32513, 32589, 32630}, {32514, 32579, 32612}, {32532, 32559}, {32543, 32582}, {32585, 32625}, {32595, 32622}, {32600, 32689, 32690}, {32601, 32631, 32635, 32659}, {32604, 32650}, {32606, 32656, 32665}, {32607, 32674}, {32613, 32628}, {32619, 32660, 32672}, {32626, 32661}, {32627, 32668}, {32632, 32638, 32639}, {32642, 32687}, {32658, 32678}, {32666, 32670} {0, 1} {11008, 11010}
L32568 = [1, 2, 3, 5, 6, 10, 11, 13], L32569 = [1, 2, 3, 5, 6, 10, 12, 13], L32574 = [1, 2, 3, 5, 6, 11, 13, 15], L32575 = [1, 2, 3, 5, 7, 8, 9, 10], L32576 = [1, 2, 3, 5, 7, 8, 9, 11], L32578 = [1, 2, 3, 5, 7, 8, 9, 13], L32579 = [1, 2, 3, 5, 7, 8, 9, 14], L32580 = [1, 2, 3, 5, 7, 8, 10, 11], L32582 = [1, 2, 3, 5, 7, 8, 11, 14], L32584 = [1, 2, 3, 5, 7, 8, 13, 14], L32585 = [1, 2, 3, 5, 7, 9, 10, 13], L32587 = [1, 2, 3, 5, 7, 9, 11, 14], L32589 = [1, 2, 3, 5, 7, 9, 13, 15], L32594 = [1, 2, 3, 5, 7, 11, 13, 14], L32595 = [1, 2, 3, 5, 7, 11, 13, 15], L32596 = [1, 2, 3, 5, 7, 12, 13, 15], L32600 = [1, 2, 3, 5, 8, 9, 11, 12], L32601 = [1, 2, 3, 5, 8, 9, 11, 15], L32602 = [1, 2, 3, 5, 8, 9, 12, 14], L32604 = [1, 2, 3, 5, 8, 10, 12, 14], L32606 = [1, 2, 3, 5, 8, 11, 12, 15], L32607 = [1, 2, 3, 5, 9, 10, 12, 13], L32611 = [1, 2, 3, 5, 9, 10, 13, 15], L32612 = [1, 2, 3, 5, 9, 11, 12, 14], L32613 = [1, 2, 3, 5, 9, 11, 12, 15], L32619 = [1, 2, 3, 5, 11, 12, 13, 14], L32620 = [1, 2, 3, 5, 11, 12, 13, 15], L32621 = [1, 2, 3, 6, 7, 8, 9, 10], L32622 = [1, 2, 3, 6, 7, 8, 9, 13], L32623 = [1, 2, 3, 6, 7, 8, 9, 14], L32624 = [1, 2, 3, 6, 7, 8, 10, 11 L32625 = [1, 2, 3, 6, 7, 8, 10, 12], L32626 = [1, 2, 3, 6, 7, 8, 10, 13], L32627 = [1, 2, 3, 6, 7, 8, 11, 12], L32628 = [1, 2, 3, 6, 7, 8, 11, 13], L32630 = [1, 2, 3, 6, 7, 8, 13, 14], L32631 = [1, 2, 3, 6, 7, 9, 13, 14], L32632 = [1, 2, 3, 6, 7, 10, 11, 13], L32635 = [1, 2, 3, 6, 7, 10, 13, 15], L32638 = [1, 2, 3, 6, 8, 9, 10, 14], L32639 = [1, 2, 3, 6, 8, 9, 13, 14], L32642 = [1, 2, 3, 6, 8, 10, 13, 14], L32650 = [1, 2, 3, 7, 8, 9, 13, 14], L32655 = [1, 2, 3, 7, 9, 10, 12, 15], L32656 = [1, 2, 3, 7, 9, 10, 13, 15], L32658 = [1, 2, 3, 7, 9, 12, 13, 15], L32659 = [1, 2, 3, 7, 10, 12, 13, 15], L32660 = [1, 2, 3, 7, 11, 12, 13, 14], L32661 = [1, 2, 3, 7, 11, 12, 13, 15], L32665 = [1, 2, 3, 8, 9, 10, 13, 14], L32666 = [1, 2, 3, 8, 9, 10, 13, 15], L32668 = [1, 2, 3, 8, 9, 12, 13, 15], L32670 = [1, 2, 3, 8, 10, 12, 13, 15], L32672 = [1, 2, 3, 9, 10, 12, 13, 14], L32674 = [1, 2, 4, 5, 7, 8, 9, 10], L32678 = [1, 2, 4, 5, 7, 11, 13, 15], L32687 = [1, 2, 5, 6, 8, 9, 10, 12], L32689 = [1, 2, 5, 8, 9, 10, 12, 14], L32690 = [1, 2, 6, 7, 8, 9, 10, 13]. q = 32 : L47 = [0, 0, 0, 0, 0, 1, 3, 7], L49 = [0, 0, 0, 0, 0, 1, 3, 9], L301 = [0, 0, 0, 0, 1, 2, 7, 9], L307 = [0, 0, 0, 0, 1, 2, 7, 15], L357 = [0, 0, 0, 0, 1, 3, 5, 7], L359 = [0, 0, 0, 0, 1, 3, 5, 9], L362 = [0, 0, 0, 0, 1, 3, 5, 13], L366 = [0, 0, 0, 0, 1, 3, 7, 8], L367 = [0, 0, 0, 0, 1, 3, 7, 9], L371 = [0, 0, 0, 0, 1, 3, 7, 16], L373 = [0, 0, 0, 0, 1, 3, 8, 9], L382 = [0, 0, 0, 0, 1, 3, 9, 16], L480 = [0, 0, 0, 0, 1, 6, 7, 9], L483 = [0, 0, 0, 0, 1, 6, 7, 15], L1151 = [0, 0, 0, 1, 1, 7, 7, 9], L1154 = [0, 0, 0, 1, 1, 7, 7, 15], L1396 = [0, 0, 0, 1, 2, 2, 7, 9], L1402 = [0, 0, 0, 1, 2, 2, 7, 15], L1459 = [0, 0, 0, 1, 2, 3, 5, 10], L1468 = [0, 0, 0, 1, 2, 3, 6, 9], L1503 = [0, 0, 0, 1, 2, 3, 10, 13], L1505 = [0, 0, 0, 1, 2, 3, 10, 15], L1561 = [0, 0, 0, 1, 2, 4, 7, 9], L1567 = [0, 0, 0, 1, 2, 4, 7, 15], L1610 = [0, 0, 0, 1, 2, 5, 6, 11], L1614 = [0, 0, 0, 1, 2, 5, 6, 15], L1652 = [0, 0, 0, 1, 2, 5, 13, 14], L1670 = [0, 0, 0, 1, 2, 6, 7, 9], L1672 = [0, 0, 0, 1, 2, 6, 7, 11], L1675 = [0, 0, 0, 1, 2, 6, 7, 15], L1686 = [0, 0, 0, 1, 2, 6, 9, 11], L1708 = [0, 0, 0, 1, 2, 7, 8, 9], L1714 = [0, 0, 0, 1, 2, 7, 8, 15], L1716 = [0, 0, 0, 1, 2, 7, 9, 10], L1718 = [0, 0, 0, 1, 2, 7, 9, 12], L1722 = [0, 0, 0, 1, 2, 7, 9, 16], L1726 = [0, 0, 0, 1, 2, 7, 10, 15], L1734 = [0, 0, 0, 1, 2, 7, 12, 15], L1739 = [0, 0, 0, 1, 2, 7, 15, 16 L1811 = [0, 0, 0, 1, 2, 11, 13, 14], L1855 = [0, 0, 0, 1, 3, 4, 5, 13], L1860 = [0, 0, 0, 1, 3, 4, 7, 9], L1862 =
APPENDIX
225
Table 6. (continued) m = 8 q I indexes of I-isospectral families 32 {0} {47, 49}, {301, 307}, {357, 359}, {366, 373}, {371, 382}, {480, 483}, {1151, 1154}, {1396, 1402}, {1459, 1468}, {1503, 1614}, {1505, 1610}, {1561, 1567}, {1652, 1811}, {1670, 1675}, {1672, 1686}, {1708, 1714}, {1716, 1726}, {1718, 1734}, {1722, 1739}, {1862, 1877}, {1904, 1911}, {1905, 1906, 1908, 1918}, {1909, 1919}, {1922, 1929}, {1936, 1954}, {1941, 1963}, {1952, 1987}, {2119, 2122}, {2253, 2256}, {2283, 2286}, {2289, 2295}, {2291, 2297}, {4694, 4697}, {5417, 5420}, {5423, 5429}, {5426, 5433}, {5970, 5976}, {6137, 6143}, {6254, 6260}, {6301, 6307}, {6309, 6321}, {6311, 6330}, {6313, 6335}, {6315, 6337},
[0, 0, 0, 1, 3, 4, 7, 12], L1877 = [0, 0, 0, 1, 3, 4, 9, 12], L1887 = [0, 0, 0, 1, 3, 4, 11, 13], L1904 = [0, 0, 0, 1, 3, 5, 7, 8], L1905 = [0, 0, 0, 1, 3, 5, 7, 9], L1906 = [0, 0, 0, 1, 3, 5, 7, 11], L1908 = [0, 0, 0, 1, 3, 5, 7, 13], L1909 = [0, 0, 0, 1, 3, 5, 7, 16], L1911 = [0, 0, 0, 1, 3, 5, 8, 9], L1914 = [0, 0, 0, 1, 3, 5, 8, 13], L1918 = [0, 0, 0, 1, 3, 5, 9, 11], L1919 = [0, 0, 0, 1, 3, 5, 9, 16], L1922 = [0, 0, 0, 1, 3, 5, 11, 15], L1925 = [0, 0, 0, 1, 3, 5, 12, 13], L1929 = [0, 0, 0, 1, 3, 5, 13, 15], L1930 = [0, 0, 0, 1, 3, 5, 13, 16], L1936 = [0, 0, 0, 1, 3, 7, 8, 8], L1937 = [0, 0, 0, 1, 3, 7, 8, 9], L1941 = [0, 0, 0, 1, 3, 7, 8, 16], L1943 = [0, 0, 0, 1, 3, 7, 9, 16], L1952 = [0, 0, 0, 1, 3, 7, 16, 16], L1954 = [0, 0, 0, 1, 3, 8, 8, 9], L1963 = [0, 0, 0, 1, 3, 8, 9, 16], L1987 = [0, 0, 0, 1, 3, 9, 16, 16], L2119 = [0, 0, 0, 1, 4, 6, 7, 9], L2122 = [0, 0, 0, 1, 4, 6, 7, 15], L2253 = [0, 0, 0, 1, 6, 6, 7, 9], L2256 = [0, 0, 0, 1, 6, 6, 7, 15], L2283 = [0, 0, 0, 1, 6, 7, 8, 9], L2286 = [0, 0, 0, 1, 6, 7, 8, 15], L2289 = [0, 0, 0, 1, 6, 7, 9, 12], L2291 = [0, 0, 0, 1, 6, 7, 9, 16], L2295 = [0, 0, 0, 1, 6, 7, 12, 15], L2297 = [0, 0, 0, 1, 6, 7, 15, 16], L4694 = [0, 0, 1, 1, 4, 7, 7, 9], L4697 = [0, 0, 1, 1, 4, 7, 7, 15], L5417 = [0, 0, 1, 1, 7, 7, 8, 9], L5420 = [0, 0, 1, 1, 7, 7, 8, 15], L5423 = [0, 0, 1, 1, 7, 7, 9, 12], L5426 = [0, 0, 1, 1, 7, 7, 9, 16], L5429 = [0, 0, 1, 1, 7, 7, 12, 15], L5433 = [0, 0, 1, 1, 7, 7, 15, 16], L5970 = [0, 0, 1, 2, 2, 2, 7, 9], L5976 = [0, 0, 1, 2, 2, 2, 7, 15], L6137 = [0, 0, 1, 2, 2, 4, 7, 9], L6143 = [0, 0, 1, 2, 2, 4, 7, 15], L6254 = [0, 0, 1, 2, 2, 6, 7, 9], L6260 = [0, 0, 1, 2, 2, 6, 7, 15], L6301 = [0, 0, 1, 2, 2, 7, 8, 9], L6307 = [0, 0, 1, 2, 2, 7, 8, 15], L6309 = [0, 0, 1, 2, 2, 7, 9, 10], L6311 = [0, 0, 1, 2, 2, 7, 9, 12], L6313 = [0, 0, 1, 2, 2, 7, 9, 14], L6315 = [0, 0, 1, 2, 2, 7, 9, 16], L6321 = [0, 0, 1, 2, 2, 7, 10, 15], L6330 = [0, 0, 1, 2, 2, 7, 12, 15], L6335 = [0, 0, 1, 2, 2, 7, 14, 15], L6337 = [0, 0, 1, 2, 2, 7, 15, 16], L6553 = [0, 0, 1, 2, 3, 5, 8, 10], L6560 = [0, 0, 1, 2, 3, 5, 9, 10], L6572 = [0, 0, 1, 2, 3, 5, 10, 16], L6593 = [0, 0, 1, 2, 3, 6, 7, 10], L6596 = [0, 0, 1, 2, 3, 6, 7, 14], L6600 = [0, 0, 1, 2, 3, 6, 8, 9], L6608 = [0, 0, 1, 2, 3, 6, 9, 10], L6609 = [0, 0, 1, 2, 3, 6, 9, 11], L6611 = [0, 0, 1, 2, 3, 6, 9, 14], L6612 = [0, 0, 1, 2, 3, 6, 9, 16], L6620 = [0, 0, 1, 2, 3, 6, 11, 13], L6621 = [0, 0, 1, 2, 3, 6, 11, 14], L6646 = [0, 0, 1, 2, 3, 7, 9, 10], L6656 = [0, 0, 1, 2, 3, 7, 10, 14], L6657 = [0, 0, 1, 2, 3, 7, 10, 15], L6693 = [0, 0, 1, 2, 3, 8, 10, 13 L6695 = [0, 0, 1, 2, 3, 8, 10, 15], L6718 = [0, 0, 1, 2, 3, 9, 10, 14], L6729 = [0, 0, 1, 2, 3, 9, 12, 15], L6749 = [0, 0, 1, 2, 3, 10, 13, 15], L6750 = [0, 0, 1, 2, 3, 10, 13, 16], L6754 = [0, 0, 1, 2, 3, 10, 15, 16], L6829 = [0, 0, 1, 2, 4, 4, 7, 9], L6835 = [0, 0, 1, 2, 4, 4, 7, 15], L6940 = [0, 0, 1, 2, 4, 6, 7, 9], L6945 = [0, 0, 1, 2, 4, 6, 7, 15], L6984 = [0, 0, 1, 2, 4, 7, 8, 9], L6990 = [0, 0, 1, 2, 4, 7, 8, 15], L6992 = [0, 0, 1, 2, 4, 7, 9, 10], L6993 = [0, 0, 1, 2, 4, 7, 9, 11], L6994 = [0, 0, 1, 2, 4, 7, 9, 12], L6998 = [0, 0, 1, 2, 4, 7, 9, 16], L7002 = [0, 0, 1, 2, 4, 7, 10, 15], L7010 = [0, 0, 1, 2, 4, 7, 12, 15], L7015 = [0, 0, 1, 2, 4, 7, 15, 16], L7135 = [0, 0, 1, 2, 5, 6, 8, 11], L7139 = [0, 0, 1, 2, 5, 6, 8, 15], L7141 = [0, 0, 1, 2, 5, 6, 9, 10], L7151 = [0, 0, 1, 2, 5, 6, 11, 13], L7153 = [0, 0, 1, 2, 5, 6, 11, 15], L7154 = [0, 0, 1, 2, 5, 6, 11, 16], L7163 = [0, 0, 1, 2, 5, 6, 15, 16], L7221 = [0, 0, 1, 2, 5, 8, 13, 14], L7270 = [0, 0, 1, 2, 5, 13, 14, 16], L7290 = [0, 0, 1, 2, 6, 6, 7, 9], L7295 = [0, 0, 1, 2, 6, 6, 7, 15], L7328 = [0, 0, 1, 2, 6, 7, 8, 9], L7330 = [0, 0, 1, 2, 6, 7, 8, 11], L7333 = [0, 0, 1, 2, 6, 7, 8, 15], L7335 = [0, 0, 1, 2, 6, 7, 9, 10], L7337 = [0, 0, 1, 2, 6, 7, 9, 12], L7338 = [0, 0, 1, 2, 6, 7, 9, 14], L7340 = [0, 0, 1, 2, 6, 7, 9, 16], L7344 = [0, 0, 1, 2, 6, 7, 10, 15], L7347 = [0, 0, 1, 2, 6, 7, 11, 16], L7350 = [0, 0, 1, 2, 6, 7, 12, 15], L7352 = [0, 0, 1, 2, 6, 7, 14, 15], L7354 = [0, 0, 1, 2, 6, 7, 15, 16], L7365 = [0, 0, 1, 2, 6, 8, 9, 11], L7391 = [0, 0, 1, 2, 6, 9, 11, 16], L7434 = [0, 0, 1, 2, 7, 8, 8, 9], L7440 = [0, 0, 1, 2, 7, 8, 8, 15], L7442 = [0, 0, 1, 2, 7, 8, 9, 10], L7444 = [0, 0, 1, 2, 7, 8, 9, 12], L7448 =
226
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 32 {0} {6553, 6600}, {6560, 6609}, {6572, 6612}, {6593, 6611}, {6596, 6608}, (cont.) {6620, 6646}, {6621, 6656}, {6657, 7151}, {6693, 7139}, {6695, 7135}, {6718, 7141}, {6729, 6993}, {6749, 7153}, {6750, 7163}, {6754, 7154}, {6829, 6835}, {6940, 6945}, {6984, 6990}, {6992, 7002}, {6994, 7010}, {6998, 7015}, {7221, 7587}, {7270, 7685}, {7290, 7295}, {7328, 7333}, {7330, 7365}, {7335, 7344}, {7337, 7350}, {7338, 7352}, {7340, 7354}, {7347, 7391}, {7434, 7440}, {7442, 7452}, {7444, 7460}, {7448, 7465}, {7467, 7488}, {7468, 7492}, {7471, 7495}, {7475, 7505}, {7479, 7510}, {7484, 7515}, {7794, 7795}, {7796, 7809}, {7797, 7798, 7808, 7810}, {7813, 7840}, {7815, 7823, 7839, 7850}, {7833, 7865}, {7849, 7901}, {7897, 7898}, {7956, 7972}, {7957, 7958, 7960, 7979}, {7961, 7980}, {7965, 7966, 7969, 7997}, {7970, 7998}, {7983, 7990}, {8005, 8019},
[0, 0, 1, 2, 7, 8, 9, 16], L7452 = [0, 0, 1, 2, 7, 8, 10, 15], L7460 = [0, 0, 1, 2, 7, 8, 12, 15], L7465 = [0, 0, 1, 2, 7, 8, 15, 16 L7467 = [0, 0, 1, 2, 7, 9, 10, 10], L7468 = [0, 0, 1, 2, 7, 9, 10, 12], L7471 = [0, 0, 1, 2, 7, 9, 10, 16], L7475 = [0, 0, 1, 2, 7, 9, 12, 12], L7479 = [0, 0, 1, 2, 7, 9, 12, 16], L7484 = [0, 0, 1, 2, 7, 9, 16, 16], L7488 = [0, 0, 1, 2, 7, 10, 10, L7492 = [0, 0, 1, 2, 7, 10, 12, 15], L7495 = [0, 0, 1, 2, 7, 10, 15, 16], L7505 = [0, 0, 1, 2, 7, 12, 12, 15], L7510 = [0, 0, 1, 2, 7, 12, 15, 16], L7515 = [0, 0, 1, 2, 7, 15, 16, 16], L7587 = [0, 0, 1, 2, 8, 11, 13, 14], L7685 = [0, 0, 1, 2, 11, 13, 14, 16], L7743 = [0, 0, 1, 3, 4, 4, 5, 13], L7748 = [0, 0, 1, 3, 4, 4, 7, 9], L7776 = [0, 0, 1, 3, 4, 4, 11, 13], L7794 = [0, 0, 1, 3, 4, 5, 7, 9], L7795 = [0, 0, 1, 3, 4, 5, 7, 11], L7796 = [0, 0, 1, 3, 4, 5, 7, 12], L7797 = [0, 0, 1, 3, 4, 5, 7, 13], L7798 = [0, 0, 1, 3, 4, 5, 7, 15], L7804 = [0, 0, 1, 3, 4, 5, 8, 13], L7808 = [0, 0, 1, 3, 4, 5, 9, 11], L7809 = [0, 0, 1, 3, 4, 5, 9, 12], L7810 = [0, 0, 1, 3, 4, 5, 9, 15], L7813 = [0, 0, 1, 3, 4, 5, 11, 13], L7815 = [0, 0, 1, 3, 4, 5, 11, 15], L7818 = [0, 0, 1, 3, 4, 5, 12, 13], L7823 = [0, 0, 1, 3, 4, 5, 13, 15], L7824 = [0, 0, 1, 3, 4, 5, 13, 16], L7831 = [0, 0, 1, 3, 4, 7, 8, 9], L7833 = [0, 0, 1, 3, 4, 7, 8, 12], L7838 = [0, 0, 1, 3, 4, 7, 9, 12], L7839 = [0, 0, 1, 3, 4, 7, 9, 13], L7840 = [0, 0, 1, 3, 4, 7, 9, 15], L7841 = [0, 0, 1, 3, 4, 7, 9, 16], L7849 = [0, 0, 1, 3, 4, 7, 12, 16], L7850 = [0, 0, 1, 3, 4, 7, 13, 15], L7865 = [0, 0, 1, 3, 4, 8, 9, 12], L7875 = [0, 0, 1, 3, 4, 8, 11, 13 L7897 = [0, 0, 1, 3, 4, 9, 11, 13], L7898 = [0, 0, 1, 3, 4, 9, 11, 15], L7901 = [0, 0, 1, 3, 4, 9, 12, 16], L7925 = [0, 0, 1, 3, 4, 11, 13, 16], L7956 = [0, 0, 1, 3, 5, 7, 8, 8], L7957 = [0, 0, 1, 3, 5, 7, 8, 9], L7958 = [0, 0, 1, 3, 5, 7, 8, 11], L7960 = [0, 0, 1, 3, 5, 7, 8, 13], L7961 = [0, 0, 1, 3, 5, 7, 8, 16], L7962 = [0, 0, 1, 3, 5, 7, 9, 11], L7963 = [0, 0, 1, 3, 5, 7, 9, 13], L7965 = [0, 0, 1, 3, 5, 7, 9, 16], L7966 = [0, 0, 1, 3, 5, 7, 11, 16], L7969 = [0, 0, 1, 3, 5, 7, 13, 16], L7970 = [0, 0, 1, 3, 5, 7, 16, 16], L7972 = [0, 0, 1, 3, 5, 8, 8, 9], L7975 = [0, 0, 1, 3, 5, 8, 8, 13], L7979 = [0, 0, 1, 3, 5, 8, 9, 11], L7980 = [0, 0, 1, 3, 5, 8, 9, 16], L7983 = [0, 0, 1, 3, 5, 8, 11, 15], L7986 = [0, 0, 1, 3, 5, 8, 12, 13], L7990 = [0, 0, 1, 3, 5, 8, 13, 15], L7991 = [0, 0, 1, 3, 5, 8, 13, 16], L7997 = [0, 0, 1, 3, 5, 9, 11, 16], L7998 = [0, 0, 1, 3, 5, 9, 16, 16], L8005 = [0, 0, 1, 3, 5, 11, 15, 16], L8008 = [0, 0, 1, 3, 5, 12, 12, 13], L8012 = [0, 0, 1, 3, 5, 12, 13, 16], L8019 = [0, 0, 1, 3, 5, 13, 15, 16], L8020 = [0, 0, 1, 3, 5, 13, 16, 16], L8028 = [0, 0, 1, 3, 7, 8, 8, 8], L8029 = [0, 0, 1, 3, 7, 8, 8, 9], L8033 = [0, 0, 1, 3, 7, 8, 8, 16], L8035 = [0, 0, 1, 3, 7, 8, 9, 16], L8044 = [0, 0, 1, 3, 7, 8, 16, 16], L8047 = [0, 0, 1, 3, 7, 9, 16, 16], L8063 = [0, 0, 1, 3, 7, 16, 16, 16], L8065 = [0, 0, 1, 3, 8, 8, 8, 9], L8074 = [0, 0, 1, 3, 8, 8, 9, 16], L8098 = [0, 0, 1, 3, 8, 9, 16, 16], L8149 = [0, 0, 1, 3, 9, 16, 16, 16], L8324 = [0, 0, 1, 4, 4, 6, 7, 9], L8327 = [0, 0, 1, 4, 4, 6, 7, 15], L8481 = [0, 0, 1, 4, 6, 6, 7, 9], L8484 = [0, 0, 1, 4, 6, 6, 7, 15], L8511 = [0, 0, 1, 4, 6, 7, 8, 9], L8514 = [0, 0, 1, 4, 6, 7, 8, 15], L8517 = [0, 0, 1, 4, 6, 7, 9, 12], L8519 = [0, 0, 1, 4, 6, 7, 9, 16], L8523 = [0, 0, 1, 4, 6, 7, 12, 15], L8525 = [0, 0, 1, 4, 6, 7, 15, 16], L8782 = [0, 0, 1, 6, 6, 6, 7, 9], L8785 = [0, 0, 1, 6, 6, 6, 7, 15], L8812 = [0, 0, 1, 6, 6, 7, 8, 9], L8815 = [0, 0, 1, 6, 6, 7, 8, 15], L8817 = [0, 0, 1, 6, 6, 7, 9, 10], L8818 = [0, 0, 1, 6, 6, 7, 9, 12], L8820 = [0, 0, 1, 6, 6, 7, 9, 16], L8823 = [0, 0, 1, 6, 6, 7, 10, 15], L8826 = [0, 0, 1, 6, 6, 7, 12, 15], L8828 = [0, 0, 1, 6, 6, 7, 15, 16], L8890 = [0, 0, 1, 6, 7, 8, 8, 9], L8893 = [0, 0, 1, 6, 7, 8, 8, 15], L8896 = [0, 0, 1, 6, 7, 8, 9, 12], L8898 = [0, 0, 1, 6, 7, 8, 9, 16],
APPENDIX
227
Table 6. (continued) m = 8 q I indexes of I-isospectral families 32 {0} {8028, 8065}, {8033, 8074}, {8044, 8098}, {8063, 8149}, {8324, 8327}, (cont.) {8481, 8484}, {8511, 8514}, {8517, 8523}, {8519, 8525}, {8782, 8785}, {8812, 8815}, {8817, 8823}, {8818, 8826}, {8820, 8828}, {8890, 8893}, {8896, 8902}, {8898, 8904}, {8909, 8918}, {8911, 8920}, {8913, 8922}, {15363, 15386}, {18131, 18134}, {18871, 18874}, {18877, 18883}, {18880, 18887}, {20496, 20503}, {21004, 21007}, {21010, 21016}, {21013, 21020}, {21025, 21035}, {21028, 21039}, {21032, 21043}, {22166, 22172}, {22333, 22339}, {22451, 22457}, {22498, 22504}, {22506, 22518}, {22508, 22527}, {22510, 22532}, {22512, 22534}, {23056, 23062}, {23174, 23180}, {23221, 23227}, {23229, 23241}, {23231, 23250}, {23233, 23255}, {23235, 23257}, {23594, 23599}, {23633, 23639}, {23641, 23653}, {23643, 23662}, {23645, 23667}, {23647, 23669}, {23754, 24707}, {23782, 23788}, {23790, 23802}, {23792, 23811}, {23794, 23816}, {23796, 23818}, {23820, 23847},
L8902 = [0, 0, 1, 6, 7, 8, 12, 15], L8904 = [0, 0, 1, 6, 7, 8, 15, 16], L8909 = [0, 0, 1, 6, 7, 9, 12, 12], L8911 = [0, 0, 1, 6, 7, 9, 12, 16], L8913 = [0, 0, 1, 6, 7, 9, 16, 16], L8918 = [0, 0, 1, 6, 7, 12, 12, 15], L8920 = [0, 0, 1, 6, 7, 12, 15, 16], L8922 = [0, 0, 1, 6, 7, 15, 16, 16], L15363 = [0, 1, 1, 2, 7, 7, 9, 14], L15386 = [0, 1, 1, 2, 7, 7, 14, 15], L18131 = [0, 1, 1, 4, 4, 7, 7, 9], L18134 = [0, 1, 1, 4, 4, 7, 7, 15], L18871 = [0, 1, 1, 4, 7, 7, 8, 9], L18874 = [0, 1, 1, 4, 7, 7, 8, 15], L18877 = [0, 1, 1, 4, 7, 7, 9, 12], L18880 = [0, 1, 1, 4, 7, 7, 9, 16], L18883 = [0, 1, 1, 4, 7, 7, 12, 15], L18887 = [0, 1, 1, 4, 7, 7, 15, 16], L20496 = [0, 1, 1, 6, 7, 7, 9, 10], L20503 = [0, 1, 1, 6, 7, 7, 10, 15], L21004 = [0, 1, 1, 7, 7, 8, 8, 9], L21007 = [0, 1, 1, 7, 7, 8, 8, 15], L21010 = [0, 1, 1, 7, 7, 8, 9, 12], L21013 = [0, 1, 1, 7, 7, 8, 9, 16], L21016 = [0, 1, 1, 7, 7, 8, 12, 15], L21020 = [0, 1, 1, 7, 7, 8, 15, 16], L21025 = [0, 1, 1, 7, 7, 9, 12, 12], L21028 = [0, 1, 1, 7, 7, 9, 12, 16], L21032 = [0, 1, 1, 7, 7, 9, 16, 16], L21035 = [0, 1, 1, 7, 7, 12, 12, 15], L21039 = [0, 1, 1, 7, 7, 12, 15, 16], L21043 = [0, 1, 1, 7, 7, 15, 16, 16], L22166 = [0, 1, 2, 2, 2, 2, 7, 9], L22172 = [0, 1, 2, 2, 2, 2, 7, 15], L22333 = [0, 1, 2, 2, 2, 4, 7, 9], L22339 = [0, 1, 2, 2, 2, 4, 7, 15], L22451 = [0, 1, 2, 2, 2, 6, 7, 9], L22457 = [0, 1, 2, 2, 2, 6, 7, 15], L22498 = [0, 1, 2, 2, 2, 7, 8, 9], L22504 = [0, 1, 2, 2, 2, 7, 8, 15], L22506 = [0, 1, 2, 2, 2, 7, 9, 10], L22508 = [0, 1, 2, 2, 2, 7, 9, 12], L22510 = [0, 1, 2, 2, 2, 7, 9, 14], L22512 = [0, 1, 2, 2, 2, 7, 9, 16], L22518 = [0, 1, 2, 2, 2, 7, 10, 15], L22527 = [0, 1, 2, 2, 2, 7, 12, 1 L22532 = [0, 1, 2, 2, 2, 7, 14, 15], L22534 = [0, 1, 2, 2, 2, 7, 15, 16], L23056 = [0, 1, 2, 2, 4, 4, 7, 9], L23062 = [0, 1, 2, 2, 4, 4, 7, 15], L23174 = [0, 1, 2, 2, 4, 6, 7, 9], L23180 = [0, 1, 2, 2, 4, 6, 7, 15], L23221 = [0, 1, 2, 2, 4, 7, 8, 9], L23227 = [0, 1, 2, 2, 4, 7, 8, 15], L23229 = [0, 1, 2, 2, 4, 7, 9, 10], L23231 = [0, 1, 2, 2, 4, 7, 9, 12], L23233 = [0, 1, 2, 2, 4, 7, 9, 14], L23235 = [0, 1, 2, 2, 4, 7, 9, 16], L23241 = [0, 1, 2, 2, 4, 7, 10, 15], L23250 = [0, 1, 2, 2, 4, 7, 12, 1 L23255 = [0, 1, 2, 2, 4, 7, 14, 15], L23257 = [0, 1, 2, 2, 4, 7, 15, 16], L23594 = [0, 1, 2, 2, 6, 6, 7, 9], L23599 = [0, 1, 2, 2, 6, 6, 7, 15], L23633 = [0, 1, 2, 2, 6, 7, 8, 9], L23639 = [0, 1, 2, 2, 6, 7, 8, 15], L23641 = [0, 1, 2, 2, 6, 7, 9, 10], L23643 = [0, 1, 2, 2, 6, 7, 9, 12], L23645 = [0, 1, 2, 2, 6, 7, 9, 14], L23647 = [0, 1, 2, 2, 6, 7, 9, 16], L23653 = [0, 1, 2, 2, 6, 7, 10, 15], L23662 = [0, 1, 2, 2, 6, 7, 12, 15], L23667 = [0, 1, 2, 2, 6, 7, 14, 15], L23669 = [0, 1, 2, 2, 6, 7, 15, 16], L23754 = [0, 1, 2, 2, 6, 11, 13, 14], L23782 = [0, 1, 2, 2, 7, 8, 8, 9], L23788 = [0, 1, 2, 2, 7, 8, 8, 15], L23790 = [0, 1, 2, 2, 7, 8, 9, 10], L23792 = [0, 1, 2, 2, 7, 8, 9, 12], L23794 = [0, 1, 2, 2, 7, 8, 9, 14], L23796 = [0, 1, 2, 2, 7, 8, 9, 16], L23802 = [0, 1, 2, 2, 7, 8, 10, 15], L23811 = [0, 1, 2, 2, 7, 8, 12, 15], L23816 = [0, 1, 2, 2, 7, 8, 14, 15], L23818 = [0, 1, 2, 2, 7, 8, 15, 16], L23820 = [0, 1, 2, 2, 7, 9, 10, 10], L23822 = [0, 1, 2, 2, 7, 9, 10, 12], L23824 = [0, 1, 2, 2, 7, 9, 10, 14], L23826 = [0, 1, 2, 2, 7, 9, 10, 16], L23831 = [0, 1, 2, 2, 7, 9, 12, 12], L23833 = [0, 1, 2, 2, 7, 9, 12, 14], L23835 = [0, 1, 2, 2, 7, 9, 12, 16], L23840 = [0, 1, 2, 2, 7, 9, 14, 16], L23842 = [0, 1, 2, 2, 7, 9, 16, 16], L23847 = [0, 1, 2, 2, 7, 10, 10, 15], L23856 = [0, 1, 2, 2, 7, 10, 12, 15], L23860 = [0, 1, 2, 2, 7, 10, 14, 15], L23862 = [0, 1, 2, 2, 7, 10, 15, 16],
228
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 32 {0} {23822, 23856}, {23824, 23860}, {23826, 23862}, {23831, 23875}, {23833, 23880}, (cont.) {23835, 23882}, {23840, 23888}, {23842, 23890}, {24258, 24301}, {24260, 24307}, {24348, 24498}, {24415, 24531}, {24419, 24569}, {24441, 25540, 25552}, {24445, 25570}, {24447, 25562}, {24500, 24512, 24515}, {24501, 24513, 24516}, {24525, 24641}, {24527, 24535, 24643, 24650}, {24534, 24703}, {24551, 24558}, {24560, 24623, 24704}, {24561, 24622, 24708}, {24573, 24627}, {24576, 24637}, {24582, 24725}, {24589, 24734}, {24601, 24737}, {24620, 25555}, {24621, 24766}, {24624, 24767}, {24646, 24792}, {24649, 24796}, {24656, 24771}, {24697, 24736}, {24700, 24733}, {24709, 24793, 25559}, {24712, 24770}, {24721, 24765}, {24745, 24837}, {24746, 24847}, {24797, 24871}, {24800, 24903}, {24848, 26258}, {24867, 26233}, {24868, 24900, 26222, 26229}, {24870, 26224}, {24904, 26291}, {24951, 26246}, {24953, 26242}, {24976, 26248}, {24987, 25884}, {25007, 26260}, {25008, 26270}, {25012, 26261}, {25065, 26273},
L23875 = [0, 1, 2, 2, 7, 12, 12, 15], L23880 = [0, 1, 2, 2, 7, 12, 14, 15], L23882 = [0, 1, 2, 2, 7, 12, 15, 16], L23888 = [0, 1, 2, 2, 7, 14, 15, 16], L23890 = [0, 1, 2, 2, 7, 15, 16, 16], L24258 = [0, 1, 2, 3, 4, 5, 10, 12], L24260 = [0, 1, 2, 3, 4, 5, 10, 14], L24301 = [0, 1, 2, 3, 4, 6, 9, 12], L24307 = [0, 1, 2, 3, 4, 6, 10, 11], L24348 = [0, 1, 2, 3, 4, 7, 10, 11], L24415 = [0, 1, 2, 3, 4, 9, 10, 14], L24419 = [0, 1, 2, 3, 4, 9, 11, 13], L24441 = [0, 1, 2, 3, 4, 10, 11, 14], L24445 = [0, 1, 2, 3, 4, 10, 12, 13], L24447 = [0, 1, 2, 3, 4, 10, 12, 15], L24498 = [0, 1, 2, 3, 5, 6, 7, 12], L24500 = [0, 1, 2, 3, 5, 6, 7, 14], L24501 = [0, 1, 2, 3, 5, 6, 7, 15], L24512 = [0, 1, 2, 3, 5, 6, 9, 10], L24513 = [0, 1, 2, 3, 5, 6, 9, 11], L24515 = [0, 1, 2, 3, 5, 6, 9, 14], L24516 = [0, 1, 2, 3, 5, 6, 9, 15], L24525 = [0, 1, 2, 3, 5, 6, 11, 13], L24527 = [0, 1, 2, 3, 5, 6, 11, 15], L24531 = [0, 1, 2, 3, 5, 6, 12, 14], L24534 = [0, 1, 2, 3, 5, 6, 13, 14], L24535 = [0, 1, 2, 3, 5, 6, 13, 15], L24538 = [0, 1, 2, 3, 5, 6, 14, 15], L24551 = [0, 1, 2, 3, 5, 7, 9, 10], L24558 = [0, 1, 2, 3, 5, 7, 10, 11], L24560 = [0, 1, 2, 3, 5, 7, 10, 13], L24561 = [0, 1, 2, 3, 5, 7, 10, 14], L24569 = [0, 1, 2, 3, 5, 7, 12, 13], L24573 = [0, 1, 2, 3, 5, 7, 13, 14], L24576 = [0, 1, 2, 3, 5, 7, 14, 15], L24582 = [0, 1, 2, 3, 5, 8, 8, 10], L24589 = [0, 1, 2, 3, 5, 8, 9, 10], L24601 = [0, 1, 2, 3, 5, 8, 10, 16], L24620 = [0, 1, 2, 3, 5, 9, 10, 12], L24621 = [0, 1, 2, 3, 5, 9, 10, 13], L24622 = [0, 1, 2, 3, 5, 9, 10, 14], L24623 = [0, 1, 2, 3, 5, 9, 10, 15], L24624 = [0, 1, 2, 3, 5, 9, 10, 16], L24627 = [0, 1, 2, 3, 5, 9, 11, 14], L24637 = [0, 1, 2, 3, 5, 9, 14, 15], L24641 = [0, 1, 2, 3, 5, 10, 11, 13], L24643 = [0, 1, 2, 3, 5, 10, 11, 15], L24646 = [0, 1, 2, 3, 5, 10, 12, 13], L24649 = [0, 1, 2, 3, 5, 10, 13, 14], L24650 = [0, 1, 2, 3, 5, 10, 13, 15], L24653 = [0, 1, 2, 3, 5, 10, 14, 15], L24656 = [0, 1, 2, 3, 5, 10, 16, 16], L24697 = [0, 1, 2, 3, 6, 7, 8, 10], L24700 = [0, 1, 2, 3, 6, 7, 8, 14], L24703 = [0, 1, 2, 3, 6, 7, 9, 10], L24704 = [0, 1, 2, 3, 6, 7, 9, 11], L24707 = [0, 1, 2, 3, 6, 7, 10, 10], L24708 = [0, 1, 2, 3, 6, 7, 10, 11], L24709 = [0, 1, 2, 3, 6, 7, 10, 12], L24710 = [0, 1, 2, 3, 6, 7, 10, 14], L24712 = [0, 1, 2, 3, 6, 7, 10, 16], L24721 = [0, 1, 2, 3, 6, 7, 14, 16], L24725 = [0, 1, 2, 3, 6, 8, 8, 9], L24733 = [0, 1, 2, 3, 6, 8, 9, 10], L24734 = [0, 1, 2, 3, 6, 8, 9, 11], L24736 = [0, 1, 2, 3, 6, 8, 9, 14], L24737 = [0, 1, 2, 3, 6, 8, 9, 16], L24745 = [0, 1, 2, 3, 6, 8, 11, 13], L24746 = [0, 1, 2, 3, 6, 8, 11, 1 L24763 = [0, 1, 2, 3, 6, 9, 10, 13], L24764 = [0, 1, 2, 3, 6, 9, 10, 14], L24765 = [0, 1, 2, 3, 6, 9, 10, 16], L24766 = [0, 1, 2, 3, 6, 9, 11, 13], L24767 = [0, 1, 2, 3, 6, 9, 11, 16], L24770 = [0, 1, 2, 3, 6, 9, 14, 16], L24771 = [0, 1, 2, 3, 6, 9, 16, 16], L24792 = [0, 1, 2, 3, 6, 11, 12, 13], L24793 = [0, 1, 2, 3, 6, 11, 12, 14], L24796 = [0, 1, 2, 3, 6, 11, 13, 14], L24797 = [0, 1, 2, 3, 6, 11, 13, 16], L24799 = [0, 1, 2, 3, 6, 11, 14, 15], L24800 = [0, 1, 2, 3, 6, 11, 14, 16], L24837 = [0, 1, 2, 3, 7, 8, 9, 10], L24847 = [0, 1, 2, 3, 7, 8, 10, 14], L24848 = [0, 1, 2, 3, 7, 8, 10, 15], L24867 = [0, 1, 2, 3, 7, 9, 10, 12], L24868 = [0, 1, 2, 3, 7, 9, 10, 13], L24870 = [0, 1, 2, 3, 7, 9, 10, 15], L24871 = [0, 1, 2, 3, 7, 9, 10, 16], L24900 = [0, 1, 2, 3, 7, 10, 13, 15], L24903 = [0, 1, 2, 3, 7, 10, 14, 16], L24904 = [0, 1, 2, 3, 7, 10, 15, 16], L24951 = [0, 1, 2, 3, 8, 8, 10, 13], L24953 = [0, 1, 2, 3, 8, 8, 10, 15], L24976 = [0, 1, 2, 3, 8, 9, 10, 14], L24987 = [0, 1, 2, 3, 8, 9, 12, 15],
APPENDIX
229
Table 6. (continued) m = 8 q I indexes of I-isospectral families 32 {0} {25088, 25915}, {25131, 26295}, {25132, 26312}, {25138, 26296}, {25239, 25245}, (cont.) {25350, 25355}, {25395, 25401}, {25403, 25413}, {25405, 25421}, {25409, 25426}, {25652, 26354}, {25686, 26120}, {25714, 25719}, {25752, 25757}, {25759, 25768}, {25761, 25774}, {25762, 25776}, {25764, 25778}, {25770, 25820}, {25875, 25881}, {25883, 25893}, {25885, 25901}, {25889, 25906}, {25908, 25929}, {25909, 25933}, {25912, 25936}, {25916, 25946}, {25925, 25956}, {26405, 27164}, {26454, 27262}, {26533, 27428}, {26555, 26560}, {26593, 26598}, {26600, 26609}, {26602, 26615}, {26603, 26617}, {26605, 26619}, {26700, 26705}, {26702, 26778}, {26707, 26716}, {26709, 26722}, {26710, 26724}, {26712, 26726}, {26719, 26804}, {26728, 26745}, {26729, 26749}, {26732, 26752}, {26735, 26759}, {26736, 26761}, {26738, 26763}, {26740, 26765}, {26742, 26767}, {26756, 26856}, {26930, 26936}, {26938, 26948}, {26940, 26956}, {26944, 26961}, {26963, 26984}, {26964, 26988}, {26967, 26991},
L25007 = [0, 1, 2, 3, 8, 10, 13, 15], L25008 = [0, 1, 2, 3, 8, 10, 13, 16], L25012 = [0, 1, 2, 3, 8, 10, 15, 16], L25065 = [0, 1, 2, 3, 9, 10, 14, 16], L25088 = [0, 1, 2, 3, 9, 12, 15, 16], L25131 = [0, 1, 2, 3, 10, 13, 15, 16], L25132 = [0, 1, 2, 3, 10, 13, 16, 16], L25138 = [0, 1, 2, 3, 10, 15, 16, 16], L25239 = [0, 1, 2, 4, 4, 4, 7, 9], L25245 = [0, 1, 2, 4, 4, 4, 7, 15], L25350 = [0, 1, 2, 4, 4, 6, 7, 9], L25355 = [0, 1, 2, 4, 4, 6, 7, 15], L25395 = [0, 1, 2, 4, 4, 7, 8, 9], L25401 = [0, 1, 2, 4, 4, 7, 8, 15], L25403 = [0, 1, 2, 4, 4, 7, 9, 10], L25405 = [0, 1, 2, 4, 4, 7, 9, 12], L25409 = [0, 1, 2, 4, 4, 7, 9, 16], L25413 = [0, 1, 2, 4, 4, 7, 10, 15], L25421 = [0, 1, 2, 4, 4, 7, 12, 15], L25426 = [0, 1, 2, 4, 4, 7, 15, 16], L25540 = [0, 1, 2, 4, 5, 6, 7, 14], L25552 = [0, 1, 2, 4, 5, 6, 9, 10], L25555 = [0, 1, 2, 4, 5, 6, 9, 13], L25559 = [0, 1, 2, 4, 5, 6, 10, 13], L25562 = [0, 1, 2, 4, 5, 6, 11, 12], L25570 = [0, 1, 2, 4, 5, 6, 12, 15], L25652 = [0, 1, 2, 4, 5, 9, 11, 13], L25686 = [0, 1, 2, 4, 5, 12, 13, 14], L25714 = [0, 1, 2, 4, 6, 6, 7, 9], L25719 = [0, 1, 2, 4, 6, 6, 7, 15], L25752 = [0, 1, 2, 4, 6, 7, 8, 9], L25757 = [0, 1, 2, 4, 6, 7, 8, 15], L25759 = [0, 1, 2, 4, 6, 7, 9, 10], L25761 = [0, 1, 2, 4, 6, 7, 9, 12], L25762 = [0, 1, 2, 4, 6, 7, 9, 14], L25764 = [0, 1, 2, 4, 6, 7, 9, 16], L25768 = [0, 1, 2, 4, 6, 7, 10, 15], L25770 = [0, 1, 2, 4, 6, 7, 11, 12], L25774 = [0, 1, 2, 4, 6, 7, 12, 15], L25776 = [0, 1, 2, 4, 6, 7, 14, 15], L25778 = [0, 1, 2, 4, 6, 7, 15, 16], L25820 = [0, 1, 2, 4, 6, 9, 11, 12], L25875 = [0, 1, 2, 4, 7, 8, 8, 9], L25881 = [0, 1, 2, 4, 7, 8, 8, 15], L25883 = [0, 1, 2, 4, 7, 8, 9, 10], L25884 = [0, 1, 2, 4, 7, 8, 9, 11], L25885 = [0, 1, 2, 4, 7, 8, 9, 12], L25889 = [0, 1, 2, 4, 7, 8, 9, 16], L25893 = [0, 1, 2, 4, 7, 8, 10, 15], L25901 = [0, 1, 2, 4, 7, 8, 12, 15], L25906 = [0, 1, 2, 4, 7, 8, 15, 16], L25908 = [0, 1, 2, 4, 7, 9, 10, 10], L25909 = [0, 1, 2, 4, 7, 9, 10, 12], L25912 = [0, 1, 2, 4, 7, 9, 10, 16], L25915 = [0, 1, 2, 4, 7, 9, 11, 16], L25916 = [0, 1, 2, 4, 7, 9, 12, 12], L25920 = [0, 1, 2, 4, 7, 9, 12, 16], L25925 = [0, 1, 2, 4, 7, 9, 16, 16], L25929 = [0, 1, 2, 4, 7, 10, 10, 15], L25933 = [0, 1, 2, 4, 7, 10, 12, 15], L25936 = [0, 1, 2, 4, 7, 10, 15, 16], L25946 = [0, 1, 2, 4, 7, 12, 12, 15], L25951 = [0, 1, 2, 4, 7, 12, 15, 16], L25956 = [0, 1, 2, 4, 7, 15, 16, 16], L26120 = [0, 1, 2, 4, 11, 12, 13, 14], L26222 = [0, 1, 2, 5, 6, 7, 9, 11], L26224 = [0, 1, 2, 5, 6, 7, 9, 15], L26229 = [0, 1, 2, 5, 6, 7, 11, 15], L26233 = [0, 1, 2, 5, 6, 7, 12, 15], L26242 = [0, 1, 2, 5, 6, 8, 8, 11], L26246 = [0, 1, 2, 5, 6, 8, 8, 15], L26248 = [0, 1, 2, 5, 6, 8, 9, 10], L26258 = [0, 1, 2, 5, 6, 8, 11, 13 L26260 = [0, 1, 2, 5, 6, 8, 11, 15], L26261 = [0, 1, 2, 5, 6, 8, 11, 16], L26270 = [0, 1, 2, 5, 6, 8, 15, 16], L26273 = [0, 1, 2, 5, 6, 9, 10, 16], L26291 = [0, 1, 2, 5, 6, 11, 13, 16], L26295 = [0, 1, 2, 5, 6, 11, 15, 16], L26296 = [0, 1, 2, 5, 6, 11, 16, 16], L26312 = [0, 1, 2, 5, 6, 15, 16, 16], L26354 = [0, 1, 2, 5, 7, 11, 12, 13], L26405 = [0, 1, 2, 5, 8, 8, 13, 14], L26454 = [0, 1, 2, 5, 8, 13, 14, 16], L26533 = [0, 1, 2, 5, 13, 14, 16, 16], L26555 = [0, 1, 2, 6, 6, 6, 7, 9], L26560 = [0, 1, 2, 6, 6, 6, 7, 15], L26593 = [0, 1, 2, 6, 6, 7, 8, 9], L26598 = [0, 1, 2, 6, 6, 7, 8, 15], L26600 = [0, 1, 2, 6, 6, 7, 9, 10], L26602 = [0, 1, 2, 6, 6, 7, 9, 12], L26603 = [0, 1, 2, 6, 6, 7, 9, 14], L26605 = [0, 1, 2, 6, 6, 7, 9, 16], L26609 = [0, 1, 2, 6, 6, 7, 10, 15], L26615 = [0, 1, 2, 6, 6, 7, 12, 15], L26617 = [0, 1, 2, 6, 6, 7, 14, 15], L26619 = [0, 1, 2, 6, 6, 7, 15, 16], L26700 = [0, 1, 2, 6, 7, 8, 8, 9], L26702 = [0, 1, 2, 6, 7, 8, 8, 11], L26705 = [0, 1, 2, 6, 7, 8, 8, 15], L26707 = [0, 1, 2, 6, 7, 8, 9, 10], L26709 = [0, 1, 2, 6, 7, 8, 9, 12],
230
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 32 {0} {26971, 27001}, {26975, 27006}, {26980, 27011}, {27013, 27048}, {27014, 27052}, (cont.) {27017, 27055}, {27018, 27059}, {27021, 27062}, {27024, 27065}, {27030, 27077}, {27034, 27082}, {27039, 27087}, {27044, 27092}, {27554, 27555}, {27557, 27558, 27568, 27570}, {27573, 27600}, {27575, 27583, 27599, 27611}, {27607, 27663}, {27660, 27661}, {27726, 27727}, {27728, 27756}, {27729, 27730, 27755, 27757}, {27733, 27737, 27741, 27777}, {27736, 27739}, {27742, 27780}, {27744, 27745, 27779, 27781}, {27760, 27829}, {27762, 27770, 27828, 27839}, {27785, 27800}, {27789, 27851}, {27793, 27810, 27850, 27870}, {27822, 27885}, {27869, 27990}, {27917, 27918}, {27986, 27987}, {28089, 28116}, {28090, 28091, 28093, 28123}, {28094, 28124}, {28098, 28099, 28102, 28141}, {28103, 28142}, {28108, 28109, 28113, 28172}, {28114, 28173}, {28127, 28134}, {28149, 28163}, {28184, 28207}, {28218, 28284}, {28223, 28293}, {28234, 28317}, {28253, 28368}, {28282, 28462}, {28698, 28701}, {28864, 28867}, {28894, 28897},
L26710 = [0, 1, 2, 6, 7, 8, 9, 14], L26712 = [0, 1, 2, 6, 7, 8, 9, 16], L26716 = [0, 1, 2, 6, 7, 8, 10, 15], L26719 = [0, 1, 2, 6, 7, 8, 11, 16], L26722 = [0, 1, 2, 6, 7, 8, 12, 15], L26724 = [0, 1, 2, 6, 7, 8, 14, 15], L26726 = [0, 1, 2, 6, 7, 8, 15, 16], L26728 = [0, 1, 2, 6, 7, 9, 10, 10], L26729 = [0, 1, 2, 6, 7, 9, 10, 12], L26732 = [0, 1, 2, 6, 7, 9, 10, 16], L26735 = [0, 1, 2, 6, 7, 9, 12, 12], L26736 = [0, 1, 2, 6, 7, 9, 12, 14], L26738 = [0, 1, 2, 6, 7, 9, 12, 16], L26740 = [0, 1, 2, 6, 7, 9, 14, 16], L26742 = [0, 1, 2, 6, 7, 9, 16, 16], L26745 = [0, 1, 2, 6, 7, 10, 10, 15], L26749 = [0, 1, 2, 6, 7, 10, 12, 15], L26752 = [0, 1, 2, 6, 7, 10, 15, 16], L26756 = [0, 1, 2, 6, 7, 11, 16, 16], L26759 = [0, 1, 2, 6, 7, 12, 12, 15], L26761 = [0, 1, 2, 6, 7, 12, 14, 15], L26763 = [0, 1, 2, 6, 7, 12, 15, 16], L26765 = [0, 1, 2, 6, 7, 14, 15, 16], L26767 = [0, 1, 2, 6, 7, 15, 16, 16], L26778 = [0, 1, 2, 6, 8, 8, 9, 11], L26804 = [0, 1, 2, 6, 8, 9, 11, 16], L26856 = [0, 1, 2, 6, 9, 11, 16, 16], L26930 = [0, 1, 2, 7, 8, 8, 8, 9], L26936 = [0, 1, 2, 7, 8, 8, 8, 15], L26938 = [0, 1, 2, 7, 8, 8, 9, 10], L26940 = [0, 1, 2, 7, 8, 8, 9, 12], L26944 = [0, 1, 2, 7, 8, 8, 9, 16], L26948 = [0, 1, 2, 7, 8, 8, 10, 15], L26956 = [0, 1, 2, 7, 8, 8, 12, 15], L26961 = [0, 1, 2, 7, 8, 8, 15, 16], L26963 = [0, 1, 2, 7, 8, 9, 10, 10], L26964 = [0, 1, 2, 7, 8, 9, 10, 12], L26967 = [0, 1, 2, 7, 8, 9, 10, 16], L26971 = [0, 1, 2, 7, 8, 9, 12, 12], L26975 = [0, 1, 2, 7, 8, 9, 12, 16], L26980 = [0, 1, 2, 7, 8, 9, 16, 16], L26984 = [0, 1, 2, 7, 8, 10, 10, 15], L26988 = [0, 1, 2, 7, 8, 10, 12, 15], L26991 = [0, 1, 2, 7, 8, 10, 15, 16], L27001 = [0, 1, 2, 7, 8, 12, 12, 15], L27006 = [0, 1, 2, 7, 8, 12, 15, 16], L27011 = [0, 1, 2, 7, 8, 15, 16, 16], L27013 = [0, 1, 2, 7, 9, 10, 10, 10], L27014 = [0, 1, 2, 7, 9, 10, 10, 12], L27017 = [0, 1, 2, 7, 9, 10, 10, 16], L27018 = [0, 1, 2, 7, 9, 10, 12, 12], L27021 = [0, 1, 2, 7, 9, 10, 12, 16], L27024 = [0, 1, 2, 7, 9, 10, 16, 16], L27030 = [0, 1, 2, 7, 9, 12, 12, 12], L27034 = [0, 1, 2, 7, 9, 12, 12, 16], L27039 = [0, 1, 2, 7, 9, 12, 16, 16], L27044 = [0, 1, 2, 7, 9, 16, 16, 16], L27048 = [0, 1, 2, 7, 10, 10, 10, 15], L27052 = [0, 1, 2, 7, 10, 10, 12, 15], L27055 = [0, 1, 2, 7, 10, 10, 15, 16], L27059 = [0, 1, 2, 7, 10, 12, 12, 15], L27062 = [0, 1, 2, 7, 10, 12, 15, 16], L27065 = [0, 1, 2, 7, 10, 15, 16, 16], L27077 = [0, 1, 2, 7, 12, 12, 12, 15], L27082 = [0, 1, 2, 7, 12, 12, 15, 16], L27087 = [0, 1, 2, 7, 12, 15, 16, 16], L27092 = [0, 1, 2, 7, 15, 16, 16, 16], L27164 = [0, 1, 2, 8, 8, 11, 13, 14], L27262 = [0, 1, 2, 8, 11, 13, 14, 16], L27428 = [0, 1, 2, 11, 13, 14, 16, 16], L27503 = [0, 1, 3, 4, 4, 4, 5, 13], L27508 = [0, 1, 3, 4, 4, 4, 7, 9], L27536 = [0, 1, 3, 4, 4, 4, 11, 13], L27554 = [0, 1, 3, 4, 4, 5, 7, 9], L27555 = [0, 1, 3, 4, 4, 5, 7, 11], L27557 = [0, 1, 3, 4, 4, 5, 7, 13], L27558 = [0, 1, 3, 4, 4, 5, 7, 15], L27564 = [0, 1, 3, 4, 4, 5, 8, 13], L27568 = [0, 1, 3, 4, 4, 5, 9, 11], L27570 = [0, 1, 3, 4, 4, 5, 9, 15], L27573 = [0, 1, 3, 4, 4, 5, 11, 13], L27575 = [0, 1, 3, 4, 4, 5, 11, 15], L27578 = [0, 1, 3, 4, 4, 5, 12, 13], L27583 = [0, 1, 3, 4, 4, 5, 13, 15], L27584 = [0, 1, 3, 4, 4, 5, 13, 16], L27591 = [0, 1, 3, 4, 4, 7, 8, 9], L27598 = [0, 1, 3, 4, 4, 7, 9, 12
APPENDIX
231
Table 6. (continued) m = 8 q I indexes of I-isospectral families 32 {0} {28900, 28906}, {28902, 28908}, {29211, 29214}, {29241, 29244}, {29246, 29252}, (cont.) {29247, 29255}, {29249, 29257}, {29319, 29322}, {29325, 29331}, {29327, 29333}, {29338, 29347}, {29342, 29351}, {29811, 29814}, {29841, 29844}, {29846, 29852}, {29847, 29855}, {29849, 29857}, {29920, 29923}, {29925, 29931}, {29926, 29934}, {29928, 29936}, {29939, 29950}, {29941, 29952}, {29942, 29955}, {29944, 29957}, {29946, 29959}, {30083, 30086}, {30089, 30095}, {30091, 30097}, {30102, 30111}, {30104, 30113}, {30106, 30115}, {30122, 30134}, {30124, 30136}, {30126, 30138}, {30128, 30140}, {51932, 51955}, {54553, 54576}, {54586, 54610}, {54601, 54655}, {54609, 54667}, {56683, 58898}, {57038, 58969}, {62288, 62291}, {63030, 63033}, {63036, 63042}, {63039, 63046}, {64725, 64732}, {65233, 65236}, {65239, 65245}, {65242, 65249}, {65254, 65264}, {65257, 65268}, {65261, 65272}, {69300, 69307}, {69320, 69332}, {69322, 69337}, {69325, 69341}, {70453, 70456}, {70459, 70465},
L27599 = [0, 1, 3, 4, 4, 7, 9, 13], L27600 = [0, 1, 3, 4, 4, 7, 9, 15], L27601 = [0, 1, 3, 4, 4, 7, 9, 16], L27607 = [0, 1, 3, 4, 4, 7, 12, 12], L27611 = [0, 1, 3, 4, 4, 7, 13, 15], L27637 = [0, 1, 3, 4, 4, 8, 11, 13], L27660 = [0, 1, 3, 4, 4, 9, 11, 13], L27661 = [0, 1, 3, 4, 4, 9, 11, 15], L27663 = [0, 1, 3, 4, 4, 9, 12, 12], L27689 = [0, 1, 3, 4, 4, 11, 12, 13], L27694 = [0, 1, 3, 4, 4, 11, 13, 16], L27726 = [0, 1, 3, 4, 5, 7, 8, 9], L27727 = [0, 1, 3, 4, 5, 7, 8, 11], L27728 = [0, 1, 3, 4, 5, 7, 8, 12], L27729 = [0, 1, 3, 4, 5, 7, 8, 13], L27730 = [0, 1, 3, 4, 5, 7, 8, 15], L27732 = [0, 1, 3, 4, 5, 7, 9, 11], L27733 = [0, 1, 3, 4, 5, 7, 9, 12], L27734 = [0, 1, 3, 4, 5, 7, 9, 13], L27735 = [0, 1, 3, 4, 5, 7, 9, 15], L27736 = [0, 1, 3, 4, 5, 7, 9, 16], L27737 = [0, 1, 3, 4, 5, 7, 11, 12], L27738 = [0, 1, 3, 4, 5, 7, 11, 1 L27739 = [0, 1, 3, 4, 5, 7, 11, 16], L27741 = [0, 1, 3, 4, 5, 7, 12, 13], L27742 = [0, 1, 3, 4, 5, 7, 12, 16], L27743 = [0, 1, 3, 4, 5, 7, 13, 15], L27744 = [0, 1, 3, 4, 5, 7, 13, 16], L27745 = [0, 1, 3, 4, 5, 7, 15, 16], L27751 = [0, 1, 3, 4, 5, 8, 8, 13], L27755 = [0, 1, 3, 4, 5, 8, 9, 11], L27756 = [0, 1, 3, 4, 5, 8, 9, 12], L27757 = [0, 1, 3, 4, 5, 8, 9, 15], L27760 = [0, 1, 3, 4, 5, 8, 11, 13], L27762 = [0, 1, 3, 4, 5, 8, 11, 15], L27765 = [0, 1, 3, 4, 5, 8, 12, 13], L27770 = [0, 1, 3, 4, 5, 8, 13, 15], L27771 = [0, 1, 3, 4, 5, 8, 13, 16], L27777 = [0, 1, 3, 4, 5, 9, 11, 12], L27778 = [0, 1, 3, 4, 5, 9, 11, 15], L27779 = [0, 1, 3, 4, 5, 9, 11, 16], L27780 = [0, 1, 3, 4, 5, 9, 12, 16], L27781 = [0, 1, 3, 4, 5, 9, 15, 16], L27785 = [0, 1, 3, 4, 5, 11, 12, 15], L27788 = [0, 1, 3, 4, 5, 11, 13, 15], L27789 = [0, 1, 3, 4, 5, 11, 13, 16], L27793 = [0, 1, 3, 4, 5, 11, 15, 16], L27796 = [0, 1, 3, 4, 5, 12, 12, 13], L27800 = [0, 1, 3, 4, 5, 12, 13, 15], L27801 = [0, 1, 3, 4, 5, 12, 13, 16], L27810 = [0, 1, 3, 4, 5, 13, 15, 16], L27811 = [0, 1, 3, 4, 5, 13, 16, 16], L27820 = [0, 1, 3, 4, 7, 8, 8, 9], L27822 = [0, 1, 3, 4, 7, 8, 8, 12], L27827 = [0, 1, 3, 4, 7, 8, 9, 12], L27828 = [0, 1, 3, 4, 7, 8, 9, 13], L27829 = [0, 1, 3, 4, 7, 8, 9, 15], L27830 = [0, 1, 3, 4, 7, 8, 9, 16], L27838 = [0, 1, 3, 4, 7, 8, 12, 16], L27839 = [0, 1, 3, 4, 7, 8, 13, 15], L27848 = [0, 1, 3, 4, 7, 9, 12, 16], L27849 = [0, 1, 3, 4, 7, 9, 13, 15], L27850 = [0, 1, 3, 4, 7, 9, 13, 16], L27851 = [0, 1, 3, 4, 7, 9, 15, 16], L27852 = [0, 1, 3, 4, 7, 9, 16, 16], L27869 = [0, 1, 3, 4, 7, 12, 16, 16], L27870 = [0, 1, 3, 4, 7, 13, 15, 16], L27885 = [0, 1, 3, 4, 8, 8, 9, 12], L27895 = [0, 1, 3, 4, 8, 8, 11, 13], L27917 = [0, 1, 3, 4, 8, 9, 11, 13], L27918 = [0, 1, 3, 4, 8, 9, 11, 15], L27921 = [0, 1, 3, 4, 8, 9, 12, 16], L27945 = [0, 1, 3, 4, 8, 11, 13, 16], L27986 = [0, 1, 3, 4, 9, 11, 13, 16], L27987 = [0, 1, 3, 4, 9, 11, 15, 16], L27990 = [0, 1, 3, 4, 9, 12, 16, 16], L28040 = [0, 1, 3, 4, 11, 13, 16, 16], L28089 = [0, 1, 3, 5, 7, 8, 8, 8], L28090 = [0, 1, 3, 5, 7, 8, 8, 9], L28091 = [0, 1, 3, 5, 7, 8, 8, 11], L28093 = [0, 1, 3, 5, 7, 8, 8, 13], L28094 = [0, 1, 3, 5, 7, 8, 8, 16], L28095 = [0, 1, 3, 5, 7, 8, 9, 11], L28096 = [0, 1, 3, 5, 7, 8, 9, 13], L28098 = [0, 1, 3, 5, 7, 8, 9, 16], L28099 = [0, 1, 3, 5, 7, 8, 11, 16], L28102 = [0, 1, 3, 5, 7, 8, 13, 16], L28103 = [0, 1, 3, 5, 7, 8, 16, 16], L28105 = [0, 1, 3, 5, 7, 9, 11, 16], L28106 = [0, 1, 3, 5, 7, 9, 13, 16], L28108 = [0, 1, 3, 5, 7, 9, 16, 16], L28109 = [0, 1, 3, 5, 7, 11, 16, 16], L28113 = [0, 1, 3, 5, 7, 13, 16, 16], L28114 = [0, 1, 3, 5, 7, 16, 16, 16], L28116 = [0, 1, 3, 5, 8, 8, 8, 9], L28119 = [0, 1, 3, 5, 8, 8, 8, 13], L28123 = [0, 1, 3, 5, 8, 8, 9, 11], L28124 =
232
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 32 {0} {70462, 70469}, {70474, 70484}, {70477, 70488}, {70481, 70492}, {70500, 70514}, (cont.) {70503, 70518}, {70507, 70522}, {70511, 70526}, {72682, 72688}, {72849, 72855}, {72967, 72973}, {73014, 73020}, {73022, 73034}, {73024, 73043}, {73026, 73048}, {73028, 73050}, {73574, 73580}, {73692, 73698}, {73739, 73745}, {73747, 73759}, {73749, 73768}, {73751, 73773}, {73753, 73775}, {74120, 74126}, {74167, 74173}, {74175, 74187}, {74177, 74196}, {74179, 74201}, {74181, 74203}, {74317, 74323}, {74325, 74337}, {74327, 74346}, {74329, 74351}, {74331, 74353}, {74355, 74383}, {74357, 74392}, {74359, 74397}, {74361, 74399}, {74366, 74413}, {74368, 74418}, {74370, 74420}, {74373, 74426}, {74375, 74428}, {74377, 74430}, {75969, 75975}, {76087, 76093}, {76134, 76140}, {76142, 76154}, {76144, 76163}, {76146, 76168}, {76148, 76170}, {76509, 76514}, {76554, 76560}, {76562, 76574}, {76564, 76583}, {76566, 76588}, {76568, 76590}, {76703, 76709}, {76711, 76723}, {76713, 76732},
[0, 1, 3, 5, 8, 8, 9, 16], L28127 = [0, 1, 3, 5, 8, 8, 11, 15], L28130 = [0, 1, 3, 5, 8, 8, 12, 13], L28134 = [0, 1, 3, 5, 8, 8, 13, 15], L28135 = [0, 1, 3, 5, 8, 8, 13, 16], L28141 = [0, 1, 3, 5, 8, 9, 11, 16], L28142 = [0, 1, 3, 5, 8, 9, 16, 16], L28149 = [0, 1, 3, 5, 8, 11, 15, 16], L28152 = [0, 1, 3, 5, 8, 12, 12, 13], L28156 = [0, 1, 3, 5, 8, 12, 13, 16], L28163 = [0, 1, 3, 5, 8, 13, 15, 16], L28164 = [0, 1, 3, 5, 8, 13, 16, 16], L28172 = [0, 1, 3, 5, 9, 11, 16, 16], L28173 = [0, 1, 3, 5, 9, 16, 16, 16], L28184 = [0, 1, 3, 5, 11, 15, 16, 16], L28187 = [0, 1, 3, 5, 12, 12, 12, 13], L28191 = [0, 1, 3, 5, 12, 12, 13, 16], L28197 = [0, 1, 3, 5, 12, 13, 16, 16], L28207 = [0, 1, 3, 5, 13, 15, 16, 16], L28208 = [0, 1, 3, 5, 13, 16, 16, 16], L28218 = [0, 1, 3, 7, 8, 8, 8, 8], L28219 = [0, 1, 3, 7, 8, 8, 8, 9], L28223 = [0, 1, 3, 7, 8, 8, 8, 16], L28225 = [0, 1, 3, 7, 8, 8, 9, 16], L28234 = [0, 1, 3, 7, 8, 8, 16, 16], L28237 = [0, 1, 3, 7, 8, 9, 16, 16], L28253 = [0, 1, 3, 7, 8, 16, 16, 16], L28257 = [0, 1, 3, 7, 9, 16, 16, 16], L28282 = [0, 1, 3, 7, 16, 16, 16, 16], L28284 = [0, 1, 3, 8, 8, 8, 8, 9], L28293 = [0, 1, 3, 8, 8, 8, 9, 16], L28317 = [0, 1, 3, 8, 8, 9, 16, 16], L28368 = [0, 1, 3, 8, 9, 16, 16, 16], L28462 = [0, 1, 3, 9, 16, 16, 16, 16], L28698 = [0, 1, 4, 4, 4, 6, 7, 9], L28701 = [0, 1, 4, 4, 4, 6, 7, 15], L28864 = [0, 1, 4, 4, 6, 6, 7, 9], L28867 = [0, 1, 4, 4, 6, 6, 7, 15], L28894 = [0, 1, 4, 4, 6, 7, 8, 9], L28897 = [0, 1, 4, 4, 6, 7, 8, 15], L28900 = [0, 1, 4, 4, 6, 7, 9, 12], L28902 = [0, 1, 4, 4, 6, 7, 9, 16], L28906 = [0, 1, 4, 4, 6, 7, 12, 15], L28908 = [0, 1, 4, 4, 6, 7, 15, 16], L29211 = [0, 1, 4, 6, 6, 6, 7, 9], L29214 = [0, 1, 4, 6, 6, 6, 7, 15], L29241 = [0, 1, 4, 6, 6, 7, 8, 9], L29244 = [0, 1, 4, 6, 6, 7, 8, 15], L29246 = [0, 1, 4, 6, 6, 7, 9, 10], L29247 = [0, 1, 4, 6, 6, 7, 9, 12], L29249 = [0, 1, 4, 6, 6, 7, 9, 16], L29252 = [0, 1, 4, 6, 6, 7, 10, 15], L29255 = [0, 1, 4, 6, 6, 7, 12, 15], L29257 = [0, 1, 4, 6, 6, 7, 15, 16], L29319 = [0, 1, 4, 6, 7, 8, 8, 9], L29322 = [0, 1, 4, 6, 7, 8, 8, 15], L29325 = [0, 1, 4, 6, 7, 8, 9, 12], L29327 = [0, 1, 4, 6, 7, 8, 9, 16], L29331 = [0, 1, 4, 6, 7, 8, 12, 15], L29333 = [0, 1, 4, 6, 7, 8, 15, 16], L29338 = [0, 1, 4, 6, 7, 9, 12, 12], L29340 = [0, 1, 4, 6, 7, 9, 12, 16], L29342 = [0, 1, 4, 6, 7, 9, 16, 16], L29347 = [0, 1, 4, 6, 7, 12, 12, 15], L29349 = [0, 1, 4, 6, 7, 12, 15, 16], L29351 = [0, 1, 4, 6, 7, 15, 16, 16], L29811 = [0, 1, 6, 6, 6, 6, 7, 9], L29814 = [0, 1, 6, 6, 6, 6, 7, 15], L29841 = [0, 1, 6, 6, 6, 7, 8, 9], L29844 = [0, 1, 6, 6, 6, 7, 8, 15], L29846 = [0, 1, 6, 6, 6, 7, 9, 10], L29847 = [0, 1, 6, 6, 6, 7, 9, 12], L29849 = [0, 1, 6, 6, 6, 7, 9, 16], L29852 = [0, 1, 6, 6, 6, 7, 10, 15], L29855 = [0, 1, 6, 6, 6, 7, 12, 15], L29857 = [0, 1, 6, 6, 6, 7, 15, 16], L29920 = [0, 1, 6, 6, 7, 8, 8, 9], L29923 = [0, 1, 6, 6, 7, 8, 8, 15], L29925 = [0, 1, 6, 6, 7, 8, 9, 10], L29926 = [0, 1, 6, 6, 7, 8, 9, 12], L29928 = [0, 1, 6, 6, 7, 8, 9, 16], L29931 = [0, 1, 6, 6, 7, 8, 10, 15], L29934 = [0, 1, 6, 6, 7, 8, 12, 15], L29936 = [0, 1, 6, 6, 7, 8, 15, 16], L29939 = [0, 1, 6, 6, 7, 9, 10, 12], L29941 = [0, 1, 6, 6, 7, 9, 10, 16], L29942 = [0, 1, 6, 6, 7, 9, 12, 12], L29944 = [0, 1, 6, 6, 7, 9, 12, 16], L29946 = [0, 1, 6, 6, 7, 9, 16, 16], L29950 = [0, 1, 6, 6, 7, 10, 12, 15], L29952 = [0, 1, 6, 6, 7, 10, 15, 16], L29955 = [0, 1, 6, 6, 7, 12, 12, 15], L29957 = [0, 1, 6, 6, 7, 12, 15, 16], L29959 = [0, 1, 6, 6, 7, 15, 16, 16], L30083 = [0, 1, 6, 7, 8, 8, 8, 9], L30086 = [0, 1, 6, 7, 8, 8, 8, 15], L30089 = [0, 1, 6, 7, 8, 8, 9, 12], L30091 = [0, 1, 6, 7, 8, 8, 9, 16], L30095 = [0, 1, 6, 7, 8, 8, 12, 15], L30097 = [0, 1, 6, 7, 8, 8, 15, 16], L30102 = [0, 1, 6, 7, 8, 9, 12, 12], L30104 =
APPENDIX
233
Table 6. (continued) m = 8 q I indexes of I-isospectral families 32 {0} {76715, 76737}, {76717, 76739}, {76741, 76768}, {76743, 76777}, {76745, 76781}, (cont.) {76747, 76783}, {76752, 76796}, {76754, 76801}, {76756, 76803}, {76761, 76809}, {76763, 76811}, {77647, 77652}, {77686, 77691}, {77693, 77703}, {77695, 77710}, {77696, 77713}, {77698, 77715}, {77802, 77808}, {77810, 77822}, {77812, 77831}, {77814, 77836}, {77816, 77838}, {77840, 77867}, {77842, 77876}, {77846, 77883}, {77851, 77896}, {77853, 77901}, {77855, 77903}, {77858, 77908}, {77860, 77910}, {77862, 77912}, {77997, 80503}, {78123, 80530}, {78165, 78171}, {78173, 78185}, {78175, 78194}, {78177, 78199}, {78179, 78201}, {78203, 78230}, {78205, 78239}, {78207, 78243}, {78209, 78245}, {78214, 78258}, {78216, 78263}, {78218, 78265}, {78223, 78271}, {78225, 78273}, {78275, 78328}, {78276, 78333}, {78278, 78337}, {78280, 78339}, {78285, 78352}, {78287, 78356}, {78289, 78358}, {78293, 78362}, {78295, 78364}, {78304, 78381}, {78306, 78386}, {78308, 78388}, {78313, 78394},
[0, 1, 6, 7, 8, 9, 12, 16], L30106 = [0, 1, 6, 7, 8, 9, 16, 16], L30111 = [0, 1, 6, 7, 8, 12, 12, 15], L30113 = [0, 1, 6, 7, 8, 12, 15, 16], L30115 = [0, 1, 6, 7, 8, 15, 16, 16], L30122 = [0, 1, 6, 7, 9, 12, 12, 12], L30124 = [0, 1, 6, 7, 9, 12, 12, 16], L30126 = [0, 1, 6, 7, 9, 12, 16, 16], L30128 = [0, 1, 6, 7, 9, 16, 16, 16], L30134 = [0, 1, 6, 7, 12, 12, 12, 15], L30136 = [0, 1, 6, 7, 12, 12, 15, 16], L30138 = [0, 1, 6, 7, 12, 15, 16, 16], L30140 = [0, 1, 6, 7, 15, 16, 16, 16], L51932 = [1, 1, 2, 4, 7, 7, 9, 14], L51955 = [1, 1, 2, 4, 7, 7, 14, 15], L54553 = [1, 1, 2, 7, 7, 8, 9, 14], L54576 = [1, 1, 2, 7, 7, 8, 14, 15], L54586 = [1, 1, 2, 7, 7, 9, 9, 15], L54601 = [1, 1, 2, 7, 7, 9, 12, 1 L54609 = [1, 1, 2, 7, 7, 9, 14, 16], L54610 = [1, 1, 2, 7, 7, 9, 15, 15], L54655 = [1, 1, 2, 7, 7, 12, 14, 15], L54667 = [1, 1, 2, 7, 7, 14, 15, 16], L56625 = [1, 1, 3, 3, 5, 11, 15, 15], L56683 = [1, 1, 3, 3, 7, 7, 11, 13], L56752 = [1, 1, 3, 3, 7, 9, 11, 13], L56761 = [1, 1, 3, 3, 7, 9, 13, 13], L57038 = [1, 1, 3, 3, 9, 11, 13, 15], L58898 = [1, 1, 3, 5, 5, 7, 7, 11], L58918 = [1, 1, 3, 5, 5, 7, 11, 13], L58927 = [1, 1, 3, 5, 5, 7, 13, 15], L58967 = [1, 1, 3, 5, 5, 9, 11, 13], L58969 = [1, 1, 3, 5, 5, 9, 11, 15], L59291 = [1, 1, 3, 5, 7, 7, 9, 11], L59311 = [1, 1, 3, 5, 7, 7, 15, 15], L59358 = [1, 1, 3, 5, 7, 9, 9, 11], L59619 = [1, 1, 3, 5, 9, 9, 15, 15], L62288 = [1, 1, 4, 4, 4, 7, 7, 9], L62291 = [1, 1, 4, 4, 4, 7, 7, 15], L63030 = [1, 1, 4, 4, 7, 7, 8, 9], L63033 = [1, 1, 4, 4, 7, 7, 8, 15], L63036 = [1, 1, 4, 4, 7, 7, 9, 12], L63039 = [1, 1, 4, 4, 7, 7, 9, 16], L63042 = [1, 1, 4, 4, 7, 7, 12, 15 L63046 = [1, 1, 4, 4, 7, 7, 15, 16], L64725 = [1, 1, 4, 6, 7, 7, 9, 10], L64732 = [1, 1, 4, 6, 7, 7, 10, 15], L65233 = [1, 1, 4, 7, 7, 8, 8, 9], L65236 = [1, 1, 4, 7, 7, 8, 8, 15], L65239 = [1, 1, 4, 7, 7, 8, 9, 12], L65242 = [1, 1, 4, 7, 7, 8, 9, 16], L65245 = [1, 1, 4, 7, 7, 8, 12, 15], L65249 = [1, 1, 4, 7, 7, 8, 15, 16], L65254 = [1, 1, 4, 7, 7, 9, 12, 12], L65257 = [1, 1, 4, 7, 7, 9, 12, 16], L65261 = [1, 1, 4, 7, 7, 9, 16, 16], L65264 = [1, 1, 4, 7, 7, 12, 12, 15], L65268 = [1, 1, 4, 7, 7, 12, 15, 16], L65272 = [1, 1, 4, 7, 7, 15, 16, 16], L69300 = [1, 1, 6, 7, 7, 8, 9, 10], L69307 = [1, 1, 6, 7, 7, 8, 10, 15], L69320 = [1, 1, 6, 7, 7, 9, 9, 15], L69322 = [1, 1, 6, 7, 7, 9, 10, 1 L69325 = [1, 1, 6, 7, 7, 9, 10, 16], L69332 = [1, 1, 6, 7, 7, 9, 15, 15], L69337 = [1, 1, 6, 7, 7, 10, 12, 15], L69341 = [1, 1, 6, 7, 7, 10, 15, 16], L70453 = [1, 1, 7, 7, 8, 8, 8, 9], L70456 = [1, 1, 7, 7, 8, 8, 8, 15], L70459 = [1, 1, 7, 7, 8, 8, 9, 12], L70462 = [1, 1, 7, 7, 8, 8, 9, 16], L70465 = [1, 1, 7, 7, 8, 8, 12, 15], L70469 = [1, 1, 7, 7, 8, 8, 15, 1 L70474 = [1, 1, 7, 7, 8, 9, 12, 12], L70477 = [1, 1, 7, 7, 8, 9, 12, 16], L70481 = [1, 1, 7, 7, 8, 9, 16, 16], L70484 = [1, 1, 7, 7, 8, 12, 12, 15], L70488 = [1, 1, 7, 7, 8, 12, 15, 16], L70492 = [1, 1, 7, 7, 8, 15, 16, 16], L70500 = [1, 1, 7, 7, 9, 12, 12, 12], L70503 = [1, 1, 7, 7, 9, 12, 12, 16], L70507 = [1, 1, 7, 7, 9, 12, 16, 16], L70511 = [1, 1, 7, 7, 9, 16, 16, 16], L70514 = [1, 1, 7, 7, 12, 12, 12, 15], L70518 = [1, 1, 7, 7, 12, 12, 15, 16], L70522 = [1, 1, 7, 7, 12, 15, 16, 16], L70526 = [1, 1, 7, 7, 15, 16, 16, 16], L72682 = [1, 2, 2, 2, 2, 2, 7, 9], L72688 = [1, 2, 2, 2, 2, 2, 7, 15], L72849 = [1, 2, 2, 2, 2, 4, 7, 9], L72855 = [1, 2, 2, 2, 2, 4, 7, 15], L72967 = [1, 2, 2, 2, 2, 6, 7, 9], L72973 = [1, 2, 2, 2, 2, 6, 7, 15], L73014 = [1, 2, 2, 2, 2, 7, 8, 9], L73020 = [1, 2, 2, 2, 2, 7, 8, 15], L73022 = [1, 2, 2, 2, 2, 7, 9, 10], L73024 = [1, 2, 2, 2, 2, 7, 9, 12], L73026 = [1, 2, 2, 2, 2, 7, 9, 14], L73028 = [1, 2, 2, 2, 2, 7, 9, 16], L73034 = [1, 2, 2, 2, 2, 7, 10, 15], L73043 = [1, 2, 2, 2, 2, 7, 12, 15], L73048 =
234
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 32 {0} {78315, 78396}, {78321, 78402}, {78323, 78404}, {79258, 79260, 79295}, (cont.) {79271, 79279}, {79302, 79306}, {79318, 79373}, {79321, 79383}, {79342, 79492}, {79344, 79498}, {79365, 79453}, {79366, 79529}, {79367, 79467, 79468, 79532, 79643, 79843}, {79390, 79398}, {79396, 79536}, {79401, 79525}, {79402, 79552}, {79455, 79475}, {79461, 79535}, {79471, 79524}, {79477, 79539}, {79530, 79671, 80021}, {79567, 79644}, {79568, 79676}, {79574, 80128}, {79620, 80004}, {79645, 79680}, {79672, 80028, 80182, 80206}, {79673, 80029}, {79677, 82638}, {79758, 80064}, {79762, 80171}, {79784, 82558, 82589}, {79788, 82607}, {79790, 82599}, {79849, 82616}, {79855, 80129}, {79864, 80231}, {79872, 82252}, {79909, 82577, 82618}, {79918, 82640}, {79919, 82657}, {79923, 82641}, {80006, 80045, 80048}, {80007, 80046, 80049}, {80009, 80019}, {80010, 80011}, {80012, 80015, 80017, 80075}, {80013, 80022}, {80023, 80078, 80081, 80084}, {80024, 80085}, {80030, 80082}, {80032, 80076, 80184, 80365}, {80033, 80079, 80087},
[1, 2, 2, 2, 2, 7, 14, 15], L73050 = [1, 2, 2, 2, 2, 7, 15, 16], L73574 = [1, 2, 2, 2, 4, 4, 7, 9], L73580 = [1, 2, 2, 2, 4, 4, 7, 15 L73692 = [1, 2, 2, 2, 4, 6, 7, 9], L73698 = [1, 2, 2, 2, 4, 6, 7, 15], L73739 = [1, 2, 2, 2, 4, 7, 8, 9], L73745 = [1, 2, 2, 2, 4, 7, 8, 15], L73747 = [1, 2, 2, 2, 4, 7, 9, 10], L73749 = [1, 2, 2, 2, 4, 7, 9, 12], L73751 = [1, 2, 2, 2, 4, 7, 9, 14], L73753 = [1, 2, 2, 2, 4, 7, 9, 16], L73759 = [1, 2, 2, 2, 4, 7, 10, 15], L73768 = [1, 2, 2, 2, 4, 7, 12, 15], L73773 = [1, 2, 2, 2, 4, 7, 14, 15], L73775 = [1, 2, 2, 2, 4, 7, 15, 16], L74120 = [1, 2, 2, 2, 6, 6, 7, 9], L74126 = [1, 2, 2, 2, 6, 6, 7, 15], L74167 = [1, 2, 2, 2, 6, 7, 8, 9], L74173 = [1, 2, 2, 2, 6, 7, 8, 15], L74175 = [1, 2, 2, 2, 6, 7, 9, 10], L74177 = [1, 2, 2, 2, 6, 7, 9, 12], L74179 = [1, 2, 2, 2, 6, 7, 9, 14], L74181 = [1, 2, 2, 2, 6, 7, 9, 16], L74187 = [1, 2, 2, 2, 6, 7, 10, 15], L74196 = [1, 2, 2, 2, 6, 7, 12, 15], L74201 = [1, 2, 2, 2, 6, 7, 14, 15], L74203 = [1, 2, 2, 2, 6, 7, 15, 16], L74317 = [1, 2, 2, 2, 7, 8, 8, 9], L74323 = [1, 2, 2, 2, 7, 8, 8, 15], L74325 = [1, 2, 2, 2, 7, 8, 9, 10], L74327 = [1, 2, 2, 2, 7, 8, 9, 12], L74329 = [1, 2, 2, 2, 7, 8, 9, 14], L74331 = [1, 2, 2, 2, 7, 8, 9, 16], L74337 = [1, 2, 2, 2, 7, 8, 10, 15], L74346 = [1, 2, 2, 2, 7, 8, 12, 15], L74351 = [1, 2, 2, 2, 7, 8, 14, 15], L74353 = [1, 2, 2, 2, 7, 8, 15, 16], L74355 = [1, 2, 2, 2, 7, 9, 10, 10], L74357 = [1, 2, 2, 2, 7, 9, 10, 12], L74359 = [1, 2, 2, 2, 7, 9, 10, 14], L74361 = [1, 2, 2, 2, 7, 9, 10, 16], L74366 = [1, 2, 2, 2, 7, 9, 12, 12], L74368 = [1, 2, 2, 2, 7, 9, 12, 14], L74370 = [1, 2, 2, 2, 7, 9, 12, 16], L74373 = [1, 2, 2, 2, 7, 9, 14, 14], L74375 = [1, 2, 2, 2, 7, 9, 14, 16], L74377 = [1, 2, 2, 2, 7, 9, 16, 16], L74383 = [1, 2, 2, 2, 7, 10, 10, 15], L74392 = [1, 2, 2, 2, 7, 10, 12, 15], L74397 = [1, 2, 2, 2, 7, 10, 14, 15], L74399 = [1, 2, 2, 2, 7, 10, 15, 16], L74413 = [1, 2, 2, 2, 7, 12, 12, 15], L74418 = [1, 2, 2, 2, 7, 12, 14, 15], L74420 = [1, 2, 2, 2, 7, 12, 15, 16], L74426 = [1, 2, 2, 2, 7, 14, 14, 15], L74428 = [1, 2, 2, 2, 7, 14, 15, 16], L74430 = [1, 2, 2, 2, 7, 15, 16, 16], L75969 = [1, 2, 2, 4, 4, 4, 7, 9], L75975 = [1, 2, 2, 4, 4, 4, 7, 15], L76087 = [1, 2, 2, 4, 4, 6, 7, 9], L76093 = [1, 2, 2, 4, 4, 6, 7, 15], L76134 = [1, 2, 2, 4, 4, 7, 8, 9], L76140 = [1, 2, 2, 4, 4, 7, 8, 15], L76142 = [1, 2, 2, 4, 4, 7, 9, 10], L76144 = [1, 2, 2, 4, 4, 7, 9, 12], L76146 = [1, 2, 2, 4, 4, 7, 9, 14], L76148 = [1, 2, 2, 4, 4, 7, 9, 16], L76154 = [1, 2, 2, 4, 4, 7, 10, 15 L76163 = [1, 2, 2, 4, 4, 7, 12, 15], L76168 = [1, 2, 2, 4, 4, 7, 14, 15], L76170 = [1, 2, 2, 4, 4, 7, 15, 16], L76509 = [1, 2, 2, 4, 6, 6, 7, 9], L76514 = [1, 2, 2, 4, 6, 6, 7, 15], L76554 = [1, 2, 2, 4, 6, 7, 8, 9], L76560 = [1, 2, 2, 4, 6, 7, 8, 15], L76562 = [1, 2, 2, 4, 6, 7, 9, 10], L76564 = [1, 2, 2, 4, 6, 7, 9, 12], L76566 = [1, 2, 2, 4, 6, 7, 9, 14], L76568 = [1, 2, 2, 4, 6, 7, 9, 16], L76574 = [1, 2, 2, 4, 6, 7, 10, 15], L76583 = [1, 2, 2, 4, 6, 7, 12, 15], L76588 = [1, 2, 2, 4, 6, 7, 14, 15], L76590 = [1, 2, 2, 4, 6, 7, 15, 16], L76703 = [1, 2, 2, 4, 7, 8, 8, 9], L76709 = [1, 2, 2, 4, 7, 8, 8, 15], L76711 = [1, 2, 2, 4, 7, 8, 9, 10], L76713 = [1, 2, 2, 4, 7, 8, 9, 12], L76715 = [1, 2, 2, 4, 7, 8, 9, 14], L76717 = [1, 2, 2, 4, 7, 8, 9, 16], L76723 = [1, 2, 2, 4, 7, 8, 10, 15], L76732 = [1, 2, 2, 4, 7, 8, 12, 15], L76737 = [1, 2, 2, 4, 7, 8, 14, 15], L76739 = [1, 2, 2, 4, 7, 8, 15, 16], L76741 = [1, 2, 2, 4, 7, 9, 10, 10],
APPENDIX
235
Table 6. (continued) m = 8 q I indexes of I-isospectral families 32 {0} {80034, 80083, 80088}, {80058, 80305}, {80060, 80068, 80307, 80314}, (cont.) {80067, 80499}, {80080, 80203}, {80109, 80125}, {80112, 80397}, {80113, 80398}, {80115, 80400}, {80117, 80135, 80402, 80416}, {80133, 80414}, {80134, 80522}, {80153, 80160}, {80162, 80287, 80500}, {80163, 80286, 80504}, {80175, 80291}, {80178, 80301}, {80183, 80363}, {80185, 80204}, {80187, 80189, 80197, 80219}, {80209, 80531}, {80210, 80367, 80523}, {80211, 80366, 80532}, {80229, 80371}, {80232, 80386}, {80237, 80376}, {80240, 80392}, {80246, 80559}, {80253, 80568}, {80265, 80571}, {80284, 82592}, {80285, 80600}, {80288, 80601}, {80310, 80626}, {80313, 80630}, {80320, 80605}, {80360, 82620}, {80362, 82626}, {80364, 80670}, {80368, 80671}, {80409, 80726}, {80415, 80733}, {80424, 80675}, {80493, 80570}, {80496, 80567}, {80505, 80627, 82596}, {80508, 80604}, {80517, 80599}, {80536, 80729, 82633}, {80540, 80674}, {80555, 80669}, {80579, 80792}, {80580, 80802}, {80631, 80826},
L76743 = [1, 2, 2, 4, 7, 9, 10, 12], L76745 = [1, 2, 2, 4, 7, 9, 10, 14], L76747 = [1, 2, 2, 4, 7, 9, 10, 16], L76752 = [1, 2, 2, 4, 7, 9, 12, 12], L76754 = [1, 2, 2, 4, 7, 9, 12, 14], L76756 = [1, 2, 2, 4, 7, 9, 12, 16], L76761 = [1, 2, 2, 4, 7, 9, 14, 16], L76763 = [1, 2, 2, 4, 7, 9, 16, 16], L76768 = [1, 2, 2, 4, 7, 10, 10, 15], L76777 = [1, 2, 2, 4, 7, 10, 12, 15], L76781 = [1, 2, 2, 4, 7, 10, 14, 15], L76783 = [1, 2, 2, 4, 7, 10, 15, 16], L76796 = [1, 2, 2, 4, 7, 12, 12, 15], L76801 = [1, 2, 2, 4, 7, 12, 14, 15], L76803 = [1, 2, 2, 4, 7, 12, 15, 16], L76809 = [1, 2, 2, 4, 7, 14, 15, 16], L76811 = [1, 2, 2, 4, 7, 15, 16, 16], L77647 = [1, 2, 2, 6, 6, 6, 7, 9], L77652 = [1, 2, 2, 6, 6, 6, 7, 15], L77686 = [1, 2, 2, 6, 6, 7, 8, 9], L77691 = [1, 2, 2, 6, 6, 7, 8, 15], L77693 = [1, 2, 2, 6, 6, 7, 9, 10], L77695 = [1, 2, 2, 6, 6, 7, 9, 12], L77696 = [1, 2, 2, 6, 6, 7, 9, 14], L77698 = [1, 2, 2, 6, 6, 7, 9, 16], L77703 = [1, 2, 2, 6, 6, 7, 10, 15], L77710 = [1, 2, 2, 6, 6, 7, 12, 15], L77713 = [1, 2, 2, 6, 6, 7, 14, 15], L77715 = [1, 2, 2, 6, 6, 7, 15, 16], L77802 = [1, 2, 2, 6, 7, 8, 8, 9], L77808 = [1, 2, 2, 6, 7, 8, 8, 15], L77810 = [1, 2, 2, 6, 7, 8, 9, 10], L77812 = [1, 2, 2, 6, 7, 8, 9, 12], L77814 = [1, 2, 2, 6, 7, 8, 9, 14], L77816 = [1, 2, 2, 6, 7, 8, 9, 16], L77822 = [1, 2, 2, 6, 7, 8, 10, 15], L77831 = [1, 2, 2, 6, 7, 8, 12, 15], L77836 = [1, 2, 2, 6, 7, 8, 14, 15], L77838 = [1, 2, 2, 6, 7, 8, 15, 16], L77840 = [1, 2, 2, 6, 7, 9, 10, 10], L77842 = [1, 2, 2, 6, 7, 9, 10, 12], L77844 = [1, 2, 2, 6, 7, 9, 10, 14], L77846 = [1, 2, 2, 6, 7, 9, 10, 16], L77851 = [1, 2, 2, 6, 7, 9, 12, 12], L77853 = [1, 2, 2, 6, 7, 9, 12, 14], L77855 = [1, 2, 2, 6, 7, 9, 12, 16], L77858 = [1, 2, 2, 6, 7, 9, 14, 14], L77860 = [1, 2, 2, 6, 7, 9, 14, 16], L77862 = [1, 2, 2, 6, 7, 9, 16, 16], L77867 = [1, 2, 2, 6, 7, 10, 10, 15], L77876 = [1, 2, 2, 6, 7, 10, 12, 15], L77881 = [1, 2, 2, 6, 7, 10, 14, 15], L77883 = [1, 2, 2, 6, 7, 10, 15, 16], L77896 = [1, 2, 2, 6, 7, 12, 12, 15], L77901 = [1, 2, 2, 6, 7, 12, 14, 15], L77903 = [1, 2, 2, 6, 7, 12, 15, 16], L77908 = [1, 2, 2, 6, 7, 14, 14, 15], L77910 = [1, 2, 2, 6, 7, 14, 15, 16], L77912 = [1, 2, 2, 6, 7, 15, 16, 16], L77997 = [1, 2, 2, 6, 8, 11, 13, 14], L78123 = [1, 2, 2, 6, 11, 13, 14, 16], L78165 = [1, 2, 2, 7, 8, 8, 8, 9], L78171 = [1, 2, 2, 7, 8, 8, 8, 15], L78173 = [1, 2, 2, 7, 8, 8, 9, 10], L78175 = [1, 2, 2, 7, 8, 8, 9, 12], L78177 = [1, 2, 2, 7, 8, 8, 9, 14], L78179 = [1, 2, 2, 7, 8, 8, 9, 16], L78185 = [1, 2, 2, 7, 8, 8, 10, 15], L78194 = [1, 2, 2, 7, 8, 8, 12, 1 L78199 = [1, 2, 2, 7, 8, 8, 14, 15], L78201 = [1, 2, 2, 7, 8, 8, 15, 16], L78203 = [1, 2, 2, 7, 8, 9, 10, 10], L78205 = [1, 2, 2, 7, 8, 9, 10, 12], L78207 = [1, 2, 2, 7, 8, 9, 10, 14], L78209 = [1, 2, 2, 7, 8, 9, 10, 16], L78214 = [1, 2, 2, 7, 8, 9, 12, 12], L78216 = [1, 2, 2, 7, 8, 9, 12, 14], L78218 = [1, 2, 2, 7, 8, 9, 12, 16], L78223 = [1, 2, 2, 7, 8, 9, 14, 16], L78225 = [1, 2, 2, 7, 8, 9, 16, 16], L78230 = [1, 2, 2, 7, 8, 10, 10, 15], L78239 = [1, 2, 2, 7, 8, 10, 12, 15], L78243 = [1, 2, 2, 7, 8, 10, 14, 15], L78245 = [1, 2, 2, 7, 8, 10, 15, 16], L78258 = [1, 2, 2, 7, 8, 12, 12, 15], L78263 = [1, 2, 2, 7, 8, 12, 14, 15], L78265 = [1, 2, 2, 7, 8, 12, 15, 16], L78271 = [1, 2, 2, 7, 8, 14, 15, 16], L78273 = [1, 2, 2, 7, 8, 15, 16, 16], L78275 = [1, 2, 2, 7, 9, 10, 10, 10], L78276 = [1, 2, 2, 7, 9, 10, 10, 12], L78278 = [1, 2, 2, 7, 9, 10, 10, 14], L78280 = [1, 2, 2, 7, 9, 10, 10, 16], L78285 = [1, 2, 2, 7, 9, 10, 12, 12], L78287 = [1, 2, 2, 7, 9, 10, 12, 14], L78289 = [1, 2, 2, 7, 9, 10, 12, 16],
236
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 32 {0} {80634, 80858}, {80734, 80905}, {80739, 80968}, {80803, 84107}, {80822, 84054}, (cont.) {80823, 80855, 84043, 84050}, {80825, 84045}, {80859, 84140}, {80895, 80957}, {80898, 84082}, {80900, 84062}, {80901, 80965, 84063, 84074}, {80904, 84067}, {80959, 81303}, {80969, 84191}, {81027, 84095}, {81029, 84091}, {81052, 84097}, {81063, 83351}, {81083, 84109}, {81084, 84119}, {81088, 84110}, {81141, 84122}, {81164, 83382}, {81207, 84144}, {81208, 84161}, {81214, 84145}, {81310, 84164}, {81345, 83441}, {81427, 84197}, {81428, 84223}, {81436, 84198}, {81570, 81576}, {81681, 81686}, {81726, 81732}, {81734, 81744}, {81736, 81752}, {81740, 81757}, {82047, 82052}, {82085, 82090}, {82092, 82101}, {82094, 82107}, {82095, 82109}, {82097, 82111}, {82214, 82220}, {82222, 82232}, {82224, 82240}, {82228, 82245}, {82247, 82268}, {82248, 82272}, {82251, 82275}, {82255, 82285}, {82259, 82290}, {82264, 82295}, {82562, 82570}, {82783, 84265}, {82817, 83668}, {82841, 84309},
L78293 L78306 L78315 L78328 L78339 L78358 L78381 L78394 L78404 L79271 L79302 L79321 L79365 L79373 L79396 L79401 L79455 L79468 L79477 L79524 L79530 L79536 L79552 L79574 L79644 L79671 L79676 L79758 L79788 L79849 L79872 L79918
= [1, 2, 2, 7, 9, 10, 14, 16], L78295 = [1, 2, 2, 7, 9, 10, 16, 16], L78304 = [1, 2, 2, 7, 9, 12, 12, 12], = [1, 2, 2, 7, 9, 12, 12, 14], L78308 = [1, 2, 2, 7, 9, 12, 12, 16], L78313 = [1, 2, 2, 7, 9, 12, 14, 16], = [1, 2, 2, 7, 9, 12, 16, 16], L78321 = [1, 2, 2, 7, 9, 14, 16, 16], L78323 = [1, 2, 2, 7, 9, 16, 16, 16], = [1, 2, 2, 7, 10, 10, 10, 15], L78333 = [1, 2, 2, 7, 10, 10, 12, 15], L78337 = [1, 2, 2, 7, 10, 10, 14, 15], = [1, 2, 2, 7, 10, 10, 15, 16], L78352 = [1, 2, 2, 7, 10, 12, 12, 15], L78356 = [1, 2, 2, 7, 10, 12, 14, 15], = [1, 2, 2, 7, 10, 12, 15, 16], L78362 = [1, 2, 2, 7, 10, 14, 15, 16], L78364 = [1, 2, 2, 7, 10, 15, 16, 16], = [1, 2, 2, 7, 12, 12, 12, 15], L78386 = [1, 2, 2, 7, 12, 12, 14, 15], L78388 = [1, 2, 2, 7, 12, 12, 15, 16], = [1, 2, 2, 7, 12, 14, 15, 16], L78396 = [1, 2, 2, 7, 12, 15, 16, 16], L78402 = [1, 2, 2, 7, 14, 15, 16, 16], = [1, 2, 2, 7, 15, 16, 16, 16], L79258 = [1, 2, 3, 4, 5, 6, 9, 13], L79260 = [1, 2, 3, 4, 5, 6, 9, 15], = [1, 2, 3, 4, 5, 6, 11, 15], L79279 = [1, 2, 3, 4, 5, 6, 13, 15], L79295 = [1, 2, 3, 4, 5, 7, 9, 10], = [1, 2, 3, 4, 5, 7, 10, 11], L79306 = [1, 2, 3, 4, 5, 7, 10, 15], L79318 = [1, 2, 3, 4, 5, 7, 13, 14], = [1, 2, 3, 4, 5, 7, 14, 15], L79342 = [1, 2, 3, 4, 5, 8, 10, 12], L79344 = [1, 2, 3, 4, 5, 8, 10, 14], = [1, 2, 3, 4, 5, 9, 10, 11], L79366 = [1, 2, 3, 4, 5, 9, 10, 12], L79367 = [1, 2, 3, 4, 5, 9, 10, 13], = [1, 2, 3, 4, 5, 9, 11, 14], L79383 = [1, 2, 3, 4, 5, 9, 14, 15], L79390 = [1, 2, 3, 4, 5, 10, 11, 15], = [1, 2, 3, 4, 5, 10, 12, 16], L79397 = [1, 2, 3, 4, 5, 10, 13, 14], L79398 = [1, 2, 3, 4, 5, 10, 13, 15], = [1, 2, 3, 4, 5, 10, 14, 15], L79402 = [1, 2, 3, 4, 5, 10, 14, 16], L79453 = [1, 2, 3, 4, 6, 7, 9, 11], = [1, 2, 3, 4, 6, 7, 9, 13], L79461 = [1, 2, 3, 4, 6, 7, 10, 12], L79467 = [1, 2, 3, 4, 6, 7, 11, 13], = [1, 2, 3, 4, 6, 7, 11, 15], L79471 = [1, 2, 3, 4, 6, 7, 12, 14], L79475 = [1, 2, 3, 4, 6, 7, 13, 15], = [1, 2, 3, 4, 6, 7, 14, 15], L79492 = [1, 2, 3, 4, 6, 8, 9, 12], L79498 = [1, 2, 3, 4, 6, 8, 10, 11], = [1, 2, 3, 4, 6, 9, 10, 12], L79525 = [1, 2, 3, 4, 6, 9, 10, 13], L79529 = [1, 2, 3, 4, 6, 9, 11, 12], = [1, 2, 3, 4, 6, 9, 11, 13], L79532 = [1, 2, 3, 4, 6, 9, 11, 15], L79535 = [1, 2, 3, 4, 6, 9, 12, 14], = [1, 2, 3, 4, 6, 9, 12, 16], L79539 = [1, 2, 3, 4, 6, 9, 14, 15], L79549 = [1, 2, 3, 4, 6, 10, 11, 13], = [1, 2, 3, 4, 6, 10, 11, 16], L79567 = [1, 2, 3, 4, 6, 11, 12, 13], L79568 = [1, 2, 3, 4, 6, 11, 12, 14], = [1, 2, 3, 4, 6, 11, 14, 15], L79620 = [1, 2, 3, 4, 7, 8, 10, 11], L79643 = [1, 2, 3, 4, 7, 9, 10, 11], = [1, 2, 3, 4, 7, 9, 10, 12], L79645 = [1, 2, 3, 4, 7, 9, 10, 13], L79646 = [1, 2, 3, 4, 7, 9, 10, 14], = [1, 2, 3, 4, 7, 10, 11, 13], L79672 = [1, 2, 3, 4, 7, 10, 11, 15], L79673 = [1, 2, 3, 4, 7, 10, 11, 16], = [1, 2, 3, 4, 7, 10, 12, 14], L79677 = [1, 2, 3, 4, 7, 10, 12, 15], L79680 = [1, 2, 3, 4, 7, 10, 13, 15], = [1, 2, 3, 4, 8, 9, 10, 14], L79762 = [1, 2, 3, 4, 8, 9, 11, 13], L79784 = [1, 2, 3, 4, 8, 10, 11, 14], = [1, 2, 3, 4, 8, 10, 12, 13], L79790 = [1, 2, 3, 4, 8, 10, 12, 15], L79843 = [1, 2, 3, 4, 9, 10, 11, 13], = [1, 2, 3, 4, 9, 10, 12, 14], L79855 = [1, 2, 3, 4, 9, 10, 14, 16], L79864 = [1, 2, 3, 4, 9, 11, 13, 16], = [1, 2, 3, 4, 9, 12, 12, 15], L79905 = [1, 2, 3, 4, 10, 11, 13, 14], L79909 = [1, 2, 3, 4, 10, 11, 14, 16], = [1, 2, 3, 4, 10, 12, 13, 15], L79919 = [1, 2, 3, 4, 10, 12, 13, 16], L79923 = [1, 2, 3, 4, 10, 12, 15, 16],
APPENDIX
237
Table 6. (continued) m = 8 q I indexes of I-isospectral families 32 {0} {82900, 83832}, {82933, 82938}, {82971, 82976}, {82978, 82987}, {82980, 82993}, (cont.) {82981, 82995}, {82983, 82997}, {83078, 83083}, {83085, 83094}, {83087, 83100}, {83088, 83102}, {83090, 83104}, {83096, 83187}, {83106, 83123}, {83107, 83127}, {83110, 83130}, {83113, 83137}, {83114, 83139}, {83116, 83141}, {83118, 83143}, {83120, 83145}, {83133, 83251}, {83342, 83348}, {83350, 83360}, {83352, 83368}, {83356, 83373}, {83375, 83396}, {83376, 83400}, {83379, 83403}, {83383, 83413}, {83387, 83418}, {83392, 83423}, {83425, 83460}, {83426, 83464}, {83429, 83467}, {83430, 83471}, {83433, 83474}, {83436, 83477}, {83442, 83489}, {83446, 83494}, {83451, 83499}, {83456, 83504}, {84061, 84072}, {84366, 85793}, {84415, 85891}, {84494, 86057}, {84609, 86314}, {84633, 84638}, {84671, 84676}, {84678, 84687}, {84680, 84693}, {84681, 84695}, {84683, 84697}, {84778, 84783}, {84785, 84794}, {84787, 84800}, {84788, 84802}, {84790, 84804}, {84806, 84824}, {84807, 84828},
L80004 = [1, 2, 3, 5, 6, 7, 8, 12], L80006 = [1, 2, 3, 5, 6, 7, 8, 14], L80007 = [1, 2, 3, 5, 6, 7, 8, 15], L80009 = [1, 2, 3, 5, 6, 7, 9, 10], L80010 = [1, 2, 3, 5, 6, 7, 9, 11], L80011 = [1, 2, 3, 5, 6, 7, 9, 13], L80012 = [1, 2, 3, 5, 6, 7, 9, 14], L80013 = [1, 2, 3, 5, 6, 7, 9, 15], L80015 = [1, 2, 3, 5, 6, 7, 10, 11], L80017 = [1, 2, 3, 5, 6, 7, 10, 13], L80018 = [1, 2, 3, 5, 6, 7, 10, 14], L80019 = [1, 2, 3, 5, 6, 7, 10, 15], L80021 = [1, 2, 3, 5, 6, 7, 11, 12], L80022 = [1, 2, 3, 5, 6, 7, 11, 13], L80023 = [1, 2, 3, 5, 6, 7, 11, 14], L80024 = [1, 2, 3, 5, 6, 7, 11, 15], L80028 = [1, 2, 3, 5, 6, 7, 12, 15], L80029 = [1, 2, 3, 5, 6, 7, 12, 16], L80030 = [1, 2, 3, 5, 6, 7, 13, 15], L80032 = [1, 2, 3, 5, 6, 7, 14, 15], L80033 = [1, 2, 3, 5, 6, 7, 14, 16], L80034 = [1, 2, 3, 5, 6, 7, 15, 16], L80045 = [1, 2, 3, 5, 6, 8, 9, 10], L80046 = [1, 2, 3, 5, 6, 8, 9, 11], L80048 = [1, 2, 3, 5, 6, 8, 9, 14], L80049 = [1, 2, 3, 5, 6, 8, 9, 15], L80058 = [1, 2, 3, 5, 6, 8, 11, 13], L80060 = [1, 2, 3, 5, 6, 8, 11, 15], L80064 = [1, 2, 3, 5, 6, 8, 12, 14], L80067 = [1, 2, 3, 5, 6, 8, 13, 14], L80068 = [1, 2, 3, 5, 6, 8, 13, 15], L80071 = [1, 2, 3, 5, 6, 8, 14, 15], L80075 = [1, 2, 3, 5, 6, 9, 10, 11], L80076 = [1, 2, 3, 5, 6, 9, 10, 13], L80077 = [1, 2, 3, 5, 6, 9, 10, 14], L80078 = [1, 2, 3, 5, 6, 9, 10, 15], L80079 = [1, 2, 3, 5, 6, 9, 10, 16], L80080 = [1, 2, 3, 5, 6, 9, 11, 13], L80081 = [1, 2, 3, 5, 6, 9, 11, 14], L80082 = [1, 2, 3, 5, 6, 9, 11, 15], L80083 = [1, 2, 3, 5, 6, 9, 11, 16], L80084 = [1, 2, 3, 5, 6, 9, 13, 14], L80085 = [1, 2, 3, 5, 6, 9, 13, 15], L80087 = [1, 2, 3, 5, 6, 9, 14, 16], L80088 = [1, 2, 3, 5, 6, 9, 15, 16], L80098 = [1, 2, 3, 5, 6, 10, 13, 14], L80109 = [1, 2, 3, 5, 6, 11, 12, 15], L80111 = [1, 2, 3, 5, 6, 11, 13, 14], L80112 = [1, 2, 3, 5, 6, 11, 13, 15], L80113 = [1, 2, 3, 5, 6, 11, 13, 16], L80115 = [1, 2, 3, 5, 6, 11, 14, 15], L80117 = [1, 2, 3, 5, 6, 11, 15, 16], L80124 = [1, 2, 3, 5, 6, 12, 13, 14], L80125 = [1, 2, 3, 5, 6, 12, 13, 15], L80128 = [1, 2, 3, 5, 6, 12, 14, 15], L80129 = [1, 2, 3, 5, 6, 12, 14, 16], L80133 = [1, 2, 3, 5, 6, 13, 14, 15], L80134 = [1, 2, 3, 5, 6, 13, 14, 16], L80135 = [1, 2, 3, 5, 6, 13, 15, 16], L80140 = [1, 2, 3, 5, 6, 14, 15, 16], L80153 = [1, 2, 3, 5, 7, 8, 9, 10], L80160 = [1, 2, 3, 5, 7, 8, 10, 11], L80162 = [1, 2, 3, 5, 7, 8, 10, 13], L80163 = [1, 2, 3, 5, 7, 8, 10, 14], L80171 = [1, 2, 3, 5, 7, 8, 12, 13], L80175 = [1, 2, 3, 5, 7, 8, 13, 14], L80178 = [1, 2, 3, 5, 7, 8, 14, 15], L80182 = [1, 2, 3, 5, 7, 9, 10, 12], L80183 = [1, 2, 3, 5, 7, 9, 10, 13], L80184 = [1, 2, 3, 5, 7, 9, 10, 14], L80185 = [1, 2, 3, 5, 7, 9, 10, 16], L80187 = [1, 2, 3, 5, 7, 9, 11, 13], L80189 = [1, 2, 3, 5, 7, 9, 11, 15], L80197 = [1, 2, 3, 5, 7, 9, 13, 15], L80203 = [1, 2, 3, 5, 7, 10, 11, 13], L80204 = [1, 2, 3, 5, 7, 10, 11, 16], L80206 = [1, 2, 3, 5, 7, 10, 12, 13], L80209 = [1, 2, 3, 5, 7, 10, 13, 14], L80210 = [1, 2, 3, 5, 7, 10, 13, 16], L80211 = [1, 2, 3, 5, 7, 10, 14, 16], L80219 = [1, 2, 3, 5, 7, 11, 13, 15], L80229 = [1, 2, 3, 5, 7, 12, 13, 14], L80231 = [1, 2, 3, 5, 7, 12, 13, 16], L80232 = [1, 2, 3, 5, 7, 12, 14, 15], L80237 = [1, 2, 3, 5, 7, 13, 14, 16], L80240 = [1, 2, 3, 5, 7, 14, 15, 16], L80246 = [1, 2, 3, 5, 8, 8, 8, 10], L80253 = [1, 2, 3, 5, 8, 8, 9, 10], L80265 = [1, 2, 3, 5, 8, 8, 10, 16], L80284 = [1, 2, 3, 5, 8, 9, 10, 12], L80285 = [1, 2, 3, 5, 8, 9, 10, 13], L80286 = [1, 2, 3, 5, 8, 9, 10, 14], L80287 = [1, 2, 3, 5, 8, 9, 10, 15], L80288 = [1, 2, 3, 5, 8, 9, 10, 16], L80291 = [1, 2, 3, 5, 8, 9, 11, 14], L80301 = [1, 2, 3, 5, 8, 9, 14, 15], L80305 = [1, 2, 3, 5, 8, 10, 11, 13], L80307 =
238
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 32 {0} {84810, 84832}, {84813, 84839}, {84814, 84841}, {84816, 84843}, {84818, 84845}, (cont.) {84820, 84847}, {85013, 85018}, {85015, 85157}, {85020, 85029}, {85022, 85035}, {85023, 85037}, {85025, 85039}, {85032, 85183}, {85041, 85058}, {85042, 85062}, {85045, 85065}, {85048, 85072}, {85049, 85074}, {85051, 85076}, {85053, 85078}, {85055, 85080}, {85069, 85235}, {85082, 85111}, {85083, 85114}, {85085, 85116}, {85086, 85120}, {85089, 85123}, {85093, 85126}, {85097, 85134}, {85098, 85136}, {85100, 85138}, {85102, 85140}, {85104, 85142}, {85106, 85144}, {85108, 85146}, {85131, 85324}, {85441, 85447}, {85449, 85459}, {85451, 85467}, {85455, 85472}, {85474, 85495}, {85475, 85499}, {85478, 85502}, {85482, 85512}, {85486, 85517}, {85491, 85522}, {85524, 85559}, {85525, 85563}, {85528, 85566}, {85529, 85570}, {85532, 85573}, {85535, 85576}, {85541, 85588}, {85545, 85593}, {85550, 85598}, {85555, 85603}, {85605, 85657}, {85606, 85661}, {85609, 85664}, {85610, 85668},
[1, 2, 3, 5, 8, 10, 11, 15], L80310 = [1, 2, 3, 5, 8, 10, 12, 13], L80313 = [1, 2, 3, 5, 8, 10, 13, 14], L80314 = [1, 2, 3, 5, 8, 10, 13, 15], L80317 = [1, 2, 3, 5, 8, 10, 14, 15], L80320 = [1, 2, 3, 5, 8, 10, 16, 16], L80360 = [1, 2, 3, 5, 9, 10, 12, 13], L80362 = [1, 2, 3, 5, 9, 10, 12, 16], L80363 = [1, 2, 3, 5, 9, 10, 13, 15], L80364 = [1, 2, 3, 5, 9, 10, 13, 16], L80365 = [1, 2, 3, 5, 9, 10, 14, 15], L80366 = [1, 2, 3, 5, 9, 10, 14, 16], L80367 = [1, 2, 3, 5, 9, 10, 15, 16], L80368 = [1, 2, 3, 5, 9, 10, 16, 16], L80371 = [1, 2, 3, 5, 9, 11, 12, 14], L80376 = [1, 2, 3, 5, 9, 11, 14, 16], L80386 = [1, 2, 3, 5, 9, 12, 14, 15], L80392 = [1, 2, 3, 5, 9, 14, 15, 16], L80396 = [1, 2, 3, 5, 10, 11, 13, 14], L80397 = [1, 2, 3, 5, 10, 11, 13, 15], L80398 = [1, 2, 3, 5, 10, 11, 13, 16], L80400 = [1, 2, 3, 5, 10, 11, 14, 15], L80402 = [1, 2, 3, 5, 10, 11, 15, 16], L80409 = [1, 2, 3, 5, 10, 12, 13, 16], L80414 = [1, 2, 3, 5, 10, 13, 14, 15], L80415 = [1, 2, 3, 5, 10, 13, 14, 16], L80416 = [1, 2, 3, 5, 10, 13, 15, 16], L80421 = [1, 2, 3, 5, 10, 14, 15, 16], L80424 = [1, 2, 3, 5, 10, 16, 16, 16], L80493 = [1, 2, 3, 6, 7, 8, 8, 10], L80496 = [1, 2, 3, 6, 7, 8, 8, 14], L80499 = [1, 2, 3, 6, 7, 8, 9, 10], L80500 = [1, 2, 3, 6, 7, 8, 9, 11], L80503 = [1, 2, 3, 6, 7, 8, 10, 10 L80504 = [1, 2, 3, 6, 7, 8, 10, 11], L80505 = [1, 2, 3, 6, 7, 8, 10, 12], L80506 = [1, 2, 3, 6, 7, 8, 10, 14], L80508 = [1, 2, 3, 6, 7, 8, 10, 16], L80517 = [1, 2, 3, 6, 7, 8, 14, 16], L80521 = [1, 2, 3, 6, 7, 9, 10, 14], L80522 = [1, 2, 3, 6, 7, 9, 10, 16], L80523 = [1, 2, 3, 6, 7, 9, 11, 16], L80530 = [1, 2, 3, 6, 7, 10, 10, 16], L80531 = [1, 2, 3, 6, 7, 10, 11, 15], L80532 = [1, 2, 3, 6, 7, 10, 11, 16], L80536 = [1, 2, 3, 6, 7, 10, 12, 16], L80538 = [1, 2, 3, 6, 7, 10, 14, 16], L80540 = [1, 2, 3, 6, 7, 10, 16, 16], L80555 = [1, 2, 3, 6, 7, 14, 16, 16], L80559 = [1, 2, 3, 6, 8, 8, 8, 9], L80567 = [1, 2, 3, 6, 8, 8, 9, 10], L80568 = [1, 2, 3, 6, 8, 8, 9, 11], L80570 = [1, 2, 3, 6, 8, 8, 9, 14], L80571 = [1, 2, 3, 6, 8, 8, 9, 16], L80579 = [1, 2, 3, 6, 8, 8, 11, 13], L80580 = [1, 2, 3, 6, 8, 8, 11, 1 L80597 = [1, 2, 3, 6, 8, 9, 10, 13], L80598 = [1, 2, 3, 6, 8, 9, 10, 14], L80599 = [1, 2, 3, 6, 8, 9, 10, 16], L80600 = [1, 2, 3, 6, 8, 9, 11, 13], L80601 = [1, 2, 3, 6, 8, 9, 11, 16], L80604 = [1, 2, 3, 6, 8, 9, 14, 16], L80605 = [1, 2, 3, 6, 8, 9, 16, 16], L80626 = [1, 2, 3, 6, 8, 11, 12, 13], L80627 = [1, 2, 3, 6, 8, 11, 12, 14], L80630 = [1, 2, 3, 6, 8, 11, 13, 14], L80631 = [1, 2, 3, 6, 8, 11, 13, 16], L80633 = [1, 2, 3, 6, 8, 11, 14, 15], L80634 = [1, 2, 3, 6, 8, 11, 14, 16], L80667 = [1, 2, 3, 6, 9, 10, 13, 16], L80668 = [1, 2, 3, 6, 9, 10, 14, 16], L80669 = [1, 2, 3, 6, 9, 10, 16, 16], L80670 = [1, 2, 3, 6, 9, 11, 13, 16], L80671 = [1, 2, 3, 6, 9, 11, 16, 16], L80674 = [1, 2, 3, 6, 9, 14, 16, 16], L80675 = [1, 2, 3, 6, 9, 16, 16, 16], L80725 = [1, 2, 3, 6, 11, 12, 13, 14], L80726 = [1, 2, 3, 6, 11, 12, 13, 16], L80729 = [1, 2, 3, 6, 11, 12, 14, 16], L80733 = [1, 2, 3, 6, 11, 13, 14, 16], L80734 = [1, 2, 3, 6, 11, 13, 16, 16], L80738 = [1, 2, 3, 6, 11, 14, 15, 16], L80739 = [1, 2, 3, 6, 11, 14, 16, 16], L80792 = [1, 2, 3, 7, 8, 8, 9, 10], L80802 = [1, 2, 3, 7, 8, 8, 10, 14], L80803 = [1, 2, 3, 7, 8, 8, 10, 15], L80822 = [1, 2, 3, 7, 8, 9, 10, 12], L80823 = [1, 2, 3, 7, 8, 9, 10, 13], L80825 = [1, 2, 3, 7, 8, 9, 10, 15], L80826 = [1, 2, 3, 7, 8, 9, 10, 16], L80855 = [1, 2, 3, 7, 8, 10, 13, 15], L80858 = [1, 2, 3, 7, 8, 10, 14, 16], L80859 = [1, 2, 3, 7, 8, 10, 15, 16], L80895 = [1, 2, 3, 7, 9, 10, 12, 13], L80898 = [1, 2, 3, 7, 9, 10, 12, 16], L80900 = [1, 2, 3, 7, 9, 10, 13, 15], L80901 = [1, 2, 3, 7, 9, 10, 13, 16], L80904 = [1, 2, 3, 7, 9, 10, 15, 16],
APPENDIX
239
Table 6. (continued) m = 8 q I indexes of I-isospectral families 32 {0} {85613, 85671}, {85616, 85674}, {85617, 85678}, {85620, 85681}, {85623, 85684}, (cont.) {85626, 85687}, {85634, 85701}, {85638, 85706}, {85643, 85711}, {85648, 85716}, {85653, 85721}, {86460, 86461}, {86463, 86464, 86474, 86476}, {86479, 86506}, {86481, 86489, 86505, 86517}, {86566, 86567}, {86633, 86634}, {86636, 86637, 86663, 86665}, {86640, 86644}, {86643, 86646}, {86647, 86688}, {86648, 86649, 86685, 86689}, {86652, 86653, 86687, 86691}, {86668, 86741}, {86670, 86678, 86740, 86752}, {86696, 86712, 86762, 86785}, {86700, 86767}, {86704, 86722, 86766, 86789}, {86748, 86841}, {86784, 86922}, {86838, 86839}, {86915, 86916}, {86918, 86919}, {87032, 87033}, {87034, 87083}, {87035, 87036, 87082, 87084}, {87039, 87043, 87047, 87104}, {87042, 87045}, {87048, 87107}, {87050, 87051, 87106, 87108}, {87059, 87063, 87068, 87146}, {87062, 87065}, {87069, 87149}, {87071, 87072, 87148, 87150}, {87087, 87219}, {87089, 87097, 87218, 87229}, {87112, 87127}, {87116, 87241}, {87120, 87137, 87240, 87260},
L80905 = [1, 2, 3, 7, 9, 10, 16, 16], L80957 = [1, 2, 3, 7, 10, 12, 13, 15], L80959 = [1, 2, 3, 7, 10, 12, 14, 15], L80965 = [1, 2, 3, 7, 10, 13, 15, 16], L80968 = [1, 2, 3, 7, 10, 14, 16, 16], L80969 = [1, 2, 3, 7, 10, 15, 16, 16], L81027 = [1, 2, 3, 8, 8, 8, 10, 13], L81029 = [1, 2, 3, 8, 8, 8, 10, 15], L81052 = [1, 2, 3, 8, 8, 9, 10, 14], L81063 = [1, 2, 3, 8, 8, 9, 12, 15], L81083 = [1, 2, 3, 8, 8, 10, 13, 15], L81084 = [1, 2, 3, 8, 8, 10, 13, 16], L81088 = [1, 2, 3, 8, 8, 10, 15, 16], L81141 = [1, 2, 3, 8, 9, 10, 14, 16], L81164 = [1, 2, 3, 8, 9, 12, 15, 16], L81207 = [1, 2, 3, 8, 10, 13, 15, 16], L81208 = [1, 2, 3, 8, 10, 13, 16, 16], L81214 = [1, 2, 3, 8, 10, 15, 16, 16], L81303 = [1, 2, 3, 9, 10, 12, 14, 15], L81310 = [1, 2, 3, 9, 10, 14, 16, 16], L81345 = [1, 2, 3, 9, 12, 15, 16, 16], L81427 = [1, 2, 3, 10, 13, 15, 16, 16], L81428 = [1, 2, 3, 10, 13, 16, 16, 16], L81436 = [1, 2, 3, 10, 15, 16, 16, 16], L81570 = [1, 2, 4, 4, 4, 4, 7, 9], L81576 = [1, 2, 4, 4, 4, 4, 7, 15], L81681 = [1, 2, 4, 4, 4, 6, 7, 9], L81686 = [1, 2, 4, 4, 4, 6, 7, 15], L81726 = [1, 2, 4, 4, 4, 7, 8, 9], L81732 = [1, 2, 4, 4, 4, 7, 8, 15], L81734 = [1, 2, 4, 4, 4, 7, 9, 10], L81736 = [1, 2, 4, 4, 4, 7, 9, 12], L81740 = [1, 2, 4, 4, 4, 7, 9, 16], L81744 = [1, 2, 4, 4, 4, 7, 10, 15], L81752 = [1, 2, 4, 4, 4, 7, 12, 15], L81757 = [1, 2, 4, 4, 4, 7, 15, 16], L82047 = [1, 2, 4, 4, 6, 6, 7, 9], L82052 = [1, 2, 4, 4, 6, 6, 7, 15 L82085 = [1, 2, 4, 4, 6, 7, 8, 9], L82090 = [1, 2, 4, 4, 6, 7, 8, 15], L82092 = [1, 2, 4, 4, 6, 7, 9, 10], L82094 = [1, 2, 4, 4, 6, 7, 9, 12], L82095 = [1, 2, 4, 4, 6, 7, 9, 14], L82097 = [1, 2, 4, 4, 6, 7, 9, 16], L82101 = [1, 2, 4, 4, 6, 7, 10, 15 L82107 = [1, 2, 4, 4, 6, 7, 12, 15], L82109 = [1, 2, 4, 4, 6, 7, 14, 15], L82111 = [1, 2, 4, 4, 6, 7, 15, 16], L82214 = [1, 2, 4, 4, 7, 8, 8, 9], L82220 = [1, 2, 4, 4, 7, 8, 8, 15], L82222 = [1, 2, 4, 4, 7, 8, 9, 10], L82224 = [1, 2, 4, 4, 7, 8, 9, 12], L82228 = [1, 2, 4, 4, 7, 8, 9, 16], L82232 = [1, 2, 4, 4, 7, 8, 10, 15], L82240 = [1, 2, 4, 4, 7, 8, 12, 1 L82245 = [1, 2, 4, 4, 7, 8, 15, 16], L82247 = [1, 2, 4, 4, 7, 9, 10, 10], L82248 = [1, 2, 4, 4, 7, 9, 10, 12], L82251 = [1, 2, 4, 4, 7, 9, 10, 16], L82252 = [1, 2, 4, 4, 7, 9, 11, 12], L82255 = [1, 2, 4, 4, 7, 9, 12, 12], L82259 = [1, 2, 4, 4, 7, 9, 12, 16], L82264 = [1, 2, 4, 4, 7, 9, 16, 16], L82268 = [1, 2, 4, 4, 7, 10, 10, 15], L82272 = [1, 2, 4, 4, 7, 10, 12, 15], L82275 = [1, 2, 4, 4, 7, 10, 15, 16], L82285 = [1, 2, 4, 4, 7, 12, 12, 15], L82290 = [1, 2, 4, 4, 7, 12, 15, 16], L82295 = [1, 2, 4, 4, 7, 15, 16, 16], L82558 = [1, 2, 4, 5, 6, 7, 8, 14], L82562 = [1, 2, 4, 5, 6, 7, 9, 11], L82570 = [1, 2, 4, 5, 6, 7, 11, 15], L82577 = [1, 2, 4, 5, 6, 7, 14, 16], L82589 = [1, 2, 4, 5, 6, 8, 9, 10], L82592 = [1, 2, 4, 5, 6, 8, 9, 13], L82596 = [1, 2, 4, 5, 6, 8, 10, 13], L82599 = [1, 2, 4, 5, 6, 8, 11, 12], L82607 = [1, 2, 4, 5, 6, 8, 12, 15], L82616 = [1, 2, 4, 5, 6, 9, 10, 12], L82618 = [1, 2, 4, 5, 6, 9, 10, 16], L82620 = [1, 2, 4, 5, 6, 9, 11, 13], L82626 = [1, 2, 4, 5, 6, 9, 13, 16], L82633 = [1, 2, 4, 5, 6, 10, 13, 16], L82638 = [1, 2, 4, 5, 6, 11, 12, 13], L82640 = [1, 2, 4, 5, 6, 11, 12, 15], L82641 = [1, 2, 4, 5, 6, 11, 12, 16], L82657 = [1, 2, 4, 5, 6, 12, 15, 16], L82783 = [1, 2, 4, 5, 8, 9, 11, 13], L82817 = [1, 2, 4, 5, 8, 12, 13, 14], L82841 = [1, 2, 4, 5, 9, 11, 13, 16], L82900 = [1, 2, 4, 5, 12, 13, 14, 16], L82933 = [1, 2, 4, 6, 6, 6, 7, 9], L82938 = [1, 2, 4, 6, 6, 6, 7, 15], L82971 = [1, 2, 4, 6, 6, 7, 8, 9], L82976 = [1, 2, 4, 6, 6, 7, 8, 15],
240
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 32 {0} {87158, 87184}, {87164, 87277}, {87170, 87198, 87276, 87307}, {87212, 87322}, (cont.) {87228, 87358}, {87259, 87427}, {87306, 87545}, {87354, 87355}, {87423, 87424}, {87541, 87542}, {87708, 87748}, {87709, 87710, 87712, 87755}, {87713, 87756}, {87717, 87718, 87721, 87773}, {87722, 87774}, {87727, 87728, 87732, 87804}, {87733, 87805}, {87739, 87740, 87745, 87850}, {87746, 87851}, {87759, 87766}, {87781, 87795}, {87816, 87839}, {87866, 87900}, {87913, 88020}, {87918, 88029}, {87929, 88053}, {87948, 88104}, {87977, 88198}, {88018, 88355}, {88676, 88679}, {88844, 88847}, {88874, 88877}, {88880, 88886}, {88882, 88888}, {89214, 89217}, {89244, 89247}, {89249, 89255}, {89250, 89258}, {89252, 89260}, {89322, 89325}, {89328, 89334}, {89330, 89336}, {89341, 89350}, {89343, 89352}, {89345, 89354}, {89894, 89897}, {89924, 89927}, {89929, 89935}, {89930, 89938}, {89932, 89940}, {90003, 90006}, {90008, 90014}, {90009, 90017}, {90011, 90019}, {90022, 90033},
L82978 = [1, 2, 4, 6, 6, 7, 9, 10], L82980 = [1, 2, 4, 6, 6, 7, 9, 12], L82981 = [1, 2, 4, 6, 6, 7, 9, 14], L82983 = [1, 2, 4, 6, 6, 7, 9, 16], L82987 = [1, 2, 4, 6, 6, 7, 10, 15], L82993 = [1, 2, 4, 6, 6, 7, 12, 15], L82995 = [1, 2, 4, 6, 6, 7, 14, 15], L82997 = [1, 2, 4, 6, 6, 7, 15, 16], L83078 = [1, 2, 4, 6, 7, 8, 8, 9], L83083 = [1, 2, 4, 6, 7, 8, 8, 15 L83085 = [1, 2, 4, 6, 7, 8, 9, 10], L83087 = [1, 2, 4, 6, 7, 8, 9, 12], L83088 = [1, 2, 4, 6, 7, 8, 9, 14], L83090 = [1, 2, 4, 6, 7, 8, 9, 16], L83094 = [1, 2, 4, 6, 7, 8, 10, 15], L83096 = [1, 2, 4, 6, 7, 8, 11, 12], L83100 = [1, 2, 4, 6, 7, 8, 12, 15], L83102 = [1, 2, 4, 6, 7, 8, 14, 15], L83104 = [1, 2, 4, 6, 7, 8, 15, 16], L83106 = [1, 2, 4, 6, 7, 9, 10, 10], L83107 = [1, 2, 4, 6, 7, 9, 10, 12], L83110 = [1, 2, 4, 6, 7, 9, 10, 16], L83113 = [1, 2, 4, 6, 7, 9, 12, 12], L83114 = [1, 2, 4, 6, 7, 9, 12, 14], L83116 = [1, 2, 4, 6, 7, 9, 12, 16], L83118 = [1, 2, 4, 6, 7, 9, 14, 16], L83120 = [1, 2, 4, 6, 7, 9, 16, 16], L83123 = [1, 2, 4, 6, 7, 10, 10, 15], L83127 = [1, 2, 4, 6, 7, 10, 12, 15], L83130 = [1, 2, 4, 6, 7, 10, 15, 16], L83133 = [1, 2, 4, 6, 7, 11, 12, 16], L83137 = [1, 2, 4, 6, 7, 12, 12, 15], L83139 = [1, 2, 4, 6, 7, 12, 14, 15], L83141 = [1, 2, 4, 6, 7, 12, 15, 16], L83143 = [1, 2, 4, 6, 7, 14, 15, 16], L83145 = [1, 2, 4, 6, 7, 15, 16, 16], L83187 = [1, 2, 4, 6, 8, 9, 11, 12], L83251 = [1, 2, 4, 6, 9, 11, 12, 16], L83342 = [1, 2, 4, 7, 8, 8, 8, 9], L83348 = [1, 2, 4, 7, 8, 8, 8, 15], L83350 = [1, 2, 4, 7, 8, 8, 9, 10 L83351 = [1, 2, 4, 7, 8, 8, 9, 11], L83352 = [1, 2, 4, 7, 8, 8, 9, 12], L83356 = [1, 2, 4, 7, 8, 8, 9, 16], L83360 = [1, 2, 4, 7, 8, 8, 10, 15], L83368 = [1, 2, 4, 7, 8, 8, 12, 15], L83373 = [1, 2, 4, 7, 8, 8, 15, 16], L83375 = [1, 2, 4, 7, 8, 9, 10, 10], L83376 = [1, 2, 4, 7, 8, 9, 10, 12], L83379 = [1, 2, 4, 7, 8, 9, 10, 16], L83382 = [1, 2, 4, 7, 8, 9, 11, 16], L83383 = [1, 2, 4, 7, 8, 9, 12, 12], L83387 = [1, 2, 4, 7, 8, 9, 12, 16], L83392 = [1, 2, 4, 7, 8, 9, 16, 16], L83396 = [1, 2, 4, 7, 8, 10, 10, 15], L83400 = [1, 2, 4, 7, 8, 10, 12, 15], L83403 = [1, 2, 4, 7, 8, 10, 15, 16], L83413 = [1, 2, 4, 7, 8, 12, 12, 15], L83418 = [1, 2, 4, 7, 8, 12, 15, 16], L83423 = [1, 2, 4, 7, 8, 15, 16, 16], L83425 = [1, 2, 4, 7, 9, 10, 10, 10], L83426 = [1, 2, 4, 7, 9, 10, 10, 12], L83429 = [1, 2, 4, 7, 9, 10, 10, 16], L83430 = [1, 2, 4, 7, 9, 10, 12, 12], L83433 = [1, 2, 4, 7, 9, 10, 12, 16], L83436 = [1, 2, 4, 7, 9, 10, 16, 16], L83441 = [1, 2, 4, 7, 9, 11, 16, 16], L83442 = [1, 2, 4, 7, 9, 12, 12, 12], L83446 = [1, 2, 4, 7, 9, 12, 12, 16], L83451 = [1, 2, 4, 7, 9, 12, 16, 16], L83456 = [1, 2, 4, 7, 9, 16, 16, 16], L83460 = [1, 2, 4, 7, 10, 10, 10, 15], L83464 = [1, 2, 4, 7, 10, 10, 12, 15], L83467 = [1, 2, 4, 7, 10, 10, 15, 16], L83471 = [1, 2, 4, 7, 10, 12, 12, 15], L83474 = [1, 2, 4, 7, 10, 12, 15, 16], L83477 = [1, 2, 4, 7, 10, 15, 16, 16], L83489 = [1, 2, 4, 7, 12, 12, 12, 15], L83494 = [1, 2, 4, 7, 12, 12, 15, 16], L83499 = [1, 2, 4, 7, 12, 15, 16, 16], L83504 = [1, 2, 4, 7, 15, 16, 16, 16], L83668 = [1, 2, 4, 8, 11, 12, 13, 14], L83832 = [1, 2, 4, 11, 12, 13, 14, 16], L84043 = [1, 2, 5, 6, 7, 8, 9, 11], L84045 = [1, 2, 5, 6, 7, 8, 9, 15], L84050 = [1, 2, 5, 6, 7, 8, 11, 15], L84054 = [1, 2, 5, 6, 7, 8, 12, 1 L84061 = [1, 2, 5, 6, 7, 9, 11, 12], L84062 = [1, 2, 5, 6, 7, 9, 11, 15], L84063 = [1, 2, 5, 6, 7, 9, 11, 16], L84067 = [1, 2, 5, 6, 7, 9, 15, 16], L84072 = [1, 2, 5, 6, 7, 11, 12, 15], L84074 = [1, 2, 5, 6, 7, 11, 15, 16], L84082 = [1, 2, 5, 6, 7, 12, 15, 16], L84091 = [1, 2, 5, 6, 8, 8, 8, 11], L84095 = [1, 2, 5, 6, 8, 8, 8, 15], L84097 = [1, 2, 5, 6, 8, 8, 9, 10], L84107 = [1, 2, 5, 6, 8, 8, 11, 13], L84109 = [1, 2, 5, 6, 8, 8, 11, 15],
APPENDIX
241
Table 6. (continued) m = 8 q I indexes of I-isospectral families 32 {0} {90024, 90035}, {90025, 90038}, {90027, 90040}, {90029, 90042}, {90166, 90169}, (cont.) {90172, 90178}, {90174, 90180}, {90185, 90194}, {90187, 90196}, {90189, 90198}, {90205, 90217}, {90207, 90219}, {90209, 90221}, {90211, 90223}, {90989, 90992}, {91019, 91022}, {91024, 91030}, {91025, 91033}, {91027, 91035}, {91098, 91101}, {91103, 91109}, {91104, 91112}, {91106, 91114}, {91116, 91127}, {91117, 91130}, {91119, 91132}, {91120, 91135}, {91122, 91137}, {91124, 91139}, {91266, 91269}, {91271, 91277}, {91272, 91280}, {91274, 91282}, {91285, 91296}, {91287, 91298}, {91288, 91301}, {91290, 91303}, {91292, 91305}, {91310, 91326}, {91312, 91328}, {91314, 91330}, {91315, 91333}, {91317, 91335}, {91319, 91337}, {91321, 91339}, {91563, 91566}, {91569, 91575}, {91571, 91577}, {91582, 91591}, {91584, 91593}, {91586, 91595}, {91602, 91614}, {91604, 91616}, {91606, 91618}, {91608, 91620}, {91629, 91644}, {91631, 91646}, {91633, 91648}, {91635, 91650}, {91637, 91652}
L84110 = [1, 2, 5, 6, 8, 8, 11, 16], L84119 = [1, 2, 5, 6, 8, 8, 15, 16], L84122 = [1, 2, 5, 6, 8, 9, 10, 16], L84140 = [1, 2, 5, 6, 8, 11, 13, 16], L84144 = [1, 2, 5, 6, 8, 11, 15, 16], L84145 = [1, 2, 5, 6, 8, 11, 16, 16], L84161 = [1, 2, 5, 6, 8, 15, 16, 16], L84164 = [1, 2, 5, 6, 9, 10, 16, 16], L84191 = [1, 2, 5, 6, 11, 13, 16, 16], L84197 = [1, 2, 5, 6, 11, 15, 16, 16], L84198 = [1, 2, 5, 6, 11, 16, 16, 16], L84223 = [1, 2, 5, 6, 15, 16, 16, 16], L84265 = [1, 2, 5, 7, 8, 11, 12, 13], L84309 = [1, 2, 5, 7, 11, 12, 13, 16], L84366 = [1, 2, 5, 8, 8, 8, 13, 14], L84415 = [1, 2, 5, 8, 8, 13, 14, 16], L84494 = [1, 2, 5, 8, 13, 14, 16, 16], L84609 = [1, 2, 5, 13, 14, 16, 16, 16], L84633 = [1, 2, 6, 6, 6, 6, 7, 9], L84638 = [1, 2, 6, 6, 6, 6, 7, 15], L84671 = [1, 2, 6, 6, 6, 7, 8, 9], L84676 = [1, 2, 6, 6, 6, 7, 8, 15], L84678 = [1, 2, 6, 6, 6, 7, 9, 10], L84680 = [1, 2, 6, 6, 6, 7, 9, 12], L84681 = [1, 2, 6, 6, 6, 7, 9, 14], L84683 = [1, 2, 6, 6, 6, 7, 9, 16], L84687 = [1, 2, 6, 6, 6, 7, 10, 15], L84693 = [1, 2, 6, 6, 6, 7, 12, 15], L84695 = [1, 2, 6, 6, 6, 7, 14, 15], L84697 = [1, 2, 6, 6, 6, 7, 15, 16], L84778 = [1, 2, 6, 6, 7, 8, 8, 9], L84783 = [1, 2, 6, 6, 7, 8, 8, 15], L84785 = [1, 2, 6, 6, 7, 8, 9, 10], L84787 = [1, 2, 6, 6, 7, 8, 9, 12], L84788 = [1, 2, 6, 6, 7, 8, 9, 14], L84790 = [1, 2, 6, 6, 7, 8, 9, 16], L84794 = [1, 2, 6, 6, 7, 8, 10, 15], L84800 = [1, 2, 6, 6, 7, 8, 12, 15], L84802 = [1, 2, 6, 6, 7, 8, 14, 15], L84804 = [1, 2, 6, 6, 7, 8, 15, 16], L84806 = [1, 2, 6, 6, 7, 9, 10, 10], L84807 = [1, 2, 6, 6, 7, 9, 10, 12], L84808 = [1, 2, 6, 6, 7, 9, 10, 14], L84810 = [1, 2, 6, 6, 7, 9, 10, 16], L84813 = [1, 2, 6, 6, 7, 9, 12, 12], L84814 = [1, 2, 6, 6, 7, 9, 12, 14], L84816 = [1, 2, 6, 6, 7, 9, 12, 16], L84818 = [1, 2, 6, 6, 7, 9, 14, 16], L84820 = [1, 2, 6, 6, 7, 9, 16, 16], L84824 = [1, 2, 6, 6, 7, 10, 10, 15], L84828 = [1, 2, 6, 6, 7, 10, 12, 15], L84830 = [1, 2, 6, 6, 7, 10, 14, 15], L84832 = [1, 2, 6, 6, 7, 10, 15, 16], L84839 = [1, 2, 6, 6, 7, 12, 12, 15], L84841 = [1, 2, 6, 6, 7, 12, 14, 15], L84843 = [1, 2, 6, 6, 7, 12, 15, 16], L84845 = [1, 2, 6, 6, 7, 14, 15, 16], L84847 = [1, 2, 6, 6, 7, 15, 16, 16], L85013 = [1, 2, 6, 7, 8, 8, 8, 9], L85015 = [1, 2, 6, 7, 8, 8, 8, 11], L85018 = [1, 2, 6, 7, 8, 8, 8, 15], L85020 = [1, 2, 6, 7, 8, 8, 9, 10], L85022 = [1, 2, 6, 7, 8, 8, 9, 12], L85023 = [1, 2, 6, 7, 8, 8, 9, 14], L85025 = [1, 2, 6, 7, 8, 8, 9, 16], L85029 = [1, 2, 6, 7, 8, 8, 10, 15 L85032 = [1, 2, 6, 7, 8, 8, 11, 16], L85035 = [1, 2, 6, 7, 8, 8, 12, 15], L85037 = [1, 2, 6, 7, 8, 8, 14, 15], L85039 = [1, 2, 6, 7, 8, 8, 15, 16], L85041 = [1, 2, 6, 7, 8, 9, 10, 10], L85042 = [1, 2, 6, 7, 8, 9, 10, 12], L85045 = [1, 2, 6, 7, 8, 9, 10, 16], L85048 = [1, 2, 6, 7, 8, 9, 12, 12], L85049 = [1, 2, 6, 7, 8, 9, 12, 14], L85051 = [1, 2, 6, 7, 8, 9, 12, 16], L85053 = [1, 2, 6, 7, 8, 9, 14, 16], L85055 = [1, 2, 6, 7, 8, 9, 16, 16], L85058 = [1, 2, 6, 7, 8, 10, 10, 15], L85062 = [1, 2, 6, 7, 8, 10, 12, 15], L85065 = [1, 2, 6, 7, 8, 10, 15, 16], L85069 = [1, 2, 6, 7, 8, 11, 16, 16], L85072 = [1, 2, 6, 7, 8, 12, 12, 15], L85074 = [1, 2, 6, 7, 8, 12, 14, 15], L85076 = [1, 2, 6, 7, 8, 12, 15, 16], L85078 = [1, 2, 6, 7, 8, 14, 15, 16], L85080 = [1, 2, 6, 7, 8, 15, 16, 16], L85082 = [1, 2, 6, 7, 9, 10, 10, 10], L85083 = [1, 2, 6, 7, 9, 10, 10, 12], L85085 = [1, 2, 6, 7, 9, 10, 10, 16], L85086 = [1, 2, 6, 7, 9, 10, 12, 12], L85089 = [1, 2, 6, 7, 9, 10, 12, 16], L85093 = [1, 2, 6, 7, 9, 10, 16, 16], L85097 = [1, 2, 6, 7, 9, 12, 12, 12], L85098 = [1, 2, 6, 7, 9, 12, 12, 14], L85100 = [1, 2, 6, 7, 9, 12, 12, 16], L85102 = [1, 2, 6, 7, 9, 12, 14, 16], L85104 = [1, 2, 6, 7, 9, 12, 16, 16], L85106 = [1, 2, 6, 7, 9, 14, 16, 16], L85108 = [1, 2, 6, 7, 9, 16, 16, 16], L85111 = [1, 2, 6, 7, 10, 10, 10, 15], L85114 = [1, 2, 6, 7, 10, 10, 12, 15],
242
EMILIO A. LAURET
Table 6. (continued) m = 8 q I indexes of I-isospectral families 32 {0, 1} {362, 367}, {1855, 1860}, {1887, 1925}, {1906, 1908}, {1914, 1937}, (cont.) {1930, 1943}, {7743, 7748}, {7776, 8008}, {7804, 7831}, {7818, 7838}, {7824, 7841}, {7875, 7986}, {7925, 8012}, {7958, 7960}, {7962, 7963}, {7966, 7969}, {7975, 8029}, {7991, 8035}, {8020, 8047}, {24500, 24512}, {24538, 24653}, {24561, 24708}, {27503, 27508}, {27536, 28187}, {27564, 27591}, {27578, 27598}, {27584, 27601}, {27637, 28152}, {27689, 27796}, {27694, 28191}, {27732, 27734}, {27735, 27738}, {27737, 27741}, {27743, 27778}, {27751, 27820}, {27765, 27827}, {27771, 27830}, {27788, 27849}, {27801, 27848}, {27811, 27852}, {27895, 28130}, {27945, 28156}, {28040, 28197}, {28091, 28093}, {28095, 28096}, {28099, 28102}, {28105, 28106}, {28109, 28113}, {28119, 28219}, {28135, 28225}, {28164, 28237}, {28208, 28257}, {56625, 56761}, {56752, 58927}, {58918, 59291}, {58967, 59358}, {59311, 59619}, {79397, 80124}, {80006, 80045}, {80033, 80079},
L85116 = [1, 2, 6, 7, 10, 10, 15, 16], L85120 = [1, 2, 6, 7, 10, 12, 12, 15], L85123 = [1, 2, 6, 7, 10, 12, 15, 16], L85126 = [1, 2, 6, 7, 10, 15, 16, 16], L85131 = [1, 2, 6, 7, 11, 16, 16, 16], L85134 = [1, 2, 6, 7, 12, 12, 12, 15], L85136 = [1, 2, 6, 7, 12, 12, 14, 15], L85138 = [1, 2, 6, 7, 12, 12, 15, 16], L85140 = [1, 2, 6, 7, 12, 14, 15, 16], L85142 = [1, 2, 6, 7, 12, 15, 16, 16], L85144 = [1, 2, 6, 7, 14, 15, 16, 16], L85146 = [1, 2, 6, 7, 15, 16, 16, 16], L85157 = [1, 2, 6, 8, 8, 8, 9, 11], L85183 = [1, 2, 6, 8, 8, 9, 11, 16], L85235 = [1, 2, 6, 8, 9, 11, 16, 16], L85324 = [1, 2, 6, 9, 11, 16, 16, 16], L85441 = [1, 2, 7, 8, 8, 8, 8, 9], L85447 = [1, 2, 7, 8, 8, 8, 8, 15], L85449 = [1, 2, 7, 8, 8, 8, 9, 10], L85451 = [1, 2, 7, 8, 8, 8, 9, 12], L85455 = [1, 2, 7, 8, 8, 8, 9, 16], L85459 = [1, 2, 7, 8, 8, 8, 10, 15], L85467 = [1, 2, 7, 8, 8, 8, 12, 15], L85472 = [1, 2, 7, 8, 8, 8, 15, 16], L85474 = [1, 2, 7, 8, 8, 9, 10, 10], L85475 = [1, 2, 7, 8, 8, 9, 10, 12], L85478 = [1, 2, 7, 8, 8, 9, 10, 16], L85482 = [1, 2, 7, 8, 8, 9, 12, 12], L85486 = [1, 2, 7, 8, 8, 9, 12, 16], L85491 = [1, 2, 7, 8, 8, 9, 16, 16], L85495 = [1, 2, 7, 8, 8, 10, 10, 15], L85499 = [1, 2, 7, 8, 8, 10, 12, 15], L85502 = [1, 2, 7, 8, 8, 10, 15, 16], L85512 = [1, 2, 7, 8, 8, 12, 12, 15], L85517 = [1, 2, 7, 8, 8, 12, 15, 16], L85522 = [1, 2, 7, 8, 8, 15, 16, 16], L85524 = [1, 2, 7, 8, 9, 10, 10, 10], L85525 = [1, 2, 7, 8, 9, 10, 10, 12], L85528 = [1, 2, 7, 8, 9, 10, 10, 16], L85529 = [1, 2, 7, 8, 9, 10, 12, 12], L85532 = [1, 2, 7, 8, 9, 10, 12, 16], L85535 = [1, 2, 7, 8, 9, 10, 16, 16], L85541 = [1, 2, 7, 8, 9, 12, 12, 12], L85545 = [1, 2, 7, 8, 9, 12, 12, 16], L85550 = [1, 2, 7, 8, 9, 12, 16, 16], L85555 = [1, 2, 7, 8, 9, 16, 16, 16], L85559 = [1, 2, 7, 8, 10, 10, 10, 15], L85563 = [1, 2, 7, 8, 10, 10, 12, 15], L85566 = [1, 2, 7, 8, 10, 10, 15, 16], L85570 = [1, 2, 7, 8, 10, 12, 12, 15], L85573 = [1, 2, 7, 8, 10, 12, 15, 16], L85576 = [1, 2, 7, 8, 10, 15, 16, 16], L85588 = [1, 2, 7, 8, 12, 12, 12, 15], L85593 = [1, 2, 7, 8, 12, 12, 15, 16], L85598 = [1, 2, 7, 8, 12, 15, 16, 16], L85603 = [1, 2, 7, 8, 15, 16, 16, 16], L85605 = [1, 2, 7, 9, 10, 10, 10, 10], L85606 = [1, 2, 7, 9, 10, 10, 10, 12], L85609 = [1, 2, 7, 9, 10, 10, 10, 16], L85610 = [1, 2, 7, 9, 10, 10, 12, 12], L85613 = [1, 2, 7, 9, 10, 10, 12, 16], L85616 = [1, 2, 7, 9, 10, 10, 16, 16], L85617 = [1, 2, 7, 9, 10, 12, 12, 12], L85620 = [1, 2, 7, 9, 10, 12, 12, 16], L85623 = [1, 2, 7, 9, 10, 12, 16, 16], L85626 = [1, 2, 7, 9, 10, 16, 16, 16], L85634 = [1, 2, 7, 9, 12, 12, 12, 12], L85638 = [1, 2, 7, 9, 12, 12, 12, 16], L85643 = [1, 2, 7, 9, 12, 12, 16, 16], L85648 = [1, 2, 7, 9, 12, 16, 16, 16], L85653 = [1, 2, 7, 9, 16, 16, 16, 16], L85657 = [1, 2, 7, 10, 10, 10, 10, 15], L85661 = [1, 2, 7, 10, 10, 10, 12, 15], L85664 = [1, 2, 7, 10, 10, 10, 15, 16], L85668 = [1, 2, 7, 10, 10, 12, 12, 15], L85671 = [1, 2, 7, 10, 10, 12, 15, 16], L85674 = [1, 2, 7, 10, 10, 15, 16, 16], L85678 = [1, 2, 7, 10, 12, 12, 12, 15], L85681 = [1, 2, 7, 10, 12, 12, 15, 16], L85684 = [1, 2, 7, 10, 12, 15, 16, 16], L85687 = [1, 2, 7, 10, 15, 16, 16, 16], L85701 = [1, 2, 7, 12, 12, 12, 12, 15], L85706 = [1, 2, 7, 12, 12, 12, 15, 16], L85711 = [1, 2, 7, 12, 12, 15, 16, 16], L85716 = [1, 2, 7, 12, 15, 16, 16, 16], L85721 = [1, 2, 7, 15, 16, 16, 16, 16], L85793 = [1, 2, 8, 8, 8, 11, 13, 14], L85891 = [1, 2, 8, 8, 11, 13, 14, 16], L86057 = [1, 2, 8, 11, 13, 14, 16, 16], L86314 = [1, 2, 11, 13, 14, 16, 16, 16], L86409 = [1, 3, 4, 4, 4, 4, 5, 13], L86414 = [1, 3, 4, 4, 4, 4, 7, 9], L86442 = [1, 3, 4, 4, 4, 4, 11, 13], L86460 =
APPENDIX
243
Table 6. (continued) m = 8 q I indexes of I-isospectral families 32 {0, 1} {80071, 80317}, {80111, 80396}, {80140, 80421}, {80163, 80504}, {80211, 80532}, (cont.) {86409, 86414}, {86442, 87869}, {86470, 86497}, {86484, 86504}, {86490, 86507}, {86543, 87819}, {86596, 87173}, {86601, 87873}, {86639, 86641}, {86642, 86645}, {86651, 86686}, {86659, 86732}, {86673, 86739}, {86679, 86742}, {86699, 86765}, {86707, 86761}, {86713, 86764}, {86723, 86768}, {86815, 87784}, {86867, 87123}, {86872, 87823}, {86974, 87177}, {86982, 87879}, {87038, 87040}, {87041, 87044}, {87043, 87047}, {87049, 87105}, {87053, 87057}, {87056, 87060}, {87061, 87064}, {87063, 87068}, {87070, 87147}, {87078, 87210}, {87092, 87217}, {87098, 87220}, {87115, 87239}, {87128, 87238}, {87138, 87242}, {87163, 87275}, {87185, 87274}, {87199, 87278}, {87332, 87762}, {87382, 87788}, {87477, 87829}, {87637, 87887}, {87710, 87712}, {87714, 87715}, {87718, 87721}, {87724, 87725}, {87728, 87732}, {87736, 87737}, {87740, 87745}, {87751, 87914}, {87767, 87920}, {87796, 87932}, {87840, 87952}, {87901, 87982}
[1, 3, 4, 4, 4, 5, 7, 9], L86461 = [1, 3, 4, 4, 4, 5, 7, 11], L86463 = [1, 3, 4, 4, 4, 5, 7, 13], L86464 = [1, 3, 4, 4, 4, 5, 7, 15], L86470 = [1, 3, 4, 4, 4, 5, 8, 13], L86474 = [1, 3, 4, 4, 4, 5, 9, 11], L86476 = [1, 3, 4, 4, 4, 5, 9, 15], L86479 = [1, 3, 4, 4, 4, 5, 11, 13], L86481 = [1, 3, 4, 4, 4, 5, 11, 15], L86484 = [1, 3, 4, 4, 4, 5, 12, 13], L86489 = [1, 3, 4, 4, 4, 5, 13, 15], L86490 = [1, 3, 4, 4, 4, 5, 13, 16], L86497 = [1, 3, 4, 4, 4, 7, 8, 9], L86504 = [1, 3, 4, 4, 4, 7, 9, 12 L86505 = [1, 3, 4, 4, 4, 7, 9, 13], L86506 = [1, 3, 4, 4, 4, 7, 9, 15], L86507 = [1, 3, 4, 4, 4, 7, 9, 16], L86517 = [1, 3, 4, 4, 4, 7, 13, 15], L86543 = [1, 3, 4, 4, 4, 8, 11, 13], L86566 = [1, 3, 4, 4, 4, 9, 11, 13], L86567 = [1, 3, 4, 4, 4, 9, 11, 15], L86596 = [1, 3, 4, 4, 4, 11, 12, 13], L86601 = [1, 3, 4, 4, 4, 11, 13, 16], L86633 = [1, 3, 4, 4, 5, 7, 8, 9], L86634 = [1, 3, 4, 4, 5, 7, 8, 11], L86636 = [1, 3, 4, 4, 5, 7, 8, 13], L86637 = [1, 3, 4, 4, 5, 7, 8, 15], L86639 = [1, 3, 4, 4, 5, 7, 9, 11], L86640 = [1, 3, 4, 4, 5, 7, 9, 12], L86641 = [1, 3, 4, 4, 5, 7, 9, 13], L86642 = [1, 3, 4, 4, 5, 7, 9, 15], L86643 = [1, 3, 4, 4, 5, 7, 9, 16], L86644 = [1, 3, 4, 4, 5, 7, 11, 12], L86645 = [1, 3, 4, 4, 5, 7, 11, 1 L86646 = [1, 3, 4, 4, 5, 7, 11, 16], L86647 = [1, 3, 4, 4, 5, 7, 12, 12], L86648 = [1, 3, 4, 4, 5, 7, 12, 13], L86649 = [1, 3, 4, 4, 5, 7, 12, 15], L86651 = [1, 3, 4, 4, 5, 7, 13, 15], L86652 = [1, 3, 4, 4, 5, 7, 13, 16], L86653 = [1, 3, 4, 4, 5, 7, 15, 16], L86659 = [1, 3, 4, 4, 5, 8, 8, 13], L86663 = [1, 3, 4, 4, 5, 8, 9, 11], L86665 = [1, 3, 4, 4, 5, 8, 9, 15], L86668 = [1, 3, 4, 4, 5, 8, 11, 13], L86670 = [1, 3, 4, 4, 5, 8, 11, 15], L86673 = [1, 3, 4, 4, 5, 8, 12, 13], L86678 = [1, 3, 4, 4, 5, 8, 13, 15], L86679 = [1, 3, 4, 4, 5, 8, 13, 16], L86685 = [1, 3, 4, 4, 5, 9, 11, 12], L86686 = [1, 3, 4, 4, 5, 9, 11, 15], L86687 = [1, 3, 4, 4, 5, 9, 11, 16], L86688 = [1, 3, 4, 4, 5, 9, 12, 12], L86689 = [1, 3, 4, 4, 5, 9, 12, 15], L86691 = [1, 3, 4, 4, 5, 9, 15, 16], L86694 = [1, 3, 4, 4, 5, 11, 12, 13], L86696 = [1, 3, 4, 4, 5, 11, 12, 15], L86699 = [1, 3, 4, 4, 5, 11, 13, 15], L86700 = [1, 3, 4, 4, 5, 11, 13, 16], L86704 = [1, 3, 4, 4, 5, 11, 15, 16], L86707 = [1, 3, 4, 4, 5, 12, 12, 13], L86712 = [1, 3, 4, 4, 5, 12, 13, 15], L86713 = [1, 3, 4, 4, 5, 12, 13, 16], L86722 = [1, 3, 4, 4, 5, 13, 15, 16], L86723 = [1, 3, 4, 4, 5, 13, 16, 16], L86732 = [1, 3, 4, 4, 7, 8, 8, 9], L86739 = [1, 3, 4, 4, 7, 8, 9, 12], L86740 = [1, 3, 4, 4, 7, 8, 9, 13 L86741 = [1, 3, 4, 4, 7, 8, 9, 15], L86742 = [1, 3, 4, 4, 7, 8, 9, 16], L86748 = [1, 3, 4, 4, 7, 8, 12, 12], L86752 = [1, 3, 4, 4, 7, 8, 13, 15], L86761 = [1, 3, 4, 4, 7, 9, 12, 12], L86762 = [1, 3, 4, 4, 7, 9, 12, 13], L86763 = [1, 3, 4, 4, 7, 9, 12, 15], L86764 = [1, 3, 4, 4, 7, 9, 12, 16], L86765 = [1, 3, 4, 4, 7, 9, 13, 15], L86766 = [1, 3, 4, 4, 7, 9, 13, 16], L86767 = [1, 3, 4, 4, 7, 9, 15, 16], L86768 = [1, 3, 4, 4, 7, 9, 16, 16], L86784 = [1, 3, 4, 4, 7, 12, 12, 16], L86785 = [1, 3, 4, 4, 7, 12, 13, 15], L86789 = [1, 3, 4, 4, 7, 13, 15, 16], L86815 = [1, 3, 4, 4, 8, 8, 11, 13], L86838 = [1, 3, 4, 4, 8, 9, 11, 13], L86839 = [1, 3, 4, 4, 8, 9, 11, 15], L86841 = [1, 3, 4, 4, 8, 9, 12, 12], L86867 = [1, 3, 4, 4, 8, 11, 12, 13], L86872 = [1, 3, 4, 4, 8, 11, 13, 16], L86915 = [1, 3, 4, 4, 9, 11, 12, 13], L86916 = [1, 3, 4, 4, 9, 11, 12, 15], L86918 = [1, 3, 4, 4, 9, 11, 13, 16], L86919 = [1, 3, 4, 4, 9, 11, 15, 16], L86922 = [1, 3, 4, 4, 9, 12, 12, 16], L86974 = [1, 3, 4, 4, 11, 12, 13, 16], L86982 = [1, 3, 4, 4, 11, 13, 16, 16], L87032 = [1, 3, 4, 5, 7, 8, 8, 9], L87033 = [1, 3, 4, 5, 7, 8, 8, 11], L87034 = [1, 3, 4, 5, 7, 8, 8, 12], L87035 = [1, 3, 4, 5, 7, 8, 8, 13], L87036 = [1, 3, 4, 5, 7, 8, 8, 15], L87038 = [1, 3, 4, 5, 7, 8, 9, 11],
244
EMILIO A. LAURET
Table 6. (continued) m = 8 q 32
I {0, 1, 2}
indexes of I-isospectral families {24763, 24799}, {79905, 80725}, {80597, 80633}, {80667, 80738}, {87054, 87055} (cont.) {0, 3} {86694, 86763} {0, 1, 2, 3} {79549, 79646} {0, 7} {24710, 24764}, {25920, 25951}, {27838, 27921}, {29340, 29349}, {77844, 77881}, {80018, 80077}, {80506, 80598}, {80538, 80668}, {84808, 84830} {0, 1, 6, 7} {80098, 80521}
L87039 = [1, 3, 4, 5, 7, 8, 9, 12], L87040 = [1, 3, 4, 5, 7, 8, 9, 13], L87041 = [1, 3, 4, 5, 7, 8, 9, 15], L87042 = [1, 3, 4, 5, 7, 8, 9, 16], L87043 = [1, 3, 4, 5, 7, 8, 11, 12], L87044 = [1, 3, 4, 5, 7, 8, 11, 13], L87045 = [1, 3, 4, 5, 7, 8, 11, 16], L87047 = [1, 3, 4, 5, 7, 8, 12, 13], L87048 = [1, 3, 4, 5, 7, 8, 12, 16], L87049 = [1, 3, 4, 5, 7, 8, 13, 15], L87050 = [1, 3, 4, 5, 7, 8, 13, 16], L87051 = [1, 3, 4, 5, 7, 8, 15, 16], L87053 = [1, 3, 4, 5, 7, 9, 11, 12], L87054 = [1, 3, 4, 5, 7, 9, 11, 13], L87055 = [1, 3, 4, 5, 7, 9, 11, 15], L87056 = [1, 3, 4, 5, 7, 9, 11, 16], L87057 = [1, 3, 4, 5, 7, 9, 12, 13], L87059 = [1, 3, 4, 5, 7, 9, 12, 16], L87060 = [1, 3, 4, 5, 7, 9, 13, 16], L87061 = [1, 3, 4, 5, 7, 9, 15, 16], L87062 = [1, 3, 4, 5, 7, 9, 16, 16], L87063 = [1, 3, 4, 5, 7, 11, 12, 16], L87064 = [1, 3, 4, 5, 7, 11, 13, 16], L87065 = [1, 3, 4, 5, 7, 11, 16, 16], L87068 = [1, 3, 4, 5, 7, 12, 13, 16], L87069 = [1, 3, 4, 5, 7, 12, 16, 16], L87070 = [1, 3, 4, 5, 7, 13, 15, 16], L87071 = [1, 3, 4, 5, 7, 13, 16, 16], L87072 = [1, 3, 4, 5, 7, 15, 16, 16], L87078 = [1, 3, 4, 5, 8, 8, 8, 13], L87082 = [1, 3, 4, 5, 8, 8, 9, 11], L87083 = [1, 3, 4, 5, 8, 8, 9, 12], L87084 = [1, 3, 4, 5, 8, 8, 9, 15], L87087 = [1, 3, 4, 5, 8, 8, 11, 13 L87089 = [1, 3, 4, 5, 8, 8, 11, 15], L87092 = [1, 3, 4, 5, 8, 8, 12, 13], L87097 = [1, 3, 4, 5, 8, 8, 13, 15], L87098 = [1, 3, 4, 5, 8, 8, 13, 16], L87104 = [1, 3, 4, 5, 8, 9, 11, 12], L87105 = [1, 3, 4, 5, 8, 9, 11, 15], L87106 = [1, 3, 4, 5, 8, 9, 11, 16], L87107 = [1, 3, 4, 5, 8, 9, 12, 16], L87108 = [1, 3, 4, 5, 8, 9, 15, 16], L87112 = [1, 3, 4, 5, 8, 11, 12, 15], L87115 = [1, 3, 4, 5, 8, 11, 13, 15], L87116 = [1, 3, 4, 5, 8, 11, 13, 16], L87120 = [1, 3, 4, 5, 8, 11, 15, 16], L87123 = [1, 3, 4, 5, 8, 12, 12, 13], L87127 = [1, 3, 4, 5, 8, 12, 13, 15], L87128 = [1, 3, 4, 5, 8, 12, 13, 16], L87137 = [1, 3, 4, 5, 8, 13, 15, 16], L87138 = [1, 3, 4, 5, 8, 13, 16, 16], L87146 = [1, 3, 4, 5, 9, 11, 12, 16], L87147 = [1, 3, 4, 5, 9, 11, 15, 16], L87148 = [1, 3, 4, 5, 9, 11, 16, 16], L87149 = [1, 3, 4, 5, 9, 12, 16, 16], L87150 = [1, 3, 4, 5, 9, 15, 16, 16], L87158 = [1, 3, 4, 5, 11, 12, 15, 16], L87163 = [1, 3, 4, 5, 11, 13, 15, 16], L87164 = [1, 3, 4, 5, 11, 13, 16, 16], L87170 = [1, 3, 4, 5, 11, 15, 16, 16], L87173 = [1, 3, 4, 5, 12, 12, 12, 13], L87177 = [1, 3, 4, 5, 12, 12, 13, 16], L87184 = [1, 3, 4, 5, 12, 13, 15, 16], L87185 = [1, 3, 4, 5, 12, 13, 16, 16], L87198 = [1, 3, 4, 5, 13, 15, 16, 16], L87199 = [1, 3, 4, 5, 13, 16, 16, 16], L87210 = [1, 3, 4, 7, 8, 8, 8, 9], L87212 = [1, 3, 4, 7, 8, 8, 8, 12], L87217 = [1, 3, 4, 7, 8, 8, 9, 12], L87218 = [1, 3, 4, 7, 8, 8, 9, 13], L87219 = [1, 3, 4, 7, 8, 8, 9, 15], L87220 = [1, 3, 4, 7, 8, 8, 9, 16], L87228 = [1, 3, 4, 7, 8, 8, 12, 16 L87229 = [1, 3, 4, 7, 8, 8, 13, 15], L87238 = [1, 3, 4, 7, 8, 9, 12, 16], L87239 = [1, 3, 4, 7, 8, 9, 13, 15], L87240 = [1, 3, 4, 7, 8, 9, 13, 16], L87241 = [1, 3, 4, 7, 8, 9, 15, 16], L87242 = [1, 3, 4, 7, 8, 9, 16, 16], L87259 = [1, 3, 4, 7, 8, 12, 16, 16], L87260 = [1, 3, 4, 7, 8, 13, 15, 16], L87274 = [1, 3, 4, 7, 9, 12, 16, 16], L87275 = [1, 3, 4, 7, 9, 13, 15, 16], L87276 = [1, 3, 4, 7, 9, 13, 16, 16], L87277 = [1, 3, 4, 7, 9, 15, 16, 16], L87278 = [1, 3, 4, 7, 9, 16, 16, 16], L87306 = [1, 3, 4, 7, 12, 16, 16, 16], L87307 = [1, 3, 4, 7, 13, 15, 16, 16], L87322 = [1, 3, 4, 8, 8, 8, 9, 12], L87332 = [1, 3, 4, 8, 8, 8, 11, 13], L87354 = [1, 3, 4, 8, 8, 9, 11, 13], L87355 = [1, 3, 4, 8, 8, 9, 11, 15], L87358 = [1, 3, 4, 8, 8, 9, 12, 16], L87382 = [1, 3, 4, 8, 8, 11, 13, 16], L87423 = [1, 3, 4, 8, 9, 11, 13, 16], L87424 = [1, 3, 4, 8, 9, 11, 15, 16], L87427 = [1, 3, 4, 8, 9, 12, 16, 16], L87477 = [1, 3, 4, 8, 11, 13, 16, 16], L87541 = [1, 3, 4, 9, 11, 13, 16, 16], L87542 = [1, 3, 4, 9, 11, 15, 16, 16], L87545 = [1, 3, 4, 9, 12, 16, 16, 16], L87637 = [1, 3, 4, 11, 13, 16, 16, 16], L87708 = [1, 3, 5, 7, 8, 8, 8, 8], L87709 = [1, 3, 5, 7, 8, 8, 8, 9], L87710 = [1, 3, 5, 7, 8, 8, 8, 11], L87712 = [1, 3, 5, 7, 8, 8, 8, 13], L87713 = [1, 3, 5, 7, 8, 8, 8, 16], L87714 = [1, 3, 5, 7, 8, 8, 9, 11], L87715 = [1, 3, 5, 7, 8, 8, 9, 13], L87717 = [1, 3, 5, 7, 8, 8, 9, 16], L87718 = [1, 3, 5, 7, 8, 8, 11, 16], L87721 = [1, 3, 5, 7, 8, 8, 13, 16], L87722 = [1, 3, 5, 7, 8, 8, 16, 16],
APPENDIX
245
L87724 = [1, 3, 5, 7, 8, 9, 11, 16], L87725 = [1, 3, 5, 7, 8, 9, 13, 16], L87727 = [1, 3, 5, 7, 8, 9, 16, 16], L87728 = [1, 3, 5, 7, 8, 11, 16, 16], L87732 = [1, 3, 5, 7, 8, 13, 16, 16], L87733 = [1, 3, 5, 7, 8, 16, 16, 16], L87736 = [1, 3, 5, 7, 9, 11, 16, 16], L87737 = [1, 3, 5, 7, 9, 13, 16, 16], L87739 = [1, 3, 5, 7, 9, 16, 16, 16], L87740 = [1, 3, 5, 7, 11, 16, 16, 16], L87745 = [1, 3, 5, 7, 13, 16, 16, 16], L87746 = [1, 3, 5, 7, 16, 16, 16, 16], L87748 = [1, 3, 5, 8, 8, 8, 8, 9], L87751 = [1, 3, 5, 8, 8, 8, 8, 13], L87755 = [1, 3, 5, 8, 8, 8, 9, 11], L87756 = [1, 3, 5, 8, 8, 8, 9, 16], L87759 = [1, 3, 5, 8, 8, 8, 11, 15], L87762 = [1, 3, 5, 8, 8, 8, 12, 13], L87766 = [1, 3, 5, 8, 8, 8, 13, 15], L87767 = [1, 3, 5, 8, 8, 8, 13, 16], L87773 = [1, 3, 5, 8, 8, 9, 11, 16], L87774 = [1, 3, 5, 8, 8, 9, 16, 16], L87781 = [1, 3, 5, 8, 8, 11, 15, 16], L87784 = [1, 3, 5, 8, 8, 12, 12, 13], L87788 = [1, 3, 5, 8, 8, 12, 13, 16], L87795 = [1, 3, 5, 8, 8, 13, 15, 16], L87796 = [1, 3, 5, 8, 8, 13, 16, 16], L87804 = [1, 3, 5, 8, 9, 11, 16, 16], L87805 = [1, 3, 5, 8, 9, 16, 16, 16], L87816 = [1, 3, 5, 8, 11, 15, 16, 16], L87819 = [1, 3, 5, 8, 12, 12, 12, 13], L87823 = [1, 3, 5, 8, 12, 12, 13, 16], L87829 = [1, 3, 5, 8, 12, 13, 16, 16], L87839 = [1, 3, 5, 8, 13, 15, 16, 16], L87840 = [1, 3, 5, 8, 13, 16, 16, 16], L87850 = [1, 3, 5, 9, 11, 16, 16, 16], L87851 = [1, 3, 5, 9, 16, 16, 16, 16], L87866 = [1, 3, 5, 11, 15, 16, 16, 16], L87869 = [1, 3, 5, 12, 12, 12, 12, 13], L87873 = [1, 3, 5, 12, 12, 12, 13, 16], L87879 = [1, 3, 5, 12, 12, 13, 16, 16], L87887 = [1, 3, 5, 12, 13, 16, 16, 16], L87900 = [1, 3, 5, 13, 15, 16, 16, 16], L87901 = [1, 3, 5, 13, 16, 16, 16, 16], L87913 = [1, 3, 7, 8, 8, 8, 8, 8], L87914 = [1, 3, 7, 8, 8, 8, 8, 9], L87918 = [1, 3, 7, 8, 8, 8, 8, 16], L87920 = [1, 3, 7, 8, 8, 8, 9, 16], L87929 = [1, 3, 7, 8, 8, 8, 16, 16], L87932 = [1, 3, 7, 8, 8, 9, 16, 16], L87948 = [1, 3, 7, 8, 8, 16, 16, 16], L87952 = [1, 3, 7, 8, 9, 16, 16, 16], L87977 = [1, 3, 7, 8, 16, 16, 16, 16], L87982 = [1, 3, 7, 9, 16, 16, 16, 16], L88018 = [1, 3, 7, 16, 16, 16, 16, 16], L88020 = [1, 3, 8, 8, 8, 8, 8, 9], L88029 = [1, 3, 8, 8, 8, 8, 9, 16], L88053 = [1, 3, 8, 8, 8, 9, 16, 16], L88104 = [1, 3, 8, 8, 9, 16, 16, 16], L88198 = [1, 3, 8, 9, 16, 16, 16, 16], L88355 = [1, 3, 9, 16, 16, 16, 16, 16], L88676 = [1, 4, 4, 4, 4, 6, 7, 9], L88679 = [1, 4, 4, 4, 4, 6, 7, 15], L88844 = [1, 4, 4, 4, 6, 6, 7, 9], L88847 = [1, 4, 4, 4, 6, 6, 7, 15], L88874 = [1, 4, 4, 4, 6, 7, 8, 9], L88877 = [1, 4, 4, 4, 6, 7, 8, 15], L88880 = [1, 4, 4, 4, 6, 7, 9, 12], L88882 = [1, 4, 4, 4, 6, 7, 9, 16], L88886 = [1, 4, 4, 4, 6, 7, 12, 15], L88888 = [1, 4, 4, 4, 6, 7, 15, 16], L89214 = [1, 4, 4, 6, 6, 6, 7, 9], L89217 = [1, 4, 4, 6, 6, 6, 7, 15], L89244 = [1, 4, 4, 6, 6, 7, 8, 9], L89247 = [1, 4, 4, 6, 6, 7, 8, 15], L89249 = [1, 4, 4, 6, 6, 7, 9, 10], L89250 = [1, 4, 4, 6, 6, 7, 9, 12], L89252 = [1, 4, 4, 6, 6, 7, 9, 16], L89255 = [1, 4, 4, 6, 6, 7, 10, 15], L89258 = [1, 4, 4, 6, 6, 7, 12, 15], L89260 = [1, 4, 4, 6, 6, 7, 15, 16], L89322 = [1, 4, 4, 6, 7, 8, 8, 9], L89325 = [1, 4, 4, 6, 7, 8, 8, 15], L89328 = [1, 4, 4, 6, 7, 8, 9, 12], L89330 = [1, 4, 4, 6, 7, 8, 9, 16], L89334 = [1, 4, 4, 6, 7, 8, 12, 15], L89336 = [1, 4, 4, 6, 7, 8, 15, 16], L89341 = [1, 4, 4, 6, 7, 9, 12, 12], L89343 = [1, 4, 4, 6, 7, 9, 12, 16], L89345 = [1, 4, 4, 6, 7, 9, 16, 16], L89350 = [1, 4, 4, 6, 7, 12, 12, 15], L89352 = [1, 4, 4, 6, 7, 12, 15, 16], L89354 = [1, 4, 4, 6, 7, 15, 16, 16], L89894 = [1, 4, 6, 6, 6, 6, 7, 9], L89897 = [1, 4, 6, 6, 6, 6, 7, 15], L89924 = [1, 4, 6, 6, 6, 7, 8, 9], L89927 = [1, 4, 6, 6, 6, 7, 8, 15], L89929 = [1, 4, 6, 6, 6, 7, 9, 10], L89930 = [1, 4, 6, 6, 6, 7, 9, 12], L89932 = [1, 4, 6, 6, 6, 7, 9, 16], L89935 = [1, 4, 6, 6, 6, 7, 10, 15], L89938 = [1, 4, 6, 6, 6, 7, 12, 15], L89940 = [1, 4, 6, 6, 6, 7, 15, 16], L90003 = [1, 4, 6, 6, 7, 8, 8, 9], L90006 = [1, 4, 6, 6, 7, 8, 8, 15], L90008 = [1, 4, 6, 6, 7, 8, 9, 10], L90009 = [1, 4, 6, 6, 7, 8, 9, 12], L90011 = [1, 4, 6, 6, 7, 8, 9, 16], L90014 = [1, 4, 6, 6, 7, 8, 10, 15], L90017 = [1, 4, 6, 6, 7, 8, 12, 1 L90019 = [1, 4, 6, 6, 7, 8, 15, 16], L90022 = [1, 4, 6, 6, 7, 9, 10, 12], L90024 = [1, 4, 6, 6, 7, 9, 10, 16], L90025 = [1, 4, 6, 6, 7, 9, 12, 12], L90027 = [1, 4, 6, 6, 7, 9, 12, 16], L90029 = [1, 4, 6, 6, 7, 9, 16, 16], L90033 = [1, 4, 6, 6, 7, 10, 12, 15], L90035 = [1, 4, 6, 6, 7, 10, 15, 16], L90038 = [1, 4, 6, 6, 7, 12, 12, 15], L90040 = [1, 4, 6, 6, 7, 12, 15, 16], L90042 = [1, 4, 6, 6, 7, 15, 16, 16], L90166 = [1, 4, 6, 7, 8, 8, 8, 9], L90169 = [1, 4, 6, 7, 8, 8, 8, 15], L90172 = [1, 4, 6, 7, 8, 8, 9, 12], L90174 = [1, 4, 6, 7, 8, 8, 9, 16], L90178 = [1, 4, 6, 7, 8, 8, 12, 15], L90180 = [1, 4, 6, 7, 8, 8, 15, 16], L90185 = [1, 4, 6, 7, 8, 9, 12, 12], L90187 = [1, 4, 6, 7, 8, 9, 12, 16], L90189 = [1, 4, 6, 7, 8, 9, 16, 16], L90194 = [1, 4, 6, 7, 8, 12, 12, 15], L90196 = [1, 4, 6, 7, 8, 12, 15, 16], L90198 = [1, 4, 6, 7, 8, 15, 16, 16], L90205 = [1, 4, 6, 7, 9, 12, 12, 12], L90207 = [1, 4, 6, 7, 9, 12, 12, 16], L90209 = [1, 4, 6, 7, 9, 12, 16, 16], L90211 = [1, 4, 6, 7, 9, 16, 16, 16], L90217 = [1, 4, 6, 7, 12, 12, 12, 15], L90219 = [1, 4, 6, 7, 12, 12, 15, 16], L90221 = [1, 4, 6, 7, 12, 15, 16, 16], L90223 = [1, 4, 6, 7, 15, 16, 16, 16], L90989 = [1, 6, 6, 6, 6, 6, 7, 9], L90992 = [1, 6, 6, 6, 6, 6, 7, 15], L91019 = [1, 6, 6, 6, 6, 7, 8, 9], L91022 = [1, 6, 6, 6, 6, 7, 8, 15], L91024 = [1, 6, 6, 6, 6, 7, 9, 10], L91025 = [1, 6, 6, 6, 6, 7, 9, 12], L91027 = [1, 6, 6, 6, 6, 7, 9, 16], L91030 = [1, 6, 6, 6, 6, 7, 10, 15], L91033 = [1, 6, 6, 6, 6, 7, 12, 15], L91035 = [1, 6, 6, 6, 6, 7, 15, 16], L91098 = [1, 6, 6, 6, 7, 8, 8, 9], L91101 = [1, 6, 6, 6, 7, 8, 8, 15], L91103 =
246
EMILIO A. LAURET
[1, 6, 6, 6, 7, 8, 9, 10], L91104 = [1, 6, 6, 6, 7, 8, 9, 12], L91106 = [1, 6, 6, 6, 7, 8, 9, 16], L91109 = [1, 6, 6, 6, 7, 8, 10, 15 L91112 = [1, 6, 6, 6, 7, 8, 12, 15], L91114 = [1, 6, 6, 6, 7, 8, 15, 16], L91116 = [1, 6, 6, 6, 7, 9, 10, 10], L91117 = [1, 6, 6, 6, 7, 9, 10, 12], L91119 = [1, 6, 6, 6, 7, 9, 10, 16], L91120 = [1, 6, 6, 6, 7, 9, 12, 12], L91122 = [1, 6, 6, 6, 7, 9, 12, 16], L91124 = [1, 6, 6, 6, 7, 9, 16, 16], L91127 = [1, 6, 6, 6, 7, 10, 10, 15], L91130 = [1, 6, 6, 6, 7, 10, 12, 15], L91132 = [1, 6, 6, 6, 7, 10, 15, 16], L91135 = [1, 6, 6, 6, 7, 12, 12, 15], L91137 = [1, 6, 6, 6, 7, 12, 15, 16], L91139 = [1, 6, 6, 6, 7, 15, 16, 16], L91266 = [1, 6, 6, 7, 8, 8, 8, 9], L91269 = [1, 6, 6, 7, 8, 8, 8, 15], L91271 = [1, 6, 6, 7, 8, 8, 9, 10], L91272 = [1, 6, 6, 7, 8, 8, 9, 12], L91274 = [1, 6, 6, 7, 8, 8, 9, 16], L91277 = [1, 6, 6, 7, 8, 8, 10, 15], L91280 = [1, 6, 6, 7, 8, 8, 12, 15], L91282 = [1, 6, 6, 7, 8, 8, 15, 16], L91285 = [1, 6, 6, 7, 8, 9, 10, 12], L91287 = [1, 6, 6, 7, 8, 9, 10, 16], L91288 = [1, 6, 6, 7, 8, 9, 12, 12], L91290 = [1, 6, 6, 7, 8, 9, 12, 16], L91292 = [1, 6, 6, 7, 8, 9, 16, 16], L91296 = [1, 6, 6, 7, 8, 10, 12, 15], L91298 = [1, 6, 6, 7, 8, 10, 15, 16], L91301 = [1, 6, 6, 7, 8, 12, 12, 15], L91303 = [1, 6, 6, 7, 8, 12, 15, 16], L91305 = [1, 6, 6, 7, 8, 15, 16, 16], L91310 = [1, 6, 6, 7, 9, 10, 12, 12], L91312 = [1, 6, 6, 7, 9, 10, 12, 16], L91314 = [1, 6, 6, 7, 9, 10, 16, 16], L91315 = [1, 6, 6, 7, 9, 12, 12, 12], L91317 = [1, 6, 6, 7, 9, 12, 12, 16], L91319 = [1, 6, 6, 7, 9, 12, 16, 16], L91321 = [1, 6, 6, 7, 9, 16, 16, 16], L91326 = [1, 6, 6, 7, 10, 12, 12, 15], L91328 = [1, 6, 6, 7, 10, 12, 15, 16], L91330 = [1, 6, 6, 7, 10, 15, 16, 16], L91333 = [1, 6, 6, 7, 12, 12, 12, 15], L91335 = [1, 6, 6, 7, 12, 12, 15, 16], L91337 = [1, 6, 6, 7, 12, 15, 16, 16], L91339 = [1, 6, 6, 7, 15, 16, 16, 16], L91563 = [1, 6, 7, 8, 8, 8, 8, 9], L91566 = [1, 6, 7, 8, 8, 8, 8, 15], L91569 = [1, 6, 7, 8, 8, 8, 9, 12], L91571 = [1, 6, 7, 8, 8, 8, 9, 16], L91575 = [1, 6, 7, 8, 8, 8, 12, 15], L91577 = [1, 6, 7, 8, 8, 8, 15, 1 L91582 = [1, 6, 7, 8, 8, 9, 12, 12], L91584 = [1, 6, 7, 8, 8, 9, 12, 16], L91586 = [1, 6, 7, 8, 8, 9, 16, 16], L91591 = [1, 6, 7, 8, 8, 12, 12, 15], L91593 = [1, 6, 7, 8, 8, 12, 15, 16], L91595 = [1, 6, 7, 8, 8, 15, 16, 16], L91602 = [1, 6, 7, 8, 9, 12, 12, 12], L91604 = [1, 6, 7, 8, 9, 12, 12, 16], L91606 = [1, 6, 7, 8, 9, 12, 16, 16], L91608 = [1, 6, 7, 8, 9, 16, 16, 16], L91614 = [1, 6, 7, 8, 12, 12, 12, 15], L91616 = [1, 6, 7, 8, 12, 12, 15, 16], L91618 = [1, 6, 7, 8, 12, 15, 16, 16], L91620 = [1, 6, 7, 8, 15, 16, 16, 16], L91629 = [1, 6, 7, 9, 12, 12, 12, 12], L91631 = [1, 6, 7, 9, 12, 12, 12, 16], L91633 = [1, 6, 7, 9, 12, 12, 16, 16], L91635 = [1, 6, 7, 9, 12, 16, 16, 16], L91637 = [1, 6, 7, 9, 16, 16, 16, 16], L91644 = [1, 6, 7, 12, 12, 12, 12, 15], L91646 = [1, 6, 7, 12, 12, 12, 15, 16], L91648 = [1, 6, 7, 12, 12, 15, 16, 16], L91650 = [1, 6, 7, 12, 15, 16, 16, 16], L91652 = [1, 6, 7, 15, 16, 16, 16, 16].
APPENDIX
247
8. Computational results for dimension 17
q = 4 : L17 = [0, 0, 0, 1, 1, 1, 1, 2, 2], L24 = [0, 0, 1, 1, 1, 1, 2, 2, 2]. q = 5 : L14 = [0, 0, 0, 1, 1, 1, 2, 2, 2], L18 = [0, 0, 1, 1, 1, 1, 2, 2, 2]. q = 7 : L28 = [0, 0, 0, 1, 1, 2, 2, 3, 3], L40 = [0, 0, 1, 1, 1, 2, 2, 3, 3], L53 = [0, 1, 1, 1, 1, 2, 2, 3, 3], L55 = [0, 1, 1, 1, 2, 2, 2, 3, 3]. q = 8 : L96 = [0, 0, 0, 1, 2, 2, 3, 4, 4], L142 = [0, 0, 1, 1, 2, 2, 3, 3, 4], L154 = [0, 0, 1, 2, 2, 2, 2, 3, 4], L158 = [0, 0, 1, 2, 2, 3, 4, 4, 4], L194 = [0, 1, 1, 1, 1, 3, 3, 3, 3], L223 = [0, 1, 1, 2, 2, 2, 3, 3, 4], L226 = [0, 1, 1, 2, 2, 3, 3, 4, 4], L240 = [0, 1, 2, 2, 2, 2, 3, 4, 4], L300 = [1, 1, 1, 1, 3, 3, 3, 3, 4]. q = 10 : L167 = [0, 0, 0, 1, 1, 2, 3, 4, 5], L273 = [0, 0, 1, 1, 1, 2, 3, 4, 5], L305 = [0, 0, 1, 1, 2, 2, 3, 4, 5], L311 = [0, 0, 1, 1, 2, 3, 3, 4, 5], L314 = [0, 0, 1, 1, 2, 3, 4, 4, 5], L315 = [0, 0, 1, 1, 2, 3, 4, 5, 5], L346 = [0, 0, 1, 2, 2, 2, 4, 4, 4], L350 = [0, 0, 1, 2, 2, 3, 4, 4, 5], L351 = [0, 0, 1, 2, 2, 3, 4, 5, 5], L380 = [0, 0, 2, 2, 2, 4, 4, 4, 5], L473 = [0, 1, 1, 1, 2, 2, 3, 4, 5], L482 = [0, 1, 1, 1, 2, 3, 3, 4, 5], L493 = [0, 1, 1, 1, 3, 3, 3, 5, 5], L522 = [0, 1, 1, 2, 2, 2, 3, 4, 5], L529 = [0, 1, 1, 2, 2, 3, 3, 4, 5], L532 = [0, 1, 1, 2, 2, 3, 4, 4, 5], L533 = [0, 1, 1, 2, 2, 3, 4, 5, 5], L540 = [0, 1, 1, 2, 3, 3, 4, 5, 5], L544 = [0, 1, 1, 2, 3, 4, 4, 5, 5], L584 = [0, 1, 2, 2, 2, 3, 4, 4, 5], L585 = [0, 1, 2, 2, 2, 3, 4, 5, 5], L592 = [0, 1, 2, 2, 3, 4, 4, 5, 5], L593 = [0, 1, 2, 2, 3, 4, 5, 5, 5], L746 = [1, 1, 1, 1, 3, 3, 3, 5, 5], L797 = [1, 1, 1, 2, 3, 3, 3, 5, 5], L813 = [1, 1, 1, 3, 3, 3, 5, 5, 5]. q = 11 : L9 = [0, 0, 0, 0, 0, 0, 1, 2, 3], L10 = [0, 0, 0, 0, 0, 0, 1, 2, 4], L50 = [0, 0, 0, 0, 1, 2, 3, 4, 5], L91 = [0, 0, 0, 1, 1, 2, 3, 4, 5], L141 = [0, 0, 1, 1, 1, 2, 3, 4, 5], L153 = [0, 0, 1, 1, 2, 2, 3, 3, 4], L154 = [0, 0, 1, 1, 2, 2, 3, 3, 5], L155 = [0, 0, 1, 1, 2, 2, 3, 4, 4], L156 = [0, 0, 1, 1, 2, 2, 3, 4, 5], L158 = [0, 0, 1, 1, 2, 3, 3, 4, 5], L208 = [0, 1, 1, 1, 1, 2, 3, 4, 5], L237 = [0, 1, 1, 1, 2, 2, 3, 4, 5], L245 = [0, 1, 1, 1, 2, 3, 3, 4, 5], L247 = [0, 1, 1, 1, 2, 3, 4, 4, 5], L248 = [0, 1, 1, 1, 2, 3, 4, 5, 5], L256 = [0, 1, 1, 2, 2, 3, 3, 4, 5], L257 = [0, 1, 1, 2, 2, 3, 4, 4, 5]. q = 12 : L678 = [0, 0, 1, 1, 2, 3, 4, 5, 6], L783 = [0, 0, 1, 2, 2, 3, 4, 5, 6], L808 = [0, 0, 1, 2, 3, 3, 4, 5, 6], L921 = [0, 0, 2, 3, 3, 3, 3, 6, 6], L942 = [0, 0, 3, 3, 3, 3, 4, 6, 6], L1133 = [0, 1, 1, 1, 2, 3, 4, 5, 6], L1253 = [0, 1, 1, 2, 2, 3, 4, 5, 6], L1261 = [0, 1, 1, 2, 2, 4, 4, 5, 5], L1293 = [0, 1, 1, 2, 3, 4, 4, 5, 6], L1295 = [0, 1, 1, 2, 3, 4, 5, 5, 6 L1296 = [0, 1, 1, 2, 3, 4, 5, 6, 6], L1447 = [0, 1, 2, 2, 3, 3, 4, 5, 6], L1490 = [0, 1, 2, 3, 3, 4, 4, 5, 6], L1492 = [0, 1, 2, 3, 3, 4, 5, 6, 6], L1501 = [0, 1, 2, 3, 4, 4, 5, 6, 6], L2198 = [1, 1, 2, 2, 2, 4, 4, 5, 5], L2241 = [1, 1, 2, 2, 4, 4, 4, 5, 5 L2244 = [1, 1, 2, 2, 4, 4, 5, 5, 6].
Table 7. n = 9 q 4 5 7 8
I {2, 3, 6, 7} {3, 4, 8} {4, 5, 6} {4, 5} {2, 3, 6, 7} {2, 3, 4, 5, 6, 7} 10 {8} {3, 4, 8} 11
12
{0} {7, 8} {0, 6, 7, 8} {6, 7} {2, 3, 6, 7} {6, 7, 8}
indexes of I-isospectral families {17, 24} {14, 18} {28, 40, 53, 55} {96, 158}, {154, 240} {142, 223, 226}, {194, 300} {142, 226} {167, 351}, {273, 544}, {305, 522, 532, 592}, {311, 473, 529, 533}, {314, 585}, {315, 593} {311, 529}, {346, 380}, {350, 584}, {482, 540}, {493, 797}, {532, 592}, {746, 813} {9, 10}, {153, 154, 155} {50, 91, 141, 156, 158, 208, 237, 245, 247, 248, 256, 257} {256, 257} {678, 1296}, {1253, 1293} {808, 1492}, {921, 942}, {1261, 2244}, {1447, 1490}, {2198, 2241} {783, 1501}, {1133, 1295}
248
EMILIO A. LAURET
Table 7. (continued) m = 9 q 13
I {0}
indexes of I-isospectral families {11, 12}, {13, 14}, {34, 35, 36}, {271, 273}, {492, 495}, {493, 494}, {496, 502}, {503, 505}, {834, 835, 836, 838}, {837, 840}, {841, 842} {0, 1} {34, 35}, {835, 836} {5, 6, 7, 8} {158, 289, 457, 501, 506, 507} 14 {0} {66, 68}, {198, 200}, {479, 481}, {806, 810}, {975, 979}, {1017, 1019}, {1621, 1660}, {1664, 1668}, {1925, 1929}, {1977, 1979}, {3095, 3152}, {3157, 3161}, {3535, 3539}, {3598, 3600} {5} {477, 1016}, {1015, 1976} {4, 5, 6} {865, 1667, 3066, 3155}, {990, 1101, 1900, 1940, 1943, 2081}, {1014, 1927}, {1460, 1747, 2700, 2811, 2820, 3160}, {1634, 1924, 1944, 2090}, {1682, 1974}, {2461, 2797, 2821, 3268}
q = 13 : L11 = [0, 0, 0, 0, 0, 0, 1, 2, 3], L12 = [0, 0, 0, 0, 0, 0, 1, 2, 4], L13 = [0, 0, 0, 0, 0, 0, 1, 2, 5], L14 = [0, 0, 0, 0, 0, 0, 1, 3, 4], L34 = [0, 0, 0, 0, 0, 1, 2, 3, 4], L35 = [0, 0, 0, 0, 0, 1, 2, 3, 5], L36 = [0, 0, 0, 0, 0, 1, 2, 3, 6], L158 = [0, 0, 0, 1, 2, 3, 4, 5, 6], L271 = [0, 0, 1, 1, 2, 2, 3, 3, 5], L273 = [0, 0, 1, 1, 2, 2, 3, 4, 4], L289 = [0, 0, 1, 1, 2, 3, 4, 5, 6], L457 = [0, 1, 1, 1, 2, 3, 4, 5, 6], L492 = [0, 1, 1, 2, 2, 3, 3, 4, 4], L493 = [0, 1, 1, 2, 2, 3, 3, 4, 5], L494 = [0, 1, 1, 2, 2, 3, 3, 4, 6], L495 = [0, 1, 1, 2, 2, 3, 3, 5, 5], L496 = [0, 1, 1, 2, 2, 3, 3, 5, 6], L501 = [0, 1, 1, 2, 2, 3, 4, 5, 6], L502 = [0, 1, 1, 2, 2, 3, 4, 6, 6], L503 = [0, 1, 1, 2, 2, 3, 5, 5, 6], L505 = [0, 1, 1, 2, 3, 3, 4, 4, 5], L506 = [0, 1, 1, 2, 3, 3, 4, 5, 6], L507 = [0, 1, 1, 2, 3, 4, 5, 5, 6], L834 = [1, 1, 2, 2, 3, 3, 4, 4, 5], L835 = [1, 1, 2, 2, 3, 3, 4, 4, 6], L836 = [1, 1, 2, 2, 3, 3, 4, 5, 5], L837 = [1, 1, 2, 2, 3, 3, 4, 5, 6], L838 = [1, 1, 2, 2, 3, 3, 4, 6, 6], L840 = [1, 1, 2, 2, 3, 4, 4, 5, 6], L841 = [1, 1, 2, 2, 3, 4, 5, 5, 6], L842 = [1, 1, 2, 3, 3, 4, 4, 5, 6]. q = 14 : L66 = [0, 0, 0, 0, 0, 1, 2, 3, 4], L68 = [0, 0, 0, 0, 0, 1, 2, 3, 6], L198 = [0, 0, 0, 0, 1, 2, 3, 4, 7], L200 = [0, 0, 0, 0, 1, 2, 3, 6, 7], L477 = [0, 0, 0, 1, 2, 3, 4, 5, 7], L479 = [0, 0, 0, 1, 2, 3, 4, 7, 7], L481 = [0, 0, 0, 1, 2, 3, 6, 7, 7], L806 = [0, 0, 1, 1, 2, 3, 3, 4, 5], L810 = [0, 0, 1, 1, 2, 3, 3, 5, 6], L865 = [0, 0, 1, 1, 3, 3, 5, 5, 7], L975 = [0, 0, 1, 2, 2, 3, 4, 4, 6], L979 = [0, 0, 1, 2, 2, 3, 4, 6, 6], L990 = [0, 0, 1, 2, 2, 4, 4, 6, 6], L1014 = [0, 0, 1, 2, 3, 4, 5, 6, 7], L1015 = [0, 0, 1, 2, 3, 4, 5, 7, 7], L1016 = [0, 0, 1, 2, 3, 4, 6, 7, 7], L1017 = [0, 0, 1, 2, 3, 4, 7, 7, 7 L1019 = [0, 0, 1, 2, 3, 6, 7, 7, 7], L1101 = [0, 0, 2, 2, 4, 4, 6, 6, 7], L1460 = [0, 1, 1, 1, 3, 3, 5, 5, 7], L1621 = [0, 1, 1, 2, 2, 3, 5, 6, 6], L1634 = [0, 1, 1, 2, 2, 4, 4, 6, 6], L1660 = [0, 1, 1, 2, 3, 3, 4, 4, 6], L1664 = [0, 1, 1, 2, 3, 3, 4, 5, 7 L1667 = [0, 1, 1, 2, 3, 3, 5, 5, 7], L1668 = [0, 1, 1, 2, 3, 3, 5, 6, 7], L1682 = [0, 1, 1, 2, 3, 4, 5, 6, 7], L1747 = [0, 1, 1, 3, 3, 5, 5, 7, 7], L1900 = [0, 1, 2, 2, 2, 4, 4, 6, 6], L1924 = [0, 1, 2, 2, 3, 4, 4, 6, 6], L1925 = [0, 1, 2, 2, 3, 4, 4, 6, 7 L1927 = [0, 1, 2, 2, 3, 4, 5, 6, 7], L1929 = [0, 1, 2, 2, 3, 4, 6, 6, 7], L1940 = [0, 1, 2, 2, 4, 4, 4, 6, 6], L1943 = [0, 1, 2, 2, 4, 4, 6, 6, 6], L1944 = [0, 1, 2, 2, 4, 4, 6, 6, 7], L1974 = [0, 1, 2, 3, 4, 5, 6, 7, 7], L1976 = [0, 1, 2, 3, 4, 6, 7, 7, 7 L1977 = [0, 1, 2, 3, 4, 7, 7, 7, 7], L1979 = [0, 1, 2, 3, 6, 7, 7, 7, 7], L2081 = [0, 2, 2, 2, 4, 4, 6, 6, 7], L2090 = [0, 2, 2, 4, 4, 6, 6, 7, 7], L2461 = [1, 1, 1, 1, 3, 3, 5, 5, 7], L2700 = [1, 1, 1, 2, 3, 3, 5, 5, 7], L2797 = [1, 1, 1, 3, 3, 3, 5, 5, 7 L2811 = [1, 1, 1, 3, 3, 4, 5, 5, 7], L2820 = [1, 1, 1, 3, 3, 5, 5, 6, 7], L2821 = [1, 1, 1, 3, 3, 5, 5, 7, 7], L3066 = [1, 1, 2, 2, 3, 3, 5, 5, 7], L3095 = [1, 1, 2, 2, 3, 5, 6, 6, 7], L3152 = [1, 1, 2, 3, 3, 4, 4, 6, 7], L3155 = [1, 1, 2, 3, 3, 4, 5, 5, 7 L3157 = [1, 1, 2, 3, 3, 4, 5, 7, 7], L3160 = [1, 1, 2, 3, 3, 5, 5, 7, 7], L3161 = [1, 1, 2, 3, 3, 5, 6, 7, 7], L3268 = [1, 1, 3, 3, 5, 5, 7, 7, 7], L3535 = [1, 2, 2, 3, 4, 4, 6, 7, 7], L3539 = [1, 2, 2, 3, 4, 6, 6, 7, 7], L3598 = [1, 2, 3, 4, 7, 7, 7, 7, 7 L3600 = [1, 2, 3, 6, 7, 7, 7, 7, 7]. q = 15 : L18 = [0, 0, 0, 0, 0, 0, 1, 2, 6], L20 = [0, 0, 0, 0, 0, 0, 1, 3, 4], L66 = [0, 0, 0, 0, 0, 1, 2, 5, 6], L72 = [0, 0, 0, 0, 0, 1, 3, 4, 5], L175 = [0, 0, 0, 0, 1, 2, 3, 6, 6], L179 = [0, 0, 0, 0, 1, 2, 5, 5, 6], L187 = [0, 0, 0, 0, 1, 3, 3, 4, 6], L191 = [0, 0, 0, 0, 1, 3, 4, 5, 5], L408 = [0, 0, 0, 1, 2, 3, 5, 6, 6], L413 = [0, 0, 0, 1, 2, 5, 5, 5, 6], L427 = [0, 0, 0, 1, 3, 3, 4, 5, 6], L433 = [0, 0, 0, 1, 3, 4, 5, 5, 5], L686 = [0, 0, 1, 1, 2, 2, 4, 6, 7], L710 = [0, 0, 1, 1, 2, 3, 4, 4, 7], L838 = [0, 0, 1, 2, 3, 3, 6, 6, 6], L842 = [0, 0, 1, 2, 3, 4, 5, 6, 7], L846 = [0, 0, 1, 2, 3, 5, 5, 6, 6], L852 = [0, 0, 1, 2, 5, 5, 5, 5, 6], L868 = [0, 0, 1, 3, 3, 3, 4, 6, 6], L872 = [0, 0, 1, 3, 3, 3, 6, 6, 6], L874 =
APPENDIX
249
Table 7. (continued) m = 9 q 15
I {0}
indexes of I-isospectral families {18, 20}, {66, 72}, {175, 187}, {179, 191}, {408, 427}, {413, 433}, {686, 710}, {838, 868}, {846, 874}, {852, 882}, {1384, 1427}, {1609, 1649}, {1618, 1657}, {1625, 1667}, {2566, 2633}, {2584, 2652}, {2883, 2939}, {2895, 2947}, {2905, 2957}, {2913, 2969} {3, 4, 8} {842, 1602}, {872, 915}, {1434, 1614}
[0, 0, 1, 3, 3, 4, 5, 5, 6], L882 = [0, 0, 1, 3, 4, 5, 5, 5, 5], L915 = [0, 0, 3, 3, 3, 5, 6, 6, 6], L1384 = [0, 1, 1, 2, 2, 4, 5, 6, 7], L1427 = [0, 1, 1, 2, 3, 4, 4, 5, 7], L1434 = [0, 1, 1, 2, 3, 4, 5, 6, 7], L1602 = [0, 1, 2, 3, 3, 4, 5, 6, 7], L1609 = [0, 1, 2, 3, 3, 5, 6, 6, 6], L1614 = [0, 1, 2, 3, 4, 5, 5, 6, 7], L1618 = [0, 1, 2, 3, 5, 5, 5, 6, 6], L1625 = [0, 1, 2, 5, 5, 5, 5, 5, 6 L1649 = [0, 1, 3, 3, 3, 4, 5, 6, 6], L1657 = [0, 1, 3, 3, 4, 5, 5, 5, 6], L1667 = [0, 1, 3, 4, 5, 5, 5, 5, 5], L2566 = [1, 1, 2, 2, 3, 4, 6, 6, 7], L2584 = [1, 1, 2, 2, 4, 5, 5, 6, 7], L2633 = [1, 1, 2, 3, 3, 4, 4, 6, 7], L2652 = [1, 1, 2, 3, 4, 4, 5, 5, 7 L2883 = [1, 2, 3, 3, 3, 6, 6, 6, 6], L2895 = [1, 2, 3, 3, 5, 5, 6, 6, 6], L2905 = [1, 2, 3, 5, 5, 5, 5, 6, 6], L2913 = [1, 2, 5, 5, 5, 5, 5, 5, 6], L2939 = [1, 3, 3, 3, 3, 4, 6, 6, 6], L2947 = [1, 3, 3, 3, 4, 5, 5, 6, 6], L2957 = [1, 3, 3, 4, 5, 5, 5, 5, 6 L2969 = [1, 3, 4, 5, 5, 5, 5, 5, 5]. q = 16 : L78 = [0, 0, 0, 0, 0, 1, 2, 3, 5], L80 = [0, 0, 0, 0, 0, 1, 2, 3, 7], L180 = [0, 0, 0, 0, 1, 1, 3, 3, 5], L181 = [0, 0, 0, 0, 1, 1, 3, 3, 7], L233 = [0, 0, 0, 0, 1, 2, 2, 3, 5], L235 = [0, 0, 0, 0, 1, 2, 2, 3, 7], L250 = [0, 0, 0, 0, 1, 2, 3, 4, 5], L252 = [0, 0, 0, 0, 1, 2, 3, 4, 7], L256 = [0, 0, 0, 0, 1, 2, 3, 5, 8], L258 = [0, 0, 0, 0, 1, 2, 3, 7, 8], L512 = [0, 0, 0, 1, 1, 3, 3, 4, 5], L513 = [0, 0, 0, 1, 1, 3, 3, 4, 7], L517 = [0, 0, 0, 1, 1, 3, 3, 5, 8], L518 = [0, 0, 0, 1, 1, 3, 3, 7, 8], L604 = [0, 0, 0, 1, 2, 2, 2, 3, 5], L606 = [0, 0, 0, 1, 2, 2, 2, 3, 7], L621 = [0, 0, 0, 1, 2, 2, 3, 4, 5], L623 = [0, 0, 0, 1, 2, 2, 3, 4, 7], L625 = [0, 0, 0, 1, 2, 2, 3, 5, 6], L627 = [0, 0, 0, 1, 2, 2, 3, 5, 8], L629 = [0, 0, 0, 1, 2, 2, 3, 6, 7], L631 = [0, 0, 0, 1, 2, 2, 3, 7, 8], L655 = [0, 0, 0, 1, 2, 3, 4, 4, 5], L657 = [0, 0, 0, 1, 2, 3, 4, 4, 7], L661 = [0, 0, 0, 1, 2, 3, 4, 5, 8], L663 = [0, 0, 0, 1, 2, 3, 4, 7, 8], L668 = [0, 0, 0, 1, 2, 3, 5, 8, 8], L670 = [0, 0, 0, 1, 2, 3, 7, 8, 8], L708 = [0, 0, 0, 1, 3, 4, 5, 8, 8], L1155 = [0, 0, 1, 1, 2, 3, 3, 5, 6], L1158 = [0, 0, 1, 1, 2, 3, 3, 6, 7 L1248 = [0, 0, 1, 1, 3, 3, 4, 4, 5], L1249 = [0, 0, 1, 1, 3, 3, 4, 4, 7], L1253 = [0, 0, 1, 1, 3, 3, 4, 5, 8], L1254 = [0, 0, 1, 1, 3, 3, 4, 7, 8], L1259 = [0, 0, 1, 1, 3, 3, 5, 8, 8], L1260 = [0, 0, 1, 1, 3, 3, 7, 8, 8], L1391 = [0, 0, 1, 2, 2, 2, 2, 3, 5 L1393 = [0, 0, 1, 2, 2, 2, 2, 3, 7], L1408 = [0, 0, 1, 2, 2, 2, 3, 4, 5], L1410 = [0, 0, 1, 2, 2, 2, 3, 4, 7], L1412 = [0, 0, 1, 2, 2, 2, 3, 5, 6], L1414 = [0, 0, 1, 2, 2, 2, 3, 5, 8], L1416 = [0, 0, 1, 2, 2, 2, 3, 6, 7], L1418 = [0, 0, 1, 2, 2, 2, 3, 7, 8 L1443 = [0, 0, 1, 2, 2, 3, 4, 4, 5], L1445 = [0, 0, 1, 2, 2, 3, 4, 4, 7], L1447 = [0, 0, 1, 2, 2, 3, 4, 5, 6], L1449 = [0, 0, 1, 2, 2, 3, 4, 5, 8], L1451 = [0, 0, 1, 2, 2, 3, 4, 6, 7], L1453 = [0, 0, 1, 2, 2, 3, 4, 7, 8], L1457 = [0, 0, 1, 2, 2, 3, 5, 6, 8 L1459 = [0, 0, 1, 2, 2, 3, 5, 8, 8], L1461 = [0, 0, 1, 2, 2, 3, 6, 7, 8], L1463 = [0, 0, 1, 2, 2, 3, 7, 8, 8], L1477 = [0, 0, 1, 2, 2, 4, 5, 6, 8], L1498 = [0, 0, 1, 2, 3, 4, 4, 4, 5], L1500 = [0, 0, 1, 2, 3, 4, 4, 4, 7], L1504 = [0, 0, 1, 2, 3, 4, 4, 5, 8 L1506 = [0, 0, 1, 2, 3, 4, 4, 7, 8], L1509 = [0, 0, 1, 2, 3, 4, 5, 6, 8], L1511 = [0, 0, 1, 2, 3, 4, 5, 8, 8], L1513 = [0, 0, 1, 2, 3, 4, 7, 8, 8], L1518 = [0, 0, 1, 2, 3, 5, 8, 8, 8], L1520 = [0, 0, 1, 2, 3, 7, 8, 8, 8], L1537 = [0, 0, 1, 2, 4, 4, 6, 7, 8 L1567 = [0, 0, 1, 3, 4, 4, 4, 5, 8], L1569 = [0, 0, 1, 3, 4, 4, 5, 7, 8], L1573 = [0, 0, 1, 3, 4, 5, 8, 8, 8], L2560 = [0, 1, 1, 2, 3, 3, 4, 5, 6], L2563 = [0, 1, 1, 2, 3, 3, 4, 6, 7], L2569 = [0, 1, 1, 2, 3, 3, 5, 5, 7], L2572 = [0, 1, 1, 2, 3, 3, 5, 6, 8 L2573 = [0, 1, 1, 2, 3, 3, 5, 7, 7], L2576 = [0, 1, 1, 2, 3, 3, 6, 7, 8], L2715 = [0, 1, 1, 3, 3, 4, 4, 4, 5], L2716 = [0, 1, 1, 3, 3, 4, 4, 4, 7], L2720 = [0, 1, 1, 3, 3, 4, 4, 5, 8], L2721 = [0, 1, 1, 3, 3, 4, 4, 7, 8], L2726 = [0, 1, 1, 3, 3, 4, 5, 8, 8 L2727 = [0, 1, 1, 3, 3, 4, 7, 8, 8], L2729 = [0, 1, 1, 3, 3, 5, 5, 7, 7], L2733 = [0, 1, 1, 3, 3, 5, 8, 8, 8], L2734 = [0, 1, 1, 3, 3, 7, 8, 8, 8], L2921 = [0, 1, 2, 2, 2, 2, 2, 3, 5], L2923 = [0, 1, 2, 2, 2, 2, 2, 3, 7], L2938 = [0, 1, 2, 2, 2, 2, 3, 4, 5 L2940 = [0, 1, 2, 2, 2, 2, 3, 4, 7], L2942 = [0, 1, 2, 2, 2, 2, 3, 5, 6], L2944 = [0, 1, 2, 2, 2, 2, 3, 5, 8], L2946 = [0, 1, 2, 2, 2, 2, 3, 6, 7], L2948 = [0, 1, 2, 2, 2, 2, 3, 7, 8], L2973 = [0, 1, 2, 2, 2, 3, 4, 4, 5], L2975 = [0, 1, 2, 2, 2, 3, 4, 4, 7 L2977 = [0, 1, 2, 2, 2, 3, 4, 5, 6], L2979 = [0, 1, 2, 2, 2, 3, 4, 5, 8], L2981 = [0, 1, 2, 2, 2, 3, 4, 6, 7], L2983 = [0, 1, 2, 2, 2, 3, 4, 7, 8], L2985 = [0, 1, 2, 2, 2, 3, 5, 6, 6], L2987 = [0, 1, 2, 2, 2, 3, 5, 6, 8], L2989 = [0, 1, 2, 2, 2, 3, 5, 8, 8 L2991 = [0, 1, 2, 2, 2, 3, 6, 6, 7], L2993 = [0, 1, 2, 2, 2, 3, 6, 7, 8], L2995 = [0, 1, 2, 2, 2, 3, 7, 8, 8], L3032 = [0, 1, 2, 2, 3, 4, 4, 4, 5], L3034 = [0, 1, 2, 2, 3, 4, 4, 4, 7], L3036 = [0, 1, 2, 2, 3, 4, 4, 5, 6], L3038 = [0, 1, 2, 2, 3, 4, 4, 5, 8 L3040 = [0, 1, 2, 2, 3, 4, 4, 6, 7], L3042 = [0, 1, 2, 2, 3, 4, 4, 7, 8], L3046 = [0, 1, 2, 2, 3, 4, 5, 6, 8], L3048 =
250
EMILIO A. LAURET
Table 7. (continued) m = 9 q 16
I {0}
indexes of I-isospectral families {78, 80}, {180, 181}, {233, 235}, {250, 252}, {256, 258}, {512, 513}, {517, 518}, {604, 606}, {621, 623}, {625, 629}, {627, 631}, {655, 657}, {661, 663}, {668, 670}, {1155, 1158}, {1248, 1249}, {1253, 1254}, {1259, 1260}, {1391, 1393}, {1408, 1410}, {1412, 1416}, {1414, 1418}, {1443, 1445}, {1447, 1451}, {1449, 1453}, {1457, 1461}, {1459, 1463}, {1498, 1500}, {1504, 1506}, {1511, 1513}, {1518, 1520}, {2560, 2563}, {2569, 2573}, {2572, 2576}, {2715, 2716}, {2720, 2721}, {2726, 2727}, {2733, 2734}, {2921, 2923}, {2938, 2940}, {2942, 2946}, {2944, 2948}, {2973, 2975}, {2977, 2981}, {2979, 2983}, {2985, 2991}, {2987, 2993}, {2989, 2995}, {3032, 3034}, {3036, 3040}, {3038, 3042}, {3046, 3050}, {3048, 3052}, {3057, 3061}, {3059, 3063}, {3111, 3113}, {3117, 3119}, {3124, 3126}, {3131, 3133}, {3138, 3140}, {4502, 4504}, {5030, 5035}, {5032, 5038}, {5193, 5196}, {5202, 5206}, {5205, 5209}, {5217, 5221}, {5220, 5224}, {5423, 5424}, {5428, 5429}, {5434, 5435}, {5441, 5442}, {5448, 5449}, {5703, 5705}, {5720, 5722}, {5724, 5728}, {5726, 5730}, {5755, 5757}, {5759, 5763}, {5761, 5765}, {5767, 5773}, {5769, 5775}, {5771, 5777}, {5815, 5817}, {5819, 5823}, {5821, 5825}, {5827, 5833}, {5829, 5835}, {5831, 5837}, {5841, 5847}, {5843, 5849}, {5845, 5851}, {5902, 5904}, {5906, 5910}, {5908, 5912}, {5916, 5920}, {5918, 5922}, {5927, 5931}, {5929, 5933}, {5938, 5942}, {5940, 5944}, {6007, 6009}, {6013, 6015}, {6020, 6022}, {6027, 6029}, {6034, 6036}, {6041, 6043} {5} {708, 1573}, {1567, 3204} {4, 5} {1477, 3051}, {1537, 3167}, {3082, 3165} {3, 4, 5, 6} {1509, 3129} {2, 3, 6, 7} {1569, 3206}, {2729, 5437, 5444}, {3054, 5935} {2, 3, 4, 5, 6, 7} {2729, 5444}
[0, 1, 2, 2, 3, 4, 5, 8, 8], L3050 = [0, 1, 2, 2, 3, 4, 6, 7, 8], L3051 = [0, 1, 2, 2, 3, 4, 6, 8, 8], L3052 = [0, 1, 2, 2, 3, 4, 7, 8, 8 L3054 = [0, 1, 2, 2, 3, 5, 6, 6, 7], L3057 = [0, 1, 2, 2, 3, 5, 6, 8, 8], L3059 = [0, 1, 2, 2, 3, 5, 8, 8, 8], L3061 = [0, 1, 2, 2, 3, 6, 7, 8, 8], L3063 = [0, 1, 2, 2, 3, 7, 8, 8, 8], L3082 = [0, 1, 2, 2, 4, 4, 6, 7, 8], L3111 = [0, 1, 2, 3, 4, 4, 4, 4, 5 L3113 = [0, 1, 2, 3, 4, 4, 4, 4, 7], L3117 = [0, 1, 2, 3, 4, 4, 4, 5, 8], L3119 = [0, 1, 2, 3, 4, 4, 4, 7, 8], L3124 = [0, 1, 2, 3, 4, 4, 5, 8, 8], L3126 = [0, 1, 2, 3, 4, 4, 7, 8, 8], L3129 = [0, 1, 2, 3, 4, 5, 6, 8, 8], L3131 = [0, 1, 2, 3, 4, 5, 8, 8, 8 L3133 = [0, 1, 2, 3, 4, 7, 8, 8, 8], L3138 = [0, 1, 2, 3, 5, 8, 8, 8, 8], L3140 = [0, 1, 2, 3, 7, 8, 8, 8, 8], L3165 = [0, 1, 2, 4, 4, 6, 6, 7, 8], L3167 = [0, 1, 2, 4, 4, 6, 7, 8, 8], L3204 = [0, 1, 3, 4, 4, 4, 5, 8, 8], L3206 = [0, 1, 3, 4, 4, 5, 7, 8, 8 L4502 = [1, 1, 1, 3, 3, 3, 5, 5, 7], L4504 = [1, 1, 1, 3, 3, 3, 5, 7, 7], L5030 = [1, 1, 2, 2, 3, 3, 5, 5, 7], L5032 = [1, 1, 2, 2, 3, 3, 5, 6, 6], L5035 = [1, 1, 2, 2, 3, 3, 5, 7, 7], L5038 = [1, 1, 2, 2, 3, 3, 6, 6, 7], L5193 = [1, 1, 2, 3, 3, 4, 4, 5, 6 L5196 = [1, 1, 2, 3, 3, 4, 4, 6, 7], L5202 = [1, 1, 2, 3, 3, 4, 5, 5, 7], L5205 = [1, 1, 2, 3, 3, 4, 5, 6, 8], L5206 = [1, 1, 2, 3, 3, 4, 5, 7, 7], L5209 = [1, 1, 2, 3, 3, 4, 6, 7, 8], L5217 = [1, 1, 2, 3, 3, 5, 5, 7, 8], L5220 = [1, 1, 2, 3, 3, 5, 6, 8, 8 L5221 = [1, 1, 2, 3, 3, 5, 7, 7, 8], L5224 = [1, 1, 2, 3, 3, 6, 7, 8, 8], L5423 = [1, 1, 3, 3, 4, 4, 4, 4, 5], L5424 = [1, 1, 3, 3, 4, 4, 4, 4, 7], L5428 = [1, 1, 3, 3, 4, 4, 4, 5, 8], L5429 = [1, 1, 3, 3, 4, 4, 4, 7, 8], L5434 = [1, 1, 3, 3, 4, 4, 5, 8, 8 L5435 = [1, 1, 3, 3, 4, 4, 7, 8, 8], L5437 = [1, 1, 3, 3, 4, 5, 5, 7, 7], L5441 = [1, 1, 3, 3, 4, 5, 8, 8, 8], L5442 = [1, 1, 3, 3, 4, 7, 8, 8, 8], L5444 = [1, 1, 3, 3, 5, 5, 7, 7, 8], L5448 = [1, 1, 3, 3, 5, 8, 8, 8, 8], L5449 = [1, 1, 3, 3, 7, 8, 8, 8, 8 L5703 = [1, 2, 2, 2, 2, 2, 2, 3, 5], L5705 = [1, 2, 2, 2, 2, 2, 2, 3, 7], L5720 = [1, 2, 2, 2, 2, 2, 3, 4, 5], L5722 = [1, 2, 2, 2, 2, 2, 3, 4, 7], L5724 = [1, 2, 2, 2, 2, 2, 3, 5, 6], L5726 = [1, 2, 2, 2, 2, 2, 3, 5, 8], L5728 = [1, 2, 2, 2, 2, 2, 3, 6, 7 L5730 = [1, 2, 2, 2, 2, 2, 3, 7, 8], L5755 = [1, 2, 2, 2, 2, 3, 4, 4, 5], L5757 = [1, 2, 2, 2, 2, 3, 4, 4, 7], L5759 =
APPENDIX
251
Table 7. (continued) m = 9 q 17
I {0}
indexes of I-isospectral families {16, 17}, {18, 19}, {55, 56, 58}, {62, 63}, {156, 157, 158, 159, 160}, {161, 162}, {376, 377, 378, 379} {0, 1} {57, 59}, {157, 158}, {376, 377, 378} {0, 1, 2} {377, 378}
[1, 2, 2, 2, 2, 3, 4, 5, 6], L5761 = [1, 2, 2, 2, 2, 3, 4, 5, 8], L5763 = [1, 2, 2, 2, 2, 3, 4, 6, 7], L5765 = [1, 2, 2, 2, 2, 3, 4, 7, 8 L5767 = [1, 2, 2, 2, 2, 3, 5, 6, 6], L5769 = [1, 2, 2, 2, 2, 3, 5, 6, 8], L5771 = [1, 2, 2, 2, 2, 3, 5, 8, 8], L5773 = [1, 2, 2, 2, 2, 3, 6, 6, 7], L5775 = [1, 2, 2, 2, 2, 3, 6, 7, 8], L5777 = [1, 2, 2, 2, 2, 3, 7, 8, 8], L5815 = [1, 2, 2, 2, 3, 4, 4, 4, 5 L5817 = [1, 2, 2, 2, 3, 4, 4, 4, 7], L5819 = [1, 2, 2, 2, 3, 4, 4, 5, 6], L5821 = [1, 2, 2, 2, 3, 4, 4, 5, 8], L5823 = [1, 2, 2, 2, 3, 4, 4, 6, 7], L5825 = [1, 2, 2, 2, 3, 4, 4, 7, 8], L5827 = [1, 2, 2, 2, 3, 4, 5, 6, 6], L5829 = [1, 2, 2, 2, 3, 4, 5, 6, 8 L5831 = [1, 2, 2, 2, 3, 4, 5, 8, 8], L5833 = [1, 2, 2, 2, 3, 4, 6, 6, 7], L5835 = [1, 2, 2, 2, 3, 4, 6, 7, 8], L5837 = [1, 2, 2, 2, 3, 4, 7, 8, 8], L5841 = [1, 2, 2, 2, 3, 5, 6, 6, 8], L5843 = [1, 2, 2, 2, 3, 5, 6, 8, 8], L5845 = [1, 2, 2, 2, 3, 5, 8, 8, 8 L5847 = [1, 2, 2, 2, 3, 6, 6, 7, 8], L5849 = [1, 2, 2, 2, 3, 6, 7, 8, 8], L5851 = [1, 2, 2, 2, 3, 7, 8, 8, 8], L5902 = [1, 2, 2, 3, 4, 4, 4, 4, 5], L5904 = [1, 2, 2, 3, 4, 4, 4, 4, 7], L5906 = [1, 2, 2, 3, 4, 4, 4, 5, 6], L5908 = [1, 2, 2, 3, 4, 4, 4, 5, 8 L5910 = [1, 2, 2, 3, 4, 4, 4, 6, 7], L5912 = [1, 2, 2, 3, 4, 4, 4, 7, 8], L5916 = [1, 2, 2, 3, 4, 4, 5, 6, 8], L5918 = [1, 2, 2, 3, 4, 4, 5, 8, 8], L5920 = [1, 2, 2, 3, 4, 4, 6, 7, 8], L5922 = [1, 2, 2, 3, 4, 4, 7, 8, 8], L5927 = [1, 2, 2, 3, 4, 5, 6, 8, 8 L5929 = [1, 2, 2, 3, 4, 5, 8, 8, 8], L5931 = [1, 2, 2, 3, 4, 6, 7, 8, 8], L5933 = [1, 2, 2, 3, 4, 7, 8, 8, 8], L5935 = [1, 2, 2, 3, 5, 6, 6, 7, 8], L5938 = [1, 2, 2, 3, 5, 6, 8, 8, 8], L5940 = [1, 2, 2, 3, 5, 8, 8, 8, 8], L5942 = [1, 2, 2, 3, 6, 7, 8, 8, 8 L5944 = [1, 2, 2, 3, 7, 8, 8, 8, 8], L6007 = [1, 2, 3, 4, 4, 4, 4, 4, 5], L6009 = [1, 2, 3, 4, 4, 4, 4, 4, 7], L6013 = [1, 2, 3, 4, 4, 4, 4, 5, 8], L6015 = [1, 2, 3, 4, 4, 4, 4, 7, 8], L6020 = [1, 2, 3, 4, 4, 4, 5, 8, 8], L6022 = [1, 2, 3, 4, 4, 4, 7, 8, 8 L6027 = [1, 2, 3, 4, 4, 5, 8, 8, 8], L6029 = [1, 2, 3, 4, 4, 7, 8, 8, 8], L6034 = [1, 2, 3, 4, 5, 8, 8, 8, 8], L6036 = [1, 2, 3, 4, 7, 8, 8, 8, 8], L6041 = [1, 2, 3, 5, 8, 8, 8, 8, 8], L6043 = [1, 2, 3, 7, 8, 8, 8, 8, 8]. q = 17 : L16 = [0, 0, 0, 0, 0, 0, 1, 2, 5], L17 = [0, 0, 0, 0, 0, 0, 1, 2, 6], L18 = [0, 0, 0, 0, 0, 0, 1, 2, 7], L19 = [0, 0, 0, 0, 0, 0, 1, 3, 4], L55 = [0, 0, 0, 0, 0, 1, 2, 3, 5], L56 = [0, 0, 0, 0, 0, 1, 2, 3, 6], L57 = [0, 0, 0, 0, 0, 1, 2, 3, 7], L58 = [0, 0, 0, 0, 0, 1, 2, 3, 8], L59 = [0, 0, 0, 0, 0, 1, 2, 4, 5], L62 = [0, 0, 0, 0, 0, 1, 2, 6, 7], L63 = [0, 0, 0, 0, 0, 1, 3, 4, 5], L156 = [0, 0, 0, 0, 1, 2, 3, 4, 5], L157 = [0, 0, 0, 0, 1, 2, 3, 4, 6], L158 = [0, 0, 0, 0, 1, 2, 3, 4, 7], L159 = [0, 0, 0, 0, 1, 2, 3, 4, 8], L160 = [0, 0, 0, 0, 1, 2, 3, 5, 6], L161 = [0, 0, 0, 0, 1, 2, 3, 5, 8], L162 = [0, 0, 0, 0, 1, 2, 3, 6, 7], L376 = [0, 0, 0, 1, 2, 3, 4, 5, 6], L377 = [0, 0, 0, 1, 2, 3, 4, 5, 7], L378 = [0, 0, 0, 1, 2, 3, 4, 5, 8], L379 = [0, 0, 0, 1, 2, 3, 4, 6, 8]. q = 18 : L117 = [0, 0, 0, 0, 0, 1, 2, 4, 5], L119 = [0, 0, 0, 0, 0, 1, 2, 4, 7], L407 = [0, 0, 0, 0, 1, 2, 3, 4, 5], L409 = [0, 0, 0, 0, 1, 2, 3, 4, 7], L429 = [0, 0, 0, 0, 1, 2, 4, 5, 6], L432 = [0, 0, 0, 0, 1, 2, 4, 5, 9], L434 = [0, 0, 0, 0, 1, 2, 4, 6, 7], L437 = [0, 0, 0, 0, 1, 2, 4, 7, 9], L1182 = [0, 0, 0, 1, 2, 3, 3, 4, 5], L1184 = [0, 0, 0, 1, 2, 3, 3, 4, 7 L1204 = [0, 0, 0, 1, 2, 3, 4, 5, 6], L1207 = [0, 0, 0, 1, 2, 3, 4, 5, 9], L1209 = [0, 0, 0, 1, 2, 3, 4, 6, 7], L1212 = [0, 0, 0, 1, 2, 3, 4, 7, 9], L1251 = [0, 0, 0, 1, 2, 4, 5, 6, 6], L1254 = [0, 0, 0, 1, 2, 4, 5, 6, 9], L1258 = [0, 0, 0, 1, 2, 4, 5, 9, 9 L1260 = [0, 0, 0, 1, 2, 4, 6, 6, 7], L1263 = [0, 0, 0, 1, 2, 4, 6, 7, 9], L1267 = [0, 0, 0, 1, 2, 4, 7, 9, 9], L2304 = [0, 0, 1, 1, 2, 4, 5, 5, 7], L2311 = [0, 0, 1, 1, 2, 4, 5, 7, 7], L2905 = [0, 0, 1, 2, 2, 4, 4, 5, 8], L2911 = [0, 0, 1, 2, 2, 4, 4, 7, 8 L2985 = [0, 0, 1, 2, 3, 3, 3, 4, 5], L2987 = [0, 0, 1, 2, 3, 3, 3, 4, 7], L3007 = [0, 0, 1, 2, 3, 3, 4, 5, 6], L3010 = [0, 0, 1, 2, 3, 3, 4, 5, 9], L3012 = [0, 0, 1, 2, 3, 3, 4, 6, 7], L3015 = [0, 0, 1, 2, 3, 3, 4, 7, 9], L3054 = [0, 0, 1, 2, 3, 4, 5, 6, 6 L3057 = [0, 0, 1, 2, 3, 4, 5, 6, 9], L3061 = [0, 0, 1, 2, 3, 4, 5, 9, 9], L3063 = [0, 0, 1, 2, 3, 4, 6, 6, 7], L3066 = [0, 0, 1, 2, 3, 4, 6, 7, 9], L3070 = [0, 0, 1, 2, 3, 4, 7, 9, 9], L3136 = [0, 0, 1, 2, 4, 5, 6, 6, 6], L3139 = [0, 0, 1, 2, 4, 5, 6, 6, 9 L3143 = [0, 0, 1, 2, 4, 5, 6, 9, 9], L3147 = [0, 0, 1, 2, 4, 5, 9, 9, 9], L3149 = [0, 0, 1, 2, 4, 6, 6, 6, 7], L3152 = [0, 0, 1, 2, 4, 6, 6, 7, 9], L3156 = [0, 0, 1, 2, 4, 6, 7, 9, 9], L3161 = [0, 0, 1, 2, 4, 7, 9, 9, 9], L5233 = [0, 1, 1, 2, 2, 5, 7, 8, 8 L5373 = [0, 1, 1, 2, 3, 4, 5, 5, 7], L5380 = [0, 1, 1, 2, 3, 4, 5, 7, 7], L5482 = [0, 1, 1, 2, 4, 4, 5, 5, 8], L5510 = [0, 1, 1, 2, 4, 5, 5, 6, 7], L5515 = [0, 1, 1, 2, 4, 5, 5, 7, 9], L5522 = [0, 1, 1, 2, 4, 5, 6, 7, 7], L5528 = [0, 1, 1, 2, 4, 5, 7, 7, 9 L6577 = [0, 1, 2, 2, 3, 4, 4, 5, 8], L6583 = [0, 1, 2, 2, 3, 4, 4, 7, 8], L6665 = [0, 1, 2, 2, 4, 4, 5, 6, 8], L6670 = [0, 1, 2, 2, 4, 4, 5, 8, 9], L6676 = [0, 1, 2, 2, 4, 4, 6, 7, 8], L6681 = [0, 1, 2, 2, 4, 4, 7, 8, 9], L6784 = [0, 1, 2, 3, 3, 3, 3, 4, 5
252
EMILIO A. LAURET
Table 7. (continued) m = 9 q 18
I {0}
indexes of I-isospectral families {117, 119}, {407, 409}, {429, 434}, {432, 437}, {1182, 1184}, {1204, 1209}, {1207, 1212}, {1251, 1260}, {1254, 1263}, {1258, 1267}, {2304, 2311}, {2905, 2911}, {2985, 2987}, {3007, 3012}, {3010, 3015}, {3054, 3063}, {3057, 3066}, {3061, 3070}, {3136, 3149}, {3139, 3152}, {3143, 3156}, {3147, 3161}, {5233, 5482}, {5373, 5380}, {5510, 5522}, {5515, 5528}, {6577, 6583}, {6670, 6681}, {6784, 6786}, {6806, 6811}, {6809, 6814}, {6853, 6862}, {6856, 6865}, {6860, 6869}, {6935, 6948}, {6938, 6951}, {6942, 6955}, {6946, 6960}, {7062, 7079}, {7065, 7082}, {7069, 7086}, {7073, 7091}, {7077, 7097}, {11285, 11738}, {11462, 11957}, {11473, 11961}, {11629, 11636}, {11766, 11778}, {12005, 12023}, {12010, 12029}, {12016, 12037}, {13815, 13821}, {13903, 13914}, {13908, 13919}, {14046, 14063}, {14051, 14068}, {14057, 14074}, {14210, 14212}, {14232, 14237}, {14235, 14240}, {14279, 14288}, {14282, 14291}, {14286, 14295}, {14361, 14374}, {14364, 14377}, {14368, 14381}, {14372, 14386}, {14488, 14505}, {14491, 14508}, {14495, 14512}, {14499, 14517}, {14503, 14523}, {14671, 14692}, {14674, 14695}, {14678, 14699}, {14682, 14704}, {14686, 14710}, {14690, 14717} {0, 8} {6665, 6676}, {11771, 11784}
L6786 = [0, 1, 2, 3, 3, 3, 3, 4, 7], L6806 = [0, 1, 2, 3, 3, 3, 4, 5, 6], L6809 = [0, 1, 2, 3, 3, 3, 4, 5, 9], L6811 = [0, 1, 2, 3, 3, 3, 4, 6, 7], L6814 = [0, 1, 2, 3, 3, 3, 4, 7, 9], L6853 = [0, 1, 2, 3, 3, 4, 5, 6, 6], L6856 = [0, 1, 2, 3, 3, 4, 5, 6, 9 L6860 = [0, 1, 2, 3, 3, 4, 5, 9, 9], L6862 = [0, 1, 2, 3, 3, 4, 6, 6, 7], L6865 = [0, 1, 2, 3, 3, 4, 6, 7, 9], L6869 = [0, 1, 2, 3, 3, 4, 7, 9, 9], L6935 = [0, 1, 2, 3, 4, 5, 6, 6, 6], L6938 = [0, 1, 2, 3, 4, 5, 6, 6, 9], L6942 = [0, 1, 2, 3, 4, 5, 6, 9, 9 L6946 = [0, 1, 2, 3, 4, 5, 9, 9, 9], L6948 = [0, 1, 2, 3, 4, 6, 6, 6, 7], L6951 = [0, 1, 2, 3, 4, 6, 6, 7, 9], L6955 = [0, 1, 2, 3, 4, 6, 7, 9, 9], L6960 = [0, 1, 2, 3, 4, 7, 9, 9, 9], L7062 = [0, 1, 2, 4, 5, 6, 6, 6, 6], L7065 = [0, 1, 2, 4, 5, 6, 6, 6, 9 L7069 = [0, 1, 2, 4, 5, 6, 6, 9, 9], L7073 = [0, 1, 2, 4, 5, 6, 9, 9, 9], L7077 = [0, 1, 2, 4, 5, 9, 9, 9, 9], L7079 = [0, 1, 2, 4, 6, 6, 6, 6, 7], L7082 = [0, 1, 2, 4, 6, 6, 6, 7, 9], L7086 = [0, 1, 2, 4, 6, 6, 7, 9, 9], L7091 = [0, 1, 2, 4, 6, 7, 9, 9, 9 L7097 = [0, 1, 2, 4, 7, 9, 9, 9, 9], L11285 = [1, 1, 2, 2, 3, 5, 7, 8, 8], L11462 = [1, 1, 2, 2, 5, 6, 7, 8, 8], L11473 = [1, 1, 2, 2, 5, 7, 8, 8, 9], L11629 = [1, 1, 2, 3, 3, 4, 5, 5, 7], L11636 = [1, 1, 2, 3, 3, 4, 5, 7, 7], L11738 = [1, 1, 2, 3, 4, 4, 5, 5, 8], L11766 = [1, 1, 2, 3, 4, 5, 5, 6, 7], L11771 = [1, 1, 2, 3, 4, 5, 5, 7, 9], L11778 = [1, 1, 2, 3, 4, 5, 6, 7, 7], L11784 = [1, 1, 2, 3, 4, 5, 7, 7, 9], L11957 = [1, 1, 2, 4, 4, 5, 5, 6, 8], L11961 = [1, 1, 2, 4, 4, 5, 5, 8, 9], L12005 = [1, 1, 2, 4, 5, 5, 6, 6, 7], L12010 = [1, 1, 2, 4, 5, 5, 6, 7, 9], L12016 = [1, 1, 2, 4, 5, 5, 7, 9, 9], L12023 = [1, 1, 2, 4, 5, 6, 6, 7, 7], L12029 = [1, 1, 2, 4, 5, 6, 7, 7, 9], L12037 = [1, 1, 2, 4, 5, 7, 7, 9, 9], L13815 = [1, 2, 2, 3, 3, 4, 4, 5, 8], L13821 = [1, 2, 2, 3, 3, 4, 4, 7, 8], L13903 = [1, 2, 2, 3, 4, 4, 5, 6, 8], L13908 = [1, 2, 2, 3, 4, 4, 5, 8, 9], L13914 = [1, 2, 2, 3, 4, 4, 6, 7, 8], L13919 = [1, 2, 2, 3, 4, 4, 7, 8, 9], L14046 = [1, 2, 2, 4, 4, 5, 6, 6, 8], L14051 = [1, 2, 2, 4, 4, 5, 6, 8, 9], L14057 = [1, 2, 2, 4, 4, 5, 8, 9, 9], L14063 = [1, 2, 2, 4, 4, 6, 6, 7, 8], L14068 = [1, 2, 2, 4, 4, 6, 7, 8, 9], L14074 = [1, 2, 2, 4, 4, 7, 8, 9, 9], L14210 = [1, 2, 3, 3, 3, 3, 3, 4, 5], L14212 = [1, 2, 3, 3, 3, 3, 3, 4, 7], L14232 = [1, 2, 3, 3, 3, 3, 4, 5, 6], L14235 = [1, 2, 3, 3, 3, 3, 4, 5, 9], L14237 = [1, 2, 3, 3, 3, 3, 4, 6, 7], L14240 = [1, 2, 3, 3, 3, 3, 4, 7, 9], L14279 = [1, 2, 3, 3, 3, 4, 5, 6, 6], L14282 = [1, 2, 3, 3, 3, 4, 5, 6, 9], L14286 = [1, 2, 3, 3, 3, 4, 5, 9, 9], L14288 = [1, 2, 3, 3, 3, 4, 6, 6, 7], L14291 = [1, 2, 3, 3, 3, 4, 6, 7, 9], L14295 = [1, 2, 3, 3, 3, 4, 7, 9, 9], L14361 = [1, 2, 3, 3, 4, 5, 6, 6, 6], L14364 = [1, 2, 3, 3, 4, 5, 6, 6, 9], L14368 = [1, 2, 3, 3, 4, 5, 6, 9, 9], L14372 = [1, 2, 3, 3, 4, 5, 9, 9, 9], L14374 = [1, 2, 3, 3, 4, 6, 6, 6, 7], L14377 = [1, 2, 3, 3, 4, 6, 6, 7, 9], L14381 = [1, 2, 3, 3, 4, 6, 7, 9, 9], L14386 = [1, 2, 3, 3, 4, 7, 9, 9, 9], L14488 = [1, 2, 3, 4, 5, 6, 6, 6, 6], L14491 = [1, 2, 3, 4, 5, 6, 6, 6, 9], L14495 = [1, 2, 3, 4, 5, 6, 6, 9, 9],
APPENDIX
253
Table 7. (continued) m = 9 q 19
I {0}
indexes of I-isospectral families {19, 21}, {67, 68, 71}, {70, 72, 74}, {77, 79}, {209, 210}, {211, 213, 215, 217}, {214, 216, 218, 220}, {219, 222}, {548, 549, 550, 551, 552, 553, 554}, {555, 556, 557}, {1269, 1270, 1271, 1272} {0, 1} {216, 218}, {550, 551}, {552, 554}, {555, 557}, {1269, 1270, 1271} {0, 1, 2, 3} {1270, 1271}
L14499 = [1, 2, 3, 4, 5, 6, 9, 9, 9], L14503 = [1, 2, 3, 4, 5, 9, 9, 9, 9], L14505 = [1, 2, 3, 4, 6, 6, 6, 6, 7], L14508 = [1, 2, 3, 4, 6, 6, 6, 7, 9], L14512 = [1, 2, 3, 4, 6, 6, 7, 9, 9], L14517 = [1, 2, 3, 4, 6, 7, 9, 9, 9], L14523 = [1, 2, 3, 4, 7, 9, 9, 9, 9], L14671 = [1, 2, 4, 5, 6, 6, 6, 6, 6], L14674 = [1, 2, 4, 5, 6, 6, 6, 6, 9], L14678 = [1, 2, 4, 5, 6, 6, 6, 9, 9], L14682 = [1, 2, 4, 5, 6, 6, 9, 9, 9], L14686 = [1, 2, 4, 5, 6, 9, 9, 9, 9], L14690 = [1, 2, 4, 5, 9, 9, 9, 9, 9], L14692 = [1, 2, 4, 6, 6, 6, 6, 6, 7], L14695 = [1, 2, 4, 6, 6, 6, 6, 7, 9], L14699 = [1, 2, 4, 6, 6, 6, 7, 9, 9], L14704 = [1, 2, 4, 6, 6, 7, 9, 9, 9], L14710 = [1, 2, 4, 6, 7, 9, 9, 9, 9], L14717 = [1, 2, 4, 7, 9, 9, 9, 9, 9]. q = 19 : L19 = [0, 0, 0, 0, 0, 0, 1, 2, 7], L21 = [0, 0, 0, 0, 0, 0, 1, 3, 4], L67 = [0, 0, 0, 0, 0, 1, 2, 3, 5], L68 = [0, 0, 0, 0, 0, 1, 2, 3, 6], L70 = [0, 0, 0, 0, 0, 1, 2, 3, 8], L71 = [0, 0, 0, 0, 0, 1, 2, 3, 9], L72 = [0, 0, 0, 0, 0, 1, 2, 4, 5], L74 = [0, 0, 0, 0, 0, 1, 2, 4, 8], L77 = [0, 0, 0, 0, 0, 1, 2, 6, 8], L79 = [0, 0, 0, 0, 0, 1, 3, 4, 5], L209 = [0, 0, 0, 0, 1, 2, 3, 4, 5], L210 = [0, 0, 0, 0, 1, 2, 3, 4, 6], L211 = [0, 0, 0, 0, 1, 2, 3, 4, 7], L213 = [0, 0, 0, 0, 1, 2, 3, 4, 9], L214 = [0, 0, 0, 0, 1, 2, 3, 5, 6], L215 = [0, 0, 0, 0, 1, 2, 3, 5, 7], L216 = [0, 0, 0, 0, 1, 2, 3, 5, 9], L217 = [0, 0, 0, 0, 1, 2, 3, 6, 7], L218 = [0, 0, 0, 0, 1, 2, 3, 6, 8], L219 = [0, 0, 0, 0, 1, 2, 3, 7, 8], L220 = [0, 0, 0, 0, 1, 2, 3, 7, 9], L222 = [0, 0, 0, 0, 1, 2, 5, 6, 8], L548 = [0, 0, 0, 1, 2, 3, 4, 5, 6], L549 = [0, 0, 0, 1, 2, 3, 4, 5, 7], L550 = [0, 0, 0, 1, 2, 3, 4, 5, 8], L551 = [0, 0, 0, 1, 2, 3, 4, 5, 9], L552 = [0, 0, 0, 1, 2, 3, 4, 6, 7], L553 = [0, 0, 0, 1, 2, 3, 4, 6, 8], L554 = [0, 0, 0, 1, 2, 3, 4, 6, 9], L555 = [0, 0, 0, 1, 2, 3, 4, 7, 9], L556 = [0, 0, 0, 1, 2, 3, 5, 6, 9], L557 = [0, 0, 0, 1, 2, 3, 5, 7, 8], L1269 = [0, 0, 1, 2, 3, 4, 5, 6, 7], L1270 = [0, 0, 1, 2, 3, 4, 5, 6, 8], L1271 = [0, 0, 1, 2, 3, 4, 5, 6, 9], L1272 = [0, 0, 1, 2, 3, 4, 5, 8, 9]. q = 20 : L355 = [0, 0, 0, 0, 1, 1, 3, 3, 7], L357 = [0, 0, 0, 0, 1, 1, 3, 3, 9], L505 = [0, 0, 0, 0, 1, 2, 3, 4, 7], L507 = [0, 0, 0, 0, 1, 2, 3, 4, 9], L1175 = [0, 0, 0, 1, 1, 3, 3, 5, 7], L1177 = [0, 0, 0, 1, 1, 3, 3, 5, 9], L1182 = [0, 0, 0, 1, 1, 3, 3, 7, 10], L1186 = [0, 0, 0, 1, 1, 3, 3, 9, 10], L1574 = [0, 0, 0, 1, 2, 3, 4, 5, 7], L1576 = [0, 0, 0, 1, 2, 3, 4, 5, 9], L1584 = [0, 0, 0, 1, 2, 3, 4, 7, 10], L1588 = [0, 0, 0, 1, 2, 3, 4, 9, 10], L1600 = [0, 0, 0, 1, 2, 3, 5, 7, 9], L2597 = [0, 0, 1, 1, 1, 3, 5, 7, 9], L3014 = [0, 0, 1, 1, 2, 3, 3, 6, 7], L3016 = [0, 0, 1, 1, 2, 3, 3, 6, 9 L3069 = [0, 0, 1, 1, 2, 3, 5, 7, 9], L3168 = [0, 0, 1, 1, 2, 4, 6, 8, 10], L3305 = [0, 0, 1, 1, 3, 3, 4, 7, 8], L3309 = [0, 0, 1, 1, 3, 3, 4, 8, 9], L3315 = [0, 0, 1, 1, 3, 3, 5, 5, 7], L3317 = [0, 0, 1, 1, 3, 3, 5, 5, 9], L3322 = [0, 0, 1, 1, 3, 3, 5, 7, 1 L3326 = [0, 0, 1, 1, 3, 3, 5, 9, 10], L3334 = [0, 0, 1, 1, 3, 3, 7, 10, 10], L3340 = [0, 0, 1, 1, 3, 3, 9, 10, 10], L3444 = [0, 0, 1, 1, 3, 5, 6, 7, 9], L3455 = [0, 0, 1, 1, 3, 5, 7, 9, 9], L3988 = [0, 0, 1, 2, 2, 3, 4, 4, 7], L3990 = [0, 0, 1, 2, 2, 3, 4, 4, 9], L3999 = [0, 0, 1, 2, 2, 3, 4, 6, 7], L4001 = [0, 0, 1, 2, 2, 3, 4, 6, 9], L4023 = [0, 0, 1, 2, 2, 3, 5, 7, 9 L4104 = [0, 0, 1, 2, 2, 4, 6, 8, 10], L4205 = [0, 0, 1, 2, 3, 4, 4, 7, 8], L4209 = [0, 0, 1, 2, 3, 4, 4, 8, 9], L4215 = [0, 0, 1, 2, 3, 4, 5, 5, 7], L4217 = [0, 0, 1, 2, 3, 4, 5, 5, 9], L4224 = [0, 0, 1, 2, 3, 4, 5, 7, 9], L4225 = [0, 0, 1, 2, 3, 4, 5, 7, 1 L4229 = [0, 0, 1, 2, 3, 4, 5, 9, 10], L4232 = [0, 0, 1, 2, 3, 4, 6, 7, 9], L4242 = [0, 0, 1, 2, 3, 4, 7, 10, 10], L4248 = [0, 0, 1, 2, 3, 4, 9, 10, 10], L4260 = [0, 0, 1, 2, 3, 5, 5, 7, 9], L4267 = [0, 0, 1, 2, 3, 5, 6, 7, 9], L4273 = [0, 0, 1, 2, 3, 5, 7, 8, 9], L4275 = [0, 0, 1, 2, 3, 5, 7, 9, 10], L4408 = [0, 0, 1, 2, 4, 6, 6, 8, 10], L4414 = [0, 0, 1, 2, 4, 6, 8, 9, 10], L4592 = [0, 0, 1, 3, 4, 5, 7, 8, 9], L4594 = [0, 0, 1, 3, 4, 5, 7, 9, 10], L4684 = [0, 0, 1, 4, 4, 4, 8, 8, 8], L4767 = [0, 0, 1, 4, 5, 5, 6, 9, 10], L5061 = [0, 0, 2, 2, 4, 5, 6, 8, 10], L5154 = [0, 0, 2, 5, 5, 5, 5, 10, 10], L5189 = [0, 0, 4, 4, 4, 5, 8, 8, 8], L5209 = [0, 0, 4, 5, 5, 5, 5, 10, 10], L5678 = [0, 1, 1, 1, 1, 3, 5, 7, 9], L6171 = [0, 1, 1, 1, 2, 3, 5, 7, 9], L6274 = [0, 1, 1, 1, 2, 4, 6, 8, 10], L6482 = [0, 1, 1, 1, 3, 3, 5, 7, 9], L6565 = [0, 1, 1, 1, 3, 4, 5, 7, 9], L6620 = [0, 1, 1, 1, 3, 5, 5, 7, 9], L6635 = [0, 1, 1, 1, 3, 5, 6, 7, 9 L6644 = [0, 1, 1, 1, 3, 5, 7, 7, 9], L6647 = [0, 1, 1, 1, 3, 5, 7, 8, 9], L6649 = [0, 1, 1, 1, 3, 5, 7, 9, 9], L6650 =
254
EMILIO A. LAURET
Table 7. (continued) m = 9 q I indexes of I-isospectral families 20 {0} {355, 357}, {505, 507}, {1175, 1177}, {1182, 1186}, {1574, 1576}, {1584, 1588}, {3014, 3016}, {3305, 3309}, {3315, 3317}, {3322, 3326}, {3334, 3340}, {3988, 3990}, {3999, 4001}, {4205, 4209}, {4215, 4217}, {4225, 4229}, {4242, 4248}, {7640, 7642}, {7657, 7661}, {8263, 8267}, {8277, 8284}, {8290, 8292}, {8297, 8301}, {8309, 8315}, {8326, 8334}, {9639, 9641}, {9650, 9654}, {9663, 9665}, {9681, 9685}, {10060, 10064}, {10078, 10084}, {10090, 10092}, {10100, 10104}, {10117, 10123}, {10140, 10148}, {16955, 16957}, {17609, 17613}, {17642, 17644}, {17659, 17663}, {17689, 17695}, {18801, 18808}, {18822, 18826}, {18836, 18843}, {18857, 18866}, {18872, 18874}, {18879, 18883}, {18891, 18897}, {18908, 18916}, {18929, 18939}, {20925, 20927}, {20936, 20938}, {20968, 20970}, {21354, 21358}, {21364, 21366}, {21375, 21379}, {21385, 21389}, {21397, 21403}, {21412, 21414}, {21430, 21434}, {21459, 21465}, {22078, 22084}, {22100, 22104}, {22118, 22124}, {22143, 22151}, {22157, 22159}, {22167, 22171}, {22184, 22190}, {22207, 22215}, {22235, 22245}
[0, 1, 1, 1, 3, 5, 7, 9, 10], L7377 = [0, 1, 1, 2, 2, 3, 5, 7, 9], L7478 = [0, 1, 1, 2, 2, 4, 6, 8, 10], L7640 = [0, 1, 1, 2, 3, 3, 5, 6, 7], L7642 = [0, 1, 1, 2, 3, 3, 5, 6, 9], L7646 = [0, 1, 1, 2, 3, 3, 5, 7, 9], L7657 = [0, 1, 1, 2, 3, 3, 6, 7, 1 L7661 = [0, 1, 1, 2, 3, 3, 6, 9, 10], L7722 = [0, 1, 1, 2, 3, 4, 5, 7, 9], L7740 = [0, 1, 1, 2, 3, 4, 6, 8, 10], L7775 = [0, 1, 1, 2, 3, 5, 5, 7, 9], L7789 = [0, 1, 1, 2, 3, 5, 6, 7, 9], L7798 = [0, 1, 1, 2, 3, 5, 7, 7, 9], L7801 = [0, 1, 1, 2, 3, 5, 7, 8, 9], L7803 = [0, 1, 1, 2, 3, 5, 7, 9, 9], L7804 = [0, 1, 1, 2, 3, 5, 7, 9, 10], L7929 = [0, 1, 1, 2, 4, 4, 6, 8, L7981 = [0, 1, 1, 2, 4, 5, 6, 8, 10], L8012 = [0, 1, 1, 2, 4, 6, 6, 8, 10], L8018 = [0, 1, 1, 2, 4, 6, 7, 8, 10], L8023 = [0, 1, 1, 2, 4, 6, 8, 8, 10], L8025 = [0, 1, 1, 2, 4, 6, 8, 9, 10], L8026 = [0, 1, 1, 2, 4, 6, 8, 10, 10], L8263 = [0, 1, 1, 3, 3, 4, 5, 7, 8], L8264 = [0, 1, 1, 3, 3, 4, 5, 7, 9], L8267 = [0, 1, 1, 3, 3, 4, 5, 8, 9], L8277 = [0, 1, 1, 3, 3, 4, 7, 8, 10], L8284 = [0, 1, 1, 3, 3, 4, 8, 9, 10], L8290 = [0, 1, 1, 3, 3, 5, 5, 5, 7], L8292 = [0, 1, 1, 3, 3, 5, 5, 5, 9], L8296 = [0, 1, 1, 3, 3, 5, 5, 7, 9], L8297 = [0, 1, 1, 3, 3, 5, 5, 7, 10], L8301 = [0, 1, 1, 3, 3, 5, 5, 9, L8303 = [0, 1, 1, 3, 3, 5, 7, 7, 9], L8306 = [0, 1, 1, 3, 3, 5, 7, 8, 9], L8309 = [0, 1, 1, 3, 3, 5, 7, 10, 10], L8315 = [0, 1, 1, 3, 3, 5, 9, 10, 10], L8326 = [0, 1, 1, 3, 3, 7, 10, 10, 10], L8334 = [0, 1, 1, 3, 3, 9, 10, 10, 10], L8438 = [0, 1, 1, 3, 4, 5, 6, 7, 9], L8447 = [0, 1, 1, 3, 4, 5, 7, 8, 9], L8449 = [0, 1, 1, 3, 4, 5, 7, 9, 9], L8450 = [0, 1, 1, 3, 4, 5, 7, 9, 10], L8537 = [0, 1, 1, 3, 5, 5, 6, 7, 9], L8548 = [0, 1, 1, 3, 5, 5, 7, 9, 9], L8566 = [0, 1, 1, 3, 5, 6, 6, 7, L8575 = [0, 1, 1, 3, 5, 6, 7, 8, 9], L8577 = [0, 1, 1, 3, 5, 6, 7, 9, 9], L8578 = [0, 1, 1, 3, 5, 6, 7, 9, 10], L8592 = [0, 1, 1, 3, 5, 7, 8, 9, 9], L8593 = [0, 1, 1, 3, 5, 7, 8, 9, 10], L8595 = [0, 1, 1, 3, 5, 7, 9, 9, 10], L8821 = [0, 1, 1, 4, 4, 6, 6, 9, 9], L9459 = [0, 1, 2, 2, 2, 3, 5, 7, 9], L9639 = [0, 1, 2, 2, 3, 4, 4, 5, 7], L9641 = [0, 1, 2, 2, 3, 4, 4, 5, 9 L9649 = [0, 1, 2, 2, 3, 4, 4, 7, 9], L9650 = [0, 1, 2, 2, 3, 4, 4, 7, 10], L9654 = [0, 1, 2, 2, 3, 4, 4, 9, 10], L9663 = [0, 1, 2, 2, 3, 4, 5, 6, 7], L9665 = [0, 1, 2, 2, 3, 4, 5, 6, 9], L9668 = [0, 1, 2, 2, 3, 4, 5, 7, 9], L9681 = [0, 1, 2, 2, 3, 4, 6, 7, 10], L9684 = [0, 1, 2, 2, 3, 4, 6, 8, 10], L9685 = [0, 1, 2, 2, 3, 4, 6, 9, 10], L9711 = [0, 1, 2, 2, 3, 5, 5, 7, 9], L9722 = [0, 1, 2, 2, 3, 5, 6, 7, 9], L9730 = [0, 1, 2, 2, 3, 5, 7, 8, 9], L9732 = [0, 1, 2, 2, 3, 5, 7, 9, 1 L9825 = [0, 1, 2, 2, 4, 4, 6, 8, 10], L9883 = [0, 1, 2, 2, 4, 6, 6, 8, 10], L9887 = [0, 1, 2, 2, 4, 6, 7, 8, 10], L9892 = [0, 1, 2, 2, 4, 6, 8, 9, 10], L10060 = [0, 1, 2, 3, 4, 4, 5, 7, 8], L10061 = [0, 1, 2, 3, 4, 4, 5, 7, 9], L10064 = [0, 1, 2, 3, 4, 4, 5, 8, 9], L10073 = [0, 1, 2, 3, 4, 4, 6, 8, 10], L10078 = [0, 1, 2, 3, 4, 4, 7, 8, 10], L10084 = [0, 1, 2, 3, 4, 4, 8, 9, 10], L10090 = [0, 1, 2, 3, 4, 5, 5, 5, 7], L10092 = [0, 1, 2, 3, 4, 5, 5, 5, 9], L10099 = [0, 1, 2, 3, 4, 5, 5, 7, 9], L10100 = [0, 1, 2, 3, 4, 5, 5, 7, 10], L10104 = [0, 1, 2, 3, 4, 5, 5, 9, 10], L10107 = [0, 1, 2, 3, 4, 5, 6, 7, 9], L10111 = [0, 1, 2, 3, 4, 5, 6, 9, 10], L10114 = [0, 1, 2, 3, 4, 5, 7, 8, 9], L10115 = [0, 1, 2, 3, 4, 5, 7, 8, 10], L10116 = [0, 1, 2, 3, 4, 5, 7, 9, 10], L10117 = [0, 1, 2, 3, 4, 5, 7, 10, 10], L10123 = [0, 1, 2, 3, 4, 5, 9, 10, 10], L10125 = [0, 1, 2, 3, 4, 6, 7, 8, 9], L10126 = [0, 1, 2, 3, 4, 6, 7, 8, 10], L10127 = [0, 1, 2, 3, 4, 6, 7, 9, 10], L10130 = [0, 1, 2, 3, 4, 6, 8, 8, 10], L10137 = [0, 1, 2, 3, 4, 7, 8, 9, 10], L10140 = [0, 1, 2, 3, 4, 7, 10, 10, 10], L10148 = [0, 1, 2, 3, 4, 9, 10, 10, 10], L10160 = [0, 1, 2, 3, 5, 5, 5, 7, 9],
APPENDIX
255
Table 7. (continued) m = 9 q 20 (cont.)
I {2, 3} {7} {2, 3, 6, 7}
{3, 4, 8}
{0, 7, 8} L10167 L10184 L10195 L10342 L10434 L10443 L10685 L10727 L11020 L11479 L11602 L13020 L13175 L13190 L14284 L14439 L14454 L15008 L15121 L15148 L15268 L15347 L15353 L15466 L15472 L15503 L15519 L15525 L15530 L16947 L17007 L17111 L17613 L17642 L17659 L17669
indexes of I-isospectral families {10111, 10115}, {10127, 10137} {9649, 21396}, {17007, 19498}, {20941, 21355, 21386, 21394} {4767, 11027}, {5154, 5209}, {8821, 19868}, {10125, 22217}, {10382, 11025}, {10913, 11020}, {18248, 19865}, {19712, 19854}, {21456, 22129} {4592, 10683}, {4684, 5189}, {8447, 10718}, {9883, 11504}, {10114, 10727}, {10184, 22194}, {10340, 11601}, {17984, 22281}, {21296, 24277}, {21533, 22303} {15008, 15013}, {17619, 17624}
= [0, 1, 2, 3, 5, 5, 6, 7, 9], L10173 = [0, 1, 2, 3, 5, 5, 7, 8, 9], L10175 = [0, 1, 2, 3, 5, 5, 7, 9, 10], = [0, 1, 2, 3, 5, 6, 7, 9, 10], L10191 = [0, 1, 2, 3, 5, 7, 8, 8, 9], L10193 = [0, 1, 2, 3, 5, 7, 8, 9, 10], = [0, 1, 2, 3, 5, 7, 9, 10, 10], L10340 = [0, 1, 2, 4, 4, 6, 8, 8, 10], L10341 = [0, 1, 2, 4, 4, 6, 8, 9, 10], = [0, 1, 2, 4, 4, 6, 8, 10, 10], L10382 = [0, 1, 2, 4, 5, 5, 6, 9, 10], L10406 = [0, 1, 2, 4, 5, 6, 8, 9, 10], = [0, 1, 2, 4, 6, 6, 8, 8, 10], L10435 = [0, 1, 2, 4, 6, 6, 8, 9, 10], L10442 = [0, 1, 2, 4, 6, 8, 8, 9, 10], = [0, 1, 2, 4, 6, 8, 8, 10, 10], L10444 = [0, 1, 2, 4, 6, 8, 9, 10, 10], L10683 = [0, 1, 3, 4, 4, 5, 7, 8, 9], = [0, 1, 3, 4, 4, 5, 7, 9, 10], L10718 = [0, 1, 3, 4, 5, 5, 7, 8, 9], L10720 = [0, 1, 3, 4, 5, 5, 7, 9, 10], = [0, 1, 3, 4, 5, 7, 8, 9, 10], L10729 = [0, 1, 3, 4, 5, 7, 9, 10, 10], L10913 = [0, 1, 4, 4, 5, 5, 6, 9, 10], = [0, 1, 4, 5, 5, 6, 6, 9, 10], L11025 = [0, 1, 4, 5, 5, 6, 8, 9, 10], L11027 = [0, 1, 4, 5, 5, 6, 9, 10, 10], = [0, 2, 2, 4, 4, 5, 6, 8, 10], L11504 = [0, 2, 2, 4, 5, 6, 6, 8, 10], L11601 = [0, 2, 4, 4, 5, 6, 8, 8, 10], = [0, 2, 4, 4, 5, 6, 8, 10, 10], L12197 = [1, 1, 1, 1, 1, 3, 5, 7, 9], L12692 = [1, 1, 1, 1, 2, 3, 5, 7, 9], = [1, 1, 1, 1, 3, 3, 5, 7, 9], L13104 = [1, 1, 1, 1, 3, 4, 5, 7, 9], L13160 = [1, 1, 1, 1, 3, 5, 5, 7, 9], = [1, 1, 1, 1, 3, 5, 6, 7, 9], L13185 = [1, 1, 1, 1, 3, 5, 7, 7, 9], L13188 = [1, 1, 1, 1, 3, 5, 7, 8, 9], = [1, 1, 1, 1, 3, 5, 7, 9, 9], L13191 = [1, 1, 1, 1, 3, 5, 7, 9, 10], L13966 = [1, 1, 1, 2, 2, 3, 5, 7, 9], = [1, 1, 1, 2, 3, 3, 5, 7, 9], L14368 = [1, 1, 1, 2, 3, 4, 5, 7, 9], L14424 = [1, 1, 1, 2, 3, 5, 5, 7, 9], = [1, 1, 1, 2, 3, 5, 6, 7, 9], L14449 = [1, 1, 1, 2, 3, 5, 7, 7, 9], L14452 = [1, 1, 1, 2, 3, 5, 7, 8, 9], = [1, 1, 1, 2, 3, 5, 7, 9, 9], L14455 = [1, 1, 1, 2, 3, 5, 7, 9, 10], L14998 = [1, 1, 1, 3, 3, 3, 5, 7, 9], = [1, 1, 1, 3, 3, 3, 7, 7, 9], L15013 = [1, 1, 1, 3, 3, 3, 7, 9, 9], L15066 = [1, 1, 1, 3, 3, 4, 5, 7, 9], = [1, 1, 1, 3, 3, 5, 5, 7, 9], L15136 = [1, 1, 1, 3, 3, 5, 6, 7, 9], L15145 = [1, 1, 1, 3, 3, 5, 7, 7, 9], = [1, 1, 1, 3, 3, 5, 7, 8, 9], L15150 = [1, 1, 1, 3, 3, 5, 7, 9, 9], L15151 = [1, 1, 1, 3, 3, 5, 7, 9, 10], = [1, 1, 1, 3, 4, 4, 5, 7, 9], L15323 = [1, 1, 1, 3, 4, 5, 5, 7, 9], L15338 = [1, 1, 1, 3, 4, 5, 6, 7, 9], = [1, 1, 1, 3, 4, 5, 7, 7, 9], L15350 = [1, 1, 1, 3, 4, 5, 7, 8, 9], L15352 = [1, 1, 1, 3, 4, 5, 7, 9, 9], = [1, 1, 1, 3, 4, 5, 7, 9, 10], L15442 = [1, 1, 1, 3, 5, 5, 5, 7, 9], L15457 = [1, 1, 1, 3, 5, 5, 6, 7, 9], = [1, 1, 1, 3, 5, 5, 7, 7, 9], L15469 = [1, 1, 1, 3, 5, 5, 7, 8, 9], L15471 = [1, 1, 1, 3, 5, 5, 7, 9, 9], = [1, 1, 1, 3, 5, 5, 7, 9, 10], L15491 = [1, 1, 1, 3, 5, 6, 6, 7, 9], L15500 = [1, 1, 1, 3, 5, 6, 7, 7, 9], = [1, 1, 1, 3, 5, 6, 7, 8, 9], L15505 = [1, 1, 1, 3, 5, 6, 7, 9, 9], L15506 = [1, 1, 1, 3, 5, 6, 7, 9, 10], = [1, 1, 1, 3, 5, 7, 7, 8, 9], L15521 = [1, 1, 1, 3, 5, 7, 7, 9, 9], L15522 = [1, 1, 1, 3, 5, 7, 7, 9, 10], = [1, 1, 1, 3, 5, 7, 8, 8, 9], L15527 = [1, 1, 1, 3, 5, 7, 8, 9, 9], L15528 = [1, 1, 1, 3, 5, 7, 8, 9, 10], = [1, 1, 1, 3, 5, 7, 9, 9, 9], L15531 = [1, 1, 1, 3, 5, 7, 9, 9, 10], L15532 = [1, 1, 1, 3, 5, 7, 9, 10, 10], = [1, 1, 2, 2, 3, 3, 5, 7, 9], L16955 = [1, 1, 2, 2, 3, 3, 6, 6, 7], L16957 = [1, 1, 2, 2, 3, 3, 6, 6, 9], = [1, 1, 2, 2, 3, 4, 4, 7, 9], L17028 = [1, 1, 2, 2, 3, 4, 5, 7, 9], L17106 = [1, 1, 2, 2, 3, 5, 7, 7, 9], = [1, 1, 2, 2, 3, 5, 7, 9, 9], L17600 = [1, 1, 2, 3, 3, 4, 5, 7, 9], L17609 = [1, 1, 2, 3, 3, 4, 6, 7, 8], = [1, 1, 2, 3, 3, 4, 6, 8, 9], L17619 = [1, 1, 2, 3, 3, 4, 7, 7, 9], L17624 = [1, 1, 2, 3, 3, 4, 7, 9, 9], = [1, 1, 2, 3, 3, 5, 5, 6, 7], L17644 = [1, 1, 2, 3, 3, 5, 5, 6, 9], L17648 = [1, 1, 2, 3, 3, 5, 5, 7, 9], = [1, 1, 2, 3, 3, 5, 6, 7, 10], L17663 = [1, 1, 2, 3, 3, 5, 6, 9, 10], L17666 = [1, 1, 2, 3, 3, 5, 7, 7, 9], = [1, 1, 2, 3, 3, 5, 7, 8, 9], L17671 = [1, 1, 2, 3, 3, 5, 7, 9, 9], L17672 = [1, 1, 2, 3, 3, 5, 7, 9, 10],
256
EMILIO A. LAURET
Table 7. (continued) m = 9 q I indexes of I-isospectral families 20 {8} {1600, 4594}, {2597, 3455}, {3069, 8593}, {3168, 4414}, {3444, 8450}, (cont.) {4023, 10193, 23098}, {4104, 10443}, {4224, 10061, 10114, 10727, 23096}, {4232, 10137}, {4260, 10720}, {4267, 9668, 10107, 10116, 22119, 22204, 23152}, {4273, 10685}, {4275, 10729}, {4408, 10342}, {5061, 11602}, {5678, 6649}, {6171, 7803, 15528, 19447}, {6274, 8025}, {6482, 6644, 8303}, {6565, 8449}, {6620, 8548}, {6635, 8577, 15353, 19200}, {6647, 8592}, {6650, 8595}, {7377, 18004}, {7478, 9892}, {7646, 7798, 18838, 18905}, {7722, 8575, 10099, 19198, 23142}, {7740, 8018, 10126}, {7775, 19374}, {7789, 10167, 17847, 19424, 22183}, {7801, 19445}, {7804, 19448}, {7929, 10341}, {7981, 10406}, {8012, 10435},
L17689 L17818 L17844 L17949 L17983 L17998 L18006 L18801 L18823 L18836 L18843 L18872 L18879 L18888 L18897 L18903 L18916 L19054 L19154 L19183 L19200 L19356 L19374 L19408 L19424 L19445 L19450 L19854 L20925 L20938 L20968 L21354 L21364 L21375
= [1, 1, 2, 3, 3, 6, 7, 10, 10], L17695 = [1, 1, 2, 3, 3, 6, 9, 10, 10], L17765 = [1, 1, 2, 3, 4, 4, 5, 7, 9], = [1, 1, 2, 3, 4, 5, 5, 7, 9], L17832 = [1, 1, 2, 3, 4, 5, 6, 7, 9], L17841 = [1, 1, 2, 3, 4, 5, 7, 7, 9], = [1, 1, 2, 3, 4, 5, 7, 8, 9], L17846 = [1, 1, 2, 3, 4, 5, 7, 9, 9], L17847 = [1, 1, 2, 3, 4, 5, 7, 9, 10], = [1, 1, 2, 3, 5, 5, 7, 7, 9], L17954 = [1, 1, 2, 3, 5, 5, 7, 9, 9], L17981 = [1, 1, 2, 3, 5, 6, 7, 8, 9], = [1, 1, 2, 3, 5, 6, 7, 9, 9], L17984 = [1, 1, 2, 3, 5, 6, 7, 9, 10], L17996 = [1, 1, 2, 3, 5, 7, 7, 8, 9], = [1, 1, 2, 3, 5, 7, 7, 9, 10], L18003 = [1, 1, 2, 3, 5, 7, 8, 9, 9], L18004 = [1, 1, 2, 3, 5, 7, 8, 9, 10], = [1, 1, 2, 3, 5, 7, 9, 9, 10], L18248 = [1, 1, 2, 4, 4, 6, 6, 9, 9], L18790 = [1, 1, 3, 3, 4, 4, 5, 7, 9], = [1, 1, 3, 3, 4, 4, 7, 8, 8], L18808 = [1, 1, 3, 3, 4, 4, 8, 8, 9], L18822 = [1, 1, 3, 3, 4, 5, 5, 7, 8], = [1, 1, 3, 3, 4, 5, 5, 7, 9], L18826 = [1, 1, 3, 3, 4, 5, 5, 8, 9], L18832 = [1, 1, 3, 3, 4, 5, 7, 7, 9], = [1, 1, 3, 3, 4, 5, 7, 8, 10], L18837 = [1, 1, 3, 3, 4, 5, 7, 9, 9], L18838 = [1, 1, 3, 3, 4, 5, 7, 9, 10], = [1, 1, 3, 3, 4, 5, 8, 9, 10], L18857 = [1, 1, 3, 3, 4, 7, 8, 10, 10], L18866 = [1, 1, 3, 3, 4, 8, 9, 10, 10], = [1, 1, 3, 3, 5, 5, 5, 5, 7], L18874 = [1, 1, 3, 3, 5, 5, 5, 5, 9], L18878 = [1, 1, 3, 3, 5, 5, 5, 7, 9], = [1, 1, 3, 3, 5, 5, 5, 7, 10], L18883 = [1, 1, 3, 3, 5, 5, 5, 9, 10], L18885 = [1, 1, 3, 3, 5, 5, 7, 7, 9], = [1, 1, 3, 3, 5, 5, 7, 8, 9], L18890 = [1, 1, 3, 3, 5, 5, 7, 9, 10], L18891 = [1, 1, 3, 3, 5, 5, 7, 10, 10], = [1, 1, 3, 3, 5, 5, 9, 10, 10], L18899 = [1, 1, 3, 3, 5, 7, 7, 9, 9], L18900 = [1, 1, 3, 3, 5, 7, 7, 9, 10], = [1, 1, 3, 3, 5, 7, 8, 8, 9], L18905 = [1, 1, 3, 3, 5, 7, 8, 9, 10], L18908 = [1, 1, 3, 3, 5, 7, 10, 10, 10], = [1, 1, 3, 3, 5, 9, 10, 10, 10], L18929 = [1, 1, 3, 3, 7, 10, 10, 10, 10], L18939 = [1, 1, 3, 3, 9, 10, 10, 10, 10], = [1, 1, 3, 4, 4, 5, 7, 9, 9], L19055 = [1, 1, 3, 4, 4, 5, 7, 9, 10], L19153 = [1, 1, 3, 4, 5, 5, 7, 9, 9], = [1, 1, 3, 4, 5, 5, 7, 9, 10], L19180 = [1, 1, 3, 4, 5, 6, 7, 8, 9], L19182 = [1, 1, 3, 4, 5, 6, 7, 9, 9], = [1, 1, 3, 4, 5, 6, 7, 9, 10], L19197 = [1, 1, 3, 4, 5, 7, 8, 9, 9], L19198 = [1, 1, 3, 4, 5, 7, 8, 9, 10], = [1, 1, 3, 4, 5, 7, 9, 9, 10], L19201 = [1, 1, 3, 4, 5, 7, 9, 10, 10], L19329 = [1, 1, 3, 5, 5, 5, 7, 9, 9], = [1, 1, 3, 5, 5, 6, 7, 8, 9], L19358 = [1, 1, 3, 5, 5, 6, 7, 9, 9], L19373 = [1, 1, 3, 5, 5, 7, 8, 9, 9], = [1, 1, 3, 5, 5, 7, 8, 9, 10], L19376 = [1, 1, 3, 5, 5, 7, 9, 9, 10], L19406 = [1, 1, 3, 5, 6, 6, 7, 8, 9], = [1, 1, 3, 5, 6, 6, 7, 9, 9], L19421 = [1, 1, 3, 5, 6, 7, 8, 8, 9], L19423 = [1, 1, 3, 5, 6, 7, 8, 9, 9], = [1, 1, 3, 5, 6, 7, 8, 9, 10], L19426 = [1, 1, 3, 5, 6, 7, 9, 9, 10], L19444 = [1, 1, 3, 5, 7, 8, 8, 9, 9], = [1, 1, 3, 5, 7, 8, 8, 9, 10], L19447 = [1, 1, 3, 5, 7, 8, 9, 9, 10], L19448 = [1, 1, 3, 5, 7, 8, 9, 10, 10], = [1, 1, 3, 5, 7, 9, 9, 10, 10], L19498 = [1, 1, 3, 6, 6, 7, 8, 8, 9], L19712 = [1, 1, 4, 4, 4, 6, 6, 9, 9], = [1, 1, 4, 4, 6, 6, 6, 9, 9], L19865 = [1, 1, 4, 4, 6, 6, 8, 9, 9], L19868 = [1, 1, 4, 4, 6, 6, 9, 9, 10], = [1, 2, 2, 2, 3, 4, 4, 4, 7], L20927 = [1, 2, 2, 2, 3, 4, 4, 4, 9], L20936 = [1, 2, 2, 2, 3, 4, 4, 6, 7], = [1, 2, 2, 2, 3, 4, 4, 6, 9], L20941 = [1, 2, 2, 2, 3, 4, 4, 7, 9], L20960 = [1, 2, 2, 2, 3, 4, 5, 7, 9], = [1, 2, 2, 2, 3, 4, 6, 6, 7], L20970 = [1, 2, 2, 2, 3, 4, 6, 6, 9], L21296 = [1, 2, 2, 2, 6, 6, 6, 10, 10], = [1, 2, 2, 3, 4, 4, 4, 7, 8], L21355 = [1, 2, 2, 3, 4, 4, 4, 7, 9], L21358 = [1, 2, 2, 3, 4, 4, 4, 8, 9], = [1, 2, 2, 3, 4, 4, 5, 5, 7], L21366 = [1, 2, 2, 3, 4, 4, 5, 5, 9], L21374 = [1, 2, 2, 3, 4, 4, 5, 7, 9], = [1, 2, 2, 3, 4, 4, 5, 7, 10], L21379 = [1, 2, 2, 3, 4, 4, 5, 9, 10], L21385 = [1, 2, 2, 3, 4, 4, 6, 7, 8],
APPENDIX
257
Table 7. (continued) m = 9 q I indexes of I-isospectral families 20 {8} {8023, 10442}, {8026, 10444}, {8264, 8306}, {8296, 18823, 18888}, {8438, 19055}, (cont.) {8537, 19154}, {8566, 19183}, {8578, 19201}, {9459, 21545}, {9684, 9887}, {9711, 22290}, {9722, 10184, 21439, 22194, 22206}, {9730, 22313}, {9732, 22315}, {9825, 10434, 11479}, {10073, 10130}, {10127, 22232}, {10160, 23135}, {10173, 23086}, {10175, 23144}, {10191, 23046}, {10195, 23154}, {12197, 13190, 15530}, {12692, 14454}, {13020, 13185, 15150, 15521}, {13104, 15352}, {13160, 15471}, {13175, 15505}, {13188, 15527}, {13191, 15531}, {13966, 17111}, {14284, 14449, 17671}, {14368, 15503, 17846, 19423}, {14424, 17954}, {14439, 17983}, {14452, 18003}, {14455, 18006}, {14998, 15145, 18899}, {15066, 15347, 18837}, {15121, 15466, 18878, 18885}, {15136, 15500, 17666}, {15148, 15519, 18832}, {15151, 15522, 18900}, {15268, 19054}, {15323, 19153}, {15338, 19182}, {15350, 19197}, {15442, 19329}, {15457, 19358}, {15469, 19373}, {15472, 19376}, {15491, 19408}, {15506, 19426}, {15525, 19444}, {15532, 19450}, {16947, 17106}, {17028, 17981}, {17600, 17841}, {17648, 17949, 18890}, {17669, 17996}, {17672, 17998}, {17765, 19180}, {17818, 19356}, {17832, 19406}, {17844, 19421}, {18790, 18903}, {20960, 21531}, {21374, 22192}, {21417, 22174}, {21437, 22109}, {22063, 22202}, {22101, 22181}
L21386 = [1, 2, 2, 3, 4, 4, 6, 7, 9], L21389 = [1, 2, 2, 3, 4, 4, 6, 8, 9], L21394 = [1, 2, 2, 3, 4, 4, 7, 8, 9], L21396 = [1, 2, 2, 3, 4, 4, 7, 9, 10], L21397 = [1, 2, 2, 3, 4, 4, 7, 10, 10], L21403 = [1, 2, 2, 3, 4, 4, 9, 10, 10], L21412 = [1, 2, 2, 3, 4, 5, 5, 6, 7], L21414 = [1, 2, 2, 3, 4, 5, 5, 6, 9], L21417 = [1, 2, 2, 3, 4, 5, 5, 7, 9], L21430 = [1, 2, 2, 3, 4, 5, 6, 7, 10], L21434 = [1, 2, 2, 3, 4, 5, 6, 9, 10], L21437 = [1, 2, 2, 3, 4, 5, 7, 8, 9], L21439 = [1, 2, 2, 3, 4, 5, 7, 9, 10], L21456 = [1, 2, 2, 3, 4, 6, 7, 8, 9], L21459 = [1, 2, 2, 3, 4, 6, 7, 10, 10], L21465 = [1, 2, 2, 3, 4, 6, 9, 10, 10], L21531 = [1, 2, 2, 3, 5, 6, 7, 8, 9], L21533 = [1, 2, 2, 3, 5, 6, 7, 9, 10], L21545 = [1, 2, 2, 3, 5, 7, 8, 9, 10], L22063 = [1, 2, 3, 4, 4, 4, 5, 7, 9], L22078 = [1, 2, 3, 4, 4, 4, 7, 8, 8], L22084 = [1, 2, 3, 4, 4, 4, 8, 8, 9], L22100 = [1, 2, 3, 4, 4, 5, 5, 7, 8], L22101 = [1, 2, 3, 4, 4, 5, 5, 7, 9], L22104 = [1, 2, 3, 4, 4, 5, 5, 8, 9], L22109 = [1, 2, 3, 4, 4, 5, 6, 7, 9], L22118 = [1, 2, 3, 4, 4, 5, 7, 8, 10], L22119 = [1, 2, 3, 4, 4, 5, 7, 9, 10], L22124 = [1, 2, 3, 4, 4, 5, 8, 9, 10], L22129 = [1, 2, 3, 4, 4, 6, 7, 8, 9], L22143 = [1, 2, 3, 4, 4, 7, 8, 10, 10], L22151 = [1, 2, 3, 4, 4, 8, 9, 10, 10], L22157 = [1, 2, 3, 4, 5, 5, 5, 5, 7], L22159 = [1, 2, 3, 4, 5, 5, 5, 5, 9], L22167 = [1, 2, 3, 4, 5, 5, 5, 7, 10], L22171 = [1, 2, 3, 4, 5, 5, 5, 9, 10], L22174 = [1, 2, 3, 4, 5, 5, 6, 7, 9], L22181 = [1, 2, 3, 4, 5, 5, 7, 8, 9], L22183 = [1, 2, 3, 4, 5, 5, 7, 9, 10], L22184 = [1, 2, 3, 4, 5, 5, 7, 10, 10], L22190 = [1, 2, 3, 4, 5, 5, 9, 10, 10], L22192 = [1, 2, 3, 4, 5, 6, 7, 8, 9], L22194 = [1, 2, 3, 4, 5, 6, 7, 9, 10], L22202 = [1, 2, 3, 4, 5, 7, 8, 8, 9], L22204 = [1, 2, 3, 4, 5, 7, 8, 9, 10], L22206 = [1, 2, 3, 4, 5, 7, 9, 10, 10], L22207 = [1, 2, 3, 4, 5, 7, 10, 10, 10], L22215 = [1, 2, 3, 4, 5, 9, 10, 10, 10], L22217 = [1, 2, 3, 4, 6, 7, 8, 9, 10], L22232 = [1, 2, 3, 4, 7, 8, 9, 10, 10], L22235 = [1, 2, 3, 4, 7, 10, 10, 10, 10], L22245 = [1, 2, 3, 4, 9, 10, 10, 10, 10], L22281 = [1, 2, 3, 5, 5, 6, 7, 9, 10], L22290 = [1, 2, 3, 5, 5, 7, 8, 9, 10], L22303 = [1, 2, 3, 5, 6, 7, 9, 10, 10], L22313 = [1, 2, 3, 5, 7, 8, 8, 9, 10], L22315 = [1, 2, 3, 5, 7, 8, 9, 10, 10], L23046 = [1, 3, 4, 4, 4, 5, 7, 9, 10], L23086 = [1, 3, 4, 4, 5, 5, 7, 9, 10], L23096 = [1, 3, 4, 4, 5, 7, 8, 9, 10], L23098 = [1, 3, 4, 4, 5, 7, 9, 10, 10], L23135 = [1, 3, 4, 5, 5, 5, 7, 9, 10], L23142 = [1, 3, 4, 5, 5, 7, 8, 9, 10], L23144 = [1, 3, 4, 5, 5, 7, 9, 10, 10], L23152 = [1, 3, 4, 5, 7, 8, 9, 10, 10], L23154 = [1, 3, 4, 5, 7, 9, 10, 10, 10], L24277 = [2, 2, 2, 5, 6, 6, 6, 10, 10]. q = 21 : L110 = [0, 0, 0, 0, 0, 1, 2, 4, 5], L112 = [0, 0, 0, 0, 0, 1, 2, 4, 8], L121 = [0, 0, 0, 0, 0, 1, 2, 6, 9], L135 = [0, 0, 0, 0, 0, 1, 3, 4, 6], L384 = [0, 0, 0, 0, 1, 2, 3, 4, 8], L385 = [0, 0, 0, 0, 1, 2, 3, 4, 9], L387 = [0, 0, 0, 0, 1, 2, 3, 5, 6], L389 = [0, 0, 0, 0, 1, 2, 3, 5, 8], L390 = [0, 0, 0, 0, 1, 2, 3, 5, 9], L391 = [0, 0, 0, 0, 1, 2, 3, 5, 10]
258
EMILIO A. LAURET
Table 7. (continued) m = 9 q I indexes of I-isospectral families 21 {0} {110, 112}, {121, 135}, {384, 389}, {385, 387}, {390, 394}, {391, 402}, {401, 459}, {404, 408}, {426, 462}, {1150, 1155, 1165}, {1157, 1168}, {1158, 1164}, {1169, 1179}, {1170, 1190}, {1189, 1298}, {1194, 1200}, {1231, 1304}, {2946, 2959}, {2988, 3001}, {2992, 3000, 3016}, {3004, 3021}, {3005, 3015}, {3022, 3041}, {3023, 3054}, {3039, 3194}, {3053, 3233}, {3060, 3067}, {3115, 3241}, {6913, 6936}, {6915, 6931}, {6921, 6943}, {6937, 6957}, {6938, 6970}, {6969, 7291}, {6987, 7004}, {6994, 7003, 7026}, {7008, 7033}, {7009, 7025}, {7034, 7064}, {7035, 7079}, {7060, 7300}, {7078, 7353}, {7087, 7095}, {7164, 7363}, {12304, 12309}, {14946, 14965, 14996}, {14970, 15002}, {14972, 14995}, {14981, 15011}, {15003, 15035}, {15004, 15051}, {15050, 15509}, {15072, 15092}, {15081, 15091, 15123}, {15097, 15132}, {15098, 15122}, {15133, 15176}, {15134, 15193}, {15170, 15522}, {15192, 15590}, {15203, 15212}, {15306, 15602}
L394 = [0, 0, 0, 0, 1, 2, 3, 6, 8], L401 = [0, 0, 0, 0, 1, 2, 3, 8, 9], L402 = [0, 0, 0, 0, 1, 2, 3, 8, 10], L404 = [0, 0, 0, 0, 1, 2, 4, 5, 7], L408 = [0, 0, 0, 0, 1, 2, 4, 7, 8], L426 = [0, 0, 0, 0, 1, 2, 6, 7, 9], L459 = [0, 0, 0, 0, 1, 3, 4, 5, 6], L462 = [0, 0, 0, 0, 1, 3, 4, 6, 7], L1150 = [0, 0, 0, 1, 2, 3, 4, 5, 9], L1155 = [0, 0, 0, 1, 2, 3, 4, 6, 10], L1157 = [0, 0, 0, 1, 2, 3, 4, 7, 8], L1158 = [0, 0, 0, 1, 2, 3, 4, 7, 9], L1164 = [0, 0, 0, 1, 2, 3, 5, 6, 7], L1165 = [0, 0, 0, 1, 2, 3, 5, 6, 8 L1168 = [0, 0, 0, 1, 2, 3, 5, 7, 8], L1169 = [0, 0, 0, 1, 2, 3, 5, 7, 9], L1170 = [0, 0, 0, 1, 2, 3, 5, 7, 10], L1171 = [0, 0, 0, 1, 2, 3, 5, 8, 9], L1179 = [0, 0, 0, 1, 2, 3, 6, 7, 8], L1183 = [0, 0, 0, 1, 2, 3, 6, 8, 10], L1189 = [0, 0, 0, 1, 2, 3, 7, 8, L1190 = [0, 0, 0, 1, 2, 3, 7, 8, 10], L1194 = [0, 0, 0, 1, 2, 4, 5, 7, 7], L1200 = [0, 0, 0, 1, 2, 4, 7, 7, 8], L1231 = [0, 0, 0, 1, 2, 6, 7, 7, 9], L1298 = [0, 0, 0, 1, 3, 4, 5, 6, 7], L1304 = [0, 0, 0, 1, 3, 4, 6, 7, 7], L2946 = [0, 0, 1, 2, 3, 3, 4, 8, 9 L2959 = [0, 0, 1, 2, 3, 3, 5, 8, 9], L2987 = [0, 0, 1, 2, 3, 4, 5, 6, 8], L2988 = [0, 0, 1, 2, 3, 4, 5, 6, 9], L2989 = [0, 0, 1, 2, 3, 4, 5, 6, 10], L2992 = [0, 0, 1, 2, 3, 4, 5, 7, 9], L3000 = [0, 0, 1, 2, 3, 4, 6, 7, 10], L3001 = [0, 0, 1, 2, 3, 4, 6, 8, 9], L3004 = [0, 0, 1, 2, 3, 4, 7, 7, 8], L3005 = [0, 0, 1, 2, 3, 4, 7, 7, 9], L3015 = [0, 0, 1, 2, 3, 5, 6, 7, 7 L3016 = [0, 0, 1, 2, 3, 5, 6, 7, 8], L3021 = [0, 0, 1, 2, 3, 5, 7, 7, 8], L3022 = [0, 0, 1, 2, 3, 5, 7, 7, 9], L3023 = [0, 0, 1, 2, 3, 5, 7, 7, 10], L3024 = [0, 0, 1, 2, 3, 5, 7, 8, 9], L3039 = [0, 0, 1, 2, 3, 6, 6, 9, 9], L3041 = [0, 0, 1, 2, 3, 6, 7, 7, L3045 = [0, 0, 1, 2, 3, 6, 7, 8, 10], L3053 = [0, 0, 1, 2, 3, 7, 7, 8, 9], L3054 = [0, 0, 1, 2, 3, 7, 7, 8, 10], L3060 = [0, 0, 1, 2, 4, 5, 7, 7, 7], L3063 = [0, 0, 1, 2, 4, 5, 7, 8, 10], L3067 = [0, 0, 1, 2, 4, 7, 7, 7, 8], L3115 = [0, 0, 1, 2, 6, 7, 7, 7, 9], L3194 = [0, 0, 1, 3, 3, 4, 6, 6, 9], L3216 = [0, 0, 1, 3, 3, 6, 6, 9, 9], L3233 = [0, 0, 1, 3, 4, 5, 6, 7, 7 L3241 = [0, 0, 1, 3, 4, 6, 7, 7, 7], L3363 = [0, 0, 3, 3, 6, 6, 7, 9, 9], L5844 = [0, 1, 1, 2, 4, 5, 7, 8, 10], L6253 = [0, 1, 1, 3, 3, 6, 6, 9, 9], L6913 = [0, 1, 2, 3, 3, 4, 6, 8, 9], L6915 = [0, 1, 2, 3, 3, 4, 6, 9, 9], L6921 = [0, 1, 2, 3, 3, 4, 7, 8, 9 L6931 = [0, 1, 2, 3, 3, 5, 6, 6, 9], L6936 = [0, 1, 2, 3, 3, 5, 6, 8, 9], L6937 = [0, 1, 2, 3, 3, 5, 6, 9, 9], L6938 = [0, 1, 2, 3, 3, 5, 6, 9, 10], L6943 = [0, 1, 2, 3, 3, 5, 7, 8, 9], L6957 = [0, 1, 2, 3, 3, 6, 6, 8, 9], L6959 = [0, 1, 2, 3, 3, 6, 6, 9, L6969 = [0, 1, 2, 3, 3, 6, 8, 9, 9], L6970 = [0, 1, 2, 3, 3, 6, 8, 9, 10], L6986 = [0, 1, 2, 3, 4, 5, 6, 7, 8], L6987 = [0, 1, 2, 3, 4, 5, 6, 7, 9], L6988 = [0, 1, 2, 3, 4, 5, 6, 7, 10], L6989 = [0, 1, 2, 3, 4, 5, 6, 8, 9], L6994 = [0, 1, 2, 3, 4, 5, 7, 7, L6996 = [0, 1, 2, 3, 4, 5, 7, 8, 10], L7003 = [0, 1, 2, 3, 4, 6, 7, 7, 10], L7004 = [0, 1, 2, 3, 4, 6, 7, 8, 9], L7008 = [0, 1, 2, 3, 4, 7, 7, 7, 8], L7009 = [0, 1, 2, 3, 4, 7, 7, 7, 9], L7025 = [0, 1, 2, 3, 5, 6, 7, 7, 7], L7026 = [0, 1, 2, 3, 5, 6, 7, 7, 8], L7033 = [0, 1, 2, 3, 5, 7, 7, 7, 8], L7034 = [0, 1, 2, 3, 5, 7, 7, 7, 9], L7035 = [0, 1, 2, 3, 5, 7, 7, 7, 1 L7036 = [0, 1, 2, 3, 5, 7, 7, 8, 9], L7060 = [0, 1, 2, 3, 6, 6, 7, 9, 9], L7064 = [0, 1, 2, 3, 6, 7, 7, 7, 8], L7068 = [0, 1, 2, 3, 6, 7, 7, 8, 10], L7078 = [0, 1, 2, 3, 7, 7, 7, 8, 9], L7079 = [0, 1, 2, 3, 7, 7, 7, 8, 10], L7087 = [0, 1, 2, 4, 5, 7, 7, 7, 7], L7090 = [0, 1, 2, 4, 5, 7, 7, 8, 10], L7095 = [0, 1, 2, 4, 7, 7, 7, 7, 8], L7164 = [0, 1, 2, 6, 7, 7, 7, 7, L7273 = [0, 1, 3, 3, 3, 6, 6, 9, 9], L7291 = [0, 1, 3, 3, 4, 5, 6, 6, 9], L7300 = [0, 1, 3, 3, 4, 6, 6, 7, 9], L7301 = [0, 1, 3, 3, 4, 6, 6, 9, 9], L7325 = [0, 1, 3, 3, 6, 6, 6, 9, 9], L7330 = [0, 1, 3, 3, 6, 6, 7, 9, 9], L7331 = [0, 1, 3, 3, 6, 6, 8, 9, 9 L7332 = [0, 1, 3, 3, 6, 6, 9, 9, 9], L7353 = [0, 1, 3, 4, 5, 6, 7, 7, 7], L7363 = [0, 1, 3, 4, 6, 7, 7, 7, 7], L7518 =
APPENDIX
259
Table 7. (continued) m = 9 q 21 (cont.)
I {0, 1}
indexes of I-isospectral families {1171, 1183}, {2987, 2989}, {3024, 3045}, {6986, 6988}, {7036, 7068}, {15005, 15040}, {15071, 15073}, {15135, 15180} {5} {6989, 7004} {4, 5, 6} {3063, 6996, 14953, 15075}, {3216, 3363, 7273, 7325, 7332, 7518}, {5844, 7090, 12917, 13219, 13240, 15083}, {6253, 6959, 7301, 7330, 7331, 7527}, {10385, 12362, 13146, 13234, 13238, 15206}
[0, 3, 3, 3, 6, 6, 7, 9, 9], L7527 = [0, 3, 3, 6, 6, 7, 7, 9, 9], L10385 = [1, 1, 1, 2, 4, 5, 7, 8, 10], L12304 = [1, 1, 2, 2, 4, 4, 5, 5, 10], L12309 = [1, 1, 2, 2, 4, 4, 5, 8, 8], L12362 = [1, 1, 2, 2, 4, 5, 7, 8, 10], L12917 = [1, 1, 2, 3, 4, 5, 7, 8, 10], L13146 = [1, 1, 2, 4, 4, 5, 7, 8, 10], L13219 = [1, 1, 2, 4, 5, 6, 7, 8, 10], L13234 = [1, 1, 2, 4, 5, 7, 7, 8, 10], L13238 = [1, 1, 2, 4, 5, 7, 8, 8, 10], L13240 = [1, 1, 2, 4, 5, 7, 8, 9, 10], L14946 = [1, 2, 3, 3, 4, 5, 6, 9, 9], L14953 = [1, 2, 3, 3, 4, 5, 7, 8, 10], L14965 = [1, 2, 3, 3, 4, 6, 6, 9, 10], L14970 = [1, 2, 3, 3, 4, 6, 7, 8, 9], L14972 = [1, 2, 3, 3, 4, 6, 7, 9, 9], L14981 = [1, 2, 3, 3, 4, 7, 7, 8, 9], L14995 = [1, 2, 3, 3, 5, 6, 6, 7, 9], L14996 = [1, 2, 3, 3, 5, 6, 6, 8, 9], L15002 = [1, 2, 3, 3, 5, 6, 7, 8, 9], L15003 = [1, 2, 3, 3, 5, 6, 7, 9, 9], L15004 = [1, 2, 3, 3, 5, 6, 7, 9, 10], L15005 = [1, 2, 3, 3, 5, 6, 8, 9, 9], L15011 = [1, 2, 3, 3, 5, 7, 7, 8, 9], L15035 = [1, 2, 3, 3, 6, 6, 7, 8, 9], L15040 = [1, 2, 3, 3, 6, 6, 8, 9, 10], L15050 = [1, 2, 3, 3, 6, 7, 8, 9, 9], L15051 = [1, 2, 3, 3, 6, 7, 8, 9, 10], L15071 = [1, 2, 3, 4, 5, 6, 7, 7, 8], L15072 = [1, 2, 3, 4, 5, 6, 7, 7, 9], L15073 = [1, 2, 3, 4, 5, 6, 7, 7, 10], L15075 = [1, 2, 3, 4, 5, 6, 7, 8, 10], L15081 = [1, 2, 3, 4, 5, 7, 7, 7, 9], L15083 = [1, 2, 3, 4, 5, 7, 7, 8, 10], L15091 = [1, 2, 3, 4, 6, 7, 7, 7, 10], L15092 = [1, 2, 3, 4, 6, 7, 7, 8, 9], L15097 = [1, 2, 3, 4, 7, 7, 7, 7, 8], L15098 = [1, 2, 3, 4, 7, 7, 7, 7, 9], L15122 = [1, 2, 3, 5, 6, 7, 7, 7, 7], L15123 = [1, 2, 3, 5, 6, 7, 7, 7, 8], L15132 = [1, 2, 3, 5, 7, 7, 7, 7, 8], L15133 = [1, 2, 3, 5, 7, 7, 7, 7, 9], L15134 = [1, 2, 3, 5, 7, 7, 7, 7, 10], L15135 = [1, 2, 3, 5, 7, 7, 7, 8, 9], L15170 = [1, 2, 3, 6, 6, 7, 7, 9, 9], L15176 = [1, 2, 3, 6, 7, 7, 7, 7, 8], L15180 = [1, 2, 3, 6, 7, 7, 7, 8, 10], L15192 = [1, 2, 3, 7, 7, 7, 7, 8, 9], L15193 = [1, 2, 3, 7, 7, 7, 7, 8, 10], L15203 = [1, 2, 4, 5, 7, 7, 7, 7, 7], L15206 = [1, 2, 4, 5, 7, 7, 7, 8, 10], L15212 = [1, 2, 4, 7, 7, 7, 7, 7, 8], L15306 = [1, 2, 6, 7, 7, 7, 7, 7, 9], L15509 = [1, 3, 3, 4, 5, 6, 6, 7, 9], L15522 = [1, 3, 3, 4, 6, 6, 7, 7, 9], L15590 = [1, 3, 4, 5, 6, 7, 7, 7, 7], L15602 = [1, 3, 4, 6, 7, 7, 7, 7, 7]. q = 22 : L33 = [0, 0, 0, 0, 0, 0, 1, 3, 5], L34 = [0, 0, 0, 0, 0, 0, 1, 3, 7], L166 = [0, 0, 0, 0, 0, 1, 2, 8, 9], L177 = [0, 0, 0, 0, 0, 1, 3, 4, 8], L182 = [0, 0, 0, 0, 0, 1, 3, 5, 11], L184 = [0, 0, 0, 0, 0, 1, 3, 7, 11], L242 = [0, 0, 0, 0, 0, 2, 4, 6, 11], L243 = [0, 0, 0, 0, 0, 2, 4, 8, 11], L567 = [0, 0, 0, 0, 1, 2, 3, 4, 9], L570 = [0, 0, 0, 0, 1, 2, 3, 5, 6 L577 = [0, 0, 0, 0, 1, 2, 3, 6, 8], L582 = [0, 0, 0, 0, 1, 2, 3, 7, 10], L600 = [0, 0, 0, 0, 1, 2, 4, 5, 6], L623 = [0, 0, 0, 0, 1, 2, 5, 6, 7], L624 = [0, 0, 0, 0, 1, 2, 5, 6, 8], L641 = [0, 0, 0, 0, 1, 2, 6, 7, 10], L662 = [0, 0, 0, 0, 1, 2, 8, 9, 11 L686 = [0, 0, 0, 0, 1, 3, 4, 8, 11], L694 = [0, 0, 0, 0, 1, 3, 5, 11, 11], L697 = [0, 0, 0, 0, 1, 3, 7, 11, 11], L818 = [0, 0, 0, 0, 2, 4, 6, 11, 11], L819 = [0, 0, 0, 0, 2, 4, 8, 11, 11], L1880 = [0, 0, 0, 1, 2, 3, 4, 5, 7], L1881 = [0, 0, 0, 1, 2, 3, 4, 5, 8], L1882 = [0, 0, 0, 1, 2, 3, 4, 5, 9], L1883 = [0, 0, 0, 1, 2, 3, 4, 5, 10], L1885 = [0, 0, 0, 1, 2, 3, 4, 6, 7], L1886 = [0, 0, 0, 1, 2, 3, 4, 6, 8], L1887 = [0, 0, 0, 1, 2, 3, 4, 6, 9], L1888 = [0, 0, 0, 1, 2, 3, 4, 6, 1 L1892 = [0, 0, 0, 1, 2, 3, 4, 7, 10], L1898 = [0, 0, 0, 1, 2, 3, 4, 9, 10], L1899 = [0, 0, 0, 1, 2, 3, 4, 9, 11], L1903 = [0, 0, 0, 1, 2, 3, 5, 6, 7], L1904 = [0, 0, 0, 1, 2, 3, 5, 6, 8], L1907 = [0, 0, 0, 1, 2, 3, 5, 6, 11], L1908 = [0, 0, 0, 1, 2, 3, 5, 7, 8], L1913 = [0, 0, 0, 1, 2, 3, 5, 8, 10], L1922 = [0, 0, 0, 1, 2, 3, 6, 8, 9], L1924 = [0, 0, 0, 1, 2, 3, 6, 8, L1932 = [0, 0, 0, 1, 2, 3, 7, 10, 11], L1976 = [0, 0, 0, 1, 2, 4, 5, 6, 7], L1977 = [0, 0, 0, 1, 2, 4, 5, 6, 8], L1979 = [0, 0, 0, 1, 2, 4, 5, 6, 11], L1982 = [0, 0, 0, 1, 2, 4, 5, 8, 10], L1996 = [0, 0, 0, 1, 2, 4, 6, 8, 10], L2027 = [0, 0, 0, 1, 2, 5, 6, 7, 11], L2030 = [0, 0, 0, 1, 2, 5, 6, 8, 11], L2063 = [0, 0, 0, 1, 2, 6, 7, 10, 11], L2099 = [0, 0, 0, 1, 2, 8, 9, 11, 11], L2142 = [0, 0, 0, 1, 3, 4, 8, 11, 11], L2147 = [0, 0, 0, 1, 3, 5, 7, 9, 11], L2152 = [0, 0, 0, 1, 3, 5, 11, 11, 11], L2156 = [0, 0, 0, 1, 3, 7, 11, 11, 11], L2377 = [0, 0, 0, 2, 4, 6, 8, 10, 11], L2379 = [0, 0, 0, 2, 4, 6, 11, 11, 11], L2380 = [0, 0, 0, 2, 4, 8, 11, 11, 11], L3804 = [0, 0, 1, 1, 2, 4, 6, 8, 10],
260
EMILIO A. LAURET
Table 7. (continued) m = 9 q I indexes of I-isospectral families 22 {0} {33, 34}, {166, 177}, {182, 184}, {242, 243}, {567, 570}, {577, 600}, {582, 623}, {624, 641}, {662, 686}, {694, 697}, {818, 819}, {1880, 1882}, {1881, 1883, 1885, 1887}, {1886, 1888}, {1892, 1913}, {1898, 1904}, {1899, 1907}, {1903, 1908}, {1922, 1976}, {1924, 1979}, {1932, 2027}, {1977, 1982}, {2030, 2063}, {2099, 2142}, {2152, 2156}, {2379, 2380}, {4049, 4051, 4060}, {5345, 5347, 5352}, {5346, 5348, 5361}, {5350, 5357, 5362}, {5353, 5358}, {5355, 5363, 5366}, {5356, 5359, 5364, 5369}, {5368, 5371}, {5374, 5385, 5401}, {5376, 5400, 5413}, {5379, 5415}, {5391, 5402}, {5392, 5405}, {5398, 5406}, {5428, 5536}, {5431, 5541}, {5442, 5624}, {5539, 5546}, {5629, 5687}, {5742, 5811}, {5823, 5828}, {6204, 6205}, {10847, 10854}, {10852, 10856, 10876}, {13505, 13507, 13510, 13513}, {13506, 13517}, {13508, 13514, 13520},
L4049 = [0, 0, 1, 1, 3, 3, 5, 5, 9], L4051 = [0, 0, 1, 1, 3, 3, 5, 7, 7], L4060 = [0, 0, 1, 1, 3, 3, 5, 9, 9], L4232 = [0, 0, 1, 1, 3, 5, 7, 9, 11], L5172 = [0, 0, 1, 2, 2, 4, 6, 8, 10], L5345 = [0, 0, 1, 2, 3, 4, 5, 6, 7], L5346 = [0, 0, 1, 2, 3, 4, 5, 6, 8], L5347 = [0, 0, 1, 2, 3, 4, 5, 6, 9], L5348 = [0, 0, 1, 2, 3, 4, 5, 6, 10], L5350 = [0, 0, 1, 2, 3, 4, 5, 7, L5352 = [0, 0, 1, 2, 3, 4, 5, 7, 10], L5353 = [0, 0, 1, 2, 3, 4, 5, 7, 11], L5355 = [0, 0, 1, 2, 3, 4, 5, 8, 10], L5356 = [0, 0, 1, 2, 3, 4, 5, 8, 11], L5357 = [0, 0, 1, 2, 3, 4, 5, 9, 10], L5358 = [0, 0, 1, 2, 3, 4, 5, 9, 11], L5359 = [0, 0, 1, 2, 3, 4, 5, 10, 11], L5361 = [0, 0, 1, 2, 3, 4, 6, 7, 8], L5362 = [0, 0, 1, 2, 3, 4, 6, 7, 9], L5363 = [0, 0, 1, 2, 3, 4, 6, 7, 10], L5364 = [0, 0, 1, 2, 3, 4, 6, 7, 11], L5366 = [0, 0, 1, 2, 3, 4, 6, 8, 9], L5367 = [0, 0, 1, 2, 3, 4, 6, 8, 10], L5368 = [0, 0, 1, 2, 3, 4, 6, 8, 11], L5369 = [0, 0, 1, 2, 3, 4, 6, 9, 11], L5371 = [0, 0, 1, 2, 3, 4, 6, 10, 11], L5374 = [0, 0, 1, 2, 3, 4, 7, 8, 10], L5376 = [0, 0, 1, 2, 3, 4, 7, 9, 10], L5379 = [0, 0, 1, 2, 3, 4, 7, 10, 11], L5385 = [0, 0, 1, 2, 3, 4, 8, 9, 10], L5391 = [0, 0, 1, 2, 3, 4, 9, 10, 11], L5392 = [0, 0, 1, 2, 3, 4, 9, 11, 11], L5398 = [0, 0, 1, 2, 3, 5, 6, 7, 11], L5400 = [0, 0, 1, 2, 3, 5, 6, 8, 9], L5401 = [0, 0, 1, 2, 3, 5, 6, 8, 10], L5402 = [0, 0, 1, 2, 3, 5, 6, 8, 11], L5405 = [0, 0, 1, 2, 3, 5, 6, 11, 11], L5406 = [0, 0, 1, 2, 3, 5, 7, 8, 11], L5407 = [0, 0, 1, 2, 3, 5, 7, 9, 11], L5413 = [0, 0, 1, 2, 3, 5, 8, 9, 10], L5415 = [0, 0, 1, 2, 3, 5, 8, 10, 11], L5428 = [0, 0, 1, 2, 3, 6, 8, 9, 11], L5431 = [0, 0, 1, 2, 3, 6, 8, 11, 11], L5442 = [0, 0, 1, 2, 3, 7, 10, 11, 11], L5513 = [0, 0, 1, 2, 4, 4, 6, 8, 10], L5536 = [0, 0, 1, 2, 4, 5, 6, 7, 11], L5538 = [0, 0, 1, 2, 4, 5, 6, 8, 10], L5539 = [0, 0, 1, 2, 4, 5, 6, 8, 11], L5541 = [0, 0, 1, 2, 4, 5, 6, 11, 11], L5546 = [0, 0, 1, 2, 4, 5, 8, 10, 11], L5560 = [0, 0, 1, 2, 4, 6, 6, 8, 10], L5573 = [0, 0, 1, 2, 4, 6, 8, 8, 10], L5575 = [0, 0, 1, 2, 4, 6, 8, 10, 10], L5576 = [0, 0, 1, 2, 4, 6, 8, 10, 11], L5624 = [0, 0, 1, 2, 5, 6, 7, 11, 11], L5629 = [0, 0, 1, 2, 5, 6, 8, 11, 11], L5687 = [0, 0, 1, 2, 6, 7, 10, 11, 11], L5742 = [0, 0, 1, 2, 8, 9, 11, 11, 11], L5811 = [0, 0, 1, 3, 4, 8, 11, 11, 11], L5817 = [0, 0, 1, 3, 5, 7, 9, 11, 11], L5823 = [0, 0, 1, 3, 5, 11, 11, 11, 11], L5828 = [0, 0, 1, 3, 7, 11, 11, 11, 11], L6182 = [0, 0, 2, 2, 4, 6, 8, 10, 11], L6202 = [0, 0, 2, 4, 6, 8, 10, 11, 11], L6204 = [0, 0, 2, 4, 6, 11, 11, 11, 11], L6205 = [0, 0, 2, 4, 8, 11, 11, 11, 11], L7669 = [0, 1, 1, 1, 2, 4, 6, 8, 10], L8239 = [0, 1, 1, 1, 3, 5, 7, 9, 11], L9525 = [0, 1, 1, 2, 2, 4, 6, 8, 10], L9936 = [0, 1, 1, 2, 3, 4, 6, 8, 10], L10025 = [0, 1, 1, 2, 3, 5, 7, 9, 11], L10231 = [0, 1, 1, 2, 4, 4, 6, 8, 10], L10297 = [0, 1, 1, 2, 4, 5, 6, 8, 10], L10345 = [0, 1, 1, 2, 4, 6, 6, 8, 10], L10358 = [0, 1, 1, 2, 4, 6, 7, 8, 10], L10368 = [0, 1, 1, 2, 4, 6, 8, 8, 10], L10370 = [0, 1, 1, 2, 4, 6, 8, 9, 10], L10372 = [0, 1, 1, 2, 4, 6, 8, 10, 10], L10373 = [0, 1, 1, 2, 4, 6, 8, 10, 11], L10847 = [0, 1, 1, 3, 3, 5, 5, 7, 9], L10852 = [0, 1, 1, 3, 3, 5, 5, 9, 11], L10854 = [0, 1, 1, 3, 3, 5, 7, 7, 9], L10856 = [0, 1, 1, 3, 3, 5, 7, 7, 11], L10862 = [0, 1, 1, 3, 3, 5, 7, 9, 11], L10876 = [0, 1, 1, 3, 3, 5, 9, 9, 11], L11067 = [0, 1, 1, 3, 4, 5, 7, 9, 11], L11188 = [0, 1, 1, 3, 5, 5, 7, 9, 11], L11221 = [0, 1, 1, 3, 5, 6, 7, 9, 11], L11246 = [0, 1, 1, 3, 5, 7, 8, 9, 11], L11251 = [0, 1, 1, 3, 5, 7, 9, 10, 11], L11252 = [0, 1, 1, 3, 5, 7, 9, 11, 11], L12686 = [0, 1, 2, 2, 2, 4, 6, 8, 10], L12907 = [0, 1, 2, 2, 3, 4, 6, 8, 10], L12962 = [0, 1, 2, 2, 3, 5, 7, 9, 11], L13104 = [0, 1, 2, 2, 4, 4, 6, 8, 10], L13146 = [0, 1, 2, 2, 4, 5, 6, 8, 10], L13183 = [0, 1, 2, 2, 4, 6, 6, 8, 10],
APPENDIX
261
Table 7. (continued) m = 9 q I indexes of I-isospectral families 22 {0} {13512, 13515, 13532}, {13518, 13527, 13533}, {13521, 13528}, (cont.) {13525, 13535, 13541}, {13526, 13529, 13536, 13545}, {13544, 13548}, {13553, 13572, 13594}, {13556, 13593, 13610}, {13560, 13612}, {13580, 13595}, {13581, 13598}, {13588, 13599}, {13630, 13823}, {13634, 13830}, {13648, 13959}, {13828, 13837}, {13966, 14060}, {14138, 14241}, {14255, 14261}, {14818, 14819, 14821}, {14858, 14859}, {24149, 24198}, {24720, 26196}, {24835, 25726}, {26278, 26284, 26319}, {30189, 30523}, {30257, 30588}, {30700, 31149}, {31182, 31184, 31189, 31192}, {31185, 31193, 31199}, {31190, 31213}, {31191, 31194, 31214}, {31197, 31208, 31215}, {31200, 31209}, {31206, 31218, 31228}, {31207, 31210, 31219, 31233}, {31232, 31237}, {31244, 31273, 31301}, {31248, 31300, 31321}, {31253, 31323}, {31283, 31302}, {31284, 31305}, {31292, 31306}, {31347, 31665}, {31352, 31674}, {31369, 31861}, {31672, 31683}, {31870, 32013}, {32118, 32264}, {32280, 32287}, {33150, 33154}, {33151, 33152, 33155}, {33192, 33193} L13191 L13204 L13505 L13508 L13512 L13515 L13519 L13525 L13528 L13532 L13536 L13542 L13545 L13556 L13580 L13588 L13595 L13600 L13630 L13730 L13784 L13819 L13827 L13837 L13866 L13886 L13890 L13966 L14241
= [0, 1, 2, 2, 4, 6, 7, 8, 10], L13200 = [0, 1, 2, 2, 4, 6, 8, 8, 10], L13202 = [0, 1, 2, 2, 4, 6, 8, 9, 10], = [0, 1, 2, 2, 4, 6, 8, 10, 10], L13205 = [0, 1, 2, 2, 4, 6, 8, 10, 11], L13485 = [0, 1, 2, 3, 4, 4, 6, 8, 10], = [0, 1, 2, 3, 4, 5, 6, 7, 8], L13506 = [0, 1, 2, 3, 4, 5, 6, 7, 9], L13507 = [0, 1, 2, 3, 4, 5, 6, 7, 10], = [0, 1, 2, 3, 4, 5, 6, 7, 11], L13510 = [0, 1, 2, 3, 4, 5, 6, 8, 9], L13511 = [0, 1, 2, 3, 4, 5, 6, 8, 10], = [0, 1, 2, 3, 4, 5, 6, 8, 11], L13513 = [0, 1, 2, 3, 4, 5, 6, 9, 10], L13514 = [0, 1, 2, 3, 4, 5, 6, 9, 11], = [0, 1, 2, 3, 4, 5, 6, 10, 11], L13517 = [0, 1, 2, 3, 4, 5, 7, 8, 9], L13518 = [0, 1, 2, 3, 4, 5, 7, 8, 11], = [0, 1, 2, 3, 4, 5, 7, 9, 11], L13520 = [0, 1, 2, 3, 4, 5, 7, 10, 11], L13521 = [0, 1, 2, 3, 4, 5, 7, 11, 11], = [0, 1, 2, 3, 4, 5, 8, 10, 11], L13526 = [0, 1, 2, 3, 4, 5, 8, 11, 11], L13527 = [0, 1, 2, 3, 4, 5, 9, 10, 11], = [0, 1, 2, 3, 4, 5, 9, 11, 11], L13529 = [0, 1, 2, 3, 4, 5, 10, 11, 11], L13531 = [0, 1, 2, 3, 4, 6, 7, 8, 10], = [0, 1, 2, 3, 4, 6, 7, 8, 11], L13533 = [0, 1, 2, 3, 4, 6, 7, 9, 11], L13535 = [0, 1, 2, 3, 4, 6, 7, 10, 11], = [0, 1, 2, 3, 4, 6, 7, 11, 11], L13539 = [0, 1, 2, 3, 4, 6, 8, 8, 10], L13541 = [0, 1, 2, 3, 4, 6, 8, 9, 11], = [0, 1, 2, 3, 4, 6, 8, 10, 10], L13543 = [0, 1, 2, 3, 4, 6, 8, 10, 11], L13544 = [0, 1, 2, 3, 4, 6, 8, 11, 11], = [0, 1, 2, 3, 4, 6, 9, 11, 11], L13548 = [0, 1, 2, 3, 4, 6, 10, 11, 11], L13553 = [0, 1, 2, 3, 4, 7, 8, 10, 11], = [0, 1, 2, 3, 4, 7, 9, 10, 11], L13560 = [0, 1, 2, 3, 4, 7, 10, 11, 11], L13572 = [0, 1, 2, 3, 4, 8, 9, 10, 11], = [0, 1, 2, 3, 4, 9, 10, 11, 11], L13581 = [0, 1, 2, 3, 4, 9, 11, 11, 11], L13587 = [0, 1, 2, 3, 5, 6, 7, 9, 11], = [0, 1, 2, 3, 5, 6, 7, 11, 11], L13593 = [0, 1, 2, 3, 5, 6, 8, 9, 11], L13594 = [0, 1, 2, 3, 5, 6, 8, 10, 11], = [0, 1, 2, 3, 5, 6, 8, 11, 11], L13598 = [0, 1, 2, 3, 5, 6, 11, 11, 11], L13599 = [0, 1, 2, 3, 5, 7, 8, 11, 11], = [0, 1, 2, 3, 5, 7, 9, 11, 11], L13610 = [0, 1, 2, 3, 5, 8, 9, 10, 11], L13612 = [0, 1, 2, 3, 5, 8, 10, 11, 11], = [0, 1, 2, 3, 6, 8, 9, 11, 11], L13634 = [0, 1, 2, 3, 6, 8, 11, 11, 11], L13648 = [0, 1, 2, 3, 7, 10, 11, 11, 11], = [0, 1, 2, 4, 4, 4, 6, 8, 10], L13755 = [0, 1, 2, 4, 4, 5, 6, 8, 10], L13775 = [0, 1, 2, 4, 4, 6, 6, 8, 10], = [0, 1, 2, 4, 4, 6, 8, 8, 10], L13786 = [0, 1, 2, 4, 4, 6, 8, 10, 10], L13787 = [0, 1, 2, 4, 4, 6, 8, 10, 11], = [0, 1, 2, 4, 5, 6, 6, 8, 10], L13823 = [0, 1, 2, 4, 5, 6, 7, 11, 11], L13825 = [0, 1, 2, 4, 5, 6, 8, 8, 10], = [0, 1, 2, 4, 5, 6, 8, 10, 11], L13828 = [0, 1, 2, 4, 5, 6, 8, 11, 11], L13830 = [0, 1, 2, 4, 5, 6, 11, 11, 11], = [0, 1, 2, 4, 5, 8, 10, 11, 11], L13851 = [0, 1, 2, 4, 6, 6, 6, 8, 10], L13864 = [0, 1, 2, 4, 6, 6, 8, 8, 10], = [0, 1, 2, 4, 6, 6, 8, 10, 10], L13867 = [0, 1, 2, 4, 6, 6, 8, 10, 11], L13884 = [0, 1, 2, 4, 6, 8, 8, 8, 10], = [0, 1, 2, 4, 6, 8, 8, 10, 10], L13887 = [0, 1, 2, 4, 6, 8, 8, 10, 11], L13889 = [0, 1, 2, 4, 6, 8, 10, 10, 10], = [0, 1, 2, 4, 6, 8, 10, 10, 11], L13891 = [0, 1, 2, 4, 6, 8, 10, 11, 11], L13959 = [0, 1, 2, 5, 6, 7, 11, 11, 11], = [0, 1, 2, 5, 6, 8, 11, 11, 11], L14060 = [0, 1, 2, 6, 7, 10, 11, 11, 11], L14138 = [0, 1, 2, 8, 9, 11, 11, 11, 11], = [0, 1, 3, 4, 8, 11, 11, 11, 11], L14248 = [0, 1, 3, 5, 7, 9, 11, 11, 11], L14255 = [0, 1, 3, 5, 11, 11, 11, 11, 11],
262
EMILIO A. LAURET
Table 7. (continued) m = 9 q 22 (cont.)
L14261 L14819 L14832 L14858 L18889 L20546 L20639 L20647 L24198 L24640 L24720 L24729 L25726 L26271 L26284 L26296 L26654 L26717 L26922 L26984 L27025 L27037 L29487
I {0, 1}
indexes of I-isospectral families {5347, 5352}, {5355, 5363}, {13514, 13520}, {13525, 13535}, {31193, 31199}, {31206, 31218} {0, 1, 2, 3, 4} {13507, 13510}, {31184, 31189} {7, 8} {1996, 2377, 5172, 5513, 5560, 5573, 5575, 6182, 12686, 13104, 13183, 13200, 13204, 13730, 13775, 13784, 13786, 13851, 13864, 13866, 13884, 13886, 13889, 14779, 14822, 14832}, {2147, 5407, 12962, 13519, 13587, 29487, 30141, 30252, 30273, 30276, 31183, 31196}, {3804, 5367, 5538, 5576, 6202, 9525, 10231, 10345, 10368, 10372, 12907, 13146, 13191, 13202, 13205, 13485, 13539, 13542, 13755, 13787, 13819, 13825, 13867, 13887, 13890, 14836}, {4232, 5817, 10025, 11067, 11221, 11246, 11251, 13600, 23261, 24484, 24687, 24722, 24729, 26533, 26687, 26712, 26717, 26959, 26984, 26989, 27025, 27030, 27037, 30277, 31198, 31291}, {7669, 9936, 10297, 10358, 10370, 10373, 13511, 13531, 13543, 13827, 13891, 14856}, {8239, 10862, 11188, 11252, 14248, 18889, 20364, 20600, 20639, 20646, 24217, 24640, 24712, 24727, 24730, 26200, 26290, 26295, 26654, 26718, 26910, 26922, 26990, 27031, 27038, 31307}, {16922, 20046, 20546, 20629, 20644, 20647, 26271, 26281, 26296, 26924, 27039, 32272} {0, 6, 7, 8} {13511, 13531}, {26271, 26281}, {31183, 31196}
= [0, 1, 3, 7, 11, 11, 11, 11, 11], L14779 = [0, 2, 2, 2, 4, 6, 8, 10, 11], L14818 = [0, 2, 2, 4, 4, 6, 6, 8, 11], = [0, 2, 2, 4, 4, 6, 6, 10, 11], L14821 = [0, 2, 2, 4, 4, 6, 8, 8, 11], L14822 = [0, 2, 2, 4, 4, 6, 8, 10, 11], = [0, 2, 2, 4, 6, 6, 8, 10, 11], L14836 = [0, 2, 2, 4, 6, 8, 10, 11, 11], L14856 = [0, 2, 4, 6, 8, 10, 11, 11, 11], = [0, 2, 4, 6, 11, 11, 11, 11, 11], L14859 = [0, 2, 4, 8, 11, 11, 11, 11, 11], L16922 = [1, 1, 1, 1, 3, 5, 7, 9, 11], = [1, 1, 1, 2, 3, 5, 7, 9, 11], L20046 = [1, 1, 1, 3, 3, 5, 7, 9, 11], L20364 = [1, 1, 1, 3, 4, 5, 7, 9, 11], = [1, 1, 1, 3, 5, 5, 7, 9, 11], L20600 = [1, 1, 1, 3, 5, 6, 7, 9, 11], L20629 = [1, 1, 1, 3, 5, 7, 7, 9, 11], = [1, 1, 1, 3, 5, 7, 8, 9, 11], L20644 = [1, 1, 1, 3, 5, 7, 9, 9, 11], L20646 = [1, 1, 1, 3, 5, 7, 9, 10, 11], = [1, 1, 1, 3, 5, 7, 9, 11, 11], L23261 = [1, 1, 2, 2, 3, 5, 7, 9, 11], L24149 = [1, 1, 2, 3, 3, 4, 7, 9, 10], = [1, 1, 2, 3, 3, 5, 6, 8, 9], L24217 = [1, 1, 2, 3, 3, 5, 7, 9, 11], L24484 = [1, 1, 2, 3, 4, 5, 7, 9, 11], = [1, 1, 2, 3, 5, 5, 7, 9, 11], L24687 = [1, 1, 2, 3, 5, 6, 7, 9, 11], L24712 = [1, 1, 2, 3, 5, 7, 7, 9, 11], = [1, 1, 2, 3, 5, 7, 8, 9, 9], L24722 = [1, 1, 2, 3, 5, 7, 8, 9, 11], L24727 = [1, 1, 2, 3, 5, 7, 9, 9, 11], = [1, 1, 2, 3, 5, 7, 9, 10, 11], L24730 = [1, 1, 2, 3, 5, 7, 9, 11, 11], L24835 = [1, 1, 2, 3, 6, 7, 9, 9, 10], = [1, 1, 2, 5, 7, 8, 9, 9, 10], L26196 = [1, 1, 3, 3, 4, 5, 7, 8, 9], L26200 = [1, 1, 3, 3, 4, 5, 7, 9, 11], = [1, 1, 3, 3, 5, 5, 7, 9, 11], L26278 = [1, 1, 3, 3, 5, 5, 9, 11, 11], L26281 = [1, 1, 3, 3, 5, 7, 7, 9, 11], = [1, 1, 3, 3, 5, 7, 7, 11, 11], L26290 = [1, 1, 3, 3, 5, 7, 8, 9, 11], L26295 = [1, 1, 3, 3, 5, 7, 9, 10, 11], = [1, 1, 3, 3, 5, 7, 9, 11, 11], L26319 = [1, 1, 3, 3, 5, 9, 9, 11, 11], L26533 = [1, 1, 3, 4, 4, 5, 7, 9, 11], = [1, 1, 3, 4, 5, 5, 7, 9, 11], L26687 = [1, 1, 3, 4, 5, 6, 7, 9, 11], L26712 = [1, 1, 3, 4, 5, 7, 8, 9, 11], = [1, 1, 3, 4, 5, 7, 9, 10, 11], L26718 = [1, 1, 3, 4, 5, 7, 9, 11, 11], L26910 = [1, 1, 3, 5, 5, 6, 7, 9, 11], = [1, 1, 3, 5, 5, 7, 8, 9, 11], L26924 = [1, 1, 3, 5, 5, 7, 9, 11, 11], L26959 = [1, 1, 3, 5, 6, 6, 7, 9, 11], = [1, 1, 3, 5, 6, 7, 8, 9, 11], L26989 = [1, 1, 3, 5, 6, 7, 9, 10, 11], L26990 = [1, 1, 3, 5, 6, 7, 9, 11, 11], = [1, 1, 3, 5, 7, 8, 8, 9, 11], L27030 = [1, 1, 3, 5, 7, 8, 9, 10, 11], L27031 = [1, 1, 3, 5, 7, 8, 9, 11, 11], = [1, 1, 3, 5, 7, 9, 10, 10, 11], L27038 = [1, 1, 3, 5, 7, 9, 10, 11, 11], L27039 = [1, 1, 3, 5, 7, 9, 11, 11, 11], = [1, 2, 2, 2, 3, 5, 7, 9, 11], L30141 = [1, 2, 2, 3, 4, 5, 7, 9, 11], L30189 = [1, 2, 2, 3, 4, 6, 9, 10, 10],
APPENDIX
263
Table 7. (continued) m = 9 q 23
I {0}
indexes of I-isospectral families {102, 104}, {108, 110}, {114, 121}, {357, 358}, {361, 362}, {365, 369}, {368, 371, 373}, {376, 378, 386, 392}, {383, 385}, {388, 390}, {391, 396}, {1085, 1086, 1090}, {1087, 1089, 1092, 1093, 1094, 1100}, {1088, 1091}, {1095, 1105}, {1097, 1102, 1103, 1104, 1106, 1107, 1108}, {1099, 1117}, {1101, 1112, 1113, 1114, 1120}, {1109, 1110, 1111, 1118}, {1119, 1124}, {2863, 2864, 2865, 2867, 2869}, {2866, 2868, 2873, 2877, 2881}, {2870, 2872, 2874, 2876, 2880, 2883}, {2887, 2891, 2892}, {2871, 2875, 2878, 2879, 2882, 2884, 2885, 2886, 2888, 2889}, {6856, 6857, 6858, 6859, 6860, 6861, 6862, 6863, 6864, 6865, 6866, 6867}, {6868, 6869, 6870}, {15264, 15265, 15266, 15267, 15268} {0, 1} {1092, 1094}, {1102, 1108}, {2875, 2885, 2886}, {2882, 2888}, {6857, 6858, 6859}, {6861, 6863}, {6862, 6864, 6866, 6867}, {6868, 6869}, {15264, 15265, 15266, 15267} {0, 1, 2} {6858, 6859}, {6862, 6864, 6866}, {15265, 15266, 15267} {0, 1, 2, 3, 4} {6862, 6864}, {15266, 15267}
L30252 = [1, 2, 2, 3, 5, 6, 7, 9, 11], L30257 = [1, 2, 2, 3, 5, 6, 8, 8, 10], L30273 = [1, 2, 2, 3, 5, 7, 8, 9, 11], L30276 = [1, 2, 2, 3, 5, 7, 9, 10, 11], L30277 = [1, 2, 2, 3, 5, 7, 9, 11, 11], L30523 = [1, 2, 2, 4, 4, 6, 7, 8, 9], L30588 = [1, 2, 2, 4, 5, 6, 6, 7, 10], L30700 = [1, 2, 2, 4, 6, 8, 8, 9, 10], L31149 = [1, 2, 3, 4, 4, 6, 8, 8, 10], L31182 = [1, 2, 3, 4, 5, 6, 7, 8, 11], L31183 = [1, 2, 3, 4, 5, 6, 7, 9, 11], L31184 = [1, 2, 3, 4, 5, 6, 7, 10, 11], L31185 = [1, 2, 3, 4, 5, 6, 7, 11, 11], L31189 = [1, 2, 3, 4, 5, 6, 8, 9, 11], L31190 = [1, 2, 3, 4, 5, 6, 8, 10, 11], L31191 = [1, 2, 3, 4, 5, 6, 8, 11, 11], L31192 = [1, 2, 3, 4, 5, 6, 9, 10, 11], L31193 = [1, 2, 3, 4, 5, 6, 9, 11, 11], L31194 = [1, 2, 3, 4, 5, 6, 10, 11, 11], L31196 = [1, 2, 3, 4, 5, 7, 8, 9, 11], L31197 = [1, 2, 3, 4, 5, 7, 8, 11, 11], L31198 = [1, 2, 3, 4, 5, 7, 9, 11, 11], L31199 = [1, 2, 3, 4, 5, 7, 10, 11, 11], L31200 = [1, 2, 3, 4, 5, 7, 11, 11, 11], L31206 = [1, 2, 3, 4, 5, 8, 10, 11, 11], L31207 = [1, 2, 3, 4, 5, 8, 11, 11, 11], L31208 = [1, 2, 3, 4, 5, 9, 10, 11, 11], L31209 = [1, 2, 3, 4, 5, 9, 11, 11, 11], L31210 = [1, 2, 3, 4, 5, 10, 11, 11, 11], L31213 = [1, 2, 3, 4, 6, 7, 8, 10, 11], L31214 = [1, 2, 3, 4, 6, 7, 8, 11, 11], L31215 = [1, 2, 3, 4, 6, 7, 9, 11, 11], L31218 = [1, 2, 3, 4, 6, 7, 10, 11, 11], L31219 = [1, 2, 3, 4, 6, 7, 11, 11, 11], L31228 = [1, 2, 3, 4, 6, 8, 9, 11, 11], L31232 = [1, 2, 3, 4, 6, 8, 11, 11, 11], L31233 = [1, 2, 3, 4, 6, 9, 11, 11, 11], L31237 = [1, 2, 3, 4, 6, 10, 11, 11, 11], L31244 = [1, 2, 3, 4, 7, 8, 10, 11, 11], L31248 = [1, 2, 3, 4, 7, 9, 10, 11, 11], L31253 = [1, 2, 3, 4, 7, 10, 11, 11, 11], L31273 = [1, 2, 3, 4, 8, 9, 10, 11, 11], L31283 = [1, 2, 3, 4, 9, 10, 11, 11, 11], L31284 = [1, 2, 3, 4, 9, 11, 11, 11, 11], L31291 = [1, 2, 3, 5, 6, 7, 9, 11, 11], L31292 = [1, 2, 3, 5, 6, 7, 11, 11, 11], L31300 = [1, 2, 3, 5, 6, 8, 9, 11, 11], L31301 = [1, 2, 3, 5, 6, 8, 10, 11, 11], L31302 = [1, 2, 3, 5, 6, 8, 11, 11, 11], L31305 = [1, 2, 3, 5, 6, 11, 11, 11, 11], L31306 = [1, 2, 3, 5, 7, 8, 11, 11, 11], L31307 = [1, 2, 3, 5, 7, 9, 11, 11, 11], L31321 = [1, 2, 3, 5, 8, 9, 10, 11, 11], L31323 = [1, 2, 3, 5, 8, 10, 11, 11, 11], L31347 = [1, 2, 3, 6, 8, 9, 11, 11, 11], L31352 = [1, 2, 3, 6, 8, 11, 11, 11, 11], L31369 = [1, 2, 3, 7, 10, 11, 11, 11, 11], L31665 = [1, 2, 4, 5, 6, 7, 11, 11, 11], L31672 = [1, 2, 4, 5, 6, 8, 11, 11, 11], L31674 = [1, 2, 4, 5, 6, 11, 11, 11, 11], L31683 = [1, 2, 4, 5, 8, 10, 11, 11, 11], L31861 = [1, 2, 5, 6, 7, 11, 11, 11, 11], L31870 = [1, 2, 5, 6, 8, 11, 11, 11, 11], L32013 = [1, 2, 6, 7, 10, 11, 11, 11, 11], L32118 = [1, 2, 8, 9, 11, 11, 11, 11, 11], L32264 = [1, 3, 4, 8, 11, 11, 11, 11, 11] L32272 = [1, 3, 5, 7, 9, 11, 11, 11, 11], L32280 = [1, 3, 5, 11, 11, 11, 11, 11, 11], L32287 = [1, 3, 7, 11, 11, 11, 11, 11, 11 L33150 = [2, 2, 4, 4, 6, 6, 8, 10, 11], L33151 = [2, 2, 4, 4, 6, 6, 8, 11, 11], L33152 = [2, 2, 4, 4, 6, 6, 10, 11, 11], L33154 = [2, 2, 4, 4, 6, 8, 8, 10, 11], L33155 = [2, 2, 4, 4, 6, 8, 8, 11, 11], L33192 = [2, 4, 6, 11, 11, 11, 11, 11, 11], L33193 = [2, 4, 8, 11, 11, 11, 11, 11, 11]. q = 23 : L102 = [0, 0, 0, 0, 0, 1, 2, 4, 5], L104 = [0, 0, 0, 0, 0, 1, 2, 4, 8], L108 = [0, 0, 0, 0, 0, 1, 2, 5, 7], L110 = [0, 0, 0, 0, 0, 1, 2, 5, 9], L114 = [0, 0, 0, 0, 0, 1, 2, 6, 10], L121 = [0, 0, 0, 0, 0, 1, 3, 4, 9], L357 = [0, 0, 0, 0, 1, 2, 3, 4, 7], L358 = [0, 0, 0, 0, 1, 2, 3, 4, 8], L361 = [0, 0, 0, 0, 1, 2, 3, 4, 11], L362 = [0, 0, 0, 0, 1, 2, 3, 5, 6] L365 = [0, 0, 0, 0, 1, 2, 3, 5, 9], L368 = [0, 0, 0, 0, 1, 2, 3, 6, 7], L369 = [0, 0, 0, 0, 1, 2, 3, 6, 8], L371 =
264
EMILIO A. LAURET
[0, 0, 0, 0, 1, 2, 3, 6, 10], L373 = [0, 0, 0, 0, 1, 2, 3, 7, 9], L376 = [0, 0, 0, 0, 1, 2, 3, 8, 10], L378 = [0, 0, 0, 0, 1, 2, 3, 9, 1 L383 = [0, 0, 0, 0, 1, 2, 4, 5, 11], L385 = [0, 0, 0, 0, 1, 2, 4, 7, 11], L386 = [0, 0, 0, 0, 1, 2, 4, 9, 10], L388 = [0, 0, 0, 0, 1, 2, 5, 6, 8], L390 = [0, 0, 0, 0, 1, 2, 5, 6, 10], L391 = [0, 0, 0, 0, 1, 2, 6, 7, 10], L392 = [0, 0, 0, 0, 1, 2, 6, 8, 9 L396 = [0, 0, 0, 0, 1, 3, 4, 5, 7], L1085 = [0, 0, 0, 1, 2, 3, 4, 5, 8], L1086 = [0, 0, 0, 1, 2, 3, 4, 5, 9], L1087 = [0, 0, 0, 1, 2, 3, 4, 5, 10], L1088 = [0, 0, 0, 1, 2, 3, 4, 5, 11], L1089 = [0, 0, 0, 1, 2, 3, 4, 6, 7], L1090 = [0, 0, 0, 1, 2, 3, 4, 6, 8], L1091 = [0, 0, 0, 1, 2, 3, 4, 6, 9], L1092 = [0, 0, 0, 1, 2, 3, 4, 6, 10], L1093 = [0, 0, 0, 1, 2, 3, 4, 6, L1094 = [0, 0, 0, 1, 2, 3, 4, 7, 8], L1095 = [0, 0, 0, 1, 2, 3, 4, 7, 9], L1097 = [0, 0, 0, 1, 2, 3, 4, 7, 11], L1099 = [0, 0, 0, 1, 2, 3, 4, 8, 10], L1100 = [0, 0, 0, 1, 2, 3, 4, 8, 11], L1101 = [0, 0, 0, 1, 2, 3, 4, 9, 10], L1102 = [0, 0, 0, 1, 2, 3, 4, 9, 11], L1103 = [0, 0, 0, 1, 2, 3, 5, 6, 7], L1104 = [0, 0, 0, 1, 2, 3, 5, 6, 8], L1105 = [0, 0, 0, 1, 2, 3, 5, 6, L1106 = [0, 0, 0, 1, 2, 3, 5, 6, 10], L1107 = [0, 0, 0, 1, 2, 3, 5, 7, 8], L1108 = [0, 0, 0, 1, 2, 3, 5, 7, 10], L1109 = [0, 0, 0, 1, 2, 3, 5, 7, 11], L1110 = [0, 0, 0, 1, 2, 3, 5, 8, 9], L1111 = [0, 0, 0, 1, 2, 3, 5, 8, 11], L1112 = [0, 0, 0, 1, 2, 3, 5, 9, 10], L1113 = [0, 0, 0, 1, 2, 3, 5, 9, 11], L1114 = [0, 0, 0, 1, 2, 3, 6, 7, 9], L1117 = [0, 0, 0, 1, 2, 3, 6, 8, 11], L1118 = [0, 0, 0, 1, 2, 3, 6, 9, 10], L1119 = [0, 0, 0, 1, 2, 3, 8, 9, 10], L1120 = [0, 0, 0, 1, 2, 3, 8, 9, 11], L1124 = [0, 0, 0, 1, 2, 6, 8, 9, 10], L2863 = [0, 0, 1, 2, 3, 4, 5, 6, 7], L2864 = [0, 0, 1, 2, 3, 4, 5, 6, 8], L2865 = [0, 0, 1, 2, 3, 4, 5, 6, 9], L2866 = [0, 0, 1, 2, 3, 4, 5, 6, 10], L2867 = [0, 0, 1, 2, 3, 4, 5, 6, 11], L2868 = [0, 0, 1, 2, 3, 4, 5, 7, 8], L2869 = [0, 0, 1, 2, 3, 4, 5, 7, 9], L2870 = [0, 0, 1, 2, 3, 4, 5, 7, L2871 = [0, 0, 1, 2, 3, 4, 5, 7, 11], L2872 = [0, 0, 1, 2, 3, 4, 5, 8, 9], L2873 = [0, 0, 1, 2, 3, 4, 5, 8, 10], L2874 = [0, 0, 1, 2, 3, 4, 5, 8, 11], L2875 = [0, 0, 1, 2, 3, 4, 5, 9, 11], L2876 = [0, 0, 1, 2, 3, 4, 5, 10, 11], L2877 = [0, 0, 1, 2, 3, 4, 6, 7, 8], L2878 = [0, 0, 1, 2, 3, 4, 6, 7, 9], L2879 = [0, 0, 1, 2, 3, 4, 6, 7, 11], L2880 = [0, 0, 1, 2, 3, 4, 6, 8, 9], L2881 = [0, 0, 1, 2, 3, 4, 6, 8, 11], L2882 = [0, 0, 1, 2, 3, 4, 6, 9, 10], L2883 = [0, 0, 1, 2, 3, 4, 6, 9, 11], L2884 = [0, 0, 1, 2, 3, 4, 7, 8, 10], L2885 = [0, 0, 1, 2, 3, 4, 7, 9, 10], L2886 = [0, 0, 1, 2, 3, 4, 7, 9, 11], L2887 = [0, 0, 1, 2, 3, 4, 8, 9, 10], L2888 = [0, 0, 1, 2, 3, 4, 8, 9, 11], L2889 = [0, 0, 1, 2, 3, 5, 6, 7, 8], L2891 = [0, 0, 1, 2, 3, 5, 7, 8, 11], L2892 = [0, 0, 1, 2, 3, 5, 8, 9, 11], L6856 = [0, 1, 2, 3, 4, 5, 6, 7, 8], L6857 = [0, 1, 2, 3, 4, 5, 6, 7, 9], L6858 = [0, 1, 2, 3, 4, 5, 6, 7, 10], L6859 = [0, 1, 2, 3, 4, 5, 6, 7, L6860 = [0, 1, 2, 3, 4, 5, 6, 8, 9], L6861 = [0, 1, 2, 3, 4, 5, 6, 8, 10], L6862 = [0, 1, 2, 3, 4, 5, 6, 8, 11], L6863 = [0, 1, 2, 3, 4, 5, 6, 9, 10], L6864 = [0, 1, 2, 3, 4, 5, 6, 9, 11], L6865 = [0, 1, 2, 3, 4, 5, 6, 10, 11], L6866 = [0, 1, 2, 3, 4, 5, 7, 8, 9], L6867 = [0, 1, 2, 3, 4, 5, 7, 9, 10], L6868 = [0, 1, 2, 3, 4, 5, 7, 10, 11], L6869 = [0, 1, 2, 3, 4, 5, 8, 9, 11], L6870 = [0, 1, 2, 3, 4, 6, 7, 9, 11], L15264 = [1, 2, 3, 4, 5, 6, 7, 8, 9], L15265 = [1, 2, 3, 4, 5, 6, 7, 8, 10], L15266 = [1, 2, 3, 4, 5, 6, 7, 8, 11], L15267 = [1, 2, 3, 4, 5, 6, 7, 9, 10], L15268 = [1, 2, 3, 4, 5, 6, 8, 10, 11]. q = 24 : L41 = [0, 0, 0, 0, 0, 0, 1, 3, 5], L43 = [0, 0, 0, 0, 0, 0, 1, 3, 7], L213 = [0, 0, 0, 0, 0, 1, 2, 5, 7], L217 = [0, 0, 0, 0, 0, 1, 2, 5, 11], L254 = [0, 0, 0, 0, 0, 1, 3, 4, 5], L256 = [0, 0, 0, 0, 0, 1, 3, 4, 7], L262 = [0, 0, 0, 0, 0, 1, 3, 5, 6], L264 = [0, 0, 0, 0, 0, 1, 3, 5, 8], L267 = [0, 0, 0, 0, 0, 1, 3, 5, 12], L269 = [0, 0, 0, 0, 0, 1, 3, 6, 7] L275 = [0, 0, 0, 0, 0, 1, 3, 7, 8], L277 = [0, 0, 0, 0, 0, 1, 3, 7, 12], L846 = [0, 0, 0, 0, 1, 2, 2, 5, 7], L850 = [0, 0, 0, 0, 1, 2, 2, 5, 11], L899 = [0, 0, 0, 0, 1, 2, 3, 5, 10], L911 = [0, 0, 0, 0, 1, 2, 3, 7, 10], L938 = [0, 0, 0, 0, 1, 2, 4, 5, L942 = [0, 0, 0, 0, 1, 2, 4, 5, 11], L969 = [0, 0, 0, 0, 1, 2, 5, 6, 7], L973 = [0, 0, 0, 0, 1, 2, 5, 6, 11], L975 = [0, 0, 0, 0, 1, 2, 5, 7, 8], L979 = [0, 0, 0, 0, 1, 2, 5, 7, 12], L983 = [0, 0, 0, 0, 1, 2, 5, 8, 11], L988 = [0, 0, 0, 0, 1, 2, 5, 11, L1071 = [0, 0, 0, 0, 1, 3, 3, 5, 9], L1082 = [0, 0, 0, 0, 1, 3, 3, 7, 9], L1099 = [0, 0, 0, 0, 1, 3, 4, 4, 5], L1101 = [0, 0, 0, 0, 1, 3, 4, 4, 7], L1107 = [0, 0, 0, 0, 1, 3, 4, 5, 6], L1109 = [0, 0, 0, 0, 1, 3, 4, 5, 8], L1112 = [0, 0, 0, 0, 1, 3, 4, 5, 1 L1114 = [0, 0, 0, 0, 1, 3, 4, 6, 7], L1120 = [0, 0, 0, 0, 1, 3, 4, 7, 8], L1122 = [0, 0, 0, 0, 1, 3, 4, 7, 12], L1137 = [0, 0, 0, 0, 1, 3, 5, 6, 6], L1139 = [0, 0, 0, 0, 1, 3, 5, 6, 8], L1142 = [0, 0, 0, 0, 1, 3, 5, 6, 12], L1147 = [0, 0, 0, 0, 1, 3, 5, 8, L1150 = [0, 0, 0, 0, 1, 3, 5, 8, 12], L1153 = [0, 0, 0, 0, 1, 3, 5, 12, 12], L1155 = [0, 0, 0, 0, 1, 3, 6, 6, 7], L1161 = [0, 0, 0, 0, 1, 3, 6, 7, 8], L1163 = [0, 0, 0, 0, 1, 3, 6, 7, 12], L1178 = [0, 0, 0, 0, 1, 3, 7, 8, 8], L1180 = [0, 0, 0, 0, 1, 3, 7, 8, 12], L1183 = [0, 0, 0, 0, 1, 3, 7, 12, 12], L2380 = [0, 0, 0, 1, 1, 3, 5, 5, 11], L2389 = [0, 0, 0, 1, 1, 3, 5, 7, 7], L2942 = [0, 0, 0, 1, 2, 2, 2, 5, 7], L2946 = [0, 0, 0, 1, 2, 2, 2, 5, 11], L3034 = [0, 0, 0, 1, 2, 2, 4, 5, L3038 = [0, 0, 0, 1, 2, 2, 4, 5, 11], L3065 = [0, 0, 0, 1, 2, 2, 5, 6, 7], L3069 = [0, 0, 0, 1, 2, 2, 5, 6, 11], L3071 = [0, 0, 0, 1, 2, 2, 5, 7, 8], L3073 = [0, 0, 0, 1, 2, 2, 5, 7, 10], L3075 = [0, 0, 0, 1, 2, 2, 5, 7, 12], L3079 = [0, 0, 0, 1, 2, 2, 5, 8, 11], L3085 = [0, 0, 0, 1, 2, 2, 5, 10, 11], L3087 = [0, 0, 0, 1, 2, 2, 5, 11, 12], L3214 = [0, 0, 0, 1, 2, 3, 4, 5, 10], L3226 = [0, 0, 0, 1, 2, 3, 4, 7, 10], L3247 = [0, 0, 0, 1, 2, 3, 5, 6, 10],
APPENDIX
265
Table 7. (continued) m = 9 q I indexes of I-isospectral families 24 {0} {41, 43}, {213, 217}, {254, 256}, {262, 269}, {264, 275}, {267, 277}, {846, 850}, {899, 911}, {938, 942}, {969, 973}, {975, 983}, {979, 988}, {1071, 1082}, {1099, 1101}, {1107, 1114}, {1109, 1120}, {1112, 1122}, {1137, 1155}, {1139, 1161}, {1142, 1163}, {1147, 1178}, {1150, 1180}, {1153, 1183}, {2942, 2946}, {3034, 3038}, {3065, 3069}, {3071, 3079}, {3073, 3085}, {3075, 3087}, {3214, 3226}, {3247, 3277}, {3251, 3262}, {3257, 3296}, {3265, 3302}, {3344, 3348}, {3375, 3379}, {3381, 3389}, {3385, 3394}, {3456, 3460}, {3462, 3470}, {3466, 3475}, {3477, 3491}, {3481, 3496}, {3487, 3502}, {3685, 3696}, {3715, 3739}, {3723, 3756}, {3728, 3759}, {3792, 3794}, {3800, 3807}, {3802, 3813}, {3805, 3815}, {3830, 3848}, {3832, 3854}, {3835, 3856}, {3840, 3871}, {3843, 3873}, {3846, 3876}, {3906, 3942}, {3908, 3948}, {3911, 3950}, {3916, 3965}, {3919, 3967}, {3922, 3970}, {3931, 4000}, {3934, 4002}, {3937, 4005}, {3940, 4009}, {7644, 7684}, {8917, 8921}, {9009, 9013}, {9040, 9044}, {9046, 9054}, {9048, 9060}, {9050, 9062}, {9226, 9237}, {9239, 9278}, {9322, 9326}, {9353, 9357}, {9359, 9367}, {9361, 9373}, {9363, 9375}, {9438, 9442}, {9444, 9452}, {9446, 9458}, {9448, 9460}, {9462, 9478}, {9464, 9484}, {9466, 9486}, {9472, 9494}, {9474, 9496}, {9734, 9773}, {9822, 9834}, {9855, 9885}, {9859, 9870},
L3251 = [0, 0, 0, 1, 2, 3, 5, 7, 9], L3257 = [0, 0, 0, 1, 2, 3, 5, 8, 10], L3262 = [0, 0, 0, 1, 2, 3, 5, 9, 11], L3265 = [0, 0, 0, 1, 2, 3, 5, 10, 12], L3277 = [0, 0, 0, 1, 2, 3, 6, 7, 10], L3296 = [0, 0, 0, 1, 2, 3, 7, 8, 10], L3302 = [0, 0, 0, 1, 2, 3, 7, 10, 12], L3344 = [0, 0, 0, 1, 2, 4, 4, 5, 7], L3348 = [0, 0, 0, 1, 2, 4, 4, 5, 11], L3375 = [0, 0, 0, 1, 2, 4, 5, 6, 7], L3379 = [0, 0, 0, 1, 2, 4, 5, 6, 11], L3381 = [0, 0, 0, 1, 2, 4, 5, 7, 8], L3385 = [0, 0, 0, 1, 2, 4, 5, 7, 12], L3389 = [0, 0, 0, 1, 2, 4, 5, 8, 11], L3394 = [0, 0, 0, 1, 2, 4, 5, 11, 12], L3456 = [0, 0, 0, 1, 2, 5, 6, 6, 7], L3460 = [0, 0, 0, 1, 2, 5, 6, 6, 11], L3462 = [0, 0, 0, 1, 2, 5, 6, 7, 8], L3466 = [0, 0, 0, 1, 2, 5, 6, 7, L3470 = [0, 0, 0, 1, 2, 5, 6, 8, 11], L3475 = [0, 0, 0, 1, 2, 5, 6, 11, 12], L3477 = [0, 0, 0, 1, 2, 5, 7, 8, 8], L3481 = [0, 0, 0, 1, 2, 5, 7, 8, 12], L3487 = [0, 0, 0, 1, 2, 5, 7, 12, 12], L3491 = [0, 0, 0, 1, 2, 5, 8, 8, 11], L3496 = [0, 0, 0, 1, 2, 5, 8, 11, 12], L3502 = [0, 0, 0, 1, 2, 5, 11, 12, 12], L3685 = [0, 0, 0, 1, 3, 3, 4, 5, 9], L3696 = [0, 0, 0, 1, 3, 3, 4, 7, 9], L3715 = [0, 0, 0, 1, 3, 3, 5, 6, 9], L3723 = [0, 0, 0, 1, 3, 3, 5, 8, 9], L3728 = [0, 0, 0, 1, 3, 3, 5, 9, 12], L3739 = [0, 0, 0, 1, 3, 3, 6, 7, 9], L3756 = [0, 0, 0, 1, 3, 3, 7, 8, 9], L3759 = [0, 0, 0, 1, 3, 3, 7, 9, L3792 = [0, 0, 0, 1, 3, 4, 4, 4, 5], L3794 = [0, 0, 0, 1, 3, 4, 4, 4, 7], L3800 = [0, 0, 0, 1, 3, 4, 4, 5, 6], L3802 = [0, 0, 0, 1, 3, 4, 4, 5, 8], L3805 = [0, 0, 0, 1, 3, 4, 4, 5, 12], L3807 = [0, 0, 0, 1, 3, 4, 4, 6, 7], L3813 = [0, 0, 0, 1, 3, 4, 4, 7, L3815 = [0, 0, 0, 1, 3, 4, 4, 7, 12], L3830 = [0, 0, 0, 1, 3, 4, 5, 6, 6], L3832 = [0, 0, 0, 1, 3, 4, 5, 6, 8], L3835 = [0, 0, 0, 1, 3, 4, 5, 6, 12], L3840 = [0, 0, 0, 1, 3, 4, 5, 8, 8], L3843 = [0, 0, 0, 1, 3, 4, 5, 8, 12], L3846 = [0, 0, 0, 1, 3, 4, 5, 12, 12], L3848 = [0, 0, 0, 1, 3, 4, 6, 6, 7], L3854 = [0, 0, 0, 1, 3, 4, 6, 7, 8], L3856 = [0, 0, 0, 1, 3, 4, 6, 7, 12], L3871 = [0, 0, 0, 1, 3, 4, 7, 8, 8], L3873 = [0, 0, 0, 1, 3, 4, 7, 8, 12], L3876 = [0, 0, 0, 1, 3, 4, 7, 12, 12], L3906 = [0, 0, 0, 1, 3, 5, 6, 6, 6], L3908 = [0, 0, 0, 1, 3, 5, 6, 6, 8], L3911 = [0, 0, 0, 1, 3, 5, 6, 6, 12], L3916 = [0, 0, 0, 1, 3, 5, 6, 8, 8], L3919 = [0, 0, 0, 1, 3, 5, 6, 8, 12], L3922 = [0, 0, 0, 1, 3, 5, 6, 12, 12], L3931 = [0, 0, 0, 1, 3, 5, 8, 8, 8], L3934 = [0, 0, 0, 1, 3, 5, 8, 8, 12], L3937 = [0, 0, 0, 1, 3, 5, 8, 12, 12], L3940 = [0, 0, 0, 1, 3, 5, 12, 12, 12], L3942 = [0, 0, 0, 1, 3, 6, 6, 6, 7], L3948 = [0, 0, 0, 1, 3, 6, 6, 7, 8], L3950 = [0, 0, 0, 1, 3, 6, 6, 7, 12], L3965 = [0, 0, 0, 1, 3, 6, 7, 8, 8], L3967 = [0, 0, 0, 1, 3, 6, 7, 8, L3970 = [0, 0, 0, 1, 3, 6, 7, 12, 12], L4000 = [0, 0, 0, 1, 3, 7, 8, 8, 8], L4002 = [0, 0, 0, 1, 3, 7, 8, 8, 12], L4005 = [0, 0, 0, 1, 3, 7, 8, 12, 12], L4009 = [0, 0, 0, 1, 3, 7, 12, 12, 12], L7525 = [0, 0, 1, 1, 3, 4, 5, 5, 11], L7534 = [0, 0, 1, 1, 3, 4, 5, 7, 7], L7639 = [0, 0, 1, 1, 3, 5, 5, 6, 11], L7644 = [0, 0, 1, 1, 3, 5, 5, 7, 11],
266
EMILIO A. LAURET
Table 7. (continued) m = 9 q I indexes of I-isospectral families 24 {0} {9865, 9904}, {9873, 9910}, {9946, 10011}, {9950, 9961}, {9956, 10030}, (cont.) {9964, 10036}, {9968, 9987}, {9975, 9996}, {9982, 10070}, {9990, 10076}, {9999, 10084}, {10148, 10152}, {10179, 10183}, {10185, 10193}, {10189, 10198}, {10260, 10264}, {10266, 10274}, {10270, 10279}, {10281, 10295}, {10285, 10300}, {10291, 10306}, {10429, 10433}, {10435, 10443}, {10439, 10448}, {10450, 10464}, {10454, 10469}, {10460, 10475}, {10477, 10498}, {10481, 10503}, {10487, 10509}, {10494, 10516}, {10836, 10868}, {10913, 10924}, {10943, 10967}, {10951, 10984}, {10956, 10987}, {11022, 11069}, {11030, 11086}, {11035, 11089}, {11048, 11122}, {11053, 11125}, {11058, 11129}, {11186, 11188}, {11194, 11201}, {11196, 11207}, {11199, 11209}, {11224, 11242}, {11226, 11248}, {11229, 11250}, {11234, 11265}, {11237, 11267}, {11240, 11270}, {11300, 11336}, {11302, 11342}, {11305, 11344}, {11310, 11359}, {11313, 11361}, {11316, 11364}, {11325, 11394}, {11328, 11396}, {11331, 11399}, {11334, 11403}, {11455, 11516}, {11457, 11522}, {11460, 11524}, {11465, 11539}, {11468, 11541}, {11471, 11544}, {11480, 11574}, {11483, 11576}, {11486, 11579}, {11489, 11583}, {11502, 11635}, {11505, 11637}, {11508, 11640}, {11511, 11644}, {11514, 11649}, {19877, 19889}, {21290, 21330}, {21573, 21638}, {21589, 21691}, {21594, 21696}, {24160, 24164}, {24252, 24256}, {24283, 24287}, {24289, 24297}, {24291, 24303}, {24293, 24305}, {24469, 24480}, {24565, 24569}, {24596, 24600}, {24602, 24610}, {24604, 24616}, {24606, 24618}, {24681, 24685}, {24687, 24695}, {24689, 24701}, {24691, 24703}, {24705, 24721}, {24707, 24727}, {24709, 24729}, {24713, 24738}, {24715, 24740}, {24717, 24742}, {25109, 25120}, {25122, 25161}, {25203, 25214}, {25216, 25297}, {25222, 25242}, {25227, 25253}, {25229, 25255}, {25244, 25339}, {25258, 25350}, {25416, 25420}, {25447, 25451}, {25453, 25461}, {25455, 25467}, {25457, 25469}, {25532, 25536}, {25538, 25546}, {25540, 25552}, {25542, 25554}, {25556, 25572}, {25558, 25578}, {25560, 25580}, {25566, 25588}, {25568, 25590}, {25717, 25721}, {25723, 25731}, {25725, 25737}, {25727, 25739}, {25741, 25757}, {25743, 25763}, {25745, 25765}, {25751, 25773}, {25753, 25775}, {25777, 25804}, {25779, 25810}, {25781, 25812}, {25787, 25820},
L7648 = [0, 0, 1, 1, 3, 5, 5, 8, 11], L7652 = [0, 0, 1, 1, 3, 5, 5, 11, 12], L7661 = [0, 0, 1, 1, 3, 5, 6, 7, 7], L7682 = [0, 0, 1, 1, 3, 5, 7, 7, 8], L7684 = [0, 0, 1, 1, 3, 5, 7, 7, 11], L7685 = [0, 0, 1, 1, 3, 5, 7, 7, 12], L8917 = [0, 0, 1, 2, 2, 2, 2, 5, 7], L8921 = [0, 0, 1, 2, 2, 2, 2, 5, 11], L9009 = [0, 0, 1, 2, 2, 2, 4, 5, 7], L9013 = [0, 0, 1, 2, 2, 2, 4, 5, 11], L9040 = [0, 0, 1, 2, 2, 2, 5, 6, 7], L9044 = [0, 0, 1, 2, 2, 2, 5, 6, 11], L9046 = [0, 0, 1, 2, 2, 2, 5, 7, 8], L9048 = [0, 0, 1, 2, 2, 2, 5, 7, 10], L9050 = [0, 0, 1, 2, 2, 2, 5, 7, 12], L9054 = [0, 0, 1, 2, 2, 2, 5, 8, 11], L9060 = [0, 0, 1, 2, 2, 2, 5, 10, 11], L9062 = [0, 0, 1, 2, 2, 2, 5, 11, 12], L9226 = [0, 0, 1, 2, 2, 3, 5, 7, 9], L9237 = [0, 0, 1, 2, 2, 3, 5, 9, 11], L9239 = [0, 0, 1, 2, 2, 3, 5, 10, 10], L9278 = [0, 0, 1, 2, 2, 3, 7, 10, 10], L9322 = [0, 0, 1, 2, 2, 4, 4, 5, 7], L9326 = [0, 0, 1, 2, 2, 4, 4, 5, 11], L9353 = [0, 0, 1, 2, 2, 4, 5, 6, 7], L9357 = [0, 0, 1, 2, 2, 4, 5, 6, 11], L9359 = [0, 0, 1, 2, 2, 4, 5, 7, 8], L9361 = [0, 0, 1, 2, 2, 4, 5, 7, L9363 = [0, 0, 1, 2, 2, 4, 5, 7, 12], L9367 = [0, 0, 1, 2, 2, 4, 5, 8, 11], L9373 = [0, 0, 1, 2, 2, 4, 5, 10, 11], L9375 = [0, 0, 1, 2, 2, 4, 5, 11, 12], L9438 = [0, 0, 1, 2, 2, 5, 6, 6, 7], L9442 = [0, 0, 1, 2, 2, 5, 6, 6, 11], L9444 = [0, 0, 1, 2, 2, 5, 6, 7, 8], L9446 = [0, 0, 1, 2, 2, 5, 6, 7, 10], L9448 = [0, 0, 1, 2, 2, 5, 6, 7, 12], L9452 = [0, 0, 1, 2, 2, 5, 6, 8, 11], L9458 = [0, 0, 1, 2, 2, 5, 6, 10, 11], L9460 = [0, 0, 1, 2, 2, 5, 6, 11, 12], L9462 = [0, 0, 1, 2, 2, 5, 7, 8, 8], L9464 = [0, 0, 1, 2, 2, 5, 7, 8, 10], L9466 = [0, 0, 1, 2, 2, 5, 7, 8, 12], L9472 = [0, 0, 1, 2, 2, 5, 7, 10, 12], L9474 = [0, 0, 1, 2, 2, 5, 7, 12, 12], L9478 = [0, 0, 1, 2, 2, 5, 8, 8, 11], L9484 = [0, 0, 1, 2, 2, 5, 8, 10, 11], L9486 = [0, 0, 1, 2, 2, 5, 8, 11, 12], L9494 = [0, 0, 1, 2, 2, 5, 10, 11, 12],
APPENDIX
267
Table 7. (continued) m = 9 q I indexes of I-isospectral families 24 {0} {25789, 25822}, {25798, 25832}, {25800, 25834}, {26309, 26348}, {26402, 26479}, (cont.) {26414, 26437}, {26428, 26521}, {26440, 26530}, {26603, 26615}, {26636, 26666}, {26640, 26651}, {26646, 26685}, {26654, 26691}, {26727, 26792}, {26731, 26742}, {26737, 26811}, {26745, 26817}, {26749, 26768}, {26756, 26777}, {26763, 26851}, {26771, 26857}, {26780, 26865}, {26923, 27043}, {26927, 26938}, {26933, 27062}, {26941, 27068}, {26945, 26964}, {26952, 26973}, {26959, 27102}, {26967, 27108}, {26976, 27116}, {26980, 27009}, {26987, 27018}, {26997, 27028}, {27004, 27172}, {27012, 27178}, {27021, 27186}, {27031, 27196}, {27290, 27294}, {27321, 27325}, {27327, 27335}, {27331, 27340}, {27402, 27406}, {27408, 27416}, {27412, 27421}, {27423, 27437}, {27427, 27442}, {27433, 27448}, {27571, 27575}, {27577, 27585}, {27581, 27590}, {27592, 27606}, {27596, 27611}, {27602, 27617}, {27619, 27640}, {27623, 27645}, {27629, 27651}, {27636, 27658}, {27877, 27881}, {27883, 27891}, {27887, 27896}, {27898, 27912}, {27902, 27917}, {27908, 27923}, {27925, 27946}, {27929, 27951}, {27935, 27957}, {27942, 27964}, {27966, 27995}, {27970, 28000}, {27976, 28006}, {27983, 28013}, {27991, 28021}, {28600, 28632}, {28679, 28736}, {28697, 28772}, {28704, 28776}, {28846, 28857}, {28876, 28900}, {28884, 28917}, {28889, 28920}, {28955, 29002}, {28963, 29019}, {28968, 29022}, {28981, 29055}, {28986, 29058}, {28991, 29062}, {29121, 29202}, {29129, 29219}, {29134, 29222}, {29147, 29255}, {29152, 29258}, {29157, 29262}, {29176, 29319}, {29181, 29322}, {29186, 29326}, {29191, 29331}, {29421, 29423}, {29429, 29436}, {29431, 29442},
L9496 = [0, 0, 1, 2, 2, 5, 11, 12, 12], L9734 = [0, 0, 1, 2, 3, 3, 5, 9, 10], L9773 = [0, 0, 1, 2, 3, 3, 7, 9, 10], L9822 = [0, 0, 1, 2, 3, 4, 4, 5, 10], L9834 = [0, 0, 1, 2, 3, 4, 4, 7, 10], L9855 = [0, 0, 1, 2, 3, 4, 5, 6, 10], L9859 = [0, 0, 1, 2, 3, 4, 5, 7, 9], L9865 = [0, 0, 1, 2, 3, 4, 5, 8, 10], L9870 = [0, 0, 1, 2, 3, 4, 5, 9, 11], L9873 = [0, 0, 1, 2, 3, 4, 5, 10, 12], L9885 = [0, 0, 1, 2, 3, 4, 6, 7, 10], L9904 = [0, 0, 1, 2, 3, 4, 7, 8, 10], L9910 = [0, 0, 1, 2, 3, 4, 7, 10, 12], L9946 = [0, 0, 1, 2, 3, 5, 6, 6, 10], L9950 = [0, 0, 1, 2, 3, 5, 6, 7, 9], L9956 = [0, 0, 1, 2, 3, 5, 6, 8, 10], L9961 = [0, 0, 1, 2, 3, 5, 6, 9, 11], L9964 = [0, 0, 1, 2, 3, 5, 6, 10, 12], L9968 = [0, 0, 1, 2, 3, 5, 7, 8, 9], L9975 = [0, 0, 1, 2, 3, 5, 7, 9, 12], L9982 = [0, 0, 1, 2, 3, 5, 8, 8, 10], L9987 = [0, 0, 1, 2, 3, 5, 8, 9, 11], L9990 = [0, 0, 1, 2, 3, 5, 8, 10, 12], L9996 = [0, 0, 1, 2, 3, 5, 9, 11, 12], L9999 = [0, 0, 1, 2, 3, 5, 10, 12, 12], L10011 = [0, 0, 1, 2, 3, 6, 6, 7, 10], L10030 = [0, 0, 1, 2, 3, 6, 7, 8, 10], L10036 = [0, 0, 1, 2, 3, 6, 7, 10, 12], L10070 = [0, 0, 1, 2, 3, 7, 8, 8, 10], L10076 = [0, 0, 1, 2, 3, 7, 8, 10, 12], L10084 = [0, 0, 1, 2, 3, 7, 10, 12, 12], L10148 = [0, 0, 1, 2, 4, 4, 4, 5, 7], L10152 = [0, 0, 1, 2, 4, 4, 4, 5, 11], L10179 = [0, 0, 1, 2, 4, 4, 5, 6, 7], L10183 = [0, 0, 1, 2, 4, 4, 5, 6, 11], L10185 = [0, 0, 1, 2, 4, 4, 5, 7, 8], L10189 = [0, 0, 1, 2, 4, 4, 5, 7, 12], L10193 = [0, 0, 1, 2, 4, 4, 5, 8, 11], L10198 = [0, 0, 1, 2, 4, 4, 5, 11, 12], L10260 = [0, 0, 1, 2, 4, 5, 6, 6, 7], L10264 = [0, 0, 1, 2, 4, 5, 6, 6, 11], L10266 = [0, 0, 1, 2, 4, 5, 6, 7, 8], L10270 = [0, 0, 1, 2, 4, 5, 6, 7, 12], L10274 = [0, 0, 1, 2, 4, 5, 6, 8, 11], L10279 = [0, 0, 1, 2, 4, 5, 6, 11, 12], L10281 = [0, 0, 1, 2, 4, 5, 7, 8, 8], L10285 = [0, 0, 1, 2, 4, 5, 7, 8, 12], L10291 = [0, 0, 1, 2, 4, 5, 7, 12, 12], L10295 = [0, 0, 1, 2, 4, 5, 8, 8, 11], L10300 = [0, 0, 1, 2, 4, 5, 8, 11, 12], L10306 = [0, 0, 1, 2, 4, 5, 11, 12, 12], L10429 = [0, 0, 1, 2, 5, 6, 6, 6, 7], L10433 = [0, 0, 1, 2, 5, 6, 6, 6, 11], L10435 = [0, 0, 1, 2, 5, 6, 6, 7, 8], L10439 = [0, 0, 1, 2, 5, 6, 6, 7, 12], L10443 = [0, 0, 1, 2, 5, 6, 6, 8, 11], L10448 = [0, 0, 1, 2, 5, 6, 6, 11, 12], L10450 = [0, 0, 1, 2, 5, 6, 7, 8, 8], L10454 = [0, 0, 1, 2, 5, 6, 7, 8, 12], L10460 = [0, 0, 1, 2, 5, 6, 7, 12, 12], L10464 = [0, 0, 1, 2, 5, 6, 8, 8, 11], L10469 = [0, 0, 1, 2, 5, 6, 8, 11, 12], L10475 = [0, 0, 1, 2, 5, 6, 11, 12, 12], L10477 = [0, 0, 1, 2, 5, 7, 8, 8, 8], L10481 = [0, 0, 1, 2, 5, 7, 8, 8, 12], L10487 = [0, 0, 1, 2, 5, 7, 8, 12, 12], L10491 = [0, 0, 1, 2, 5, 7, 10, 11, 12], L10494 = [0, 0, 1, 2, 5, 7, 12, 12, 12], L10498 = [0, 0, 1, 2, 5, 8, 8, 8, 11], L10503 = [0, 0, 1, 2, 5, 8, 8, 11, 12], L10509 = [0, 0, 1, 2, 5, 8, 11, 12, 12], L10516 = [0, 0, 1, 2, 5, 11, 12, 12, 12],
268
EMILIO A. LAURET
Table 7. (continued) m = 9 q I indexes of I-isospectral families 24 {0} {29434, 29444}, {29459, 29477}, {29461, 29483}, {29464, 29485}, {29469, 29500}, (cont.) {29472, 29502}, {29475, 29505}, {29535, 29571}, {29537, 29577}, {29540, 29579}, {29545, 29594}, {29548, 29596}, {29551, 29599}, {29560, 29629}, {29566, 29634}, {29569, 29638}, {29690, 29751}, {29692, 29757}, {29695, 29759}, {29700, 29774}, {29703, 29776}, {29706, 29779}, {29715, 29809}, {29718, 29811}, {29721, 29814}, {29724, 29818}, {29737, 29870}, {29740, 29872}, {29743, 29875}, {29746, 29879}, {29749, 29884}, {29966, 30059}, {29968, 30065}, {29971, 30067}, {29976, 30082}, {29979, 30084}, {29982, 30087}, {29991, 30117}, {29994, 30119}, {29997, 30122}, {30000, 30126}, {30013, 30178}, {30016, 30180}, {30019, 30183}, {30022, 30187}, {30025, 30192}, {30042, 30274}, {30045, 30276}, {30048, 30279}, {30051, 30283}, {30054, 30288}, {30057, 30294}, {47646, 47660}, {49437, 49560}, {50524, 50536}, {51137, 51149}, {51176, 51196}, {51184, 51206}, {54142, 54182}, {54425, 54490}, {54441, 54543}, {54446, 54548}, {55018, 55122}, {55034, 55175}, {55039, 55180}, {55064, 55282}, {55069, 55287}, {55074, 55294}, {59807, 59811}, {59899, 59903}, {59930, 59934}, {59936, 59944}, {59938, 59950}, {59940, 59952}, {60116, 60127}, {60212, 60216}, {60243, 60247}, {60249, 60257}, {60251, 60263}, {60253, 60265}, {60328, 60332}, {60334, 60342}, {60336, 60348}, {60338, 60350}, {60352, 60368}, {60354, 60374}, {60356, 60376}, {60360, 60385}, {60362, 60387}, {60364, 60389}, {60756, 60767}, {60850, 60861}, {60869, 60889}, {60874, 60900}, {60876, 60902}, {60904, 60998}, {61066, 61070}, {61097, 61101}, {61103, 61111}, {61105, 61117}, {61107, 61119}, {61182, 61186}, {61188, 61196}, {61190, 61202}, {61192, 61204}, {61206, 61222}, {61208, 61228}, {61210, 61230}, {61214, 61239}, {61216, 61241}, {61218, 61243}, {61371, 61375}, {61377, 61385}, {61379, 61391}, {61381, 61393}, {61395, 61411}, {61397, 61417}, {61399, 61419}, {61405, 61430}, {61407, 61432},
L10836 L10924 L10956 L10987 L11035 L11058 L11089 L11129 L11194 L11201 L11224 L11234 L11242 L11265 L11300 L11310 L11321 L11331 L11342 L11361
= [0, 0, 1, 3, 3, 3, 5, 9, 9], L10868 = [0, 0, 1, 3, 3, 3, 7, 9, 9], L10913 = [0, 0, 1, 3, 3, 4, 4, 5, 9], = [0, 0, 1, 3, 3, 4, 4, 7, 9], L10943 = [0, 0, 1, 3, 3, 4, 5, 6, 9], L10951 = [0, 0, 1, 3, 3, 4, 5, 8, 9], = [0, 0, 1, 3, 3, 4, 5, 9, 12], L10967 = [0, 0, 1, 3, 3, 4, 6, 7, 9], L10984 = [0, 0, 1, 3, 3, 4, 7, 8, 9], = [0, 0, 1, 3, 3, 4, 7, 9, 12], L11022 = [0, 0, 1, 3, 3, 5, 6, 6, 9], L11030 = [0, 0, 1, 3, 3, 5, 6, 8, 9], = [0, 0, 1, 3, 3, 5, 6, 9, 12], L11048 = [0, 0, 1, 3, 3, 5, 8, 8, 9], L11053 = [0, 0, 1, 3, 3, 5, 8, 9, 12], = [0, 0, 1, 3, 3, 5, 9, 12, 12], L11069 = [0, 0, 1, 3, 3, 6, 6, 7, 9], L11086 = [0, 0, 1, 3, 3, 6, 7, 8, 9], = [0, 0, 1, 3, 3, 6, 7, 9, 12], L11122 = [0, 0, 1, 3, 3, 7, 8, 8, 9], L11125 = [0, 0, 1, 3, 3, 7, 8, 9, 12], = [0, 0, 1, 3, 3, 7, 9, 12, 12], L11186 = [0, 0, 1, 3, 4, 4, 4, 4, 5], L11188 = [0, 0, 1, 3, 4, 4, 4, 4, 7], = [0, 0, 1, 3, 4, 4, 4, 5, 6], L11196 = [0, 0, 1, 3, 4, 4, 4, 5, 8], L11199 = [0, 0, 1, 3, 4, 4, 4, 5, 12], = [0, 0, 1, 3, 4, 4, 4, 6, 7], L11207 = [0, 0, 1, 3, 4, 4, 4, 7, 8], L11209 = [0, 0, 1, 3, 4, 4, 4, 7, 12], = [0, 0, 1, 3, 4, 4, 5, 6, 6], L11226 = [0, 0, 1, 3, 4, 4, 5, 6, 8], L11229 = [0, 0, 1, 3, 4, 4, 5, 6, 12], = [0, 0, 1, 3, 4, 4, 5, 8, 8], L11237 = [0, 0, 1, 3, 4, 4, 5, 8, 12], L11240 = [0, 0, 1, 3, 4, 4, 5, 12, 12], = [0, 0, 1, 3, 4, 4, 6, 6, 7], L11248 = [0, 0, 1, 3, 4, 4, 6, 7, 8], L11250 = [0, 0, 1, 3, 4, 4, 6, 7, 12], = [0, 0, 1, 3, 4, 4, 7, 8, 8], L11267 = [0, 0, 1, 3, 4, 4, 7, 8, 12], L11270 = [0, 0, 1, 3, 4, 4, 7, 12, 12], = [0, 0, 1, 3, 4, 5, 6, 6, 6], L11302 = [0, 0, 1, 3, 4, 5, 6, 6, 8], L11305 = [0, 0, 1, 3, 4, 5, 6, 6, 12], = [0, 0, 1, 3, 4, 5, 6, 8, 8], L11313 = [0, 0, 1, 3, 4, 5, 6, 8, 12], L11316 = [0, 0, 1, 3, 4, 5, 6, 12, 12], = [0, 0, 1, 3, 4, 5, 7, 9, 11], L11325 = [0, 0, 1, 3, 4, 5, 8, 8, 8], L11328 = [0, 0, 1, 3, 4, 5, 8, 8, 12], = [0, 0, 1, 3, 4, 5, 8, 12, 12], L11334 = [0, 0, 1, 3, 4, 5, 12, 12, 12], L11336 = [0, 0, 1, 3, 4, 6, 6, 6, 7], = [0, 0, 1, 3, 4, 6, 6, 7, 8], L11344 = [0, 0, 1, 3, 4, 6, 6, 7, 12], L11359 = [0, 0, 1, 3, 4, 6, 7, 8, 8], = [0, 0, 1, 3, 4, 6, 7, 8, 12], L11364 = [0, 0, 1, 3, 4, 6, 7, 12, 12], L11394 = [0, 0, 1, 3, 4, 7, 8, 8, 8],
APPENDIX
269
Table 7. (continued) m = 9 q I indexes of I-isospectral families 24 {0} {61434, 61463}, {61436, 61469}, {61438, 61471}, {61442, 61480}, {61444, 61482}, (cont.) {61446, 61484}, {61455, 61496}, {61457, 61498}, {61459, 61500}, {62091, 62116}, {62118, 62216}, {62330, 62341}, {62343, 62382}, {62424, 62435}, {62437, 62518}, {62443, 62463}, {62448, 62474}, {62450, 62476}, {62465, 62560}, {62479, 62571}, {62635, 62646}, {62654, 62674}, {62659, 62685}, {62661, 62687}, {62676, 62843}, {62690, 62854}, {62696, 62730}, {62701, 62741}, {62703, 62743}, {62714, 62757}, {62716, 62759}, {62732, 62918}, {62746, 62929}, {62762, 62943}, {63039, 63043}, {63070, 63074}, {63076, 63084}, {63078, 63090}, {63080, 63092}, {63155, 63159}, {63161, 63169}, {63163, 63175}, {63165, 63177}, {63179, 63195}, {63181, 63201}, {63183, 63203}, {63189, 63211}, {63191, 63213}, {63340, 63344}, {63346, 63354}, {63348, 63360}, {63350, 63362}, {63364, 63380}, {63366, 63386}, {63368, 63388}, {63374, 63396}, {63376, 63398}, {63400, 63427}, {63402, 63433}, {63404, 63435}, {63410, 63443}, {63412, 63445}, {63421, 63455}, {63423, 63457}, {63686, 63690}, {63692, 63700}, {63694, 63706}, {63696, 63708}, {63710, 63726}, {63712, 63732}, {63714, 63734}, {63720, 63742}, {63722, 63744}, {63746, 63773}, {63748, 63779}, {63750, 63781}, {63756, 63789}, {63758, 63791}, {63767, 63801}, {63769, 63803}, {63805, 63845}, {63807, 63851}, {63809, 63853}, {63815, 63861}, {63817, 63863}, {63826, 63873}, {63828, 63875}, {63839, 63887}, {63841, 63889}, {64642, 64734}, {64858, 64897}, {64951, 65028}, {64963, 64986}, {64977, 65070}, {64989, 65079}, {65157, 65297}, {65169, 65192}, {65183, 65339}, {65195, 65348}, {65207, 65242}, {65218, 65255}, {65233, 65414}, {65245, 65423}, {65258, 65434}, {65540, 65552}, {65573, 65603}, {65577, 65588}, {65583, 65622}, {65591, 65628}, {65664, 65729}, {65668, 65679}, {65674, 65748}, {65682, 65754}, {65686, 65705}, {65693, 65714}, {65700, 65788}, {65708, 65794}, {65717, 65802}, {65860, 65980}, {65864, 65875}, {65870, 65999}, {65878, 66005}, {65882, 65901}, {65889, 65910}, {65896, 66039}, {65904, 66045}, {65913, 66053}, {65917, 65946}, {65924, 65955}, {65934, 65965}, {65941, 66109}, {65949, 66115}, {65958, 66123}, {65968, 66133}, {66221, 66418}, {66225, 66236}, {66231, 66437}, {66239, 66443}, {66243, 66262}, {66250, 66271}, {66257, 66477}, {66265, 66483}, {66274, 66491}, {66278, 66307}, {66285, 66316}, {66295, 66326}, {66302, 66547}, {66310, 66553}, {66319, 66561}, {66329, 66571}, {66333, 66373}, {66340, 66382}, {66350, 66392}, {66361, 66403}, {66368, 66657}, {66376, 66663}, {66385, 66671}, {66395, 66681}, {66406, 66693}, {66826, 66830}, {66857, 66861}, {66863, 66871}, {66867, 66876}, {66938, 66942}, {66944, 66952}, {66948, 66957}, {66959, 66973}, {66963, 66978}, {66969, 66984}, {67107, 67111}, {67113, 67121}, {67117, 67126}, {67128, 67142}, {67132, 67147}, {67138, 67153},
L11396 L11455 L11465 L11480 L11489 L11508 L11516 L11539 L11565
= [0, 0, 1, 3, 4, 7, 8, 8, 12], L11399 = [0, 0, 1, 3, 4, 7, 8, 12, 12], L11403 = [0, 0, 1, 3, 4, 7, 12, 12, 12], = [0, 0, 1, 3, 5, 6, 6, 6, 6], L11457 = [0, 0, 1, 3, 5, 6, 6, 6, 8], L11460 = [0, 0, 1, 3, 5, 6, 6, 6, 12], = [0, 0, 1, 3, 5, 6, 6, 8, 8], L11468 = [0, 0, 1, 3, 5, 6, 6, 8, 12], L11471 = [0, 0, 1, 3, 5, 6, 6, 12, 12], = [0, 0, 1, 3, 5, 6, 8, 8, 8], L11483 = [0, 0, 1, 3, 5, 6, 8, 8, 12], L11486 = [0, 0, 1, 3, 5, 6, 8, 12, 12], = [0, 0, 1, 3, 5, 6, 12, 12, 12], L11502 = [0, 0, 1, 3, 5, 8, 8, 8, 8], L11505 = [0, 0, 1, 3, 5, 8, 8, 8, 12], = [0, 0, 1, 3, 5, 8, 8, 12, 12], L11511 = [0, 0, 1, 3, 5, 8, 12, 12, 12], L11514 = [0, 0, 1, 3, 5, 12, 12, 12, 12], = [0, 0, 1, 3, 6, 6, 6, 6, 7], L11522 = [0, 0, 1, 3, 6, 6, 6, 7, 8], L11524 = [0, 0, 1, 3, 6, 6, 6, 7, 12], = [0, 0, 1, 3, 6, 6, 7, 8, 8], L11541 = [0, 0, 1, 3, 6, 6, 7, 8, 12], L11544 = [0, 0, 1, 3, 6, 6, 7, 12, 12], = [0, 0, 1, 3, 6, 6, 9, 11, 12], L11574 = [0, 0, 1, 3, 6, 7, 8, 8, 8], L11576 = [0, 0, 1, 3, 6, 7, 8, 8, 12],
270
EMILIO A. LAURET
Table 7. (continued) m = 9 q I indexes of I-isospectral families 24 {0} {67155, 67176}, {67159, 67181}, {67165, 67187}, {67172, 67194}, {67413, 67417}, (cont.) {67419, 67427}, {67423, 67432}, {67434, 67448}, {67438, 67453}, {67444, 67459}, {67461, 67482}, {67465, 67487}, {67471, 67493}, {67478, 67500}, {67502, 67531}, {67506, 67536}, {67512, 67542}, {67519, 67549}, {67527, 67557}, {67917, 67921}, {67923, 67931}, {67927, 67936}, {67938, 67952}, {67942, 67957}, {67948, 67963}, {67965, 67986}, {67969, 67991}, {67975, 67997}, {67982, 68004}, {68006, 68035}, {68010, 68040}, {68016, 68046}, {68023, 68053}, {68031, 68061}, {68063, 68101}, {68067, 68106}, {68073, 68112}, {68080, 68119}, {68088, 68127}, {68097, 68136}, {69014, 69087}, {69199, 69231}, {69278, 69335}, {69296, 69371}, {69303, 69375}, {69447, 69543}, {69465, 69579}, {69472, 69583}, {69497, 69644}, {69504, 69648}, {69511, 69653}, {69758, 69769}, {69788, 69812}, {69796, 69829}, {69801, 69832}, {69867, 69914}, {69875, 69931}, {69880, 69934}, {69893, 69967}, {69898, 69970}, {69903, 69974}, {70033, 70114}, {70041, 70131}, {70046, 70134}, {70059, 70167}, {70064, 70170}, {70069, 70174}, {70088, 70231}, {70093, 70234}, {70098, 70238}, {70103, 70243}, {70335, 70461}, {70343, 70478}, {70348, 70481}, {70361, 70514}, {70366, 70517}, {70371, 70521}, {70390, 70578}, {70395, 70581}, {70400, 70585}, {70405, 70590}, {70430, 70680}, {70435, 70683}, {70440, 70687}, {70445, 70692}, {70450, 70698}, {70831, 70833}, {70839, 70846}, {70841, 70852}, {70844, 70854}, {70869, 70887}, {70871, 70893}, {70874, 70895}, {70879, 70910}, {70882, 70912}, {70885, 70915}, {70945, 70981}, {70947, 70987}, {70950, 70989}, {70955, 71004}, {70958, 71006}, {70961, 71009}, {70970, 71039}, {70973, 71041}, {70976, 71044}, {70979, 71048}, {71100, 71161}, {71102, 71167}, {71105, 71169}, {71110, 71184}, {71113, 71186}, {71116, 71189}, {71125, 71219}, {71128, 71221}, {71131, 71224}, {71134, 71228}, {71147, 71280}, {71150, 71282}, {71153, 71285}, {71156, 71289}, {71159, 71294}, {71376, 71469}, {71378, 71475}, {71381, 71477}, {71386, 71492}, {71389, 71494}, {71392, 71497}, {71401, 71527}, {71404, 71529}, {71407, 71532}, {71410, 71536}, {71423, 71588}, {71426, 71590}, {71429, 71593}, {71432, 71597}, {71435, 71602}, {71452, 71684}, {71455, 71686}, {71458, 71689}, {71461, 71693}, {71464, 71698}, {71467, 71704}, {71825, 71957}, {71827, 71963}, {71830, 71965}, {71835, 71980}, {71838, 71982}, {71841, 71985}, {71850, 72015}, {71853, 72017}, {71856, 72020}, {71859, 72024}, {71872, 72076}, {71875, 72078}, {71878, 72081}, {71881, 72085}, {71884, 72090}, {71901, 72172}, {71904, 72174}, {71907, 72177}, {71910, 72181}, {71913, 72186}, {71916, 72192}, {71937, 72313}, {71940, 72315}, {71943, 72318}, {71946, 72322}, {71949, 72327}, {71952, 72333}, {71955, 72340} L11579 L11637 L11649 L13088 L13426 L17270 L19166 L20037 L20895 L21180 L21294
= [0, 0, 1, 3, 6, 7, 8, 12, 12], L11583 = [0, 0, 1, 3, 6, 7, 12, 12, 12], L11635 = [0, 0, 1, 3, 7, 8, 8, 8, 8], = [0, 0, 1, 3, 7, 8, 8, 8, 12], L11640 = [0, 0, 1, 3, 7, 8, 8, 12, 12], L11644 = [0, 0, 1, 3, 7, 8, 12, 12, 12], = [0, 0, 1, 3, 7, 12, 12, 12, 12], L12201 = [0, 0, 1, 5, 6, 6, 7, 11, 12], L12970 = [0, 0, 2, 3, 3, 4, 9, 9, 10], = [0, 0, 2, 3, 4, 6, 8, 9, 12], L13132 = [0, 0, 2, 3, 6, 6, 9, 10, 12], L13401 = [0, 0, 3, 4, 4, 6, 8, 9, 12], = [0, 0, 3, 4, 6, 6, 8, 9, 12], L13428 = [0, 0, 3, 4, 6, 6, 9, 12, 12], L13464 = [0, 0, 3, 6, 6, 8, 9, 12, 12], = [0, 1, 1, 1, 5, 7, 11, 11, 11], L19121 = [0, 1, 1, 2, 3, 5, 5, 10, 11], L19156 = [0, 1, 1, 2, 3, 5, 7, 7, 10], = [0, 1, 1, 2, 3, 5, 7, 9, 11], L19877 = [0, 1, 1, 2, 5, 5, 7, 7, 11], L19889 = [0, 1, 1, 2, 5, 5, 7, 11, 11], = [0, 1, 1, 2, 5, 7, 11, 11, 12], L20851 = [0, 1, 1, 3, 3, 5, 5, 9, 11], L20885 = [0, 1, 1, 3, 3, 5, 7, 7, 9], = [0, 1, 1, 3, 3, 5, 7, 9, 11], L20900 = [0, 1, 1, 3, 3, 5, 7, 11, 11], L21171 = [0, 1, 1, 3, 4, 4, 5, 5, 11], = [0, 1, 1, 3, 4, 4, 5, 7, 7], L21285 = [0, 1, 1, 3, 4, 5, 5, 6, 11], L21290 = [0, 1, 1, 3, 4, 5, 5, 7, 11], = [0, 1, 1, 3, 4, 5, 5, 8, 11], L21298 = [0, 1, 1, 3, 4, 5, 5, 11, 12], L21307 = [0, 1, 1, 3, 4, 5, 6, 7, 7],
APPENDIX
271
Table 7. (continued) m = 9 q 24 (cont.)
L21328 L21339 L21573 L21584 L21592 L21602 L21636 L21689 L21696 L21720 L23420 L24252 L24287 L24293 L24305 L24565 L24600
I {0, 1}
indexes of I-isospectral families {2380, 2389}, {7525, 7534}, {7639, 7661}, {7648, 7682}, {7652, 7685}, {19121, 19156}, {20851, 20885}, {20900, 21584}, {21171, 21180}, {21285, 21307}, {21294, 21328}, {21298, 21331}, {21568, 21615}, {21577, 21636}, {21581, 21639}, {21598, 21689}, {21602, 21692}, {21606, 21697}, {49117, 49152}, {49418, 49499}, {49451, 49553}, {49464, 49561}, {53093, 53127}, {53142, 54436}, {53380, 53445}, {53404, 53498}, {53411, 53503}, {53460, 55029}, {53518, 55054}, {53537, 55058}, {54023, 54032}, {54137, 54159}, {54146, 54180}, {54150, 54183}, {54420, 54467}, {54429, 54488}, {54433, 54491}, {54450, 54541}, {54454, 54544}, {54458, 54549}, {55013, 55099}, {55022, 55120}, {55026, 55123}, {55043, 55173}, {55047, 55176}, {55051, 55181}, {55078, 55280}, {55082, 55283}, {55086, 55288}, {55090, 55295} {4} {12970, 32749}, {25577, 63442}, {32699, 32743}, {32820, 76755}, {47406, 63408}, {47657, 47813}, {63200, 63432}, {75093, 75604}, {76645, 76749} {4, 5} {11565, 30167}, {13088, 32951}, {13132, 33015}, {13401, 33535}, {13426, 33526}, {13428, 13464}, {26493, 29044}, {26828, 29838}, {27091, 30165}, {29800, 30147}, {32367, 32950}, {32894, 32947}, {32938, 33011}, {33481, 33524}, {33512, 33561} {6} {21355, 29730}, {21592, 21721} {0, 5, 6} {29563, 29631}, {61403, 61428}, {62648, 62801} {7} {24787, 25935}, {63577, 67767} {6, 7} {10491, 27988}, {17270, 44608}, {20037, 23420}, {20895, 53529}, {21591, 55071}, {21720, 55345}, {27633, 27980}, {30883, 73357}, {40403, 44604}, {43567, 44575}, {47815, 51506}, {50666, 57344}, {51286, 58262}, {53137, 53513}, {54443, 55066}, {54572, 55318}, {72978, 73355}
= [0, 1, 1, 3, 4, 5, 7, 7, 8], L21330 = [0, 1, 1, 3, 4, 5, 7, 7, 11], L21331 = [0, 1, 1, 3, 4, 5, 7, 7, 12], = [0, 1, 1, 3, 4, 5, 7, 9, 11], L21355 = [0, 1, 1, 3, 4, 5, 8, 9, 12], L21568 = [0, 1, 1, 3, 5, 5, 6, 6, 11], = [0, 1, 1, 3, 5, 5, 6, 7, 11], L21577 = [0, 1, 1, 3, 5, 5, 6, 8, 11], L21581 = [0, 1, 1, 3, 5, 5, 6, 11, 12], = [0, 1, 1, 3, 5, 5, 7, 7, 9], L21589 = [0, 1, 1, 3, 5, 5, 7, 8, 11], L21591 = [0, 1, 1, 3, 5, 5, 7, 9, 11], = [0, 1, 1, 3, 5, 5, 7, 9, 12], L21594 = [0, 1, 1, 3, 5, 5, 7, 11, 12], L21598 = [0, 1, 1, 3, 5, 5, 8, 8, 11], = [0, 1, 1, 3, 5, 5, 8, 11, 12], L21606 = [0, 1, 1, 3, 5, 5, 11, 12, 12], L21615 = [0, 1, 1, 3, 5, 6, 6, 7, 7], = [0, 1, 1, 3, 5, 6, 7, 7, 8], L21638 = [0, 1, 1, 3, 5, 6, 7, 7, 11], L21639 = [0, 1, 1, 3, 5, 6, 7, 7, 12], = [0, 1, 1, 3, 5, 7, 7, 8, 8], L21691 = [0, 1, 1, 3, 5, 7, 7, 8, 11], L21692 = [0, 1, 1, 3, 5, 7, 7, 8, 12], = [0, 1, 1, 3, 5, 7, 7, 11, 12], L21697 = [0, 1, 1, 3, 5, 7, 7, 12, 12], L21718 = [0, 1, 1, 3, 5, 7, 9, 10, 11], = [0, 1, 1, 3, 5, 7, 9, 11, 11], L21721 = [0, 1, 1, 3, 5, 7, 9, 11, 12], L23151 = [0, 1, 1, 5, 5, 7, 7, 11, 11], = [0, 1, 1, 5, 7, 10, 11, 11, 12], L24160 = [0, 1, 2, 2, 2, 2, 2, 5, 7], L24164 = [0, 1, 2, 2, 2, 2, 2, 5, 11], = [0, 1, 2, 2, 2, 2, 4, 5, 7], L24256 = [0, 1, 2, 2, 2, 2, 4, 5, 11], L24283 = [0, 1, 2, 2, 2, 2, 5, 6, 7], = [0, 1, 2, 2, 2, 2, 5, 6, 11], L24289 = [0, 1, 2, 2, 2, 2, 5, 7, 8], L24291 = [0, 1, 2, 2, 2, 2, 5, 7, 10], = [0, 1, 2, 2, 2, 2, 5, 7, 12], L24297 = [0, 1, 2, 2, 2, 2, 5, 8, 11], L24303 = [0, 1, 2, 2, 2, 2, 5, 10, 11], = [0, 1, 2, 2, 2, 2, 5, 11, 12], L24469 = [0, 1, 2, 2, 2, 3, 5, 7, 9], L24480 = [0, 1, 2, 2, 2, 3, 5, 9, 11], = [0, 1, 2, 2, 2, 4, 4, 5, 7], L24569 = [0, 1, 2, 2, 2, 4, 4, 5, 11], L24596 = [0, 1, 2, 2, 2, 4, 5, 6, 7], = [0, 1, 2, 2, 2, 4, 5, 6, 11], L24602 = [0, 1, 2, 2, 2, 4, 5, 7, 8], L24604 = [0, 1, 2, 2, 2, 4, 5, 7, 10],
272
EMILIO A. LAURET
Table 7. (continued) m = 9 q 24 (cont.)
L24606 L24618 L24687 L24695 L24705 L24713 L24721 L24738 L24787 L25122 L25214 L25227 L25242 L25255 L25339 L25420 L25453 L25461 L25532 L25540 L25552 L25558 L25568 L25578 L25590 L25721 L25727 L25739 L25745 L25757
I {2, 3, 6, 7}
indexes of I-isospectral families {12201, 31264}, {23151, 58128}, {27626, 67468, 67516}, {29169, 70423}, {30885, 31262}, {32743, 76645}, {32779, 33338, 33384}, {57103, 58125}, {63409, 67162, 67509}, {70081, 70417}, {76568, 76639}, {77267, 77302} {2, 3, 4, 5, 6, 7} {27626, 67516}, {33338, 33384}, {67162, 67509} {8} {32371, 76064}, {60967, 62894}, {74986, 75371} {6, 7, 8} {11321, 30034}, {19166, 21718}, {21339, 55319}, {25228, 26994}, {25636, 27756}, {26755, 66349}, {28976, 70419}, {29556, 71444}, {29711, 71893}, {29729, 71925}, {29733, 71929}, {39418, 42334}, {41370, 53528}, {42168, 55057}, {46925, 49585, 55340}, {48697, 53526}, {49162, 54570}, {49509, 55202}, {49572, 55316}, {49582, 55335}, {49587, 55342}, {49588, 55343}, {52691, 53523}, {60875, 62713}, {62093, 65219}, {62449, 65931}, {62660, 66292}, {62702, 66347}, {62715, 66358} {0, 5, 6, 7, 8} {53394, 53502}
= [0, 1, 2, 2, 2, 4, 5, 7, 12], L24610 = [0, 1, 2, 2, 2, 4, 5, 8, 11], L24616 = [0, 1, 2, 2, 2, 4, 5, 10, 11], = [0, 1, 2, 2, 2, 4, 5, 11, 12], L24681 = [0, 1, 2, 2, 2, 5, 6, 6, 7], L24685 = [0, 1, 2, 2, 2, 5, 6, 6, 11], = [0, 1, 2, 2, 2, 5, 6, 7, 8], L24689 = [0, 1, 2, 2, 2, 5, 6, 7, 10], L24691 = [0, 1, 2, 2, 2, 5, 6, 7, 12], = [0, 1, 2, 2, 2, 5, 6, 8, 11], L24701 = [0, 1, 2, 2, 2, 5, 6, 10, 11], L24703 = [0, 1, 2, 2, 2, 5, 6, 11, 12], = [0, 1, 2, 2, 2, 5, 7, 8, 8], L24707 = [0, 1, 2, 2, 2, 5, 7, 8, 10], L24709 = [0, 1, 2, 2, 2, 5, 7, 8, 12], = [0, 1, 2, 2, 2, 5, 7, 10, 10], L24715 = [0, 1, 2, 2, 2, 5, 7, 10, 12], L24717 = [0, 1, 2, 2, 2, 5, 7, 12, 12], = [0, 1, 2, 2, 2, 5, 8, 8, 11], L24727 = [0, 1, 2, 2, 2, 5, 8, 10, 11], L24729 = [0, 1, 2, 2, 2, 5, 8, 11, 12], = [0, 1, 2, 2, 2, 5, 10, 10, 11], L24740 = [0, 1, 2, 2, 2, 5, 10, 11, 12], L24742 = [0, 1, 2, 2, 2, 5, 11, 12, 12], = [0, 1, 2, 2, 2, 6, 8, 10, 11], L25109 = [0, 1, 2, 2, 3, 4, 5, 7, 9], L25120 = [0, 1, 2, 2, 3, 4, 5, 9, 11], = [0, 1, 2, 2, 3, 4, 5, 10, 10], L25161 = [0, 1, 2, 2, 3, 4, 7, 10, 10], L25203 = [0, 1, 2, 2, 3, 5, 6, 7, 9], = [0, 1, 2, 2, 3, 5, 6, 9, 11], L25216 = [0, 1, 2, 2, 3, 5, 6, 10, 10], L25222 = [0, 1, 2, 2, 3, 5, 7, 8, 9], = [0, 1, 2, 2, 3, 5, 7, 9, 10], L25228 = [0, 1, 2, 2, 3, 5, 7, 9, 11], L25229 = [0, 1, 2, 2, 3, 5, 7, 9, 12], = [0, 1, 2, 2, 3, 5, 8, 9, 11], L25244 = [0, 1, 2, 2, 3, 5, 8, 10, 10], L25253 = [0, 1, 2, 2, 3, 5, 9, 10, 11], = [0, 1, 2, 2, 3, 5, 9, 11, 12], L25258 = [0, 1, 2, 2, 3, 5, 10, 10, 12], L25297 = [0, 1, 2, 2, 3, 6, 7, 10, 10], = [0, 1, 2, 2, 3, 7, 8, 10, 10], L25350 = [0, 1, 2, 2, 3, 7, 10, 10, 12], L25416 = [0, 1, 2, 2, 4, 4, 4, 5, 7], = [0, 1, 2, 2, 4, 4, 4, 5, 11], L25447 = [0, 1, 2, 2, 4, 4, 5, 6, 7], L25451 = [0, 1, 2, 2, 4, 4, 5, 6, 11], = [0, 1, 2, 2, 4, 4, 5, 7, 8], L25455 = [0, 1, 2, 2, 4, 4, 5, 7, 10], L25457 = [0, 1, 2, 2, 4, 4, 5, 7, 12], = [0, 1, 2, 2, 4, 4, 5, 8, 11], L25467 = [0, 1, 2, 2, 4, 4, 5, 10, 11], L25469 = [0, 1, 2, 2, 4, 4, 5, 11, 12], = [0, 1, 2, 2, 4, 5, 6, 6, 7], L25536 = [0, 1, 2, 2, 4, 5, 6, 6, 11], L25538 = [0, 1, 2, 2, 4, 5, 6, 7, 8], = [0, 1, 2, 2, 4, 5, 6, 7, 10], L25542 = [0, 1, 2, 2, 4, 5, 6, 7, 12], L25546 = [0, 1, 2, 2, 4, 5, 6, 8, 11], = [0, 1, 2, 2, 4, 5, 6, 10, 11], L25554 = [0, 1, 2, 2, 4, 5, 6, 11, 12], L25556 = [0, 1, 2, 2, 4, 5, 7, 8, 8], = [0, 1, 2, 2, 4, 5, 7, 8, 10], L25560 = [0, 1, 2, 2, 4, 5, 7, 8, 12], L25566 = [0, 1, 2, 2, 4, 5, 7, 10, 12], = [0, 1, 2, 2, 4, 5, 7, 12, 12], L25572 = [0, 1, 2, 2, 4, 5, 8, 8, 11], L25577 = [0, 1, 2, 2, 4, 5, 8, 10, 10], = [0, 1, 2, 2, 4, 5, 8, 10, 11], L25580 = [0, 1, 2, 2, 4, 5, 8, 11, 12], L25588 = [0, 1, 2, 2, 4, 5, 10, 11, 12], = [0, 1, 2, 2, 4, 5, 11, 12, 12], L25636 = [0, 1, 2, 2, 4, 6, 8, 10, 12], L25717 = [0, 1, 2, 2, 5, 6, 6, 6, 7], = [0, 1, 2, 2, 5, 6, 6, 6, 11], L25723 = [0, 1, 2, 2, 5, 6, 6, 7, 8], L25725 = [0, 1, 2, 2, 5, 6, 6, 7, 10], = [0, 1, 2, 2, 5, 6, 6, 7, 12], L25731 = [0, 1, 2, 2, 5, 6, 6, 8, 11], L25737 = [0, 1, 2, 2, 5, 6, 6, 10, 11], = [0, 1, 2, 2, 5, 6, 6, 11, 12], L25741 = [0, 1, 2, 2, 5, 6, 7, 8, 8], L25743 = [0, 1, 2, 2, 5, 6, 7, 8, 10], = [0, 1, 2, 2, 5, 6, 7, 8, 12], L25751 = [0, 1, 2, 2, 5, 6, 7, 10, 12], L25753 = [0, 1, 2, 2, 5, 6, 7, 12, 12], = [0, 1, 2, 2, 5, 6, 8, 8, 11], L25763 = [0, 1, 2, 2, 5, 6, 8, 10, 11], L25765 = [0, 1, 2, 2, 5, 6, 8, 11, 12],
APPENDIX
L25773 L25779 L25789 L25804 L25820 L25834 L26348 L26428 L26479 L26530 L26636 L26651 L26685 L26731 L26745 L26756 L26771 L26792 L26828 L26865 L26933 L26945 L26964 L26976 L26994 L27009 L27021 L27043 L27091 L27116 L27186 L27294 L27327 L27340 L27408 L27421 L27433 L27448 L27577 L27590 L27602 L27617 L27626 L27636 L27651 L27877 L27887 L27898 L27912
273
= [0, 1, 2, 2, 5, 6, 10, 11, 12], L25775 = [0, 1, 2, 2, 5, 6, 11, 12, 12], L25777 = [0, 1, 2, 2, 5, 7, 8, 8, 8], = [0, 1, 2, 2, 5, 7, 8, 8, 10], L25781 = [0, 1, 2, 2, 5, 7, 8, 8, 12], L25787 = [0, 1, 2, 2, 5, 7, 8, 10, 12], = [0, 1, 2, 2, 5, 7, 8, 12, 12], L25798 = [0, 1, 2, 2, 5, 7, 10, 12, 12], L25800 = [0, 1, 2, 2, 5, 7, 12, 12, 12], = [0, 1, 2, 2, 5, 8, 8, 8, 11], L25810 = [0, 1, 2, 2, 5, 8, 8, 10, 11], L25812 = [0, 1, 2, 2, 5, 8, 8, 11, 12], = [0, 1, 2, 2, 5, 8, 10, 11, 12], L25822 = [0, 1, 2, 2, 5, 8, 11, 12, 12], L25832 = [0, 1, 2, 2, 5, 10, 11, 12, 12], = [0, 1, 2, 2, 5, 11, 12, 12, 12], L25935 = [0, 1, 2, 2, 6, 8, 10, 10, 11], L26309 = [0, 1, 2, 3, 3, 4, 5, 9, 10], = [0, 1, 2, 3, 3, 4, 7, 9, 10], L26402 = [0, 1, 2, 3, 3, 5, 6, 9, 10], L26414 = [0, 1, 2, 3, 3, 5, 7, 9, 9], = [0, 1, 2, 3, 3, 5, 8, 9, 10], L26437 = [0, 1, 2, 3, 3, 5, 9, 9, 11], L26440 = [0, 1, 2, 3, 3, 5, 9, 10, 12], = [0, 1, 2, 3, 3, 6, 7, 9, 10], L26493 = [0, 1, 2, 3, 3, 6, 8, 9, 12], L26521 = [0, 1, 2, 3, 3, 7, 8, 9, 10], = [0, 1, 2, 3, 3, 7, 9, 10, 12], L26603 = [0, 1, 2, 3, 4, 4, 4, 5, 10], L26615 = [0, 1, 2, 3, 4, 4, 4, 7, 10], = [0, 1, 2, 3, 4, 4, 5, 6, 10], L26640 = [0, 1, 2, 3, 4, 4, 5, 7, 9], L26646 = [0, 1, 2, 3, 4, 4, 5, 8, 10], = [0, 1, 2, 3, 4, 4, 5, 9, 11], L26654 = [0, 1, 2, 3, 4, 4, 5, 10, 12], L26666 = [0, 1, 2, 3, 4, 4, 6, 7, 10], = [0, 1, 2, 3, 4, 4, 7, 8, 10], L26691 = [0, 1, 2, 3, 4, 4, 7, 10, 12], L26727 = [0, 1, 2, 3, 4, 5, 6, 6, 10], = [0, 1, 2, 3, 4, 5, 6, 7, 9], L26737 = [0, 1, 2, 3, 4, 5, 6, 8, 10], L26742 = [0, 1, 2, 3, 4, 5, 6, 9, 11], = [0, 1, 2, 3, 4, 5, 6, 10, 12], L26749 = [0, 1, 2, 3, 4, 5, 7, 8, 9], L26755 = [0, 1, 2, 3, 4, 5, 7, 9, 11], = [0, 1, 2, 3, 4, 5, 7, 9, 12], L26763 = [0, 1, 2, 3, 4, 5, 8, 8, 10], L26768 = [0, 1, 2, 3, 4, 5, 8, 9, 11], = [0, 1, 2, 3, 4, 5, 8, 10, 12], L26777 = [0, 1, 2, 3, 4, 5, 9, 11, 12], L26780 = [0, 1, 2, 3, 4, 5, 10, 12, 12], = [0, 1, 2, 3, 4, 6, 6, 7, 10], L26811 = [0, 1, 2, 3, 4, 6, 7, 8, 10], L26817 = [0, 1, 2, 3, 4, 6, 7, 10, 12], = [0, 1, 2, 3, 4, 6, 8, 9, 12], L26851 = [0, 1, 2, 3, 4, 7, 8, 8, 10], L26857 = [0, 1, 2, 3, 4, 7, 8, 10, 12], = [0, 1, 2, 3, 4, 7, 10, 12, 12], L26923 = [0, 1, 2, 3, 5, 6, 6, 6, 10], L26927 = [0, 1, 2, 3, 5, 6, 6, 7, 9], = [0, 1, 2, 3, 5, 6, 6, 8, 10], L26938 = [0, 1, 2, 3, 5, 6, 6, 9, 11], L26941 = [0, 1, 2, 3, 5, 6, 6, 10, 12], = [0, 1, 2, 3, 5, 6, 7, 8, 9], L26952 = [0, 1, 2, 3, 5, 6, 7, 9, 12], L26959 = [0, 1, 2, 3, 5, 6, 8, 8, 10], = [0, 1, 2, 3, 5, 6, 8, 9, 11], L26967 = [0, 1, 2, 3, 5, 6, 8, 10, 12], L26973 = [0, 1, 2, 3, 5, 6, 9, 11, 12], = [0, 1, 2, 3, 5, 6, 10, 12, 12], L26980 = [0, 1, 2, 3, 5, 7, 8, 8, 9], L26987 = [0, 1, 2, 3, 5, 7, 8, 9, 12], = [0, 1, 2, 3, 5, 7, 9, 10, 11], L26997 = [0, 1, 2, 3, 5, 7, 9, 12, 12], L27004 = [0, 1, 2, 3, 5, 8, 8, 8, 10], = [0, 1, 2, 3, 5, 8, 8, 9, 11], L27012 = [0, 1, 2, 3, 5, 8, 8, 10, 12], L27018 = [0, 1, 2, 3, 5, 8, 9, 11, 12], = [0, 1, 2, 3, 5, 8, 10, 12, 12], L27028 = [0, 1, 2, 3, 5, 9, 11, 12, 12], L27031 = [0, 1, 2, 3, 5, 10, 12, 12, 12], = [0, 1, 2, 3, 6, 6, 6, 7, 10], L27062 = [0, 1, 2, 3, 6, 6, 7, 8, 10], L27068 = [0, 1, 2, 3, 6, 6, 7, 10, 12], = [0, 1, 2, 3, 6, 6, 9, 11, 12], L27102 = [0, 1, 2, 3, 6, 7, 8, 8, 10], L27108 = [0, 1, 2, 3, 6, 7, 8, 10, 12], = [0, 1, 2, 3, 6, 7, 10, 12, 12], L27172 = [0, 1, 2, 3, 7, 8, 8, 8, 10], L27178 = [0, 1, 2, 3, 7, 8, 8, 10, 12], = [0, 1, 2, 3, 7, 8, 10, 12, 12], L27196 = [0, 1, 2, 3, 7, 10, 12, 12, 12], L27290 = [0, 1, 2, 4, 4, 4, 4, 5, 7], = [0, 1, 2, 4, 4, 4, 4, 5, 11], L27321 = [0, 1, 2, 4, 4, 4, 5, 6, 7], L27325 = [0, 1, 2, 4, 4, 4, 5, 6, 11], = [0, 1, 2, 4, 4, 4, 5, 7, 8], L27331 = [0, 1, 2, 4, 4, 4, 5, 7, 12], L27335 = [0, 1, 2, 4, 4, 4, 5, 8, 11], = [0, 1, 2, 4, 4, 4, 5, 11, 12], L27402 = [0, 1, 2, 4, 4, 5, 6, 6, 7], L27406 = [0, 1, 2, 4, 4, 5, 6, 6, 11], = [0, 1, 2, 4, 4, 5, 6, 7, 8], L27412 = [0, 1, 2, 4, 4, 5, 6, 7, 12], L27416 = [0, 1, 2, 4, 4, 5, 6, 8, 11], = [0, 1, 2, 4, 4, 5, 6, 11, 12], L27423 = [0, 1, 2, 4, 4, 5, 7, 8, 8], L27427 = [0, 1, 2, 4, 4, 5, 7, 8, 12], = [0, 1, 2, 4, 4, 5, 7, 12, 12], L27437 = [0, 1, 2, 4, 4, 5, 8, 8, 11], L27442 = [0, 1, 2, 4, 4, 5, 8, 11, 12], = [0, 1, 2, 4, 4, 5, 11, 12, 12], L27571 = [0, 1, 2, 4, 5, 6, 6, 6, 7], L27575 = [0, 1, 2, 4, 5, 6, 6, 6, 11], = [0, 1, 2, 4, 5, 6, 6, 7, 8], L27581 = [0, 1, 2, 4, 5, 6, 6, 7, 12], L27585 = [0, 1, 2, 4, 5, 6, 6, 8, 11], = [0, 1, 2, 4, 5, 6, 6, 11, 12], L27592 = [0, 1, 2, 4, 5, 6, 7, 8, 8], L27596 = [0, 1, 2, 4, 5, 6, 7, 8, 12], = [0, 1, 2, 4, 5, 6, 7, 12, 12], L27606 = [0, 1, 2, 4, 5, 6, 8, 8, 11], L27611 = [0, 1, 2, 4, 5, 6, 8, 11, 12], = [0, 1, 2, 4, 5, 6, 11, 12, 12], L27619 = [0, 1, 2, 4, 5, 7, 8, 8, 8], L27623 = [0, 1, 2, 4, 5, 7, 8, 8, 12], = [0, 1, 2, 4, 5, 7, 8, 10, 11], L27629 = [0, 1, 2, 4, 5, 7, 8, 12, 12], L27633 = [0, 1, 2, 4, 5, 7, 10, 11, 12], = [0, 1, 2, 4, 5, 7, 12, 12, 12], L27640 = [0, 1, 2, 4, 5, 8, 8, 8, 11], L27645 = [0, 1, 2, 4, 5, 8, 8, 11, 12], = [0, 1, 2, 4, 5, 8, 11, 12, 12], L27658 = [0, 1, 2, 4, 5, 11, 12, 12, 12], L27756 = [0, 1, 2, 4, 6, 8, 10, 10, 12], = [0, 1, 2, 5, 6, 6, 6, 6, 7], L27881 = [0, 1, 2, 5, 6, 6, 6, 6, 11], L27883 = [0, 1, 2, 5, 6, 6, 6, 7, 8], = [0, 1, 2, 5, 6, 6, 6, 7, 12], L27891 = [0, 1, 2, 5, 6, 6, 6, 8, 11], L27896 = [0, 1, 2, 5, 6, 6, 6, 11, 12], = [0, 1, 2, 5, 6, 6, 7, 8, 8], L27902 = [0, 1, 2, 5, 6, 6, 7, 8, 12], L27908 = [0, 1, 2, 5, 6, 6, 7, 12, 12], = [0, 1, 2, 5, 6, 6, 8, 8, 11], L27917 = [0, 1, 2, 5, 6, 6, 8, 11, 12], L27923 = [0, 1, 2, 5, 6, 6, 11, 12, 12],
274
L27925 L27942 L27957 L27970 L27983 L27995 L28013 L28632 L28704 L28776 L28876 L28900 L28955 L28976 L28991 L29022 L29058 L29129 L29152 L29176 L29191 L29222 L29262 L29326 L29423 L29434 L29444 L29464 L29475 L29485 L29505 L29540 L29551 L29563 L29571 L29594 L29629 L29638 L29695 L29706 L29718 L29729 L29737 L29746 L29757 L29776 L29809 L29818 L29872
EMILIO A. LAURET
= [0, 1, 2, 5, 6, 7, 8, 8, 8], L27929 = [0, 1, 2, 5, 6, 7, 8, 8, 12], L27935 = [0, 1, 2, 5, 6, 7, 8, 12, 12], = [0, 1, 2, 5, 6, 7, 12, 12, 12], L27946 = [0, 1, 2, 5, 6, 8, 8, 8, 11], L27951 = [0, 1, 2, 5, 6, 8, 8, 11, 12], = [0, 1, 2, 5, 6, 8, 11, 12, 12], L27964 = [0, 1, 2, 5, 6, 11, 12, 12, 12], L27966 = [0, 1, 2, 5, 7, 8, 8, 8, 8], = [0, 1, 2, 5, 7, 8, 8, 8, 12], L27976 = [0, 1, 2, 5, 7, 8, 8, 12, 12], L27980 = [0, 1, 2, 5, 7, 8, 10, 11, 12], = [0, 1, 2, 5, 7, 8, 12, 12, 12], L27988 = [0, 1, 2, 5, 7, 10, 11, 12, 12], L27991 = [0, 1, 2, 5, 7, 12, 12, 12, 12], = [0, 1, 2, 5, 8, 8, 8, 8, 11], L28000 = [0, 1, 2, 5, 8, 8, 8, 11, 12], L28006 = [0, 1, 2, 5, 8, 8, 11, 12, 12], = [0, 1, 2, 5, 8, 11, 12, 12, 12], L28021 = [0, 1, 2, 5, 11, 12, 12, 12, 12], L28600 = [0, 1, 3, 3, 3, 4, 5, 9, 9], = [0, 1, 3, 3, 3, 4, 7, 9, 9], L28679 = [0, 1, 3, 3, 3, 5, 6, 9, 9], L28697 = [0, 1, 3, 3, 3, 5, 8, 9, 9], = [0, 1, 3, 3, 3, 5, 9, 9, 12], L28736 = [0, 1, 3, 3, 3, 6, 7, 9, 9], L28772 = [0, 1, 3, 3, 3, 7, 8, 9, 9], = [0, 1, 3, 3, 3, 7, 9, 9, 12], L28846 = [0, 1, 3, 3, 4, 4, 4, 5, 9], L28857 = [0, 1, 3, 3, 4, 4, 4, 7, 9], = [0, 1, 3, 3, 4, 4, 5, 6, 9], L28884 = [0, 1, 3, 3, 4, 4, 5, 8, 9], L28889 = [0, 1, 3, 3, 4, 4, 5, 9, 12], = [0, 1, 3, 3, 4, 4, 6, 7, 9], L28917 = [0, 1, 3, 3, 4, 4, 7, 8, 9], L28920 = [0, 1, 3, 3, 4, 4, 7, 9, 12], = [0, 1, 3, 3, 4, 5, 6, 6, 9], L28963 = [0, 1, 3, 3, 4, 5, 6, 8, 9], L28968 = [0, 1, 3, 3, 4, 5, 6, 9, 12], = [0, 1, 3, 3, 4, 5, 7, 9, 11], L28981 = [0, 1, 3, 3, 4, 5, 8, 8, 9], L28986 = [0, 1, 3, 3, 4, 5, 8, 9, 12], = [0, 1, 3, 3, 4, 5, 9, 12, 12], L29002 = [0, 1, 3, 3, 4, 6, 6, 7, 9], L29019 = [0, 1, 3, 3, 4, 6, 7, 8, 9], = [0, 1, 3, 3, 4, 6, 7, 9, 12], L29044 = [0, 1, 3, 3, 4, 6, 9, 10, 12], L29055 = [0, 1, 3, 3, 4, 7, 8, 8, 9], = [0, 1, 3, 3, 4, 7, 8, 9, 12], L29062 = [0, 1, 3, 3, 4, 7, 9, 12, 12], L29121 = [0, 1, 3, 3, 5, 6, 6, 6, 9], = [0, 1, 3, 3, 5, 6, 6, 8, 9], L29134 = [0, 1, 3, 3, 5, 6, 6, 9, 12], L29147 = [0, 1, 3, 3, 5, 6, 8, 8, 9], = [0, 1, 3, 3, 5, 6, 8, 9, 12], L29157 = [0, 1, 3, 3, 5, 6, 9, 12, 12], L29169 = [0, 1, 3, 3, 5, 7, 9, 9, 11], = [0, 1, 3, 3, 5, 8, 8, 8, 9], L29181 = [0, 1, 3, 3, 5, 8, 8, 9, 12], L29186 = [0, 1, 3, 3, 5, 8, 9, 12, 12], = [0, 1, 3, 3, 5, 9, 12, 12, 12], L29202 = [0, 1, 3, 3, 6, 6, 6, 7, 9], L29219 = [0, 1, 3, 3, 6, 6, 7, 8, 9], = [0, 1, 3, 3, 6, 6, 7, 9, 12], L29255 = [0, 1, 3, 3, 6, 7, 8, 8, 9], L29258 = [0, 1, 3, 3, 6, 7, 8, 9, 12], = [0, 1, 3, 3, 6, 7, 9, 12, 12], L29319 = [0, 1, 3, 3, 7, 8, 8, 8, 9], L29322 = [0, 1, 3, 3, 7, 8, 8, 9, 12], = [0, 1, 3, 3, 7, 8, 9, 12, 12], L29331 = [0, 1, 3, 3, 7, 9, 12, 12, 12], L29421 = [0, 1, 3, 4, 4, 4, 4, 4, 5], = [0, 1, 3, 4, 4, 4, 4, 4, 7], L29429 = [0, 1, 3, 4, 4, 4, 4, 5, 6], L29431 = [0, 1, 3, 4, 4, 4, 4, 5, 8], = [0, 1, 3, 4, 4, 4, 4, 5, 12], L29436 = [0, 1, 3, 4, 4, 4, 4, 6, 7], L29442 = [0, 1, 3, 4, 4, 4, 4, 7, 8], = [0, 1, 3, 4, 4, 4, 4, 7, 12], L29459 = [0, 1, 3, 4, 4, 4, 5, 6, 6], L29461 = [0, 1, 3, 4, 4, 4, 5, 6, 8], = [0, 1, 3, 4, 4, 4, 5, 6, 12], L29469 = [0, 1, 3, 4, 4, 4, 5, 8, 8], L29472 = [0, 1, 3, 4, 4, 4, 5, 8, 12], = [0, 1, 3, 4, 4, 4, 5, 12, 12], L29477 = [0, 1, 3, 4, 4, 4, 6, 6, 7], L29483 = [0, 1, 3, 4, 4, 4, 6, 7, 8], = [0, 1, 3, 4, 4, 4, 6, 7, 12], L29500 = [0, 1, 3, 4, 4, 4, 7, 8, 8], L29502 = [0, 1, 3, 4, 4, 4, 7, 8, 12], = [0, 1, 3, 4, 4, 4, 7, 12, 12], L29535 = [0, 1, 3, 4, 4, 5, 6, 6, 6], L29537 = [0, 1, 3, 4, 4, 5, 6, 6, 8], = [0, 1, 3, 4, 4, 5, 6, 6, 12], L29545 = [0, 1, 3, 4, 4, 5, 6, 8, 8], L29548 = [0, 1, 3, 4, 4, 5, 6, 8, 12], = [0, 1, 3, 4, 4, 5, 6, 12, 12], L29556 = [0, 1, 3, 4, 4, 5, 7, 9, 11], L29560 = [0, 1, 3, 4, 4, 5, 8, 8, 8], = [0, 1, 3, 4, 4, 5, 8, 8, 12], L29566 = [0, 1, 3, 4, 4, 5, 8, 12, 12], L29569 = [0, 1, 3, 4, 4, 5, 12, 12, 12], = [0, 1, 3, 4, 4, 6, 6, 6, 7], L29577 = [0, 1, 3, 4, 4, 6, 6, 7, 8], L29579 = [0, 1, 3, 4, 4, 6, 6, 7, 12], = [0, 1, 3, 4, 4, 6, 7, 8, 8], L29596 = [0, 1, 3, 4, 4, 6, 7, 8, 12], L29599 = [0, 1, 3, 4, 4, 6, 7, 12, 12], = [0, 1, 3, 4, 4, 7, 8, 8, 8], L29631 = [0, 1, 3, 4, 4, 7, 8, 8, 12], L29634 = [0, 1, 3, 4, 4, 7, 8, 12, 12], = [0, 1, 3, 4, 4, 7, 12, 12, 12], L29690 = [0, 1, 3, 4, 5, 6, 6, 6, 6], L29692 = [0, 1, 3, 4, 5, 6, 6, 6, 8], = [0, 1, 3, 4, 5, 6, 6, 6, 12], L29700 = [0, 1, 3, 4, 5, 6, 6, 8, 8], L29703 = [0, 1, 3, 4, 5, 6, 6, 8, 12], = [0, 1, 3, 4, 5, 6, 6, 12, 12], L29711 = [0, 1, 3, 4, 5, 6, 7, 9, 11], L29715 = [0, 1, 3, 4, 5, 6, 8, 8, 8], = [0, 1, 3, 4, 5, 6, 8, 8, 12], L29721 = [0, 1, 3, 4, 5, 6, 8, 12, 12], L29724 = [0, 1, 3, 4, 5, 6, 12, 12, 12], = [0, 1, 3, 4, 5, 7, 8, 9, 11], L29730 = [0, 1, 3, 4, 5, 7, 8, 9, 12], L29733 = [0, 1, 3, 4, 5, 7, 9, 11, 12], = [0, 1, 3, 4, 5, 8, 8, 8, 8], L29740 = [0, 1, 3, 4, 5, 8, 8, 8, 12], L29743 = [0, 1, 3, 4, 5, 8, 8, 12, 12], = [0, 1, 3, 4, 5, 8, 12, 12, 12], L29749 = [0, 1, 3, 4, 5, 12, 12, 12, 12], L29751 = [0, 1, 3, 4, 6, 6, 6, 6, 7], = [0, 1, 3, 4, 6, 6, 6, 7, 8], L29759 = [0, 1, 3, 4, 6, 6, 6, 7, 12], L29774 = [0, 1, 3, 4, 6, 6, 7, 8, 8], = [0, 1, 3, 4, 6, 6, 7, 8, 12], L29779 = [0, 1, 3, 4, 6, 6, 7, 12, 12], L29800 = [0, 1, 3, 4, 6, 6, 9, 11, 12], = [0, 1, 3, 4, 6, 7, 8, 8, 8], L29811 = [0, 1, 3, 4, 6, 7, 8, 8, 12], L29814 = [0, 1, 3, 4, 6, 7, 8, 12, 12], = [0, 1, 3, 4, 6, 7, 12, 12, 12], L29838 = [0, 1, 3, 4, 6, 8, 9, 10, 12], L29870 = [0, 1, 3, 4, 7, 8, 8, 8, 8], = [0, 1, 3, 4, 7, 8, 8, 8, 12], L29875 = [0, 1, 3, 4, 7, 8, 8, 12, 12], L29879 = [0, 1, 3, 4, 7, 8, 12, 12, 12],
APPENDIX
L29884 L29971 L29982 L29997 L30016 L30025 L30045 L30054 L30065 L30084 L30119 L30147 L30178 L30187 L30276 L30288 L30885 L32367 L32743 L32820 L32947 L33011 L33384 L33524 L33561 L41370 L43567 L44608 L47646 L47813 L49117 L49418 L49464 L49553 L49572 L49587 L50536 L51149 L51196 L51506 L53127 L53380 L53411 L53498 L53513 L53526 L53537 L54137 L54150
275
= [0, 1, 3, 4, 7, 12, 12, 12, 12], L29966 = [0, 1, 3, 5, 6, 6, 6, 6, 6], L29968 = [0, 1, 3, 5, 6, 6, 6, 6, 8], = [0, 1, 3, 5, 6, 6, 6, 6, 12], L29976 = [0, 1, 3, 5, 6, 6, 6, 8, 8], L29979 = [0, 1, 3, 5, 6, 6, 6, 8, 12], = [0, 1, 3, 5, 6, 6, 6, 12, 12], L29991 = [0, 1, 3, 5, 6, 6, 8, 8, 8], L29994 = [0, 1, 3, 5, 6, 6, 8, 8, 12], = [0, 1, 3, 5, 6, 6, 8, 12, 12], L30000 = [0, 1, 3, 5, 6, 6, 12, 12, 12], L30013 = [0, 1, 3, 5, 6, 8, 8, 8, 8], = [0, 1, 3, 5, 6, 8, 8, 8, 12], L30019 = [0, 1, 3, 5, 6, 8, 8, 12, 12], L30022 = [0, 1, 3, 5, 6, 8, 12, 12, 12], = [0, 1, 3, 5, 6, 12, 12, 12, 12], L30034 = [0, 1, 3, 5, 7, 8, 9, 11, 12], L30042 = [0, 1, 3, 5, 8, 8, 8, 8, 8], = [0, 1, 3, 5, 8, 8, 8, 8, 12], L30048 = [0, 1, 3, 5, 8, 8, 8, 12, 12], L30051 = [0, 1, 3, 5, 8, 8, 12, 12, 12], = [0, 1, 3, 5, 8, 12, 12, 12, 12], L30057 = [0, 1, 3, 5, 12, 12, 12, 12, 12], L30059 = [0, 1, 3, 6, 6, 6, 6, 6, 7], = [0, 1, 3, 6, 6, 6, 6, 7, 8], L30067 = [0, 1, 3, 6, 6, 6, 6, 7, 12], L30082 = [0, 1, 3, 6, 6, 6, 7, 8, 8], = [0, 1, 3, 6, 6, 6, 7, 8, 12], L30087 = [0, 1, 3, 6, 6, 6, 7, 12, 12], L30117 = [0, 1, 3, 6, 6, 7, 8, 8, 8], = [0, 1, 3, 6, 6, 7, 8, 8, 12], L30122 = [0, 1, 3, 6, 6, 7, 8, 12, 12], L30126 = [0, 1, 3, 6, 6, 7, 12, 12, 12], = [0, 1, 3, 6, 6, 8, 9, 11, 12], L30165 = [0, 1, 3, 6, 6, 9, 10, 11, 12], L30167 = [0, 1, 3, 6, 6, 9, 11, 12, 12], = [0, 1, 3, 6, 7, 8, 8, 8, 8], L30180 = [0, 1, 3, 6, 7, 8, 8, 8, 12], L30183 = [0, 1, 3, 6, 7, 8, 8, 12, 12], = [0, 1, 3, 6, 7, 8, 12, 12, 12], L30192 = [0, 1, 3, 6, 7, 12, 12, 12, 12], L30274 = [0, 1, 3, 7, 8, 8, 8, 8, 8], = [0, 1, 3, 7, 8, 8, 8, 8, 12], L30279 = [0, 1, 3, 7, 8, 8, 8, 12, 12], L30283 = [0, 1, 3, 7, 8, 8, 12, 12, 12], = [0, 1, 3, 7, 8, 12, 12, 12, 12], L30294 = [0, 1, 3, 7, 12, 12, 12, 12, 12], L30883 = [0, 1, 4, 5, 6, 6, 7, 8, 11], = [0, 1, 4, 5, 6, 6, 7, 11, 12], L31262 = [0, 1, 5, 6, 6, 7, 8, 11, 12], L31264 = [0, 1, 5, 6, 6, 7, 11, 12, 12], = [0, 2, 2, 3, 4, 6, 8, 9, 12], L32371 = [0, 2, 2, 3, 4, 6, 9, 10, 10], L32699 = [0, 2, 3, 3, 4, 4, 9, 9, 10], = [0, 2, 3, 3, 4, 8, 9, 9, 10], L32749 = [0, 2, 3, 3, 4, 9, 9, 10, 12], L32779 = [0, 2, 3, 3, 6, 6, 9, 9, 12], = [0, 2, 3, 3, 8, 9, 9, 10, 12], L32894 = [0, 2, 3, 4, 4, 6, 8, 9, 12], L32938 = [0, 2, 3, 4, 6, 6, 9, 10, 12], = [0, 2, 3, 4, 6, 8, 8, 9, 12], L32950 = [0, 2, 3, 4, 6, 8, 9, 10, 12], L32951 = [0, 2, 3, 4, 6, 8, 9, 12, 12], = [0, 2, 3, 6, 6, 8, 9, 10, 12], L33015 = [0, 2, 3, 6, 6, 9, 10, 12, 12], L33338 = [0, 3, 3, 4, 6, 6, 9, 9, 12], = [0, 3, 3, 6, 6, 8, 9, 9, 12], L33481 = [0, 3, 4, 4, 6, 6, 8, 9, 12], L33512 = [0, 3, 4, 6, 6, 6, 6, 9, 12], = [0, 3, 4, 6, 6, 8, 8, 9, 12], L33526 = [0, 3, 4, 6, 6, 8, 9, 12, 12], L33535 = [0, 3, 4, 6, 8, 8, 9, 12, 12], = [0, 3, 6, 6, 6, 6, 8, 9, 12], L39418 = [1, 1, 1, 2, 3, 5, 7, 9, 11], L40403 = [1, 1, 1, 2, 5, 7, 11, 11, 11], = [1, 1, 1, 3, 3, 5, 7, 9, 11], L42168 = [1, 1, 1, 3, 5, 5, 7, 9, 11], L42334 = [1, 1, 1, 3, 5, 7, 9, 10, 11], = [1, 1, 1, 4, 5, 7, 11, 11, 11], L44575 = [1, 1, 1, 5, 7, 8, 11, 11, 11], L44604 = [1, 1, 1, 5, 7, 10, 11, 11, 11], = [1, 1, 1, 5, 7, 11, 11, 11, 12], L46925 = [1, 1, 2, 2, 3, 5, 7, 9, 11], L47406 = [1, 1, 2, 2, 4, 5, 8, 10, 10], = [1, 1, 2, 2, 5, 5, 7, 7, 11], L47657 = [1, 1, 2, 2, 5, 5, 7, 10, 10], L47660 = [1, 1, 2, 2, 5, 5, 7, 11, 11], = [1, 1, 2, 2, 5, 7, 10, 10, 11], L47815 = [1, 1, 2, 2, 5, 7, 10, 11, 11], L48697 = [1, 1, 2, 3, 3, 5, 7, 9, 11], = [1, 1, 2, 3, 4, 5, 5, 10, 11], L49152 = [1, 1, 2, 3, 4, 5, 7, 7, 10], L49162 = [1, 1, 2, 3, 4, 5, 7, 9, 11], = [1, 1, 2, 3, 5, 5, 6, 10, 11], L49437 = [1, 1, 2, 3, 5, 5, 7, 10, 11], L49451 = [1, 1, 2, 3, 5, 5, 8, 10, 11], = [1, 1, 2, 3, 5, 5, 10, 11, 12], L49499 = [1, 1, 2, 3, 5, 6, 7, 7, 10], L49509 = [1, 1, 2, 3, 5, 6, 7, 9, 11], = [1, 1, 2, 3, 5, 7, 7, 8, 10], L49560 = [1, 1, 2, 3, 5, 7, 7, 10, 11], L49561 = [1, 1, 2, 3, 5, 7, 7, 10, 12], = [1, 1, 2, 3, 5, 7, 8, 9, 11], L49582 = [1, 1, 2, 3, 5, 7, 9, 9, 11], L49585 = [1, 1, 2, 3, 5, 7, 9, 10, 11], = [1, 1, 2, 3, 5, 7, 9, 11, 11], L49588 = [1, 1, 2, 3, 5, 7, 9, 11, 12], L50524 = [1, 1, 2, 4, 5, 5, 7, 7, 11], = [1, 1, 2, 4, 5, 5, 7, 11, 11], L50666 = [1, 1, 2, 4, 5, 7, 8, 11, 11], L51137 = [1, 1, 2, 5, 5, 6, 7, 7, 11], = [1, 1, 2, 5, 5, 6, 7, 11, 11], L51176 = [1, 1, 2, 5, 5, 7, 7, 8, 11], L51184 = [1, 1, 2, 5, 5, 7, 7, 11, 12], = [1, 1, 2, 5, 5, 7, 8, 11, 11], L51206 = [1, 1, 2, 5, 5, 7, 11, 11, 12], L51286 = [1, 1, 2, 5, 6, 6, 7, 11, 11], = [1, 1, 2, 5, 7, 10, 10, 11, 11], L52691 = [1, 1, 3, 3, 3, 5, 7, 9, 11], L53093 = [1, 1, 3, 3, 4, 5, 5, 9, 11], = [1, 1, 3, 3, 4, 5, 7, 7, 9], L53137 = [1, 1, 3, 3, 4, 5, 7, 9, 11], L53142 = [1, 1, 3, 3, 4, 5, 7, 11, 11], = [1, 1, 3, 3, 5, 5, 6, 9, 11], L53394 = [1, 1, 3, 3, 5, 5, 7, 9, 11], L53404 = [1, 1, 3, 3, 5, 5, 8, 9, 11], = [1, 1, 3, 3, 5, 5, 9, 11, 12], L53445 = [1, 1, 3, 3, 5, 6, 7, 7, 9], L53460 = [1, 1, 3, 3, 5, 6, 7, 11, 11], = [1, 1, 3, 3, 5, 7, 7, 8, 9], L53502 = [1, 1, 3, 3, 5, 7, 7, 9, 11], L53503 = [1, 1, 3, 3, 5, 7, 7, 9, 12], = [1, 1, 3, 3, 5, 7, 8, 9, 11], L53518 = [1, 1, 3, 3, 5, 7, 8, 11, 11], L53523 = [1, 1, 3, 3, 5, 7, 9, 9, 11], = [1, 1, 3, 3, 5, 7, 9, 10, 11], L53528 = [1, 1, 3, 3, 5, 7, 9, 11, 11], L53529 = [1, 1, 3, 3, 5, 7, 9, 11, 12], = [1, 1, 3, 3, 5, 7, 11, 11, 12], L54023 = [1, 1, 3, 4, 4, 4, 5, 5, 11], L54032 = [1, 1, 3, 4, 4, 4, 5, 7, 7], = [1, 1, 3, 4, 4, 5, 5, 6, 11], L54142 = [1, 1, 3, 4, 4, 5, 5, 7, 11], L54146 = [1, 1, 3, 4, 4, 5, 5, 8, 11], = [1, 1, 3, 4, 4, 5, 5, 11, 12], L54159 = [1, 1, 3, 4, 4, 5, 6, 7, 7], L54180 = [1, 1, 3, 4, 4, 5, 7, 7, 8],
276
L54182 L54425 L54436 L54446 L54458 L54490 L54543 L54549 L55013 L55026 L55039 L55051 L55058 L55069 L55078 L55090 L55122 L55175 L55181 L55282 L55288 L55316 L55335 L55343 L57344 L58262 L59899 L59934 L59940 L59952 L60212 L60247 L60253 L60265 L60334 L60342 L60352 L60360 L60368 L60385 L60756 L60861 L60875 L60900 L60967 L61070 L61103 L61111 L61182
EMILIO A. LAURET
= [1, 1, 3, 4, 4, 5, 7, 7, 11], L54183 = [1, 1, 3, 4, 4, 5, 7, 7, 12], L54420 = [1, 1, 3, 4, 5, 5, 6, 6, 11], = [1, 1, 3, 4, 5, 5, 6, 7, 11], L54429 = [1, 1, 3, 4, 5, 5, 6, 8, 11], L54433 = [1, 1, 3, 4, 5, 5, 6, 11, 12], = [1, 1, 3, 4, 5, 5, 7, 7, 9], L54441 = [1, 1, 3, 4, 5, 5, 7, 8, 11], L54443 = [1, 1, 3, 4, 5, 5, 7, 9, 11], = [1, 1, 3, 4, 5, 5, 7, 11, 12], L54450 = [1, 1, 3, 4, 5, 5, 8, 8, 11], L54454 = [1, 1, 3, 4, 5, 5, 8, 11, 12], = [1, 1, 3, 4, 5, 5, 11, 12, 12], L54467 = [1, 1, 3, 4, 5, 6, 6, 7, 7], L54488 = [1, 1, 3, 4, 5, 6, 7, 7, 8], = [1, 1, 3, 4, 5, 6, 7, 7, 11], L54491 = [1, 1, 3, 4, 5, 6, 7, 7, 12], L54541 = [1, 1, 3, 4, 5, 7, 7, 8, 8], = [1, 1, 3, 4, 5, 7, 7, 8, 11], L54544 = [1, 1, 3, 4, 5, 7, 7, 8, 12], L54548 = [1, 1, 3, 4, 5, 7, 7, 11, 12], = [1, 1, 3, 4, 5, 7, 7, 12, 12], L54570 = [1, 1, 3, 4, 5, 7, 9, 10, 11], L54572 = [1, 1, 3, 4, 5, 7, 9, 11, 11], = [1, 1, 3, 5, 5, 6, 6, 6, 11], L55018 = [1, 1, 3, 5, 5, 6, 6, 7, 11], L55022 = [1, 1, 3, 5, 5, 6, 6, 8, 11], = [1, 1, 3, 5, 5, 6, 6, 11, 12], L55029 = [1, 1, 3, 5, 5, 6, 7, 7, 9], L55034 = [1, 1, 3, 5, 5, 6, 7, 8, 11], = [1, 1, 3, 5, 5, 6, 7, 11, 12], L55043 = [1, 1, 3, 5, 5, 6, 8, 8, 11], L55047 = [1, 1, 3, 5, 5, 6, 8, 11, 12], = [1, 1, 3, 5, 5, 6, 11, 12, 12], L55054 = [1, 1, 3, 5, 5, 7, 7, 8, 9], L55057 = [1, 1, 3, 5, 5, 7, 7, 9, 11], = [1, 1, 3, 5, 5, 7, 7, 9, 12], L55064 = [1, 1, 3, 5, 5, 7, 8, 8, 11], L55066 = [1, 1, 3, 5, 5, 7, 8, 9, 11], = [1, 1, 3, 5, 5, 7, 8, 11, 12], L55071 = [1, 1, 3, 5, 5, 7, 9, 11, 12], L55074 = [1, 1, 3, 5, 5, 7, 11, 12, 12], = [1, 1, 3, 5, 5, 8, 8, 8, 11], L55082 = [1, 1, 3, 5, 5, 8, 8, 11, 12], L55086 = [1, 1, 3, 5, 5, 8, 11, 12, 12], = [1, 1, 3, 5, 5, 11, 12, 12, 12], L55099 = [1, 1, 3, 5, 6, 6, 6, 7, 7], L55120 = [1, 1, 3, 5, 6, 6, 7, 7, 8], = [1, 1, 3, 5, 6, 6, 7, 7, 11], L55123 = [1, 1, 3, 5, 6, 6, 7, 7, 12], L55173 = [1, 1, 3, 5, 6, 7, 7, 8, 8], = [1, 1, 3, 5, 6, 7, 7, 8, 11], L55176 = [1, 1, 3, 5, 6, 7, 7, 8, 12], L55180 = [1, 1, 3, 5, 6, 7, 7, 11, 12], = [1, 1, 3, 5, 6, 7, 7, 12, 12], L55202 = [1, 1, 3, 5, 6, 7, 9, 10, 11], L55280 = [1, 1, 3, 5, 7, 7, 8, 8, 8], = [1, 1, 3, 5, 7, 7, 8, 8, 11], L55283 = [1, 1, 3, 5, 7, 7, 8, 8, 12], L55287 = [1, 1, 3, 5, 7, 7, 8, 11, 12], = [1, 1, 3, 5, 7, 7, 8, 12, 12], L55294 = [1, 1, 3, 5, 7, 7, 11, 12, 12], L55295 = [1, 1, 3, 5, 7, 7, 12, 12, 12], = [1, 1, 3, 5, 7, 8, 9, 10, 11], L55318 = [1, 1, 3, 5, 7, 8, 9, 11, 11], L55319 = [1, 1, 3, 5, 7, 8, 9, 11, 12], = [1, 1, 3, 5, 7, 9, 9, 10, 11], L55340 = [1, 1, 3, 5, 7, 9, 10, 10, 11], L55342 = [1, 1, 3, 5, 7, 9, 10, 11, 11], = [1, 1, 3, 5, 7, 9, 10, 11, 12], L55345 = [1, 1, 3, 5, 7, 9, 11, 11, 12], L57103 = [1, 1, 4, 5, 5, 7, 7, 11, 11], = [1, 1, 4, 5, 7, 8, 10, 11, 11], L58125 = [1, 1, 5, 5, 7, 7, 8, 11, 11], L58128 = [1, 1, 5, 5, 7, 7, 11, 11, 12], = [1, 1, 5, 6, 6, 7, 10, 11, 11], L59807 = [1, 2, 2, 2, 2, 2, 2, 5, 7], L59811 = [1, 2, 2, 2, 2, 2, 2, 5, 11], = [1, 2, 2, 2, 2, 2, 4, 5, 7], L59903 = [1, 2, 2, 2, 2, 2, 4, 5, 11], L59930 = [1, 2, 2, 2, 2, 2, 5, 6, 7], = [1, 2, 2, 2, 2, 2, 5, 6, 11], L59936 = [1, 2, 2, 2, 2, 2, 5, 7, 8], L59938 = [1, 2, 2, 2, 2, 2, 5, 7, 10], = [1, 2, 2, 2, 2, 2, 5, 7, 12], L59944 = [1, 2, 2, 2, 2, 2, 5, 8, 11], L59950 = [1, 2, 2, 2, 2, 2, 5, 10, 11], = [1, 2, 2, 2, 2, 2, 5, 11, 12], L60116 = [1, 2, 2, 2, 2, 3, 5, 7, 9], L60127 = [1, 2, 2, 2, 2, 3, 5, 9, 11], = [1, 2, 2, 2, 2, 4, 4, 5, 7], L60216 = [1, 2, 2, 2, 2, 4, 4, 5, 11], L60243 = [1, 2, 2, 2, 2, 4, 5, 6, 7], = [1, 2, 2, 2, 2, 4, 5, 6, 11], L60249 = [1, 2, 2, 2, 2, 4, 5, 7, 8], L60251 = [1, 2, 2, 2, 2, 4, 5, 7, 10], = [1, 2, 2, 2, 2, 4, 5, 7, 12], L60257 = [1, 2, 2, 2, 2, 4, 5, 8, 11], L60263 = [1, 2, 2, 2, 2, 4, 5, 10, 11], = [1, 2, 2, 2, 2, 4, 5, 11, 12], L60328 = [1, 2, 2, 2, 2, 5, 6, 6, 7], L60332 = [1, 2, 2, 2, 2, 5, 6, 6, 11], = [1, 2, 2, 2, 2, 5, 6, 7, 8], L60336 = [1, 2, 2, 2, 2, 5, 6, 7, 10], L60338 = [1, 2, 2, 2, 2, 5, 6, 7, 12], = [1, 2, 2, 2, 2, 5, 6, 8, 11], L60348 = [1, 2, 2, 2, 2, 5, 6, 10, 11], L60350 = [1, 2, 2, 2, 2, 5, 6, 11, 12], = [1, 2, 2, 2, 2, 5, 7, 8, 8], L60354 = [1, 2, 2, 2, 2, 5, 7, 8, 10], L60356 = [1, 2, 2, 2, 2, 5, 7, 8, 12], = [1, 2, 2, 2, 2, 5, 7, 10, 10], L60362 = [1, 2, 2, 2, 2, 5, 7, 10, 12], L60364 = [1, 2, 2, 2, 2, 5, 7, 12, 12], = [1, 2, 2, 2, 2, 5, 8, 8, 11], L60374 = [1, 2, 2, 2, 2, 5, 8, 10, 11], L60376 = [1, 2, 2, 2, 2, 5, 8, 11, 12], = [1, 2, 2, 2, 2, 5, 10, 10, 11], L60387 = [1, 2, 2, 2, 2, 5, 10, 11, 12], L60389 = [1, 2, 2, 2, 2, 5, 11, 12, 12], = [1, 2, 2, 2, 3, 4, 5, 7, 9], L60767 = [1, 2, 2, 2, 3, 4, 5, 9, 11], L60850 = [1, 2, 2, 2, 3, 5, 6, 7, 9], = [1, 2, 2, 2, 3, 5, 6, 9, 11], L60869 = [1, 2, 2, 2, 3, 5, 7, 8, 9], L60874 = [1, 2, 2, 2, 3, 5, 7, 9, 10], = [1, 2, 2, 2, 3, 5, 7, 9, 11], L60876 = [1, 2, 2, 2, 3, 5, 7, 9, 12], L60889 = [1, 2, 2, 2, 3, 5, 8, 9, 11], = [1, 2, 2, 2, 3, 5, 9, 10, 11], L60902 = [1, 2, 2, 2, 3, 5, 9, 11, 12], L60904 = [1, 2, 2, 2, 3, 5, 10, 10, 10], = [1, 2, 2, 2, 3, 6, 9, 10, 10], L60998 = [1, 2, 2, 2, 3, 7, 10, 10, 10], L61066 = [1, 2, 2, 2, 4, 4, 4, 5, 7], = [1, 2, 2, 2, 4, 4, 4, 5, 11], L61097 = [1, 2, 2, 2, 4, 4, 5, 6, 7], L61101 = [1, 2, 2, 2, 4, 4, 5, 6, 11], = [1, 2, 2, 2, 4, 4, 5, 7, 8], L61105 = [1, 2, 2, 2, 4, 4, 5, 7, 10], L61107 = [1, 2, 2, 2, 4, 4, 5, 7, 12], = [1, 2, 2, 2, 4, 4, 5, 8, 11], L61117 = [1, 2, 2, 2, 4, 4, 5, 10, 11], L61119 = [1, 2, 2, 2, 4, 4, 5, 11, 12], = [1, 2, 2, 2, 4, 5, 6, 6, 7], L61186 = [1, 2, 2, 2, 4, 5, 6, 6, 11], L61188 = [1, 2, 2, 2, 4, 5, 6, 7, 8],
APPENDIX
L61190 L61202 L61208 L61216 L61228 L61241 L61375 L61381 L61393 L61399 L61407 L61419 L61432 L61438 L61446 L61459 L61471 L61484 L61500 L62116 L62330 L62382 L62437 L62449 L62465 L62479 L62571 L62648 L62660 L62676 L62690 L62702 L62714 L62730 L62743 L62759 L62843 L62918 L63039 L63074 L63080 L63092 L63161 L63169 L63179 L63189 L63200 L63211 L63344
277
= [1, 2, 2, 2, 4, 5, 6, 7, 10], L61192 = [1, 2, 2, 2, 4, 5, 6, 7, 12], L61196 = [1, 2, 2, 2, 4, 5, 6, 8, 11], = [1, 2, 2, 2, 4, 5, 6, 10, 11], L61204 = [1, 2, 2, 2, 4, 5, 6, 11, 12], L61206 = [1, 2, 2, 2, 4, 5, 7, 8, 8], = [1, 2, 2, 2, 4, 5, 7, 8, 10], L61210 = [1, 2, 2, 2, 4, 5, 7, 8, 12], L61214 = [1, 2, 2, 2, 4, 5, 7, 10, 10], = [1, 2, 2, 2, 4, 5, 7, 10, 12], L61218 = [1, 2, 2, 2, 4, 5, 7, 12, 12], L61222 = [1, 2, 2, 2, 4, 5, 8, 8, 11], = [1, 2, 2, 2, 4, 5, 8, 10, 11], L61230 = [1, 2, 2, 2, 4, 5, 8, 11, 12], L61239 = [1, 2, 2, 2, 4, 5, 10, 10, 11], = [1, 2, 2, 2, 4, 5, 10, 11, 12], L61243 = [1, 2, 2, 2, 4, 5, 11, 12, 12], L61371 = [1, 2, 2, 2, 5, 6, 6, 6, 7], = [1, 2, 2, 2, 5, 6, 6, 6, 11], L61377 = [1, 2, 2, 2, 5, 6, 6, 7, 8], L61379 = [1, 2, 2, 2, 5, 6, 6, 7, 10], = [1, 2, 2, 2, 5, 6, 6, 7, 12], L61385 = [1, 2, 2, 2, 5, 6, 6, 8, 11], L61391 = [1, 2, 2, 2, 5, 6, 6, 10, 11], = [1, 2, 2, 2, 5, 6, 6, 11, 12], L61395 = [1, 2, 2, 2, 5, 6, 7, 8, 8], L61397 = [1, 2, 2, 2, 5, 6, 7, 8, 10], = [1, 2, 2, 2, 5, 6, 7, 8, 12], L61403 = [1, 2, 2, 2, 5, 6, 7, 10, 10], L61405 = [1, 2, 2, 2, 5, 6, 7, 10, 12], = [1, 2, 2, 2, 5, 6, 7, 12, 12], L61411 = [1, 2, 2, 2, 5, 6, 8, 8, 11], L61417 = [1, 2, 2, 2, 5, 6, 8, 10, 11], = [1, 2, 2, 2, 5, 6, 8, 11, 12], L61428 = [1, 2, 2, 2, 5, 6, 10, 10, 11], L61430 = [1, 2, 2, 2, 5, 6, 10, 11, 12], = [1, 2, 2, 2, 5, 6, 11, 12, 12], L61434 = [1, 2, 2, 2, 5, 7, 8, 8, 8], L61436 = [1, 2, 2, 2, 5, 7, 8, 8, 10], = [1, 2, 2, 2, 5, 7, 8, 8, 12], L61442 = [1, 2, 2, 2, 5, 7, 8, 10, 10], L61444 = [1, 2, 2, 2, 5, 7, 8, 10, 12], = [1, 2, 2, 2, 5, 7, 8, 12, 12], L61455 = [1, 2, 2, 2, 5, 7, 10, 10, 12], L61457 = [1, 2, 2, 2, 5, 7, 10, 12, 12], = [1, 2, 2, 2, 5, 7, 12, 12, 12], L61463 = [1, 2, 2, 2, 5, 8, 8, 8, 11], L61469 = [1, 2, 2, 2, 5, 8, 8, 10, 11], = [1, 2, 2, 2, 5, 8, 8, 11, 12], L61480 = [1, 2, 2, 2, 5, 8, 10, 10, 11], L61482 = [1, 2, 2, 2, 5, 8, 10, 11, 12], = [1, 2, 2, 2, 5, 8, 11, 12, 12], L61496 = [1, 2, 2, 2, 5, 10, 10, 11, 12], L61498 = [1, 2, 2, 2, 5, 10, 11, 12, 12], = [1, 2, 2, 2, 5, 11, 12, 12, 12], L62091 = [1, 2, 2, 3, 3, 5, 7, 9, 9], L62093 = [1, 2, 2, 3, 3, 5, 7, 9, 11], = [1, 2, 2, 3, 3, 5, 9, 9, 11], L62118 = [1, 2, 2, 3, 3, 5, 9, 10, 10], L62216 = [1, 2, 2, 3, 3, 7, 9, 10, 10], = [1, 2, 2, 3, 4, 4, 5, 7, 9], L62341 = [1, 2, 2, 3, 4, 4, 5, 9, 11], L62343 = [1, 2, 2, 3, 4, 4, 5, 10, 10], = [1, 2, 2, 3, 4, 4, 7, 10, 10], L62424 = [1, 2, 2, 3, 4, 5, 6, 7, 9], L62435 = [1, 2, 2, 3, 4, 5, 6, 9, 11], = [1, 2, 2, 3, 4, 5, 6, 10, 10], L62443 = [1, 2, 2, 3, 4, 5, 7, 8, 9], L62448 = [1, 2, 2, 3, 4, 5, 7, 9, 10], = [1, 2, 2, 3, 4, 5, 7, 9, 11], L62450 = [1, 2, 2, 3, 4, 5, 7, 9, 12], L62463 = [1, 2, 2, 3, 4, 5, 8, 9, 11], = [1, 2, 2, 3, 4, 5, 8, 10, 10], L62474 = [1, 2, 2, 3, 4, 5, 9, 10, 11], L62476 = [1, 2, 2, 3, 4, 5, 9, 11, 12], = [1, 2, 2, 3, 4, 5, 10, 10, 12], L62518 = [1, 2, 2, 3, 4, 6, 7, 10, 10], L62560 = [1, 2, 2, 3, 4, 7, 8, 10, 10], = [1, 2, 2, 3, 4, 7, 10, 10, 12], L62635 = [1, 2, 2, 3, 5, 6, 6, 7, 9], L62646 = [1, 2, 2, 3, 5, 6, 6, 9, 11], = [1, 2, 2, 3, 5, 6, 6, 10, 10], L62654 = [1, 2, 2, 3, 5, 6, 7, 8, 9], L62659 = [1, 2, 2, 3, 5, 6, 7, 9, 10], = [1, 2, 2, 3, 5, 6, 7, 9, 11], L62661 = [1, 2, 2, 3, 5, 6, 7, 9, 12], L62674 = [1, 2, 2, 3, 5, 6, 8, 9, 11], = [1, 2, 2, 3, 5, 6, 8, 10, 10], L62685 = [1, 2, 2, 3, 5, 6, 9, 10, 11], L62687 = [1, 2, 2, 3, 5, 6, 9, 11, 12], = [1, 2, 2, 3, 5, 6, 10, 10, 12], L62696 = [1, 2, 2, 3, 5, 7, 8, 8, 9], L62701 = [1, 2, 2, 3, 5, 7, 8, 9, 10], = [1, 2, 2, 3, 5, 7, 8, 9, 11], L62703 = [1, 2, 2, 3, 5, 7, 8, 9, 12], L62713 = [1, 2, 2, 3, 5, 7, 9, 10, 11], = [1, 2, 2, 3, 5, 7, 9, 10, 12], L62715 = [1, 2, 2, 3, 5, 7, 9, 11, 12], L62716 = [1, 2, 2, 3, 5, 7, 9, 12, 12], = [1, 2, 2, 3, 5, 8, 8, 9, 11], L62732 = [1, 2, 2, 3, 5, 8, 8, 10, 10], L62741 = [1, 2, 2, 3, 5, 8, 9, 10, 11], = [1, 2, 2, 3, 5, 8, 9, 11, 12], L62746 = [1, 2, 2, 3, 5, 8, 10, 10, 12], L62757 = [1, 2, 2, 3, 5, 9, 10, 11, 12], = [1, 2, 2, 3, 5, 9, 11, 12, 12], L62762 = [1, 2, 2, 3, 5, 10, 10, 12, 12], L62801 = [1, 2, 2, 3, 6, 6, 7, 10, 10], = [1, 2, 2, 3, 6, 7, 8, 10, 10], L62854 = [1, 2, 2, 3, 6, 7, 10, 10, 12], L62894 = [1, 2, 2, 3, 6, 9, 10, 10, 10], = [1, 2, 2, 3, 7, 8, 8, 10, 10], L62929 = [1, 2, 2, 3, 7, 8, 10, 10, 12], L62943 = [1, 2, 2, 3, 7, 10, 10, 12, 12], = [1, 2, 2, 4, 4, 4, 4, 5, 7], L63043 = [1, 2, 2, 4, 4, 4, 4, 5, 11], L63070 = [1, 2, 2, 4, 4, 4, 5, 6, 7], = [1, 2, 2, 4, 4, 4, 5, 6, 11], L63076 = [1, 2, 2, 4, 4, 4, 5, 7, 8], L63078 = [1, 2, 2, 4, 4, 4, 5, 7, 10], = [1, 2, 2, 4, 4, 4, 5, 7, 12], L63084 = [1, 2, 2, 4, 4, 4, 5, 8, 11], L63090 = [1, 2, 2, 4, 4, 4, 5, 10, 11], = [1, 2, 2, 4, 4, 4, 5, 11, 12], L63155 = [1, 2, 2, 4, 4, 5, 6, 6, 7], L63159 = [1, 2, 2, 4, 4, 5, 6, 6, 11], = [1, 2, 2, 4, 4, 5, 6, 7, 8], L63163 = [1, 2, 2, 4, 4, 5, 6, 7, 10], L63165 = [1, 2, 2, 4, 4, 5, 6, 7, 12], = [1, 2, 2, 4, 4, 5, 6, 8, 11], L63175 = [1, 2, 2, 4, 4, 5, 6, 10, 11], L63177 = [1, 2, 2, 4, 4, 5, 6, 11, 12], = [1, 2, 2, 4, 4, 5, 7, 8, 8], L63181 = [1, 2, 2, 4, 4, 5, 7, 8, 10], L63183 = [1, 2, 2, 4, 4, 5, 7, 8, 12], = [1, 2, 2, 4, 4, 5, 7, 10, 12], L63191 = [1, 2, 2, 4, 4, 5, 7, 12, 12], L63195 = [1, 2, 2, 4, 4, 5, 8, 8, 11], = [1, 2, 2, 4, 4, 5, 8, 10, 10], L63201 = [1, 2, 2, 4, 4, 5, 8, 10, 11], L63203 = [1, 2, 2, 4, 4, 5, 8, 11, 12], = [1, 2, 2, 4, 4, 5, 10, 11, 12], L63213 = [1, 2, 2, 4, 4, 5, 11, 12, 12], L63340 = [1, 2, 2, 4, 5, 6, 6, 6, 7], = [1, 2, 2, 4, 5, 6, 6, 6, 11], L63346 = [1, 2, 2, 4, 5, 6, 6, 7, 8], L63348 = [1, 2, 2, 4, 5, 6, 6, 7, 10],
278
L63350 L63362 L63368 L63380 L63396 L63402 L63409 L63421 L63432 L63442 L63455 L63686 L63694 L63706 L63712 L63722 L63734 L63746 L63756 L63769 L63781 L63801 L63807 L63817 L63839 L63851 L63863 L63887 L64734 L64951 L64986 L65070 L65169 L65195 L65219 L65245 L65297 L65414 L65540 L65577 L65591 L65628 L65674 L65686 L65705 L65717 L65754 L65802 L65870
EMILIO A. LAURET
= [1, 2, 2, 4, 5, 6, 6, 7, 12], L63354 = [1, 2, 2, 4, 5, 6, 6, 8, 11], L63360 = [1, 2, 2, 4, 5, 6, 6, 10, 11], = [1, 2, 2, 4, 5, 6, 6, 11, 12], L63364 = [1, 2, 2, 4, 5, 6, 7, 8, 8], L63366 = [1, 2, 2, 4, 5, 6, 7, 8, 10], = [1, 2, 2, 4, 5, 6, 7, 8, 12], L63374 = [1, 2, 2, 4, 5, 6, 7, 10, 12], L63376 = [1, 2, 2, 4, 5, 6, 7, 12, 12], = [1, 2, 2, 4, 5, 6, 8, 8, 11], L63386 = [1, 2, 2, 4, 5, 6, 8, 10, 11], L63388 = [1, 2, 2, 4, 5, 6, 8, 11, 12], = [1, 2, 2, 4, 5, 6, 10, 11, 12], L63398 = [1, 2, 2, 4, 5, 6, 11, 12, 12], L63400 = [1, 2, 2, 4, 5, 7, 8, 8, 8], = [1, 2, 2, 4, 5, 7, 8, 8, 10], L63404 = [1, 2, 2, 4, 5, 7, 8, 8, 12], L63408 = [1, 2, 2, 4, 5, 7, 8, 10, 10], = [1, 2, 2, 4, 5, 7, 8, 10, 11], L63410 = [1, 2, 2, 4, 5, 7, 8, 10, 12], L63412 = [1, 2, 2, 4, 5, 7, 8, 12, 12], = [1, 2, 2, 4, 5, 7, 10, 12, 12], L63423 = [1, 2, 2, 4, 5, 7, 12, 12, 12], L63427 = [1, 2, 2, 4, 5, 8, 8, 8, 11], = [1, 2, 2, 4, 5, 8, 8, 10, 10], L63433 = [1, 2, 2, 4, 5, 8, 8, 10, 11], L63435 = [1, 2, 2, 4, 5, 8, 8, 11, 12], = [1, 2, 2, 4, 5, 8, 10, 10, 12], L63443 = [1, 2, 2, 4, 5, 8, 10, 11, 12], L63445 = [1, 2, 2, 4, 5, 8, 11, 12, 12], = [1, 2, 2, 4, 5, 10, 11, 12, 12], L63457 = [1, 2, 2, 4, 5, 11, 12, 12, 12], L63577 = [1, 2, 2, 4, 6, 10, 10, 11, 12], = [1, 2, 2, 5, 6, 6, 6, 6, 7], L63690 = [1, 2, 2, 5, 6, 6, 6, 6, 11], L63692 = [1, 2, 2, 5, 6, 6, 6, 7, 8], = [1, 2, 2, 5, 6, 6, 6, 7, 10], L63696 = [1, 2, 2, 5, 6, 6, 6, 7, 12], L63700 = [1, 2, 2, 5, 6, 6, 6, 8, 11], = [1, 2, 2, 5, 6, 6, 6, 10, 11], L63708 = [1, 2, 2, 5, 6, 6, 6, 11, 12], L63710 = [1, 2, 2, 5, 6, 6, 7, 8, 8], = [1, 2, 2, 5, 6, 6, 7, 8, 10], L63714 = [1, 2, 2, 5, 6, 6, 7, 8, 12], L63720 = [1, 2, 2, 5, 6, 6, 7, 10, 12], = [1, 2, 2, 5, 6, 6, 7, 12, 12], L63726 = [1, 2, 2, 5, 6, 6, 8, 8, 11], L63732 = [1, 2, 2, 5, 6, 6, 8, 10, 11], = [1, 2, 2, 5, 6, 6, 8, 11, 12], L63742 = [1, 2, 2, 5, 6, 6, 10, 11, 12], L63744 = [1, 2, 2, 5, 6, 6, 11, 12, 12], = [1, 2, 2, 5, 6, 7, 8, 8, 8], L63748 = [1, 2, 2, 5, 6, 7, 8, 8, 10], L63750 = [1, 2, 2, 5, 6, 7, 8, 8, 12], = [1, 2, 2, 5, 6, 7, 8, 10, 12], L63758 = [1, 2, 2, 5, 6, 7, 8, 12, 12], L63767 = [1, 2, 2, 5, 6, 7, 10, 12, 12], = [1, 2, 2, 5, 6, 7, 12, 12, 12], L63773 = [1, 2, 2, 5, 6, 8, 8, 8, 11], L63779 = [1, 2, 2, 5, 6, 8, 8, 10, 11], = [1, 2, 2, 5, 6, 8, 8, 11, 12], L63789 = [1, 2, 2, 5, 6, 8, 10, 11, 12], L63791 = [1, 2, 2, 5, 6, 8, 11, 12, 12], = [1, 2, 2, 5, 6, 10, 11, 12, 12], L63803 = [1, 2, 2, 5, 6, 11, 12, 12, 12], L63805 = [1, 2, 2, 5, 7, 8, 8, 8, 8], = [1, 2, 2, 5, 7, 8, 8, 8, 10], L63809 = [1, 2, 2, 5, 7, 8, 8, 8, 12], L63815 = [1, 2, 2, 5, 7, 8, 8, 10, 12], = [1, 2, 2, 5, 7, 8, 8, 12, 12], L63826 = [1, 2, 2, 5, 7, 8, 10, 12, 12], L63828 = [1, 2, 2, 5, 7, 8, 12, 12, 12], = [1, 2, 2, 5, 7, 10, 12, 12, 12], L63841 = [1, 2, 2, 5, 7, 12, 12, 12, 12], L63845 = [1, 2, 2, 5, 8, 8, 8, 8, 11], = [1, 2, 2, 5, 8, 8, 8, 10, 11], L63853 = [1, 2, 2, 5, 8, 8, 8, 11, 12], L63861 = [1, 2, 2, 5, 8, 8, 10, 11, 12], = [1, 2, 2, 5, 8, 8, 11, 12, 12], L63873 = [1, 2, 2, 5, 8, 10, 11, 12, 12], L63875 = [1, 2, 2, 5, 8, 11, 12, 12, 12], = [1, 2, 2, 5, 10, 11, 12, 12, 12], L63889 = [1, 2, 2, 5, 11, 12, 12, 12, 12], L64642 = [1, 2, 3, 3, 3, 5, 9, 9, 10], = [1, 2, 3, 3, 3, 7, 9, 9, 10], L64858 = [1, 2, 3, 3, 4, 4, 5, 9, 10], L64897 = [1, 2, 3, 3, 4, 4, 7, 9, 10], = [1, 2, 3, 3, 4, 5, 6, 9, 10], L64963 = [1, 2, 3, 3, 4, 5, 7, 9, 9], L64977 = [1, 2, 3, 3, 4, 5, 8, 9, 10], = [1, 2, 3, 3, 4, 5, 9, 9, 11], L64989 = [1, 2, 3, 3, 4, 5, 9, 10, 12], L65028 = [1, 2, 3, 3, 4, 6, 7, 9, 10], = [1, 2, 3, 3, 4, 7, 8, 9, 10], L65079 = [1, 2, 3, 3, 4, 7, 9, 10, 12], L65157 = [1, 2, 3, 3, 5, 6, 6, 9, 10], = [1, 2, 3, 3, 5, 6, 7, 9, 9], L65183 = [1, 2, 3, 3, 5, 6, 8, 9, 10], L65192 = [1, 2, 3, 3, 5, 6, 9, 9, 11], = [1, 2, 3, 3, 5, 6, 9, 10, 12], L65207 = [1, 2, 3, 3, 5, 7, 8, 9, 9], L65218 = [1, 2, 3, 3, 5, 7, 9, 9, 12], = [1, 2, 3, 3, 5, 7, 9, 10, 11], L65233 = [1, 2, 3, 3, 5, 8, 8, 9, 10], L65242 = [1, 2, 3, 3, 5, 8, 9, 9, 11], = [1, 2, 3, 3, 5, 8, 9, 10, 12], L65255 = [1, 2, 3, 3, 5, 9, 9, 11, 12], L65258 = [1, 2, 3, 3, 5, 9, 10, 12, 12], = [1, 2, 3, 3, 6, 6, 7, 9, 10], L65339 = [1, 2, 3, 3, 6, 7, 8, 9, 10], L65348 = [1, 2, 3, 3, 6, 7, 9, 10, 12], = [1, 2, 3, 3, 7, 8, 8, 9, 10], L65423 = [1, 2, 3, 3, 7, 8, 9, 10, 12], L65434 = [1, 2, 3, 3, 7, 9, 10, 12, 12], = [1, 2, 3, 4, 4, 4, 4, 5, 10], L65552 = [1, 2, 3, 4, 4, 4, 4, 7, 10], L65573 = [1, 2, 3, 4, 4, 4, 5, 6, 10], = [1, 2, 3, 4, 4, 4, 5, 7, 9], L65583 = [1, 2, 3, 4, 4, 4, 5, 8, 10], L65588 = [1, 2, 3, 4, 4, 4, 5, 9, 11], = [1, 2, 3, 4, 4, 4, 5, 10, 12], L65603 = [1, 2, 3, 4, 4, 4, 6, 7, 10], L65622 = [1, 2, 3, 4, 4, 4, 7, 8, 10], = [1, 2, 3, 4, 4, 4, 7, 10, 12], L65664 = [1, 2, 3, 4, 4, 5, 6, 6, 10], L65668 = [1, 2, 3, 4, 4, 5, 6, 7, 9], = [1, 2, 3, 4, 4, 5, 6, 8, 10], L65679 = [1, 2, 3, 4, 4, 5, 6, 9, 11], L65682 = [1, 2, 3, 4, 4, 5, 6, 10, 12], = [1, 2, 3, 4, 4, 5, 7, 8, 9], L65693 = [1, 2, 3, 4, 4, 5, 7, 9, 12], L65700 = [1, 2, 3, 4, 4, 5, 8, 8, 10], = [1, 2, 3, 4, 4, 5, 8, 9, 11], L65708 = [1, 2, 3, 4, 4, 5, 8, 10, 12], L65714 = [1, 2, 3, 4, 4, 5, 9, 11, 12], = [1, 2, 3, 4, 4, 5, 10, 12, 12], L65729 = [1, 2, 3, 4, 4, 6, 6, 7, 10], L65748 = [1, 2, 3, 4, 4, 6, 7, 8, 10], = [1, 2, 3, 4, 4, 6, 7, 10, 12], L65788 = [1, 2, 3, 4, 4, 7, 8, 8, 10], L65794 = [1, 2, 3, 4, 4, 7, 8, 10, 12], = [1, 2, 3, 4, 4, 7, 10, 12, 12], L65860 = [1, 2, 3, 4, 5, 6, 6, 6, 10], L65864 = [1, 2, 3, 4, 5, 6, 6, 7, 9], = [1, 2, 3, 4, 5, 6, 6, 8, 10], L65875 = [1, 2, 3, 4, 5, 6, 6, 9, 11], L65878 = [1, 2, 3, 4, 5, 6, 6, 10, 12],
APPENDIX
L65882 L65901 L65913 L65931 L65946 L65958 L65980 L66039 L66109 L66133 L66231 L66243 L66262 L66274 L66292 L66307 L66319 L66333 L66349 L66361 L66376 L66392 L66406 L66443 L66491 L66561 L66663 L66693 L66857 L66867 L66938 L66948 L66959 L66973 L67107 L67117 L67128 L67142 L67155 L67165 L67181 L67413 L67423 L67434 L67448 L67461 L67471 L67487 L67502
279
= [1, 2, 3, 4, 5, 6, 7, 8, 9], L65889 = [1, 2, 3, 4, 5, 6, 7, 9, 12], L65896 = [1, 2, 3, 4, 5, 6, 8, 8, 10], = [1, 2, 3, 4, 5, 6, 8, 9, 11], L65904 = [1, 2, 3, 4, 5, 6, 8, 10, 12], L65910 = [1, 2, 3, 4, 5, 6, 9, 11, 12], = [1, 2, 3, 4, 5, 6, 10, 12, 12], L65917 = [1, 2, 3, 4, 5, 7, 8, 8, 9], L65924 = [1, 2, 3, 4, 5, 7, 8, 9, 12], = [1, 2, 3, 4, 5, 7, 9, 10, 11], L65934 = [1, 2, 3, 4, 5, 7, 9, 12, 12], L65941 = [1, 2, 3, 4, 5, 8, 8, 8, 10], = [1, 2, 3, 4, 5, 8, 8, 9, 11], L65949 = [1, 2, 3, 4, 5, 8, 8, 10, 12], L65955 = [1, 2, 3, 4, 5, 8, 9, 11, 12], = [1, 2, 3, 4, 5, 8, 10, 12, 12], L65965 = [1, 2, 3, 4, 5, 9, 11, 12, 12], L65968 = [1, 2, 3, 4, 5, 10, 12, 12, 12], = [1, 2, 3, 4, 6, 6, 6, 7, 10], L65999 = [1, 2, 3, 4, 6, 6, 7, 8, 10], L66005 = [1, 2, 3, 4, 6, 6, 7, 10, 12], = [1, 2, 3, 4, 6, 7, 8, 8, 10], L66045 = [1, 2, 3, 4, 6, 7, 8, 10, 12], L66053 = [1, 2, 3, 4, 6, 7, 10, 12, 12], = [1, 2, 3, 4, 7, 8, 8, 8, 10], L66115 = [1, 2, 3, 4, 7, 8, 8, 10, 12], L66123 = [1, 2, 3, 4, 7, 8, 10, 12, 12], = [1, 2, 3, 4, 7, 10, 12, 12, 12], L66221 = [1, 2, 3, 5, 6, 6, 6, 6, 10], L66225 = [1, 2, 3, 5, 6, 6, 6, 7, 9], = [1, 2, 3, 5, 6, 6, 6, 8, 10], L66236 = [1, 2, 3, 5, 6, 6, 6, 9, 11], L66239 = [1, 2, 3, 5, 6, 6, 6, 10, 12], = [1, 2, 3, 5, 6, 6, 7, 8, 9], L66250 = [1, 2, 3, 5, 6, 6, 7, 9, 12], L66257 = [1, 2, 3, 5, 6, 6, 8, 8, 10], = [1, 2, 3, 5, 6, 6, 8, 9, 11], L66265 = [1, 2, 3, 5, 6, 6, 8, 10, 12], L66271 = [1, 2, 3, 5, 6, 6, 9, 11, 12], = [1, 2, 3, 5, 6, 6, 10, 12, 12], L66278 = [1, 2, 3, 5, 6, 7, 8, 8, 9], L66285 = [1, 2, 3, 5, 6, 7, 8, 9, 12], = [1, 2, 3, 5, 6, 7, 9, 10, 11], L66295 = [1, 2, 3, 5, 6, 7, 9, 12, 12], L66302 = [1, 2, 3, 5, 6, 8, 8, 8, 10], = [1, 2, 3, 5, 6, 8, 8, 9, 11], L66310 = [1, 2, 3, 5, 6, 8, 8, 10, 12], L66316 = [1, 2, 3, 5, 6, 8, 9, 11, 12], = [1, 2, 3, 5, 6, 8, 10, 12, 12], L66326 = [1, 2, 3, 5, 6, 9, 11, 12, 12], L66329 = [1, 2, 3, 5, 6, 10, 12, 12, 12], = [1, 2, 3, 5, 7, 8, 8, 8, 9], L66340 = [1, 2, 3, 5, 7, 8, 8, 9, 12], L66347 = [1, 2, 3, 5, 7, 8, 9, 10, 11], = [1, 2, 3, 5, 7, 8, 9, 11, 12], L66350 = [1, 2, 3, 5, 7, 8, 9, 12, 12], L66358 = [1, 2, 3, 5, 7, 9, 10, 11, 12], = [1, 2, 3, 5, 7, 9, 12, 12, 12], L66368 = [1, 2, 3, 5, 8, 8, 8, 8, 10], L66373 = [1, 2, 3, 5, 8, 8, 8, 9, 11], = [1, 2, 3, 5, 8, 8, 8, 10, 12], L66382 = [1, 2, 3, 5, 8, 8, 9, 11, 12], L66385 = [1, 2, 3, 5, 8, 8, 10, 12, 12], = [1, 2, 3, 5, 8, 9, 11, 12, 12], L66395 = [1, 2, 3, 5, 8, 10, 12, 12, 12], L66403 = [1, 2, 3, 5, 9, 11, 12, 12, 12], = [1, 2, 3, 5, 10, 12, 12, 12, 12], L66418 = [1, 2, 3, 6, 6, 6, 6, 7, 10], L66437 = [1, 2, 3, 6, 6, 6, 7, 8, 10], = [1, 2, 3, 6, 6, 6, 7, 10, 12], L66477 = [1, 2, 3, 6, 6, 7, 8, 8, 10], L66483 = [1, 2, 3, 6, 6, 7, 8, 10, 12], = [1, 2, 3, 6, 6, 7, 10, 12, 12], L66547 = [1, 2, 3, 6, 7, 8, 8, 8, 10], L66553 = [1, 2, 3, 6, 7, 8, 8, 10, 12], = [1, 2, 3, 6, 7, 8, 10, 12, 12], L66571 = [1, 2, 3, 6, 7, 10, 12, 12, 12], L66657 = [1, 2, 3, 7, 8, 8, 8, 8, 10], = [1, 2, 3, 7, 8, 8, 8, 10, 12], L66671 = [1, 2, 3, 7, 8, 8, 10, 12, 12], L66681 = [1, 2, 3, 7, 8, 10, 12, 12, 12], = [1, 2, 3, 7, 10, 12, 12, 12, 12], L66826 = [1, 2, 4, 4, 4, 4, 4, 5, 7], L66830 = [1, 2, 4, 4, 4, 4, 4, 5, 11], = [1, 2, 4, 4, 4, 4, 5, 6, 7], L66861 = [1, 2, 4, 4, 4, 4, 5, 6, 11], L66863 = [1, 2, 4, 4, 4, 4, 5, 7, 8], = [1, 2, 4, 4, 4, 4, 5, 7, 12], L66871 = [1, 2, 4, 4, 4, 4, 5, 8, 11], L66876 = [1, 2, 4, 4, 4, 4, 5, 11, 12], = [1, 2, 4, 4, 4, 5, 6, 6, 7], L66942 = [1, 2, 4, 4, 4, 5, 6, 6, 11], L66944 = [1, 2, 4, 4, 4, 5, 6, 7, 8], = [1, 2, 4, 4, 4, 5, 6, 7, 12], L66952 = [1, 2, 4, 4, 4, 5, 6, 8, 11], L66957 = [1, 2, 4, 4, 4, 5, 6, 11, 12], = [1, 2, 4, 4, 4, 5, 7, 8, 8], L66963 = [1, 2, 4, 4, 4, 5, 7, 8, 12], L66969 = [1, 2, 4, 4, 4, 5, 7, 12, 12], = [1, 2, 4, 4, 4, 5, 8, 8, 11], L66978 = [1, 2, 4, 4, 4, 5, 8, 11, 12], L66984 = [1, 2, 4, 4, 4, 5, 11, 12, 12], = [1, 2, 4, 4, 5, 6, 6, 6, 7], L67111 = [1, 2, 4, 4, 5, 6, 6, 6, 11], L67113 = [1, 2, 4, 4, 5, 6, 6, 7, 8], = [1, 2, 4, 4, 5, 6, 6, 7, 12], L67121 = [1, 2, 4, 4, 5, 6, 6, 8, 11], L67126 = [1, 2, 4, 4, 5, 6, 6, 11, 12], = [1, 2, 4, 4, 5, 6, 7, 8, 8], L67132 = [1, 2, 4, 4, 5, 6, 7, 8, 12], L67138 = [1, 2, 4, 4, 5, 6, 7, 12, 12], = [1, 2, 4, 4, 5, 6, 8, 8, 11], L67147 = [1, 2, 4, 4, 5, 6, 8, 11, 12], L67153 = [1, 2, 4, 4, 5, 6, 11, 12, 12], = [1, 2, 4, 4, 5, 7, 8, 8, 8], L67159 = [1, 2, 4, 4, 5, 7, 8, 8, 12], L67162 = [1, 2, 4, 4, 5, 7, 8, 10, 11], = [1, 2, 4, 4, 5, 7, 8, 12, 12], L67172 = [1, 2, 4, 4, 5, 7, 12, 12, 12], L67176 = [1, 2, 4, 4, 5, 8, 8, 8, 11], = [1, 2, 4, 4, 5, 8, 8, 11, 12], L67187 = [1, 2, 4, 4, 5, 8, 11, 12, 12], L67194 = [1, 2, 4, 4, 5, 11, 12, 12, 12], = [1, 2, 4, 5, 6, 6, 6, 6, 7], L67417 = [1, 2, 4, 5, 6, 6, 6, 6, 11], L67419 = [1, 2, 4, 5, 6, 6, 6, 7, 8], = [1, 2, 4, 5, 6, 6, 6, 7, 12], L67427 = [1, 2, 4, 5, 6, 6, 6, 8, 11], L67432 = [1, 2, 4, 5, 6, 6, 6, 11, 12], = [1, 2, 4, 5, 6, 6, 7, 8, 8], L67438 = [1, 2, 4, 5, 6, 6, 7, 8, 12], L67444 = [1, 2, 4, 5, 6, 6, 7, 12, 12], = [1, 2, 4, 5, 6, 6, 8, 8, 11], L67453 = [1, 2, 4, 5, 6, 6, 8, 11, 12], L67459 = [1, 2, 4, 5, 6, 6, 11, 12, 12], = [1, 2, 4, 5, 6, 7, 8, 8, 8], L67465 = [1, 2, 4, 5, 6, 7, 8, 8, 12], L67468 = [1, 2, 4, 5, 6, 7, 8, 10, 11], = [1, 2, 4, 5, 6, 7, 8, 12, 12], L67478 = [1, 2, 4, 5, 6, 7, 12, 12, 12], L67482 = [1, 2, 4, 5, 6, 8, 8, 8, 11], = [1, 2, 4, 5, 6, 8, 8, 11, 12], L67493 = [1, 2, 4, 5, 6, 8, 11, 12, 12], L67500 = [1, 2, 4, 5, 6, 11, 12, 12, 12], = [1, 2, 4, 5, 7, 8, 8, 8, 8], L67506 = [1, 2, 4, 5, 7, 8, 8, 8, 12], L67509 = [1, 2, 4, 5, 7, 8, 8, 10, 11],
280
L67512 L67527 L67542 L67767 L67923 L67936 L67948 L67963 L67975 L67991 L68006 L68023 L68040 L68061 L68073 L68097 L68112 L68136 L69199 L69296 L69371 L69465 L69504 L69579 L69648 L69769 L69801 L69832 L69880 L69903 L69934 L69974 L70046 L70069 L70093 L70114 L70167 L70231 L70243 L70348 L70371 L70400 L70419 L70435 L70450 L70481 L70521 L70585 L70683
EMILIO A. LAURET
= [1, 2, 4, 5, 7, 8, 8, 12, 12], L67516 = [1, 2, 4, 5, 7, 8, 10, 11, 12], L67519 = [1, 2, 4, 5, 7, 8, 12, 12, 12], = [1, 2, 4, 5, 7, 12, 12, 12, 12], L67531 = [1, 2, 4, 5, 8, 8, 8, 8, 11], L67536 = [1, 2, 4, 5, 8, 8, 8, 11, 12], = [1, 2, 4, 5, 8, 8, 11, 12, 12], L67549 = [1, 2, 4, 5, 8, 11, 12, 12, 12], L67557 = [1, 2, 4, 5, 11, 12, 12, 12, 12], = [1, 2, 4, 6, 10, 10, 10, 11, 12], L67917 = [1, 2, 5, 6, 6, 6, 6, 6, 7], L67921 = [1, 2, 5, 6, 6, 6, 6, 6, 11], = [1, 2, 5, 6, 6, 6, 6, 7, 8], L67927 = [1, 2, 5, 6, 6, 6, 6, 7, 12], L67931 = [1, 2, 5, 6, 6, 6, 6, 8, 11], = [1, 2, 5, 6, 6, 6, 6, 11, 12], L67938 = [1, 2, 5, 6, 6, 6, 7, 8, 8], L67942 = [1, 2, 5, 6, 6, 6, 7, 8, 12], = [1, 2, 5, 6, 6, 6, 7, 12, 12], L67952 = [1, 2, 5, 6, 6, 6, 8, 8, 11], L67957 = [1, 2, 5, 6, 6, 6, 8, 11, 12], = [1, 2, 5, 6, 6, 6, 11, 12, 12], L67965 = [1, 2, 5, 6, 6, 7, 8, 8, 8], L67969 = [1, 2, 5, 6, 6, 7, 8, 8, 12], = [1, 2, 5, 6, 6, 7, 8, 12, 12], L67982 = [1, 2, 5, 6, 6, 7, 12, 12, 12], L67986 = [1, 2, 5, 6, 6, 8, 8, 8, 11], = [1, 2, 5, 6, 6, 8, 8, 11, 12], L67997 = [1, 2, 5, 6, 6, 8, 11, 12, 12], L68004 = [1, 2, 5, 6, 6, 11, 12, 12, 12], = [1, 2, 5, 6, 7, 8, 8, 8, 8], L68010 = [1, 2, 5, 6, 7, 8, 8, 8, 12], L68016 = [1, 2, 5, 6, 7, 8, 8, 12, 12], = [1, 2, 5, 6, 7, 8, 12, 12, 12], L68031 = [1, 2, 5, 6, 7, 12, 12, 12, 12], L68035 = [1, 2, 5, 6, 8, 8, 8, 8, 11], = [1, 2, 5, 6, 8, 8, 8, 11, 12], L68046 = [1, 2, 5, 6, 8, 8, 11, 12, 12], L68053 = [1, 2, 5, 6, 8, 11, 12, 12, 12], = [1, 2, 5, 6, 11, 12, 12, 12, 12], L68063 = [1, 2, 5, 7, 8, 8, 8, 8, 8], L68067 = [1, 2, 5, 7, 8, 8, 8, 8, 12], = [1, 2, 5, 7, 8, 8, 8, 12, 12], L68080 = [1, 2, 5, 7, 8, 8, 12, 12, 12], L68088 = [1, 2, 5, 7, 8, 12, 12, 12, 12], = [1, 2, 5, 7, 12, 12, 12, 12, 12], L68101 = [1, 2, 5, 8, 8, 8, 8, 8, 11], L68106 = [1, 2, 5, 8, 8, 8, 8, 11, 12], = [1, 2, 5, 8, 8, 8, 11, 12, 12], L68119 = [1, 2, 5, 8, 8, 11, 12, 12, 12], L68127 = [1, 2, 5, 8, 11, 12, 12, 12, 12], = [1, 2, 5, 11, 12, 12, 12, 12, 12], L69014 = [1, 3, 3, 3, 3, 5, 9, 9, 9], L69087 = [1, 3, 3, 3, 3, 7, 9, 9, 9], = [1, 3, 3, 3, 4, 4, 5, 9, 9], L69231 = [1, 3, 3, 3, 4, 4, 7, 9, 9], L69278 = [1, 3, 3, 3, 4, 5, 6, 9, 9], = [1, 3, 3, 3, 4, 5, 8, 9, 9], L69303 = [1, 3, 3, 3, 4, 5, 9, 9, 12], L69335 = [1, 3, 3, 3, 4, 6, 7, 9, 9], = [1, 3, 3, 3, 4, 7, 8, 9, 9], L69375 = [1, 3, 3, 3, 4, 7, 9, 9, 12], L69447 = [1, 3, 3, 3, 5, 6, 6, 9, 9], = [1, 3, 3, 3, 5, 6, 8, 9, 9], L69472 = [1, 3, 3, 3, 5, 6, 9, 9, 12], L69497 = [1, 3, 3, 3, 5, 8, 8, 9, 9], = [1, 3, 3, 3, 5, 8, 9, 9, 12], L69511 = [1, 3, 3, 3, 5, 9, 9, 12, 12], L69543 = [1, 3, 3, 3, 6, 6, 7, 9, 9], = [1, 3, 3, 3, 6, 7, 8, 9, 9], L69583 = [1, 3, 3, 3, 6, 7, 9, 9, 12], L69644 = [1, 3, 3, 3, 7, 8, 8, 9, 9], = [1, 3, 3, 3, 7, 8, 9, 9, 12], L69653 = [1, 3, 3, 3, 7, 9, 9, 12, 12], L69758 = [1, 3, 3, 4, 4, 4, 4, 5, 9], = [1, 3, 3, 4, 4, 4, 4, 7, 9], L69788 = [1, 3, 3, 4, 4, 4, 5, 6, 9], L69796 = [1, 3, 3, 4, 4, 4, 5, 8, 9], = [1, 3, 3, 4, 4, 4, 5, 9, 12], L69812 = [1, 3, 3, 4, 4, 4, 6, 7, 9], L69829 = [1, 3, 3, 4, 4, 4, 7, 8, 9], = [1, 3, 3, 4, 4, 4, 7, 9, 12], L69867 = [1, 3, 3, 4, 4, 5, 6, 6, 9], L69875 = [1, 3, 3, 4, 4, 5, 6, 8, 9], = [1, 3, 3, 4, 4, 5, 6, 9, 12], L69893 = [1, 3, 3, 4, 4, 5, 8, 8, 9], L69898 = [1, 3, 3, 4, 4, 5, 8, 9, 12], = [1, 3, 3, 4, 4, 5, 9, 12, 12], L69914 = [1, 3, 3, 4, 4, 6, 6, 7, 9], L69931 = [1, 3, 3, 4, 4, 6, 7, 8, 9], = [1, 3, 3, 4, 4, 6, 7, 9, 12], L69967 = [1, 3, 3, 4, 4, 7, 8, 8, 9], L69970 = [1, 3, 3, 4, 4, 7, 8, 9, 12], = [1, 3, 3, 4, 4, 7, 9, 12, 12], L70033 = [1, 3, 3, 4, 5, 6, 6, 6, 9], L70041 = [1, 3, 3, 4, 5, 6, 6, 8, 9], = [1, 3, 3, 4, 5, 6, 6, 9, 12], L70059 = [1, 3, 3, 4, 5, 6, 8, 8, 9], L70064 = [1, 3, 3, 4, 5, 6, 8, 9, 12], = [1, 3, 3, 4, 5, 6, 9, 12, 12], L70081 = [1, 3, 3, 4, 5, 7, 9, 9, 11], L70088 = [1, 3, 3, 4, 5, 8, 8, 8, 9], = [1, 3, 3, 4, 5, 8, 8, 9, 12], L70098 = [1, 3, 3, 4, 5, 8, 9, 12, 12], L70103 = [1, 3, 3, 4, 5, 9, 12, 12, 12], = [1, 3, 3, 4, 6, 6, 6, 7, 9], L70131 = [1, 3, 3, 4, 6, 6, 7, 8, 9], L70134 = [1, 3, 3, 4, 6, 6, 7, 9, 12], = [1, 3, 3, 4, 6, 7, 8, 8, 9], L70170 = [1, 3, 3, 4, 6, 7, 8, 9, 12], L70174 = [1, 3, 3, 4, 6, 7, 9, 12, 12], = [1, 3, 3, 4, 7, 8, 8, 8, 9], L70234 = [1, 3, 3, 4, 7, 8, 8, 9, 12], L70238 = [1, 3, 3, 4, 7, 8, 9, 12, 12], = [1, 3, 3, 4, 7, 9, 12, 12, 12], L70335 = [1, 3, 3, 5, 6, 6, 6, 6, 9], L70343 = [1, 3, 3, 5, 6, 6, 6, 8, 9], = [1, 3, 3, 5, 6, 6, 6, 9, 12], L70361 = [1, 3, 3, 5, 6, 6, 8, 8, 9], L70366 = [1, 3, 3, 5, 6, 6, 8, 9, 12], = [1, 3, 3, 5, 6, 6, 9, 12, 12], L70390 = [1, 3, 3, 5, 6, 8, 8, 8, 9], L70395 = [1, 3, 3, 5, 6, 8, 8, 9, 12], = [1, 3, 3, 5, 6, 8, 9, 12, 12], L70405 = [1, 3, 3, 5, 6, 9, 12, 12, 12], L70417 = [1, 3, 3, 5, 7, 8, 9, 9, 11], = [1, 3, 3, 5, 7, 8, 9, 11, 12], L70423 = [1, 3, 3, 5, 7, 9, 9, 11, 12], L70430 = [1, 3, 3, 5, 8, 8, 8, 8, 9], = [1, 3, 3, 5, 8, 8, 8, 9, 12], L70440 = [1, 3, 3, 5, 8, 8, 9, 12, 12], L70445 = [1, 3, 3, 5, 8, 9, 12, 12, 12], = [1, 3, 3, 5, 9, 12, 12, 12, 12], L70461 = [1, 3, 3, 6, 6, 6, 6, 7, 9], L70478 = [1, 3, 3, 6, 6, 6, 7, 8, 9], = [1, 3, 3, 6, 6, 6, 7, 9, 12], L70514 = [1, 3, 3, 6, 6, 7, 8, 8, 9], L70517 = [1, 3, 3, 6, 6, 7, 8, 9, 12], = [1, 3, 3, 6, 6, 7, 9, 12, 12], L70578 = [1, 3, 3, 6, 7, 8, 8, 8, 9], L70581 = [1, 3, 3, 6, 7, 8, 8, 9, 12], = [1, 3, 3, 6, 7, 8, 9, 12, 12], L70590 = [1, 3, 3, 6, 7, 9, 12, 12, 12], L70680 = [1, 3, 3, 7, 8, 8, 8, 8, 9], = [1, 3, 3, 7, 8, 8, 8, 9, 12], L70687 = [1, 3, 3, 7, 8, 8, 9, 12, 12], L70692 = [1, 3, 3, 7, 8, 9, 12, 12, 12],
APPENDIX
L70698 L70839 L70846 L70869 L70879 L70887 L70910 L70945 L70955 L70970 L70979 L70989 L71009 L71044 L71102 L71113 L71128 L71147 L71156 L71167 L71186 L71221 L71280 L71289 L71378 L71389 L71404 L71423 L71432 L71452 L71461 L71469 L71492 L71527 L71536 L71593 L71684 L71693 L71825 L71835 L71850 L71859 L71878 L71893 L71907 L71916 L71937 L71946 L71955
281
= [1, 3, 3, 7, 9, 12, 12, 12, 12], L70831 = [1, 3, 4, 4, 4, 4, 4, 4, 5], L70833 = [1, 3, 4, 4, 4, 4, 4, 4, 7], = [1, 3, 4, 4, 4, 4, 4, 5, 6], L70841 = [1, 3, 4, 4, 4, 4, 4, 5, 8], L70844 = [1, 3, 4, 4, 4, 4, 4, 5, 12], = [1, 3, 4, 4, 4, 4, 4, 6, 7], L70852 = [1, 3, 4, 4, 4, 4, 4, 7, 8], L70854 = [1, 3, 4, 4, 4, 4, 4, 7, 12], = [1, 3, 4, 4, 4, 4, 5, 6, 6], L70871 = [1, 3, 4, 4, 4, 4, 5, 6, 8], L70874 = [1, 3, 4, 4, 4, 4, 5, 6, 12], = [1, 3, 4, 4, 4, 4, 5, 8, 8], L70882 = [1, 3, 4, 4, 4, 4, 5, 8, 12], L70885 = [1, 3, 4, 4, 4, 4, 5, 12, 12], = [1, 3, 4, 4, 4, 4, 6, 6, 7], L70893 = [1, 3, 4, 4, 4, 4, 6, 7, 8], L70895 = [1, 3, 4, 4, 4, 4, 6, 7, 12], = [1, 3, 4, 4, 4, 4, 7, 8, 8], L70912 = [1, 3, 4, 4, 4, 4, 7, 8, 12], L70915 = [1, 3, 4, 4, 4, 4, 7, 12, 12], = [1, 3, 4, 4, 4, 5, 6, 6, 6], L70947 = [1, 3, 4, 4, 4, 5, 6, 6, 8], L70950 = [1, 3, 4, 4, 4, 5, 6, 6, 12], = [1, 3, 4, 4, 4, 5, 6, 8, 8], L70958 = [1, 3, 4, 4, 4, 5, 6, 8, 12], L70961 = [1, 3, 4, 4, 4, 5, 6, 12, 12], = [1, 3, 4, 4, 4, 5, 8, 8, 8], L70973 = [1, 3, 4, 4, 4, 5, 8, 8, 12], L70976 = [1, 3, 4, 4, 4, 5, 8, 12, 12], = [1, 3, 4, 4, 4, 5, 12, 12, 12], L70981 = [1, 3, 4, 4, 4, 6, 6, 6, 7], L70987 = [1, 3, 4, 4, 4, 6, 6, 7, 8], = [1, 3, 4, 4, 4, 6, 6, 7, 12], L71004 = [1, 3, 4, 4, 4, 6, 7, 8, 8], L71006 = [1, 3, 4, 4, 4, 6, 7, 8, 12], = [1, 3, 4, 4, 4, 6, 7, 12, 12], L71039 = [1, 3, 4, 4, 4, 7, 8, 8, 8], L71041 = [1, 3, 4, 4, 4, 7, 8, 8, 12], = [1, 3, 4, 4, 4, 7, 8, 12, 12], L71048 = [1, 3, 4, 4, 4, 7, 12, 12, 12], L71100 = [1, 3, 4, 4, 5, 6, 6, 6, 6], = [1, 3, 4, 4, 5, 6, 6, 6, 8], L71105 = [1, 3, 4, 4, 5, 6, 6, 6, 12], L71110 = [1, 3, 4, 4, 5, 6, 6, 8, 8], = [1, 3, 4, 4, 5, 6, 6, 8, 12], L71116 = [1, 3, 4, 4, 5, 6, 6, 12, 12], L71125 = [1, 3, 4, 4, 5, 6, 8, 8, 8], = [1, 3, 4, 4, 5, 6, 8, 8, 12], L71131 = [1, 3, 4, 4, 5, 6, 8, 12, 12], L71134 = [1, 3, 4, 4, 5, 6, 12, 12, 12], = [1, 3, 4, 4, 5, 8, 8, 8, 8], L71150 = [1, 3, 4, 4, 5, 8, 8, 8, 12], L71153 = [1, 3, 4, 4, 5, 8, 8, 12, 12], = [1, 3, 4, 4, 5, 8, 12, 12, 12], L71159 = [1, 3, 4, 4, 5, 12, 12, 12, 12], L71161 = [1, 3, 4, 4, 6, 6, 6, 6, 7], = [1, 3, 4, 4, 6, 6, 6, 7, 8], L71169 = [1, 3, 4, 4, 6, 6, 6, 7, 12], L71184 = [1, 3, 4, 4, 6, 6, 7, 8, 8], = [1, 3, 4, 4, 6, 6, 7, 8, 12], L71189 = [1, 3, 4, 4, 6, 6, 7, 12, 12], L71219 = [1, 3, 4, 4, 6, 7, 8, 8, 8], = [1, 3, 4, 4, 6, 7, 8, 8, 12], L71224 = [1, 3, 4, 4, 6, 7, 8, 12, 12], L71228 = [1, 3, 4, 4, 6, 7, 12, 12, 12], = [1, 3, 4, 4, 7, 8, 8, 8, 8], L71282 = [1, 3, 4, 4, 7, 8, 8, 8, 12], L71285 = [1, 3, 4, 4, 7, 8, 8, 12, 12], = [1, 3, 4, 4, 7, 8, 12, 12, 12], L71294 = [1, 3, 4, 4, 7, 12, 12, 12, 12], L71376 = [1, 3, 4, 5, 6, 6, 6, 6, 6], = [1, 3, 4, 5, 6, 6, 6, 6, 8], L71381 = [1, 3, 4, 5, 6, 6, 6, 6, 12], L71386 = [1, 3, 4, 5, 6, 6, 6, 8, 8], = [1, 3, 4, 5, 6, 6, 6, 8, 12], L71392 = [1, 3, 4, 5, 6, 6, 6, 12, 12], L71401 = [1, 3, 4, 5, 6, 6, 8, 8, 8], = [1, 3, 4, 5, 6, 6, 8, 8, 12], L71407 = [1, 3, 4, 5, 6, 6, 8, 12, 12], L71410 = [1, 3, 4, 5, 6, 6, 12, 12, 12], = [1, 3, 4, 5, 6, 8, 8, 8, 8], L71426 = [1, 3, 4, 5, 6, 8, 8, 8, 12], L71429 = [1, 3, 4, 5, 6, 8, 8, 12, 12], = [1, 3, 4, 5, 6, 8, 12, 12, 12], L71435 = [1, 3, 4, 5, 6, 12, 12, 12, 12], L71444 = [1, 3, 4, 5, 7, 8, 9, 11, 12], = [1, 3, 4, 5, 8, 8, 8, 8, 8], L71455 = [1, 3, 4, 5, 8, 8, 8, 8, 12], L71458 = [1, 3, 4, 5, 8, 8, 8, 12, 12], = [1, 3, 4, 5, 8, 8, 12, 12, 12], L71464 = [1, 3, 4, 5, 8, 12, 12, 12, 12], L71467 = [1, 3, 4, 5, 12, 12, 12, 12, 12], = [1, 3, 4, 6, 6, 6, 6, 6, 7], L71475 = [1, 3, 4, 6, 6, 6, 6, 7, 8], L71477 = [1, 3, 4, 6, 6, 6, 6, 7, 12], = [1, 3, 4, 6, 6, 6, 7, 8, 8], L71494 = [1, 3, 4, 6, 6, 6, 7, 8, 12], L71497 = [1, 3, 4, 6, 6, 6, 7, 12, 12], = [1, 3, 4, 6, 6, 7, 8, 8, 8], L71529 = [1, 3, 4, 6, 6, 7, 8, 8, 12], L71532 = [1, 3, 4, 6, 6, 7, 8, 12, 12], = [1, 3, 4, 6, 6, 7, 12, 12, 12], L71588 = [1, 3, 4, 6, 7, 8, 8, 8, 8], L71590 = [1, 3, 4, 6, 7, 8, 8, 8, 12], = [1, 3, 4, 6, 7, 8, 8, 12, 12], L71597 = [1, 3, 4, 6, 7, 8, 12, 12, 12], L71602 = [1, 3, 4, 6, 7, 12, 12, 12, 12], = [1, 3, 4, 7, 8, 8, 8, 8, 8], L71686 = [1, 3, 4, 7, 8, 8, 8, 8, 12], L71689 = [1, 3, 4, 7, 8, 8, 8, 12, 12], = [1, 3, 4, 7, 8, 8, 12, 12, 12], L71698 = [1, 3, 4, 7, 8, 12, 12, 12, 12], L71704 = [1, 3, 4, 7, 12, 12, 12, 12, 12], = [1, 3, 5, 6, 6, 6, 6, 6, 6], L71827 = [1, 3, 5, 6, 6, 6, 6, 6, 8], L71830 = [1, 3, 5, 6, 6, 6, 6, 6, 12], = [1, 3, 5, 6, 6, 6, 6, 8, 8], L71838 = [1, 3, 5, 6, 6, 6, 6, 8, 12], L71841 = [1, 3, 5, 6, 6, 6, 6, 12, 12], = [1, 3, 5, 6, 6, 6, 8, 8, 8], L71853 = [1, 3, 5, 6, 6, 6, 8, 8, 12], L71856 = [1, 3, 5, 6, 6, 6, 8, 12, 12], = [1, 3, 5, 6, 6, 6, 12, 12, 12], L71872 = [1, 3, 5, 6, 6, 8, 8, 8, 8], L71875 = [1, 3, 5, 6, 6, 8, 8, 8, 12], = [1, 3, 5, 6, 6, 8, 8, 12, 12], L71881 = [1, 3, 5, 6, 6, 8, 12, 12, 12], L71884 = [1, 3, 5, 6, 6, 12, 12, 12, 12], = [1, 3, 5, 6, 7, 8, 9, 11, 12], L71901 = [1, 3, 5, 6, 8, 8, 8, 8, 8], L71904 = [1, 3, 5, 6, 8, 8, 8, 8, 12], = [1, 3, 5, 6, 8, 8, 8, 12, 12], L71910 = [1, 3, 5, 6, 8, 8, 12, 12, 12], L71913 = [1, 3, 5, 6, 8, 12, 12, 12, 12], = [1, 3, 5, 6, 12, 12, 12, 12, 12], L71925 = [1, 3, 5, 7, 8, 8, 9, 11, 12], L71929 = [1, 3, 5, 7, 8, 9, 11, 12, 12], = [1, 3, 5, 8, 8, 8, 8, 8, 8], L71940 = [1, 3, 5, 8, 8, 8, 8, 8, 12], L71943 = [1, 3, 5, 8, 8, 8, 8, 12, 12], = [1, 3, 5, 8, 8, 8, 12, 12, 12], L71949 = [1, 3, 5, 8, 8, 12, 12, 12, 12], L71952 = [1, 3, 5, 8, 12, 12, 12, 12, 12], = [1, 3, 5, 12, 12, 12, 12, 12, 12], L71957 = [1, 3, 6, 6, 6, 6, 6, 6, 7], L71963 = [1, 3, 6, 6, 6, 6, 6, 7, 8],
282
EMILIO A. LAURET
Table 7. (continued) m = 9 q I indexes of I-isospectral families 25 {0} {133, 146}, {141, 142}, {143, 145, 157}, {499, 514}, {504, 508}, {509, 511}, {510, 513, 516, 524}, {515, 519, 521}, {523, 563}, {529, 534}, {538, 554}, {565, 567}, {1406, 1411}, {1456, 1463}, {1655, 1660}, {1657, 1658}, {1661, 1663, 1671}, {1662, 1666}, {1664, 1668}, {1665, 1688}, {1670, 1674, 1707}, {1673, 1706, 1711, 1712, 1717}, {1677, 1691}, {1687, 1715}, {1696, 1724}, {1699, 1722}, {1719, 1740, 1774}, {1747, 1783}, {1775, 1777}, {1779, 1782, 1815}, {4321, 4326}, {4339, 4347}, {4393, 4400}, {4455, 4465}, {4750, 4752}, {4751, 4753}, {4756, 4776}, {4762, 4792}, {4765, 4838}, {4768, 4769, 4771, 4772, 4773, 4774, 4775, 4778}, {4780, 4782, 4827, 4835}, {4785, 4789}, {4787, 4840}, {4795, 4830, 4831}, {4817, 4871}, {4819, 4826}, {4820, 4869}, {4829, 4834}, {4832, 4837, 4842, 4851}, {4839, 4845, 4848}, {4841, 4865}, {4846, 4855}, {4850, 4948}, {4886, 4895}, {4899, 4938}, {4951, 4953}, {11593, 11598}, {11611, 11619}, {11638, 11647}, {11693, 11700}, {11755, 11765}, {11839, 11849}, {12218, 12220}, {12233, 12248}, {12236, 12237, 12240, 12243}, {12238, 12242}, {12239, 12241, 12244, 12252}, {12247, 12251, 12254, 12267}, {12249, 12253, 12266}, {12250, 12259},
L71965 = [1, 3, 6, 6, 6, 6, 6, 7, 12], L71980 = [1, 3, 6, 6, 6, 6, 7, 8, 8], L71982 = [1, 3, 6, 6, 6, 6, 7, 8, 12], L71985 = [1, 3, 6, 6, 6, 6, 7, 12, 12], L72015 = [1, 3, 6, 6, 6, 7, 8, 8, 8], L72017 = [1, 3, 6, 6, 6, 7, 8, 8, 12], L72020 = [1, 3, 6, 6, 6, 7, 8, 12, 12], L72024 = [1, 3, 6, 6, 6, 7, 12, 12, 12], L72076 = [1, 3, 6, 6, 7, 8, 8, 8, 8], L72078 = [1, 3, 6, 6, 7, 8, 8, 8, 12], L72081 = [1, 3, 6, 6, 7, 8, 8, 12, 12], L72085 = [1, 3, 6, 6, 7, 8, 12, 12, 12], L72090 = [1, 3, 6, 6, 7, 12, 12, 12, 12], L72172 = [1, 3, 6, 7, 8, 8, 8, 8, 8], L72174 = [1, 3, 6, 7, 8, 8, 8, 8, 12], L72177 = [1, 3, 6, 7, 8, 8, 8, 12, 12], L72181 = [1, 3, 6, 7, 8, 8, 12, 12, 12], L72186 = [1, 3, 6, 7, 8, 12, 12, 12, 12], L72192 = [1, 3, 6, 7, 12, 12, 12, 12, 12], L72313 = [1, 3, 7, 8, 8, 8, 8, 8, 8], L72315 = [1, 3, 7, 8, 8, 8, 8, 8, 12], L72318 = [1, 3, 7, 8, 8, 8, 8, 12, 12], L72322 = [1, 3, 7, 8, 8, 8, 12, 12, 12], L72327 = [1, 3, 7, 8, 8, 12, 12, 12, 12], L72333 = [1, 3, 7, 8, 12, 12, 12, 12, 12], L72340 = [1, 3, 7, 12, 12, 12, 12, 12, 12], L72978 = [1, 4, 4, 5, 6, 6, 7, 8, 11], L73355 = [1, 4, 5, 6, 6, 7, 8, 8, 11], L73357 = [1, 4, 5, 6, 6, 7, 8, 11, 12], L74986 = [2, 2, 2, 2, 3, 6, 9, 10, 10], L75093 = [2, 2, 2, 3, 3, 3, 9, 9, 10], L75371 = [2, 2, 2, 3, 6, 9, 10, 10, 10], L75604 = [2, 2, 3, 3, 3, 9, 9, 10, 10], L76064 = [2, 2, 3, 6, 8, 9, 10, 10, 12], L76568 = [2, 3, 3, 4, 4, 8, 9, 9, 10], L76639 = [2, 3, 3, 4, 8, 8, 9, 9, 10], L76645 = [2, 3, 3, 4, 8, 9, 9, 10, 12], L76749 = [2, 3, 3, 8, 8, 9, 9, 10, 12], L76755 = [2, 3, 3, 8, 9, 9, 10, 12, 12], L77267 = [3, 3, 3, 3, 4, 9, 9, 9, 9], L77302 = [3, 3, 3, 3, 8, 9, 9, 9, 9]. q = 25 : L133 = [0, 0, 0, 0, 0, 1, 2, 4, 11], L141 = [0, 0, 0, 0, 0, 1, 2, 6, 7], L142 = [0, 0, 0, 0, 0, 1, 2, 6, 8], L143 = [0, 0, 0, 0, 0, 1, 2, 6, 9], L145 = [0, 0, 0, 0, 0, 1, 2, 6, 11], L146 = [0, 0, 0, 0, 0, 1, 2, 7, 8], L157 = [0, 0, 0, 0, 0, 1, 3, 4, 9], L499 = [0, 0, 0, 0, 1, 2, 3, 4, 11], L504 = [0, 0, 0, 0, 1, 2, 3, 5, 8], L508 = [0, 0, 0, 0, 1, 2, 3, 5, 12 L509 = [0, 0, 0, 0, 1, 2, 3, 6, 7], L510 = [0, 0, 0, 0, 1, 2, 3, 6, 8], L511 = [0, 0, 0, 0, 1, 2, 3, 6, 9], L513 = [0, 0, 0, 0, 1, 2, 3, 6, 11], L514 = [0, 0, 0, 0, 1, 2, 3, 6, 12], L515 = [0, 0, 0, 0, 1, 2, 3, 7, 8], L516 = [0, 0, 0, 0, 1, 2, 3, 7, 9 L518 = [0, 0, 0, 0, 1, 2, 3, 7, 11], L519 = [0, 0, 0, 0, 1, 2, 3, 7, 12], L521 = [0, 0, 0, 0, 1, 2, 3, 8, 12], L523 = [0, 0, 0, 0, 1, 2, 3, 9, 11], L524 = [0, 0, 0, 0, 1, 2, 3, 9, 12], L529 = [0, 0, 0, 0, 1, 2, 4, 5, 7], L534 = [0, 0, 0, 0, 1, 2, 4, 5, 1 L535 = [0, 0, 0, 0, 1, 2, 4, 7, 8], L538 = [0, 0, 0, 0, 1, 2, 4, 9, 10], L554 = [0, 0, 0, 0, 1, 2, 5, 7, 8], L563 = [0, 0, 0, 0, 1, 2, 6, 7, 8], L565 = [0, 0, 0, 0, 1, 2, 6, 7, 11], L567 = [0, 0, 0, 0, 1, 2, 6, 8, 11], L1406 = [0, 0, 0, 1, 1, 4, 4, 6, L1411 = [0, 0, 0, 1, 1, 4, 4, 9, 11], L1456 = [0, 0, 0, 1, 1, 4, 6, 9, 9], L1463 = [0, 0, 0, 1, 1, 4, 6, 11, 11], L1655 = [0, 0, 0, 1, 2, 3, 4, 5, 11], L1657 = [0, 0, 0, 1, 2, 3, 4, 6, 7], L1658 = [0, 0, 0, 1, 2, 3, 4, 6, 8], L1660 = [0, 0, 0, 1, 2, 3, 4, 6, 10], L1661 = [0, 0, 0, 1, 2, 3, 4, 6, 11], L1662 = [0, 0, 0, 1, 2, 3, 4, 6, 12], L1663 = [0, 0, 0, 1, 2, 3, 4, 7, 8], L1664 = [0, 0, 0, 1, 2, 3, 4, 7, 9], L1665 = [0, 0, 0, 1, 2, 3, 4, 7, 10], L1666 = [0, 0, 0, 1, 2, 3, 4, 7, L1668 = [0, 0, 0, 1, 2, 3, 4, 8, 9], L1670 = [0, 0, 0, 1, 2, 3, 4, 8, 11], L1671 = [0, 0, 0, 1, 2, 3, 4, 8, 12],
APPENDIX
283
Table 7. (continued) m = 9 q I indexes of I-isospectral families 25 {0} {12256, 12262}, {12257, 12261, 12263, 12271, 12278, 12281}, {12258, 12340}, (cont.) {12265, 12270, 12363}, {12269, 12362, 12367, 12368, 12373}, {12274, 12344}, {12275, 12276, 12282}, {12286, 12288}, {12291, 12295}, {12323, 12403}, {12326, 12401}, {12333, 12341}, {12338, 12371}, {12347, 12397}, {12351, 12380}, {12353, 12387}, {12355, 12378}, {12375, 12430, 12488}, {12437, 12498}, {12490, 12492}, {12494, 12497, 12549}, {28096, 28101}, {28114, 28122}, {28141, 28150}, {28171, 28180}, {28226, 28233}, {28288, 28298}, {28372, 28382}, {28460, 28470}, {28917, 28919}, {28935, 28936, 28939, 28942}, {28938, 28940, 28943, 28951}, {28946, 28950, 28953, 28966}, {28948, 28952}, {28949, 28955}, {28956, 28962}, {28959, 28990}, {28960, 28970, 29016, 29018}, {28968, 29008}, {28972, 29109}, {28975, 28977, 28981, 28985, 28989}, {28976, 28979, 28983, 28984, 28986, 28987, 28988, 28992}, {28995, 28997, 29098, 29106}, {29001, 29005}, {29003, 29111}, {29011, 29101, 29102}, {29022, 29024}, {29027, 29031}, {29059, 29165}, {29062, 29163}, {29069, 29077}, {29083, 29159}, {29087, 29142}, {29089, 29149}, {29090, 29097}, {29091, 29140}, {29100, 29105}, {29103, 29108, 29113, 29122}, {29110, 29116, 29119}, {29112, 29136}, {29117, 29126}, {29121, 29278}, {29191, 29200}, {29204, 29268}, {29281, 29283}
L1673 = [0, 0, 0, 1, 2, 3, 4, 9, 11], L1674 = [0, 0, 0, 1, 2, 3, 4, 9, 12], L1677 = [0, 0, 0, 1, 2, 3, 4, 10, 12], L1687 = [0, 0, 0, 1, 2, 3, 5, 6, 8], L1688 = [0, 0, 0, 1, 2, 3, 5, 6, 9], L1691 = [0, 0, 0, 1, 2, 3, 5, 6, 12], L1696 = [0, 0, 0, 1, 2, 3, 5, 7, 12], L1699 = [0, 0, 0, 1, 2, 3, 5, 8, 12], L1706 = [0, 0, 0, 1, 2, 3, 6, 7, 8], L1707 = [0, 0, 0, 1, 2, 3, 6, 7, 9], L1711 = [0, 0, 0, 1, 2, 3, 6, 8, 12], L1712 = [0, 0, 0, 1, 2, 3, 6, 9, 11], L1715 = [0, 0, 0, 1, 2, 3, 6, 10, 12], L1717 = [0, 0, 0, 1, 2, 3, 7, 8, 11], L1719 = [0, 0, 0, 1, 2, 3, 7, 9, 10], L1722 = [0, 0, 0, 1, 2, 3, 7, 10, 12], L1724 = [0, 0, 0, 1, 2, 3, 8, 10, 12], L1740 = [0, 0, 0, 1, 2, 4, 5, 7, 12], L1747 = [0, 0, 0, 1, 2, 4, 5, 10, 11], L1774 = [0, 0, 0, 1, 2, 5, 6, 7, 8], L1775 = [0, 0, 0, 1, 2, 5, 6, 7, 10], L1777 = [0, 0, 0, 1, 2, 5, 6, 8, 10], L1779 = [0, 0, 0, 1, 2, 5, 6, 9, 10], L1782 = [0, 0, 0, 1, 2, 5, 6, 10, 11], L1783 = [0, 0, 0, 1, 2, 5, 7, 8, 10], L1815 = [0, 0, 0, 1, 3, 4, 5, 9, 10], L4321 = [0, 0, 1, 1, 4, 4, 5, 6, 11], L4326 = [0, 0, 1, 1, 4, 4, 5, 9, 11], L4330 = [0, 0, 1, 1, 4, 4, 6, 6, 9], L4332 = [0, 0, 1, 1, 4, 4, 6, 6, 11], L4339 = [0, 0, 1, 1, 4, 4, 6, 10, 11], L4340 = [0, 0, 1, 1, 4, 4, 6, 11, 11], L4347 = [0, 0, 1, 1, 4, 4, 9, 10, 11], L4348 = [0, 0, 1, 1, 4, 4, 9, 11, 11], L4393 = [0, 0, 1, 1, 4, 5, 6, 9, 9], L4400 = [0, 0, 1, 1, 4, 5, 6, 11, 11], L4455 = [0, 0, 1, 1, 4, 6, 9, 9, 10], L4465 = [0, 0, 1, 1, 4, 6, 10, 11, 11], L4750 = [0, 0, 1, 2, 3, 4, 5, 6, 11], L4751 = [0, 0, 1, 2, 3, 4, 5, 6, 12], L4752 = [0, 0, 1, 2, 3, 4, 5, 7, 8], L4753 = [0, 0, 1, 2, 3, 4, 5, 7, 9], L4755 = [0, 0, 1, 2, 3, 4, 5, 7, L4756 = [0, 0, 1, 2, 3, 4, 5, 7, 12], L4757 = [0, 0, 1, 2, 3, 4, 5, 8, 9], L4762 = [0, 0, 1, 2, 3, 4, 5, 9, 11], L4763 = [0, 0, 1, 2, 3, 4, 5, 9, 12], L4765 = [0, 0, 1, 2, 3, 4, 5, 10, 11], L4768 = [0, 0, 1, 2, 3, 4, 6, 7, 8], L4769 = [0, 0, 1, 2, 3, 4, 6, 7, 9], L4771 = [0, 0, 1, 2, 3, 4, 6, 7, 11], L4772 = [0, 0, 1, 2, 3, 4, 6, 7, 12], L4773 = [0, 0, 1, 2, 3, 4, 6, 8, 9], L4774 = [0, 0, 1, 2, 3, 4, 6, 8, 11], L4775 = [0, 0, 1, 2, 3, 4, 6, 8, 12], L4776 = [0, 0, 1, 2, 3, 4, 6, 9, 10], L4777 = [0, 0, 1, 2, 3, 4, 6, 9, 11], L4778 = [0, 0, 1, 2, 3, 4, 6, 9, 12], L4780 = [0, 0, 1, 2, 3, 4, 6, 10, 11], L4782 = [0, 0, 1, 2, 3, 4, 7, 8, 10], L4783 = [0, 0, 1, 2, 3, 4, 7, 8, 12], L4785 = [0, 0, 1, 2, 3, 4, 7, 9, 12], L4787 = [0, 0, 1, 2, 3, 4, 7, 10, 12], L4789 = [0, 0, 1, 2, 3, 4, 8, 9, 11], L4792 = [0, 0, 1, 2, 3, 4, 8, 10, 12], L4795 = [0, 0, 1, 2, 3, 4, 9, 10, 12], L4817 = [0, 0, 1, 2, 3, 5, 5, 7, 12], L4819 = [0, 0, 1, 2, 3, 5, 5, 8, 10], L4820 = [0, 0, 1, 2, 3, 5, 5, 8, 12], L4826 = [0, 0, 1, 2, 3, 5, 5, 10, 12], L4827 = [0, 0, 1, 2, 3, 5, 6, 7, 8], L4828 = [0, 0, 1, 2, 3, 5, 6, 7, 9], L4829 = [0, 0, 1, 2, 3, 5, 6, 7, 10], L4830 = [0, 0, 1, 2, 3, 5, 6, 7, 11], L4831 = [0, 0, 1, 2, 3, 5, 6, 8, 9], L4832 = [0, 0, 1, 2, 3, 5, 6, 8, 10], L4834 =
284
EMILIO A. LAURET
Table 7. (continued) m = 9 q 25 (cont.)
I {0, 1}
indexes of I-isospectral families {518, 535}, {519, 521}, {1674, 1707}, {1712, 1717}, {4330, 4332}, {4340, 4348}, {4755, 4757}, {4763, 4828}, {4772, 4773, 4774, 4778}, {4782, 4835}, {4795, 4831}, {4844, 4896}, {4845, 4848}, {11602, 11604}, {11612, 11620}, {11625, 11628}, {11639, 11648}, {12231, 12334}, {12246, 12255}, {12270, 12363}, {12271, 12278}, {12275, 12276}, {12284, 12289}, {12301, 12337}, {12368, 12373}, {28105, 28107}, {28115, 28123}, {28128, 28131}, {28142, 28151}, {28157, 28160}, {28172, 28181}, {28930, 29070}, {28945, 28954}, {28958, 28961}, {28969, 29099}, {28984, 28986, 28987, 28992}, {28997, 29106}, {29011, 29102}, {29020, 29025}, {29037, 29073}, {29115, 29201}, {29116, 29119} {0, 1, 2} {4772, 4778}, {28978, 28980}, {28984, 28992}, {28993, 28999} {0, 1, 2, 3, 4} {4777, 4783}, {12277, 12279}, {28991, 28998} {3, 4, 8} {5023, 12588, 12593}
[0, 0, 1, 2, 3, 5, 6, 9, 10], L4835 = [0, 0, 1, 2, 3, 5, 6, 9, 11], L4837 = [0, 0, 1, 2, 3, 5, 6, 10, 11], L4838 = [0, 0, 1, 2, 3, 5, 6, 10, 12], L4839 = [0, 0, 1, 2, 3, 5, 7, 8, 10], L4840 = [0, 0, 1, 2, 3, 5, 7, 8, 11], L4841 = [0, 0, 1, 2, 3, 5, 7, 8, 12], L4842 = [0, 0, 1, 2, 3, 5, 7, 9, 10], L4844 = [0, 0, 1, 2, 3, 5, 7, 10, 11], L4845 = [0, 0, 1, 2, 3, 5, 7, 10, 12], L4846 = [0, 0, 1, 2, 3, 5, 8, 9, 12], L4848 = [0, 0, 1, 2, 3, 5, 8, 10, 12], L4850 = [0, 0, 1, 2, 3, 5, 9, 10, 11], L4851 = [0, 0, 1, 2, 3, 5, 9, 10, 12], L4855 = [0, 0, 1, 2, 3, 6, 7, 8, 10], L4865 = [0, 0, 1, 2, 3, 7, 8, 10, 12], L4869 = [0, 0, 1, 2, 3, 7, 10, 10, 12], L4871 = [0, 0, 1, 2, 3, 8, 10, 10, 12], L4886 = [0, 0, 1, 2, 4, 5, 5, 7, 10], L4895 = [0, 0, 1, 2, 4, 5, 5, 10, 12], L4896 = [0, 0, 1, 2, 4, 5, 7, 8, 10], L4899 = [0, 0, 1, 2, 4, 5, 9, 10, 10], L4938 = [0, 0, 1, 2, 5, 5, 7, 8, 10], L4948 = [0, 0, 1, 2, 5, 6, 7, 8, 10], L4951 = [0, 0, 1, 2, 5, 6, 7, 10, 11], L4953 = [0, 0, 1, 2, 5, 6, 8, 10, 11], L5023 = [0, 0, 1, 4, 5, 6, 9, 10, 11], L11593 = [0, 1, 1, 4, 4, 5, 5, 6, 11], L11598 = [0, 1, 1, 4, 4, 5, 5, 9, 11], L11602 = [0, 1, 1, 4, 4, 5, 6, 6, 9], L11604 = [0, 1, 1, 4, 4, 5, 6, 6, 11], L11611 = [0, 1, 1, 4, 4, 5, 6, 10, 11], L11612 = [0, 1, 1, 4, 4, 5, 6, 11, 11], L11619 = [0, 1, 1, 4, 4, 5, 9, 10, 11], L11620 = [0, 1, 1, 4, 4, 5, 9, 11, 11], L11625 = [0, 1, 1, 4, 4, 6, 6, 9, 10], L11628 = [0, 1, 1, 4, 4, 6, 6, 10, 11], L11638 = [0, 1, 1, 4, 4, 6, 10, 10, 11], L11639 = [0, 1, 1, 4, 4, 6, 10, 11, 11], L11647 = [0, 1, 1, 4, 4, 9, 10, 10, 11], L11648 = [0, 1, 1, 4, 4, 9, 10, 11, 11], L11693 = [0, 1, 1, 4, 5, 5, 6, 9, 9], L11700 = [0, 1, 1, 4, 5, 5, 6, 11, 11], L11755 = [0, 1, 1, 4, 5, 6, 9, 9, 10], L11765 = [0, 1, 1, 4, 5, 6, 10, 11, 11], L11839 = [0, 1, 1, 4, 6, 9, 9, 10, 10], L11849 = [0, 1, 1, 4, 6, 10, 10, 11, 11], L12218 = [0, 1, 2, 3, 4, 5, 5, 6, 11], L12220 = [0, 1, 2, 3, 4, 5, 5, 7, 8], L12231 = [0, 1, 2, 3, 4, 5, 5, 9, 12], L12233 = [0, 1, 2, 3, 4, 5, 5, 10, 11], L12236 = [0, 1, 2, 3, 4, 5, 6, 7, 8], L12237 = [0, 1, 2, 3, 4, 5, 6, 7, 9], L12238 = [0, 1, 2, 3, 4, 5, 6, 7, 10], L12239 = [0, 1, 2, 3, 4, 5, 6, 7, 11], L12240 = [0, 1, 2, 3, 4, 5, 6, 7, 12], L12241 = [0, 1, 2, 3, 4, 5, 6, 8, 9], L12242 = [0, 1, 2, 3, 4, 5, 6, 8, 10], L12243 = [0, 1, 2, 3, 4, 5, 6, 8, 11], L12244 = [0, 1, 2, 3, 4, 5, 6, 8, 12], L12246 = [0, 1, 2, 3, 4, 5, 6, 9, 11], L12247 = [0, 1, 2, 3, 4, 5, 6, 9, 12], L12248 = [0, 1, 2, 3, 4, 5, 6, 10, 10], L12249 = [0, 1, 2, 3, 4, 5, 6, 10, 11], L12250 = [0, 1, 2, 3, 4, 5, 6, 10, 12], L12251 = [0, 1, 2, 3, 4, 5, 6, 11, 12], L12252 = [0, 1, 2, 3, 4, 5, 7, 8, 9], L12253 = [0, 1, 2, 3, 4, 5, 7, 8, 10], L12254 = [0, 1, 2, 3, 4, 5, 7, 8, 11], L12255 = [0, 1, 2, 3, 4, 5, 7, 8, 12], L12256 = [0, 1, 2, 3, 4, 5, 7, 9, 10], L12257 = [0, 1, 2, 3, 4, 5, 7, 9, 12], L12258 = [0, 1, 2, 3, 4, 5, 7, 10, 10], L12259 = [0, 1, 2, 3, 4, 5, 7, 10, 11], L12261 = [0, 1, 2, 3, 4, 5, 7, 11, 12], L12262 = [0, 1, 2, 3, 4, 5, 8, 9, 10], L12263 = [0, 1, 2, 3, 4, 5, 8, 9, 11], L12265 = [0, 1, 2, 3, 4, 5, 8, 10, 11], L12266 = [0, 1, 2, 3, 4, 5, 8, 10, 12], L12267 = [0, 1, 2, 3, 4, 5, 8, 11, 12], L12269 = [0, 1, 2, 3, 4, 5, 9, 10, 11], L12270 = [0, 1, 2, 3, 4, 5, 9, 10, 12], L12271 = [0, 1, 2, 3, 4, 5, 9, 11, 12], L12274 = [0, 1, 2, 3, 4, 5, 10, 10, 12], L12275 = [0, 1, 2, 3, 4, 6, 7, 8, 9], L12276 = [0, 1, 2, 3, 4, 6, 7, 8, 11], L12277 = [0, 1, 2, 3, 4, 6, 7, 8, 12], L12278 = [0, 1, 2, 3, 4, 6, 7, 9, 10], L12279 = [0, 1, 2, 3, 4, 6, 7, 9, 11], L12281 = [0, 1, 2, 3, 4, 6, 7, 10, 12], L12282 = [0, 1, 2, 3, 4, 6, 7, 11, 12], L12284 = [0, 1, 2, 3, 4, 6, 9, 10, 11], L12286 = [0, 1, 2, 3, 4, 6, 10, 10, 11], L12288 =
APPENDIX
285
[0, 1, 2, 3, 4, 7, 8, 10, 10], L12289 = [0, 1, 2, 3, 4, 7, 8, 10, 12], L12291 = [0, 1, 2, 3, 4, 7, 9, 10, 12], L12295 = [0, 1, 2, 3, 4, 8, 9, 10, 11], L12301 = [0, 1, 2, 3, 4, 9, 10, 10, 12], L12323 = [0, 1, 2, 3, 5, 5, 5, 7, 12], L12326 = [0, 1, 2, 3, 5, 5, 5, 8, 12], L12333 = [0, 1, 2, 3, 5, 5, 6, 7, 8], L12334 = [0, 1, 2, 3, 5, 5, 6, 7, 9], L12337 = [0, 1, 2, 3, 5, 5, 6, 8, 9], L12338 = [0, 1, 2, 3, 5, 5, 6, 8, 10], L12340 = [0, 1, 2, 3, 5, 5, 6, 9, 10], L12341 = [0, 1, 2, 3, 5, 5, 6, 9, 11], L12344 = [0, 1, 2, 3, 5, 5, 6, 10, 12], L12347 = [0, 1, 2, 3, 5, 5, 7, 8, 12], L12351 = [0, 1, 2, 3, 5, 5, 7, 10, 12], L12353 = [0, 1, 2, 3, 5, 5, 8, 9, 12], L12355 = [0, 1, 2, 3, 5, 5, 8, 10, 12], L12362 = [0, 1, 2, 3, 5, 6, 7, 8, 10], L12363 = [0, 1, 2, 3, 5, 6, 7, 9, 10], L12367 = [0, 1, 2, 3, 5, 6, 8, 10, 12], L12368 = [0, 1, 2, 3, 5, 6, 9, 10, 11], L12371 = [0, 1, 2, 3, 5, 6, 10, 10, 12], L12373 = [0, 1, 2, 3, 5, 7, 8, 10, 11], L12375 = [0, 1, 2, 3, 5, 7, 9, 10, 10], L12378 = [0, 1, 2, 3, 5, 7, 10, 10, 12], L12380 = [0, 1, 2, 3, 5, 8, 10, 10, 12], L12387 = [0, 1, 2, 3, 6, 7, 8, 10, 10], L12397 = [0, 1, 2, 3, 7, 8, 10, 10, 12], L12401 = [0, 1, 2, 3, 7, 10, 10, 10, 12], L12403 = [0, 1, 2, 3, 8, 10, 10, 10, 12], L12430 = [0, 1, 2, 4, 5, 5, 7, 10, 12], L12437 = [0, 1, 2, 4, 5, 5, 10, 10, 11], L12488 = [0, 1, 2, 5, 5, 6, 7, 8, 10], L12490 = [0, 1, 2, 5, 5, 6, 7, 10, 10], L12492 = [0, 1, 2, 5, 5, 6, 8, 10, 10], L12494 = [0, 1, 2, 5, 5, 6, 9, 10, 10], L12497 = [0, 1, 2, 5, 5, 6, 10, 10, 11], L12498 = [0, 1, 2, 5, 5, 7, 8, 10, 10], L12549 = [0, 1, 3, 4, 5, 5, 9, 10, 10], L12588 = [0, 1, 4, 5, 5, 6, 9, 10, 11], L12593 = [0, 1, 4, 5, 6, 9, 10, 10, 11], L28096 = [1, 1, 4, 4, 5, 5, 5, 6, 11], L28101 = [1, 1, 4, 4, 5, 5, 5, 9, 11], L28105 = [1, 1, 4, 4, 5, 5, 6, 6, 9], L28107 = [1, 1, 4, 4, 5, 5, 6, 6, 11], L28114 = [1, 1, 4, 4, 5, 5, 6, 10, 11], L28115 = [1, 1, 4, 4, 5, 5, 6, 11, 11], L28122 = [1, 1, 4, 4, 5, 5, 9, 10, 11], L28123 = [1, 1, 4, 4, 5, 5, 9, 11, 11], L28128 = [1, 1, 4, 4, 5, 6, 6, 9, 10], L28131 = [1, 1, 4, 4, 5, 6, 6, 10, 11], L28141 = [1, 1, 4, 4, 5, 6, 10, 10, 11], L28142 = [1, 1, 4, 4, 5, 6, 10, 11, 11], L28150 = [1, 1, 4, 4, 5, 9, 10, 10, 11], L28151 = [1, 1, 4, 4, 5, 9, 10, 11, 11], L28157 = [1, 1, 4, 4, 6, 6, 9, 10, 10], L28160 = [1, 1, 4, 4, 6, 6, 10, 10, 11], L28171 = [1, 1, 4, 4, 6, 10, 10, 10, 11], L28172 = [1, 1, 4, 4, 6, 10, 10, 11, 11], L28180 = [1, 1, 4, 4, 9, 10, 10, 10, 11], L28181 = [1, 1, 4, 4, 9, 10, 10, 11, 11], L28226 = [1, 1, 4, 5, 5, 5, 6, 9, 9], L28233 = [1, 1, 4, 5, 5, 5, 6, 11, 11], L28288 = [1, 1, 4, 5, 5, 6, 9, 9, 10], L28298 = [1, 1, 4, 5, 5, 6, 10, 11, 11], L28372 = [1, 1, 4, 5, 6, 9, 9, 10, 10], L28382 = [1, 1, 4, 5, 6, 10, 10, 11, 11], L28460 = [1, 1, 4, 6, 9, 9, 10, 10, 10], L28470 = [1, 1, 4, 6, 10, 10, 10, 11, 11], L28917 = [1, 2, 3, 4, 5, 5, 5, 6, 11], L28919 = [1, 2, 3, 4, 5, 5, 5, 7, 8], L28930 = [1, 2, 3, 4, 5, 5, 5, 9, 12], L28935 = [1, 2, 3, 4, 5, 5, 6, 7, 8], L28936 = [1, 2, 3, 4, 5, 5, 6, 7, 9], L28938 = [1, 2, 3, 4, 5, 5, 6, 7, 11], L28939 = [1, 2, 3, 4, 5, 5, 6, 7, 12], L28940 = [1, 2, 3, 4, 5, 5, 6, 8, 9], L28942 = [1, 2, 3, 4, 5, 5, 6, 8, 11], L28943 = [1, 2, 3, 4, 5, 5, 6, 8, 12], L28945 = [1, 2, 3, 4, 5, 5, 6, 9, 11], L28946 = [1, 2, 3, 4, 5, 5, 6, 9, 12], L28948 = [1, 2, 3, 4, 5, 5, 6, 10, 11], L28949 = [1, 2, 3, 4, 5, 5, 6, 10, 12], L28950 = [1, 2, 3, 4, 5, 5, 6, 11, 12], L28951 = [1, 2, 3, 4, 5, 5, 7, 8, 9], L28952 = [1, 2, 3, 4, 5, 5, 7, 8, 10], L28953 = [1, 2, 3, 4, 5, 5, 7, 8, 11], L28954 = [1, 2, 3, 4, 5, 5, 7, 8, 12], L28955 = [1, 2, 3, 4, 5, 5, 7, 9, 10], L28956 = [1, 2, 3, 4, 5, 5, 7, 9, 12], L28958 = [1, 2, 3, 4, 5, 5, 7, 10, 11], L28959 = [1, 2, 3, 4, 5, 5, 7, 10, 12], L28960 = [1, 2, 3, 4, 5, 5, 7, 11, 12], L28961 = [1, 2, 3, 4, 5, 5, 8, 9, 10], L28962 = [1, 2, 3, 4, 5, 5, 8, 9, 11], L28966 = [1, 2, 3, 4, 5, 5, 8, 11, 12], L28968 = [1, 2, 3, 4, 5, 5, 9, 10, 11], L28969 = [1, 2, 3, 4, 5, 5, 9, 10, 12], L28970 = [1, 2, 3, 4, 5, 5, 9, 11, 12], L28972 = [1, 2, 3, 4, 5, 5, 10, 10, 11], L28975 = [1, 2, 3, 4, 5, 6, 7, 8, 9], L28976 = [1, 2, 3, 4, 5, 6, 7, 8, 10], L28977 = [1, 2, 3, 4, 5, 6, 7, 8, 11], L28978 = [1, 2, 3, 4, 5, 6, 7, 8, 12], L28979 = [1, 2, 3, 4, 5, 6, 7, 9, 10], L28980 = [1, 2, 3, 4, 5, 6, 7, 9, 11], L28981 = [1, 2, 3, 4, 5, 6, 7, 9, 12], L28983 = [1, 2, 3, 4, 5, 6, 7, 10, 11], L28984 = [1, 2, 3, 4, 5, 6, 7, 10, 12], L28985 = [1, 2, 3, 4, 5, 6, 7, 11, 12], L28986 = [1, 2, 3, 4, 5, 6, 8, 9, 10], L28987 = [1, 2, 3, 4, 5, 6, 8, 10, 11], L28988 = [1, 2, 3, 4, 5, 6, 8, 10, 12], L28989 = [1, 2, 3, 4, 5, 6, 8, 11, 12], L28990 = [1, 2, 3, 4, 5, 6, 9, 10, 10], L28991 = [1, 2, 3, 4, 5, 6, 9, 10, 11], L28992 = [1, 2, 3, 4, 5, 6, 9, 10, 12], L28993 = [1, 2, 3, 4, 5, 6, 9, 11, 12], L28995 = [1, 2, 3, 4, 5, 6, 10, 10, 11], L28997 = [1, 2, 3, 4, 5, 7, 8, 10, 10], L28998 = [1, 2, 3, 4, 5, 7, 8, 10, 12], L28999 = [1, 2, 3, 4, 5, 7, 8, 11, 12], L29001 = [1, 2, 3, 4, 5, 7, 9, 10, 12], L29003 = [1, 2, 3, 4, 5, 7, 10, 10, 12], L29005 = [1, 2, 3, 4, 5, 8, 9, 10, 11], L29008 = [1, 2, 3, 4, 5, 8, 10, 10, 12], L29011 = [1, 2, 3, 4, 5, 9, 10, 10, 12], L29016 = [1, 2, 3, 4, 6, 7, 9, 10, 10], L29018 = [1, 2, 3, 4, 6, 7, 10, 10, 12], L29020 = [1, 2, 3, 4, 6, 9, 10, 10, 11], L29022 = [1, 2, 3, 4, 6, 10, 10, 10, 11], L29024 = [1, 2, 3, 4, 7, 8, 10, 10, 10], L29025 = [1, 2, 3, 4, 7, 8, 10, 10, 12], L29027 = [1, 2, 3, 4, 7, 9, 10, 10, 12], L29031 = [1, 2, 3, 4, 8, 9, 10, 10, 11], L29037 = [1, 2, 3, 4, 9, 10, 10, 10, 12], L29059 = [1, 2, 3, 5, 5, 5, 5, 7, 12], L29062 = [1, 2, 3, 5, 5, 5, 5, 8, 12], L29069 = [1, 2, 3, 5, 5, 5, 6, 7, 8], L29070 = [1, 2, 3, 5, 5, 5, 6, 7, 9], L29073 = [1, 2, 3, 5, 5, 5, 6, 8, 9], L29077 = [1, 2, 3, 5, 5, 5, 6, 9, 11], L29083 = [1, 2, 3, 5, 5, 5, 7, 8, 12], L29087 = [1, 2, 3, 5, 5, 5, 7, 10, 12], L29089 = [1, 2, 3, 5, 5, 5, 8, 9, 12], L29090 = [1, 2, 3, 5, 5, 5, 8, 10, 10],
286
EMILIO A. LAURET
Table 7. (continued) m = 9 q I indexes of I-isospectral families 26 {0} {39, 42}, {40, 44}, {218, 244}, {233, 282}, {246, 247}, {249, 251, 252}, {254, 263}, {257, 269}, {360, 361}, {362, 364}, {902, 961}, {952, 965}, {994, 1045}, {1020, 1088}, {1044, 1077}, {1057, 1181}, {1093, 1095}, {1099, 1104, 1105}, {1108, 1129}, {1114, 1141}, {1352, 1353, 1354}, {1355, 1356}, {1357, 1359}, {3289, 3351}, {3298, 3317}, {3323, 3345}, {3334, 3372}, {3352, 3470}, {3359, 3501}, {3368, 3661}, {3400, 3575}, {3405, 3578}, {3485, 3500}, {3544, 3586}, {3557, 3589}, {3660, 3766}, {3716, 3857}, {3764, 3835}, {3786, 4052}, {3866, 3869}, {3875, 3885, 3886}, {3890, 3931}, {3900, 3951}, {4385, 4386, 4387}, {4388, 4389}, {4390, 4392}, {7493, 7495}, {7534, 7541}, {10497, 10500, 10504}, {10501, 10503}, {10509, 10527}, {10514, 10608}, {10516, 10525}, {10524, 10531}, {10532, 10534}, {10541, 10617}, {10550, 10614}, {10551, 10552, 10963}, {10553, 10694}, {10560, 10572}, {10571, 10610}, {10578, 10615}, {10579, 10623}, {10587, 10648}, {10609, 10620}, {10630, 10679}, {10637, 10680}, {10646, 10962}, {10661, 10739}, {10675, 10974}, {10696, 11049}, {10698, 10977}, {10712, 11050}, {10730, 10971}, {10731, 11365}, {10774, 11133}, {10793, 11195}, {10800, 11199}, {11005, 11048}, {11046, 11061}, {11134, 11215}, {11156, 11219}, {11362, 11547}, {11461, 11714}, {11544, 11677}, {11577, 12077}, {11659, 11661}, {11727, 11731}, {11738, 11754, 11755}, {11760, 11831}, {11775, 11861}, {12670, 12671, 12672}, {12673, 12674}, {12675, 12677},
L29091 = [1, 2, 3, 5, 5, 5, 8, 10, 12], L29097 = [1, 2, 3, 5, 5, 5, 10, 10, 12], L29098 = [1, 2, 3, 5, 5, 6, 7, 8, 10], L29099 = [1, 2, 3, 5, 5, 6, 7, 9, 10], L29100 = [1, 2, 3, 5, 5, 6, 7, 10, 10], L29101 = [1, 2, 3, 5, 5, 6, 7, 10, 11], L29102 = [1, 2, 3, 5, 5, 6, 8, 9, 10], L29103 = [1, 2, 3, 5, 5, 6, 8, 10, 10], L29105 = [1, 2, 3, 5, 5, 6, 9, 10, 10], L29106 = [1, 2, 3, 5, 5, 6, 9, 10, 11], L29108 = [1, 2, 3, 5, 5, 6, 10, 10, 11], L29109 = [1, 2, 3, 5, 5, 6, 10, 10, 12], L29110 = [1, 2, 3, 5, 5, 7, 8, 10, 10], L29111 = [1, 2, 3, 5, 5, 7, 8, 10, 11], L29112 = [1, 2, 3, 5, 5, 7, 8, 10, 12], L29113 = [1, 2, 3, 5, 5, 7, 9, 10, 10], L29115 = [1, 2, 3, 5, 5, 7, 10, 10, 11], L29116 = [1, 2, 3, 5, 5, 7, 10, 10, 12], L29117 = [1, 2, 3, 5, 5, 8, 9, 10, 12], L29119 = [1, 2, 3, 5, 5, 8, 10, 10, 12], L29121 = [1, 2, 3, 5, 5, 9, 10, 10, 11], L29122 = [1, 2, 3, 5, 5, 9, 10, 10, 12], L29126 = [1, 2, 3, 5, 6, 7, 8, 10, 10], L29136 = [1, 2, 3, 5, 7, 8, 10, 10, 12], L29140 = [1, 2, 3, 5, 7, 10, 10, 10, 12], L29142 = [1, 2, 3, 5, 8, 10, 10, 10, 12], L29149 = [1, 2, 3, 6, 7, 8, 10, 10, 10], L29159 = [1, 2, 3, 7, 8, 10, 10, 10, 12], L29163 = [1, 2, 3, 7, 10, 10, 10, 10, 12], L29165 = [1, 2, 3, 8, 10, 10, 10, 10, 12], L29191 = [1, 2, 4, 5, 5, 5, 7, 10, 10], L29200 = [1, 2, 4, 5, 5, 5, 10, 10, 12], L29201 = [1, 2, 4, 5, 5, 7, 8, 10, 10], L29204 = [1, 2, 4, 5, 5, 9, 10, 10, 10], L29268 = [1, 2, 5, 5, 5, 7, 8, 10, 10], L29278 = [1, 2, 5, 5, 6, 7, 8, 10, 10], L29281 = [1, 2, 5, 5, 6, 7, 10, 10, 11], L29283 = [1, 2, 5, 5, 6, 8, 10, 10, 11]. q = 26 : L39 = [0, 0, 0, 0, 0, 0, 1, 3, 5], L40 = [0, 0, 0, 0, 0, 0, 1, 3, 7], L42 = [0, 0, 0, 0, 0, 0, 1, 3, 9], L44 = [0, 0, 0, 0, 0, 0, 1, 3, 11], L218 = [0, 0, 0, 0, 0, 1, 2, 7, 8], L233 = [0, 0, 0, 0, 0, 1, 2, 10, 11], L244 = [0, 0, 0, 0, 0, 1, 3, 4, 8], L246 = [0, 0, 0, 0, 0, 1, 3, 4, 10], L247 = [0, 0, 0, 0, 0, 1, 3, 4, 12], L249 = [0, 0, 0, 0, 0, 1, 3, 5, 7 L251 = [0, 0, 0, 0, 0, 1, 3, 5, 9], L252 = [0, 0, 0, 0, 0, 1, 3, 5, 11], L254 = [0, 0, 0, 0, 0, 1, 3, 5, 13], L257 = [0, 0, 0, 0, 0, 1, 3, 7, 13], L263 = [0, 0, 0, 0, 0, 1, 3, 9, 13], L269 = [0, 0, 0, 0, 0, 1, 3, 11, 13], L282 = [0, 0, 0, 0, 0, 1, 4, 5, 8], L360 = [0, 0, 0, 0, 0, 2, 4, 6, 13], L361 = [0, 0, 0, 0, 0, 2, 4, 8, 13], L362 = [0, 0, 0, 0, 0, 2, 4, 10, L364 = [0, 0, 0, 0, 0, 2, 6, 8, 13], L902 = [0, 0, 0, 0, 1, 2, 3, 9, 12], L952 = [0, 0, 0, 0, 1, 2, 4, 10, 11], L961 = [0, 0, 0, 0, 1, 2, 5, 6, 7], L965 = [0, 0, 0, 0, 1, 2, 5, 6, 12], L994 = [0, 0, 0, 0, 1, 2, 6, 7, 8], L1020 = [0, 0, 0, 0, 1, 2, 7, 8, 13], L1044 = [0, 0, 0, 0, 1, 2, 9, 10, 11], L1045 = [0, 0, 0, 0, 1, 2, 9, 10, 12], L1057 = [0, 0, 0, 0, 1, 2, 10, 11, 13], L1077 = [0, 0, 0, 0, 1, 3, 4, 5, 8], L1088 = [0, 0, 0, 0, 1, 3, 4, 8, 13], L1093 = [0, 0, 0, 0, 1, 3, 4, 10, 13], L1095 = [0, 0, 0, 0, 1, 3, 4, 12, 13], L1099 = [0, 0, 0, 0, 1, 3, 5, 7, 13], L1104 =
APPENDIX
287
Table 7. (continued) m = 9 q I indexes of I-isospectral families 26 {0} {22588, 22592}, {22621, 22625}, {22622, 22642}, {22634, 22651}, (cont.) {22682, 22744}, {22699, 22714}, {29654, 29656, 29659}, {29655, 29679}, {29661, 29664, 29666, 29686}, {29665, 29677, 29688}, {29669, 29751}, {29671, 29678, 29752}, {29672, 29681, 29690}, {29682, 29894}, {29684, 29689}, {29698, 29735}, {29699, 29717, 29734, 29809}, {29701, 29742}, {29702, 29765}, {29705, 29743}, {29710, 29764, 29799, 29912}, {29715, 29897}, {29718, 29737}, {29731, 29732, 29758}, {29733, 29753}, {29757, 29761}, {29774, 29840}, {29775, 29915}, {29791, 29909}, {29793, 30587}, {29794, 29795, 30591}, {29796, 30042}, {29798, 29896}, {29811, 29834}, {29831, 29895}, {29832, 29901}, {29846, 29911}, {29847, 29922}, {29856, 29964}, {29862, 29965}, {29900, 29918}, {29934, 30117}, {29935, 30014}, {29943, 30015}, {29962, 30590}, {29984, 30120}, {30007, 30047}, {30008, 30611}, {30048, 30758}, {30051, 30615}, {30074, 30759}, {30105, 30604}, {30107, 30607}, {30108, 31305}, {30181, 30898}, {30210, 31004}, {30219, 31008}, {30657, 30756}, {30754, 30780}, {30899, 31034}, {30932, 31039}, {31300, 31592}, {31457, 31871}, {31588, 31813}, {31634, 32505}, {31788, 31791}, {31889, 31894}, {31902, 31926, 31927}, {31933, 32046}, {31954, 32088}, {33402, 33405}, {33488, 33489, 33490}, {33491, 33492}, {33493, 33495}, {55186, 55246}, {61161, 61167}, {61196, 61203, 61207, 61227}, {61204, 61275}, {61228, 61234}, {61230, 61276}, {61248, 61281}, {61253, 61298}, {61367, 61491}, {61396, 61423}, {73333, 74278}, {75938, 75940, 75945, 75947}, {75939, 75941, 75948, 75959, 75961, 75963}, {75943, 75950, 75960, 75973, 75993, 76004}, {75944, 75992}, {75949, 75952, 75962}, {75951, 75997}, {75964, 76117}, {75966, 75971, 75995, 76077}, {75967, 75972, 75975, 76006},
[0, 0, 0, 0, 1, 3, 5, 9, 13], L1105 = [0, 0, 0, 0, 1, 3, 5, 11, 13], L1108 = [0, 0, 0, 0, 1, 3, 5, 13, 13], L1114 = [0, 0, 0, 0, 1, 3, 7, 13, 13], L1129 = [0, 0, 0, 0, 1, 3, 9, 13, 13], L1141 = [0, 0, 0, 0, 1, 3, 11, 13, 13], L1181 = [0, 0, 0, 0, 1, 4, 5, 8, 13], L1352 = [0, 0, 0, 0, 2, 4, 6, 8, 13], L1353 = [0, 0, 0, 0, 2, 4, 6, 10, 13], L1354 = [0, 0, 0, 0, 2, 4, 6, 12, 13], L1355 = [0, 0, 0, 0, 2, 4, 6, 13, 13], L1356 = [0, 0, 0, 0, 2, 4, 8, 13, 13], L1357 = [0, 0, 0, 0, 2, 4, 10, 13, 13], L1359 = [0, 0, 0, 0, 2, 6, 8, 13, 13], L3289 = [0, 0, 0, 1, 2, 3, 4, 7, 8], L3298 = [0, 0, 0, 1, 2, 3, 4, 8, 11], L3317 = [0, 0, 0, 1, 2, 3, 5, 6, 10], L3323 = [0, 0, 0, 1, 2, 3, 5, 7, 10], L3334 = [0, 0, 0, 1, 2, 3, 5, 9, 12], L3345 = [0, 0, 0, 1, 2, 3, 6, 7, 9], L3351 = [0, 0, 0, 1, 2, 3, 6, 8, 9], L3352 = [0, 0, 0, 1, 2, 3, 6, 8, L3359 = [0, 0, 0, 1, 2, 3, 6, 10, 11], L3368 = [0, 0, 0, 1, 2, 3, 7, 8, 10], L3372 = [0, 0, 0, 1, 2, 3, 7, 9, 10], L3400 = [0, 0, 0, 1, 2, 3, 9, 10, 12], L3405 = [0, 0, 0, 1, 2, 3, 9, 12, 13], L3470 = [0, 0, 0, 1, 2, 4, 5, 6, 12], L3485 = [0, 0, 0, 1, 2, 4, 5, 10, 12], L3500 = [0, 0, 0, 1, 2, 4, 6, 7, 8], L3501 = [0, 0, 0, 1, 2, 4, 6, 7, 9], L3544 = [0, 0, 0, 1, 2, 4, 9, 10, 11], L3557 = [0, 0, 0, 1, 2, 4, 10, 11, 13], L3575 = [0, 0, 0, 1, 2, 5, 6, 7, 8], L3578 = [0, 0, 0, 1, 2, 5, 6, 7, 13], L3586 = [0, 0, 0, 1, 2, 5, 6, 11, 12], L3589 = [0, 0, 0, 1, 2, 5, 6, 12, 13], L3660 = [0, 0, 0, 1, 2, 6, 7, 8, 13], L3661 = [0, 0, 0, 1, 2, 6, 7, 9, 10], L3716 = [0, 0, 0, 1, 2, 7, 8, 13, 13], L3764 = [0, 0, 0, 1, 2, 9, 10, 11, 13], L3766 = [0, 0, 0, 1, 2, 9, 10, 12, 13], L3786 = [0, 0, 0, 1, 2, 10, 11, 13, 13], L3835 = [0, 0, 0, 1, 3, 4, 5, 8, 13], L3857 = [0, 0, 0, 1, 3, 4, 8, 13, 13], L3866 = [0, 0, 0, 1, 3, 4, 10, 13, 13],
288
EMILIO A. LAURET
Table 7. (continued) m = 9 q I indexes of I-isospectral families 26 {0} {75974, 75994, 76008}, {75979, 76118}, {75982, 75996, 76119}, (cont.) {75983, 75999, 76010}, {76000, 76345}, {76001, 76346}, {76003, 76009}, {76026, 76033, 76086, 76095}, {76028, 76045, 76085, 76194}, {76029, 76088}, {76031, 76058, 76087, 76210}, {76034, 76099}, {76036, 76142}, {76040, 76100}, {76048, 76141, 76196, 76373}, {76055, 76349}, {76059, 76090}, {76080, 76125}, {76081, 76082, 76131}, {76083, 76120}, {76129, 76135}, {76157, 76265}, {76158, 76377}, {76182, 76368}, {76186, 77564}, {76187, 76188, 77568}, {76189, 76567}, {76195, 76348}, {76212, 76253}, {76249, 76347}, {76250, 76353}, {76273, 76371}, {76274, 76385}, {76290, 76447}, {76298, 76448}, {76352, 76380}, {76403, 76683}, {76404, 76519}, {76412, 76520}, {76445, 77567}, {76473, 76686}, {76511, 76578}, {76512, 77598}, {76579, 77856}, {76583, 77603}, {76617, 77857}, {76667, 77589}, {76669, 77593}, {76670, 78729}, {76784, 78070}, {76825, 78235}, {76836, 78239}, {77661, 77853}, {77851, 77893}, {78071, 78277}, {78117, 78283}, {78722, 79153}, {78954, 79590}, {79148, 79504}, {79209, 80634}, {79471, 79475}, {79614, 79620}, {79629, 79662, 79663}, {79670, 79839}, {79698, 79895}, {82085, 82089}, {82086, 82087}, {82090, 82101}, {82091, 82097}, {82104, 82125}, {82188, 82189, 82190}, {82191, 82192}, {82193, 82195} L3869 = [0, 0, 0, 1, 3, 4, 12, 13, 13], L3875 = [0, 0, 0, 1, 3, 5, 7, 13, 13], L3885 = [0, 0, 0, 1, 3, 5, 9, 13, 13], L3886 = [0, 0, 0, 1, 3, 5, 11, 13, 13], L3890 = [0, 0, 0, 1, 3, 5, 13, 13, 13], L3900 = [0, 0, 0, 1, 3, 7, 13, 13, 13], L3931 = [0, 0, 0, 1, 3, 9, 13, 13, 13], L3951 = [0, 0, 0, 1, 3, 11, 13, 13, 13], L4052 = [0, 0, 0, 1, 4, 5, 8, 13, 13], L4385 = [0, 0, 0, 2, 4, 6, 8, 13, 13], L4386 = [0, 0, 0, 2, 4, 6, 10, 13, 13], L4387 = [0, 0, 0, 2, 4, 6, 12, 13, 13], L4388 = [0, 0, 0, 2, 4, 6, 13, 13, 13], L4389 = [0, 0, 0, 2, 4, 8, 13, 13, 13], L4390 = [0, 0, 0, 2, 4, 10, 13, 13, 13], L4392 = [0, 0, 0, 2, 6, 8, 13, 13, 13], L7493 = [0, 0, 1, 1, 3, 3, 4, 9, 10], L7495 = [0, 0, 1, 1, 3, 3, 4, 9, 12], L7534 = [0, 0, 1, 1, 3, 3, 5, 11, 11], L7541 = [0, 0, 1, 1, 3, 3, 7, 7, 9], L10497 = [0, 0, 1, 2, 3, 4, 5, 6, 11], L10500 = [0, 0, 1, 2, 3, 4, 5, 7, 8], L10501 = [0, 0, 1, 2, 3, 4, 5, 7, 9], L10503 = [0, 0, 1, 2, 3, 4, 5, 7, 11], L10504 = [0, 0, 1, 2, 3, 4, 5, 7, 12], L10509 = [0, 0, 1, 2, 3, 4, 5, 8, 11], L10514 = [0, 0, 1, 2, 3, 4, 5, 9, 12], L10516 = [0, 0, 1, 2, 3, 4, 5, 10, 11], L10517 = [0, 0, 1, 2, 3, 4, 5, 10, 12], L10524 = [0, 0, 1, 2, 3, 4, 6, 7, 8], L10525 = [0, 0, 1, 2, 3, 4, 6, 7, 9], L10527 = [0, 0, 1, 2, 3, 4, 6, 7, 11], L10531 = [0, 0, 1, 2, 3, 4, 6, 8, 9], L10532 = [0, 0, 1, 2, 3, 4, 6, 8, 10], L10534 = [0, 0, 1, 2, 3, 4, 6, 8, 12], L10536 = [0, 0, 1, 2, 3, 4, 6, 9, 10], L10541 = [0, 0, 1, 2, 3, 4, 6, 10, 11], L10550 = [0, 0, 1, 2, 3, 4, 7, 8, 9], L10551 = [0, 0, 1, 2, 3, 4, 7, 8, 10], L10552 = [0, 0, 1, 2, 3, 4, 7, 8, 12], L10553 = [0, 0, 1, 2, 3, 4, 7, 8, 13], L10554 = [0, 0, 1, 2, 3, 4, 7, 9, 10], L10560 = [0, 0, 1, 2, 3, 4, 7, 10, 12], L10571 = [0, 0, 1, 2, 3, 4, 8, 9, 11], L10572 = [0, 0, 1, 2, 3, 4, 8, 9, 12], L10578 = [0, 0, 1, 2, 3, 4, 8, 11, 12], L10579 = [0, 0, 1, 2, 3, 4, 8, 11, 13], L10587 = [0, 0, 1, 2, 3, 4, 9, 11, 12], L10608 = [0, 0, 1, 2, 3, 5, 6, 7, 8], L10609 = [0, 0, 1, 2, 3, 5, 6, 7, 9], L10610 = [0, 0, 1, 2, 3, 5, 6, 7, 10], L10614 = [0, 0, 1, 2, 3, 5, 6, 8, 9], L10615 = [0, 0, 1, 2, 3, 5, 6, 8, 10], L10616 = [0, 0, 1, 2, 3, 5, 6, 8, 11], L10617 = [0, 0, 1, 2, 3, 5, 6, 8, 12], L10620 = [0, 0, 1, 2, 3, 5, 6, 9, 11], L10623 = [0, 0, 1, 2, 3, 5, 6, 10, 13], L10630 = [0, 0, 1, 2, 3, 5, 7, 8, 10], L10637 = [0, 0, 1, 2, 3, 5, 7, 10, 13], L10646 = [0, 0, 1, 2, 3, 5, 8, 9, 12], L10648 = [0, 0, 1, 2, 3, 5, 8, 10, 11], L10661 = [0, 0, 1, 2, 3, 5, 9, 12, 13], L10675 = [0, 0, 1, 2, 3, 6, 7, 8, 10], L10679 = [0, 0, 1, 2, 3, 6, 7, 9, 10], L10680 = [0, 0, 1, 2, 3, 6, 7, 9, 13], L10694 = [0, 0, 1, 2, 3, 6, 8, 9, 13], L10696 = [0, 0, 1, 2, 3, 6, 8, 10, 11], L10698 = [0, 0, 1, 2, 3, 6, 8, 10, 13], L10712 = [0, 0, 1, 2, 3, 6, 10, 11, 13], L10730 = [0, 0, 1, 2, 3, 7, 8, 10, 12], L10731 = [0, 0, 1, 2, 3, 7, 8, 10, 13], L10739 = [0, 0, 1, 2, 3, 7, 9, 10, 13],
APPENDIX
289
Table 7. (continued) m = 9 q 26 (cont.)
L10774 L10962 L10974 L11046 L11050 L11133 L11195 L11219 L11461 L11577 L11677 L11731 L11754 L11775 L12077 L12671 L12674 L21243 L22621 L22634 L22682 L22744 L29654 L29659 L29665 L29671 L29678 L29681 L29686 L29690 L29701 L29705
I {0, 1}
indexes of I-isospectral families {251, 252}, {1104, 1105}, {1352, 1353}, {3885, 3886}, {4385, 4386}, {10517, 10536}, {10554, 10616}, {11754, 11755}, {12670, 12671}, {29680, 29730}, {29704, 29739}, {29710, 29799}, {29720, 29766}, {29800, 29913}, {31926, 31927}, {33488, 33489}, {61207, 61227}, {75948, 75959}, {75960, 75973}, {75998, 76078}, {76026, 76033}, {76039, 76096}, {76048, 76196}, {76062, 76143}, {76085, 76194}, {76197, 76374}, {79662, 79663}, {82188, 82189} {0, 1, 2} {75945, 75947}, {75966, 75995} {5, 6, 7, 8} {11062, 12668, 28787, 30477, 30716, 30771, 30778, 30781, 33439}, {11736, 29940, 73142, 76002, 76351, 76407}, {21243, 29756, 30597, 30753, 30782, 33486}, {23633, 31900, 56409, 62473, 63324, 63490, 63515, 63520, 76409}, {45809, 61283, 63135, 63457, 63521, 79627}
= [0, 0, 1, 2, 3, 8, 10, 11, 12], L10793 = [0, 0, 1, 2, 3, 9, 10, 12, 13], L10800 = [0, 0, 1, 2, 3, 9, 12, 13, 13], = [0, 0, 1, 2, 4, 5, 6, 7, 9], L10963 = [0, 0, 1, 2, 4, 5, 6, 7, 10], L10971 = [0, 0, 1, 2, 4, 5, 6, 9, 12], = [0, 0, 1, 2, 4, 5, 6, 11, 12], L10977 = [0, 0, 1, 2, 4, 5, 6, 12, 13], L11005 = [0, 0, 1, 2, 4, 5, 10, 12, 13], = [0, 0, 1, 2, 4, 6, 7, 8, 10], L11048 = [0, 0, 1, 2, 4, 6, 7, 8, 13], L11049 = [0, 0, 1, 2, 4, 6, 7, 9, 10], = [0, 0, 1, 2, 4, 6, 7, 9, 13], L11061 = [0, 0, 1, 2, 4, 6, 8, 10, 11], L11062 = [0, 0, 1, 2, 4, 6, 8, 10, 12], = [0, 0, 1, 2, 4, 9, 10, 11, 12], L11134 = [0, 0, 1, 2, 4, 9, 10, 11, 13], L11156 = [0, 0, 1, 2, 4, 10, 11, 13, 13], = [0, 0, 1, 2, 5, 6, 7, 8, 13], L11199 = [0, 0, 1, 2, 5, 6, 7, 13, 13], L11215 = [0, 0, 1, 2, 5, 6, 11, 12, 13], = [0, 0, 1, 2, 5, 6, 12, 13, 13], L11362 = [0, 0, 1, 2, 6, 7, 8, 13, 13], L11365 = [0, 0, 1, 2, 6, 7, 9, 10, 13], = [0, 0, 1, 2, 7, 8, 13, 13, 13], L11544 = [0, 0, 1, 2, 9, 10, 11, 13, 13], L11547 = [0, 0, 1, 2, 9, 10, 12, 13, 13], = [0, 0, 1, 2, 10, 11, 13, 13, 13], L11659 = [0, 0, 1, 3, 4, 4, 10, 10, 12], L11661 = [0, 0, 1, 3, 4, 4, 10, 12, 12], = [0, 0, 1, 3, 4, 5, 8, 13, 13], L11714 = [0, 0, 1, 3, 4, 8, 13, 13, 13], L11727 = [0, 0, 1, 3, 4, 10, 13, 13, 13], = [0, 0, 1, 3, 4, 12, 13, 13, 13], L11736 = [0, 0, 1, 3, 5, 7, 9, 11, 13], L11738 = [0, 0, 1, 3, 5, 7, 13, 13, 13], = [0, 0, 1, 3, 5, 9, 13, 13, 13], L11755 = [0, 0, 1, 3, 5, 11, 13, 13, 13], L11760 = [0, 0, 1, 3, 5, 13, 13, 13, 13], = [0, 0, 1, 3, 7, 13, 13, 13, 13], L11831 = [0, 0, 1, 3, 9, 13, 13, 13, 13], L11861 = [0, 0, 1, 3, 11, 13, 13, 13, 13], = [0, 0, 1, 4, 5, 8, 13, 13, 13], L12668 = [0, 0, 2, 4, 6, 8, 10, 12, 13], L12670 = [0, 0, 2, 4, 6, 8, 13, 13, 13], = [0, 0, 2, 4, 6, 10, 13, 13, 13], L12672 = [0, 0, 2, 4, 6, 12, 13, 13, 13], L12673 = [0, 0, 2, 4, 6, 13, 13, 13, 13], = [0, 0, 2, 4, 8, 13, 13, 13, 13], L12675 = [0, 0, 2, 4, 10, 13, 13, 13, 13], L12677 = [0, 0, 2, 6, 8, 13, 13, 13, 13], = [0, 1, 1, 2, 4, 6, 8, 10, 12], L22588 = [0, 1, 1, 3, 3, 4, 9, 10, 13], L22592 = [0, 1, 1, 3, 3, 4, 9, 12, 13], = [0, 1, 1, 3, 3, 5, 5, 9, 9], L22622 = [0, 1, 1, 3, 3, 5, 5, 9, 11], L22625 = [0, 1, 1, 3, 3, 5, 5, 11, 11], = [0, 1, 1, 3, 3, 5, 7, 7, 11], L22642 = [0, 1, 1, 3, 3, 5, 7, 9, 9], L22651 = [0, 1, 1, 3, 3, 5, 7, 11, 11], = [0, 1, 1, 3, 3, 5, 9, 11, 11], L22699 = [0, 1, 1, 3, 3, 5, 11, 11, 13], L22714 = [0, 1, 1, 3, 3, 7, 7, 9, 13], = [0, 1, 1, 3, 3, 7, 9, 11, 11], L23633 = [0, 1, 1, 3, 5, 7, 9, 11, 13], L28787 = [0, 1, 2, 2, 4, 6, 8, 10, 12], = [0, 1, 2, 3, 4, 5, 6, 7, 10], L29655 = [0, 1, 2, 3, 4, 5, 6, 7, 11], L29656 = [0, 1, 2, 3, 4, 5, 6, 7, 12], = [0, 1, 2, 3, 4, 5, 6, 8, 9], L29661 = [0, 1, 2, 3, 4, 5, 6, 8, 11], L29664 = [0, 1, 2, 3, 4, 5, 6, 9, 10], = [0, 1, 2, 3, 4, 5, 6, 9, 11], L29666 = [0, 1, 2, 3, 4, 5, 6, 9, 12], L29669 = [0, 1, 2, 3, 4, 5, 6, 10, 12], = [0, 1, 2, 3, 4, 5, 6, 11, 12], L29672 = [0, 1, 2, 3, 4, 5, 6, 11, 13], L29677 = [0, 1, 2, 3, 4, 5, 7, 8, 9], = [0, 1, 2, 3, 4, 5, 7, 8, 10], L29679 = [0, 1, 2, 3, 4, 5, 7, 8, 11], L29680 = [0, 1, 2, 3, 4, 5, 7, 8, 12], = [0, 1, 2, 3, 4, 5, 7, 8, 13], L29682 = [0, 1, 2, 3, 4, 5, 7, 9, 10], L29684 = [0, 1, 2, 3, 4, 5, 7, 9, 13], = [0, 1, 2, 3, 4, 5, 7, 10, 12], L29688 = [0, 1, 2, 3, 4, 5, 7, 11, 12], L29689 = [0, 1, 2, 3, 4, 5, 7, 11, 13], = [0, 1, 2, 3, 4, 5, 7, 12, 13], L29698 = [0, 1, 2, 3, 4, 5, 8, 9, 11], L29699 = [0, 1, 2, 3, 4, 5, 8, 9, 12], = [0, 1, 2, 3, 4, 5, 8, 10, 11], L29702 = [0, 1, 2, 3, 4, 5, 8, 10, 12], L29704 = [0, 1, 2, 3, 4, 5, 8, 11, 12], = [0, 1, 2, 3, 4, 5, 8, 11, 13], L29710 = [0, 1, 2, 3, 4, 5, 9, 10, 12], L29715 = [0, 1, 2, 3, 4, 5, 9, 12, 13],
290
L29717 L29730 L29733 L29737 L29743 L29753 L29758 L29765 L29775 L29794 L29798 L29809 L29832 L29846 L29862 L29896 L29901 L29912 L29918 L29935 L29962 L29984 L30014 L30047 L30074 L30108 L30181 L30477 L30591 L30607 L30657 L30754 L30759 L30780 L30898 L31004 L31039 L31457 L31634 L31813 L31894 L31926 L31954 L32505 L33439 L33489 L33492 L45809 L56409
EMILIO A. LAURET
= [0, 1, 2, 3, 4, 5, 10, 11, 12], L29718 = [0, 1, 2, 3, 4, 5, 10, 11, 13], L29720 = [0, 1, 2, 3, 4, 5, 10, 12, 13], = [0, 1, 2, 3, 4, 6, 7, 8, 9], L29731 = [0, 1, 2, 3, 4, 6, 7, 8, 10], L29732 = [0, 1, 2, 3, 4, 6, 7, 8, 12], = [0, 1, 2, 3, 4, 6, 7, 8, 13], L29734 = [0, 1, 2, 3, 4, 6, 7, 9, 10], L29735 = [0, 1, 2, 3, 4, 6, 7, 9, 11], = [0, 1, 2, 3, 4, 6, 7, 9, 13], L29739 = [0, 1, 2, 3, 4, 6, 7, 10, 11], L29742 = [0, 1, 2, 3, 4, 6, 7, 11, 12], = [0, 1, 2, 3, 4, 6, 7, 11, 13], L29751 = [0, 1, 2, 3, 4, 6, 8, 9, 10], L29752 = [0, 1, 2, 3, 4, 6, 8, 9, 11], = [0, 1, 2, 3, 4, 6, 8, 9, 13], L29756 = [0, 1, 2, 3, 4, 6, 8, 10, 12], L29757 = [0, 1, 2, 3, 4, 6, 8, 10, 13], = [0, 1, 2, 3, 4, 6, 8, 11, 12], L29761 = [0, 1, 2, 3, 4, 6, 8, 12, 13], L29764 = [0, 1, 2, 3, 4, 6, 9, 10, 11], = [0, 1, 2, 3, 4, 6, 9, 10, 12], L29766 = [0, 1, 2, 3, 4, 6, 9, 10, 13], L29774 = [0, 1, 2, 3, 4, 6, 10, 11, 12], = [0, 1, 2, 3, 4, 6, 10, 11, 13], L29791 = [0, 1, 2, 3, 4, 7, 8, 9, 13], L29793 = [0, 1, 2, 3, 4, 7, 8, 10, 12], = [0, 1, 2, 3, 4, 7, 8, 10, 13], L29795 = [0, 1, 2, 3, 4, 7, 8, 12, 13], L29796 = [0, 1, 2, 3, 4, 7, 8, 13, 13], = [0, 1, 2, 3, 4, 7, 9, 10, 11], L29799 = [0, 1, 2, 3, 4, 7, 9, 10, 12], L29800 = [0, 1, 2, 3, 4, 7, 9, 10, 13], = [0, 1, 2, 3, 4, 7, 10, 11, 12], L29811 = [0, 1, 2, 3, 4, 7, 10, 12, 13], L29831 = [0, 1, 2, 3, 4, 8, 9, 11, 12], = [0, 1, 2, 3, 4, 8, 9, 11, 13], L29834 = [0, 1, 2, 3, 4, 8, 9, 12, 13], L29840 = [0, 1, 2, 3, 4, 8, 10, 11, 12], = [0, 1, 2, 3, 4, 8, 11, 12, 13], L29847 = [0, 1, 2, 3, 4, 8, 11, 13, 13], L29856 = [0, 1, 2, 3, 4, 9, 10, 11, 12], = [0, 1, 2, 3, 4, 9, 11, 12, 13], L29894 = [0, 1, 2, 3, 5, 6, 7, 8, 9], L29895 = [0, 1, 2, 3, 5, 6, 7, 8, 10], = [0, 1, 2, 3, 5, 6, 7, 8, 11], L29897 = [0, 1, 2, 3, 5, 6, 7, 8, 13], L29900 = [0, 1, 2, 3, 5, 6, 7, 9, 13], = [0, 1, 2, 3, 5, 6, 7, 10, 13], L29909 = [0, 1, 2, 3, 5, 6, 8, 9, 13], L29911 = [0, 1, 2, 3, 5, 6, 8, 10, 13], = [0, 1, 2, 3, 5, 6, 8, 11, 12], L29913 = [0, 1, 2, 3, 5, 6, 8, 11, 13], L29915 = [0, 1, 2, 3, 5, 6, 8, 12, 13], = [0, 1, 2, 3, 5, 6, 9, 11, 13], L29922 = [0, 1, 2, 3, 5, 6, 10, 13, 13], L29934 = [0, 1, 2, 3, 5, 7, 8, 10, 11], = [0, 1, 2, 3, 5, 7, 8, 10, 13], L29940 = [0, 1, 2, 3, 5, 7, 9, 11, 13], L29943 = [0, 1, 2, 3, 5, 7, 10, 13, 13], = [0, 1, 2, 3, 5, 8, 9, 12, 13], L29964 = [0, 1, 2, 3, 5, 8, 10, 11, 12], L29965 = [0, 1, 2, 3, 5, 8, 10, 11, 13], = [0, 1, 2, 3, 5, 9, 12, 13, 13], L30007 = [0, 1, 2, 3, 6, 7, 8, 10, 12], L30008 = [0, 1, 2, 3, 6, 7, 8, 10, 13], = [0, 1, 2, 3, 6, 7, 9, 10, 13], L30015 = [0, 1, 2, 3, 6, 7, 9, 13, 13], L30042 = [0, 1, 2, 3, 6, 8, 9, 13, 13], = [0, 1, 2, 3, 6, 8, 10, 11, 12], L30048 = [0, 1, 2, 3, 6, 8, 10, 11, 13], L30051 = [0, 1, 2, 3, 6, 8, 10, 13, 13], = [0, 1, 2, 3, 6, 10, 11, 13, 13], L30105 = [0, 1, 2, 3, 7, 8, 10, 11, 12], L30107 = [0, 1, 2, 3, 7, 8, 10, 12, 13], = [0, 1, 2, 3, 7, 8, 10, 13, 13], L30117 = [0, 1, 2, 3, 7, 9, 10, 11, 12], L30120 = [0, 1, 2, 3, 7, 9, 10, 13, 13], = [0, 1, 2, 3, 8, 10, 11, 12, 13], L30210 = [0, 1, 2, 3, 9, 10, 12, 13, 13], L30219 = [0, 1, 2, 3, 9, 12, 13, 13, 13], = [0, 1, 2, 4, 4, 6, 8, 10, 12], L30587 = [0, 1, 2, 4, 5, 6, 7, 8, 10], L30590 = [0, 1, 2, 4, 5, 6, 7, 9, 13], = [0, 1, 2, 4, 5, 6, 7, 10, 13], L30597 = [0, 1, 2, 4, 5, 6, 8, 10, 12], L30604 = [0, 1, 2, 4, 5, 6, 9, 11, 12], = [0, 1, 2, 4, 5, 6, 9, 12, 13], L30611 = [0, 1, 2, 4, 5, 6, 11, 12, 13], L30615 = [0, 1, 2, 4, 5, 6, 12, 13, 13], = [0, 1, 2, 4, 5, 10, 12, 13, 13], L30716 = [0, 1, 2, 4, 6, 6, 8, 10, 12], L30753 = [0, 1, 2, 4, 6, 7, 8, 10, 12], = [0, 1, 2, 4, 6, 7, 8, 10, 13], L30756 = [0, 1, 2, 4, 6, 7, 8, 13, 13], L30758 = [0, 1, 2, 4, 6, 7, 9, 10, 13], = [0, 1, 2, 4, 6, 7, 9, 13, 13], L30771 = [0, 1, 2, 4, 6, 8, 8, 10, 12], L30778 = [0, 1, 2, 4, 6, 8, 10, 10, 12], = [0, 1, 2, 4, 6, 8, 10, 11, 13], L30781 = [0, 1, 2, 4, 6, 8, 10, 12, 12], L30782 = [0, 1, 2, 4, 6, 8, 10, 12, 13], = [0, 1, 2, 4, 9, 10, 11, 12, 13], L30899 = [0, 1, 2, 4, 9, 10, 11, 13, 13], L30932 = [0, 1, 2, 4, 10, 11, 13, 13, 13], = [0, 1, 2, 5, 6, 7, 8, 13, 13], L31008 = [0, 1, 2, 5, 6, 7, 13, 13, 13], L31034 = [0, 1, 2, 5, 6, 11, 12, 13, 13], = [0, 1, 2, 5, 6, 12, 13, 13, 13], L31300 = [0, 1, 2, 6, 7, 8, 13, 13, 13], L31305 = [0, 1, 2, 6, 7, 9, 10, 13, 13], = [0, 1, 2, 7, 8, 13, 13, 13, 13], L31588 = [0, 1, 2, 9, 10, 11, 13, 13, 13], L31592 = [0, 1, 2, 9, 10, 12, 13, 13, 13], = [0, 1, 2, 10, 11, 13, 13, 13, 13], L31788 = [0, 1, 3, 4, 4, 10, 10, 12, 13], L31791 = [0, 1, 3, 4, 4, 10, 12, 12, 13], = [0, 1, 3, 4, 5, 8, 13, 13, 13], L31871 = [0, 1, 3, 4, 8, 13, 13, 13, 13], L31889 = [0, 1, 3, 4, 10, 13, 13, 13, 13], = [0, 1, 3, 4, 12, 13, 13, 13, 13], L31900 = [0, 1, 3, 5, 7, 9, 11, 13, 13], L31902 = [0, 1, 3, 5, 7, 13, 13, 13, 13], = [0, 1, 3, 5, 9, 13, 13, 13, 13], L31927 = [0, 1, 3, 5, 11, 13, 13, 13, 13], L31933 = [0, 1, 3, 5, 13, 13, 13, 13, 13], = [0, 1, 3, 7, 13, 13, 13, 13, 13], L32046 = [0, 1, 3, 9, 13, 13, 13, 13, 13], L32088 = [0, 1, 3, 11, 13, 13, 13, 13, 13 = [0, 1, 4, 5, 8, 13, 13, 13, 13], L33402 = [0, 2, 2, 4, 4, 6, 6, 10, 13], L33405 = [0, 2, 2, 4, 4, 6, 8, 8, 13], = [0, 2, 2, 4, 6, 8, 10, 12, 13], L33486 = [0, 2, 4, 6, 8, 10, 12, 13, 13], L33488 = [0, 2, 4, 6, 8, 13, 13, 13, 13], = [0, 2, 4, 6, 10, 13, 13, 13, 13], L33490 = [0, 2, 4, 6, 12, 13, 13, 13, 13], L33491 = [0, 2, 4, 6, 13, 13, 13, 13, 13] = [0, 2, 4, 8, 13, 13, 13, 13, 13], L33493 = [0, 2, 4, 10, 13, 13, 13, 13, 13], L33495 = [0, 2, 6, 8, 13, 13, 13, 13, 13 = [1, 1, 1, 3, 5, 7, 9, 11, 13], L55186 = [1, 1, 2, 3, 3, 5, 8, 9, 11], L55246 = [1, 1, 2, 3, 3, 6, 7, 9, 11], = [1, 1, 2, 3, 5, 7, 9, 11, 13], L61161 = [1, 1, 3, 3, 4, 9, 10, 13, 13], L61167 = [1, 1, 3, 3, 4, 9, 12, 13, 13],
APPENDIX
L61196 L61207 L61230 L61253 L61281 L61367 L61491 L63324 L63515 L73142 L75938 L75941 L75945 L75949 L75952 L75961 L75964 L75971 L75974 L75982 L75993 L75996 L75999 L76002 L76006 L76010 L76029 L76034 L76040 L76055 L76062 L76080 L76083 L76087 L76095 L76100 L76119 L76129 L76141 L76157 L76186 L76189 L76196 L76212 L76253 L76274 L76345 L76348 L76352
291
= [1, 1, 3, 3, 5, 5, 7, 7, 11], L61203 = [1, 1, 3, 3, 5, 5, 7, 9, 9], L61204 = [1, 1, 3, 3, 5, 5, 7, 9, 11], = [1, 1, 3, 3, 5, 5, 7, 11, 11], L61227 = [1, 1, 3, 3, 5, 5, 9, 9, 11], L61228 = [1, 1, 3, 3, 5, 5, 9, 9, 13], = [1, 1, 3, 3, 5, 5, 9, 11, 13], L61234 = [1, 1, 3, 3, 5, 5, 11, 11, 13], L61248 = [1, 1, 3, 3, 5, 7, 7, 9, 11], = [1, 1, 3, 3, 5, 7, 7, 11, 13], L61275 = [1, 1, 3, 3, 5, 7, 9, 9, 11], L61276 = [1, 1, 3, 3, 5, 7, 9, 9, 13], = [1, 1, 3, 3, 5, 7, 9, 11, 11], L61283 = [1, 1, 3, 3, 5, 7, 9, 11, 13], L61298 = [1, 1, 3, 3, 5, 7, 11, 11, 13], = [1, 1, 3, 3, 5, 9, 11, 11, 13], L61396 = [1, 1, 3, 3, 5, 11, 11, 13, 13], L61423 = [1, 1, 3, 3, 7, 7, 9, 13, 13], = [1, 1, 3, 3, 7, 9, 11, 11, 13], L62473 = [1, 1, 3, 4, 5, 7, 9, 11, 13], L63135 = [1, 1, 3, 5, 5, 7, 9, 11, 13], = [1, 1, 3, 5, 6, 7, 9, 11, 13], L63457 = [1, 1, 3, 5, 7, 7, 9, 11, 13], L63490 = [1, 1, 3, 5, 7, 8, 9, 11, 13], = [1, 1, 3, 5, 7, 9, 10, 11, 13], L63520 = [1, 1, 3, 5, 7, 9, 11, 12, 13], L63521 = [1, 1, 3, 5, 7, 9, 11, 13, 13], = [1, 2, 2, 3, 5, 7, 9, 11, 13], L73333 = [1, 2, 2, 3, 6, 8, 8, 10, 12], L74278 = [1, 2, 2, 4, 6, 6, 8, 9, 12], = [1, 2, 3, 4, 5, 6, 7, 8, 9], L75939 = [1, 2, 3, 4, 5, 6, 7, 8, 10], L75940 = [1, 2, 3, 4, 5, 6, 7, 8, 11], = [1, 2, 3, 4, 5, 6, 7, 8, 12], L75943 = [1, 2, 3, 4, 5, 6, 7, 9, 10], L75944 = [1, 2, 3, 4, 5, 6, 7, 9, 11], = [1, 2, 3, 4, 5, 6, 7, 9, 12], L75947 = [1, 2, 3, 4, 5, 6, 7, 10, 11], L75948 = [1, 2, 3, 4, 5, 6, 7, 10, 12], = [1, 2, 3, 4, 5, 6, 7, 10, 13], L75950 = [1, 2, 3, 4, 5, 6, 7, 11, 12], L75951 = [1, 2, 3, 4, 5, 6, 7, 11, 13], = [1, 2, 3, 4, 5, 6, 7, 12, 13], L75959 = [1, 2, 3, 4, 5, 6, 8, 9, 10], L75960 = [1, 2, 3, 4, 5, 6, 8, 9, 11], = [1, 2, 3, 4, 5, 6, 8, 9, 12], L75962 = [1, 2, 3, 4, 5, 6, 8, 9, 13], L75963 = [1, 2, 3, 4, 5, 6, 8, 10, 11], = [1, 2, 3, 4, 5, 6, 8, 10, 12], L75966 = [1, 2, 3, 4, 5, 6, 8, 11, 12], L75967 = [1, 2, 3, 4, 5, 6, 8, 11, 13], = [1, 2, 3, 4, 5, 6, 9, 10, 12], L75972 = [1, 2, 3, 4, 5, 6, 9, 10, 13], L75973 = [1, 2, 3, 4, 5, 6, 9, 11, 12], = [1, 2, 3, 4, 5, 6, 9, 11, 13], L75975 = [1, 2, 3, 4, 5, 6, 9, 12, 13], L75979 = [1, 2, 3, 4, 5, 6, 10, 12, 13], = [1, 2, 3, 4, 5, 6, 11, 12, 13], L75983 = [1, 2, 3, 4, 5, 6, 11, 13, 13], L75992 = [1, 2, 3, 4, 5, 7, 8, 9, 11], = [1, 2, 3, 4, 5, 7, 8, 9, 12], L75994 = [1, 2, 3, 4, 5, 7, 8, 9, 13], L75995 = [1, 2, 3, 4, 5, 7, 8, 10, 12], = [1, 2, 3, 4, 5, 7, 8, 10, 13], L75997 = [1, 2, 3, 4, 5, 7, 8, 11, 13], L75998 = [1, 2, 3, 4, 5, 7, 8, 12, 13], = [1, 2, 3, 4, 5, 7, 8, 13, 13], L76000 = [1, 2, 3, 4, 5, 7, 9, 10, 11], L76001 = [1, 2, 3, 4, 5, 7, 9, 10, 13], = [1, 2, 3, 4, 5, 7, 9, 11, 13], L76003 = [1, 2, 3, 4, 5, 7, 9, 13, 13], L76004 = [1, 2, 3, 4, 5, 7, 10, 11, 12], = [1, 2, 3, 4, 5, 7, 10, 12, 13], L76008 = [1, 2, 3, 4, 5, 7, 11, 12, 13], L76009 = [1, 2, 3, 4, 5, 7, 11, 13, 13], = [1, 2, 3, 4, 5, 7, 12, 13, 13], L76026 = [1, 2, 3, 4, 5, 8, 9, 10, 12], L76028 = [1, 2, 3, 4, 5, 8, 9, 11, 12], = [1, 2, 3, 4, 5, 8, 9, 11, 13], L76031 = [1, 2, 3, 4, 5, 8, 9, 12, 13], L76033 = [1, 2, 3, 4, 5, 8, 10, 11, 12], = [1, 2, 3, 4, 5, 8, 10, 11, 13], L76036 = [1, 2, 3, 4, 5, 8, 10, 12, 13], L76039 = [1, 2, 3, 4, 5, 8, 11, 12, 13], = [1, 2, 3, 4, 5, 8, 11, 13, 13], L76045 = [1, 2, 3, 4, 5, 9, 10, 11, 12], L76048 = [1, 2, 3, 4, 5, 9, 10, 12, 13], = [1, 2, 3, 4, 5, 9, 12, 13, 13], L76058 = [1, 2, 3, 4, 5, 10, 11, 12, 13], L76059 = [1, 2, 3, 4, 5, 10, 11, 13, 13], = [1, 2, 3, 4, 5, 10, 12, 13, 13], L76077 = [1, 2, 3, 4, 6, 7, 8, 9, 12], L76078 = [1, 2, 3, 4, 6, 7, 8, 9, 13], = [1, 2, 3, 4, 6, 7, 8, 10, 12], L76081 = [1, 2, 3, 4, 6, 7, 8, 10, 13], L76082 = [1, 2, 3, 4, 6, 7, 8, 12, 13], = [1, 2, 3, 4, 6, 7, 8, 13, 13], L76085 = [1, 2, 3, 4, 6, 7, 9, 10, 11], L76086 = [1, 2, 3, 4, 6, 7, 9, 10, 12], = [1, 2, 3, 4, 6, 7, 9, 10, 13], L76088 = [1, 2, 3, 4, 6, 7, 9, 11, 13], L76090 = [1, 2, 3, 4, 6, 7, 9, 13, 13], = [1, 2, 3, 4, 6, 7, 10, 11, 12], L76096 = [1, 2, 3, 4, 6, 7, 10, 11, 13], L76099 = [1, 2, 3, 4, 6, 7, 11, 12, 13], = [1, 2, 3, 4, 6, 7, 11, 13, 13], L76117 = [1, 2, 3, 4, 6, 8, 9, 10, 12], L76118 = [1, 2, 3, 4, 6, 8, 9, 10, 13], = [1, 2, 3, 4, 6, 8, 9, 11, 13], L76120 = [1, 2, 3, 4, 6, 8, 9, 13, 13], L76125 = [1, 2, 3, 4, 6, 8, 10, 11, 12], = [1, 2, 3, 4, 6, 8, 10, 13, 13], L76131 = [1, 2, 3, 4, 6, 8, 11, 12, 13], L76135 = [1, 2, 3, 4, 6, 8, 12, 13, 13], = [1, 2, 3, 4, 6, 9, 10, 11, 13], L76142 = [1, 2, 3, 4, 6, 9, 10, 12, 13], L76143 = [1, 2, 3, 4, 6, 9, 10, 13, 13], = [1, 2, 3, 4, 6, 10, 11, 12, 13], L76158 = [1, 2, 3, 4, 6, 10, 11, 13, 13], L76182 = [1, 2, 3, 4, 7, 8, 9, 13, 13], = [1, 2, 3, 4, 7, 8, 10, 12, 13], L76187 = [1, 2, 3, 4, 7, 8, 10, 13, 13], L76188 = [1, 2, 3, 4, 7, 8, 12, 13, 13], = [1, 2, 3, 4, 7, 8, 13, 13, 13], L76194 = [1, 2, 3, 4, 7, 9, 10, 11, 12], L76195 = [1, 2, 3, 4, 7, 9, 10, 11, 13], = [1, 2, 3, 4, 7, 9, 10, 12, 13], L76197 = [1, 2, 3, 4, 7, 9, 10, 13, 13], L76210 = [1, 2, 3, 4, 7, 10, 11, 12, 13], = [1, 2, 3, 4, 7, 10, 12, 13, 13], L76249 = [1, 2, 3, 4, 8, 9, 11, 12, 13], L76250 = [1, 2, 3, 4, 8, 9, 11, 13, 13], = [1, 2, 3, 4, 8, 9, 12, 13, 13], L76265 = [1, 2, 3, 4, 8, 10, 11, 12, 13], L76273 = [1, 2, 3, 4, 8, 11, 12, 13, 13], = [1, 2, 3, 4, 8, 11, 13, 13, 13], L76290 = [1, 2, 3, 4, 9, 10, 11, 12, 13], L76298 = [1, 2, 3, 4, 9, 11, 12, 13, 13], = [1, 2, 3, 5, 6, 7, 8, 9, 11], L76346 = [1, 2, 3, 5, 6, 7, 8, 9, 13], L76347 = [1, 2, 3, 5, 6, 7, 8, 10, 13], = [1, 2, 3, 5, 6, 7, 8, 11, 13], L76349 = [1, 2, 3, 5, 6, 7, 8, 13, 13], L76351 = [1, 2, 3, 5, 6, 7, 9, 11, 13], = [1, 2, 3, 5, 6, 7, 9, 13, 13], L76353 = [1, 2, 3, 5, 6, 7, 10, 13, 13], L76368 = [1, 2, 3, 5, 6, 8, 9, 13, 13],
292
EMILIO A. LAURET
L76371 = [1, 2, 3, 5, 6, 8, 10, 13, 13], L76373 = [1, 2, 3, 5, 6, 8, 11, 12, 13], L76374 = [1, 2, 3, 5, 6, 8, 11, 13, 13], L76377 = [1, 2, 3, 5, 6, 8, 12, 13, 13], L76380 = [1, 2, 3, 5, 6, 9, 11, 13, 13], L76385 = [1, 2, 3, 5, 6, 10, 13, 13, 13], L76403 = [1, 2, 3, 5, 7, 8, 10, 11, 13], L76404 = [1, 2, 3, 5, 7, 8, 10, 13, 13], L76407 = [1, 2, 3, 5, 7, 9, 10, 11, 13], L76409 = [1, 2, 3, 5, 7, 9, 11, 13, 13], L76412 = [1, 2, 3, 5, 7, 10, 13, 13, 13], L76445 = [1, 2, 3, 5, 8, 9, 12, 13, 13], L76447 = [1, 2, 3, 5, 8, 10, 11, 12, 13], L76448 = [1, 2, 3, 5, 8, 10, 11, 13, 13], L76473 = [1, 2, 3, 5, 9, 12, 13, 13, 13], L76511 = [1, 2, 3, 6, 7, 8, 10, 12, 13], L76512 = [1, 2, 3, 6, 7, 8, 10, 13, 13], L76519 = [1, 2, 3, 6, 7, 9, 10, 13, 13], L76520 = [1, 2, 3, 6, 7, 9, 13, 13, 13], L76567 = [1, 2, 3, 6, 8, 9, 13, 13, 13], L76578 = [1, 2, 3, 6, 8, 10, 11, 12, 13], L76579 = [1, 2, 3, 6, 8, 10, 11, 13, 13], L76583 = [1, 2, 3, 6, 8, 10, 13, 13, 13], L76617 = [1, 2, 3, 6, 10, 11, 13, 13, 13], L76667 = [1, 2, 3, 7, 8, 10, 11, 12, 13], L76669 = [1, 2, 3, 7, 8, 10, 12, 13, 13], L76670 = [1, 2, 3, 7, 8, 10, 13, 13, 13], L76683 = [1, 2, 3, 7, 9, 10, 11, 12, 13], L76686 = [1, 2, 3, 7, 9, 10, 13, 13, 13], L76784 = [1, 2, 3, 8, 10, 11, 12, 13, 13], L76825 = [1, 2, 3, 9, 10, 12, 13, 13, 13], L76836 = [1, 2, 3, 9, 12, 13, 13, 13, 13], L77564 = [1, 2, 4, 5, 6, 7, 8, 10, 13], L77567 = [1, 2, 4, 5, 6, 7, 9, 13, 13], L77568 = [1, 2, 4, 5, 6, 7, 10, 13, 13], L77589 = [1, 2, 4, 5, 6, 9, 11, 12, 13], L77593 = [1, 2, 4, 5, 6, 9, 12, 13, 13], L77598 = [1, 2, 4, 5, 6, 11, 12, 13, 13], L77603 = [1, 2, 4, 5, 6, 12, 13, 13, 13], L77661 = [1, 2, 4, 5, 10, 12, 13, 13, 13], L77851 = [1, 2, 4, 6, 7, 8, 10, 13, 13], L77853 = [1, 2, 4, 6, 7, 8, 13, 13, 13], L77856 = [1, 2, 4, 6, 7, 9, 10, 13, 13], L77857 = [1, 2, 4, 6, 7, 9, 13, 13, 13], L77893 = [1, 2, 4, 6, 8, 10, 11, 13, 13], L78070 = [1, 2, 4, 9, 10, 11, 12, 13, 13], L78071 = [1, 2, 4, 9, 10, 11, 13, 13, 13], L78117 = [1, 2, 4, 10, 11, 13, 13, 13, 13 L78235 = [1, 2, 5, 6, 7, 8, 13, 13, 13], L78239 = [1, 2, 5, 6, 7, 13, 13, 13, 13], L78277 = [1, 2, 5, 6, 11, 12, 13, 13, 13], L78283 = [1, 2, 5, 6, 12, 13, 13, 13, 13], L78722 = [1, 2, 6, 7, 8, 13, 13, 13, 13], L78729 = [1, 2, 6, 7, 9, 10, 13, 13, 13], L78954 = [1, 2, 7, 8, 13, 13, 13, 13, 13], L79148 = [1, 2, 9, 10, 11, 13, 13, 13, 13], L79153 = [1, 2, 9, 10, 12, 13, 13, 13, 1 L79209 = [1, 2, 10, 11, 13, 13, 13, 13, 13], L79471 = [1, 3, 4, 4, 10, 10, 12, 13, 13], L79475 = [1, 3, 4, 4, 10, 12, 12, 13, 1 L79504 = [1, 3, 4, 5, 8, 13, 13, 13, 13], L79590 = [1, 3, 4, 8, 13, 13, 13, 13, 13], L79614 = [1, 3, 4, 10, 13, 13, 13, 13, 13] L79620 = [1, 3, 4, 12, 13, 13, 13, 13, 13], L79627 = [1, 3, 5, 7, 9, 11, 13, 13, 13], L79629 = [1, 3, 5, 7, 13, 13, 13, 13, 13] L79662 = [1, 3, 5, 9, 13, 13, 13, 13, 13], L79663 = [1, 3, 5, 11, 13, 13, 13, 13, 13], L79670 = [1, 3, 5, 13, 13, 13, 13, 13, 1 L79698 = [1, 3, 7, 13, 13, 13, 13, 13, 13], L79839 = [1, 3, 9, 13, 13, 13, 13, 13, 13], L79895 = [1, 3, 11, 13, 13, 13, 13, 13 L80634 = [1, 4, 5, 8, 13, 13, 13, 13, 13], L82085 = [2, 2, 4, 4, 6, 6, 8, 8, 13], L82086 = [2, 2, 4, 4, 6, 6, 8, 10, 13], L82087 = [2, 2, 4, 4, 6, 6, 8, 12, 13], L82089 = [2, 2, 4, 4, 6, 6, 10, 10, 13], L82090 = [2, 2, 4, 4, 6, 6, 10, 12, 13], L82091 = [2, 2, 4, 4, 6, 6, 10, 13, 13], L82097 = [2, 2, 4, 4, 6, 8, 8, 13, 13], L82101 = [2, 2, 4, 4, 6, 8, 12, 12, 13], L82104 = [2, 2, 4, 4, 6, 10, 10, 12, 13], L82125 = [2, 2, 4, 6, 6, 8, 8, 10, 13], L82188 = [2, 4, 6, 8, 13, 13, 13, 13, 13], L82189 = [2, 4, 6, 10, 13, 13, 13, 13, 13], L82190 = [2, 4, 6, 12, 13, 13, 13, 13, 13], L82191 = [2, 4, 6, 13, 13, 13, 13, 13, L82192 = [2, 4, 8, 13, 13, 13, 13, 13, 13], L82193 = [2, 4, 10, 13, 13, 13, 13, 13, 13], L82195 = [2, 6, 8, 13, 13, 13, 13, 13 q = 27 : L162 = [0, 0, 0, 0, 0, 1, 2, 4, 11], L165 = [0, 0, 0, 0, 0, 1, 2, 5, 7], L168 = [0, 0, 0, 0, 0, 1, 2, 5, 10], L177 = [0, 0, 0, 0, 0, 1, 2, 7, 8], L179 = [0, 0, 0, 0, 0, 1, 2, 7, 10], L687 = [0, 0, 0, 0, 1, 2, 3, 5, 10], L690 = [0, 0, 0, 0, 1, 2, 3, 5, 13], L704 = [0, 0, 0, 0, 1, 2, 3, 7, 13], L716 = [0, 0, 0, 0, 1, 2, 3, 10, 13], L720 = [0, 0, 0, 0, 1, 2, 4, 5, 7], L721 = [0, 0, 0, 0, 1, 2, 4, 5, 8], L723 = [0, 0, 0, 0, 1, 2, 4, 5, 10], L724 = [0, 0, 0, 0, 1, 2, 4, 5, 11 L727 = [0, 0, 0, 0, 1, 2, 4, 7, 8], L730 = [0, 0, 0, 0, 1, 2, 4, 7, 11], L732 = [0, 0, 0, 0, 1, 2, 4, 7, 13], L736 = [0, 0, 0, 0, 1, 2, 4, 9, 11], L738 = [0, 0, 0, 0, 1, 2, 4, 10, 11], L739 = [0, 0, 0, 0, 1, 2, 4, 10, 12], L748 = [0, 0, 0, 0, 1, 2, 5, 7, 8], L749 = [0, 0, 0, 0, 1, 2, 5, 7, 9], L750 = [0, 0, 0, 0, 1, 2, 5, 7, 11], L751 = [0, 0, 0, 0, 1, 2, 5, 7, 12 L755 = [0, 0, 0, 0, 1, 2, 5, 9, 10], L781 = [0, 0, 0, 0, 1, 2, 7, 8, 9], L786 = [0, 0, 0, 0, 1, 2, 7, 9, 10], L2478 = [0, 0, 0, 1, 2, 3, 4, 5, 12], L2480 = [0, 0, 0, 1, 2, 3, 4, 6, 7], L2481 = [0, 0, 0, 1, 2, 3, 4, 6, 8], L2483 = [0, 0, 0, 1, 2, 3, 4, 6, L2487 = [0, 0, 0, 1, 2, 3, 4, 7, 8], L2489 = [0, 0, 0, 1, 2, 3, 4, 7, 10], L2492 = [0, 0, 0, 1, 2, 3, 4, 7, 13], L2496 = [0, 0, 0, 1, 2, 3, 4, 8, 12], L2504 = [0, 0, 0, 1, 2, 3, 4, 10, 12], L2507 = [0, 0, 0, 1, 2, 3, 4, 11, 13], L2511 = [0, 0, 0, 1, 2, 3, 5, 6, 8], L2525 = [0, 0, 0, 1, 2, 3, 5, 8, 12], L2528 = [0, 0, 0, 1, 2, 3, 5, 9, 10], L2531 = [0, 0, 0, 1, 2, 3, 5, 9, 13], L2561 = [0, 0, 0, 1, 2, 3, 6, 10, 13], L2563 = [0, 0, 0, 1, 2, 3, 6, 11, 13], L2574 = [0, 0, 0, 1, 2, 3, 7, 9, 13], L2575 = [0, 0, 0, 1, 2, 3, 7, 10, 12], L2576 = [0, 0, 0, 1, 2, 3, 7, 11, 12], L2583 = [0, 0, 0, 1, 2, 3, 8, 10, 12], L2593 = [0, 0, 0, 1, 2, 3, 9, 10, 13], L2602 = [0, 0, 0, 1, 2, 4, 5, 7, 8], L2603 = [0, 0, 0, 1, 2, 4, 5, 7, 9], L2604 = [0, 0, 0, 1, 2, 4, 5, 7, 10], L2605 = [0, 0, 0, 1, 2, 4, 5, 7, 11], L2607 = [0, 0, 0, 1, 2, 4, 5, 7, 13], L2608 = [0, 0, 0, 1, 2, 4, 5, 8, 9], L2609 = [0, 0, 0, 1, 2, 4, 5, 8, 10], L2610 = [0, 0, 0, 1, 2, 4, 5, 8, 11], L2611 = [0, 0, 0, 1, 2, 4, 5, 8, 13], L2613 = [0, 0, 0, 1, 2, 4, 5, 9, 10], L2614 = [0, 0, 0, 1, 2, 4, 5, 9, 11], L2617 = [0, 0, 0, 1, 2, 4, 5, 10, 13], L2618 = [0, 0, 0, 1, 2, 4, 5, 11, 12],
APPENDIX
293
Table 7. (continued) m = 9 q I indexes of I-isospectral families 27 {0} {162, 165, 168}, {177, 179}, {687, 690}, {704, 716}, {720, 721}, {723, 724, 727, 732}, {736, 749, 755}, {738, 748}, {739, 751}, {781, 786}, {2478, 2483}, {2480, 2481}, {2487, 2489}, {2492, 2507}, {2496, 2511}, {2504, 2563}, {2525, 2561}, {2528, 2531}, {2574, 2593}, {2575, 2699}, {2576, 2705}, {2583, 2710}, {2602, 2604, 2610}, {2603, 2608}, {2605, 2611, 2617}, {2613, 2614, 2620, 2625}, {2618, 2649}, {2633, 2661, 2669}, {2635, 2659}, {2636, 2663}, {2724, 2733}, {7662, 7800}, {7710, 7711}, {7718, 7723, 7744}, {7728, 7748}, {7731, 7746, 7761}, {7737, 7739}, {7738, 7743}, {7752, 7756}, {7754, 7805, 7807}, {7755, 7809, 7819}, {7758, 7764}, {7767, 7791}, {7776, 7810}, {7779, 7811}, {7788, 7910}, {7793, 8041}, {7813, 7821}, {7825, 7913}, {7833, 7899}, {7838, 7908}, {7843, 7846}, {7886, 7891}, {7923, 8128}, {7924, 8129}, {7930, 7954}, {7931, 8126}, {7932, 8136}, {7942, 8144}, {7967, 7971, 7981}, {7968, 7969, 7975}, {7970, 7979}, {7972, 7982, 7988}, {7984, 7985, 7993, 7998}, {7989, 8040}, {8010, 8057, 8067}, {8012, 8054}, {8013, 8059}, {8164, 8177}, {21088, 21093}, {21178, 21202}, {21196, 21429}, {21267, 21273}, {21269, 21274}, {21275, 21328}, {21277, 21278}, {21282, 21284, 21333, 21344}, {21283, 21313}, {21285, 21303, 21310, 21332, 21339},
L2620 = [0, 0, 0, 1, 2, 4, 7, 8, 9], L2623 = [0, 0, 0, 1, 2, 4, 7, 9, 11], L2625 = [0, 0, 0, 1, 2, 4, 7, 9, 13], L2633 = [0, 0, 0, 1, 2, 4, 9, 9, 11], L2635 = [0, 0, 0, 1, 2, 4, 9, 10, 11], L2636 = [0, 0, 0, 1, 2, 4, 9, 10, 12], L2649 = [0, 0, 0, 1, 2, 5, 6, 7, 8], L2659 = [0, 0, 0, 1, 2, 5, 7, 8, 9], L2661 = [0, 0, 0, 1, 2, 5, 7, 9, 9], L2662 = [0, 0, 0, 1, 2, 5, 7, 9, 11], L2663 = [0, 0, 0, 1, 2, 5, 7, 9, 12], L2669 = [0, 0, 0, 1, 2, 5, 9, 9, 10], L2699 = [0, 0, 0, 1, 2, 6, 7, 8, 12], L2705 = [0, 0, 0, 1, 2, 6, 7, 11, 12], L2710 = [0, 0, 0, 1, 2, 6, 8, 10, 12], L2724 = [0, 0, 0, 1, 2, 7, 8, 9, 9], L2733 = [0, 0, 0, 1, 2, 7, 9, 9, 10], L7662 = [0, 0, 1, 2, 3, 3, 6, 11, 13], L7710 = [0, 0, 1, 2, 3, 4, 5, 6, 10], L7711 = [0, 0, 1, 2, 3, 4, 5, 6, 11], L7718 = [0, 0, 1, 2, 3, 4, 5, 7, 12], L7719 = [0, 0, 1, 2, 3, 4, 5, 7, 13], L7721 = [0, 0, 1, 2, 3, 4, 5, 8, 10], L7723 = [0, 0, 1, 2, 3, 4, 5, 8, 12], L7728 = [0, 0, 1, 2, 3, 4, 5, 9, 12], L7731 = [0, 0, 1, 2, 3, 4, 5, 10, 12], L7732 = [0, 0, 1, 2, 3, 4, 5, 10, 13], L7734 = [0, 0, 1, 2, 3, 4, 5, 11, 13], L7737 = [0, 0, 1, 2, 3, 4, 6, 7, 8], L7738 = [0, 0, 1, 2, 3, 4, 6, 7, 9], L7739 = [0, 0, 1, 2, 3, 4, 6, 7, 10], L7743 = [0, 0, 1, 2, 3, 4, 6, 8, 9], L7744 = [0, 0, 1, 2, 3, 4, 6, 8, 11], L7746 = [0, 0, 1, 2, 3, 4, 6, 8, 13], L7748 = [0, 0, 1, 2, 3, 4, 6, 9, 10], L7752 = [0, 0, 1, 2, 3, 4, 6, 10, 11], L7754 = [0, 0, 1, 2, 3, 4, 6, 10, 13], L7755 = [0, 0, 1, 2, 3, 4, 6, 11, 12], L7756 = [0, 0, 1, 2, 3, 4, 6, 11, 13], L7758 = [0, 0, 1, 2, 3, 4, 7, 8, 9], L7759 = [0, 0, 1, 2, 3, 4, 7, 8, 10], L7760 = [0, 0, 1, 2, 3, 4, 7, 8, 11], L7761 = [0, 0, 1, 2, 3, 4, 7, 8, 12], L7764 = [0, 0, 1, 2, 3, 4, 7, 9, 10], L7767 = [0, 0, 1, 2, 3, 4, 7, 9, 13], L7776 = [0, 0, 1, 2, 3, 4, 8, 9, 12], L7779 = [0, 0, 1, 2, 3, 4, 8, 10, 12], L7780 = [0, 0, 1, 2, 3, 4, 8, 10, 13], L7788 = [0, 0, 1, 2, 3, 4, 9, 10, 12], L7791 = [0, 0, 1, 2, 3, 4, 9, 11, 13], L7793 = [0, 0, 1, 2, 3, 4, 10, 11, 12], L7800 = [0, 0, 1, 2, 3, 5, 6, 6, 8], L7805 = [0, 0, 1, 2, 3, 5, 6, 7, 8], L7807 = [0, 0, 1, 2, 3, 5, 6, 7, 10], L7809 = [0, 0, 1, 2, 3, 5, 6, 7, L7810 = [0, 0, 1, 2, 3, 5, 6, 8, 9], L7811 = [0, 0, 1, 2, 3, 5, 6, 8, 10], L7813 = [0, 0, 1, 2, 3, 5, 6, 8, 13], L7819 = [0, 0, 1, 2, 3, 5, 6, 10, 12], L7821 = [0, 0, 1, 2, 3, 5, 6, 11, 13], L7825 = [0, 0, 1, 2, 3, 5, 7, 8, 12], L7832 = [0, 0, 1, 2, 3, 5, 7, 10, 11], L7833 = [0, 0, 1, 2, 3, 5, 7, 11, 12], L7838 = [0, 0, 1, 2, 3, 5, 8, 9, 12], L7843 = [0, 0, 1, 2, 3, 5, 9, 9, 10], L7846 = [0, 0, 1, 2, 3, 5, 9, 9, 13], L7886 = [0, 0, 1, 2, 3, 6, 7, 8, 12], L7891 = [0, 0, 1, 2, 3, 6, 7, 10, 12], L7899 = [0, 0, 1, 2, 3, 6, 8, 10, 13], L7908 = [0, 0, 1, 2, 3, 6, 9, 10, 13], L7910 = [0, 0, 1, 2, 3, 6, 9, 11, 13], L7913 = [0, 0, 1, 2, 3, 6, 10, 11, 13], L7923 = [0, 0, 1, 2, 3, 7, 8, 10, 12], L7924 = [0, 0, 1, 2, 3, 7, 8, 11, 12], L7930 = [0, 0, 1, 2, 3, 7, 9, 9, 13], L7931 = [0, 0, 1, 2, 3, 7, 9, 10, 12],
294
EMILIO A. LAURET
Table 7. (continued) m = 9 q I indexes of I-isospectral families 27 {0} {21289, 21290, 21299}, {21291, 21312}, {21292, 21298, 21309}, (cont.) {21296, 21307, 21346}, {21300, 21342, 21372, 21441}, {21301, 21311, 21371}, {21317, 21351}, {21320, 21348, 21369}, {21326, 21362}, {21327, 21373, 21397}, {21331, 21335}, {21334, 21345}, {21355, 21359}, {21357, 21440, 21444}, {21361, 21442}, {21363, 21448}, {21366, 21375}, {21378, 21407}, {21384, 21453}, {21391, 21449}, {21394, 21450}, {21404, 21601}, {21409, 21776}, {21452, 21462}, {21467, 21604}, {21476, 21588}, {21483, 21599}, {21489, 21492}, {21618, 21912}, {21619, 21913}, {21621, 21915}, {21629, 21658}, {21630, 21910}, {21631, 21924}, {21644, 21935}, {21675, 21680, 21692}, {21676, 21677, 21684}, {21679, 21690}, {21681, 21693, 21699}, {21695, 21696, 21706, 21711}, {21700, 21775}, {21727, 21797, 21809}, {21729, 21793}, {21730, 21799}, {21961, 21978}, {52923, 52989}, {52926, 52927, 52937}, {52929, 52935, 52947}, {52939, 52949, 53047}, {52966, 53050, 53082}, {52968, 53138}, {52977, 52981}, {52998, 53006}, {53010, 53040}, {53021, 53124}, {53037, 53296}, {53158, 53294}, {53166, 53171}, {53317, 53348}, {53318, 53814}, {53319, 53823}, {53330, 53832}, {53342, 53657}, {53430, 53431, 53433, 53439, 53441, 53451}, {53432, 53440, 53454}, {53435, 53448}, {53437, 53449}, {53442, 53455, 53469}, {53443, 53453, 53505}, {53450, 53520}, {53457, 53458}, {53462, 53464, 53527, 53538}, {53463, 53503}, {53465, 53491, 53500, 53526, 53533}, {53468, 53480, 53504}, {53470, 53652}, {53473, 53474, 53487}, {53475, 53502}, {53476, 53486, 53499}, {53484, 53497, 53544}, {53488, 53536, 53574, 53673}, {53489, 53501, 53573}, {53509, 53549}, {53512, 53546, 53571}, {53518, 53560}, {53519, 53575, 53603}, {53525, 53529}, {53528, 53543}, {53553, 53557}, {53555, 53672, 53677}, {53556, 53679, 53695}, {53559, 53674}, {53561, 53681}, {53568, 53577}, {53580, 53613}, {53586, 53687}, {53597, 53683}, {53600, 53684}, {53610, 53899}, {53615, 54122}, {53686, 53697}, {53703, 53902}, {53713, 53884}, {53722, 53897}, {53729, 53732}, {53857, 53870}, {53920, 54320}, {53921, 54321}, {53923, 54323}, {53935, 53969}, {53936, 54318}, {53937, 54336}, {53953, 54350}, {53990, 53996, 54010}, {53991, 53992, 54000}, {53995, 54008}, {53997, 54011, 54017}, {54013, 54014, 54026, 54031}, {54018, 54121}, {54051, 54148, 54162}, {54053, 54143}, {54054, 54150}, {54382, 54403} L7932 L7967 L7970 L7974 L7980 L7984
= [0, 0, 1, 2, 3, 7, 9, 11, 12], L7942 = [0, 0, 1, 2, 3, 8, 9, 10, 12], L7954 = [0, 0, 1, 2, 3, 9, 9, 10, 13], = [0, 0, 1, 2, 4, 5, 7, 8, 9], L7968 = [0, 0, 1, 2, 4, 5, 7, 8, 10], L7969 = [0, 0, 1, 2, 4, 5, 7, 8, 11], = [0, 0, 1, 2, 4, 5, 7, 9, 9], L7971 = [0, 0, 1, 2, 4, 5, 7, 9, 10], L7972 = [0, 0, 1, 2, 4, 5, 7, 9, 11], = [0, 0, 1, 2, 4, 5, 7, 9, 13], L7975 = [0, 0, 1, 2, 4, 5, 7, 10, 13], L7979 = [0, 0, 1, 2, 4, 5, 8, 9, 9], = [0, 0, 1, 2, 4, 5, 8, 9, 10], L7981 = [0, 0, 1, 2, 4, 5, 8, 9, 11], L7982 = [0, 0, 1, 2, 4, 5, 8, 9, 13], = [0, 0, 1, 2, 4, 5, 9, 9, 10], L7985 = [0, 0, 1, 2, 4, 5, 9, 9, 11], L7988 = [0, 0, 1, 2, 4, 5, 9, 10, 13],
APPENDIX
295
Table 7. (continued) m = 9 q 27 (cont.)
I {0, 1}
indexes of I-isospectral families {723, 724}, {2613, 2614}, {7719, 7721}, {7732, 7759}, {7734, 7760}, {7780, 7832}, {7984, 7985}, {20969, 20971}, {20984, 21019}, {21040, 21103}, {21270, 21272}, {21282, 21284}, {21285, 21332}, {21297, 21305}, {21300, 21441}, {21303, 21310}, {21321, 21367}, {21323, 21368}, {21395, 21475}, {21695, 21696}, {52588, 52590}, {52603, 52639}, {52660, 52724}, {52907, 52909}, {52922, 52997}, {52934, 52943}, {52941, 52948}, {52952, 53016}, {52962, 53044}, {52970, 53049}, {53008, 53067}, {53018, 53146}, {53076, 53190}, {53084, 53196}, {53431, 53433}, {53438, 53447}, {53443, 53453}, {53462, 53464}, {53465, 53526}, {53468, 53480}, {53477, 53478, 53479}, {53485, 53495}, {53488, 53673}, {53491, 53500}, {53513, 53569}, {53515, 53570}, {53601, 53712}, {54013, 54014} {0, 1, 2} {730, 750}, {2607, 2609}, {2611, 2617}, {2623, 2662}, {7968, 7969}, {7974, 7980}, {7982, 7988}, {7996, 8058}, {21341, 21447}, {21676, 21677}, {21683, 21691}, {21693, 21699}, {21709, 21798}, {53445, 53452}, {53455, 53469}, {53535, 53680}, {53991, 53992}, {53999, 54009}, {54011, 54017}, {54029, 54149} {0, 8} {21358, 21446, 21460}, {21568, 21577}
L7989 = [0, 0, 1, 2, 4, 5, 9, 11, 12], L7993 = [0, 0, 1, 2, 4, 7, 8, 9, 9], L7996 = [0, 0, 1, 2, 4, 7, 9, 9, 11], L7998 = [0, 0, 1, 2, 4, 7, 9, 9, 13], L8010 = [0, 0, 1, 2, 4, 9, 9, 9, 11], L8012 = [0, 0, 1, 2, 4, 9, 9, 10, 11], L8013 = [0, 0, 1, 2, 4, 9, 9, 10, 12], L8040 = [0, 0, 1, 2, 5, 6, 7, 8, 9], L8041 = [0, 0, 1, 2, 5, 6, 7, 8, 12], L8054 = [0, 0, 1, 2, 5, 7, 8, 9, 9], L8057 = [0, 0, 1, 2, 5, 7, 9, 9, 9], L8058 = [0, 0, 1, 2, 5, 7, 9, 9, 11], L8059 = [0, 0, 1, 2, 5, 7, 9, 9, 12], L8067 = [0, 0, 1, 2, 5, 9, 9, 9, 10], L8126 = [0, 0, 1, 2, 6, 7, 8, 9, 12], L8128 = [0, 0, 1, 2, 6, 7, 8, 10, 12], L8129 = [0, 0, 1, 2, 6, 7, 8, 11, 12], L8136 = [0, 0, 1, 2, 6, 7, 9, 11, 12], L8144 = [0, 0, 1, 2, 6, 8, 9, 10, 12], L8164 = [0, 0, 1, 2, 7, 8, 9, 9, 9], L8177 = [0, 0, 1, 2, 7, 9, 9, 9, 10], L20969 = [0, 1, 2, 3, 3, 4, 5, 7, 13], L20971 = [0, 1, 2, 3, 3, 4, 5, 8, 10], L20984 = [0, 1, 2, 3, 3, 4, 5, 11, 13], L21019 = [0, 1, 2, 3, 3, 4, 7, 8, 11], L21040 = [0, 1, 2, 3, 3, 4, 8, 10, 13], L21088 = [0, 1, 2, 3, 3, 5, 6, 10, 12], L21093 = [0, 1, 2, 3, 3, 5, 6, 12, 13], L21103 = [0, 1, 2, 3, 3, 5, 7, 10, 11], L21178 = [0, 1, 2, 3, 3, 6, 7, 12, 13], L21196 = [0, 1, 2, 3, 3, 6, 9, 11, 13], L21202 = [0, 1, 2, 3, 3, 6, 10, 12, 13], L21267 = [0, 1, 2, 3, 4, 5, 6, 7, 10], L21269 = [0, 1, 2, 3, 4, 5, 6, 7, 12], L21270 = [0, 1, 2, 3, 4, 5, 6, 7, 13], L21272 = [0, 1, 2, 3, 4, 5, 6, 8, 10], L21273 = [0, 1, 2, 3, 4, 5, 6, 8, 11], L21274 = [0, 1, 2, 3, 4, 5, 6, 8, 12], L21275 = [0, 1, 2, 3, 4, 5, 6, 8, 13], L21277 = [0, 1, 2, 3, 4, 5, 6, 9, 10], L21278 = [0, 1, 2, 3, 4, 5, 6, 9, 11], L21282 = [0, 1, 2, 3, 4, 5, 6, 10, 12], L21283 = [0, 1, 2, 3, 4, 5, 6, 10, 13], L21284 = [0, 1, 2, 3, 4, 5, 6, 11, 12], L21285 = [0, 1, 2, 3, 4, 5, 6, 11, 13], L21289 = [0, 1, 2, 3, 4, 5, 7, 8, 10], L21290 = [0, 1, 2, 3, 4, 5, 7, 8, 11], L21291 = [0, 1, 2, 3, 4, 5, 7, 8, 12], L21292 = [0, 1, 2, 3, 4, 5, 7, 8, 13], L21296 = [0, 1, 2, 3, 4, 5, 7, 9, 12], L21297 = [0, 1, 2, 3, 4, 5, 7, 9, 13], L21298 = [0, 1, 2, 3, 4, 5, 7, 10, 11], L21299 = [0, 1, 2, 3, 4, 5, 7, 10, 13], L21300 = [0, 1, 2, 3, 4, 5, 7, 11, 12], L21301 = [0, 1, 2, 3, 4, 5, 7, 11, 13], L21303 = [0, 1, 2, 3, 4, 5, 7, 12, 13], L21305 = [0, 1, 2, 3, 4, 5, 8, 9, 10], L21307 = [0, 1, 2, 3, 4, 5, 8, 9, 12], L21309 = [0, 1, 2, 3, 4, 5, 8, 10, 11], L21310 = [0, 1, 2, 3, 4, 5, 8, 10, 12], L21311 = [0, 1, 2, 3, 4, 5, 8, 10, 13], L21312 = [0, 1, 2, 3, 4, 5, 8, 11, 12], L21313 = [0, 1, 2, 3, 4, 5, 8, 12, 13], L21317 = [0, 1, 2, 3, 4, 5, 9, 9, 12], L21320 = [0, 1, 2, 3, 4, 5, 9, 10, 12], L21321 = [0, 1, 2, 3, 4, 5, 9, 10, 13], L21323 = [0, 1, 2, 3, 4, 5, 9, 11, 13], L21326 = [0, 1, 2, 3, 4, 5, 10, 11, 12], L21327 = [0, 1, 2, 3, 4, 5, 10, 11, 13], L21328 = [0, 1, 2, 3, 4, 5, 10, 12, 13], L21331 = [0, 1, 2, 3, 4, 6, 7, 8, 9], L21332 = [0, 1, 2, 3, 4, 6, 7, 8, 11], L21333 = [0, 1, 2, 3, 4, 6, 7, 8, 12], L21334 = [0, 1, 2, 3, 4, 6, 7, 9, 9], L21335 = [0, 1, 2, 3, 4, 6, 7, 9, 10], L21339 = [0, 1, 2, 3, 4, 6, 7, 10, 11], L21341 = [0, 1, 2, 3, 4, 6, 7, 11, 12], L21342 = [0, 1, 2, 3, 4, 6, 7, 11, 13], L21344 =
296
EMILIO A. LAURET
[0, 1, 2, 3, 4, 6, 7, 12, 13], L21345 = [0, 1, 2, 3, 4, 6, 8, 9, 9], L21346 = [0, 1, 2, 3, 4, 6, 8, 9, 11], L21348 = [0, 1, 2, 3, 4, 6, 8, 9, 13], L21351 = [0, 1, 2, 3, 4, 6, 9, 9, 10], L21355 = [0, 1, 2, 3, 4, 6, 9, 10, 11], L21357 = [0, 1, 2, 3, 4, 6, 9, 10, 13], L21358 = [0, 1, 2, 3, 4, 6, 9, 11, 12], L21359 = [0, 1, 2, 3, 4, 6, 9, 11, 13], L21361 = [0, 1, 2, 3, 4, 6, 10, 11, 12], L21362 = [0, 1, 2, 3, 4, 6, 10, 11, 13], L21363 = [0, 1, 2, 3, 4, 6, 10, 12, 12], L21366 = [0, 1, 2, 3, 4, 7, 8, 9, 9], L21367 = [0, 1, 2, 3, 4, 7, 8, 9, 10], L21368 = [0, 1, 2, 3, 4, 7, 8, 9, 11], L21369 = [0, 1, 2, 3, 4, 7, 8, 9, 12], L21371 = [0, 1, 2, 3, 4, 7, 8, 10, 11], L21372 = [0, 1, 2, 3, 4, 7, 8, 10, 12], L21373 = [0, 1, 2, 3, 4, 7, 8, 11, 13], L21375 = [0, 1, 2, 3, 4, 7, 9, 9, 10], L21378 = [0, 1, 2, 3, 4, 7, 9, 9, 13], L21384 = [0, 1, 2, 3, 4, 7, 10, 11, 12], L21391 = [0, 1, 2, 3, 4, 8, 9, 9, 12], L21394 = [0, 1, 2, 3, 4, 8, 9, 10, 12], L21395 = [0, 1, 2, 3, 4, 8, 9, 10, 13], L21397 = [0, 1, 2, 3, 4, 8, 10, 11, 13], L21404 = [0, 1, 2, 3, 4, 9, 9, 10, 12], L21407 = [0, 1, 2, 3, 4, 9, 9, 11, 13], L21409 = [0, 1, 2, 3, 4, 9, 10, 11, 12], L21429 = [0, 1, 2, 3, 5, 6, 6, 8, 9], L21440 = [0, 1, 2, 3, 5, 6, 7, 8, 9], L21441 = [0, 1, 2, 3, 5, 6, 7, 8, 10], L21442 = [0, 1, 2, 3, 5, 6, 7, 8, 12], L21444 = [0, 1, 2, 3, 5, 6, 7, 9, 10], L21446 = [0, 1, 2, 3, 5, 6, 7, 9, 12], L21447 = [0, 1, 2, 3, 5, 6, 7, 11, 12], L21448 = [0, 1, 2, 3, 5, 6, 7, 12, 12], L21449 = [0, 1, 2, 3, 5, 6, 8, 9, 9], L21450 = [0, 1, 2, 3, 5, 6, 8, 9, 10], L21452 = [0, 1, 2, 3, 5, 6, 8, 9, 13], L21453 = [0, 1, 2, 3, 5, 6, 8, 10, 13], L21460 = [0, 1, 2, 3, 5, 6, 9, 10, 12], L21462 = [0, 1, 2, 3, 5, 6, 9, 11, 13], L21467 = [0, 1, 2, 3, 5, 7, 8, 9, 12], L21475 = [0, 1, 2, 3, 5, 7, 9, 10, 11], L21476 = [0, 1, 2, 3, 5, 7, 9, 11, 12], L21483 = [0, 1, 2, 3, 5, 8, 9, 9, 12], L21489 = [0, 1, 2, 3, 5, 9, 9, 9, 10], L21492 = [0, 1, 2, 3, 5, 9, 9, 9, 13], L21568 = [0, 1, 2, 3, 6, 7, 8, 9, 12], L21577 = [0, 1, 2, 3, 6, 7, 9, 10, 12], L21588 = [0, 1, 2, 3, 6, 8, 9, 10, 13], L21599 = [0, 1, 2, 3, 6, 9, 9, 10, 13], L21601 = [0, 1, 2, 3, 6, 9, 9, 11, 13], L21604 = [0, 1, 2, 3, 6, 9, 10, 11, 13], L21618 = [0, 1, 2, 3, 7, 8, 9, 10, 12], L21619 = [0, 1, 2, 3, 7, 8, 9, 11, 12], L21621 = [0, 1, 2, 3, 7, 8, 10, 11, 12], L21629 = [0, 1, 2, 3, 7, 9, 9, 9, 13], L21630 = [0, 1, 2, 3, 7, 9, 9, 10, 12], L21631 = [0, 1, 2, 3, 7, 9, 9, 11, 12], L21644 = [0, 1, 2, 3, 8, 9, 9, 10, 12], L21658 = [0, 1, 2, 3, 9, 9, 9, 10, 13], L21675 = [0, 1, 2, 4, 5, 7, 8, 9, 9], L21676 = [0, 1, 2, 4, 5, 7, 8, 9, 10], L21677 = [0, 1, 2, 4, 5, 7, 8, 9, 11], L21679 = [0, 1, 2, 4, 5, 7, 9, 9, 9], L21680 = [0, 1, 2, 4, 5, 7, 9, 9, 10], L21681 = [0, 1, 2, 4, 5, 7, 9, 9, 11], L21683 = [0, 1, 2, 4, 5, 7, 9, 9, 13], L21684 = [0, 1, 2, 4, 5, 7, 9, 10, 13], L21690 = [0, 1, 2, 4, 5, 8, 9, 9, 9], L21691 = [0, 1, 2, 4, 5, 8, 9, 9, 10], L21692 = [0, 1, 2, 4, 5, 8, 9, 9, 11], L21693 = [0, 1, 2, 4, 5, 8, 9, 9, 13], L21695 = [0, 1, 2, 4, 5, 9, 9, 9, 10], L21696 = [0, 1, 2, 4, 5, 9, 9, 9, 11], L21699 = [0, 1, 2, 4, 5, 9, 9, 10, 13], L21700 = [0, 1, 2, 4, 5, 9, 9, 11, 12], L21706 = [0, 1, 2, 4, 7, 8, 9, 9, 9], L21709 = [0, 1, 2, 4, 7, 9, 9, 9, 11], L21711 = [0, 1, 2, 4, 7, 9, 9, 9, 13], L21727 = [0, 1, 2, 4, 9, 9, 9, 9, 11], L21729 = [0, 1, 2, 4, 9, 9, 9, 10, 11], L21730 = [0, 1, 2, 4, 9, 9, 9, 10, 12], L21775 = [0, 1, 2, 5, 6, 7, 8, 9, 9], L21776 = [0, 1, 2, 5, 6, 7, 8, 9, 12], L21793 = [0, 1, 2, 5, 7, 8, 9, 9, 9], L21797 = [0, 1, 2, 5, 7, 9, 9, 9, 9], L21798 = [0, 1, 2, 5, 7, 9, 9, 9, 11], L21799 = [0, 1, 2, 5, 7, 9, 9, 9, 12], L21809 = [0, 1, 2, 5, 9, 9, 9, 9, 10], L21910 = [0, 1, 2, 6, 7, 8, 9, 9, 12], L21912 = [0, 1, 2, 6, 7, 8, 9, 10, 12], L21913 = [0, 1, 2, 6, 7, 8, 9, 11, 12], L21915 = [0, 1, 2, 6, 7, 8, 10, 11, 12], L21924 = [0, 1, 2, 6, 7, 9, 9, 11, 12], L21935 = [0, 1, 2, 6, 8, 9, 9, 10, 12], L21961 = [0, 1, 2, 7, 8, 9, 9, 9, 9], L21978 = [0, 1, 2, 7, 9, 9, 9, 9, 10], L52588 = [1, 2, 3, 3, 3, 4, 5, 7, 13], L52590 = [1, 2, 3, 3, 3, 4, 5, 8, 10], L52603 = [1, 2, 3, 3, 3, 4, 5, 11, 13], L52639 = [1, 2, 3, 3, 3, 4, 7, 8, 11], L52660 = [1, 2, 3, 3, 3, 4, 8, 10, 13], L52724 = [1, 2, 3, 3, 3, 5, 7, 10, 11], L52907 = [1, 2, 3, 3, 4, 5, 6, 7, 13], L52909 = [1, 2, 3, 3, 4, 5, 6, 8, 10], L52922 = [1, 2, 3, 3, 4, 5, 6, 11, 13], L52923 = [1, 2, 3, 3, 4, 5, 6, 12, 12], L52926 = [1, 2, 3, 3, 4, 5, 7, 8, 10], L52927 = [1, 2, 3, 3, 4, 5, 7, 8, 11], L52929 = [1, 2, 3, 3, 4, 5, 7, 8, 13], L52934 = [1, 2, 3, 3, 4, 5, 7, 9, 13], L52935 = [1, 2, 3, 3, 4, 5, 7, 10, 11], L52937 = [1, 2, 3, 3, 4, 5, 7, 10, 13], L52939 = [1, 2, 3, 3, 4, 5, 7, 11, 13], L52941 = [1, 2, 3, 3, 4, 5, 7, 12, 13], L52943 = [1, 2, 3, 3, 4, 5, 8, 9, 10], L52947 = [1, 2, 3, 3, 4, 5, 8, 10, 11], L52948 = [1, 2, 3, 3, 4, 5, 8, 10, 12], L52949 = [1, 2, 3, 3, 4, 5, 8, 10, 13], L52952 = [1, 2, 3, 3, 4, 5, 8, 12, 13], L52962 = [1, 2, 3, 3, 4, 5, 9, 11, 13], L52966 = [1, 2, 3, 3, 4, 5, 10, 11, 13], L52968 = [1, 2, 3, 3, 4, 5, 10, 12, 13], L52970 = [1, 2, 3, 3, 4, 5, 11, 12, 13], L52977 = [1, 2, 3, 3, 4, 6, 6, 7, 12], L52981 = [1, 2, 3, 3, 4, 6, 6, 8, 12], L52989 = [1, 2, 3, 3, 4, 6, 6, 10, 12], L52997 = [1, 2, 3, 3, 4, 6, 7, 8, 11], L52998 = [1, 2, 3, 3, 4, 6, 7, 8, 12], L53006 = [1, 2, 3, 3, 4, 6, 7, 10, 12], L53008 = [1, 2, 3, 3, 4, 6, 7, 11, 13], L53010 = [1, 2, 3, 3, 4, 6, 7, 12, 13], L53016 = [1, 2, 3, 3, 4, 6, 8, 10, 11], L53018 = [1, 2, 3, 3, 4, 6, 8, 10, 13], L53021 = [1, 2, 3, 3, 4, 6, 8, 12, 12], L53037 = [1, 2, 3, 3, 4, 6, 10, 12, 12], L53040 = [1, 2, 3, 3, 4, 6, 11, 12, 13], L53044 = [1, 2, 3, 3, 4, 7, 8, 9, 11], L53047 = [1, 2, 3, 3, 4, 7, 8, 10, 11], L53049 = [1, 2, 3, 3, 4, 7, 8, 11, 12], L53050 = [1, 2, 3, 3, 4, 7, 8, 11, 13], L53067 = [1, 2, 3, 3, 4, 7, 11, 12, 13], L53076 = [1, 2, 3, 3, 4, 8, 9, 10, 13], L53082 = [1, 2, 3, 3, 4, 8, 10, 11, 13],
APPENDIX
L53084 L53146 L53171 L53294 L53318 L53342 L53431 L53435 L53439 L53442 L53447 L53450 L53453 L53457 L53463 L53468 L53473 L53476 L53479 L53485 L53488 L53495 L53500 L53503 L53509 L53515 L53520 L53527 L53533 L53538 L53546 L53555 L53559 L53568 L53571 L53575 L53586 L53601 L53613 L53657 L53674 L53680 L53684 L53695 L53712 L53729 L53823 L53870 L53899
297
= [1, 2, 3, 3, 4, 8, 10, 12, 13], L53124 = [1, 2, 3, 3, 5, 6, 6, 8, 12], L53138 = [1, 2, 3, 3, 5, 6, 7, 8, 10], = [1, 2, 3, 3, 5, 6, 7, 10, 11], L53158 = [1, 2, 3, 3, 5, 6, 8, 12, 12], L53166 = [1, 2, 3, 3, 5, 6, 9, 10, 12], = [1, 2, 3, 3, 5, 6, 9, 12, 13], L53190 = [1, 2, 3, 3, 5, 7, 9, 10, 11], L53196 = [1, 2, 3, 3, 5, 7, 10, 11, 12], = [1, 2, 3, 3, 6, 6, 10, 12, 13], L53296 = [1, 2, 3, 3, 6, 6, 11, 12, 13], L53317 = [1, 2, 3, 3, 6, 7, 9, 12, 13], = [1, 2, 3, 3, 6, 7, 10, 12, 12], L53319 = [1, 2, 3, 3, 6, 7, 11, 12, 12], L53330 = [1, 2, 3, 3, 6, 8, 10, 12, 12], = [1, 2, 3, 3, 6, 9, 9, 11, 13], L53348 = [1, 2, 3, 3, 6, 9, 10, 12, 13], L53430 = [1, 2, 3, 4, 5, 6, 7, 8, 10], = [1, 2, 3, 4, 5, 6, 7, 8, 11], L53432 = [1, 2, 3, 4, 5, 6, 7, 8, 12], L53433 = [1, 2, 3, 4, 5, 6, 7, 8, 13], = [1, 2, 3, 4, 5, 6, 7, 9, 10], L53437 = [1, 2, 3, 4, 5, 6, 7, 9, 12], L53438 = [1, 2, 3, 4, 5, 6, 7, 9, 13], = [1, 2, 3, 4, 5, 6, 7, 10, 11], L53440 = [1, 2, 3, 4, 5, 6, 7, 10, 12], L53441 = [1, 2, 3, 4, 5, 6, 7, 10, 13], = [1, 2, 3, 4, 5, 6, 7, 11, 12], L53443 = [1, 2, 3, 4, 5, 6, 7, 11, 13], L53445 = [1, 2, 3, 4, 5, 6, 7, 12, 13], = [1, 2, 3, 4, 5, 6, 8, 9, 10], L53448 = [1, 2, 3, 4, 5, 6, 8, 9, 11], L53449 = [1, 2, 3, 4, 5, 6, 8, 9, 12], = [1, 2, 3, 4, 5, 6, 8, 9, 13], L53451 = [1, 2, 3, 4, 5, 6, 8, 10, 11], L53452 = [1, 2, 3, 4, 5, 6, 8, 10, 12], = [1, 2, 3, 4, 5, 6, 8, 10, 13], L53454 = [1, 2, 3, 4, 5, 6, 8, 11, 12], L53455 = [1, 2, 3, 4, 5, 6, 8, 12, 13], = [1, 2, 3, 4, 5, 6, 9, 9, 10], L53458 = [1, 2, 3, 4, 5, 6, 9, 9, 11], L53462 = [1, 2, 3, 4, 5, 6, 9, 10, 12], = [1, 2, 3, 4, 5, 6, 9, 10, 13], L53464 = [1, 2, 3, 4, 5, 6, 9, 11, 12], L53465 = [1, 2, 3, 4, 5, 6, 9, 11, 13], = [1, 2, 3, 4, 5, 6, 10, 11, 13], L53469 = [1, 2, 3, 4, 5, 6, 10, 12, 13], L53470 = [1, 2, 3, 4, 5, 6, 11, 12, 12], = [1, 2, 3, 4, 5, 7, 8, 9, 10], L53474 = [1, 2, 3, 4, 5, 7, 8, 9, 11], L53475 = [1, 2, 3, 4, 5, 7, 8, 9, 12], = [1, 2, 3, 4, 5, 7, 8, 9, 13], L53477 = [1, 2, 3, 4, 5, 7, 8, 10, 11], L53478 = [1, 2, 3, 4, 5, 7, 8, 10, 13], = [1, 2, 3, 4, 5, 7, 8, 11, 13], L53480 = [1, 2, 3, 4, 5, 7, 8, 12, 13], L53484 = [1, 2, 3, 4, 5, 7, 9, 9, 12], = [1, 2, 3, 4, 5, 7, 9, 9, 13], L53486 = [1, 2, 3, 4, 5, 7, 9, 10, 11], L53487 = [1, 2, 3, 4, 5, 7, 9, 10, 13], = [1, 2, 3, 4, 5, 7, 9, 11, 12], L53489 = [1, 2, 3, 4, 5, 7, 9, 11, 13], L53491 = [1, 2, 3, 4, 5, 7, 9, 12, 13], = [1, 2, 3, 4, 5, 8, 9, 9, 10], L53497 = [1, 2, 3, 4, 5, 8, 9, 9, 12], L53499 = [1, 2, 3, 4, 5, 8, 9, 10, 11], = [1, 2, 3, 4, 5, 8, 9, 10, 12], L53501 = [1, 2, 3, 4, 5, 8, 9, 10, 13], L53502 = [1, 2, 3, 4, 5, 8, 9, 11, 12], = [1, 2, 3, 4, 5, 8, 9, 12, 13], L53504 = [1, 2, 3, 4, 5, 8, 10, 11, 12], L53505 = [1, 2, 3, 4, 5, 8, 10, 12, 13], = [1, 2, 3, 4, 5, 9, 9, 9, 12], L53512 = [1, 2, 3, 4, 5, 9, 9, 10, 12], L53513 = [1, 2, 3, 4, 5, 9, 9, 10, 13], = [1, 2, 3, 4, 5, 9, 9, 11, 13], L53518 = [1, 2, 3, 4, 5, 9, 10, 11, 12], L53519 = [1, 2, 3, 4, 5, 9, 10, 11, 13], = [1, 2, 3, 4, 5, 9, 10, 12, 13], L53525 = [1, 2, 3, 4, 6, 7, 8, 9, 9], L53526 = [1, 2, 3, 4, 6, 7, 8, 9, 11], = [1, 2, 3, 4, 6, 7, 8, 9, 12], L53528 = [1, 2, 3, 4, 6, 7, 9, 9, 9], L53529 = [1, 2, 3, 4, 6, 7, 9, 9, 10], = [1, 2, 3, 4, 6, 7, 9, 10, 11], L53535 = [1, 2, 3, 4, 6, 7, 9, 11, 12], L53536 = [1, 2, 3, 4, 6, 7, 9, 11, 13], = [1, 2, 3, 4, 6, 7, 9, 12, 13], L53543 = [1, 2, 3, 4, 6, 8, 9, 9, 9], L53544 = [1, 2, 3, 4, 6, 8, 9, 9, 11], = [1, 2, 3, 4, 6, 8, 9, 9, 13], L53549 = [1, 2, 3, 4, 6, 9, 9, 9, 10], L53553 = [1, 2, 3, 4, 6, 9, 9, 10, 11], = [1, 2, 3, 4, 6, 9, 9, 10, 13], L53556 = [1, 2, 3, 4, 6, 9, 9, 11, 12], L53557 = [1, 2, 3, 4, 6, 9, 9, 11, 13], = [1, 2, 3, 4, 6, 9, 10, 11, 12], L53560 = [1, 2, 3, 4, 6, 9, 10, 11, 13], L53561 = [1, 2, 3, 4, 6, 9, 10, 12, 12], = [1, 2, 3, 4, 7, 8, 9, 9, 9], L53569 = [1, 2, 3, 4, 7, 8, 9, 9, 10], L53570 = [1, 2, 3, 4, 7, 8, 9, 9, 11], = [1, 2, 3, 4, 7, 8, 9, 9, 12], L53573 = [1, 2, 3, 4, 7, 8, 9, 10, 11], L53574 = [1, 2, 3, 4, 7, 8, 9, 10, 12], = [1, 2, 3, 4, 7, 8, 9, 11, 13], L53577 = [1, 2, 3, 4, 7, 9, 9, 9, 10], L53580 = [1, 2, 3, 4, 7, 9, 9, 9, 13], = [1, 2, 3, 4, 7, 9, 10, 11, 12], L53597 = [1, 2, 3, 4, 8, 9, 9, 9, 12], L53600 = [1, 2, 3, 4, 8, 9, 9, 10, 12], = [1, 2, 3, 4, 8, 9, 9, 10, 13], L53603 = [1, 2, 3, 4, 8, 9, 10, 11, 13], L53610 = [1, 2, 3, 4, 9, 9, 9, 10, 12], = [1, 2, 3, 4, 9, 9, 9, 11, 13], L53615 = [1, 2, 3, 4, 9, 9, 10, 11, 12], L53652 = [1, 2, 3, 5, 6, 6, 7, 8, 12], = [1, 2, 3, 5, 6, 6, 8, 9, 9], L53672 = [1, 2, 3, 5, 6, 7, 8, 9, 9], L53673 = [1, 2, 3, 5, 6, 7, 8, 9, 10], = [1, 2, 3, 5, 6, 7, 8, 9, 12], L53677 = [1, 2, 3, 5, 6, 7, 9, 9, 10], L53679 = [1, 2, 3, 5, 6, 7, 9, 9, 12], = [1, 2, 3, 5, 6, 7, 9, 11, 12], L53681 = [1, 2, 3, 5, 6, 7, 9, 12, 12], L53683 = [1, 2, 3, 5, 6, 8, 9, 9, 9], = [1, 2, 3, 5, 6, 8, 9, 9, 10], L53686 = [1, 2, 3, 5, 6, 8, 9, 9, 13], L53687 = [1, 2, 3, 5, 6, 8, 9, 10, 13], = [1, 2, 3, 5, 6, 9, 9, 10, 12], L53697 = [1, 2, 3, 5, 6, 9, 9, 11, 13], L53703 = [1, 2, 3, 5, 7, 8, 9, 9, 12], = [1, 2, 3, 5, 7, 9, 9, 10, 11], L53713 = [1, 2, 3, 5, 7, 9, 9, 11, 12], L53722 = [1, 2, 3, 5, 8, 9, 9, 9, 12], = [1, 2, 3, 5, 9, 9, 9, 9, 10], L53732 = [1, 2, 3, 5, 9, 9, 9, 9, 13], L53814 = [1, 2, 3, 6, 6, 7, 8, 12, 12], = [1, 2, 3, 6, 6, 7, 11, 12, 12], L53832 = [1, 2, 3, 6, 6, 8, 10, 12, 12], L53857 = [1, 2, 3, 6, 7, 8, 9, 9, 12], = [1, 2, 3, 6, 7, 9, 9, 10, 12], L53884 = [1, 2, 3, 6, 8, 9, 9, 10, 13], L53897 = [1, 2, 3, 6, 9, 9, 9, 10, 13], = [1, 2, 3, 6, 9, 9, 9, 11, 13], L53902 = [1, 2, 3, 6, 9, 9, 10, 11, 13], L53920 = [1, 2, 3, 7, 8, 9, 9, 10, 12],
298
L53921 L53936 L53969 L53992 L53997 L54008 L54011 L54017 L54029 L54053 L54122 L54149 L54318 L54323 L54382
EMILIO A. LAURET
= [1, 2, 3, 7, 8, 9, 9, 11, 12], L53923 = [1, 2, 3, 7, 8, 9, 10, 11, 12], L53935 = [1, 2, 3, 7, 9, 9, 9, 9, 13], = [1, 2, 3, 7, 9, 9, 9, 10, 12], L53937 = [1, 2, 3, 7, 9, 9, 9, 11, 12], L53953 = [1, 2, 3, 8, 9, 9, 9, 10, 12], = [1, 2, 3, 9, 9, 9, 9, 10, 13], L53990 = [1, 2, 4, 5, 7, 8, 9, 9, 9], L53991 = [1, 2, 4, 5, 7, 8, 9, 9, 10], = [1, 2, 4, 5, 7, 8, 9, 9, 11], L53995 = [1, 2, 4, 5, 7, 9, 9, 9, 9], L53996 = [1, 2, 4, 5, 7, 9, 9, 9, 10], = [1, 2, 4, 5, 7, 9, 9, 9, 11], L53999 = [1, 2, 4, 5, 7, 9, 9, 9, 13], L54000 = [1, 2, 4, 5, 7, 9, 9, 10, 13], = [1, 2, 4, 5, 8, 9, 9, 9, 9], L54009 = [1, 2, 4, 5, 8, 9, 9, 9, 10], L54010 = [1, 2, 4, 5, 8, 9, 9, 9, 11], = [1, 2, 4, 5, 8, 9, 9, 9, 13], L54013 = [1, 2, 4, 5, 9, 9, 9, 9, 10], L54014 = [1, 2, 4, 5, 9, 9, 9, 9, 11], = [1, 2, 4, 5, 9, 9, 9, 10, 13], L54018 = [1, 2, 4, 5, 9, 9, 9, 11, 12], L54026 = [1, 2, 4, 7, 8, 9, 9, 9, 9], = [1, 2, 4, 7, 9, 9, 9, 9, 11], L54031 = [1, 2, 4, 7, 9, 9, 9, 9, 13], L54051 = [1, 2, 4, 9, 9, 9, 9, 9, 11], = [1, 2, 4, 9, 9, 9, 9, 10, 11], L54054 = [1, 2, 4, 9, 9, 9, 9, 10, 12], L54121 = [1, 2, 5, 6, 7, 8, 9, 9, 9], = [1, 2, 5, 6, 7, 8, 9, 9, 12], L54143 = [1, 2, 5, 7, 8, 9, 9, 9, 9], L54148 = [1, 2, 5, 7, 9, 9, 9, 9, 9], = [1, 2, 5, 7, 9, 9, 9, 9, 11], L54150 = [1, 2, 5, 7, 9, 9, 9, 9, 12], L54162 = [1, 2, 5, 9, 9, 9, 9, 9, 10], = [1, 2, 6, 7, 8, 9, 9, 9, 12], L54320 = [1, 2, 6, 7, 8, 9, 9, 10, 12], L54321 = [1, 2, 6, 7, 8, 9, 9, 11, 12], = [1, 2, 6, 7, 8, 9, 10, 11, 12], L54336 = [1, 2, 6, 7, 9, 9, 9, 11, 12], L54350 = [1, 2, 6, 8, 9, 9, 9, 10, 12], = [1, 2, 7, 8, 9, 9, 9, 9, 9], L54403 = [1, 2, 7, 9, 9, 9, 9, 9, 10].
APPENDIX
299
9. Summarizing table for dimension 5 There are 3 cases that are obstructed by [La, Prop. 2.2 ] (hole obstruction), among 8 cases. Lens spaces Lens orbifolds ∅, {0}, {0, 1, 2}. ∃ {2}. @ Prop. 2.2 {0, 2}, {1}, {1, 2}. @ Thm. 4.7 {0, 1}. @ Rem. 4.8 {0, 1}. @ Thm. 4.11 {2}.
300
EMILIO A. LAURET
10. Summarizing table for dimension 7 There are 7 cases that are obstructed by [La, Prop. 2.2 ] (hole obstruction), among 16 cases. Lens spaces Lens orbifolds ∅, {0}, {0, 1}, {0, 1, 2, 3}. ∃ {2}, {3}. @ Prop. 2.2 {0, 1, 3}, {0, 2}, {0, 2, 3}, {1}, (hole obstruction) {1, 2}, {1, 2, 3}, {1, 3}. @ Thm. 4.7 {0, 1, 2}. @ Rem. 4.8 {0, 1, 2}. @ Thm. 4.11 {0, 3}, {2, 3}. @ Rem. 4.13 {0, 3}. @? {2}, {3}. {2, 3}.
APPENDIX
301
11. Summarizing table for dimension 9 There are 16 cases that are obstructed by [La, Prop. 2.2 ] (hole obstruction), among 32 cases. Lens spaces Lens orbifolds ∅, {0}, {0, 1}, {0, 1, 2}, {0, 1, 2, 3, 4}. ∃ {2, 3}, {2, 3, 4}, {3, 4}, {4}. @ Prop. 2.2 {0, 1, 2, 4}, {0, 1, 3}, {0, 1, 3, 4}, {0, 2}, {0, 2, 3}, (hole {0, 2, 3, 4}, {0, 2, 4}, {1}, {1, 2}, {1, 2, 3}, obstruction) {1, 2, 3, 4}, {1, 2, 4}, {1, 3}, {1, 3, 4}, {1, 4}, {2, 4}. @ Thm. 4.7 {0, 1, 2, 3}. @ Rem. 4.8 {0, 1, 2, 3}. @ Thm. 4.11 {0, 1, 4}, {0, 3, 4}, {2, 3, 4}. @ Rem. 4.13 {0, 1, 4}, {0, 3, 4}. {0, 3}, {0, 4}, {2}, {3}. @? {2, 3}, {3, 4}, {4}.
302
EMILIO A. LAURET
12. Summarizing table for dimension 11 For reason of space, we do not include in the next table any case I such that its non-existence is due to the hole obstruction in [La, Prop. 2.2 ]. There are 36 such cases among 64. Lens spaces Lens orbifolds ∅, {0}, {0, 1}, {0, 1, 2}, {0, 1, 2, 3}, {0, 1, 2, 3, 4, 5}, {4, 5}. ∃ {0, 3}, {0, 5}, {2, 3, 4}, {3}, {3, 4, 5}, {4}, {5}. @ Thm. 4.7 {0, 1, 2, 3, 4}. @ Rem. 4.8 {0, 1, 2, 3, 4}. {0, 1, 2, 5}, {0, 1, 4, 5}, @ Thm. 4.11 {0, 3, 4, 5}, {2, 3, 4, 5}. {0, 1, 2, 5}, {0, 1, 4, 5}, @ Rem. 4.13 {0, 3, 4, 5}. {0, 4}, {0, 1, 4}, {0, 1, 5}, {0, 3, 4}, {0, 4, 5}, {2}, {2, 3}, {2, 5}, {3, 4}. @? {0, 3}, {0, 5}, {2, 3, 4}, {2, 3, 4, 5}. {3}, {3, 4, 5}, {4}, {5}.
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13. Summarizing table for dimension 13 Similarly as above, we do not show the subsets I obstructed by the hole obstruction. Such subsets are 79 among 128. Lens spaces Lens orbifolds ∅, {0}, {0, 1}, {0, 1, 2}, {0, 1, 2, 3}, {0, 1, 2, 3, 4}, {0, 1, 2, 3, 4, 5, 6}, {4}, {6}. ∃ {0, 1, 6}, {0, 3, 4}, {0, 5, 6}, {0, 6}, {2}, {2, 3, 6}, {2, 5}, {2, 5, 6}, {3}, {3, 4, 5, 6}, {4, 5}, {4, 5, 6}, {5}, {5, 6}. @ Thm. 4.7 {0, 1, 2, 3, 4, 5}. @ Rem. 4.8 {0, 1, 2, 3, 4, 5}. {0, 1, 2, 3, 6}, {0, 1, 2, 5, 6}, @ Thm. 4.11 {0, 1, 4, 5, 6}, {0, 3, 4, 5, 6}, {2, 3, 4, 5, 6}. {0, 1, 2, 3, 6}, {0, 1, 2, 5, 6}, @ Rem. 4.13 {0, 1, 4, 5, 6}, {0, 3, 4, 5, 6}. {0, 1, 2, 5}, {0, 1, 2, 6}, {0, 1, 4}, {0, 1, 4, 5}, {0, 1, 5}, {0, 1, 5, 6}, {0, 3}, {0, 3, 4, 5}, {0, 3, 6}, {0, 4}, {0, 4, 5}, {0, 4, 5, 6}, {0, 5}, {2, 3}, {2, 3, 4}, @? {2, 3, 4, 5}, {2, 6}, {3, 4}, {3, 4, 5}, {3, 6}. {0, 1, 6}, {0, 3, 4}, {0, 5, 6}, {2, 3, 4, 5, 6}. {0, 6}, {2}, {2, 3, 6}, {2, 5}, {2, 5, 6}, {3}, {3, 4, 5, 6}, {4, 5}, {4, 5, 6}, {5}, {5, 6}.
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14. Summarizing table for dimension 15 Similarly as above, we do not show the subsets I obstructed by the hole obstruction. Such subsets are 170 among 28 = 256. In Table 6 does not appear any I-isospectral family for I = {0, 1, 2, 3, 4, 5, 6, 7}, that is, p-isospectral for all p. However, such pairs exist, but the smallest order of their fundamental groups is equal to 100. The author expects that there are some more subsets I such that there exists a pair of Iisospectral lens spaces and lens orbifolds with fundamental group of order q higher than 27. For example, there should exist a pair of {0, 1, 2, 3}-isospectral lens spaces with fundamental group of order q > 27. Lens spaces Lens orbifolds ∅, {0}, {0, 1}, {0, 1, 2}, {0, 1, 2, 3, 4}, {0, 1, 2, 3, 4, 5, 6, 7}. {0, 1, 2, 3}, {0, 1, 4}, {0, 1, 6, 7}, {0, 1, 7}, {0, 3}, {0, 5}, {0, 7}, ∃ {2, 3, 4, 5, 6}, {3, 4, 5}, {3, 4, 5, 6, 7}, {4}, {4, 5}, {4, 5, 6, 7}, {5}, {5, 6, 7}, {6, 7}, {7}. @ Thm. 4.7 {0, 1, 2, 3, 4, 5, 6}. @ Rem. 4.8 {0, 1, 2, 3, 4, 5, 6}. {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, @ Thm. 4.11 {0, 1, 2, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 7}, {2, 3, 4, 5, 6, 7}. {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 6, 7}, @ Rem. 4.13 {0, 1, 2, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 7}. {0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 7}, {0, 1, 2, 5}, {0, 1, 2, 5, 6}, {0, 1, 2, 6}, {0, 1, 2, 6}, {0, 1, 2, 6, 7}, {0, 1, 2, 7}, {0, 1, 4, 5}, {0, 1, 4, 5, 6}, {0, 1, 4, 7}, {0, 1, 5}, {0, 1, 5, 6}, {0, 1, 5, 6, 7}, {0, 1, 6}, {0, 3, 4}, {0, 3, 4, 5}, {0, 3, 4, 5, 6}, {0, 3, 4, 7}, {0, 3, 6}, {0, 3, 6, 7}, {0, 3, 7}, {0, 4}, {0, 4, 5}, @? {0, 4, 5, 6}, {0, 4, 5, 6, 7}, {0, 4, 7}, {0, 5, 6}, {0, 5, 6, 7}, {0, 6}, {0, 6, 7}, {2}, {2, 3}, {2, 3, 4}, {2, 3, 4, 5}, {2, 3, 4, 7}, {2, 3, 6}, {2, 3, 6, 7}, {2, 3, 7}, {2, 5}, {2, 5, 6}, {2, 5, 6, 7}, {2, 6}, {2, 6, 7}, {2, 7}, {3}, {3, 4}, {3, 4, 5, 6}, {3, 4, 7}, {3, 6}, {3, 6, 7}, {3, 7}, {4, 5, 6}, {4, 7}, {5, 6}, {6}. {0, 1, 2, 3}, {0, 1, 4}, {0, 1, 6, 7}, {2, 3, 4, 5, 6, 7}, {0, 1, 7}, {0, 3}, {0, 5}, {0, 7}, {2, 3, 4, 5, 6}, {3, 4, 5}, {3, 4, 5, 6, 7}, {4}, {4, 5}, {4, 5, 6, 7}, {5}, {5, 6, 7}, {6, 7}, {7}.
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15. Summarizing table for dimension 17 Lens spaces Lens orbifolds ∅, {0}, {0, 1}, {0, 1, 2}, {0, 1, 2, 3, 4}, {0, 1, 2, 3, 4, 5, 6, 7, 8}, {0, 7, 8}. {0, 1, 2, 3}, {0, 5, 6, 7}, {0, 6, 7, 8}, {0, 8}, {2, 3}, {2, 3, 4, 5, 6, 7}, {2, 3, 6, 7}, ∃ {3, 4, 5, 6}, {3, 4, 8}, {4}, {4, 5}, {4, 5, 6}, {5}, {5, 6, 7, 8}, {6}, {6, 7}, {6, 7, 8}, {7}, {7, 8}, {8}. @ Thm. 4.7 {0, 1, 2, 3, 4, 5, 6, 7}. @ Rem. 4.8 {0, 1, 2, 3, 4, 5, 6, 7}. {0, 1, 2, 3, 4, 5, 8}, {0, 1, 2, 3, 4, 7, 8}, @ Thm. 4.11 {0, 1, 2, 3, 6, 7, 8}, {0, 1, 2, 5, 6, 7, 8}, {0, 1, 4, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 7, 8}. {0, 1, 2, 3, 4, 5, 8}, {0, 1, 2, 3, 4, 7, 8}, @ Rem. 4.13 {0, 1, 2, 3, 6, 7, 8}, {0, 1, 2, 5, 6, 7, 8}, {0, 1, 4, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 7, 8}. {0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 5, 6}, {0, 1, 2, 3, 4, 7}, {0, 1, 2, 3, 4, 8}, {0, 1, 2, 3, 6}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 3, 7}, {0, 1, 2, 3, 7, 8}, {0, 1, 2, 3, 8}, {0, 1, 2, 5}, {0, 1, 2, 5, 6}, {0, 1, 2, 5, 6, 7}, {0, 1, 2, 5, 8}, {0, 1, 2, 6}, {0, 1, 2, 6, 7}, {0, 1, 2, 6, 7, 8}, {0, 1, 2, 7}, {0, 1, 2, 7, 8}, {0, 1, 2, 8}, {0, 1, 4}, {0, 1, 4, 5}, {0, 1, 4, 5, 6}, {0, 1, 4, 5, 6, 7}, {0, 1, 4, 5, 8}, {0, 1, 4, 7}, {0, 1, 4, 7, 8}, {0, 1, 4, 8}, {0, 1, 5}, {0, 1, 5, 6}, {0, 1, 5, 6, 7}, {0, 1, 5, 6, 7, 8}, {0, 1, 5, 8}, {0, 1, 6}, {0, 1, 6, 7}, {0, 1, 6, 7, 8}, {0, 1, 7}, {0, 1, 7, 8}, {0, 1, 8}, {0, 3}, {0, 3, 4}, {0, 3, 4, 5}, {0, 3, 4, 5, 6}, {0, 3, 4, 5, 6, 7}, {0, 3, 4, 5, 8}, {0, 3, 4, 7}, {0, 3, 4, 7, 8}, {0, 3, 4, 8}, {0, 3, 6}, {0, 3, 6, 7}, {0, 3, 6, 7, 8}, {0, 3, 6, 7}, {0, 3, 7, 8}, {0, 3, 8}, {0, 4}, {0, 4, 5}, {0, 4, 5, 6}, {0, 4, 5, 6, 7}, {0, 4, 5, 6, 7, 8}, @? {0, 4, 5, 8}, {0, 4, 7}, {0, 4, 7, 8}, {0, 4, 8}, {0, 5}, {0, 5, 6}, {0, 5, 6, 7, 8}, {0, 5, 8}, {0, 6}, {0, 6, 7}, {0, 7}, {2}, {2, 3, 4}, {2, 3, 4, 5}, {2, 3, 4, 5, 6}, {2, 3, 4, 5, 8}, {2, 3, 4, 7}, {2, 3, 4, 7, 8}, {2, 3, 4, 8}, {2, 3, 6}, {2, 3, 6, 7, 8}, {2, 3, 7}, {2, 3, 7, 8}, {2, 3, 8}, {2, 5}, {2, 5, 6}, {2, 5, 6, 7}, {2, 5, 6, 7, 8}, {2, 5, 8}, {2, 6}, {2, 6, 7}, {2, 6, 7, 8}, {2, 7}, {2, 7, 8}, {2, 8}, {3}, {3, 4}, {3, 4, 5}, {3, 4, 5, 6, 7}, {3, 4, 5, 6, 7, 8}, {3, 4, 5, 8}, {3, 4, 7}, {3, 4, 7, 8}, {3, 6}, {3, 6, 7}, {3, 6, 7, 8}, {3, 7}, {3, 7, 8}, {3, 8}, {4, 5, 6, 7}, {4, 5, 6, 7, 8}, {4, 5, 8}, {4, 7}, {4, 7, 8}, {4, 8}, {5, 6}, {5, 6, 7}, {5, 8}. {0, 1, 2, 3}, {0, 5, 6, 7}, {0, 6, 7, 8}, {2, 3, 4, 5, 6, 7, 8}. {0, 8}, {2, 3}, {2, 3, 4, 5, 6, 7}, {2, 3, 6, 7}, {3, 4, 5, 6}, {3, 4, 8}, {4}, {4, 5}, {4, 5, 6}, {5}, {5, 6, 7, 8}, {6}, {6, 7}, {6, 7, 8}, {7}, {7, 8}, {8}.
Similarly as in the previous two cases, we do not show the subsets I obstructed by the hole obstruction. In this case, such subsets are 361 among 29 = 512.
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In Table 7 does not appear any {0, 1, 2, 3, 4, 5, 6, 7, 8}-isospectral family, that is, p-isospectral for all p. However, such pairs exist. For example, one can check that L(132 ; 130 , 132 , 133 , 134 , 135 , 136 , 137 , 138 , 139 ), L(132 ; 130 , 131 , 132 , 133 , 134 , 135 , 136 , 137 , 139 ), are p-isospectral for all p by [DD14, Thm. 1]. The author expects that there are many more subsets I such that there exists a pair of I-isospectral lens spaces or lens orbifolds with fundamental group of order q higher than 27.
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16. Existence and non-existence distribution For a fixed dimension 2n − 1, the next table shows the number of subsets I of {0, . . . , n − 1} such that there exists a (2n − 1)-dimensional I-isospectral family in the computational results. Furthermore, it shows the number of subsets I obstructed by [La, Prop. 2.2 ] (hole obstruction) or by the results in [La, §4] (i.e. Theorem 4.7 or Remark 4.8, Theorem 4.11 or Remark 4.13), and also the number of cases that we do not know the reason for their non-existence. In a fixed dimension, the left (resp. right) column considers lens spaces (resp. lens orbifolds). existence or reason dimension for the non-existence 5 7 9 11 13 15 17 ∃ 3 4 4 6 5 9 7 14 9 18 6 23 7 27 @ Prop. 2.2 3 7 16 36 79 170 361 @ Sect. 4 2 1 3 2 4 3 5 4 6 5 7 6 8 7 @? 0 0 2 1 7 4 16 10 34 26 73 57 136 117 Total 8 16 32 64 128 256 512
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17. Algorithms 17.1. Lens spaces. We will explain the algorithm which gives, for n and q positive integers fixed, the set of classes (up to isometry) of (2n−1)-dimensional lens orbifolds with fundamental group of order q. Each of them is determined by an integer vector s = (s1 , . . . , sn ) of length n satisfying gcd(q, s1 , . . . , sn ) = 1. One can assume that 0 ≤ s1 ≤ s2 ≤ · · · ≤ sn ≤ q/2 by the isometry condition in [La, §2.2]. We consider the lexicographic order in the set S := {(s1 , . . . , sn ) ∈ Zn : 0 ≤ s1 ≤ s2 ≤ · · · ≤ sn ≤ q/2}. The next algorithm returns a representative set of (2n − 1)-dimensional lens orbifolds, where each element is the smallest element (with respect to the lexicographic order in S) in its isometry class. Algorithm 17.1. Let n and q positive integer numbers. (1) Initialize sol as an empty list and set s = [0, . . . , 0, 1]. (2) Given s, check if gcd(q, s) = 1 and L(q; s) is not isometric to any L(q; s0 ) with s0 ∈ S smaller than s. (3) In the affirmative case, add s to sol. Else, take the next element to s in S, and call it again s. If s is the largest element in S, go to (4), otherwise go back to (2). (4) Return sol. For small values of n and q, Tables 8, 9 and 10 show the number of (2n − 1)-dimensional lens orbifolds, lens spaces and lens spaces in L0 (n; q) respectively, with fundamental group of order q. We recall that L0 (n; q), which was introduced in [La, §2.4], is given by lens spaces L(q; s1 , . . . , sn ) satisfying that si 6≡ ±sj (mod q) for all i 6= j. Ikeda used this set to give several interesting examples (see [La, §2.4]). 17.2. Isospectralities. The next algorithm returns, for n and q positive integers and each subset I of {0, 1, . . . , n − 1}, the set of families of (2n − 1)-dimensional lens orbifolds with fundamental group of order q such that they are I-isospectral. We recall that a family is Iisospectral if they are p-isospectral pairwise for every p ∈ I and, for any p0 6∈ I, there are two elements in the family such that they are not p0 -isospectral. Briefly, the algorithm calculates for each lens orbifolds L as above, the generating functions p FL (z) ∈ C(x) for 0 ≤ p ≤ n − 1 as in Ikeda’s formula [La, (2.6)] and it compares these numbers to obtain the I-isospectralities. In order to have a very fast algorithm, we replace the field C(x) by a finite field Fπ with order a huge prime π of around 20 digits. As a consequence, there is a probability of π1 ∼ 10120 for two different power series in C(x) to induce the same associated number in Fπ . In conclusion, if the computational results do not show that two lens orbifolds are I-isospectral, then this is a proof for this fact. On the other hand, if the computational results show that two lens orbifolds are I-isospectral, then there is a very tiny probability that they are already I 0 -isospectral for some I 0 strictly contained in I. Algorithm 17.2. Let n and q positive integer numbers. (1) Pick randomly a prime number π less than 1020 . Let Fπ be the finite field with π elements. Pick any primitive q-root of unity ξ in Fπ and pick randomly an element z0 in Fπ . (2) Compute the representative set S of (2n − 1)-dimensional lens orbifolds with fundamental group of order q. p (3) Compute for each s in S and 0 ≤ p ≤ n − 1, the number FL(q;s) (z0 ) in Fπ as in [La, (2.6)], by replacing ξq = e2πi/q by ξ, z by z0 and any integer number by its class in Fπ .
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Table 8. The number of lens orbifolds in each dimension and q fixed. q 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
3 2 2 3 3 5 3 5 4 7 4 9 5 8 8 8 6 11 6 12 10 11 7 16 9 13 10 15 9 22 9 14 14 16 14 21 11 17 16 22
dimension 5 7 9 11 13 3 4 5 6 7 3 4 5 6 7 6 10 15 21 28 5 8 11 15 19 13 26 45 71 105 7 12 19 29 41 14 31 59 102 164 11 23 42 71 112 23 57 119 224 389 11 25 51 93 159 36 103 243 505 958 15 37 79 159 291 33 99 247 548 1111 31 89 215 464 921 35 115 313 749 1627 21 64 163 380 809 57 209 620 1598 3716 25 80 223 558 1273 66 253 789 2137 5216 49 176 527 1398 3371 61 247 823 2384 6209 33 124 397 1125 2893 104 461 1631 4960 13486 45 183 620 1864 5048 81 368 1363 4396 12681 59 260 948 3016 8630 104 506 1983 6693 20156 49 221 833 2777 8315 177 931 3871 13739 43359 55 259 1035 3621 11373 105 568 2479 9266 30735 97 495 2083 7613 24913 123 692 3143 12274 42511 99 518 2253 8562 29183 190 1163 5599 22819 82044 75 410 1873 7493 26721 147 906 4503 19129 71831 129 753 3611 14994 55485 206 1322 6757 29456 113596
15 17 8 9 8 9 36 45 24 29 148 201 56 75 250 365 168 243 638 997 258 401 1696 2843 508 843 2100 3755 1714 3025 3279 6218 1619 3049 7975 16045 2703 5407 11735 24711 7535 15823 14863 33197 6871 15269 33603 77987 12621 29420 33499 82199 22659 55379 55413 141315 22865 58395 124677 332025 32691 87175 92615 257722 74476 206297 133701 387709 90848 261803 266971 799969 86836 260429 243993 762067 186696 579507 396681 1274559
(4) Initialize sol as a list with 2n empty lists, indexed by the subsets of {0, . . . , n − 1}. (5) Run over the pairs of lens orbifolds {L(q; s), L(q; s0 )}, and compare for every 0 ≤ p ≤ p−1 p−1 p n−1, when they are p-isospectral by checking FL(q;s) (z0 ) = FL(q;s 0 ) (z0 ) and FL(q;s) (z0 ) = p FL(q;s 0 ) (z0 ).
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Table 9. The number of lens spaces in each dimension and q fixed. dimension q 3 5 7 9 11 13 15 17 2 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 3 3 4 4 5 5 5 2 2 6 1 1 1 1 1 1 1 1 5 7 10 12 15 19 7 2 4 8 2 2 3 3 4 4 5 5 5 7 10 12 15 19 9 2 4 10 2 2 3 3 4 4 5 5 26 42 66 99 143 11 3 7 14 12 2 2 3 3 4 4 5 5 13 4 10 22 42 80 132 217 335 14 2 4 5 7 10 12 15 19 15 3 5 10 14 22 30 43 55 16 3 5 10 14 22 30 43 55 17 5 15 43 99 217 429 810 1430 5 7 10 12 15 19 18 2 4 19 5 19 55 143 335 715 1430 2704 20 3 5 10 14 22 30 43 55 21 4 10 22 42 80 132 217 335 22 3 7 14 26 42 66 99 143 23 6 26 91 273 728 1768 3978 8398 24 4 5 11 14 24 30 45 55 25 6 22 73 201 504 1144 2438 4862 26 4 10 22 42 80 132 217 335 27 5 19 55 143 335 715 1430 2704 28 4 10 22 42 80 132 217 335 29 8 40 172 612 1944 5538 14550 35530 30 3 5 10 14 22 30 43 55 31 8 46 204 776 2586 7752 21318 54484 32 5 15 43 99 217 429 810 1430 33 6 22 73 201 504 1144 2438 4862 34 5 15 43 99 217 429 810 1430 35 7 31 116 364 1038 2652 6310 14000 42 80 132 217 335 36 4 10 22 37 10 64 335 1463 5620 19228 60115 173593 38 5 19 55 143 335 715 1430 2704 39 7 31 116 364 1038 2652 6310 14000 40 6 15 46 99 222 429 819 1430 (6) Add the pair {L(q; s), L(q; s0 )} in the entry of sol according to {p : L(q; s) and L(q; s0 ) are p-isospectral} ⊂ {0, . . . , n − 1}. In case some of them was already in a list inside this entry, add the other element to the same list.
APPENDIX
Table 10. The number of lens spaces used by Ikeda in each dimension and q fixed. That is, the lens spaces L(q; s1 , . . . , sn ) satisfying si 6≡ ±sj (mod q) for all i 6= j. q 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
3 0 0 0 1 0 1 1 1 1 2 1 3 1 2 2 4 1 4 2 3 2 5 3 5 3 4 3 7 2 7 4 5 4 6 3 9 4 6 5
dimension 5 7 9 11 13 15 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 4 3 1 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 7 10 7 4 1 1 0 1 0 0 0 0 0 0 10 14 14 10 4 1 1 1 1 0 0 0 0 0 4 3 1 1 0 0 0 2 1 1 0 0 0 0 15 30 42 42 30 15 5 1 1 0 0 0 0 0 12 22 26 22 12 5 1 4 3 1 1 0 0 0 10 14 14 10 4 1 1 4 3 1 1 0 0 0 26 73 143 217 246 217 143 1 1 0 0 0 0 0 31 91 201 335 429 429 335 7 10 7 4 1 1 0 12 22 26 22 12 5 1 7 10 7 4 1 1 0 19 43 66 80 66 43 19 4 3 1 1 0 0 0 46 172 476 1038 1768 2438 2704 10 14 14 10 4 1 1 19 43 66 80 66 43 19 7 12 7 5 1 1 0
311
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(7) Return the list sol, which for each subset I of {0, . . . , n − 1}, it gives the list of all families in S which are I-isospectral. The author thanks to Peter Doyle to share this clever idea to compute the numbers in the field Fπ in place of the field C(x). He communicated to the author that this idea was explained by John Voight.
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18. Non-singular matrix In Subsection 4.5 in [La] we define the matrix (0) (n−2) A1 (z) . . . A1 (z) .. ... (18.1) A = ... , . (0) (n−2) An (z) . . . An (z) which has coefficients in C(z) and its size is n × (n − 1). Lemma 4.9 ensures that for n ≤ 9, any square matrix obtained by deleting one row from A is non-singular. Here, we include the (non-zero) determinant of such matrices calculated by Sage [Sa]. In each table, the fist column indicates the row deleted and the second one indicates the determinant of the corresponding obtained matrix. n=2 row determinant 1
z2 + 1
2
1 n=3
row
determinant
1
z6 − z4 + z2 − 1
2
z4 − 1
3
z2 − 1 n=4
row
determinant
1
z 12 − 3 z 10 + 3 z 8 − 3 z 4 + 3 z 2 − 1
2
z 10 − 3 z 8 + 4 z 6 − 4 z 4 + 3 z 2 − 1
3
z8 − 2 z6 + 2 z2 − 1
4
z6 − 3 z4 + 3 z2 − 1 n=5
row 1
determinant z
20
− 6z
18
+ 15 z
16
− 20 z
14
+ 16 z 12 − 12 z 10 + 16 z 8 − 20 z 6 + 15 z 4 − 6 z 2 + 1
2
z 18 − 6 z 16 + 15 z 14 − 19 z 12 + 9 z 10 + 9 z 8 − 19 z 6 + 15 z 4 − 6 z 2 + 1
3
z 16 − 6 z 14 + 16 z 12 − 26 z 10 + 30 z 8 − 26 z 6 + 16 z 4 − 6 z 2 + 1
4
z 14 − 5 z 12 + 9 z 10 − 5 z 8 − 5 z 6 + 9 z 4 − 5 z 2 + 1
5
z 12 − 6 z 10 + 15 z 8 − 20 z 6 + 15 z 4 − 6 z 2 + 1
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n=6 row
determinant
1
− 10 z + 45 z − 120 z 24 + 210 z 22 − 251 z 20 + 200 z 18 −75 z 16 − 75 z 14 + 200 z 12 − 251 z 10 + 210 z 8 − 120 z 6 + 45 z 4 − 10 z 2 + 1
2
z 28 − 10 z 26 + 45 z 24 − 120 z 22 + 211 z 20 − 262 z 18 + 255 z 16 −240 z 14 + 255 z 12 − 262 z 10 + 211 z 8 − 120 z 6 + 45 z 4 − 10 z 2 + 1
3
z 26 − 10 z 24 + 45 z 22 − 119 z 20 + 200 z 18 − 207 z 16 +90 z 14 + 90 z 12 − 207 z 10 + 200 z 8 − 119 z 6 + 45 z 4 − 10 z 2 + 1
4
z 24 − 10 z 22 + 46 z 20 − 130 z 18 + 255 z 16 − 372 z 14 +420 z 12 − 372 z 10 + 255 z 8 − 130 z 6 + 46 z 4 − 10 z 2 + 1
5
z 22 − 9 z 20 + 35 z 18 − 75 z 16 + 90 z 14 −42 z 12 − 42 z 10 + 90 z 8 − 75 z 6 + 35 z 4 − 9 z 2 + 1
6
z 20 − 10 z 18 + 45 z 16 − 120 z 14 + 210 z 12 −252 z 10 + 210 z 8 − 120 z 6 + 45 z 4 − 10 z 2 + 1
z
30
28
26
n=7 row
determinant
1
z 42 − 15 z 40 + 105 z 38 − 455 z 36 + 1365 z 34 − 3003 z 32 + 5006 z 30 −6450 z 28 + 6540 z 26 − 5460 z 24 + 4368 z 22 − 4368 z 20 + 5460 z 18 − 6540 z 16 +6450 z 14 − 5006 z 12 + 3003 z 10 − 1365 z 8 + 455 z 6 − 105 z 4 + 15 z 2 − 1
2
z 40 − 15 z 38 + 105 z 36 − 455 z 34 + 1365 z 32 − 3002 z 30 + 4990 z 28 −6330 z 26 + 5980 z 24 − 3640 z 22 + 3640 z 18 − 5980 z 16 + 6330 z 14 − 4990 z 12 +3002 z 10 − 1365 z 8 + 455 z 6 − 105 z 4 + 15 z 2 − 1
3
z 38 − 15 z 36 + 105 z 34 − 455 z 32 + 1366 z 30 − 3018 z 28 + 5110 z 26 −6890 z 24 + 7800 z 22 − 8008 z 20 + 8008 z 18 − 7800 z 16 + 6890 z 14 − 5110 z 12 +3018 z 10 − 1366 z 8 + 455 z 6 − 105 z 4 + 15 z 2 − 1
4
z 36 − 15 z 34 + 105 z 32 − 454 z 30 + 1350 z 28 − 2898 z 26 + 4550 z 24 −5070 z 22 + 3432 z 20 − 3432 z 16 + 5070 z 14 − 4550 z 12 + 2898 z 10 − 1350 z 8 +454 z 6 − 105 z 4 + 15 z 2 − 1
5
z 34 − 15 z 32 + 106 z 30 − 470 z 28 + 1470 z 26 − 3458 z 24 + 6370 z 22 −9438 z 20 + 11440 z 18 − 11440 z 16 + 9438 z 14 − 6370 z 12 + 3458 z 10 − 1470 z 8 +470 z 6 − 106 z 4 + 15 z 2 − 1
6
z 32 − 14 z 30 + 90 z 28 − 350 z 26 + 910 z 24 − 1638 z 22 + 2002 z 20 −1430 z + 1430 z 14 − 2002 z 12 + 1638 z 10 − 910 z 8 + 350 z 6 − 90 z 4 + 14 z 2 − 1 18
7
z 30 − 15 z 28 + 105 z 26 − 455 z 24 + 1365 z 22 − 3003 z 20 + 5005 z 18 −6435 z + 6435 z 14 − 5005 z 12 + 3003 z 10 − 1365 z 8 + 455 z 6 − 105 z 4 + 15 z 2 − 1 16
APPENDIX
n=8 row
determinant 56
54
52
50
1
z − 21 z + 210 z − 1330 z + 5985 z 48 − 20349 z 46 + 54264 z 44 − 116279 z 42 +203469 z 40 − 293720 z 38 + 351386 z 36 − 346731 z 34 + 273581 z 32 − 149226 z 30 +149226 z 26 − 273581 z 24 + 346731 z 22 − 351386 z 20 + 293720 z 18 − 203469 z 16 +116279 z 14 − 54264 z 12 + 20349 z 10 − 5985 z 8 + 1330 z 6 − 210 z 4 + 21 z 2 − 1
2
z 54 − 21 z 52 + 210 z 50 − 1330 z 48 + 5985 z 46 − 20349 z 44 + 54265 z 42 − 116301 z 40 +203700 z 38 − 295260 z 36 + 358701 z 34 − 373065 z 32 + 348194 z 30 − 319770 z 28 +319770 z 26 − 348194 z 24 + 373065 z 22 − 358701 z 20 + 295260 z 18 − 203700 z 16 +116301 z 14 − 54265 z 12 + 20349 z 10 − 5985 z 8 + 1330 z 6 − 210 z 4 + 21 z 2 − 1
3
z 52 − 21 z 50 + 210 z 48 − 1330 z 46 + 5985 z 44 − 20348 z 42 + 54243 z 40 − 116070 z 38 +202160 z 36 − 287945 z 34 + 332367 z 32 − 298452 z 30 + 177650 z 28 − 177650 z 24 +298452 z 22 − 332367 z 20 + 287945 z 18 − 202160 z 16 + 116070 z 14 − 54243 z 12 +20348 z 10 − 5985 z 8 + 1330 z 6 − 210 z 4 + 21 z 2 − 1
4
z 50 − 21 z 48 + 210 z 46 − 1330 z 44 + 5986 z 42 − 20370 z 40 + 54474 z 38 − 117610 z 36 +209475 z 34 − 314279 z 32 + 406980 z 30 − 468996 z 28 + 497420 z 26 − 497420 z 24 +468996 z 22 − 406980 z 20 + 314279 z 18 − 209475 z 16 + 117610 z 14 − 54474 z 12 +20370 z 10 − 5986 z 8 + 1330 z 6 − 210 z 4 + 21 z 2 − 1
5
z 48 − 21 z 46 + 210 z 44 − 1329 z 42 + 5964 z 40 − 20139 z 38 + 52934 z 36 − 110295 z 34 +183141 z 32 − 239666 z 30 + 236436 z 28 − 149226 z 26 + 149226 z 22 − 236436 z 20 +239666 z 18 − 183141 z 16 + 110295 z 14 − 52934 z 12 + 20139 z 10 − 5964 z 8 +1329 z 6 − 210 z 4 + 21 z 2 − 1
6
z 46 − 21 z 44 + 211 z 42 − 1351 z 40 + 6195 z 38 − 21679 z 36 + 60249 z 34 − 136629 z 32 +257754 z 30 − 410210 z 28 + 556206 z 26 − 646646 z 24 + 646646 z 22 − 556206 z 20 +410210 z 18 − 257754 z 16 + 136629 z 14 − 60249 z 12 + 21679 z 10 − 6195 z 8 +1351 z 6 − 211 z 4 + 21 z 2 − 1
7
z 44 − 20 z 42 + 189 z 40 − 1120 z 38 + 4655 z 36 − 14364 z 34 + 33915 z 32 − 62016 z 30 +87210 z 28 − 90440 z 26 + 58786 z 24 − 58786 z 20 + 90440 z 18 − 87210 z 16 +62016 z 14 − 33915 z 12 + 14364 z 10 − 4655 z 8 + 1120 z 6 − 189 z 4 + 20 z 2 − 1
8
z 42 − 21 z 40 + 210 z 38 − 1330 z 36 + 5985 z 34 − 20349 z 32 + 54264 z 30 − 116280 z 28 +203490 z 26 − 293930 z 24 + 352716 z 22 − 352716 z 20 + 293930 z 18 −203490 z 16 + 116280 z 14 − 54264 z 12 + 20349 z 10 − 5985 z 8 + 1330 z 6 − 210 z 4 +21 z 2 − 1
315
316
EMILIO A. LAURET
n=9 row
determinant 72
70
68
1
z − 28 z + 378 z − 3276 z 66 + 20475 z 64 − 98280 z 62 + 376740 z 60 −1184040 z 58 + 3108106 z 56 − 6906928 z 54 + 13123488 z 52 − 21477456 z 50 +30442230 z 48 − 37540440 z 46 + 40493340 z 44 − 38626200 z 42 + 33529860 z 40 −28381080 z 38 + 26246220 z 36 − 28381080 z 34 + 33529860 z 32 − 38626200 z 30 +40493340 z 28 − 37540440 z 26 + 30442230 z 24 − 21477456 z 22 + 13123488 z 20 −6906928 z 18 + 3108106 z 16 − 1184040 z 14 + 376740 z 12 − 98280 z 10 +20475 z 8 − 3276 z 6 + 378 z 4 − 28 z 2 + 1
2
z 70 − 28 z 68 + 378 z 66 − 3276 z 64 + 20475 z 62 − 98280 z 60 + 376740 z 58 −1184039 z 56 + 3108077 z 54 − 6906522 z 52 + 13119834 z 50 − 21453705 z 48 +30323475 z 46 − 37065420 z 44 + 38932560 z 42 − 34334055 z 40 + 23514855 z 38 −8351070 z 36 − 8351070 z 34 + 23514855 z 32 − 34334055 z 30 + 38932560 z 28 −37065420 z 26 + 30323475 z 24 − 21453705 z 22 + 13119834 z 20 − 6906522 z 18 +3108077 z 16 − 1184039 z 14 + 376740 z 12 − 98280 z 10 + 20475 z 8 −3276 z 6 + 378 z 4 − 28 z 2 + 1
3
z 68 − 28 z 66 + 378 z 64 − 3276 z 62 + 20475 z 60 − 98280 z 58 + 376741 z 56 −1184068 z 54 + 3108483 z 52 − 6910176 z 50 + 13143585 z 48 − 21572460 z 46 +30798495 z 44 − 38626200 z 42 + 43224705 z 40 − 44349060 z 38 + 43544865 z 36 −42948360 z 34 + 43544865 z 32 − 44349060 z 30 + 43224705 z 28 − 38626200 z 26 +30798495 z 24 − 21572460 z 22 + 13143585 z 20 − 6910176 z 18 + 3108483 z 16 −1184068 z 14 + 376741 z 12 − 98280 z 10 + 20475 z 8 − 3276 z 6 +378 z 4 − 28 z 2 + 1
4
z 66 − 28 z 64 + 378 z 62 − 3276 z 60 + 20475 z 58 − 98279 z 56 + 376712 z 54 −1183662 z 52 + 3104829 z 50 − 6886425 z 48 + 13024830 z 46 − 21097440 z 44 +29237715 z 42 − 34334055 z 40 + 33209700 z 38 − 24319050 z 36 + 8947575 z 34 +8947575 z 32 − 24319050 z 30 + 33209700 z 28 − 34334055 z 26 + 29237715 z 24 −21097440 z 22 + 13024830 z 20 − 6886425 z 18 + 3104829 z 16 − 1183662 z 14 +376712 z 12 − 98279 z 10 + 20475 z 8 − 3276 z 6 + 378 z 4 − 28 z 2 + 1
5
z 64 − 28 z 62 + 378 z 60 − 3276 z 58 + 20476 z 56 − 98308 z 54 + 377118 z 52 −1187316 z 50 + 3128580 z 48 − 7005180 z 46 + 13499850 z 44 − 22658220 z 42 +33529860 z 40 − 44349060 z 38 + 53239710 z 36 − 58916340 z 34 + 60843510 z 32 −58916340 z 30 + 53239710 z 28 − 44349060 z 26 + 33529860 z 24 − 22658220 z 22 +13499850 z 20 − 7005180 z 18 + 3128580 z 16 − 1187316 z 14 + 377118 z 12 −98308 z 10 + 20476 z 8 − 3276 z 6 + 378 z 4 − 28 z 2 + 1
6
z 62 − 28 z 60 + 378 z 58 − 3275 z 56 + 20447 z 54 − 97902 z 52 + 373464 z 50 −1163565 z 48 + 3009825 z 46 − 6530160 z 44 + 11939070 z 42 − 18366075 z 40 +23514855 z 38 − 24319050 z 36 + 18642420 z 34 − 7020405 z 32 − 7020405 z 30 +18642420 z 28 − 24319050 z 26 + 23514855 z 24 − 18366075 z 22 + 11939070 z 20 −6530160 z 18 + 3009825 z 16 − 1163565 z 14 + 373464 z 12 − 97902 z 10 +20447 z 8 − 3275 z 6 + 378 z 4 − 28 z 2 + 1
APPENDIX
n = 9 (cont.) row
determinant 60
58
56
7
z − 28 z + 379 z − 3304 z 54 + 20853 z 52 − 101556 z 50 + 397215 z 48 −1282320 z 46 + 3484845 z 44 − 8090940 z 42 + 16231215 z 40 − 28381080 z 38 +43544865 z 36 − 58916340 z 34 + 70538355 z 32 − 74884320 z 30 + 70538355 z 28 −58916340 z 26 + 43544865 z 24 − 28381080 z 22 + 16231215 z 20 − 8090940 z 18 +3484845 z 16 − 1282320 z 14 + 397215 z 12 − 101556 z 10 + 20853 z 8 −3304 z 6 + 379 z 4 − 28 z 2 + 1
8
z 58 − 27 z 56 + 350 z 54 − 2898 z 52 + 17199 z 50 − 77805 z 48 + 278460 z 46 −807300 z 44 + 1924065 z 42 − 3798795 z 40 + 6216210 z 38 − 8351070 z 36 +8947575 z 34 − 7020405 z 32 + 2674440 z 30 + 2674440 z 28 − 7020405 z 26 +8947575 z 24 − 8351070 z 22 + 6216210 z 20 − 3798795 z 18 + 1924065 z 16 −807300 z 14 + 278460 z 12 − 77805 z 10 + 17199 z 8 − 2898 z 6 +350 z 4 − 27 z 2 + 1
9
z 56 − 28 z 54 + 378 z 52 − 3276 z 50 + 20475 z 48 − 98280 z 46 + 376740 z 44 −1184040 z 42 + 3108105 z 40 − 6906900 z 38 + 13123110 z 36 − 21474180 z 34 +30421755 z 32 − 37442160 z 30 + 40116600 z 28 − 37442160 z 26 + 30421755 z 24 −21474180 z 22 + 13123110 z 20 − 6906900 z 18 + 3108105 z 16 − 1184040 z 14 +376740 z 12 − 98280 z 10 + 20475 z 8 − 3276 z 6 + 378 z 4 − 28 z 2 + 1
317
318
EMILIO A. LAURET
References [DD14] D. DeFord, P. Doyle. Cyclic groups with the same Hodge series. arXiv:1404.2574 (2014). [La] E.A. Lauret. A computational study on lens spaces isospectral on forms. arXiv:1703.03077 (2017). [Sa] W.A. Stein et al. Sage Mathematics Software (Version 4.3). The Sage Development Team, 2009, www.sagemath.org. ´ rdoba, Medina Allende s/n, Ciudad CIEM–FaMAF (CONICET), Universidad Nacional de Co ´ rdoba, Argentina. Universitaria, 5000 Co E-mail address:
[email protected] 
