Properties

Label 126.4
Level 126
Weight 4
Dimension 328
Nonzero newspaces 10
Newform subspaces 28
Sturm bound 3456
Trace bound 9

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Defining parameters

Level: \( N \) = \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 28 \)
Sturm bound: \(3456\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(126))\).

Total New Old
Modular forms 1392 328 1064
Cusp forms 1200 328 872
Eisenstein series 192 0 192

Trace form

\( 328q - 8q^{2} - 6q^{3} + 16q^{4} - 48q^{5} + 36q^{6} - 44q^{7} + 16q^{8} + 210q^{9} + O(q^{10}) \) \( 328q - 8q^{2} - 6q^{3} + 16q^{4} - 48q^{5} + 36q^{6} - 44q^{7} + 16q^{8} + 210q^{9} + 60q^{10} - 12q^{11} - 48q^{12} - 250q^{13} - 464q^{14} - 420q^{15} + 64q^{16} + 330q^{17} + 24q^{18} + 488q^{19} + 264q^{20} + 756q^{21} + 732q^{22} + 1578q^{23} + 144q^{24} + 826q^{25} + 500q^{26} - 792q^{27} - 8q^{28} - 1164q^{29} - 264q^{30} - 1978q^{31} - 128q^{32} - 2274q^{33} - 1092q^{34} - 1920q^{35} - 1032q^{36} + 158q^{37} - 616q^{38} + 2424q^{39} + 240q^{40} + 3642q^{41} + 816q^{42} + 1202q^{43} + 888q^{44} + 2796q^{45} - 504q^{46} + 1902q^{47} + 288q^{48} - 3224q^{49} + 1408q^{50} + 3582q^{51} - 760q^{52} - 2046q^{53} - 1188q^{54} + 900q^{55} - 224q^{56} - 5046q^{57} + 1632q^{58} - 3930q^{59} - 2160q^{60} + 5720q^{61} + 824q^{62} - 8622q^{63} - 512q^{64} - 7092q^{65} - 5376q^{66} - 4648q^{67} - 3072q^{68} - 6912q^{69} - 804q^{70} - 1608q^{71} + 48q^{72} - 3034q^{73} + 1304q^{74} + 5214q^{75} - 256q^{76} + 8622q^{77} + 8280q^{78} + 4382q^{79} + 960q^{80} + 294q^{81} + 5016q^{82} + 5262q^{83} - 744q^{84} + 5424q^{85} - 4492q^{86} + 1692q^{87} - 2352q^{88} - 4950q^{89} - 4224q^{90} - 6970q^{91} + 528q^{92} + 2748q^{93} - 3000q^{94} + 1374q^{95} - 384q^{96} - 2470q^{97} + 3172q^{98} + 1032q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(126))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
126.4.a \(\chi_{126}(1, \cdot)\) 126.4.a.a 1 1
126.4.a.b 1
126.4.a.c 1
126.4.a.d 1
126.4.a.e 1
126.4.a.f 1
126.4.a.g 1
126.4.a.h 1
126.4.d \(\chi_{126}(125, \cdot)\) 126.4.d.a 8 1
126.4.e \(\chi_{126}(25, \cdot)\) 126.4.e.a 24 2
126.4.e.b 24
126.4.f \(\chi_{126}(43, \cdot)\) 126.4.f.a 6 2
126.4.f.b 8
126.4.f.c 10
126.4.f.d 12
126.4.g \(\chi_{126}(37, \cdot)\) 126.4.g.a 2 2
126.4.g.b 2
126.4.g.c 2
126.4.g.d 2
126.4.g.e 4
126.4.g.f 4
126.4.g.g 4
126.4.h \(\chi_{126}(67, \cdot)\) 126.4.h.a 24 2
126.4.h.b 24
126.4.k \(\chi_{126}(17, \cdot)\) 126.4.k.a 16 2
126.4.l \(\chi_{126}(5, \cdot)\) 126.4.l.a 48 2
126.4.m \(\chi_{126}(41, \cdot)\) 126.4.m.a 48 2
126.4.t \(\chi_{126}(47, \cdot)\) 126.4.t.a 48 2

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(126))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(126)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T \))(\( 1 + 2 T \))(\( 1 + 2 T \))(\( 1 + 2 T \))(\( 1 + 2 T \))(\( 1 - 2 T \))(\( 1 - 2 T \))(\( 1 - 2 T \))(\( ( 1 + 4 T^{2} )^{4} \))(\( ( 1 - 2 T + 4 T^{2} )^{3} \))(\( ( 1 + 2 T + 4 T^{2} )^{4} \))(\( ( 1 - 2 T + 4 T^{2} )^{5} \))(\( ( 1 + 2 T + 4 T^{2} )^{6} \))(\( 1 + 2 T + 4 T^{2} \))(\( 1 + 2 T + 4 T^{2} \))(\( 1 + 2 T + 4 T^{2} \))(\( 1 - 2 T + 4 T^{2} \))(\( ( 1 + 2 T + 4 T^{2} )^{2} \))(\( ( 1 - 2 T + 4 T^{2} )^{2} \))(\( ( 1 - 2 T + 4 T^{2} )^{2} \))(\( ( 1 - 4 T^{2} + 16 T^{4} )^{4} \))
$3$ (\( 1 + 12 T + 90 T^{2} + 567 T^{3} + 2430 T^{4} + 8748 T^{5} + 19683 T^{6} \))(\( 1 - 9 T + 3 T^{2} + 153 T^{3} - 621 T^{4} + 4131 T^{5} + 2187 T^{6} - 177147 T^{7} + 531441 T^{8} \))(\( 1 - 4 T - 26 T^{2} + 141 T^{3} + 657 T^{4} - 6966 T^{5} + 17739 T^{6} + 102789 T^{7} - 511758 T^{8} - 2125764 T^{9} + 14348907 T^{10} \))(\( 1 + 7 T + 19 T^{2} - 9 T^{3} + 156 T^{4} + 6732 T^{5} + 45144 T^{6} + 181764 T^{7} + 113724 T^{8} - 177147 T^{9} + 10097379 T^{10} + 100442349 T^{11} + 387420489 T^{12} \))
$5$ (\( 1 + 18 T + 125 T^{2} \))(\( 1 + 6 T + 125 T^{2} \))(\( 1 + 2 T + 125 T^{2} \))(\( 1 - 12 T + 125 T^{2} \))(\( 1 - 22 T + 125 T^{2} \))(\( 1 + 22 T + 125 T^{2} \))(\( 1 - 6 T + 125 T^{2} \))(\( 1 - 14 T + 125 T^{2} \))(\( ( 1 + 260 T^{2} + 40950 T^{4} + 4062500 T^{6} + 244140625 T^{8} )^{2} \))(\( 1 + 9 T - 252 T^{2} - 765 T^{3} + 52335 T^{4} + 17748 T^{5} - 7682339 T^{6} + 2218500 T^{7} + 817734375 T^{8} - 1494140625 T^{9} - 61523437500 T^{10} + 274658203125 T^{11} + 3814697265625 T^{12} \))(\( 1 - T - 229 T^{2} + 3870 T^{3} + 26462 T^{4} - 678974 T^{5} + 5524510 T^{6} + 62332725 T^{7} - 997334831 T^{8} + 7791590625 T^{9} + 86320468750 T^{10} - 1326121093750 T^{11} + 6460449218750 T^{12} + 118103027343750 T^{13} - 873565673828125 T^{14} - 476837158203125 T^{15} + 59604644775390625 T^{16} \))(\( 1 - T - 301 T^{2} - 870 T^{3} + 31605 T^{4} + 194547 T^{5} - 3044247 T^{6} + 20595045 T^{7} + 729791997 T^{8} - 3671065021 T^{9} - 123882340706 T^{10} - 458883127625 T^{11} + 11402999953125 T^{12} + 40224697265625 T^{13} - 743224365234375 T^{14} + 5937103271484375 T^{15} + 120563507080078125 T^{16} - 414848327636718750 T^{17} - 17940998077392578125 T^{18} - 7450580596923828125 T^{19} + \)\(93\!\cdots\!25\)\( T^{20} \))(\( 1 + 9 T - 180 T^{2} - 1521 T^{3} + 19107 T^{4} + 372528 T^{5} + 459779 T^{6} - 72054954 T^{7} - 517873473 T^{8} + 7703414145 T^{9} + 104359259034 T^{10} - 437900872275 T^{11} - 16486035015144 T^{12} - 54737609034375 T^{13} + 1630613422406250 T^{14} + 15045730751953125 T^{15} - 126433953369140625 T^{16} - 2198942687988281250 T^{17} + 1753917694091796875 T^{18} + \)\(17\!\cdots\!00\)\( T^{19} + \)\(11\!\cdots\!75\)\( T^{20} - \)\(11\!\cdots\!25\)\( T^{21} - \)\(16\!\cdots\!00\)\( T^{22} + \)\(10\!\cdots\!25\)\( T^{23} + \)\(14\!\cdots\!25\)\( T^{24} \))(\( 1 + 15 T + 100 T^{2} + 1875 T^{3} + 15625 T^{4} \))(\( 1 + 6 T - 89 T^{2} + 750 T^{3} + 15625 T^{4} \))(\( 1 - 7 T - 76 T^{2} - 875 T^{3} + 15625 T^{4} \))(\( 1 + 9 T - 44 T^{2} + 1125 T^{3} + 15625 T^{4} \))(\( 1 - 7 T - 165 T^{2} + 252 T^{3} + 24046 T^{4} + 31500 T^{5} - 2578125 T^{6} - 13671875 T^{7} + 244140625 T^{8} \))(\( 1 + 7 T - 165 T^{2} - 252 T^{3} + 24046 T^{4} - 31500 T^{5} - 2578125 T^{6} + 13671875 T^{7} + 244140625 T^{8} \))(\( 1 - 5 T + 105 T^{2} + 1650 T^{3} - 12350 T^{4} + 206250 T^{5} + 1640625 T^{6} - 9765625 T^{7} + 244140625 T^{8} \))(\( 1 - 394 T^{2} + 76359 T^{4} - 10015094 T^{6} + 788280437 T^{8} + 16569847068 T^{10} - 16690045259414 T^{12} + 3346113778728272 T^{14} - 478450853619491574 T^{16} + 52283027792629250000 T^{18} - \)\(40\!\cdots\!50\)\( T^{20} + \)\(63\!\cdots\!00\)\( T^{22} + \)\(46\!\cdots\!25\)\( T^{24} - \)\(93\!\cdots\!50\)\( T^{26} + \)\(11\!\cdots\!75\)\( T^{28} - \)\(89\!\cdots\!50\)\( T^{30} + \)\(35\!\cdots\!25\)\( T^{32} \))
$7$ (\( 1 - 7 T \))(\( 1 - 7 T \))(\( 1 + 7 T \))(\( 1 - 7 T \))(\( 1 + 7 T \))(\( 1 + 7 T \))(\( 1 - 7 T \))(\( 1 + 7 T \))(\( ( 1 - 20 T + 714 T^{2} - 6860 T^{3} + 117649 T^{4} )^{2} \))(\( ( 1 + 7 T + 49 T^{2} )^{3} \))(\( ( 1 - 7 T + 49 T^{2} )^{4} \))(\( ( 1 - 7 T + 49 T^{2} )^{5} \))(\( ( 1 + 7 T + 49 T^{2} )^{6} \))(\( 1 - 35 T + 343 T^{2} \))(\( 1 + 7 T + 343 T^{2} \))(\( 1 + 20 T + 343 T^{2} \))(\( 1 + 28 T + 343 T^{2} \))(\( 1 - 6 T - 77 T^{2} - 2058 T^{3} + 117649 T^{4} \))(\( 1 - 6 T - 77 T^{2} - 2058 T^{3} + 117649 T^{4} \))(\( 1 - 659 T^{2} + 117649 T^{4} \))(\( ( 1 + 32 T + 784 T^{2} + 15428 T^{3} + 218197 T^{4} + 5291804 T^{5} + 92236816 T^{6} + 1291315424 T^{7} + 13841287201 T^{8} )^{2} \))
$11$ (\( 1 - 72 T + 1331 T^{2} \))(\( 1 + 30 T + 1331 T^{2} \))(\( 1 - 8 T + 1331 T^{2} \))(\( 1 + 48 T + 1331 T^{2} \))(\( 1 - 26 T + 1331 T^{2} \))(\( 1 + 26 T + 1331 T^{2} \))(\( 1 - 30 T + 1331 T^{2} \))(\( 1 - 28 T + 1331 T^{2} \))(\( ( 1 - 1760 T^{2} + 1142322 T^{4} - 3117947360 T^{6} + 3138428376721 T^{8} )^{2} \))(\( 1 + 48 T - 1548 T^{2} - 52818 T^{3} + 4005756 T^{4} + 50678940 T^{5} - 4988044937 T^{6} + 67453669140 T^{7} + 7096441105116 T^{8} - 124542081143238 T^{9} - 4858287127164108 T^{10} + 200507912131951248 T^{11} + 5559917313492231481 T^{12} \))(\( 1 - 5 T - 2182 T^{2} + 158451 T^{3} + 2427827 T^{4} - 279627664 T^{5} + 9980471089 T^{6} + 295406959071 T^{7} - 17130347878430 T^{8} + 393186662523501 T^{9} + 17681013342899929 T^{10} - 659347404668523824 T^{11} + 7619561150569415267 T^{12} + \)\(66\!\cdots\!01\)\( T^{13} - \)\(12\!\cdots\!42\)\( T^{14} - \)\(37\!\cdots\!55\)\( T^{15} + \)\(98\!\cdots\!41\)\( T^{16} \))(\( 1 + 4 T - 1042 T^{2} + 83862 T^{3} - 908685 T^{4} - 53419476 T^{5} + 5068864797 T^{6} - 159103286790 T^{7} - 1107846728709 T^{8} + 155641631537038 T^{9} - 8086448925305819 T^{10} + 207159011575797578 T^{11} - 1962618058558444749 T^{12} - \)\(37\!\cdots\!90\)\( T^{13} + \)\(15\!\cdots\!37\)\( T^{14} - \)\(22\!\cdots\!76\)\( T^{15} - \)\(50\!\cdots\!85\)\( T^{16} + \)\(62\!\cdots\!82\)\( T^{17} - \)\(10\!\cdots\!22\)\( T^{18} + \)\(52\!\cdots\!84\)\( T^{19} + \)\(17\!\cdots\!01\)\( T^{20} \))(\( 1 + 39 T - 2520 T^{2} - 98511 T^{3} + 4200858 T^{4} + 166018395 T^{5} - 2352513325 T^{6} - 118166518746 T^{7} - 3231760999734 T^{8} + 139986175826808 T^{9} + 20302211720476080 T^{10} - 28620601462635930 T^{11} - 33593892498584782176 T^{12} - 38094020546768422830 T^{13} + \)\(35\!\cdots\!80\)\( T^{14} + \)\(33\!\cdots\!28\)\( T^{15} - \)\(10\!\cdots\!14\)\( T^{16} - \)\(49\!\cdots\!46\)\( T^{17} - \)\(13\!\cdots\!25\)\( T^{18} + \)\(12\!\cdots\!45\)\( T^{19} + \)\(41\!\cdots\!78\)\( T^{20} - \)\(12\!\cdots\!81\)\( T^{21} - \)\(43\!\cdots\!20\)\( T^{22} + \)\(90\!\cdots\!09\)\( T^{23} + \)\(30\!\cdots\!61\)\( T^{24} \))(\( 1 + 9 T - 1250 T^{2} + 11979 T^{3} + 1771561 T^{4} \))(\( 1 + 30 T - 431 T^{2} + 39930 T^{3} + 1771561 T^{4} \))(\( 1 - 35 T - 106 T^{2} - 46585 T^{3} + 1771561 T^{4} \))(\( 1 + 57 T + 1918 T^{2} + 75867 T^{3} + 1771561 T^{4} \))(\( 1 + 25 T + 171 T^{2} - 55200 T^{3} - 2397320 T^{4} - 73471200 T^{5} + 302936931 T^{6} + 58948692275 T^{7} + 3138428376721 T^{8} \))(\( 1 - 25 T + 171 T^{2} + 55200 T^{3} - 2397320 T^{4} + 73471200 T^{5} + 302936931 T^{6} - 58948692275 T^{7} + 3138428376721 T^{8} \))(\( 1 - 67 T + 1041 T^{2} - 52662 T^{3} + 4142284 T^{4} - 70093122 T^{5} + 1844195001 T^{6} - 157982495297 T^{7} + 3138428376721 T^{8} \))(\( 1 + 6418 T^{2} + 20891655 T^{4} + 46350180590 T^{6} + 78873694695509 T^{8} + 106612660360887156 T^{10} + \)\(11\!\cdots\!30\)\( T^{12} + \)\(10\!\cdots\!56\)\( T^{14} + \)\(11\!\cdots\!86\)\( T^{16} + \)\(18\!\cdots\!16\)\( T^{18} + \)\(36\!\cdots\!30\)\( T^{20} + \)\(59\!\cdots\!36\)\( T^{22} + \)\(77\!\cdots\!69\)\( T^{24} + \)\(80\!\cdots\!90\)\( T^{26} + \)\(64\!\cdots\!55\)\( T^{28} + \)\(35\!\cdots\!78\)\( T^{30} + \)\(97\!\cdots\!81\)\( T^{32} \))
$13$ (\( 1 + 34 T + 2197 T^{2} \))(\( 1 - 2 T + 2197 T^{2} \))(\( 1 + 42 T + 2197 T^{2} \))(\( 1 - 56 T + 2197 T^{2} \))(\( 1 + 54 T + 2197 T^{2} \))(\( 1 + 54 T + 2197 T^{2} \))(\( 1 - 2 T + 2197 T^{2} \))(\( 1 - 18 T + 2197 T^{2} \))(\( ( 1 - 628 T^{2} + 8341014 T^{4} - 3031236052 T^{6} + 23298085122481 T^{8} )^{2} \))(\( 1 - 57 T - 1509 T^{2} + 144284 T^{3} + 343773 T^{4} - 71899659 T^{5} - 1052243778 T^{6} - 157963550823 T^{7} + 1659326610357 T^{8} + 1530059587533932 T^{9} - 35156810449823829 T^{10} - 2917595901803173149 T^{11} + \)\(11\!\cdots\!29\)\( T^{12} \))(\( 1 - 21 T - 6604 T^{2} + 143907 T^{3} + 25185493 T^{4} - 450600480 T^{5} - 68065247446 T^{6} + 460246830006 T^{7} + 156900588822904 T^{8} + 1011162285523182 T^{9} - 328537948959579814 T^{10} - 4778392507633499040 T^{11} + \)\(58\!\cdots\!33\)\( T^{12} + \)\(73\!\cdots\!99\)\( T^{13} - \)\(74\!\cdots\!16\)\( T^{14} - \)\(51\!\cdots\!73\)\( T^{15} + \)\(54\!\cdots\!61\)\( T^{16} \))(\( 1 + 57 T - 2639 T^{2} - 414342 T^{3} - 11429214 T^{4} + 363918366 T^{5} + 48121007283 T^{6} + 2700501812667 T^{7} + 69897322886739 T^{8} - 5081263940463408 T^{9} - 463466824639109940 T^{10} - 11163536877198107376 T^{11} + \)\(33\!\cdots\!51\)\( T^{12} + \)\(28\!\cdots\!91\)\( T^{13} + \)\(11\!\cdots\!23\)\( T^{14} + \)\(18\!\cdots\!62\)\( T^{15} - \)\(12\!\cdots\!06\)\( T^{16} - \)\(10\!\cdots\!46\)\( T^{17} - \)\(14\!\cdots\!79\)\( T^{18} + \)\(67\!\cdots\!69\)\( T^{19} + \)\(26\!\cdots\!49\)\( T^{20} \))(\( 1 + 21 T - 2658 T^{2} - 104705 T^{3} - 2227800 T^{4} - 32484903 T^{5} + 11922001282 T^{6} + 751379742459 T^{7} - 6266410381188 T^{8} - 1919095618877219 T^{9} + 8423860931042862 T^{10} + 1800597822926896239 T^{11} - 20313077878481962214 T^{12} + \)\(39\!\cdots\!83\)\( T^{13} + \)\(40\!\cdots\!58\)\( T^{14} - \)\(20\!\cdots\!87\)\( T^{15} - \)\(14\!\cdots\!28\)\( T^{16} + \)\(38\!\cdots\!63\)\( T^{17} + \)\(13\!\cdots\!78\)\( T^{18} - \)\(80\!\cdots\!39\)\( T^{19} - \)\(12\!\cdots\!00\)\( T^{20} - \)\(12\!\cdots\!85\)\( T^{21} - \)\(69\!\cdots\!42\)\( T^{22} + \)\(12\!\cdots\!13\)\( T^{23} + \)\(12\!\cdots\!41\)\( T^{24} \))(\( ( 1 + 88 T + 2197 T^{2} )^{2} \))(\( ( 1 - 53 T + 2197 T^{2} )^{2} \))(\( ( 1 - 66 T + 2197 T^{2} )^{2} \))(\( ( 1 + 70 T + 2197 T^{2} )^{2} \))(\( ( 1 + 49 T + 3788 T^{2} + 107653 T^{3} + 4826809 T^{4} )^{2} \))(\( ( 1 + 49 T + 3788 T^{2} + 107653 T^{3} + 4826809 T^{4} )^{2} \))(\( ( 1 - 41 T + 4478 T^{2} - 90077 T^{3} + 4826809 T^{4} )^{2} \))(\( ( 1 - 5078 T^{2} + 17369173 T^{4} - 48053748314 T^{6} + 104714590798984 T^{8} - 231946264845750026 T^{10} + \)\(40\!\cdots\!13\)\( T^{12} - \)\(57\!\cdots\!62\)\( T^{14} + \)\(54\!\cdots\!61\)\( T^{16} )^{2} \))
$17$ (\( 1 + 6 T + 4913 T^{2} \))(\( 1 + 66 T + 4913 T^{2} \))(\( 1 - 2 T + 4913 T^{2} \))(\( 1 - 114 T + 4913 T^{2} \))(\( 1 - 74 T + 4913 T^{2} \))(\( 1 + 74 T + 4913 T^{2} \))(\( 1 - 66 T + 4913 T^{2} \))(\( 1 + 74 T + 4913 T^{2} \))(\( ( 1 - 748 T^{2} - 19329786 T^{4} - 18054901612 T^{6} + 582622237229761 T^{8} )^{2} \))(\( ( 1 - 24 T + 5220 T^{2} - 78585 T^{3} + 25645860 T^{4} - 579301656 T^{5} + 118587876497 T^{6} )^{2} \))(\( ( 1 + 23 T + 9893 T^{2} + 281573 T^{3} + 69040201 T^{4} + 1383368149 T^{5} + 238792970117 T^{6} + 2727521159431 T^{7} + 582622237229761 T^{8} )^{2} \))(\( ( 1 + 50 T + 9032 T^{2} - 95527 T^{3} + 17002011 T^{4} - 2908646206 T^{5} + 83530880043 T^{6} - 2305789553863 T^{7} + 1071085700520904 T^{8} + 29131111861488050 T^{9} + 2862423051509815793 T^{10} )^{2} \))(\( ( 1 - 87 T + 18387 T^{2} - 973779 T^{3} + 142589430 T^{4} - 5461941786 T^{5} + 770598533284 T^{6} - 26834519994618 T^{7} + 3441762205295670 T^{8} - 115478383787372163 T^{9} + 10712675075943615507 T^{10} - \)\(24\!\cdots\!91\)\( T^{11} + \)\(14\!\cdots\!09\)\( T^{12} )^{2} \))(\( 1 + 84 T + 2143 T^{2} + 412692 T^{3} + 24137569 T^{4} \))(\( 1 + 84 T + 2143 T^{2} + 412692 T^{3} + 24137569 T^{4} \))(\( 1 - 59 T - 1432 T^{2} - 289867 T^{3} + 24137569 T^{4} \))(\( 1 - 51 T - 2312 T^{2} - 250563 T^{3} + 24137569 T^{4} \))(\( 1 - 98 T + 2202 T^{2} + 237552 T^{3} - 16532417 T^{4} + 1167092976 T^{5} + 53150926938 T^{6} - 11621611896706 T^{7} + 582622237229761 T^{8} \))(\( 1 + 98 T + 2202 T^{2} - 237552 T^{3} - 16532417 T^{4} - 1167092976 T^{5} + 53150926938 T^{6} + 11621611896706 T^{7} + 582622237229761 T^{8} \))(\( 1 + 92 T + 1902 T^{2} - 300288 T^{3} - 22661357 T^{4} - 1475314944 T^{5} + 45909656238 T^{6} + 10910084637724 T^{7} + 582622237229761 T^{8} \))(\( 1 - 27988 T^{2} + 407517960 T^{4} - 4164237444008 T^{6} + 33768844539997826 T^{8} - \)\(23\!\cdots\!92\)\( T^{10} + \)\(14\!\cdots\!32\)\( T^{12} - \)\(78\!\cdots\!68\)\( T^{14} + \)\(39\!\cdots\!95\)\( T^{16} - \)\(18\!\cdots\!92\)\( T^{18} + \)\(82\!\cdots\!52\)\( T^{20} - \)\(32\!\cdots\!28\)\( T^{22} + \)\(11\!\cdots\!46\)\( T^{24} - \)\(34\!\cdots\!92\)\( T^{26} + \)\(80\!\cdots\!60\)\( T^{28} - \)\(13\!\cdots\!32\)\( T^{30} + \)\(11\!\cdots\!41\)\( T^{32} \))
$19$ (\( 1 - 92 T + 6859 T^{2} \))(\( 1 + 52 T + 6859 T^{2} \))(\( 1 + 124 T + 6859 T^{2} \))(\( 1 - 2 T + 6859 T^{2} \))(\( 1 - 116 T + 6859 T^{2} \))(\( 1 - 116 T + 6859 T^{2} \))(\( 1 + 52 T + 6859 T^{2} \))(\( 1 - 80 T + 6859 T^{2} \))(\( ( 1 - 13516 T^{2} + 139733526 T^{4} - 635872127596 T^{6} + 2213314919066161 T^{8} )^{2} \))(\( ( 1 + 141 T + 19551 T^{2} + 1828069 T^{3} + 134100309 T^{4} + 6633469221 T^{5} + 322687697779 T^{6} )^{2} \))(\( ( 1 + 94 T + 13819 T^{2} + 1292485 T^{3} + 131846581 T^{4} + 8865154615 T^{5} + 650127029539 T^{6} + 30332643591226 T^{7} + 2213314919066161 T^{8} )^{2} \))(\( ( 1 - 49 T + 33438 T^{2} - 1299768 T^{3} + 452869533 T^{4} - 13223211027 T^{5} + 3106232126847 T^{6} - 61148730655608 T^{7} + 10790031238334202 T^{8} - 108452431034241889 T^{9} + 15181127029874798299 T^{10} )^{2} \))(\( ( 1 - 96 T + 16242 T^{2} - 1387075 T^{3} + 147989907 T^{4} - 8990040816 T^{5} + 1098100012983 T^{6} - 61662689956944 T^{7} + 6962315553923067 T^{8} - 447592038396806425 T^{9} + 35948660915472586962 T^{10} - \)\(14\!\cdots\!04\)\( T^{11} + \)\(10\!\cdots\!41\)\( T^{12} )^{2} \))(\( 1 + 104 T + 3957 T^{2} + 713336 T^{3} + 47045881 T^{4} \))(\( 1 - 97 T + 2550 T^{2} - 665323 T^{3} + 47045881 T^{4} \))(\( 1 + 137 T + 11910 T^{2} + 939683 T^{3} + 47045881 T^{4} \))(\( 1 + 5 T - 6834 T^{2} + 34295 T^{3} + 47045881 T^{4} \))(\( 1 - 119 T - 2663 T^{2} - 369614 T^{3} + 138870796 T^{4} - 2535182426 T^{5} - 125283181103 T^{6} - 38399836035701 T^{7} + 2213314919066161 T^{8} \))(\( 1 - 119 T - 2663 T^{2} - 369614 T^{3} + 138870796 T^{4} - 2535182426 T^{5} - 125283181103 T^{6} - 38399836035701 T^{7} + 2213314919066161 T^{8} \))(\( 1 + 43 T - 9305 T^{2} - 110252 T^{3} + 64683544 T^{4} - 756218468 T^{5} - 437761922705 T^{6} + 13875571004497 T^{7} + 2213314919066161 T^{8} \))(\( ( 1 - 342 T + 64753 T^{2} - 8811630 T^{3} + 884748151 T^{4} - 63434432124 T^{5} + 2868005943988 T^{6} - 17252084465172 T^{7} - 6756956753687042 T^{8} - 118332047346614748 T^{9} + \)\(13\!\cdots\!28\)\( T^{10} - \)\(20\!\cdots\!96\)\( T^{11} + \)\(19\!\cdots\!11\)\( T^{12} - \)\(13\!\cdots\!70\)\( T^{13} + \)\(67\!\cdots\!73\)\( T^{14} - \)\(24\!\cdots\!98\)\( T^{15} + \)\(48\!\cdots\!21\)\( T^{16} )^{2} \))
$23$ (\( 1 - 180 T + 12167 T^{2} \))(\( 1 + 114 T + 12167 T^{2} \))(\( 1 + 76 T + 12167 T^{2} \))(\( 1 - 120 T + 12167 T^{2} \))(\( 1 + 58 T + 12167 T^{2} \))(\( 1 - 58 T + 12167 T^{2} \))(\( 1 - 114 T + 12167 T^{2} \))(\( 1 - 112 T + 12167 T^{2} \))(\( ( 1 - 44240 T^{2} + 782190978 T^{4} - 6549107729360 T^{6} + 21914624432020321 T^{8} )^{2} \))(\( 1 - 30 T - 27864 T^{2} - 50214 T^{3} + 465205518 T^{4} + 4868880918 T^{5} - 6432386973797 T^{6} + 59239674129306 T^{7} + 68867112424835502 T^{8} - 90443079742703082 T^{9} - \)\(61\!\cdots\!44\)\( T^{10} - \)\(79\!\cdots\!10\)\( T^{11} + \)\(32\!\cdots\!69\)\( T^{12} \))(\( 1 - 374 T + 45833 T^{2} - 3344556 T^{3} + 859764083 T^{4} - 169835114038 T^{5} + 17527026209797 T^{6} - 1808539479332106 T^{7} + 222811406401501087 T^{8} - 22004499845033733702 T^{9} + \)\(25\!\cdots\!33\)\( T^{10} - \)\(30\!\cdots\!94\)\( T^{11} + \)\(18\!\cdots\!43\)\( T^{12} - \)\(89\!\cdots\!92\)\( T^{13} + \)\(14\!\cdots\!77\)\( T^{14} - \)\(14\!\cdots\!02\)\( T^{15} + \)\(48\!\cdots\!41\)\( T^{16} \))(\( 1 - 176 T - 16963 T^{2} + 4074570 T^{3} + 145120950 T^{4} - 32207984022 T^{5} - 3753997456998 T^{6} + 77561240932902 T^{7} + 90834726823288194 T^{8} + 327761157511899022 T^{9} - \)\(13\!\cdots\!36\)\( T^{10} + \)\(39\!\cdots\!74\)\( T^{11} + \)\(13\!\cdots\!66\)\( T^{12} + \)\(13\!\cdots\!26\)\( T^{13} - \)\(82\!\cdots\!58\)\( T^{14} - \)\(85\!\cdots\!54\)\( T^{15} + \)\(47\!\cdots\!50\)\( T^{16} + \)\(16\!\cdots\!10\)\( T^{17} - \)\(81\!\cdots\!83\)\( T^{18} - \)\(10\!\cdots\!72\)\( T^{19} + \)\(71\!\cdots\!49\)\( T^{20} \))(\( 1 + 168 T - 30690 T^{2} - 5031030 T^{3} + 671215752 T^{4} + 75186503268 T^{5} - 13911824846515 T^{6} - 831691242061002 T^{7} + 240399305045183286 T^{8} + 7651682166907611198 T^{9} - \)\(33\!\cdots\!60\)\( T^{10} - \)\(39\!\cdots\!02\)\( T^{11} + \)\(40\!\cdots\!12\)\( T^{12} - \)\(48\!\cdots\!34\)\( T^{13} - \)\(49\!\cdots\!40\)\( T^{14} + \)\(13\!\cdots\!74\)\( T^{15} + \)\(52\!\cdots\!06\)\( T^{16} - \)\(22\!\cdots\!14\)\( T^{17} - \)\(45\!\cdots\!35\)\( T^{18} + \)\(29\!\cdots\!64\)\( T^{19} + \)\(32\!\cdots\!32\)\( T^{20} - \)\(29\!\cdots\!10\)\( T^{21} - \)\(21\!\cdots\!10\)\( T^{22} + \)\(14\!\cdots\!44\)\( T^{23} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 + 84 T - 5111 T^{2} + 1022028 T^{3} + 148035889 T^{4} \))(\( 1 - 84 T - 5111 T^{2} - 1022028 T^{3} + 148035889 T^{4} \))(\( 1 + 7 T - 12118 T^{2} + 85169 T^{3} + 148035889 T^{4} \))(\( 1 - 69 T - 7406 T^{2} - 839523 T^{3} + 148035889 T^{4} \))(\( 1 - 122 T - 3714 T^{2} + 699792 T^{3} + 16756087 T^{4} + 8514369264 T^{5} - 549805291746 T^{6} - 219740624698486 T^{7} + 21914624432020321 T^{8} \))(\( 1 + 122 T - 3714 T^{2} - 699792 T^{3} + 16756087 T^{4} - 8514369264 T^{5} - 549805291746 T^{6} + 219740624698486 T^{7} + 21914624432020321 T^{8} \))(\( 1 - 148 T - 2526 T^{2} - 14208 T^{3} + 182283043 T^{4} - 172868736 T^{5} - 373938655614 T^{6} - 266570593896524 T^{7} + 21914624432020321 T^{8} \))(\( 1 + 12628 T^{2} - 152323560 T^{4} - 5115483863896 T^{6} - 8486672803469662 T^{8} + \)\(85\!\cdots\!76\)\( T^{10} + \)\(10\!\cdots\!92\)\( T^{12} - \)\(70\!\cdots\!60\)\( T^{14} - \)\(22\!\cdots\!13\)\( T^{16} - \)\(10\!\cdots\!40\)\( T^{18} + \)\(23\!\cdots\!32\)\( T^{20} + \)\(27\!\cdots\!44\)\( T^{22} - \)\(40\!\cdots\!42\)\( T^{24} - \)\(36\!\cdots\!04\)\( T^{26} - \)\(16\!\cdots\!60\)\( T^{28} + \)\(19\!\cdots\!12\)\( T^{30} + \)\(23\!\cdots\!81\)\( T^{32} \))
$29$ (\( 1 - 114 T + 24389 T^{2} \))(\( 1 + 72 T + 24389 T^{2} \))(\( 1 + 254 T + 24389 T^{2} \))(\( 1 - 54 T + 24389 T^{2} \))(\( 1 - 208 T + 24389 T^{2} \))(\( 1 + 208 T + 24389 T^{2} \))(\( 1 - 72 T + 24389 T^{2} \))(\( 1 + 190 T + 24389 T^{2} \))(\( ( 1 - 60080 T^{2} + 1874061042 T^{4} - 35736985125680 T^{6} + 353814783205469041 T^{8} )^{2} \))(\( 1 + 117 T - 9810 T^{2} - 8104923 T^{3} - 655891011 T^{4} + 63017592930 T^{5} + 36858066204589 T^{6} + 1536936073969770 T^{7} - 390139269377067531 T^{8} - \)\(11\!\cdots\!87\)\( T^{9} - \)\(34\!\cdots\!10\)\( T^{10} + \)\(10\!\cdots\!33\)\( T^{11} + \)\(21\!\cdots\!61\)\( T^{12} \))(\( 1 - 271 T - 38803 T^{2} + 7520976 T^{3} + 3235076084 T^{4} - 303059385266 T^{5} - 105997401830390 T^{6} + 1727808215476197 T^{7} + 3339594708008059465 T^{8} + 42139514567248968633 T^{9} - \)\(63\!\cdots\!90\)\( T^{10} - \)\(43\!\cdots\!54\)\( T^{11} + \)\(11\!\cdots\!44\)\( T^{12} + \)\(64\!\cdots\!24\)\( T^{13} - \)\(81\!\cdots\!83\)\( T^{14} - \)\(13\!\cdots\!59\)\( T^{15} + \)\(12\!\cdots\!81\)\( T^{16} \))(\( 1 - 271 T + 30308 T^{2} + 859431 T^{3} - 1142086404 T^{4} + 230977779267 T^{5} - 8621337963525 T^{6} - 2893872700229829 T^{7} + 441721949420441463 T^{8} - 6158611865910596854 T^{9} - \)\(37\!\cdots\!25\)\( T^{10} - \)\(15\!\cdots\!06\)\( T^{11} + \)\(26\!\cdots\!23\)\( T^{12} - \)\(41\!\cdots\!01\)\( T^{13} - \)\(30\!\cdots\!25\)\( T^{14} + \)\(19\!\cdots\!83\)\( T^{15} - \)\(24\!\cdots\!44\)\( T^{16} + \)\(44\!\cdots\!99\)\( T^{17} + \)\(37\!\cdots\!48\)\( T^{18} - \)\(82\!\cdots\!39\)\( T^{19} + \)\(74\!\cdots\!01\)\( T^{20} \))(\( 1 + 117 T - 73917 T^{2} - 18394002 T^{3} + 2335957965 T^{4} + 1076730678981 T^{5} + 12119605015271 T^{6} - 37846909889286489 T^{7} - 3695723963917029504 T^{8} + \)\(80\!\cdots\!54\)\( T^{9} + \)\(17\!\cdots\!67\)\( T^{10} - \)\(77\!\cdots\!73\)\( T^{11} - \)\(49\!\cdots\!17\)\( T^{12} - \)\(18\!\cdots\!97\)\( T^{13} + \)\(10\!\cdots\!07\)\( T^{14} + \)\(11\!\cdots\!26\)\( T^{15} - \)\(13\!\cdots\!64\)\( T^{16} - \)\(32\!\cdots\!61\)\( T^{17} + \)\(25\!\cdots\!31\)\( T^{18} + \)\(55\!\cdots\!49\)\( T^{19} + \)\(29\!\cdots\!65\)\( T^{20} - \)\(56\!\cdots\!18\)\( T^{21} - \)\(55\!\cdots\!17\)\( T^{22} + \)\(21\!\cdots\!13\)\( T^{23} + \)\(44\!\cdots\!21\)\( T^{24} \))(\( ( 1 + 51 T + 24389 T^{2} )^{2} \))(\( ( 1 - 180 T + 24389 T^{2} )^{2} \))(\( ( 1 + 106 T + 24389 T^{2} )^{2} \))(\( ( 1 + 114 T + 24389 T^{2} )^{2} \))(\( ( 1 + 73 T + 47746 T^{2} + 1780397 T^{3} + 594823321 T^{4} )^{2} \))(\( ( 1 - 73 T + 47746 T^{2} - 1780397 T^{3} + 594823321 T^{4} )^{2} \))(\( ( 1 + 77 T + 9574 T^{2} + 1877953 T^{3} + 594823321 T^{4} )^{2} \))(\( ( 1 - 101890 T^{2} + 5352676057 T^{4} - 193574296614130 T^{6} + 5334177008360889700 T^{8} - \)\(11\!\cdots\!30\)\( T^{10} + \)\(18\!\cdots\!37\)\( T^{12} - \)\(21\!\cdots\!90\)\( T^{14} + \)\(12\!\cdots\!81\)\( T^{16} )^{2} \))
$31$ (\( 1 - 56 T + 29791 T^{2} \))(\( 1 + 196 T + 29791 T^{2} \))(\( 1 + 72 T + 29791 T^{2} \))(\( 1 - 236 T + 29791 T^{2} \))(\( 1 + 252 T + 29791 T^{2} \))(\( 1 + 252 T + 29791 T^{2} \))(\( 1 + 196 T + 29791 T^{2} \))(\( 1 - 72 T + 29791 T^{2} \))(\( ( 1 - 101884 T^{2} + 4332769926 T^{4} - 90422425035004 T^{6} + 787662783788549761 T^{8} )^{2} \))(\( 1 - 165 T - 58344 T^{2} + 5495873 T^{3} + 3154650147 T^{4} - 144414314946 T^{5} - 93229664138193 T^{6} - 4302246856556286 T^{7} + 2799763617729691107 T^{8} + \)\(14\!\cdots\!83\)\( T^{9} - \)\(45\!\cdots\!84\)\( T^{10} - \)\(38\!\cdots\!15\)\( T^{11} + \)\(69\!\cdots\!41\)\( T^{12} \))(\( 1 - 243 T - 6151 T^{2} - 8914860 T^{3} + 2490318622 T^{4} + 117491450778 T^{5} + 42742085844890 T^{6} - 10211221082121813 T^{7} - 951217853496050879 T^{8} - \)\(30\!\cdots\!83\)\( T^{9} + \)\(37\!\cdots\!90\)\( T^{10} + \)\(31\!\cdots\!38\)\( T^{11} + \)\(19\!\cdots\!42\)\( T^{12} - \)\(20\!\cdots\!60\)\( T^{13} - \)\(42\!\cdots\!91\)\( T^{14} - \)\(50\!\cdots\!33\)\( T^{15} + \)\(62\!\cdots\!21\)\( T^{16} \))(\( 1 + 207 T - 46508 T^{2} + 1023921 T^{3} + 3373726146 T^{4} - 207266976279 T^{5} - 42783940115355 T^{6} + 18727602911272737 T^{7} - 264199487255837433 T^{8} - \)\(12\!\cdots\!12\)\( T^{9} + \)\(92\!\cdots\!41\)\( T^{10} - \)\(35\!\cdots\!92\)\( T^{11} - \)\(23\!\cdots\!73\)\( T^{12} + \)\(49\!\cdots\!27\)\( T^{13} - \)\(33\!\cdots\!55\)\( T^{14} - \)\(48\!\cdots\!29\)\( T^{15} + \)\(23\!\cdots\!86\)\( T^{16} + \)\(21\!\cdots\!51\)\( T^{17} - \)\(28\!\cdots\!68\)\( T^{18} + \)\(38\!\cdots\!77\)\( T^{19} + \)\(55\!\cdots\!01\)\( T^{20} \))(\( 1 + 129 T - 12567 T^{2} - 7893260 T^{3} - 949545831 T^{4} + 185873195055 T^{5} + 78862123021051 T^{6} + 5178642965572077 T^{7} - 940227613501467312 T^{8} - \)\(29\!\cdots\!26\)\( T^{9} - \)\(15\!\cdots\!35\)\( T^{10} + \)\(52\!\cdots\!39\)\( T^{11} + \)\(18\!\cdots\!59\)\( T^{12} + \)\(15\!\cdots\!49\)\( T^{13} - \)\(13\!\cdots\!35\)\( T^{14} - \)\(77\!\cdots\!46\)\( T^{15} - \)\(74\!\cdots\!32\)\( T^{16} + \)\(12\!\cdots\!27\)\( T^{17} + \)\(55\!\cdots\!91\)\( T^{18} + \)\(38\!\cdots\!05\)\( T^{19} - \)\(58\!\cdots\!51\)\( T^{20} - \)\(14\!\cdots\!60\)\( T^{21} - \)\(69\!\cdots\!67\)\( T^{22} + \)\(21\!\cdots\!39\)\( T^{23} + \)\(48\!\cdots\!81\)\( T^{24} \))(\( 1 + 185 T + 4434 T^{2} + 5511335 T^{3} + 887503681 T^{4} \))(\( 1 + 179 T + 2250 T^{2} + 5332589 T^{3} + 887503681 T^{4} \))(\( 1 + 75 T - 24166 T^{2} + 2234325 T^{3} + 887503681 T^{4} \))(\( 1 + 23 T - 29262 T^{2} + 685193 T^{3} + 887503681 T^{4} \))(\( 1 + 98 T - 14551 T^{2} - 3471846 T^{3} - 590152420 T^{4} - 103429764186 T^{5} - 12914066062231 T^{6} + 2591082971745758 T^{7} + 787662783788549761 T^{8} \))(\( 1 + 98 T - 14551 T^{2} - 3471846 T^{3} - 590152420 T^{4} - 103429764186 T^{5} - 12914066062231 T^{6} + 2591082971745758 T^{7} + 787662783788549761 T^{8} \))(\( 1 - 520 T + 144563 T^{2} - 34452600 T^{3} + 6891960488 T^{4} - 1026377406600 T^{5} + 128300194636403 T^{6} - 13748603523548920 T^{7} + 787662783788549761 T^{8} \))(\( ( 1 + 624 T + 258856 T^{2} + 80535936 T^{3} + 20284367635 T^{4} + 4269891758076 T^{5} + 807618224093992 T^{6} + 140828748444307164 T^{7} + 24234290471489389816 T^{8} + \)\(41\!\cdots\!24\)\( T^{9} + \)\(71\!\cdots\!52\)\( T^{10} + \)\(11\!\cdots\!96\)\( T^{11} + \)\(15\!\cdots\!35\)\( T^{12} + \)\(18\!\cdots\!36\)\( T^{13} + \)\(18\!\cdots\!96\)\( T^{14} + \)\(12\!\cdots\!44\)\( T^{15} + \)\(62\!\cdots\!21\)\( T^{16} )^{2} \))
$37$ (\( 1 + 34 T + 50653 T^{2} \))(\( 1 + 286 T + 50653 T^{2} \))(\( 1 - 398 T + 50653 T^{2} \))(\( 1 - 146 T + 50653 T^{2} \))(\( 1 - 50 T + 50653 T^{2} \))(\( 1 - 50 T + 50653 T^{2} \))(\( 1 + 286 T + 50653 T^{2} \))(\( 1 + 346 T + 50653 T^{2} \))(\( ( 1 + 40 T + 8394 T^{2} + 2026120 T^{3} + 2565726409 T^{4} )^{4} \))(\( ( 1 + 399 T + 119733 T^{2} + 21982651 T^{3} + 6064835649 T^{4} + 1023724837191 T^{5} + 129961739795077 T^{6} )^{2} \))(\( ( 1 + 181 T + 42844 T^{2} - 12321968 T^{3} - 3161946908 T^{4} - 624144645104 T^{5} + 109925982267196 T^{6} + 23523074902908937 T^{7} + 6582952005840035281 T^{8} )^{2} \))(\( ( 1 - 253 T + 219543 T^{2} - 41177991 T^{3} + 20787830616 T^{4} - 2973160844616 T^{5} + 1052965984192248 T^{6} - 105651458978264319 T^{7} + 28532190239830589811 T^{8} - \)\(16\!\cdots\!93\)\( T^{9} + \)\(33\!\cdots\!93\)\( T^{10} )^{2} \))(\( ( 1 - 471 T + 176214 T^{2} - 27200506 T^{3} + 5859394857 T^{4} - 618987544479 T^{5} + 278778183772128 T^{6} - 31353576090494787 T^{7} + 15033604125363678513 T^{8} - \)\(35\!\cdots\!62\)\( T^{9} + \)\(11\!\cdots\!34\)\( T^{10} - \)\(15\!\cdots\!03\)\( T^{11} + \)\(16\!\cdots\!29\)\( T^{12} )^{2} \))(\( 1 + 44 T - 48717 T^{2} + 2228732 T^{3} + 2565726409 T^{4} \))(\( 1 - 145 T - 29628 T^{2} - 7344685 T^{3} + 2565726409 T^{4} \))(\( 1 + 11 T - 50532 T^{2} + 557183 T^{3} + 2565726409 T^{4} \))(\( 1 - 253 T + 13356 T^{2} - 12815209 T^{3} + 2565726409 T^{4} \))(\( 1 + 289 T - 17387 T^{2} - 115022 T^{3} + 3386108842 T^{4} - 5826209366 T^{5} - 44610285073283 T^{6} + 37558942800777253 T^{7} + 6582952005840035281 T^{8} \))(\( 1 + 289 T - 17387 T^{2} - 115022 T^{3} + 3386108842 T^{4} - 5826209366 T^{5} - 44610285073283 T^{6} + 37558942800777253 T^{7} + 6582952005840035281 T^{8} \))(\( 1 + 7 T - 74033 T^{2} - 190568 T^{3} + 2919934318 T^{4} - 9652840904 T^{5} - 189948423237497 T^{6} + 909732178565539 T^{7} + 6582952005840035281 T^{8} \))(\( ( 1 - 626 T + 68505 T^{2} + 5417630 T^{3} + 11688623387 T^{4} - 4034655563880 T^{5} + 166838405422072 T^{6} - 87806835110147336 T^{7} + 54081687093359460678 T^{8} - \)\(44\!\cdots\!08\)\( T^{9} + \)\(42\!\cdots\!48\)\( T^{10} - \)\(52\!\cdots\!60\)\( T^{11} + \)\(76\!\cdots\!47\)\( T^{12} + \)\(18\!\cdots\!90\)\( T^{13} + \)\(11\!\cdots\!45\)\( T^{14} - \)\(53\!\cdots\!62\)\( T^{15} + \)\(43\!\cdots\!61\)\( T^{16} )^{2} \))
$41$ (\( 1 + 6 T + 68921 T^{2} \))(\( 1 - 378 T + 68921 T^{2} \))(\( 1 + 462 T + 68921 T^{2} \))(\( 1 + 126 T + 68921 T^{2} \))(\( 1 - 126 T + 68921 T^{2} \))(\( 1 + 126 T + 68921 T^{2} \))(\( 1 + 378 T + 68921 T^{2} \))(\( 1 + 162 T + 68921 T^{2} \))(\( ( 1 + 186164 T^{2} + 18160658406 T^{4} + 884298405921524 T^{6} + 22563490300366186081 T^{8} )^{2} \))(\( 1 - 384 T - 98100 T^{2} + 12598554 T^{3} + 22850508924 T^{4} - 1950427947300 T^{5} - 1344970654506389 T^{6} - 134425444555863300 T^{7} + \)\(10\!\cdots\!84\)\( T^{8} + \)\(41\!\cdots\!94\)\( T^{9} - \)\(22\!\cdots\!00\)\( T^{10} - \)\(59\!\cdots\!84\)\( T^{11} + \)\(10\!\cdots\!21\)\( T^{12} \))(\( 1 + 213 T - 84590 T^{2} - 65999067 T^{3} - 3185697689 T^{4} + 5013788714586 T^{5} + 1428680211356995 T^{6} - 164868593391514353 T^{7} - \)\(12\!\cdots\!52\)\( T^{8} - \)\(11\!\cdots\!13\)\( T^{9} + \)\(67\!\cdots\!95\)\( T^{10} + \)\(16\!\cdots\!46\)\( T^{11} - \)\(71\!\cdots\!09\)\( T^{12} - \)\(10\!\cdots\!67\)\( T^{13} - \)\(90\!\cdots\!90\)\( T^{14} + \)\(15\!\cdots\!33\)\( T^{15} + \)\(50\!\cdots\!61\)\( T^{16} \))(\( 1 - 606 T + 141758 T^{2} - 11799990 T^{3} - 9146715435 T^{4} + 6326595493920 T^{5} - 1959244960115487 T^{6} + 306846938252397024 T^{7} + 29161393147252058763 T^{8} - \)\(36\!\cdots\!98\)\( T^{9} + \)\(12\!\cdots\!09\)\( T^{10} - \)\(25\!\cdots\!58\)\( T^{11} + \)\(13\!\cdots\!83\)\( T^{12} + \)\(10\!\cdots\!64\)\( T^{13} - \)\(44\!\cdots\!47\)\( T^{14} + \)\(98\!\cdots\!20\)\( T^{15} - \)\(98\!\cdots\!35\)\( T^{16} - \)\(87\!\cdots\!90\)\( T^{17} + \)\(72\!\cdots\!38\)\( T^{18} - \)\(21\!\cdots\!86\)\( T^{19} + \)\(24\!\cdots\!01\)\( T^{20} \))(\( 1 + 255 T - 270090 T^{2} - 70026909 T^{3} + 42113492442 T^{4} + 10426716654555 T^{5} - 4573113056761063 T^{6} - 1008782128875463884 T^{7} + \)\(38\!\cdots\!16\)\( T^{8} + \)\(62\!\cdots\!50\)\( T^{9} - \)\(28\!\cdots\!02\)\( T^{10} - \)\(17\!\cdots\!44\)\( T^{11} + \)\(19\!\cdots\!42\)\( T^{12} - \)\(12\!\cdots\!24\)\( T^{13} - \)\(13\!\cdots\!82\)\( T^{14} + \)\(20\!\cdots\!50\)\( T^{15} + \)\(87\!\cdots\!96\)\( T^{16} - \)\(15\!\cdots\!84\)\( T^{17} - \)\(49\!\cdots\!23\)\( T^{18} + \)\(77\!\cdots\!55\)\( T^{19} + \)\(21\!\cdots\!62\)\( T^{20} - \)\(24\!\cdots\!29\)\( T^{21} - \)\(65\!\cdots\!90\)\( T^{22} + \)\(42\!\cdots\!55\)\( T^{23} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( ( 1 - 168 T + 68921 T^{2} )^{2} \))(\( ( 1 + 126 T + 68921 T^{2} )^{2} \))(\( ( 1 - 498 T + 68921 T^{2} )^{2} \))(\( ( 1 - 42 T + 68921 T^{2} )^{2} \))(\( ( 1 + 168 T + 68921 T^{2} )^{4} \))(\( ( 1 - 168 T + 68921 T^{2} )^{4} \))(\( ( 1 - 426 T + 171106 T^{2} - 29360346 T^{3} + 4750104241 T^{4} )^{2} \))(\( ( 1 + 499084 T^{2} + 111962587672 T^{4} + 14766698141272708 T^{6} + \)\(12\!\cdots\!54\)\( T^{8} + \)\(70\!\cdots\!28\)\( T^{10} + \)\(25\!\cdots\!32\)\( T^{12} + \)\(53\!\cdots\!64\)\( T^{14} + \)\(50\!\cdots\!61\)\( T^{16} )^{2} \))
$43$ (\( 1 - 164 T + 79507 T^{2} \))(\( 1 - 164 T + 79507 T^{2} \))(\( 1 - 212 T + 79507 T^{2} \))(\( 1 + 376 T + 79507 T^{2} \))(\( 1 - 164 T + 79507 T^{2} \))(\( 1 - 164 T + 79507 T^{2} \))(\( 1 - 164 T + 79507 T^{2} \))(\( 1 + 412 T + 79507 T^{2} \))(\( ( 1 - 260 T + 155106 T^{2} - 20671820 T^{3} + 6321363049 T^{4} )^{4} \))(\( 1 - 771 T + 193974 T^{2} - 50785663 T^{3} + 29084759433 T^{4} - 7431715027980 T^{5} + 1134363686777763 T^{6} - 590873366729605860 T^{7} + \)\(18\!\cdots\!17\)\( T^{8} - \)\(25\!\cdots\!09\)\( T^{9} + \)\(77\!\cdots\!74\)\( T^{10} - \)\(24\!\cdots\!97\)\( T^{11} + \)\(25\!\cdots\!49\)\( T^{12} \))(\( 1 - 238 T - 60675 T^{2} + 5271292 T^{3} - 2134721566 T^{4} + 2420831216454 T^{5} + 42843939153790 T^{6} - 184810086452079577 T^{7} + 50838540246961940772 T^{8} - \)\(14\!\cdots\!39\)\( T^{9} + \)\(27\!\cdots\!10\)\( T^{10} + \)\(12\!\cdots\!22\)\( T^{11} - \)\(85\!\cdots\!66\)\( T^{12} + \)\(16\!\cdots\!44\)\( T^{13} - \)\(15\!\cdots\!75\)\( T^{14} - \)\(47\!\cdots\!34\)\( T^{15} + \)\(15\!\cdots\!01\)\( T^{16} \))(\( 1 + 409 T - 147884 T^{2} - 63366165 T^{3} + 18856178688 T^{4} + 6736200070353 T^{5} - 1316077911054483 T^{6} - 465265088271859539 T^{7} + 29975304785830751439 T^{8} + \)\(10\!\cdots\!90\)\( T^{9} - \)\(10\!\cdots\!35\)\( T^{10} + \)\(81\!\cdots\!30\)\( T^{11} + \)\(18\!\cdots\!11\)\( T^{12} - \)\(23\!\cdots\!77\)\( T^{13} - \)\(52\!\cdots\!83\)\( T^{14} + \)\(21\!\cdots\!71\)\( T^{15} + \)\(47\!\cdots\!12\)\( T^{16} - \)\(12\!\cdots\!95\)\( T^{17} - \)\(23\!\cdots\!84\)\( T^{18} + \)\(51\!\cdots\!63\)\( T^{19} + \)\(10\!\cdots\!49\)\( T^{20} \))(\( 1 + 942 T + 269535 T^{2} - 42289388 T^{3} - 44197958085 T^{4} - 9092664308136 T^{5} + 377606091677815 T^{6} + 691280609795093763 T^{7} + \)\(28\!\cdots\!65\)\( T^{8} + \)\(77\!\cdots\!03\)\( T^{9} + \)\(49\!\cdots\!65\)\( T^{10} - \)\(52\!\cdots\!11\)\( T^{11} - \)\(23\!\cdots\!20\)\( T^{12} - \)\(41\!\cdots\!77\)\( T^{13} + \)\(31\!\cdots\!85\)\( T^{14} + \)\(39\!\cdots\!29\)\( T^{15} + \)\(11\!\cdots\!65\)\( T^{16} + \)\(21\!\cdots\!41\)\( T^{17} + \)\(95\!\cdots\!35\)\( T^{18} - \)\(18\!\cdots\!48\)\( T^{19} - \)\(70\!\cdots\!85\)\( T^{20} - \)\(53\!\cdots\!16\)\( T^{21} + \)\(27\!\cdots\!15\)\( T^{22} + \)\(75\!\cdots\!06\)\( T^{23} + \)\(63\!\cdots\!01\)\( T^{24} \))(\( ( 1 - 326 T + 79507 T^{2} )^{2} \))(\( ( 1 + 325 T + 79507 T^{2} )^{2} \))(\( ( 1 - 260 T + 79507 T^{2} )^{2} \))(\( ( 1 + 124 T + 79507 T^{2} )^{2} \))(\( ( 1 - 307 T + 161298 T^{2} - 24408649 T^{3} + 6321363049 T^{4} )^{2} \))(\( ( 1 - 307 T + 161298 T^{2} - 24408649 T^{3} + 6321363049 T^{4} )^{2} \))(\( ( 1 + 107 T + 86220 T^{2} + 8507249 T^{3} + 6321363049 T^{4} )^{2} \))(\( ( 1 + 278 T + 270019 T^{2} + 50229506 T^{3} + 29430654334 T^{4} + 3993597333542 T^{5} + 1706888129127931 T^{6} + 139720746118442354 T^{7} + 39959630797262576401 T^{8} )^{4} \))
$47$ (\( 1 + 168 T + 103823 T^{2} \))(\( 1 - 228 T + 103823 T^{2} \))(\( 1 - 264 T + 103823 T^{2} \))(\( 1 - 12 T + 103823 T^{2} \))(\( 1 + 444 T + 103823 T^{2} \))(\( 1 - 444 T + 103823 T^{2} \))(\( 1 + 228 T + 103823 T^{2} \))(\( 1 + 24 T + 103823 T^{2} \))(\( ( 1 + 149372 T^{2} + 24974240454 T^{4} + 1610112952123388 T^{6} + \)\(11\!\cdots\!41\)\( T^{8} )^{2} \))(\( 1 + 81 T + 5646 T^{2} + 117759825 T^{3} + 4672110435 T^{4} + 803885546034 T^{5} + 5629933175771815 T^{6} + 83461809045887982 T^{7} + 50361684419732858115 T^{8} + \)\(13\!\cdots\!75\)\( T^{9} + \)\(65\!\cdots\!86\)\( T^{10} + \)\(97\!\cdots\!83\)\( T^{11} + \)\(12\!\cdots\!89\)\( T^{12} \))(\( 1 - 675 T + 37387 T^{2} + 77590386 T^{3} - 14073185960 T^{4} - 2780172589698 T^{5} + 544267648367926 T^{6} - 322605518680562283 T^{7} + \)\(21\!\cdots\!97\)\( T^{8} - \)\(33\!\cdots\!09\)\( T^{9} + \)\(58\!\cdots\!54\)\( T^{10} - \)\(31\!\cdots\!66\)\( T^{11} - \)\(16\!\cdots\!60\)\( T^{12} + \)\(93\!\cdots\!98\)\( T^{13} + \)\(46\!\cdots\!43\)\( T^{14} - \)\(87\!\cdots\!25\)\( T^{15} + \)\(13\!\cdots\!81\)\( T^{16} \))(\( 1 - 675 T + 82088 T^{2} + 71665155 T^{3} - 35492469408 T^{4} + 6293893465017 T^{5} + 471660448117893 T^{6} - 576532697538573243 T^{7} + \)\(15\!\cdots\!03\)\( T^{8} - \)\(11\!\cdots\!46\)\( T^{9} - \)\(91\!\cdots\!55\)\( T^{10} - \)\(12\!\cdots\!58\)\( T^{11} + \)\(16\!\cdots\!87\)\( T^{12} - \)\(64\!\cdots\!81\)\( T^{13} + \)\(54\!\cdots\!13\)\( T^{14} + \)\(75\!\cdots\!31\)\( T^{15} - \)\(44\!\cdots\!12\)\( T^{16} + \)\(93\!\cdots\!85\)\( T^{17} + \)\(11\!\cdots\!28\)\( T^{18} - \)\(94\!\cdots\!25\)\( T^{19} + \)\(14\!\cdots\!49\)\( T^{20} \))(\( 1 + 81 T - 175251 T^{2} - 34020648 T^{3} + 4943762067 T^{4} + 2148298867035 T^{5} + 2642290614165335 T^{6} + 411972632863814385 T^{7} - \)\(24\!\cdots\!18\)\( T^{8} - \)\(11\!\cdots\!70\)\( T^{9} - \)\(12\!\cdots\!27\)\( T^{10} + \)\(55\!\cdots\!07\)\( T^{11} + \)\(42\!\cdots\!63\)\( T^{12} + \)\(57\!\cdots\!61\)\( T^{13} - \)\(13\!\cdots\!83\)\( T^{14} - \)\(12\!\cdots\!90\)\( T^{15} - \)\(28\!\cdots\!38\)\( T^{16} + \)\(49\!\cdots\!55\)\( T^{17} + \)\(33\!\cdots\!15\)\( T^{18} + \)\(27\!\cdots\!45\)\( T^{19} + \)\(66\!\cdots\!27\)\( T^{20} - \)\(47\!\cdots\!24\)\( T^{21} - \)\(25\!\cdots\!99\)\( T^{22} + \)\(12\!\cdots\!87\)\( T^{23} + \)\(15\!\cdots\!21\)\( T^{24} \))(\( 1 + 138 T - 84779 T^{2} + 14327574 T^{3} + 10779215329 T^{4} \))(\( 1 + 366 T + 30133 T^{2} + 37999218 T^{3} + 10779215329 T^{4} \))(\( 1 + 171 T - 74582 T^{2} + 17753733 T^{3} + 10779215329 T^{4} \))(\( 1 - 201 T - 63422 T^{2} - 20868423 T^{3} + 10779215329 T^{4} \))(\( 1 - 672 T + 158834 T^{2} - 57189888 T^{3} + 28038541539 T^{4} - 5937625741824 T^{5} + 1712105887566386 T^{6} - 752055677925059424 T^{7} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 + 672 T + 158834 T^{2} + 57189888 T^{3} + 28038541539 T^{4} + 5937625741824 T^{5} + 1712105887566386 T^{6} + 752055677925059424 T^{7} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 - 576 T + 89606 T^{2} - 19885824 T^{3} + 13421113923 T^{4} - 2064605905152 T^{5} + 965882368770374 T^{6} - 644619152507193792 T^{7} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 - 436840 T^{2} + 90860267532 T^{4} - 12019016866813616 T^{6} + \)\(12\!\cdots\!94\)\( T^{8} - \)\(11\!\cdots\!44\)\( T^{10} + \)\(11\!\cdots\!60\)\( T^{12} - \)\(12\!\cdots\!92\)\( T^{14} + \)\(12\!\cdots\!19\)\( T^{16} - \)\(13\!\cdots\!68\)\( T^{18} + \)\(13\!\cdots\!60\)\( T^{20} - \)\(14\!\cdots\!16\)\( T^{22} + \)\(16\!\cdots\!14\)\( T^{24} - \)\(17\!\cdots\!84\)\( T^{26} + \)\(14\!\cdots\!72\)\( T^{28} - \)\(73\!\cdots\!60\)\( T^{30} + \)\(18\!\cdots\!61\)\( T^{32} \))
$53$ (\( 1 + 654 T + 148877 T^{2} \))(\( 1 - 348 T + 148877 T^{2} \))(\( 1 - 162 T + 148877 T^{2} \))(\( 1 + 174 T + 148877 T^{2} \))(\( 1 - 12 T + 148877 T^{2} \))(\( 1 + 12 T + 148877 T^{2} \))(\( 1 + 348 T + 148877 T^{2} \))(\( 1 + 318 T + 148877 T^{2} \))(\( ( 1 - 522320 T^{2} + 112512272658 T^{4} - 11576889104899280 T^{6} + \)\(49\!\cdots\!41\)\( T^{8} )^{2} \))(\( ( 1 - 522 T + 190134 T^{2} - 48782187 T^{3} + 28306579518 T^{4} - 11569796509338 T^{5} + 3299763591802133 T^{6} )^{2} \))(\( ( 1 - 54 T + 236591 T^{2} - 19653129 T^{3} + 33755250168 T^{4} - 2925898886133 T^{5} + 5243888363871239 T^{6} - 178187233957315182 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} )^{2} \))(\( ( 1 + 450 T + 345232 T^{2} + 146943009 T^{3} + 77594979187 T^{4} + 33037648375266 T^{5} + 11552107716422999 T^{6} + 3256897916857897161 T^{7} + \)\(11\!\cdots\!56\)\( T^{8} + \)\(22\!\cdots\!50\)\( T^{9} + \)\(73\!\cdots\!57\)\( T^{10} )^{2} \))(\( ( 1 - 90 T + 756729 T^{2} - 44452305 T^{3} + 252967751055 T^{4} - 10326303249633 T^{5} + 48393394788297022 T^{6} - 1537349048895612141 T^{7} + \)\(56\!\cdots\!95\)\( T^{8} - \)\(14\!\cdots\!65\)\( T^{9} + \)\(37\!\cdots\!89\)\( T^{10} - \)\(65\!\cdots\!30\)\( T^{11} + \)\(10\!\cdots\!89\)\( T^{12} )^{2} \))(\( 1 - 639 T + 259444 T^{2} - 95132403 T^{3} + 22164361129 T^{4} \))(\( 1 + 768 T + 440947 T^{2} + 114337536 T^{3} + 22164361129 T^{4} \))(\( 1 + 417 T + 25012 T^{2} + 62081709 T^{3} + 22164361129 T^{4} \))(\( 1 + 393 T + 5572 T^{2} + 58508661 T^{3} + 22164361129 T^{4} \))(\( 1 + 375 T - 781 T^{2} - 58630500 T^{3} - 23104532418 T^{4} - 8728732948500 T^{5} - 17310366041749 T^{6} + 1237411346925799875 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 - 375 T - 781 T^{2} + 58630500 T^{3} - 23104532418 T^{4} + 8728732948500 T^{5} - 17310366041749 T^{6} - 1237411346925799875 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 + 243 T - 250441 T^{2} + 2851848 T^{3} + 64828660998 T^{4} + 424574574696 T^{5} - 5550864765507889 T^{6} + 801842552807918319 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 + 649378 T^{2} + 244319710347 T^{4} + 58070741955199790 T^{6} + \)\(89\!\cdots\!57\)\( T^{8} + \)\(57\!\cdots\!60\)\( T^{10} - \)\(12\!\cdots\!54\)\( T^{12} - \)\(48\!\cdots\!76\)\( T^{14} - \)\(90\!\cdots\!50\)\( T^{16} - \)\(10\!\cdots\!04\)\( T^{18} - \)\(59\!\cdots\!14\)\( T^{20} + \)\(62\!\cdots\!40\)\( T^{22} + \)\(21\!\cdots\!17\)\( T^{24} + \)\(31\!\cdots\!10\)\( T^{26} + \)\(28\!\cdots\!87\)\( T^{28} + \)\(17\!\cdots\!02\)\( T^{30} + \)\(58\!\cdots\!61\)\( T^{32} \))
$59$ (\( 1 - 492 T + 205379 T^{2} \))(\( 1 - 348 T + 205379 T^{2} \))(\( 1 - 772 T + 205379 T^{2} \))(\( 1 + 138 T + 205379 T^{2} \))(\( 1 - 124 T + 205379 T^{2} \))(\( 1 + 124 T + 205379 T^{2} \))(\( 1 + 348 T + 205379 T^{2} \))(\( 1 - 200 T + 205379 T^{2} \))(\( ( 1 + 253196 T^{2} + 35242060086 T^{4} + 10679942395766636 T^{6} + \)\(17\!\cdots\!81\)\( T^{8} )^{2} \))(\( 1 + 21 T - 237354 T^{2} - 181685679 T^{3} + 5748229293 T^{4} + 21030301905816 T^{5} + 14406231366999691 T^{6} + 4319182375114584264 T^{7} + \)\(24\!\cdots\!13\)\( T^{8} - \)\(15\!\cdots\!81\)\( T^{9} - \)\(42\!\cdots\!74\)\( T^{10} + \)\(76\!\cdots\!79\)\( T^{11} + \)\(75\!\cdots\!21\)\( T^{12} \))(\( 1 - 202 T - 531049 T^{2} + 16684212 T^{3} + 159300075830 T^{4} + 10988486623156 T^{5} - 38404349933253128 T^{6} - 1299442121783896557 T^{7} + \)\(80\!\cdots\!84\)\( T^{8} - \)\(26\!\cdots\!03\)\( T^{9} - \)\(16\!\cdots\!48\)\( T^{10} + \)\(95\!\cdots\!84\)\( T^{11} + \)\(28\!\cdots\!30\)\( T^{12} + \)\(60\!\cdots\!88\)\( T^{13} - \)\(39\!\cdots\!29\)\( T^{14} - \)\(31\!\cdots\!18\)\( T^{15} + \)\(31\!\cdots\!61\)\( T^{16} \))(\( 1 - 625 T + 76718 T^{2} - 79101585 T^{3} - 20565592434 T^{4} + 47175299491233 T^{5} - 12073281842585217 T^{6} + 5706376133235544023 T^{7} - \)\(34\!\cdots\!73\)\( T^{8} - \)\(13\!\cdots\!26\)\( T^{9} + \)\(51\!\cdots\!21\)\( T^{10} - \)\(28\!\cdots\!54\)\( T^{11} - \)\(14\!\cdots\!93\)\( T^{12} + \)\(49\!\cdots\!97\)\( T^{13} - \)\(21\!\cdots\!77\)\( T^{14} + \)\(17\!\cdots\!67\)\( T^{15} - \)\(15\!\cdots\!14\)\( T^{16} - \)\(12\!\cdots\!15\)\( T^{17} + \)\(24\!\cdots\!98\)\( T^{18} - \)\(40\!\cdots\!75\)\( T^{19} + \)\(13\!\cdots\!01\)\( T^{20} \))(\( 1 + 444 T - 665211 T^{2} - 377119914 T^{3} + 206650399647 T^{4} + 143703237077472 T^{5} - 47289423923096413 T^{6} - 35326833829575968871 T^{7} + \)\(10\!\cdots\!57\)\( T^{8} + \)\(63\!\cdots\!55\)\( T^{9} - \)\(17\!\cdots\!93\)\( T^{10} - \)\(55\!\cdots\!39\)\( T^{11} + \)\(30\!\cdots\!00\)\( T^{12} - \)\(11\!\cdots\!81\)\( T^{13} - \)\(75\!\cdots\!13\)\( T^{14} + \)\(55\!\cdots\!45\)\( T^{15} + \)\(18\!\cdots\!17\)\( T^{16} - \)\(12\!\cdots\!29\)\( T^{17} - \)\(35\!\cdots\!73\)\( T^{18} + \)\(22\!\cdots\!48\)\( T^{19} + \)\(65\!\cdots\!67\)\( T^{20} - \)\(24\!\cdots\!66\)\( T^{21} - \)\(88\!\cdots\!11\)\( T^{22} + \)\(12\!\cdots\!76\)\( T^{23} + \)\(56\!\cdots\!41\)\( T^{24} \))(\( 1 - 159 T - 180098 T^{2} - 32655261 T^{3} + 42180533641 T^{4} \))(\( 1 + 264 T - 135683 T^{2} + 54220056 T^{3} + 42180533641 T^{4} \))(\( 1 + 17 T - 205090 T^{2} + 3491443 T^{3} + 42180533641 T^{4} \))(\( 1 - 219 T - 157418 T^{2} - 44978001 T^{3} + 42180533641 T^{4} \))(\( 1 - 763 T + 205407 T^{2} + 25938948 T^{3} - 19796216048 T^{4} + 5327315201292 T^{5} + 8664176873596887 T^{6} - 6609865809633718457 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} \))(\( 1 + 763 T + 205407 T^{2} - 25938948 T^{3} - 19796216048 T^{4} - 5327315201292 T^{5} + 8664176873596887 T^{6} + 6609865809633718457 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} \))(\( 1 + 7 T - 200565 T^{2} - 1471008 T^{3} - 1944620216 T^{4} - 302114152032 T^{5} - 8459938729707165 T^{6} + 60640970730584573 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} \))(\( 1 - 1113586 T^{2} + 660589172571 T^{4} - 264167429023970894 T^{6} + \)\(78\!\cdots\!53\)\( T^{8} - \)\(17\!\cdots\!40\)\( T^{10} + \)\(32\!\cdots\!06\)\( T^{12} - \)\(51\!\cdots\!48\)\( T^{14} + \)\(90\!\cdots\!98\)\( T^{16} - \)\(21\!\cdots\!68\)\( T^{18} + \)\(58\!\cdots\!86\)\( T^{20} - \)\(13\!\cdots\!40\)\( T^{22} + \)\(24\!\cdots\!33\)\( T^{24} - \)\(35\!\cdots\!94\)\( T^{26} + \)\(37\!\cdots\!11\)\( T^{28} - \)\(26\!\cdots\!66\)\( T^{30} + \)\(10\!\cdots\!21\)\( T^{32} \))
$61$ (\( 1 + 250 T + 226981 T^{2} \))(\( 1 + 106 T + 226981 T^{2} \))(\( 1 - 30 T + 226981 T^{2} \))(\( 1 - 380 T + 226981 T^{2} \))(\( 1 + 162 T + 226981 T^{2} \))(\( 1 + 162 T + 226981 T^{2} \))(\( 1 + 106 T + 226981 T^{2} \))(\( 1 + 198 T + 226981 T^{2} \))(\( ( 1 - 500884 T^{2} + 126472292886 T^{4} - 25805731191435124 T^{6} + \)\(26\!\cdots\!21\)\( T^{8} )^{2} \))(\( 1 - 780 T - 154002 T^{2} + 55626026 T^{3} + 154589202702 T^{4} - 18121545839646 T^{5} - 34168567588346793 T^{6} - 4113246596228688726 T^{7} + \)\(79\!\cdots\!22\)\( T^{8} + \)\(65\!\cdots\!66\)\( T^{9} - \)\(40\!\cdots\!42\)\( T^{10} - \)\(46\!\cdots\!80\)\( T^{11} + \)\(13\!\cdots\!81\)\( T^{12} \))(\( 1 - 1212 T + 239267 T^{2} - 3162822 T^{3} + 187949681281 T^{4} - 58043170902294 T^{5} - 44955529435193749 T^{6} + 9664786778799768882 T^{7} + \)\(71\!\cdots\!33\)\( T^{8} + \)\(21\!\cdots\!42\)\( T^{9} - \)\(23\!\cdots\!89\)\( T^{10} - \)\(67\!\cdots\!54\)\( T^{11} + \)\(49\!\cdots\!01\)\( T^{12} - \)\(19\!\cdots\!22\)\( T^{13} + \)\(32\!\cdots\!27\)\( T^{14} - \)\(37\!\cdots\!32\)\( T^{15} + \)\(70\!\cdots\!41\)\( T^{16} \))(\( 1 + 1014 T + 165103 T^{2} - 332338248 T^{3} - 225006447660 T^{4} - 35168008104360 T^{5} + 46595345587937658 T^{6} + 37345473318007694844 T^{7} + \)\(87\!\cdots\!46\)\( T^{8} - \)\(58\!\cdots\!78\)\( T^{9} - \)\(51\!\cdots\!96\)\( T^{10} - \)\(13\!\cdots\!18\)\( T^{11} + \)\(44\!\cdots\!06\)\( T^{12} + \)\(43\!\cdots\!04\)\( T^{13} + \)\(12\!\cdots\!18\)\( T^{14} - \)\(21\!\cdots\!60\)\( T^{15} - \)\(30\!\cdots\!60\)\( T^{16} - \)\(10\!\cdots\!28\)\( T^{17} + \)\(11\!\cdots\!23\)\( T^{18} + \)\(16\!\cdots\!94\)\( T^{19} + \)\(36\!\cdots\!01\)\( T^{20} \))(\( 1 + 978 T + 356718 T^{2} + 365578534 T^{3} + 258773030058 T^{4} + 48525405780120 T^{5} + 27404413522391593 T^{6} + 20211315787211565798 T^{7} - \)\(41\!\cdots\!26\)\( T^{8} - \)\(48\!\cdots\!50\)\( T^{9} - \)\(15\!\cdots\!94\)\( T^{10} - \)\(15\!\cdots\!12\)\( T^{11} - \)\(11\!\cdots\!00\)\( T^{12} - \)\(35\!\cdots\!72\)\( T^{13} - \)\(80\!\cdots\!34\)\( T^{14} - \)\(56\!\cdots\!50\)\( T^{15} - \)\(10\!\cdots\!46\)\( T^{16} + \)\(12\!\cdots\!98\)\( T^{17} + \)\(37\!\cdots\!33\)\( T^{18} + \)\(15\!\cdots\!20\)\( T^{19} + \)\(18\!\cdots\!78\)\( T^{20} + \)\(58\!\cdots\!14\)\( T^{21} + \)\(12\!\cdots\!18\)\( T^{22} + \)\(80\!\cdots\!18\)\( T^{23} + \)\(18\!\cdots\!61\)\( T^{24} \))(\( 1 + 722 T + 294303 T^{2} + 163880282 T^{3} + 51520374361 T^{4} \))(\( 1 + 818 T + 442143 T^{2} + 185670458 T^{3} + 51520374361 T^{4} \))(\( 1 + 51 T - 224380 T^{2} + 11576031 T^{3} + 51520374361 T^{4} \))(\( 1 - 709 T + 275700 T^{2} - 160929529 T^{3} + 51520374361 T^{4} \))(\( 1 - 406 T - 274558 T^{2} + 5914608 T^{3} + 104132072759 T^{4} + 1342503638448 T^{5} - 14145330943807438 T^{6} - 4747823313690661246 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} \))(\( 1 - 406 T - 274558 T^{2} + 5914608 T^{3} + 104132072759 T^{4} + 1342503638448 T^{5} - 14145330943807438 T^{6} - 4747823313690661246 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} \))(\( 1 + 224 T - 410950 T^{2} + 1604736 T^{3} + 149727814859 T^{4} + 364244582016 T^{5} - 21172297843652950 T^{6} + 2619488724794847584 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} \))(\( ( 1 - 1632 T + 1515286 T^{2} - 1024044096 T^{3} + 507147724594 T^{4} - 151439337874440 T^{5} - 5780390636265536 T^{6} + 36949211391126580368 T^{7} - \)\(24\!\cdots\!01\)\( T^{8} + \)\(83\!\cdots\!08\)\( T^{9} - \)\(29\!\cdots\!96\)\( T^{10} - \)\(17\!\cdots\!40\)\( T^{11} + \)\(13\!\cdots\!74\)\( T^{12} - \)\(61\!\cdots\!96\)\( T^{13} + \)\(20\!\cdots\!66\)\( T^{14} - \)\(50\!\cdots\!52\)\( T^{15} + \)\(70\!\cdots\!41\)\( T^{16} )^{2} \))
$67$ (\( 1 + 124 T + 300763 T^{2} \))(\( 1 - 596 T + 300763 T^{2} \))(\( 1 + 764 T + 300763 T^{2} \))(\( 1 + 484 T + 300763 T^{2} \))(\( 1 + 860 T + 300763 T^{2} \))(\( 1 + 860 T + 300763 T^{2} \))(\( 1 - 596 T + 300763 T^{2} \))(\( 1 + 716 T + 300763 T^{2} \))(\( ( 1 + 920 T + 460326 T^{2} + 276701960 T^{3} + 90458382169 T^{4} )^{4} \))(\( 1 - 384 T - 173424 T^{2} + 85131122 T^{3} - 33547873104 T^{4} + 5955243494544 T^{5} + 20959014584590071 T^{6} + 1791116899149537072 T^{7} - \)\(30\!\cdots\!76\)\( T^{8} + \)\(23\!\cdots\!34\)\( T^{9} - \)\(14\!\cdots\!64\)\( T^{10} - \)\(94\!\cdots\!12\)\( T^{11} + \)\(74\!\cdots\!09\)\( T^{12} \))(\( 1 + 139 T - 800538 T^{2} - 280034389 T^{3} + 334951438031 T^{4} + 134625567082980 T^{5} - 75122243735690903 T^{6} - 22025505408916196753 T^{7} + \)\(16\!\cdots\!74\)\( T^{8} - \)\(66\!\cdots\!39\)\( T^{9} - \)\(67\!\cdots\!07\)\( T^{10} + \)\(36\!\cdots\!60\)\( T^{11} + \)\(27\!\cdots\!91\)\( T^{12} - \)\(68\!\cdots\!27\)\( T^{13} - \)\(59\!\cdots\!42\)\( T^{14} + \)\(30\!\cdots\!13\)\( T^{15} + \)\(66\!\cdots\!21\)\( T^{16} \))(\( 1 + 1580 T + 457078 T^{2} - 492353118 T^{3} - 151288423989 T^{4} + 272492358188232 T^{5} + 156620513772519213 T^{6} - 17275056958151207898 T^{7} - \)\(21\!\cdots\!29\)\( T^{8} + \)\(12\!\cdots\!82\)\( T^{9} + \)\(14\!\cdots\!53\)\( T^{10} + \)\(36\!\cdots\!66\)\( T^{11} - \)\(19\!\cdots\!01\)\( T^{12} - \)\(46\!\cdots\!06\)\( T^{13} + \)\(12\!\cdots\!93\)\( T^{14} + \)\(67\!\cdots\!76\)\( T^{15} - \)\(11\!\cdots\!01\)\( T^{16} - \)\(10\!\cdots\!06\)\( T^{17} + \)\(30\!\cdots\!38\)\( T^{18} + \)\(31\!\cdots\!40\)\( T^{19} + \)\(60\!\cdots\!49\)\( T^{20} \))(\( 1 + 663 T - 345408 T^{2} - 313195211 T^{3} + 124178257866 T^{4} + 138437340834975 T^{5} + 24439199330529559 T^{6} - 5495930641369742310 T^{7} - \)\(78\!\cdots\!46\)\( T^{8} - \)\(10\!\cdots\!68\)\( T^{9} + \)\(48\!\cdots\!72\)\( T^{10} + \)\(16\!\cdots\!94\)\( T^{11} - \)\(45\!\cdots\!20\)\( T^{12} + \)\(49\!\cdots\!22\)\( T^{13} + \)\(43\!\cdots\!68\)\( T^{14} - \)\(27\!\cdots\!96\)\( T^{15} - \)\(64\!\cdots\!06\)\( T^{16} - \)\(13\!\cdots\!30\)\( T^{17} + \)\(18\!\cdots\!31\)\( T^{18} + \)\(30\!\cdots\!25\)\( T^{19} + \)\(83\!\cdots\!86\)\( T^{20} - \)\(63\!\cdots\!53\)\( T^{21} - \)\(20\!\cdots\!92\)\( T^{22} + \)\(12\!\cdots\!81\)\( T^{23} + \)\(54\!\cdots\!81\)\( T^{24} \))(\( 1 - 166 T - 273207 T^{2} - 49926658 T^{3} + 90458382169 T^{4} \))(\( 1 - 523 T - 27234 T^{2} - 157299049 T^{3} + 90458382169 T^{4} \))(\( 1 + 439 T - 108042 T^{2} + 132034957 T^{3} + 90458382169 T^{4} \))(\( 1 + 419 T - 125202 T^{2} + 126019697 T^{3} + 90458382169 T^{4} \))(\( 1 - 1041 T + 270341 T^{2} - 220498374 T^{3} + 245132424828 T^{4} - 66317752459362 T^{5} + 24454609493949629 T^{6} - 28322002306543039827 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 - 1041 T + 270341 T^{2} - 220498374 T^{3} + 245132424828 T^{4} - 66317752459362 T^{5} + 24454609493949629 T^{6} - 28322002306543039827 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 + 687 T - 206863 T^{2} + 53109222 T^{3} + 228403689708 T^{4} + 15973288936386 T^{5} - 18712492310625847 T^{6} + 18690889130254628589 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( ( 1 - 34 T - 432501 T^{2} - 244602470 T^{3} + 53207716205 T^{4} + 93841766718504 T^{5} + 32666276223725578 T^{6} - 16291345166027326324 T^{7} - \)\(98\!\cdots\!62\)\( T^{8} - \)\(48\!\cdots\!12\)\( T^{9} + \)\(29\!\cdots\!82\)\( T^{10} + \)\(25\!\cdots\!88\)\( T^{11} + \)\(43\!\cdots\!05\)\( T^{12} - \)\(60\!\cdots\!10\)\( T^{13} - \)\(32\!\cdots\!09\)\( T^{14} - \)\(75\!\cdots\!78\)\( T^{15} + \)\(66\!\cdots\!21\)\( T^{16} )^{2} \))
$71$ (\( 1 + 36 T + 357911 T^{2} \))(\( 1 + 630 T + 357911 T^{2} \))(\( 1 - 236 T + 357911 T^{2} \))(\( 1 + 576 T + 357911 T^{2} \))(\( 1 + 238 T + 357911 T^{2} \))(\( 1 - 238 T + 357911 T^{2} \))(\( 1 - 630 T + 357911 T^{2} \))(\( 1 + 392 T + 357911 T^{2} \))(\( ( 1 - 330800 T^{2} - 18493280958 T^{4} - 42375573921066800 T^{6} + \)\(16\!\cdots\!41\)\( T^{8} )^{2} \))(\( ( 1 - 57 T + 367377 T^{2} - 182634123 T^{3} + 131488269447 T^{4} - 7301716183497 T^{5} + 45848500718449031 T^{6} )^{2} \))(\( ( 1 + 1295 T + 1795244 T^{2} + 1349389658 T^{3} + 1011484858822 T^{4} + 482961401884438 T^{5} + 229971266107471724 T^{6} + 59373808430391495145 T^{7} + \)\(16\!\cdots\!41\)\( T^{8} )^{2} \))(\( ( 1 + 377 T + 1027598 T^{2} + 447481346 T^{3} + 629752049547 T^{4} + 197285081855177 T^{5} + 225395185805416317 T^{6} + 57322487471951237666 T^{7} + \)\(47\!\cdots\!38\)\( T^{8} + \)\(61\!\cdots\!57\)\( T^{9} + \)\(58\!\cdots\!51\)\( T^{10} )^{2} \))(\( ( 1 - 507 T + 1252677 T^{2} - 859117431 T^{3} + 774357559413 T^{4} - 595730339250105 T^{5} + 322202396876351290 T^{6} - \)\(21\!\cdots\!55\)\( T^{7} + \)\(99\!\cdots\!73\)\( T^{8} - \)\(39\!\cdots\!61\)\( T^{9} + \)\(20\!\cdots\!57\)\( T^{10} - \)\(29\!\cdots\!57\)\( T^{11} + \)\(21\!\cdots\!61\)\( T^{12} )^{2} \))(\( ( 1 + 1086 T + 357911 T^{2} )^{2} \))(\( ( 1 - 342 T + 357911 T^{2} )^{2} \))(\( ( 1 - 784 T + 357911 T^{2} )^{2} \))(\( ( 1 - 96 T + 357911 T^{2} )^{2} \))(\( ( 1 + 1652 T + 1360270 T^{2} + 591268972 T^{3} + 128100283921 T^{4} )^{2} \))(\( ( 1 - 1652 T + 1360270 T^{2} - 591268972 T^{3} + 128100283921 T^{4} )^{2} \))(\( ( 1 + 472 T + 637018 T^{2} + 168933992 T^{3} + 128100283921 T^{4} )^{2} \))(\( ( 1 - 846568 T^{2} + 615050624116 T^{4} - 295332039745995832 T^{6} + \)\(11\!\cdots\!02\)\( T^{8} - \)\(37\!\cdots\!72\)\( T^{10} + \)\(10\!\cdots\!56\)\( T^{12} - \)\(17\!\cdots\!48\)\( T^{14} + \)\(26\!\cdots\!81\)\( T^{16} )^{2} \))
$73$ (\( 1 - 1010 T + 389017 T^{2} \))(\( 1 + 1042 T + 389017 T^{2} \))(\( 1 - 418 T + 389017 T^{2} \))(\( 1 + 1150 T + 389017 T^{2} \))(\( 1 + 146 T + 389017 T^{2} \))(\( 1 + 146 T + 389017 T^{2} \))(\( 1 + 1042 T + 389017 T^{2} \))(\( 1 - 538 T + 389017 T^{2} \))(\( ( 1 - 1300228 T^{2} + 714352822374 T^{4} - 196768998379293892 T^{6} + \)\(22\!\cdots\!21\)\( T^{8} )^{2} \))(\( ( 1 + 117 T + 506133 T^{2} - 134410025 T^{3} + 196894341261 T^{4} + 17706104475813 T^{5} + 58871586708267913 T^{6} )^{2} \))(\( ( 1 + 2000 T + 2663509 T^{2} + 2429329973 T^{3} + 1727799097657 T^{4} + 945050658106541 T^{5} + 403080073728788101 T^{6} + \)\(11\!\cdots\!00\)\( T^{7} + \)\(22\!\cdots\!21\)\( T^{8} )^{2} \))(\( ( 1 - 1559 T + 2512827 T^{2} - 2340059841 T^{3} + 2135659109352 T^{4} - 1352009407465440 T^{5} + 830807699742786984 T^{6} - \)\(35\!\cdots\!49\)\( T^{7} + \)\(14\!\cdots\!51\)\( T^{8} - \)\(35\!\cdots\!39\)\( T^{9} + \)\(89\!\cdots\!57\)\( T^{10} )^{2} \))(\( ( 1 - 144 T + 1127475 T^{2} + 206515139 T^{3} + 530063310042 T^{4} + 279359611038441 T^{5} + 193985398904607132 T^{6} + \)\(10\!\cdots\!97\)\( T^{7} + \)\(80\!\cdots\!38\)\( T^{8} + \)\(12\!\cdots\!07\)\( T^{9} + \)\(25\!\cdots\!75\)\( T^{10} - \)\(12\!\cdots\!08\)\( T^{11} + \)\(34\!\cdots\!69\)\( T^{12} )^{2} \))(\( 1 + 218 T - 341493 T^{2} + 84805706 T^{3} + 151334226289 T^{4} \))(\( 1 - 43 T - 387168 T^{2} - 16727731 T^{3} + 151334226289 T^{4} \))(\( 1 + 295 T - 301992 T^{2} + 114760015 T^{3} + 151334226289 T^{4} \))(\( 1 - 313 T - 291048 T^{2} - 121762321 T^{3} + 151334226289 T^{4} \))(\( 1 - 189 T - 297259 T^{2} + 84115206 T^{3} - 54354622146 T^{4} + 32722245092502 T^{5} - 44985460772441851 T^{6} - 11126729887862635557 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 - 189 T - 297259 T^{2} + 84115206 T^{3} - 54354622146 T^{4} + 32722245092502 T^{5} - 44985460772441851 T^{6} - 11126729887862635557 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 - 921 T + 270053 T^{2} + 184058166 T^{3} - 147013032042 T^{4} + 71601755562822 T^{5} + 40868261812023317 T^{6} - 54220731358314747873 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( ( 1 + 1566 T + 2128687 T^{2} + 2053394010 T^{3} + 1723582499653 T^{4} + 1269244514774412 T^{5} + 891506081517645706 T^{6} + \)\(57\!\cdots\!32\)\( T^{7} + \)\(37\!\cdots\!86\)\( T^{8} + \)\(22\!\cdots\!44\)\( T^{9} + \)\(13\!\cdots\!34\)\( T^{10} + \)\(74\!\cdots\!56\)\( T^{11} + \)\(39\!\cdots\!13\)\( T^{12} + \)\(18\!\cdots\!70\)\( T^{13} + \)\(73\!\cdots\!03\)\( T^{14} + \)\(21\!\cdots\!18\)\( T^{15} + \)\(52\!\cdots\!41\)\( T^{16} )^{2} \))
$79$ (\( 1 - 56 T + 493039 T^{2} \))(\( 1 + 88 T + 493039 T^{2} \))(\( 1 - 552 T + 493039 T^{2} \))(\( 1 - 776 T + 493039 T^{2} \))(\( 1 + 984 T + 493039 T^{2} \))(\( 1 + 984 T + 493039 T^{2} \))(\( 1 + 88 T + 493039 T^{2} \))(\( 1 - 240 T + 493039 T^{2} \))(\( ( 1 - 112 T + 406014 T^{2} - 55220368 T^{3} + 243087455521 T^{4} )^{4} \))(\( 1 - 1383 T - 79770 T^{2} + 85607285 T^{3} + 1022858230077 T^{4} - 449447630663196 T^{5} - 164486295934003209 T^{6} - \)\(22\!\cdots\!44\)\( T^{7} + \)\(24\!\cdots\!17\)\( T^{8} + \)\(10\!\cdots\!15\)\( T^{9} - \)\(47\!\cdots\!70\)\( T^{10} - \)\(40\!\cdots\!17\)\( T^{11} + \)\(14\!\cdots\!61\)\( T^{12} \))(\( 1 - 1545 T + 135641 T^{2} + 576786432 T^{3} + 262453195432 T^{4} - 392965726353228 T^{5} - 106866556646468452 T^{6} + 77122026263059272753 T^{7} + \)\(55\!\cdots\!45\)\( T^{8} + \)\(38\!\cdots\!67\)\( T^{9} - \)\(25\!\cdots\!92\)\( T^{10} - \)\(47\!\cdots\!32\)\( T^{11} + \)\(15\!\cdots\!12\)\( T^{12} + \)\(16\!\cdots\!68\)\( T^{13} + \)\(19\!\cdots\!01\)\( T^{14} - \)\(10\!\cdots\!55\)\( T^{15} + \)\(34\!\cdots\!81\)\( T^{16} \))(\( 1 + 1383 T - 186275 T^{2} - 1277635176 T^{3} - 438797938893 T^{4} + 428758795115217 T^{5} + 196355568892051485 T^{6} - \)\(14\!\cdots\!33\)\( T^{7} - \)\(71\!\cdots\!57\)\( T^{8} + \)\(47\!\cdots\!15\)\( T^{9} + \)\(58\!\cdots\!02\)\( T^{10} + \)\(23\!\cdots\!85\)\( T^{11} - \)\(17\!\cdots\!97\)\( T^{12} - \)\(17\!\cdots\!27\)\( T^{13} + \)\(11\!\cdots\!85\)\( T^{14} + \)\(12\!\cdots\!83\)\( T^{15} - \)\(63\!\cdots\!73\)\( T^{16} - \)\(90\!\cdots\!04\)\( T^{17} - \)\(65\!\cdots\!75\)\( T^{18} + \)\(23\!\cdots\!97\)\( T^{19} + \)\(84\!\cdots\!01\)\( T^{20} \))(\( 1 + 609 T - 777696 T^{2} - 395547173 T^{3} - 71141975565 T^{4} - 224471826664896 T^{5} - 23213681995587389 T^{6} + \)\(14\!\cdots\!40\)\( T^{7} + \)\(21\!\cdots\!71\)\( T^{8} + \)\(97\!\cdots\!03\)\( T^{9} - \)\(56\!\cdots\!46\)\( T^{10} - \)\(50\!\cdots\!55\)\( T^{11} - \)\(18\!\cdots\!56\)\( T^{12} - \)\(24\!\cdots\!45\)\( T^{13} - \)\(13\!\cdots\!66\)\( T^{14} + \)\(11\!\cdots\!57\)\( T^{15} + \)\(12\!\cdots\!11\)\( T^{16} + \)\(42\!\cdots\!60\)\( T^{17} - \)\(33\!\cdots\!29\)\( T^{18} - \)\(15\!\cdots\!84\)\( T^{19} - \)\(24\!\cdots\!65\)\( T^{20} - \)\(68\!\cdots\!07\)\( T^{21} - \)\(66\!\cdots\!96\)\( T^{22} + \)\(25\!\cdots\!51\)\( T^{23} + \)\(20\!\cdots\!21\)\( T^{24} \))(\( 1 - 583 T - 153150 T^{2} - 287441737 T^{3} + 243087455521 T^{4} \))(\( 1 - 1171 T + 878202 T^{2} - 577348669 T^{3} + 243087455521 T^{4} \))(\( 1 - 495 T - 248014 T^{2} - 244054305 T^{3} + 243087455521 T^{4} \))(\( 1 + 461 T - 280518 T^{2} + 227290979 T^{3} + 243087455521 T^{4} \))(\( 1 + 524 T - 316753 T^{2} - 206848476 T^{3} - 28794145744 T^{4} - 101984365758564 T^{5} - 76998680798643313 T^{6} + 62802236294891999156 T^{7} + \)\(59\!\cdots\!41\)\( T^{8} \))(\( 1 + 524 T - 316753 T^{2} - 206848476 T^{3} - 28794145744 T^{4} - 101984365758564 T^{5} - 76998680798643313 T^{6} + 62802236294891999156 T^{7} + \)\(59\!\cdots\!41\)\( T^{8} \))(\( 1 - 526 T - 757051 T^{2} - 25063374 T^{3} + 689091996644 T^{4} - 12357220853586 T^{5} - 184029601289628571 T^{6} - 63041939486857235794 T^{7} + \)\(59\!\cdots\!41\)\( T^{8} \))(\( ( 1 - 1372 T - 683760 T^{2} + 670974472 T^{3} + 1671648709715 T^{4} - 819563027847396 T^{5} - 1007117883840661376 T^{6} + 11914106711294176424 T^{7} + \)\(77\!\cdots\!56\)\( T^{8} + \)\(58\!\cdots\!36\)\( T^{9} - \)\(24\!\cdots\!96\)\( T^{10} - \)\(98\!\cdots\!24\)\( T^{11} + \)\(98\!\cdots\!15\)\( T^{12} + \)\(19\!\cdots\!28\)\( T^{13} - \)\(98\!\cdots\!60\)\( T^{14} - \)\(97\!\cdots\!88\)\( T^{15} + \)\(34\!\cdots\!81\)\( T^{16} )^{2} \))
$83$ (\( 1 + 228 T + 571787 T^{2} \))(\( 1 - 1440 T + 571787 T^{2} \))(\( 1 + 1036 T + 571787 T^{2} \))(\( 1 + 378 T + 571787 T^{2} \))(\( 1 - 656 T + 571787 T^{2} \))(\( 1 + 656 T + 571787 T^{2} \))(\( 1 + 1440 T + 571787 T^{2} \))(\( 1 - 1072 T + 571787 T^{2} \))(\( ( 1 + 1341548 T^{2} + 1086206614614 T^{4} + 438606204012435212 T^{6} + \)\(10\!\cdots\!61\)\( T^{8} )^{2} \))(\( 1 + 12 T - 1053864 T^{2} + 404096754 T^{3} + 510613483716 T^{4} - 216835757815308 T^{5} - 223075525460746457 T^{6} - \)\(12\!\cdots\!96\)\( T^{7} + \)\(16\!\cdots\!04\)\( T^{8} + \)\(75\!\cdots\!62\)\( T^{9} - \)\(11\!\cdots\!04\)\( T^{10} + \)\(73\!\cdots\!84\)\( T^{11} + \)\(34\!\cdots\!09\)\( T^{12} \))(\( 1 + 142 T - 981853 T^{2} + 1435324800 T^{3} + 772358229251 T^{4} - 1109364392322268 T^{5} + 801541976606778769 T^{6} + \)\(60\!\cdots\!94\)\( T^{7} - \)\(56\!\cdots\!45\)\( T^{8} + \)\(34\!\cdots\!78\)\( T^{9} + \)\(26\!\cdots\!61\)\( T^{10} - \)\(20\!\cdots\!04\)\( T^{11} + \)\(82\!\cdots\!11\)\( T^{12} + \)\(87\!\cdots\!00\)\( T^{13} - \)\(34\!\cdots\!77\)\( T^{14} + \)\(28\!\cdots\!86\)\( T^{15} + \)\(11\!\cdots\!21\)\( T^{16} \))(\( 1 - 2054 T + 1266392 T^{2} - 374773266 T^{3} + 294709461831 T^{4} + 250915131604590 T^{5} - 568927087641465645 T^{6} + \)\(19\!\cdots\!50\)\( T^{7} + \)\(32\!\cdots\!03\)\( T^{8} - \)\(67\!\cdots\!40\)\( T^{9} + \)\(82\!\cdots\!73\)\( T^{10} - \)\(38\!\cdots\!80\)\( T^{11} + \)\(10\!\cdots\!07\)\( T^{12} + \)\(35\!\cdots\!50\)\( T^{13} - \)\(60\!\cdots\!45\)\( T^{14} + \)\(15\!\cdots\!30\)\( T^{15} + \)\(10\!\cdots\!79\)\( T^{16} - \)\(74\!\cdots\!78\)\( T^{17} + \)\(14\!\cdots\!32\)\( T^{18} - \)\(13\!\cdots\!58\)\( T^{19} + \)\(37\!\cdots\!49\)\( T^{20} \))(\( 1 + 516 T - 1599093 T^{2} - 1071061890 T^{3} + 826242107706 T^{4} + 689232801242982 T^{5} - 525580521208635910 T^{6} - \)\(20\!\cdots\!40\)\( T^{7} + \)\(68\!\cdots\!11\)\( T^{8} + \)\(16\!\cdots\!84\)\( T^{9} - \)\(40\!\cdots\!51\)\( T^{10} - \)\(75\!\cdots\!58\)\( T^{11} + \)\(16\!\cdots\!99\)\( T^{12} - \)\(42\!\cdots\!46\)\( T^{13} - \)\(13\!\cdots\!19\)\( T^{14} + \)\(31\!\cdots\!52\)\( T^{15} + \)\(73\!\cdots\!71\)\( T^{16} - \)\(12\!\cdots\!80\)\( T^{17} - \)\(18\!\cdots\!90\)\( T^{18} + \)\(13\!\cdots\!06\)\( T^{19} + \)\(94\!\cdots\!26\)\( T^{20} - \)\(69\!\cdots\!30\)\( T^{21} - \)\(59\!\cdots\!57\)\( T^{22} + \)\(11\!\cdots\!08\)\( T^{23} + \)\(12\!\cdots\!81\)\( T^{24} \))(\( ( 1 - 597 T + 571787 T^{2} )^{2} \))(\( ( 1 - 810 T + 571787 T^{2} )^{2} \))(\( ( 1 + 932 T + 571787 T^{2} )^{2} \))(\( ( 1 - 588 T + 571787 T^{2} )^{2} \))(\( ( 1 + 287 T + 781978 T^{2} + 164102869 T^{3} + 326940373369 T^{4} )^{2} \))(\( ( 1 - 287 T + 781978 T^{2} - 164102869 T^{3} + 326940373369 T^{4} )^{2} \))(\( ( 1 - 221 T + 945628 T^{2} - 126364927 T^{3} + 326940373369 T^{4} )^{2} \))(\( ( 1 + 1807270 T^{2} + 2072146786669 T^{4} + 1731956241551621794 T^{6} + \)\(11\!\cdots\!68\)\( T^{8} + \)\(56\!\cdots\!86\)\( T^{10} + \)\(22\!\cdots\!09\)\( T^{12} + \)\(63\!\cdots\!30\)\( T^{14} + \)\(11\!\cdots\!21\)\( T^{16} )^{2} \))
$89$ (\( 1 + 390 T + 704969 T^{2} \))(\( 1 + 1374 T + 704969 T^{2} \))(\( 1 + 30 T + 704969 T^{2} \))(\( 1 - 390 T + 704969 T^{2} \))(\( 1 + 954 T + 704969 T^{2} \))(\( 1 - 954 T + 704969 T^{2} \))(\( 1 - 1374 T + 704969 T^{2} \))(\( 1 + 810 T + 704969 T^{2} \))(\( ( 1 + 1098356 T^{2} + 554819824806 T^{4} + 545862382814760116 T^{6} + \)\(24\!\cdots\!21\)\( T^{8} )^{2} \))(\( ( 1 + 648 T + 2158218 T^{2} + 892587411 T^{3} + 1521476785242 T^{4} + 322043876542728 T^{5} + 350356403707485209 T^{6} )^{2} \))(\( ( 1 + 132 T + 738863 T^{2} - 1004820993 T^{3} - 79516549278 T^{4} - 708367650614217 T^{5} + 367201087583317343 T^{6} + 46247045289388047588 T^{7} + \)\(24\!\cdots\!21\)\( T^{8} )^{2} \))(\( ( 1 + 1158 T + 2860408 T^{2} + 2357049225 T^{3} + 3485716165171 T^{4} + 2177745438521502 T^{5} + 2457321839244434699 T^{6} + \)\(11\!\cdots\!25\)\( T^{7} + \)\(10\!\cdots\!72\)\( T^{8} + \)\(28\!\cdots\!18\)\( T^{9} + \)\(17\!\cdots\!49\)\( T^{10} )^{2} \))(\( ( 1 - 378 T + 1887921 T^{2} - 145222173 T^{3} + 2059926377013 T^{4} - 210799284432813 T^{5} + 1856379068523125962 T^{6} - \)\(14\!\cdots\!97\)\( T^{7} + \)\(10\!\cdots\!93\)\( T^{8} - \)\(50\!\cdots\!57\)\( T^{9} + \)\(46\!\cdots\!41\)\( T^{10} - \)\(65\!\cdots\!22\)\( T^{11} + \)\(12\!\cdots\!81\)\( T^{12} )^{2} \))(\( 1 + 1038 T + 372475 T^{2} + 731757822 T^{3} + 496981290961 T^{4} \))(\( 1 + 600 T - 344969 T^{2} + 422981400 T^{3} + 496981290961 T^{4} \))(\( 1 + 873 T + 57160 T^{2} + 615437937 T^{3} + 496981290961 T^{4} \))(\( 1 + 1017 T + 329320 T^{2} + 716953473 T^{3} + 496981290961 T^{4} \))(\( 1 - 2394 T + 3029186 T^{2} - 3093316128 T^{3} + 2763749199855 T^{4} - 2180691977440032 T^{5} + 1505448768840987746 T^{6} - \)\(83\!\cdots\!46\)\( T^{7} + \)\(24\!\cdots\!21\)\( T^{8} \))(\( 1 + 2394 T + 3029186 T^{2} + 3093316128 T^{3} + 2763749199855 T^{4} + 2180691977440032 T^{5} + 1505448768840987746 T^{6} + \)\(83\!\cdots\!46\)\( T^{7} + \)\(24\!\cdots\!21\)\( T^{8} \))(\( 1 - 774 T - 367486 T^{2} + 343173024 T^{3} + 14930800239 T^{4} + 241926343556256 T^{5} - 182633666690094046 T^{6} - \)\(27\!\cdots\!66\)\( T^{7} + \)\(24\!\cdots\!21\)\( T^{8} \))(\( 1 - 2824192 T^{2} + 4312528809732 T^{4} - 4399354202928484352 T^{6} + \)\(29\!\cdots\!78\)\( T^{8} - \)\(76\!\cdots\!52\)\( T^{10} - \)\(10\!\cdots\!40\)\( T^{12} + \)\(18\!\cdots\!64\)\( T^{14} - \)\(15\!\cdots\!57\)\( T^{16} + \)\(90\!\cdots\!04\)\( T^{18} - \)\(25\!\cdots\!40\)\( T^{20} - \)\(94\!\cdots\!12\)\( T^{22} + \)\(18\!\cdots\!98\)\( T^{24} - \)\(13\!\cdots\!52\)\( T^{26} + \)\(64\!\cdots\!52\)\( T^{28} - \)\(21\!\cdots\!32\)\( T^{30} + \)\(37\!\cdots\!81\)\( T^{32} \))
$97$ (\( 1 + 70 T + 912673 T^{2} \))(\( 1 + 34 T + 912673 T^{2} \))(\( 1 + 1190 T + 912673 T^{2} \))(\( 1 + 1330 T + 912673 T^{2} \))(\( 1 - 526 T + 912673 T^{2} \))(\( 1 - 526 T + 912673 T^{2} \))(\( 1 + 34 T + 912673 T^{2} \))(\( 1 - 1354 T + 912673 T^{2} \))(\( ( 1 - 1044772 T^{2} + 650240778054 T^{4} - 870265827533681188 T^{6} + \)\(69\!\cdots\!41\)\( T^{8} )^{2} \))(\( 1 + 741 T - 1142418 T^{2} + 174586793 T^{3} + 917682825771 T^{4} - 758251433847708 T^{5} - 1257258664172531199 T^{6} - \)\(69\!\cdots\!84\)\( T^{7} + \)\(76\!\cdots\!59\)\( T^{8} + \)\(13\!\cdots\!81\)\( T^{9} - \)\(79\!\cdots\!38\)\( T^{10} + \)\(46\!\cdots\!13\)\( T^{11} + \)\(57\!\cdots\!89\)\( T^{12} \))(\( 1 - 638 T - 197967 T^{2} + 1627259216 T^{3} - 1785731534086 T^{4} + 398431063574808 T^{5} + 521780813880337198 T^{6} - \)\(12\!\cdots\!03\)\( T^{7} + \)\(97\!\cdots\!70\)\( T^{8} - \)\(11\!\cdots\!19\)\( T^{9} + \)\(43\!\cdots\!42\)\( T^{10} + \)\(30\!\cdots\!36\)\( T^{11} - \)\(12\!\cdots\!26\)\( T^{12} + \)\(10\!\cdots\!88\)\( T^{13} - \)\(11\!\cdots\!63\)\( T^{14} - \)\(33\!\cdots\!86\)\( T^{15} + \)\(48\!\cdots\!81\)\( T^{16} \))(\( 1 + 719 T - 2604542 T^{2} + 345832659 T^{3} + 5202837068988 T^{4} - 2101030174081203 T^{5} - 4448197018744740159 T^{6} + \)\(39\!\cdots\!91\)\( T^{7} + \)\(21\!\cdots\!07\)\( T^{8} - \)\(16\!\cdots\!36\)\( T^{9} - \)\(28\!\cdots\!17\)\( T^{10} - \)\(14\!\cdots\!28\)\( T^{11} + \)\(18\!\cdots\!03\)\( T^{12} + \)\(30\!\cdots\!47\)\( T^{13} - \)\(30\!\cdots\!19\)\( T^{14} - \)\(13\!\cdots\!79\)\( T^{15} + \)\(30\!\cdots\!32\)\( T^{16} + \)\(18\!\cdots\!23\)\( T^{17} - \)\(12\!\cdots\!02\)\( T^{18} + \)\(31\!\cdots\!47\)\( T^{19} + \)\(40\!\cdots\!49\)\( T^{20} \))(\( 1 + 2292 T + 1459695 T^{2} - 209121686 T^{3} - 814101959409 T^{4} - 944536516563864 T^{5} - 187888036098838625 T^{6} + \)\(46\!\cdots\!91\)\( T^{7} - \)\(69\!\cdots\!41\)\( T^{8} - \)\(14\!\cdots\!77\)\( T^{9} - \)\(13\!\cdots\!55\)\( T^{10} + \)\(13\!\cdots\!71\)\( T^{11} + \)\(17\!\cdots\!34\)\( T^{12} + \)\(12\!\cdots\!83\)\( T^{13} - \)\(11\!\cdots\!95\)\( T^{14} - \)\(11\!\cdots\!09\)\( T^{15} - \)\(48\!\cdots\!81\)\( T^{16} + \)\(29\!\cdots\!63\)\( T^{17} - \)\(10\!\cdots\!25\)\( T^{18} - \)\(49\!\cdots\!08\)\( T^{19} - \)\(39\!\cdots\!29\)\( T^{20} - \)\(91\!\cdots\!18\)\( T^{21} + \)\(58\!\cdots\!55\)\( T^{22} + \)\(83\!\cdots\!84\)\( T^{23} + \)\(33\!\cdots\!21\)\( T^{24} \))(\( ( 1 + 169 T + 912673 T^{2} )^{2} \))(\( ( 1 - 386 T + 912673 T^{2} )^{2} \))(\( ( 1 + 290 T + 912673 T^{2} )^{2} \))(\( ( 1 + 1834 T + 912673 T^{2} )^{2} \))(\( ( 1 + 63 T + 667132 T^{2} + 57498399 T^{3} + 832972004929 T^{4} )^{2} \))(\( ( 1 + 63 T + 667132 T^{2} + 57498399 T^{3} + 832972004929 T^{4} )^{2} \))(\( ( 1 - 1953 T + 2366992 T^{2} - 1782450369 T^{3} + 832972004929 T^{4} )^{2} \))(\( ( 1 - 864362 T^{2} + 1022031804529 T^{4} - 68730029451677666 T^{6} + \)\(12\!\cdots\!24\)\( T^{8} - \)\(57\!\cdots\!14\)\( T^{10} + \)\(70\!\cdots\!89\)\( T^{12} - \)\(49\!\cdots\!18\)\( T^{14} + \)\(48\!\cdots\!81\)\( T^{16} )^{2} \))
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