Properties

Label 105.4
Level 105
Weight 4
Dimension 728
Nonzero newspaces 12
Newform subspaces 27
Sturm bound 3072
Trace bound 4

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Defining parameters

Level: \( N \) = \( 105\( 105 = 3 \cdot 5 \cdot 7 \) \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 27 \)
Sturm bound: \(3072\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(105))\).

Total New Old
Modular forms 1248 784 464
Cusp forms 1056 728 328
Eisenstein series 192 56 136

Trace form

\( 728q - 8q^{2} - 6q^{3} + 36q^{4} + 12q^{5} + 48q^{6} + 104q^{7} - 36q^{8} - 54q^{9} + O(q^{10}) \) \( 728q - 8q^{2} - 6q^{3} + 36q^{4} + 12q^{5} + 48q^{6} + 104q^{7} - 36q^{8} - 54q^{9} + 120q^{10} + 112q^{11} - 36q^{12} - 184q^{13} + 360q^{14} - 174q^{15} - 404q^{16} - 56q^{17} - 144q^{18} - 628q^{19} - 172q^{20} - 606q^{21} + 128q^{22} + 912q^{23} + 1044q^{24} + 1574q^{25} + 1948q^{26} - 408q^{27} + 2268q^{28} - 472q^{29} - 1722q^{30} - 868q^{31} - 1828q^{32} - 306q^{33} - 1576q^{34} - 2012q^{35} - 2244q^{36} - 2364q^{37} - 4748q^{38} - 2028q^{39} - 1712q^{40} + 728q^{41} - 3360q^{42} - 1432q^{43} - 448q^{44} + 321q^{45} + 2456q^{46} + 880q^{47} + 6252q^{48} + 3832q^{49} + 3700q^{50} + 7002q^{51} + 10584q^{52} + 3976q^{53} + 8736q^{54} + 7812q^{55} + 9468q^{56} + 2460q^{57} + 4904q^{58} + 3616q^{59} - 1704q^{60} - 8124q^{61} - 7056q^{62} - 6618q^{63} - 22284q^{64} - 8936q^{65} - 12588q^{66} - 14204q^{67} - 14920q^{68} - 3600q^{69} - 19800q^{70} - 4072q^{71} + 7896q^{72} + 3644q^{73} - 724q^{74} + 6645q^{75} + 11104q^{76} + 216q^{77} + 1320q^{78} + 8068q^{79} + 3752q^{80} - 9546q^{81} - 1944q^{82} - 288q^{83} - 7476q^{84} + 3516q^{85} + 388q^{86} - 3396q^{87} + 11520q^{88} + 5256q^{89} - 9876q^{90} - 3248q^{91} + 7296q^{92} - 4986q^{93} - 7864q^{94} - 7952q^{95} + 4896q^{96} - 5592q^{97} + 12932q^{98} + 13956q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(105))\)

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
105.4.a \(\chi_{105}(1, \cdot)\) 105.4.a.a 1 1
105.4.a.b 1
105.4.a.c 2
105.4.a.d 2
105.4.a.e 2
105.4.a.f 2
105.4.a.g 2
105.4.b \(\chi_{105}(41, \cdot)\) 105.4.b.a 16 1
105.4.b.b 16
105.4.d \(\chi_{105}(64, \cdot)\) 105.4.d.a 6 1
105.4.d.b 10
105.4.g \(\chi_{105}(104, \cdot)\) 105.4.g.a 4 1
105.4.g.b 40
105.4.i \(\chi_{105}(16, \cdot)\) 105.4.i.a 2 2
105.4.i.b 4
105.4.i.c 6
105.4.i.d 10
105.4.i.e 10
105.4.j \(\chi_{105}(8, \cdot)\) 105.4.j.a 72 2
105.4.m \(\chi_{105}(13, \cdot)\) 105.4.m.a 48 2
105.4.p \(\chi_{105}(59, \cdot)\) 105.4.p.a 88 2
105.4.q \(\chi_{105}(4, \cdot)\) 105.4.q.a 4 2
105.4.q.b 44
105.4.s \(\chi_{105}(26, \cdot)\) 105.4.s.a 32 2
105.4.s.b 32
105.4.u \(\chi_{105}(52, \cdot)\) 105.4.u.a 96 4
105.4.x \(\chi_{105}(2, \cdot)\) 105.4.x.a 176 4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(105))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(105)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 8 T^{2} \))(\( 1 - 5 T + 8 T^{2} \))(\( 1 + 7 T + 24 T^{2} + 56 T^{3} + 64 T^{4} \))(\( 1 + 4 T + 15 T^{2} + 32 T^{3} + 64 T^{4} \))(\( 1 + 2 T + 9 T^{2} + 16 T^{3} + 64 T^{4} \))(\( 1 - T - 8 T^{3} + 64 T^{4} \))(\( 1 - 3 T + 8 T^{2} - 24 T^{3} + 64 T^{4} \))(\( 1 - 32 T^{2} + 546 T^{4} - 6384 T^{6} + 58041 T^{8} - 418032 T^{10} + 2282084 T^{12} - 8044480 T^{14} + 27741696 T^{16} - 514846720 T^{18} + 9347416064 T^{20} - 109584580608 T^{22} + 973766393856 T^{24} - 6854767804416 T^{26} + 37520834297856 T^{28} - 140737488355328 T^{30} + 281474976710656 T^{32} \))(\( 1 - 32 T^{2} + 546 T^{4} - 6384 T^{6} + 58041 T^{8} - 418032 T^{10} + 2282084 T^{12} - 8044480 T^{14} + 27741696 T^{16} - 514846720 T^{18} + 9347416064 T^{20} - 109584580608 T^{22} + 973766393856 T^{24} - 6854767804416 T^{26} + 37520834297856 T^{28} - 140737488355328 T^{30} + 281474976710656 T^{32} \))(\( 1 - 21 T^{2} + 267 T^{4} - 2607 T^{6} + 17088 T^{8} - 86016 T^{10} + 262144 T^{12} \))(\( 1 - 13 T^{2} + 115 T^{4} - 1151 T^{6} + 11968 T^{8} - 114560 T^{10} + 765952 T^{12} - 4714496 T^{14} + 30146560 T^{16} - 218103808 T^{18} + 1073741824 T^{20} \))(\( ( 1 + 8 T^{2} )^{4} \))(\( 1 + 3 T + T^{2} + 24 T^{3} + 64 T^{4} \))(\( 1 - 4 T - 2 T^{2} - 8 T^{3} + 132 T^{4} - 64 T^{5} - 128 T^{6} - 2048 T^{7} + 4096 T^{8} \))(\( 1 + 3 T - 7 T^{2} - 20 T^{3} + 26 T^{4} - 32 T^{5} - 444 T^{6} - 256 T^{7} + 1664 T^{8} - 10240 T^{9} - 28672 T^{10} + 98304 T^{11} + 262144 T^{12} \))(\( 1 + 3 T - 3 T^{2} - 16 T^{3} - 6 T^{4} - 28 T^{5} + 688 T^{6} + 3056 T^{7} - 280 T^{8} - 9504 T^{9} + 1552 T^{10} - 76032 T^{11} - 17920 T^{12} + 1564672 T^{13} + 2818048 T^{14} - 917504 T^{15} - 1572864 T^{16} - 33554432 T^{17} - 50331648 T^{18} + 402653184 T^{19} + 1073741824 T^{20} \))(\( 1 - T - 9 T^{2} + 50 T^{3} - 14 T^{4} - 400 T^{5} + 1136 T^{6} + 248 T^{7} - 8984 T^{8} + 1680 T^{9} + 23312 T^{10} + 13440 T^{11} - 574976 T^{12} + 126976 T^{13} + 4653056 T^{14} - 13107200 T^{15} - 3670016 T^{16} + 104857600 T^{17} - 150994944 T^{18} - 134217728 T^{19} + 1073741824 T^{20} \))(\( 1 - 9 T^{2} + 17 T^{4} - 576 T^{6} + 4096 T^{8} \))
$3$ (\( 1 + 3 T \))(\( 1 + 3 T \))(\( ( 1 + 3 T )^{2} \))(\( ( 1 - 3 T )^{2} \))(\( ( 1 + 3 T )^{2} \))(\( ( 1 - 3 T )^{2} \))(\( ( 1 - 3 T )^{2} \))(\( 1 + 2 T + 13 T^{2} + 66 T^{3} + 906 T^{4} + 6354 T^{5} + 22347 T^{6} + 169506 T^{7} + 544266 T^{8} + 4576662 T^{9} + 16290963 T^{10} + 125065782 T^{11} + 481485546 T^{12} + 947027862 T^{13} + 5036466357 T^{14} + 20920706406 T^{15} + 282429536481 T^{16} \))(\( 1 - 2 T + 13 T^{2} - 66 T^{3} + 906 T^{4} - 6354 T^{5} + 22347 T^{6} - 169506 T^{7} + 544266 T^{8} - 4576662 T^{9} + 16290963 T^{10} - 125065782 T^{11} + 481485546 T^{12} - 947027862 T^{13} + 5036466357 T^{14} - 20920706406 T^{15} + 282429536481 T^{16} \))(\( ( 1 + 9 T^{2} )^{3} \))(\( ( 1 + 9 T^{2} )^{5} \))(\( 1 + 26 T^{2} + 729 T^{4} \))(\( 1 - 3 T + 9 T^{2} \))(\( ( 1 - 3 T + 9 T^{2} )^{2} \))(\( ( 1 - 3 T + 9 T^{2} )^{3} \))(\( ( 1 + 3 T + 9 T^{2} )^{5} \))(\( ( 1 + 3 T + 9 T^{2} )^{5} \))(\( 1 - 9 T^{2} + 81 T^{4} \))
$5$ (\( 1 - 5 T \))(\( 1 - 5 T \))(\( ( 1 + 5 T )^{2} \))(\( ( 1 + 5 T )^{2} \))(\( ( 1 - 5 T )^{2} \))(\( ( 1 - 5 T )^{2} \))(\( ( 1 + 5 T )^{2} \))(\( ( 1 + 5 T )^{16} \))(\( ( 1 - 5 T )^{16} \))(\( 1 + 14 T - 85 T^{2} - 2700 T^{3} - 10625 T^{4} + 218750 T^{5} + 1953125 T^{6} \))(\( 1 + 14 T + 285 T^{2} + 1152 T^{3} + 2830 T^{4} - 184700 T^{5} + 353750 T^{6} + 18000000 T^{7} + 556640625 T^{8} + 3417968750 T^{9} + 30517578125 T^{10} \))(\( ( 1 + 125 T^{2} )^{2} \))(\( 1 - 5 T + 25 T^{2} \))(\( ( 1 - 5 T + 25 T^{2} )^{2} \))(\( ( 1 + 5 T + 25 T^{2} )^{3} \))(\( ( 1 + 5 T + 25 T^{2} )^{5} \))(\( ( 1 - 5 T + 25 T^{2} )^{5} \))(\( 1 + 4 T - 109 T^{2} + 500 T^{3} + 15625 T^{4} \))
$7$ (\( 1 - 7 T \))(\( 1 - 7 T \))(\( ( 1 + 7 T )^{2} \))(\( ( 1 + 7 T )^{2} \))(\( ( 1 + 7 T )^{2} \))(\( ( 1 + 7 T )^{2} \))(\( ( 1 - 7 T )^{2} \))(\( 1 + 4 T - 156 T^{2} + 6132 T^{3} - 105180 T^{4} - 971292 T^{5} + 27927452 T^{6} - 282573004 T^{7} + 781972086 T^{8} - 96922540372 T^{9} + 3285636800348 T^{10} - 39195135650244 T^{11} - 1455826587801180 T^{12} + 29112047178970476 T^{13} - 254032521274030044 T^{14} + 2234183456333136028 T^{15} + \)\(19\!\cdots\!01\)\( T^{16} \))(\( 1 + 4 T - 156 T^{2} + 6132 T^{3} - 105180 T^{4} - 971292 T^{5} + 27927452 T^{6} - 282573004 T^{7} + 781972086 T^{8} - 96922540372 T^{9} + 3285636800348 T^{10} - 39195135650244 T^{11} - 1455826587801180 T^{12} + 29112047178970476 T^{13} - 254032521274030044 T^{14} + 2234183456333136028 T^{15} + \)\(19\!\cdots\!01\)\( T^{16} \))(\( ( 1 + 49 T^{2} )^{3} \))(\( ( 1 + 49 T^{2} )^{5} \))(\( ( 1 - 343 T^{2} )^{2} \))(\( 1 + 28 T + 343 T^{2} \))(\( 1 - 50 T + 1239 T^{2} - 17150 T^{3} + 117649 T^{4} \))(\( 1 + 2 T + 98 T^{2} - 10192 T^{3} + 33614 T^{4} + 235298 T^{5} + 40353607 T^{6} \))(\( 1 + 32 T + 157 T^{2} - 708 T^{3} - 124187 T^{4} - 5295724 T^{5} - 42596141 T^{6} - 83295492 T^{7} + 6335516299 T^{8} + 442921190432 T^{9} + 4747561509943 T^{10} \))(\( 1 - 56 T + 1761 T^{2} - 46900 T^{3} + 1033445 T^{4} - 19485732 T^{5} + 354471635 T^{6} - 5517738100 T^{7} + 71062701927 T^{8} - 775112083256 T^{9} + 4747561509943 T^{10} \))(\( 1 - 286 T^{2} + 117649 T^{4} \))
$11$ (\( 1 - 42 T + 1331 T^{2} \))(\( 1 - 12 T + 1331 T^{2} \))(\( 1 + 26 T + 2406 T^{2} + 34606 T^{3} + 1771561 T^{4} \))(\( 1 + 92 T + 4758 T^{2} + 122452 T^{3} + 1771561 T^{4} \))(\( 1 + 16 T - 474 T^{2} + 21296 T^{3} + 1771561 T^{4} \))(\( 1 + 22 T + 2718 T^{2} + 29282 T^{3} + 1771561 T^{4} \))(\( 1 - 62 T + 3582 T^{2} - 82522 T^{3} + 1771561 T^{4} \))(\( 1 - 8606 T^{2} + 34825461 T^{4} - 88052496450 T^{6} + 162187796573166 T^{8} - 257506228706019606 T^{10} + \)\(41\!\cdots\!51\)\( T^{12} - \)\(67\!\cdots\!62\)\( T^{14} + \)\(97\!\cdots\!10\)\( T^{16} - \)\(11\!\cdots\!82\)\( T^{18} + \)\(12\!\cdots\!71\)\( T^{20} - \)\(14\!\cdots\!86\)\( T^{22} + \)\(15\!\cdots\!06\)\( T^{24} - \)\(15\!\cdots\!50\)\( T^{26} + \)\(10\!\cdots\!21\)\( T^{28} - \)\(47\!\cdots\!26\)\( T^{30} + \)\(97\!\cdots\!81\)\( T^{32} \))(\( 1 - 8606 T^{2} + 34825461 T^{4} - 88052496450 T^{6} + 162187796573166 T^{8} - 257506228706019606 T^{10} + \)\(41\!\cdots\!51\)\( T^{12} - \)\(67\!\cdots\!62\)\( T^{14} + \)\(97\!\cdots\!10\)\( T^{16} - \)\(11\!\cdots\!82\)\( T^{18} + \)\(12\!\cdots\!71\)\( T^{20} - \)\(14\!\cdots\!86\)\( T^{22} + \)\(15\!\cdots\!06\)\( T^{24} - \)\(15\!\cdots\!50\)\( T^{26} + \)\(10\!\cdots\!21\)\( T^{28} - \)\(47\!\cdots\!26\)\( T^{30} + \)\(97\!\cdots\!81\)\( T^{32} \))(\( ( 1 + 66 T + 3717 T^{2} + 169572 T^{3} + 4947327 T^{4} + 116923026 T^{5} + 2357947691 T^{6} )^{2} \))(\( ( 1 - 66 T + 4555 T^{2} - 210928 T^{3} + 10802758 T^{4} - 383496700 T^{5} + 14378470898 T^{6} - 373671818608 T^{7} + 10740451732505 T^{8} - 207136272863586 T^{9} + 4177248169415651 T^{10} )^{2} \))(\( ( 1 - 72 T + 1331 T^{2} )^{2}( 1 + 72 T + 1331 T^{2} )^{2} \))(\( 1 - 45 T + 694 T^{2} - 59895 T^{3} + 1771561 T^{4} \))(\( 1 - 32 T + 994 T^{2} + 84224 T^{3} - 3133605 T^{4} + 112102144 T^{5} + 1760931634 T^{6} - 75454326112 T^{7} + 3138428376721 T^{8} \))(\( 1 - T - 3484 T^{2} + 9399 T^{3} + 7500248 T^{4} - 14944861 T^{5} - 11409671290 T^{6} - 19891609991 T^{7} + 13287146847128 T^{8} + 22162350347709 T^{9} - 10934284464495964 T^{10} - 4177248169415651 T^{11} + 5559917313492231481 T^{12} \))(\( 1 + 43 T - 1018 T^{2} - 184703 T^{3} - 5534545 T^{4} + 50464234 T^{5} + 12689409820 T^{6} + 504310395110 T^{7} + 6113678102337 T^{8} - 534835812328359 T^{9} - 31491030462599406 T^{10} - 711866466209045829 T^{11} + 10830753692654238057 T^{12} + \)\(11\!\cdots\!10\)\( T^{13} + \)\(39\!\cdots\!20\)\( T^{14} + \)\(21\!\cdots\!34\)\( T^{15} - \)\(30\!\cdots\!45\)\( T^{16} - \)\(13\!\cdots\!33\)\( T^{17} - \)\(10\!\cdots\!38\)\( T^{18} + \)\(56\!\cdots\!53\)\( T^{19} + \)\(17\!\cdots\!01\)\( T^{20} \))(\( 1 - 33 T - 670 T^{2} + 29721 T^{3} - 422065 T^{4} + 60807414 T^{5} + 3843117816 T^{6} - 264648812490 T^{7} + 484736115169 T^{8} + 178222331833149 T^{9} - 2105070196908054 T^{10} + 237213923669921319 T^{11} + 858739596924908809 T^{12} - \)\(62\!\cdots\!90\)\( T^{13} + \)\(12\!\cdots\!36\)\( T^{14} + \)\(25\!\cdots\!14\)\( T^{15} - \)\(23\!\cdots\!65\)\( T^{16} + \)\(21\!\cdots\!31\)\( T^{17} - \)\(65\!\cdots\!70\)\( T^{18} - \)\(43\!\cdots\!43\)\( T^{19} + \)\(17\!\cdots\!01\)\( T^{20} \))(\( ( 1 - 45 T + 694 T^{2} - 59895 T^{3} + 1771561 T^{4} )^{2} \))
$13$ (\( 1 - 20 T + 2197 T^{2} \))(\( 1 - 30 T + 2197 T^{2} \))(\( 1 - 14 T + 2386 T^{2} - 30758 T^{3} + 4826809 T^{4} \))(\( 1 - 8 T - 2810 T^{2} - 17576 T^{3} + 4826809 T^{4} \))(\( 1 + 76 T + 5806 T^{2} + 166972 T^{3} + 4826809 T^{4} \))(\( 1 + 22 T + 4450 T^{2} + 48334 T^{3} + 4826809 T^{4} \))(\( 1 + 6 T + 3378 T^{2} + 13182 T^{3} + 4826809 T^{4} \))(\( 1 - 20914 T^{2} + 214906317 T^{4} - 1458997385978 T^{6} + 7394431445805782 T^{8} - 29817361723357747734 T^{10} + \)\(99\!\cdots\!23\)\( T^{12} - \)\(27\!\cdots\!70\)\( T^{14} + \)\(65\!\cdots\!94\)\( T^{16} - \)\(13\!\cdots\!30\)\( T^{18} + \)\(23\!\cdots\!63\)\( T^{20} - \)\(33\!\cdots\!86\)\( T^{22} + \)\(40\!\cdots\!02\)\( T^{24} - \)\(38\!\cdots\!22\)\( T^{26} + \)\(27\!\cdots\!97\)\( T^{28} - \)\(12\!\cdots\!66\)\( T^{30} + \)\(29\!\cdots\!21\)\( T^{32} \))(\( 1 - 20914 T^{2} + 214906317 T^{4} - 1458997385978 T^{6} + 7394431445805782 T^{8} - 29817361723357747734 T^{10} + \)\(99\!\cdots\!23\)\( T^{12} - \)\(27\!\cdots\!70\)\( T^{14} + \)\(65\!\cdots\!94\)\( T^{16} - \)\(13\!\cdots\!30\)\( T^{18} + \)\(23\!\cdots\!63\)\( T^{20} - \)\(33\!\cdots\!86\)\( T^{22} + \)\(40\!\cdots\!02\)\( T^{24} - \)\(38\!\cdots\!22\)\( T^{26} + \)\(27\!\cdots\!97\)\( T^{28} - \)\(12\!\cdots\!66\)\( T^{30} + \)\(29\!\cdots\!21\)\( T^{32} \))(\( 1 - 8946 T^{2} + 38833239 T^{4} - 104657523868 T^{6} + 187440627504351 T^{8} - 208424669505715026 T^{10} + \)\(11\!\cdots\!29\)\( T^{12} \))(\( 1 - 13662 T^{2} + 97034245 T^{4} - 454371436584 T^{6} + 1533415610487218 T^{8} - 3873561618402720820 T^{10} + \)\(74\!\cdots\!62\)\( T^{12} - \)\(10\!\cdots\!04\)\( T^{14} + \)\(10\!\cdots\!05\)\( T^{16} - \)\(74\!\cdots\!82\)\( T^{18} + \)\(26\!\cdots\!49\)\( T^{20} \))(\( ( 1 - 2774 T^{2} + 4826809 T^{4} )^{2} \))(\( ( 1 + 31 T + 2197 T^{2} )^{2} \))(\( ( 1 - 14 T + 3091 T^{2} - 30758 T^{3} + 4826809 T^{4} )^{2} \))(\( ( 1 + 79 T + 6542 T^{2} + 346439 T^{3} + 14372774 T^{4} + 381317911 T^{5} + 10604499373 T^{6} )^{2} \))(\( ( 1 - 123 T + 9911 T^{2} - 514334 T^{3} + 26762121 T^{4} - 1198576829 T^{5} + 58796379837 T^{6} - 2482591980206 T^{7} + 105101193285803 T^{8} - 2865664470065163 T^{9} + 51185893014090757 T^{10} )^{2} \))(\( ( 1 + 23 T + 5115 T^{2} + 67458 T^{3} + 14193793 T^{4} + 48898957 T^{5} + 31183763221 T^{6} + 325606881522 T^{7} + 54242014292895 T^{8} + 535855957817063 T^{9} + 51185893014090757 T^{10} )^{2} \))(\( ( 1 - 3025 T^{2} + 4826809 T^{4} )^{2} \))
$17$ (\( 1 - 66 T + 4913 T^{2} \))(\( 1 + 134 T + 4913 T^{2} \))(\( 1 - 16 T + 6558 T^{2} - 78608 T^{3} + 24137569 T^{4} \))(\( 1 + 44 T + 630 T^{2} + 216172 T^{3} + 24137569 T^{4} \))(\( 1 + 124 T + 13638 T^{2} + 609212 T^{3} + 24137569 T^{4} \))(\( 1 - 116 T + 9030 T^{2} - 569908 T^{3} + 24137569 T^{4} \))(\( 1 - 40 T + 8750 T^{2} - 196520 T^{3} + 24137569 T^{4} \))(\( ( 1 + 36 T + 21865 T^{2} + 564630 T^{3} + 242030590 T^{4} + 4401615030 T^{5} + 1804180591495 T^{6} + 24001984689648 T^{7} + 10050190098418018 T^{8} + 117921750780240624 T^{9} + 43548533515671375655 T^{10} + \)\(52\!\cdots\!10\)\( T^{11} + \)\(14\!\cdots\!90\)\( T^{12} + \)\(16\!\cdots\!90\)\( T^{13} + \)\(30\!\cdots\!85\)\( T^{14} + \)\(24\!\cdots\!12\)\( T^{15} + \)\(33\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 - 36 T + 21865 T^{2} - 564630 T^{3} + 242030590 T^{4} - 4401615030 T^{5} + 1804180591495 T^{6} - 24001984689648 T^{7} + 10050190098418018 T^{8} - 117921750780240624 T^{9} + 43548533515671375655 T^{10} - \)\(52\!\cdots\!10\)\( T^{11} + \)\(14\!\cdots\!90\)\( T^{12} - \)\(16\!\cdots\!90\)\( T^{13} + \)\(30\!\cdots\!85\)\( T^{14} - \)\(24\!\cdots\!12\)\( T^{15} + \)\(33\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 - 18630 T^{2} + 165676335 T^{4} - 961084533780 T^{6} + 3999023967729615 T^{8} - 10854252279590447430 T^{10} + \)\(14\!\cdots\!09\)\( T^{12} \))(\( 1 - 3586 T^{2} - 9840163 T^{4} - 226703927544 T^{6} + 917313320435074 T^{8} + 2772044023815717620 T^{10} + \)\(22\!\cdots\!06\)\( T^{12} - \)\(13\!\cdots\!84\)\( T^{14} - \)\(13\!\cdots\!67\)\( T^{16} - \)\(12\!\cdots\!06\)\( T^{18} + \)\(81\!\cdots\!49\)\( T^{20} \))(\( ( 1 + 754 T^{2} + 24137569 T^{4} )^{2} \))(\( 1 + 96 T + 4303 T^{2} + 471648 T^{3} + 24137569 T^{4} \))(\( 1 - 20 T - 7214 T^{2} + 44240 T^{3} + 31870227 T^{4} + 217351120 T^{5} - 174128422766 T^{6} - 2371757529940 T^{7} + 582622237229761 T^{8} \))(\( 1 - 72 T - 9451 T^{2} + 322376 T^{3} + 92742014 T^{4} - 1453634728 T^{5} - 466825538823 T^{6} - 7141707418664 T^{7} + 2238566762123966 T^{8} + 38229885273596872 T^{9} - 5506362764058471211 T^{10} - \)\(20\!\cdots\!96\)\( T^{11} + \)\(14\!\cdots\!09\)\( T^{12} \))(\( 1 + 124 T - 13393 T^{2} - 1317332 T^{3} + 223226567 T^{4} + 13464256864 T^{5} - 1978738682246 T^{6} - 55979698376512 T^{7} + 15589925656986105 T^{8} + 163083275563038492 T^{9} - 82630650088387671747 T^{10} + \)\(80\!\cdots\!96\)\( T^{11} + \)\(37\!\cdots\!45\)\( T^{12} - \)\(66\!\cdots\!64\)\( T^{13} - \)\(11\!\cdots\!06\)\( T^{14} + \)\(38\!\cdots\!52\)\( T^{15} + \)\(31\!\cdots\!03\)\( T^{16} - \)\(91\!\cdots\!44\)\( T^{17} - \)\(45\!\cdots\!53\)\( T^{18} + \)\(20\!\cdots\!52\)\( T^{19} + \)\(81\!\cdots\!49\)\( T^{20} \))(\( 1 - 136 T + 17627 T^{2} - 1261192 T^{3} + 51283667 T^{4} + 1474736384 T^{5} - 302802583826 T^{6} + 22322448865408 T^{7} + 436909427829105 T^{8} - 170853787341953928 T^{9} + 16229413764409058493 T^{10} - \)\(83\!\cdots\!64\)\( T^{11} + \)\(10\!\cdots\!45\)\( T^{12} + \)\(26\!\cdots\!76\)\( T^{13} - \)\(17\!\cdots\!86\)\( T^{14} + \)\(42\!\cdots\!12\)\( T^{15} + \)\(72\!\cdots\!03\)\( T^{16} - \)\(87\!\cdots\!64\)\( T^{17} + \)\(59\!\cdots\!67\)\( T^{18} - \)\(22\!\cdots\!28\)\( T^{19} + \)\(81\!\cdots\!49\)\( T^{20} \))(\( 1 + 6462 T^{2} + 17619875 T^{4} + 155976970878 T^{6} + 582622237229761 T^{8} \))
$19$ (\( 1 - 38 T + 6859 T^{2} \))(\( 1 + 92 T + 6859 T^{2} \))(\( 1 - 174 T + 18414 T^{2} - 1193466 T^{3} + 47045881 T^{4} \))(\( 1 + 108 T + 13254 T^{2} + 740772 T^{3} + 47045881 T^{4} \))(\( 1 + 96 T + 13974 T^{2} + 658464 T^{3} + 47045881 T^{4} \))(\( 1 - 102 T + 13134 T^{2} - 699618 T^{3} + 47045881 T^{4} \))(\( 1 + 122 T + 17398 T^{2} + 836798 T^{3} + 47045881 T^{4} \))(\( 1 - 62236 T^{2} + 1887129552 T^{4} - 37632525907604 T^{6} + 561272609523528140 T^{8} - \)\(67\!\cdots\!72\)\( T^{10} + \)\(67\!\cdots\!96\)\( T^{12} - \)\(57\!\cdots\!48\)\( T^{14} + \)\(42\!\cdots\!62\)\( T^{16} - \)\(27\!\cdots\!88\)\( T^{18} + \)\(14\!\cdots\!56\)\( T^{20} - \)\(69\!\cdots\!52\)\( T^{22} + \)\(27\!\cdots\!40\)\( T^{24} - \)\(86\!\cdots\!04\)\( T^{26} + \)\(20\!\cdots\!12\)\( T^{28} - \)\(31\!\cdots\!96\)\( T^{30} + \)\(23\!\cdots\!41\)\( T^{32} \))(\( 1 - 62236 T^{2} + 1887129552 T^{4} - 37632525907604 T^{6} + 561272609523528140 T^{8} - \)\(67\!\cdots\!72\)\( T^{10} + \)\(67\!\cdots\!96\)\( T^{12} - \)\(57\!\cdots\!48\)\( T^{14} + \)\(42\!\cdots\!62\)\( T^{16} - \)\(27\!\cdots\!88\)\( T^{18} + \)\(14\!\cdots\!56\)\( T^{20} - \)\(69\!\cdots\!52\)\( T^{22} + \)\(27\!\cdots\!40\)\( T^{24} - \)\(86\!\cdots\!04\)\( T^{26} + \)\(20\!\cdots\!12\)\( T^{28} - \)\(31\!\cdots\!96\)\( T^{30} + \)\(23\!\cdots\!41\)\( T^{32} \))(\( ( 1 - 138 T + 26205 T^{2} - 1963716 T^{3} + 179740095 T^{4} - 6492331578 T^{5} + 322687697779 T^{6} )^{2} \))(\( ( 1 + 174 T + 30655 T^{2} + 3260120 T^{3} + 355132498 T^{4} + 29134734196 T^{5} + 2435853803782 T^{6} + 153375217565720 T^{7} + 9891991375415245 T^{8} + 385116795917512014 T^{9} + 15181127029874798299 T^{10} )^{2} \))(\( ( 1 - 6859 T^{2} )^{4} \))(\( 1 + 149 T + 15342 T^{2} + 1021991 T^{3} + 47045881 T^{4} \))(\( 1 + 18 T - 5283 T^{2} - 145998 T^{3} - 17829748 T^{4} - 1001400282 T^{5} - 248543389323 T^{6} + 5808378560022 T^{7} + 2213314919066161 T^{8} \))(\( 1 - 29 T - 17643 T^{2} + 128566 T^{3} + 205239771 T^{4} - 153240385 T^{5} - 1627200213666 T^{6} - 1051075800715 T^{7} + 9655685842933251 T^{8} + 41486666552654914 T^{9} - 39049515117084278523 T^{10} - \)\(44\!\cdots\!71\)\( T^{11} + \)\(10\!\cdots\!41\)\( T^{12} \))(\( 1 + 37 T - 21904 T^{2} + 94257 T^{3} + 282384930 T^{4} - 7197449657 T^{5} - 2269051553590 T^{6} + 80463620556965 T^{7} + 13988764492770637 T^{8} - 261602777288079214 T^{9} - 83432723067784841076 T^{10} - \)\(17\!\cdots\!26\)\( T^{11} + \)\(65\!\cdots\!97\)\( T^{12} + \)\(25\!\cdots\!35\)\( T^{13} - \)\(50\!\cdots\!90\)\( T^{14} - \)\(10\!\cdots\!43\)\( T^{15} + \)\(29\!\cdots\!30\)\( T^{16} + \)\(67\!\cdots\!83\)\( T^{17} - \)\(10\!\cdots\!84\)\( T^{18} + \)\(12\!\cdots\!43\)\( T^{19} + \)\(23\!\cdots\!01\)\( T^{20} \))(\( 1 - 39 T - 9880 T^{2} + 624565 T^{3} + 34233842 T^{4} - 5416345181 T^{5} + 257964611298 T^{6} + 32510372903289 T^{7} - 4724786288080355 T^{8} - 95041416218862726 T^{9} + 40077725082249793964 T^{10} - \)\(65\!\cdots\!34\)\( T^{11} - \)\(22\!\cdots\!55\)\( T^{12} + \)\(10\!\cdots\!31\)\( T^{13} + \)\(57\!\cdots\!78\)\( T^{14} - \)\(82\!\cdots\!19\)\( T^{15} + \)\(35\!\cdots\!22\)\( T^{16} + \)\(44\!\cdots\!35\)\( T^{17} - \)\(48\!\cdots\!80\)\( T^{18} - \)\(13\!\cdots\!21\)\( T^{19} + \)\(23\!\cdots\!01\)\( T^{20} \))(\( ( 1 - 135 T + 11366 T^{2} - 925965 T^{3} + 47045881 T^{4} )^{2} \))
$23$ (\( 1 - 12 T + 12167 T^{2} \))(\( 1 - 112 T + 12167 T^{2} \))(\( 1 - 184 T + 19470 T^{2} - 2238728 T^{3} + 148035889 T^{4} \))(\( 1 + 320 T + 47934 T^{2} + 3893440 T^{3} + 148035889 T^{4} \))(\( 1 + 16 T + 15150 T^{2} + 194672 T^{3} + 148035889 T^{4} \))(\( 1 - 260 T + 34734 T^{2} - 3163420 T^{3} + 148035889 T^{4} \))(\( 1 - 16 T + 782 T^{2} - 194672 T^{3} + 148035889 T^{4} \))(\( 1 - 117596 T^{2} + 6684538896 T^{4} - 244668948162228 T^{6} + 6501673619798663820 T^{8} - \)\(13\!\cdots\!00\)\( T^{10} + \)\(22\!\cdots\!84\)\( T^{12} - \)\(33\!\cdots\!88\)\( T^{14} + \)\(42\!\cdots\!78\)\( T^{16} - \)\(49\!\cdots\!32\)\( T^{18} + \)\(50\!\cdots\!64\)\( T^{20} - \)\(43\!\cdots\!00\)\( T^{22} + \)\(31\!\cdots\!20\)\( T^{24} - \)\(17\!\cdots\!72\)\( T^{26} + \)\(70\!\cdots\!56\)\( T^{28} - \)\(18\!\cdots\!84\)\( T^{30} + \)\(23\!\cdots\!81\)\( T^{32} \))(\( 1 - 117596 T^{2} + 6684538896 T^{4} - 244668948162228 T^{6} + 6501673619798663820 T^{8} - \)\(13\!\cdots\!00\)\( T^{10} + \)\(22\!\cdots\!84\)\( T^{12} - \)\(33\!\cdots\!88\)\( T^{14} + \)\(42\!\cdots\!78\)\( T^{16} - \)\(49\!\cdots\!32\)\( T^{18} + \)\(50\!\cdots\!64\)\( T^{20} - \)\(43\!\cdots\!00\)\( T^{22} + \)\(31\!\cdots\!20\)\( T^{24} - \)\(17\!\cdots\!72\)\( T^{26} + \)\(70\!\cdots\!56\)\( T^{28} - \)\(18\!\cdots\!84\)\( T^{30} + \)\(23\!\cdots\!81\)\( T^{32} \))(\( 1 - 48042 T^{2} + 1101997215 T^{4} - 16142068432204 T^{6} + 163135137398049135 T^{8} - \)\(10\!\cdots\!82\)\( T^{10} + \)\(32\!\cdots\!69\)\( T^{12} \))(\( 1 - 68862 T^{2} + 2443463533 T^{4} - 58952757931656 T^{6} + 1054996500313105346 T^{8} - \)\(14\!\cdots\!64\)\( T^{10} + \)\(15\!\cdots\!94\)\( T^{12} - \)\(12\!\cdots\!76\)\( T^{14} + \)\(79\!\cdots\!77\)\( T^{16} - \)\(33\!\cdots\!42\)\( T^{18} + \)\(71\!\cdots\!49\)\( T^{20} \))(\( ( 1 + 12167 T^{2} )^{4} \))(\( 1 - 141 T + 7714 T^{2} - 1715547 T^{3} + 148035889 T^{4} \))(\( 1 - 68 T - 19514 T^{2} + 13328 T^{3} + 378346947 T^{4} + 162161776 T^{5} - 2888772337946 T^{6} - 122478380979484 T^{7} + 21914624432020321 T^{8} \))(\( 1 - 63 T - 28408 T^{2} + 920141 T^{3} + 561102572 T^{4} - 7607171815 T^{5} - 7549311617142 T^{6} - 92556459473105 T^{7} + 83063318066206508 T^{8} + 1657314411071226283 T^{9} - \)\(62\!\cdots\!68\)\( T^{10} - \)\(16\!\cdots\!41\)\( T^{11} + \)\(32\!\cdots\!69\)\( T^{12} \))(\( 1 + 77 T - 40526 T^{2} - 3164693 T^{3} + 912830895 T^{4} + 63875502782 T^{5} - 14990398295836 T^{6} - 743770274612358 T^{7} + 208475820275483873 T^{8} + 3628111953906564439 T^{9} - \)\(26\!\cdots\!78\)\( T^{10} + \)\(44\!\cdots\!13\)\( T^{11} + \)\(30\!\cdots\!97\)\( T^{12} - \)\(13\!\cdots\!54\)\( T^{13} - \)\(32\!\cdots\!56\)\( T^{14} + \)\(17\!\cdots\!74\)\( T^{15} + \)\(29\!\cdots\!55\)\( T^{16} - \)\(12\!\cdots\!39\)\( T^{17} - \)\(19\!\cdots\!66\)\( T^{18} + \)\(44\!\cdots\!19\)\( T^{19} + \)\(71\!\cdots\!49\)\( T^{20} \))(\( 1 - 133 T - 7186 T^{2} - 4075423 T^{3} + 803226335 T^{4} + 26486527262 T^{5} + 7194420605464 T^{6} - 2387572288321298 T^{7} - 21820426257674127 T^{8} - 4470686607756087351 T^{9} + \)\(40\!\cdots\!02\)\( T^{10} - \)\(54\!\cdots\!17\)\( T^{11} - \)\(32\!\cdots\!03\)\( T^{12} - \)\(43\!\cdots\!74\)\( T^{13} + \)\(15\!\cdots\!44\)\( T^{14} + \)\(70\!\cdots\!34\)\( T^{15} + \)\(26\!\cdots\!15\)\( T^{16} - \)\(16\!\cdots\!29\)\( T^{17} - \)\(34\!\cdots\!26\)\( T^{18} - \)\(77\!\cdots\!51\)\( T^{19} + \)\(71\!\cdots\!49\)\( T^{20} \))(\( 1 + 20365 T^{2} + 266697336 T^{4} + 3014750879485 T^{6} + 21914624432020321 T^{8} \))
$29$ (\( 1 + 258 T + 24389 T^{2} \))(\( 1 + 58 T + 24389 T^{2} \))(\( 1 + 32 T + 19046 T^{2} + 780448 T^{3} + 594823321 T^{4} \))(\( 1 + 236 T + 61982 T^{2} + 5755804 T^{3} + 594823321 T^{4} \))(\( 1 - 188 T + 34286 T^{2} - 4585132 T^{3} + 594823321 T^{4} \))(\( 1 + 196 T + 20942 T^{2} + 4780244 T^{3} + 594823321 T^{4} \))(\( 1 - 352 T + 78278 T^{2} - 8584928 T^{3} + 594823321 T^{4} \))(\( 1 - 183566 T^{2} + 18491724525 T^{4} - 1301548714278762 T^{6} + 70543734053026546350 T^{8} - \)\(30\!\cdots\!86\)\( T^{10} + \)\(11\!\cdots\!35\)\( T^{12} - \)\(34\!\cdots\!26\)\( T^{14} + \)\(91\!\cdots\!18\)\( T^{16} - \)\(20\!\cdots\!46\)\( T^{18} + \)\(39\!\cdots\!35\)\( T^{20} - \)\(65\!\cdots\!46\)\( T^{22} + \)\(88\!\cdots\!50\)\( T^{24} - \)\(96\!\cdots\!62\)\( T^{26} + \)\(81\!\cdots\!25\)\( T^{28} - \)\(48\!\cdots\!06\)\( T^{30} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( 1 - 183566 T^{2} + 18491724525 T^{4} - 1301548714278762 T^{6} + 70543734053026546350 T^{8} - \)\(30\!\cdots\!86\)\( T^{10} + \)\(11\!\cdots\!35\)\( T^{12} - \)\(34\!\cdots\!26\)\( T^{14} + \)\(91\!\cdots\!18\)\( T^{16} - \)\(20\!\cdots\!46\)\( T^{18} + \)\(39\!\cdots\!35\)\( T^{20} - \)\(65\!\cdots\!46\)\( T^{22} + \)\(88\!\cdots\!50\)\( T^{24} - \)\(96\!\cdots\!62\)\( T^{26} + \)\(81\!\cdots\!25\)\( T^{28} - \)\(48\!\cdots\!06\)\( T^{30} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( ( 1 + 170 T + 65051 T^{2} + 6611676 T^{3} + 1586528839 T^{4} + 101119964570 T^{5} + 14507145975869 T^{6} )^{2} \))(\( ( 1 + 370 T + 160385 T^{2} + 37125560 T^{3} + 8745786530 T^{4} + 1370740158092 T^{5} + 213300987680170 T^{6} + 22083148893184760 T^{7} + 2326728607339749565 T^{8} + \)\(13\!\cdots\!70\)\( T^{9} + \)\(86\!\cdots\!49\)\( T^{10} )^{2} \))(\( ( 1 - 54 T + 24389 T^{2} )^{2}( 1 + 54 T + 24389 T^{2} )^{2} \))(\( ( 1 - 48 T + 24389 T^{2} )^{2} \))(\( ( 1 + 332 T + 76262 T^{2} + 8097148 T^{3} + 594823321 T^{4} )^{2} \))(\( ( 1 - 220 T + 74711 T^{2} - 10703064 T^{3} + 1822126579 T^{4} - 130861130620 T^{5} + 14507145975869 T^{6} )^{2} \))(\( ( 1 - 360 T + 130325 T^{2} - 27401400 T^{3} + 6029894570 T^{4} - 923796431136 T^{5} + 147063098667730 T^{6} - 16298991748049400 T^{7} + 1890643799305127425 T^{8} - \)\(12\!\cdots\!60\)\( T^{9} + \)\(86\!\cdots\!49\)\( T^{10} )^{2} \))(\( ( 1 - 272 T + 89713 T^{2} - 18586464 T^{3} + 4032454334 T^{4} - 595833637376 T^{5} + 98347528751926 T^{6} - 11055662242126944 T^{7} + 1301479586933135597 T^{8} - 96237621031887579152 T^{9} + \)\(86\!\cdots\!49\)\( T^{10} )^{2} \))(\( ( 1 - 184 T + 24389 T^{2} )^{4} \))
$31$ (\( 1 - 146 T + 29791 T^{2} \))(\( 1 + 224 T + 29791 T^{2} \))(\( 1 - 330 T + 85430 T^{2} - 9831030 T^{3} + 887503681 T^{4} \))(\( 1 + 60 T + 8462 T^{2} + 1787460 T^{3} + 887503681 T^{4} \))(\( 1 + 120 T + 60590 T^{2} + 3574920 T^{3} + 887503681 T^{4} \))(\( 1 - 150 T + 36542 T^{2} - 4468650 T^{3} + 887503681 T^{4} \))(\( 1 - 66 T + 45870 T^{2} - 1966206 T^{3} + 887503681 T^{4} \))(\( 1 - 243928 T^{2} + 30010199448 T^{4} - 2480265605366024 T^{6} + \)\(15\!\cdots\!16\)\( T^{8} - \)\(77\!\cdots\!16\)\( T^{10} + \)\(32\!\cdots\!88\)\( T^{12} - \)\(11\!\cdots\!04\)\( T^{14} + \)\(37\!\cdots\!98\)\( T^{16} - \)\(10\!\cdots\!24\)\( T^{18} + \)\(25\!\cdots\!68\)\( T^{20} - \)\(54\!\cdots\!56\)\( T^{22} + \)\(95\!\cdots\!36\)\( T^{24} - \)\(13\!\cdots\!24\)\( T^{26} + \)\(14\!\cdots\!88\)\( T^{28} - \)\(10\!\cdots\!08\)\( T^{30} + \)\(38\!\cdots\!41\)\( T^{32} \))(\( 1 - 243928 T^{2} + 30010199448 T^{4} - 2480265605366024 T^{6} + \)\(15\!\cdots\!16\)\( T^{8} - \)\(77\!\cdots\!16\)\( T^{10} + \)\(32\!\cdots\!88\)\( T^{12} - \)\(11\!\cdots\!04\)\( T^{14} + \)\(37\!\cdots\!98\)\( T^{16} - \)\(10\!\cdots\!24\)\( T^{18} + \)\(25\!\cdots\!68\)\( T^{20} - \)\(54\!\cdots\!56\)\( T^{22} + \)\(95\!\cdots\!36\)\( T^{24} - \)\(13\!\cdots\!24\)\( T^{26} + \)\(14\!\cdots\!88\)\( T^{28} - \)\(10\!\cdots\!08\)\( T^{30} + \)\(38\!\cdots\!41\)\( T^{32} \))(\( ( 1 + 366 T + 102201 T^{2} + 18296380 T^{3} + 3044669991 T^{4} + 324826347246 T^{5} + 26439622160671 T^{6} )^{2} \))(\( ( 1 - 342 T + 142051 T^{2} - 26927448 T^{3} + 6639779138 T^{4} - 944601593732 T^{5} + 197805660300158 T^{6} - 23898209219936088 T^{7} + 3755774767545476221 T^{8} - \)\(26\!\cdots\!62\)\( T^{9} + \)\(23\!\cdots\!51\)\( T^{10} )^{2} \))(\( ( 1 - 29791 T^{2} )^{4} \))(\( 1 - 178 T + 1893 T^{2} - 5302798 T^{3} + 887503681 T^{4} \))(\( 1 + 66 T - 53723 T^{2} - 99198 T^{3} + 2355896964 T^{4} - 2955207618 T^{5} - 47679360254363 T^{6} + 1745015062604286 T^{7} + 787662783788549761 T^{8} \))(\( 1 + 136 T - 8546 T^{2} - 2998636 T^{3} - 528330122 T^{4} - 8154034460 T^{5} + 25822124352518 T^{6} - 242916840597860 T^{7} - 468894928058179082 T^{8} - 79282802837385844756 T^{9} - \)\(67\!\cdots\!06\)\( T^{10} + \)\(31\!\cdots\!36\)\( T^{11} + \)\(69\!\cdots\!41\)\( T^{12} \))(\( 1 + 314 T - 25093 T^{2} - 11954934 T^{3} + 865517672 T^{4} + 110001595950 T^{5} - 90893388430871 T^{6} - 6546943301723310 T^{7} + 2772893062489254731 T^{8} + \)\(16\!\cdots\!96\)\( T^{9} - \)\(56\!\cdots\!12\)\( T^{10} + \)\(49\!\cdots\!36\)\( T^{11} + \)\(24\!\cdots\!11\)\( T^{12} - \)\(17\!\cdots\!10\)\( T^{13} - \)\(71\!\cdots\!31\)\( T^{14} + \)\(25\!\cdots\!50\)\( T^{15} + \)\(60\!\cdots\!52\)\( T^{16} - \)\(24\!\cdots\!54\)\( T^{17} - \)\(15\!\cdots\!53\)\( T^{18} + \)\(58\!\cdots\!54\)\( T^{19} + \)\(55\!\cdots\!01\)\( T^{20} \))(\( 1 - 430 T + 15907 T^{2} + 21798754 T^{3} - 2419402776 T^{4} - 860625141498 T^{5} + 180970103191009 T^{6} + 11431707811370410 T^{7} - 5289476269692339797 T^{8} - \)\(20\!\cdots\!76\)\( T^{9} + \)\(18\!\cdots\!32\)\( T^{10} - \)\(61\!\cdots\!16\)\( T^{11} - \)\(46\!\cdots\!57\)\( T^{12} + \)\(30\!\cdots\!10\)\( T^{13} + \)\(14\!\cdots\!49\)\( T^{14} - \)\(20\!\cdots\!98\)\( T^{15} - \)\(16\!\cdots\!16\)\( T^{16} + \)\(45\!\cdots\!74\)\( T^{17} + \)\(98\!\cdots\!47\)\( T^{18} - \)\(79\!\cdots\!30\)\( T^{19} + \)\(55\!\cdots\!01\)\( T^{20} \))(\( ( 1 + 170 T - 891 T^{2} + 5064470 T^{3} + 887503681 T^{4} )^{2} \))
$37$ (\( 1 - 434 T + 50653 T^{2} \))(\( 1 + 146 T + 50653 T^{2} \))(\( 1 + 132 T + 103214 T^{2} + 6686196 T^{3} + 2565726409 T^{4} \))(\( 1 - 204 T + 108830 T^{2} - 10333212 T^{3} + 2565726409 T^{4} \))(\( 1 + 132 T + 70814 T^{2} + 6686196 T^{3} + 2565726409 T^{4} \))(\( 1 + 96 T + 82550 T^{2} + 4862688 T^{3} + 2565726409 T^{4} \))(\( 1 + 188 T + 44542 T^{2} + 9522764 T^{3} + 2565726409 T^{4} \))(\( ( 1 + 406 T + 171732 T^{2} + 18546546 T^{3} + 2667303348 T^{4} - 859604603298 T^{5} + 277822176189836 T^{6} + 94739636753810282 T^{7} + 46630581522163131318 T^{8} + \)\(47\!\cdots\!46\)\( T^{9} + \)\(71\!\cdots\!24\)\( T^{10} - \)\(11\!\cdots\!46\)\( T^{11} + \)\(17\!\cdots\!88\)\( T^{12} + \)\(61\!\cdots\!78\)\( T^{13} + \)\(29\!\cdots\!28\)\( T^{14} + \)\(34\!\cdots\!22\)\( T^{15} + \)\(43\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 + 406 T + 171732 T^{2} + 18546546 T^{3} + 2667303348 T^{4} - 859604603298 T^{5} + 277822176189836 T^{6} + 94739636753810282 T^{7} + 46630581522163131318 T^{8} + \)\(47\!\cdots\!46\)\( T^{9} + \)\(71\!\cdots\!24\)\( T^{10} - \)\(11\!\cdots\!46\)\( T^{11} + \)\(17\!\cdots\!88\)\( T^{12} + \)\(61\!\cdots\!78\)\( T^{13} + \)\(29\!\cdots\!28\)\( T^{14} + \)\(34\!\cdots\!22\)\( T^{15} + \)\(43\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 - 135294 T^{2} + 11227035399 T^{4} - 635435307878212 T^{6} + 28805501217992152191 T^{8} - \)\(89\!\cdots\!14\)\( T^{10} + \)\(16\!\cdots\!29\)\( T^{12} \))(\( 1 - 160866 T^{2} + 14645741397 T^{4} - 941454249392984 T^{6} + 51314852590450172274 T^{8} - \)\(26\!\cdots\!00\)\( T^{10} + \)\(13\!\cdots\!66\)\( T^{12} - \)\(61\!\cdots\!04\)\( T^{14} + \)\(24\!\cdots\!13\)\( T^{16} - \)\(69\!\cdots\!26\)\( T^{18} + \)\(11\!\cdots\!49\)\( T^{20} \))(\( ( 1 - 50653 T^{2} )^{4} \))(\( 1 + 371 T + 86988 T^{2} + 18792263 T^{3} + 2565726409 T^{4} \))(\( 1 + 18 T - 2495 T^{2} - 1772766 T^{3} - 2574191220 T^{4} - 89795916198 T^{5} - 6401487390455 T^{6} + 2339311316311386 T^{7} + 6582952005840035281 T^{8} \))(\( 1 + 43 T - 31445 T^{2} - 2347900 T^{3} - 659210699 T^{4} + 28210346809 T^{5} + 202602319837646 T^{6} + 1428938696916277 T^{7} - 1691354299519649891 T^{8} - \)\(30\!\cdots\!00\)\( T^{9} - \)\(20\!\cdots\!45\)\( T^{10} + \)\(14\!\cdots\!99\)\( T^{11} + \)\(16\!\cdots\!29\)\( T^{12} \))(\( 1 + 225 T - 76286 T^{2} - 2361973 T^{3} + 6089794302 T^{4} - 356399592229 T^{5} - 68864532404144 T^{6} + 56856556722394743 T^{7} - 7573070672827671431 T^{8} - \)\(37\!\cdots\!02\)\( T^{9} + \)\(11\!\cdots\!48\)\( T^{10} - \)\(19\!\cdots\!06\)\( T^{11} - \)\(19\!\cdots\!79\)\( T^{12} + \)\(73\!\cdots\!11\)\( T^{13} - \)\(45\!\cdots\!64\)\( T^{14} - \)\(11\!\cdots\!97\)\( T^{15} + \)\(10\!\cdots\!58\)\( T^{16} - \)\(20\!\cdots\!01\)\( T^{17} - \)\(33\!\cdots\!46\)\( T^{18} + \)\(49\!\cdots\!25\)\( T^{19} + \)\(11\!\cdots\!49\)\( T^{20} \))(\( 1 + 3 T - 197874 T^{2} - 9191603 T^{3} + 21726300338 T^{4} + 1331144162729 T^{5} - 1659517612754472 T^{6} - 84598271217222955 T^{7} + \)\(10\!\cdots\!81\)\( T^{8} + \)\(20\!\cdots\!78\)\( T^{9} - \)\(53\!\cdots\!56\)\( T^{10} + \)\(10\!\cdots\!34\)\( T^{11} + \)\(25\!\cdots\!29\)\( T^{12} - \)\(10\!\cdots\!35\)\( T^{13} - \)\(10\!\cdots\!32\)\( T^{14} + \)\(44\!\cdots\!97\)\( T^{15} + \)\(36\!\cdots\!02\)\( T^{16} - \)\(78\!\cdots\!11\)\( T^{17} - \)\(85\!\cdots\!14\)\( T^{18} + \)\(65\!\cdots\!99\)\( T^{19} + \)\(11\!\cdots\!49\)\( T^{20} \))(\( 1 + 96265 T^{2} + 6701223816 T^{4} + 246989652762385 T^{6} + 6582952005840035281 T^{8} \))
$41$ (\( 1 + 282 T + 68921 T^{2} \))(\( 1 - 18 T + 68921 T^{2} \))(\( 1 - 200 T + 64542 T^{2} - 13784200 T^{3} + 4750104241 T^{4} \))(\( 1 - 44 T + 106326 T^{2} - 3032524 T^{3} + 4750104241 T^{4} \))(\( 1 - 100 T + 89142 T^{2} - 6892100 T^{3} + 4750104241 T^{4} \))(\( 1 + 176 T - 16914 T^{2} + 12130096 T^{3} + 4750104241 T^{4} \))(\( 1 - 16 T + 18350 T^{2} - 1102736 T^{3} + 4750104241 T^{4} \))(\( ( 1 + 468 T + 326380 T^{2} + 70737084 T^{3} + 29968819300 T^{4} + 2596217207796 T^{5} + 1936320479038420 T^{6} + 145315453164258492 T^{7} + \)\(15\!\cdots\!38\)\( T^{8} + \)\(10\!\cdots\!32\)\( T^{9} + \)\(91\!\cdots\!20\)\( T^{10} + \)\(84\!\cdots\!56\)\( T^{11} + \)\(67\!\cdots\!00\)\( T^{12} + \)\(11\!\cdots\!84\)\( T^{13} + \)\(34\!\cdots\!80\)\( T^{14} + \)\(34\!\cdots\!88\)\( T^{15} + \)\(50\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 - 468 T + 326380 T^{2} - 70737084 T^{3} + 29968819300 T^{4} - 2596217207796 T^{5} + 1936320479038420 T^{6} - 145315453164258492 T^{7} + \)\(15\!\cdots\!38\)\( T^{8} - \)\(10\!\cdots\!32\)\( T^{9} + \)\(91\!\cdots\!20\)\( T^{10} - \)\(84\!\cdots\!56\)\( T^{11} + \)\(67\!\cdots\!00\)\( T^{12} - \)\(11\!\cdots\!84\)\( T^{13} + \)\(34\!\cdots\!80\)\( T^{14} - \)\(34\!\cdots\!88\)\( T^{15} + \)\(50\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 + 206 T + 68783 T^{2} + 10173252 T^{3} + 4740593143 T^{4} + 978521473646 T^{5} + 327381934393961 T^{6} )^{2} \))(\( ( 1 - 802 T + 392457 T^{2} - 146273472 T^{3} + 44792512462 T^{4} - 12012058617212 T^{5} + 3087144751393502 T^{6} - 694814239692994752 T^{7} + \)\(12\!\cdots\!77\)\( T^{8} - \)\(18\!\cdots\!62\)\( T^{9} + \)\(15\!\cdots\!01\)\( T^{10} )^{2} \))(\( ( 1 + 68921 T^{2} )^{4} \))(\( ( 1 - 225 T + 68921 T^{2} )^{2} \))(\( ( 1 - 152 T + 113850 T^{2} - 10475992 T^{3} + 4750104241 T^{4} )^{2} \))(\( ( 1 + 599 T + 272999 T^{2} + 79436618 T^{3} + 18815364079 T^{4} + 2845312440359 T^{5} + 327381934393961 T^{6} )^{2} \))(\( ( 1 - 341 T + 190073 T^{2} - 39759328 T^{3} + 16717012002 T^{4} - 3155754961314 T^{5} + 1152153184189842 T^{6} - 188860952552110048 T^{7} + 62226466416063349153 T^{8} - \)\(76\!\cdots\!21\)\( T^{9} + \)\(15\!\cdots\!01\)\( T^{10} )^{2} \))(\( ( 1 + 627 T + 298461 T^{2} + 100221404 T^{3} + 28792732854 T^{4} + 7903095350774 T^{5} + 1984423941030534 T^{6} + 476062116179374364 T^{7} + 97710739521155994021 T^{8} + \)\(14\!\cdots\!87\)\( T^{9} + \)\(15\!\cdots\!01\)\( T^{10} )^{2} \))(\( ( 1 - 247 T + 68921 T^{2} )^{4} \))
$43$ (\( 1 - 20 T + 79507 T^{2} \))(\( 1 - 340 T + 79507 T^{2} \))(\( 1 - 364 T + 172486 T^{2} - 28940548 T^{3} + 6321363049 T^{4} \))(\( 1 - 136 T + 81718 T^{2} - 10812952 T^{3} + 6321363049 T^{4} \))(\( 1 + 536 T + 200086 T^{2} + 42615752 T^{3} + 6321363049 T^{4} \))(\( 1 + 344 T + 171958 T^{2} + 27350408 T^{3} + 6321363049 T^{4} \))(\( 1 + 396 T + 95718 T^{2} + 31484772 T^{3} + 6321363049 T^{4} \))(\( ( 1 + 274 T + 391320 T^{2} + 53372706 T^{3} + 58454003724 T^{4} - 260041845822 T^{5} + 4589236205221928 T^{6} - 791278660184876446 T^{7} + \)\(30\!\cdots\!18\)\( T^{8} - \)\(62\!\cdots\!22\)\( T^{9} + \)\(29\!\cdots\!72\)\( T^{10} - \)\(13\!\cdots\!46\)\( T^{11} + \)\(23\!\cdots\!24\)\( T^{12} + \)\(16\!\cdots\!42\)\( T^{13} + \)\(98\!\cdots\!80\)\( T^{14} + \)\(55\!\cdots\!82\)\( T^{15} + \)\(15\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 + 274 T + 391320 T^{2} + 53372706 T^{3} + 58454003724 T^{4} - 260041845822 T^{5} + 4589236205221928 T^{6} - 791278660184876446 T^{7} + \)\(30\!\cdots\!18\)\( T^{8} - \)\(62\!\cdots\!22\)\( T^{9} + \)\(29\!\cdots\!72\)\( T^{10} - \)\(13\!\cdots\!46\)\( T^{11} + \)\(23\!\cdots\!24\)\( T^{12} + \)\(16\!\cdots\!42\)\( T^{13} + \)\(98\!\cdots\!80\)\( T^{14} + \)\(55\!\cdots\!82\)\( T^{15} + \)\(15\!\cdots\!01\)\( T^{16} )^{2} \))(\( 1 - 142146 T^{2} + 11474416359 T^{4} - 844942679855548 T^{6} + 72533951580623718591 T^{8} - \)\(56\!\cdots\!46\)\( T^{10} + \)\(25\!\cdots\!49\)\( T^{12} \))(\( 1 - 485758 T^{2} + 119488561781 T^{4} - 19372440245362728 T^{6} + \)\(22\!\cdots\!22\)\( T^{8} - \)\(20\!\cdots\!28\)\( T^{10} + \)\(14\!\cdots\!78\)\( T^{12} - \)\(77\!\cdots\!28\)\( T^{14} + \)\(30\!\cdots\!69\)\( T^{16} - \)\(77\!\cdots\!58\)\( T^{18} + \)\(10\!\cdots\!49\)\( T^{20} \))(\( ( 1 - 79507 T^{2} )^{4} \))(\( ( 1 - 344 T + 79507 T^{2} )^{2} \))(\( ( 1 + 842 T + 333367 T^{2} + 66944894 T^{3} + 6321363049 T^{4} )^{2} \))(\( ( 1 - 170 T + 62886 T^{2} - 25979064 T^{3} + 4999877202 T^{4} - 1074631718330 T^{5} + 502592611936843 T^{6} )^{2} \))(\( ( 1 - 32 T + 218617 T^{2} + 27320644 T^{3} + 18062796109 T^{4} + 4794346174172 T^{5} + 1436118730238263 T^{6} + 172703709456483556 T^{7} + \)\(10\!\cdots\!31\)\( T^{8} - \)\(12\!\cdots\!32\)\( T^{9} + \)\(31\!\cdots\!07\)\( T^{10} )^{2} \))(\( ( 1 - 108 T + 178357 T^{2} - 39070996 T^{3} + 22552051325 T^{4} - 3630162418200 T^{5} + 1793045944696775 T^{6} - 246981950402026804 T^{7} + 89640910487219506951 T^{8} - \)\(43\!\cdots\!08\)\( T^{9} + \)\(31\!\cdots\!07\)\( T^{10} )^{2} \))(\( ( 1 - 100450 T^{2} + 6321363049 T^{4} )^{2} \))
$47$ (\( 1 + 72 T + 103823 T^{2} \))(\( 1 - 208 T + 103823 T^{2} \))(\( 1 - 292 T + 179390 T^{2} - 30316316 T^{3} + 10779215329 T^{4} \))(\( 1 - 400 T + 106526 T^{2} - 41529200 T^{3} + 10779215329 T^{4} \))(\( 1 + 928 T + 408830 T^{2} + 96347744 T^{3} + 10779215329 T^{4} \))(\( 1 - 560 T + 248606 T^{2} - 58140880 T^{3} + 10779215329 T^{4} \))(\( 1 + 188 T + 15582 T^{2} + 19518724 T^{3} + 10779215329 T^{4} \))(\( ( 1 - 456 T + 383377 T^{2} - 113615790 T^{3} + 69441494650 T^{4} - 12502697065050 T^{5} + 6757925542629967 T^{6} - 612775938965056308 T^{7} + \)\(62\!\cdots\!18\)\( T^{8} - \)\(63\!\cdots\!84\)\( T^{9} + \)\(72\!\cdots\!43\)\( T^{10} - \)\(13\!\cdots\!50\)\( T^{11} + \)\(80\!\cdots\!50\)\( T^{12} - \)\(13\!\cdots\!70\)\( T^{13} + \)\(48\!\cdots\!53\)\( T^{14} - \)\(59\!\cdots\!32\)\( T^{15} + \)\(13\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 + 456 T + 383377 T^{2} + 113615790 T^{3} + 69441494650 T^{4} + 12502697065050 T^{5} + 6757925542629967 T^{6} + 612775938965056308 T^{7} + \)\(62\!\cdots\!18\)\( T^{8} + \)\(63\!\cdots\!84\)\( T^{9} + \)\(72\!\cdots\!43\)\( T^{10} + \)\(13\!\cdots\!50\)\( T^{11} + \)\(80\!\cdots\!50\)\( T^{12} + \)\(13\!\cdots\!70\)\( T^{13} + \)\(48\!\cdots\!53\)\( T^{14} + \)\(59\!\cdots\!32\)\( T^{15} + \)\(13\!\cdots\!81\)\( T^{16} )^{2} \))(\( 1 - 167706 T^{2} + 23309138223 T^{4} - 3026280208385068 T^{6} + \)\(25\!\cdots\!67\)\( T^{8} - \)\(19\!\cdots\!46\)\( T^{10} + \)\(12\!\cdots\!89\)\( T^{12} \))(\( 1 - 502182 T^{2} + 138597263629 T^{4} - 26712508734207432 T^{6} + \)\(39\!\cdots\!54\)\( T^{8} - \)\(45\!\cdots\!76\)\( T^{10} + \)\(42\!\cdots\!66\)\( T^{12} - \)\(31\!\cdots\!12\)\( T^{14} + \)\(17\!\cdots\!81\)\( T^{16} - \)\(67\!\cdots\!42\)\( T^{18} + \)\(14\!\cdots\!49\)\( T^{20} \))(\( ( 1 - 175646 T^{2} + 10779215329 T^{4} )^{2} \))(\( 1 + 375 T + 36802 T^{2} + 38933625 T^{3} + 10779215329 T^{4} \))(\( 1 - 212 T - 145138 T^{2} + 3723568 T^{3} + 20685730483 T^{4} + 386592000464 T^{5} - 1564473754420402 T^{6} - 237255660297786604 T^{7} + \)\(11\!\cdots\!41\)\( T^{8} \))(\( 1 - 3 T - 72204 T^{2} + 62541997 T^{3} - 2376790884 T^{4} - 2253348114927 T^{5} + 2681417930011010 T^{6} - 233949361336065921 T^{7} - 25619940730640260836 T^{8} + \)\(69\!\cdots\!99\)\( T^{9} - \)\(83\!\cdots\!64\)\( T^{10} - \)\(36\!\cdots\!29\)\( T^{11} + \)\(12\!\cdots\!89\)\( T^{12} \))(\( 1 + 25 T - 227610 T^{2} - 73101461 T^{3} + 24026193611 T^{4} + 14842831799166 T^{5} + 815012071632728 T^{6} - 1726119131867110546 T^{7} - \)\(42\!\cdots\!67\)\( T^{8} + \)\(71\!\cdots\!07\)\( T^{9} + \)\(63\!\cdots\!74\)\( T^{10} + \)\(73\!\cdots\!61\)\( T^{11} - \)\(45\!\cdots\!43\)\( T^{12} - \)\(19\!\cdots\!82\)\( T^{13} + \)\(94\!\cdots\!48\)\( T^{14} + \)\(17\!\cdots\!38\)\( T^{15} + \)\(30\!\cdots\!79\)\( T^{16} - \)\(95\!\cdots\!67\)\( T^{17} - \)\(30\!\cdots\!10\)\( T^{18} + \)\(35\!\cdots\!75\)\( T^{19} + \)\(14\!\cdots\!49\)\( T^{20} \))(\( 1 - 553 T - 156682 T^{2} + 109233557 T^{3} + 28024627643 T^{4} - 16290620541022 T^{5} - 2638343597881880 T^{6} + 1559174107875594658 T^{7} + 79078601331925068813 T^{8} - \)\(43\!\cdots\!55\)\( T^{9} - \)\(90\!\cdots\!10\)\( T^{10} - \)\(45\!\cdots\!65\)\( T^{11} + \)\(85\!\cdots\!77\)\( T^{12} + \)\(17\!\cdots\!86\)\( T^{13} - \)\(30\!\cdots\!80\)\( T^{14} - \)\(19\!\cdots\!46\)\( T^{15} + \)\(35\!\cdots\!27\)\( T^{16} + \)\(14\!\cdots\!79\)\( T^{17} - \)\(21\!\cdots\!42\)\( T^{18} - \)\(77\!\cdots\!39\)\( T^{19} + \)\(14\!\cdots\!49\)\( T^{20} \))(\( 1 - 113843 T^{2} + 2181013320 T^{4} - 1227138210699347 T^{6} + \)\(11\!\cdots\!41\)\( T^{8} \))
$53$ (\( 1 - 336 T + 148877 T^{2} \))(\( 1 + 754 T + 148877 T^{2} \))(\( 1 - 34 T + 103410 T^{2} - 5061818 T^{3} + 22164361129 T^{4} \))(\( 1 - 16 T + 260838 T^{2} - 2382032 T^{3} + 22164361129 T^{4} \))(\( 1 - 884 T + 460350 T^{2} - 131607268 T^{3} + 22164361129 T^{4} \))(\( 1 - 326 T + 204138 T^{2} - 48533902 T^{3} + 22164361129 T^{4} \))(\( 1 - 982 T + 504354 T^{2} - 146197214 T^{3} + 22164361129 T^{4} \))(\( 1 - 1082180 T^{2} + 635688438048 T^{4} - 263556066423088716 T^{6} + \)\(84\!\cdots\!28\)\( T^{8} - \)\(22\!\cdots\!00\)\( T^{10} + \)\(48\!\cdots\!76\)\( T^{12} - \)\(91\!\cdots\!00\)\( T^{14} + \)\(14\!\cdots\!94\)\( T^{16} - \)\(20\!\cdots\!00\)\( T^{18} + \)\(24\!\cdots\!16\)\( T^{20} - \)\(24\!\cdots\!00\)\( T^{22} + \)\(20\!\cdots\!68\)\( T^{24} - \)\(14\!\cdots\!84\)\( T^{26} + \)\(75\!\cdots\!08\)\( T^{28} - \)\(28\!\cdots\!20\)\( T^{30} + \)\(58\!\cdots\!61\)\( T^{32} \))(\( 1 - 1082180 T^{2} + 635688438048 T^{4} - 263556066423088716 T^{6} + \)\(84\!\cdots\!28\)\( T^{8} - \)\(22\!\cdots\!00\)\( T^{10} + \)\(48\!\cdots\!76\)\( T^{12} - \)\(91\!\cdots\!00\)\( T^{14} + \)\(14\!\cdots\!94\)\( T^{16} - \)\(20\!\cdots\!00\)\( T^{18} + \)\(24\!\cdots\!16\)\( T^{20} - \)\(24\!\cdots\!00\)\( T^{22} + \)\(20\!\cdots\!68\)\( T^{24} - \)\(14\!\cdots\!84\)\( T^{26} + \)\(75\!\cdots\!08\)\( T^{28} - \)\(28\!\cdots\!20\)\( T^{30} + \)\(58\!\cdots\!61\)\( T^{32} \))(\( 1 - 466338 T^{2} + 138876104679 T^{4} - 24411867787298428 T^{6} + \)\(30\!\cdots\!91\)\( T^{8} - \)\(22\!\cdots\!58\)\( T^{10} + \)\(10\!\cdots\!89\)\( T^{12} \))(\( 1 - 997006 T^{2} + 484698335029 T^{4} - 151727963326781416 T^{6} + \)\(34\!\cdots\!38\)\( T^{8} - \)\(57\!\cdots\!36\)\( T^{10} + \)\(75\!\cdots\!02\)\( T^{12} - \)\(74\!\cdots\!56\)\( T^{14} + \)\(52\!\cdots\!81\)\( T^{16} - \)\(24\!\cdots\!86\)\( T^{18} + \)\(53\!\cdots\!49\)\( T^{20} \))(\( ( 1 + 148877 T^{2} )^{4} \))(\( 1 - 663 T + 290692 T^{2} - 98705451 T^{3} + 22164361129 T^{4} \))(\( 1 - 368 T - 189914 T^{2} - 10150912 T^{3} + 63518934267 T^{4} - 1511237325824 T^{5} - 4209322479452906 T^{6} - 1214313001783184944 T^{7} + \)\(49\!\cdots\!41\)\( T^{8} \))(\( 1 + 331 T - 333110 T^{2} - 50610775 T^{3} + 97428261796 T^{4} + 7341212711443 T^{5} - 15286864287523616 T^{6} + 1092937724841499511 T^{7} + \)\(21\!\cdots\!84\)\( T^{8} - \)\(16\!\cdots\!75\)\( T^{9} - \)\(16\!\cdots\!10\)\( T^{10} + \)\(24\!\cdots\!67\)\( T^{11} + \)\(10\!\cdots\!89\)\( T^{12} \))(\( 1 - 317 T + 36608 T^{2} + 65490883 T^{3} - 43515633637 T^{4} + 7415247471298 T^{5} + 6175303105639036 T^{6} - 2555693600931772834 T^{7} + \)\(73\!\cdots\!25\)\( T^{8} + \)\(23\!\cdots\!61\)\( T^{9} - \)\(17\!\cdots\!72\)\( T^{10} + \)\(34\!\cdots\!97\)\( T^{11} + \)\(16\!\cdots\!25\)\( T^{12} - \)\(84\!\cdots\!22\)\( T^{13} + \)\(30\!\cdots\!76\)\( T^{14} + \)\(54\!\cdots\!86\)\( T^{15} - \)\(47\!\cdots\!93\)\( T^{16} + \)\(10\!\cdots\!99\)\( T^{17} + \)\(88\!\cdots\!48\)\( T^{18} - \)\(11\!\cdots\!29\)\( T^{19} + \)\(53\!\cdots\!49\)\( T^{20} \))(\( 1 - 1135 T + 344368 T^{2} + 107494169 T^{3} - 79422582717 T^{4} + 1522579460342 T^{5} + 9430009439322196 T^{6} - 3330261248690177614 T^{7} + \)\(61\!\cdots\!73\)\( T^{8} + \)\(99\!\cdots\!43\)\( T^{9} - \)\(11\!\cdots\!60\)\( T^{10} + \)\(14\!\cdots\!11\)\( T^{11} + \)\(13\!\cdots\!17\)\( T^{12} - \)\(10\!\cdots\!62\)\( T^{13} + \)\(46\!\cdots\!36\)\( T^{14} + \)\(11\!\cdots\!94\)\( T^{15} - \)\(86\!\cdots\!13\)\( T^{16} + \)\(17\!\cdots\!57\)\( T^{17} + \)\(83\!\cdots\!08\)\( T^{18} - \)\(40\!\cdots\!95\)\( T^{19} + \)\(53\!\cdots\!49\)\( T^{20} \))(\( 1 + 295729 T^{2} + 65291280312 T^{4} + 6554644352318041 T^{6} + \)\(49\!\cdots\!41\)\( T^{8} \))
$59$ (\( 1 + 360 T + 205379 T^{2} \))(\( 1 - 380 T + 205379 T^{2} \))(\( 1 - 364 T + 438374 T^{2} - 74757956 T^{3} + 42180533641 T^{4} \))(\( 1 + 464 T + 458102 T^{2} + 95295856 T^{3} + 42180533641 T^{4} \))(\( 1 - 104 T + 80534 T^{2} - 21359416 T^{3} + 42180533641 T^{4} \))(\( 1 + 844 T + 474182 T^{2} + 173339876 T^{3} + 42180533641 T^{4} \))(\( 1 - 516 T + 418118 T^{2} - 105975564 T^{3} + 42180533641 T^{4} \))(\( ( 1 + 276 T + 1079368 T^{2} + 269058612 T^{3} + 568125822220 T^{4} + 128160475695540 T^{5} + 191883154887630712 T^{6} + 38445761827335559668 T^{7} + \)\(46\!\cdots\!98\)\( T^{8} + \)\(78\!\cdots\!72\)\( T^{9} + \)\(80\!\cdots\!92\)\( T^{10} + \)\(11\!\cdots\!60\)\( T^{11} + \)\(10\!\cdots\!20\)\( T^{12} + \)\(98\!\cdots\!88\)\( T^{13} + \)\(81\!\cdots\!28\)\( T^{14} + \)\(42\!\cdots\!84\)\( T^{15} + \)\(31\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 - 276 T + 1079368 T^{2} - 269058612 T^{3} + 568125822220 T^{4} - 128160475695540 T^{5} + 191883154887630712 T^{6} - 38445761827335559668 T^{7} + \)\(46\!\cdots\!98\)\( T^{8} - \)\(78\!\cdots\!72\)\( T^{9} + \)\(80\!\cdots\!92\)\( T^{10} - \)\(11\!\cdots\!60\)\( T^{11} + \)\(10\!\cdots\!20\)\( T^{12} - \)\(98\!\cdots\!88\)\( T^{13} + \)\(81\!\cdots\!28\)\( T^{14} - \)\(42\!\cdots\!84\)\( T^{15} + \)\(31\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 - 880 T + 706697 T^{2} - 338588064 T^{3} + 145140723163 T^{4} - 37118869604080 T^{5} + 8662995818654939 T^{6} )^{2} \))(\( ( 1 + 704 T + 427487 T^{2} + 197865856 T^{3} + 99740405354 T^{4} + 55609053370240 T^{5} + 20484584711199166 T^{6} + 8346087395413261696 T^{7} + \)\(37\!\cdots\!93\)\( T^{8} + \)\(12\!\cdots\!24\)\( T^{9} + \)\(36\!\cdots\!99\)\( T^{10} )^{2} \))(\( ( 1 + 205379 T^{2} )^{4} \))(\( 1 - 60 T - 201779 T^{2} - 12322740 T^{3} + 42180533641 T^{4} \))(\( 1 - 140 T - 326866 T^{2} + 9000880 T^{3} + 73832727115 T^{4} + 1848591733520 T^{5} - 13787382309099106 T^{6} - 1212819414611691460 T^{7} + \)\(17\!\cdots\!81\)\( T^{8} \))(\( 1 - 1520 T + 1148735 T^{2} - 566210800 T^{3} + 199248776190 T^{4} - 35546559587920 T^{5} + 2432254555145203 T^{6} - 7300516861607421680 T^{7} + \)\(84\!\cdots\!90\)\( T^{8} - \)\(49\!\cdots\!00\)\( T^{9} + \)\(20\!\cdots\!35\)\( T^{10} - \)\(55\!\cdots\!80\)\( T^{11} + \)\(75\!\cdots\!21\)\( T^{12} \))(\( 1 + 676 T - 259179 T^{2} - 22928420 T^{3} + 159667268999 T^{4} - 15850073806032 T^{5} - 23985994336882042 T^{6} + 12685589247886825904 T^{7} + \)\(22\!\cdots\!61\)\( T^{8} - \)\(68\!\cdots\!72\)\( T^{9} + \)\(55\!\cdots\!91\)\( T^{10} - \)\(14\!\cdots\!88\)\( T^{11} + \)\(96\!\cdots\!01\)\( T^{12} + \)\(10\!\cdots\!56\)\( T^{13} - \)\(42\!\cdots\!02\)\( T^{14} - \)\(57\!\cdots\!68\)\( T^{15} + \)\(11\!\cdots\!79\)\( T^{16} - \)\(35\!\cdots\!80\)\( T^{17} - \)\(82\!\cdots\!19\)\( T^{18} + \)\(43\!\cdots\!44\)\( T^{19} + \)\(13\!\cdots\!01\)\( T^{20} \))(\( 1 - 332 T - 320471 T^{2} + 243978636 T^{3} - 20389370525 T^{4} - 31533377981208 T^{5} + 20583073309028818 T^{6} - 8827744675821656792 T^{7} + \)\(10\!\cdots\!81\)\( T^{8} + \)\(16\!\cdots\!84\)\( T^{9} - \)\(12\!\cdots\!45\)\( T^{10} + \)\(34\!\cdots\!36\)\( T^{11} + \)\(44\!\cdots\!21\)\( T^{12} - \)\(76\!\cdots\!88\)\( T^{13} + \)\(36\!\cdots\!58\)\( T^{14} - \)\(11\!\cdots\!92\)\( T^{15} - \)\(15\!\cdots\!25\)\( T^{16} + \)\(37\!\cdots\!24\)\( T^{17} - \)\(10\!\cdots\!31\)\( T^{18} - \)\(21\!\cdots\!08\)\( T^{19} + \)\(13\!\cdots\!01\)\( T^{20} \))(\( ( 1 + 4 T - 205363 T^{2} + 821516 T^{3} + 42180533641 T^{4} )^{2} \))
$61$ (\( 1 + 682 T + 226981 T^{2} \))(\( 1 - 718 T + 226981 T^{2} \))(\( 1 - 792 T + 340886 T^{2} - 179768952 T^{3} + 51520374361 T^{4} \))(\( 1 + 684 T + 535646 T^{2} + 155255004 T^{3} + 51520374361 T^{4} \))(\( 1 + 468 T + 494606 T^{2} + 106227108 T^{3} + 51520374361 T^{4} \))(\( 1 + 204 T + 455006 T^{2} + 46304124 T^{3} + 51520374361 T^{4} \))(\( 1 + 880 T + 575238 T^{2} + 199743280 T^{3} + 51520374361 T^{4} \))(\( 1 - 1803700 T^{2} + 1727735787552 T^{4} - 1138891143711322076 T^{6} + \)\(57\!\cdots\!08\)\( T^{8} - \)\(23\!\cdots\!08\)\( T^{10} + \)\(78\!\cdots\!52\)\( T^{12} - \)\(22\!\cdots\!80\)\( T^{14} + \)\(55\!\cdots\!82\)\( T^{16} - \)\(11\!\cdots\!80\)\( T^{18} + \)\(20\!\cdots\!92\)\( T^{20} - \)\(31\!\cdots\!48\)\( T^{22} + \)\(40\!\cdots\!28\)\( T^{24} - \)\(41\!\cdots\!76\)\( T^{26} + \)\(32\!\cdots\!72\)\( T^{28} - \)\(17\!\cdots\!00\)\( T^{30} + \)\(49\!\cdots\!81\)\( T^{32} \))(\( 1 - 1803700 T^{2} + 1727735787552 T^{4} - 1138891143711322076 T^{6} + \)\(57\!\cdots\!08\)\( T^{8} - \)\(23\!\cdots\!08\)\( T^{10} + \)\(78\!\cdots\!52\)\( T^{12} - \)\(22\!\cdots\!80\)\( T^{14} + \)\(55\!\cdots\!82\)\( T^{16} - \)\(11\!\cdots\!80\)\( T^{18} + \)\(20\!\cdots\!92\)\( T^{20} - \)\(31\!\cdots\!48\)\( T^{22} + \)\(40\!\cdots\!28\)\( T^{24} - \)\(41\!\cdots\!76\)\( T^{26} + \)\(32\!\cdots\!72\)\( T^{28} - \)\(17\!\cdots\!00\)\( T^{30} + \)\(49\!\cdots\!81\)\( T^{32} \))(\( ( 1 + 870 T + 582363 T^{2} + 282478148 T^{3} + 132185336103 T^{4} + 44822725694070 T^{5} + 11694146092834141 T^{6} )^{2} \))(\( ( 1 - 650 T + 689345 T^{2} - 375251480 T^{3} + 259020342850 T^{4} - 102268282520348 T^{5} + 58792696440435850 T^{6} - 19333096729119304280 T^{7} + \)\(80\!\cdots\!45\)\( T^{8} - \)\(17\!\cdots\!50\)\( T^{9} + \)\(60\!\cdots\!01\)\( T^{10} )^{2} \))(\( ( 1 - 226981 T^{2} )^{4} \))(\( 1 + 392 T - 73317 T^{2} + 88976552 T^{3} + 51520374361 T^{4} \))(\( 1 - 732 T - 44894 T^{2} - 92785392 T^{3} + 164091153819 T^{4} - 21060521061552 T^{5} - 2312955686562734 T^{6} - 8560114939954591212 T^{7} + \)\(26\!\cdots\!21\)\( T^{8} \))(\( 1 - 1160 T + 250957 T^{2} - 125991256 T^{3} + 286379252746 T^{4} - 109352485901816 T^{5} + 9150550020060557 T^{6} - 24820936602480097496 T^{7} + \)\(14\!\cdots\!06\)\( T^{8} - \)\(14\!\cdots\!96\)\( T^{9} + \)\(66\!\cdots\!97\)\( T^{10} - \)\(69\!\cdots\!60\)\( T^{11} + \)\(13\!\cdots\!81\)\( T^{12} \))(\( 1 - 188 T - 431481 T^{2} + 373005124 T^{3} + 29297127399 T^{4} - 121648932752488 T^{5} + 38284746381984330 T^{6} + 12628932742569504968 T^{7} - \)\(11\!\cdots\!39\)\( T^{8} - \)\(36\!\cdots\!84\)\( T^{9} + \)\(15\!\cdots\!05\)\( T^{10} - \)\(81\!\cdots\!04\)\( T^{11} - \)\(57\!\cdots\!79\)\( T^{12} + \)\(14\!\cdots\!88\)\( T^{13} + \)\(10\!\cdots\!30\)\( T^{14} - \)\(73\!\cdots\!88\)\( T^{15} + \)\(40\!\cdots\!19\)\( T^{16} + \)\(11\!\cdots\!64\)\( T^{17} - \)\(30\!\cdots\!21\)\( T^{18} - \)\(30\!\cdots\!48\)\( T^{19} + \)\(36\!\cdots\!01\)\( T^{20} \))(\( 1 - 584 T - 684009 T^{2} + 304553272 T^{3} + 343910273991 T^{4} - 91891274199664 T^{5} - 134703419439176310 T^{6} + 18304200035324266544 T^{7} + \)\(42\!\cdots\!49\)\( T^{8} - \)\(18\!\cdots\!52\)\( T^{9} - \)\(10\!\cdots\!07\)\( T^{10} - \)\(41\!\cdots\!12\)\( T^{11} + \)\(21\!\cdots\!89\)\( T^{12} + \)\(21\!\cdots\!04\)\( T^{13} - \)\(35\!\cdots\!10\)\( T^{14} - \)\(55\!\cdots\!64\)\( T^{15} + \)\(47\!\cdots\!71\)\( T^{16} + \)\(94\!\cdots\!92\)\( T^{17} - \)\(48\!\cdots\!69\)\( T^{18} - \)\(93\!\cdots\!64\)\( T^{19} + \)\(36\!\cdots\!01\)\( T^{20} \))(\( ( 1 + 262 T - 158337 T^{2} + 59469022 T^{3} + 51520374361 T^{4} )^{2} \))
$67$ (\( 1 - 812 T + 300763 T^{2} \))(\( 1 - 412 T + 300763 T^{2} \))(\( 1 + 788 T + 753430 T^{2} + 237001244 T^{3} + 90458382169 T^{4} \))(\( 1 - 736 T + 602470 T^{2} - 221361568 T^{3} + 90458382169 T^{4} \))(\( 1 + 1688 T + 1302310 T^{2} + 507687944 T^{3} + 90458382169 T^{4} \))(\( 1 + 104 T + 537670 T^{2} + 31279352 T^{3} + 90458382169 T^{4} \))(\( 1 + 356 T + 100374 T^{2} + 107071628 T^{3} + 90458382169 T^{4} \))(\( ( 1 - 502 T + 1342320 T^{2} - 608015510 T^{3} + 930983956700 T^{4} - 373795253912646 T^{5} + 437317641030113680 T^{6} - \)\(15\!\cdots\!94\)\( T^{7} + \)\(15\!\cdots\!78\)\( T^{8} - \)\(46\!\cdots\!22\)\( T^{9} + \)\(39\!\cdots\!20\)\( T^{10} - \)\(10\!\cdots\!62\)\( T^{11} + \)\(76\!\cdots\!00\)\( T^{12} - \)\(14\!\cdots\!30\)\( T^{13} + \)\(99\!\cdots\!80\)\( T^{14} - \)\(11\!\cdots\!34\)\( T^{15} + \)\(66\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 - 502 T + 1342320 T^{2} - 608015510 T^{3} + 930983956700 T^{4} - 373795253912646 T^{5} + 437317641030113680 T^{6} - \)\(15\!\cdots\!94\)\( T^{7} + \)\(15\!\cdots\!78\)\( T^{8} - \)\(46\!\cdots\!22\)\( T^{9} + \)\(39\!\cdots\!20\)\( T^{10} - \)\(10\!\cdots\!62\)\( T^{11} + \)\(76\!\cdots\!00\)\( T^{12} - \)\(14\!\cdots\!30\)\( T^{13} + \)\(99\!\cdots\!80\)\( T^{14} - \)\(11\!\cdots\!34\)\( T^{15} + \)\(66\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 - 1101858 T^{2} + 638460439095 T^{4} - 237880710542256316 T^{6} + \)\(57\!\cdots\!55\)\( T^{8} - \)\(90\!\cdots\!38\)\( T^{10} + \)\(74\!\cdots\!09\)\( T^{12} \))(\( 1 - 2016990 T^{2} + 1931325978405 T^{4} - 1175831601966849320 T^{6} + \)\(51\!\cdots\!30\)\( T^{8} - \)\(17\!\cdots\!32\)\( T^{10} + \)\(46\!\cdots\!70\)\( T^{12} - \)\(96\!\cdots\!20\)\( T^{14} + \)\(14\!\cdots\!45\)\( T^{16} - \)\(13\!\cdots\!90\)\( T^{18} + \)\(60\!\cdots\!49\)\( T^{20} \))(\( ( 1 - 300763 T^{2} )^{4} \))(\( 1 - 280 T - 222363 T^{2} - 84213640 T^{3} + 90458382169 T^{4} \))(\( 1 + 1066 T + 375741 T^{2} + 169588874 T^{3} + 146302956428 T^{4} + 51006058510862 T^{5} + 33988922974562229 T^{6} + 29002165666450413502 T^{7} + \)\(81\!\cdots\!61\)\( T^{8} \))(\( 1 + 806 T - 307154 T^{2} - 111681852 T^{3} + 271889672754 T^{4} + 31382224966814 T^{5} - 84826512482707274 T^{6} + 9438612127693879082 T^{7} + \)\(24\!\cdots\!26\)\( T^{8} - \)\(30\!\cdots\!44\)\( T^{9} - \)\(25\!\cdots\!94\)\( T^{10} + \)\(19\!\cdots\!58\)\( T^{11} + \)\(74\!\cdots\!09\)\( T^{12} \))(\( 1 - 1776 T + 1302831 T^{2} - 795082424 T^{3} + 523494226340 T^{4} - 209497188661456 T^{5} + 62623175581904481 T^{6} - 31980651664564177744 T^{7} + \)\(13\!\cdots\!23\)\( T^{8} + \)\(42\!\cdots\!28\)\( T^{9} - \)\(47\!\cdots\!52\)\( T^{10} + \)\(12\!\cdots\!64\)\( T^{11} + \)\(11\!\cdots\!87\)\( T^{12} - \)\(87\!\cdots\!68\)\( T^{13} + \)\(51\!\cdots\!41\)\( T^{14} - \)\(51\!\cdots\!08\)\( T^{15} + \)\(38\!\cdots\!60\)\( T^{16} - \)\(17\!\cdots\!08\)\( T^{17} + \)\(87\!\cdots\!51\)\( T^{18} - \)\(35\!\cdots\!48\)\( T^{19} + \)\(60\!\cdots\!49\)\( T^{20} \))(\( 1 + 412 T - 633285 T^{2} - 520720460 T^{3} + 54577110124 T^{4} + 159720777575348 T^{5} + 31924035283508653 T^{6} + 10162758820279347212 T^{7} + \)\(13\!\cdots\!07\)\( T^{8} - \)\(68\!\cdots\!08\)\( T^{9} - \)\(11\!\cdots\!76\)\( T^{10} - \)\(20\!\cdots\!04\)\( T^{11} + \)\(12\!\cdots\!83\)\( T^{12} + \)\(27\!\cdots\!64\)\( T^{13} + \)\(26\!\cdots\!33\)\( T^{14} + \)\(39\!\cdots\!64\)\( T^{15} + \)\(40\!\cdots\!16\)\( T^{16} - \)\(11\!\cdots\!20\)\( T^{17} - \)\(42\!\cdots\!85\)\( T^{18} + \)\(82\!\cdots\!76\)\( T^{19} + \)\(60\!\cdots\!49\)\( T^{20} \))(\( 1 - 162350 T^{2} - 64100859669 T^{4} - 14685918345137150 T^{6} + \)\(81\!\cdots\!61\)\( T^{8} \))
$71$ (\( 1 - 810 T + 357911 T^{2} \))(\( 1 + 960 T + 357911 T^{2} \))(\( 1 - 454 T + 304526 T^{2} - 162491594 T^{3} + 128100283921 T^{4} \))(\( 1 + 740 T + 757502 T^{2} + 264854140 T^{3} + 128100283921 T^{4} \))(\( 1 + 136 T + 540446 T^{2} + 48675896 T^{3} + 128100283921 T^{4} \))(\( 1 - 1670 T + 1384382 T^{2} - 597711370 T^{3} + 128100283921 T^{4} \))(\( 1 - 310 T + 664038 T^{2} - 110952410 T^{3} + 128100283921 T^{4} \))(\( 1 - 3784904 T^{2} + 6923073902136 T^{4} - 8129352290527081176 T^{6} + \)\(68\!\cdots\!04\)\( T^{8} - \)\(45\!\cdots\!12\)\( T^{10} + \)\(23\!\cdots\!20\)\( T^{12} - \)\(10\!\cdots\!80\)\( T^{14} + \)\(40\!\cdots\!02\)\( T^{16} - \)\(13\!\cdots\!80\)\( T^{18} + \)\(39\!\cdots\!20\)\( T^{20} - \)\(94\!\cdots\!32\)\( T^{22} + \)\(18\!\cdots\!24\)\( T^{24} - \)\(28\!\cdots\!76\)\( T^{26} + \)\(30\!\cdots\!56\)\( T^{28} - \)\(21\!\cdots\!64\)\( T^{30} + \)\(72\!\cdots\!61\)\( T^{32} \))(\( 1 - 3784904 T^{2} + 6923073902136 T^{4} - 8129352290527081176 T^{6} + \)\(68\!\cdots\!04\)\( T^{8} - \)\(45\!\cdots\!12\)\( T^{10} + \)\(23\!\cdots\!20\)\( T^{12} - \)\(10\!\cdots\!80\)\( T^{14} + \)\(40\!\cdots\!02\)\( T^{16} - \)\(13\!\cdots\!80\)\( T^{18} + \)\(39\!\cdots\!20\)\( T^{20} - \)\(94\!\cdots\!32\)\( T^{22} + \)\(18\!\cdots\!24\)\( T^{24} - \)\(28\!\cdots\!76\)\( T^{26} + \)\(30\!\cdots\!56\)\( T^{28} - \)\(21\!\cdots\!64\)\( T^{30} + \)\(72\!\cdots\!61\)\( T^{32} \))(\( ( 1 + 1018 T + 1108049 T^{2} + 595462884 T^{3} + 396582925639 T^{4} + 130406089031578 T^{5} + 45848500718449031 T^{6} )^{2} \))(\( ( 1 - 1470 T + 1881615 T^{2} - 1727909680 T^{3} + 1338943951990 T^{4} - 860023408325220 T^{5} + 479222768800692890 T^{6} - \)\(22\!\cdots\!80\)\( T^{7} + \)\(86\!\cdots\!65\)\( T^{8} - \)\(24\!\cdots\!70\)\( T^{9} + \)\(58\!\cdots\!51\)\( T^{10} )^{2} \))(\( ( 1 - 828 T + 357911 T^{2} )^{2}( 1 + 828 T + 357911 T^{2} )^{2} \))(\( ( 1 - 258 T + 357911 T^{2} )^{2} \))(\( ( 1 + 1208 T + 959606 T^{2} + 432356488 T^{3} + 128100283921 T^{4} )^{2} \))(\( ( 1 + 406 T + 391273 T^{2} + 58294156 T^{3} + 140040910703 T^{4} + 52008715271926 T^{5} + 45848500718449031 T^{6} )^{2} \))(\( ( 1 + 6 T + 797207 T^{2} - 67070712 T^{3} + 425455729610 T^{4} - 37303525976244 T^{5} + 152275285640444710 T^{6} - 8591777249983621752 T^{7} + \)\(36\!\cdots\!17\)\( T^{8} + \)\(98\!\cdots\!46\)\( T^{9} + \)\(58\!\cdots\!51\)\( T^{10} )^{2} \))(\( ( 1 + 142 T + 1020275 T^{2} + 238977320 T^{3} + 602260486134 T^{4} + 107445186880572 T^{5} + 215555652852706074 T^{6} + 30613062542679671720 T^{7} + \)\(46\!\cdots\!25\)\( T^{8} + \)\(23\!\cdots\!22\)\( T^{9} + \)\(58\!\cdots\!51\)\( T^{10} )^{2} \))(\( ( 1 + 1138 T + 357911 T^{2} )^{4} \))
$73$ (\( 1 + 124 T + 389017 T^{2} \))(\( 1 - 1066 T + 389017 T^{2} \))(\( 1 - 778 T + 794698 T^{2} - 302655226 T^{3} + 151334226289 T^{4} \))(\( 1 - 424 T + 748558 T^{2} - 164943208 T^{3} + 151334226289 T^{4} \))(\( 1 - 508 T + 13078 T^{2} - 197620636 T^{3} + 151334226289 T^{4} \))(\( 1 + 386 T + 152218 T^{2} + 150160562 T^{3} + 151334226289 T^{4} \))(\( 1 - 326 T + 789802 T^{2} - 126819542 T^{3} + 151334226289 T^{4} \))(\( 1 - 3366328 T^{2} + 5803283641176 T^{4} - 6783928049764768040 T^{6} + \)\(60\!\cdots\!24\)\( T^{8} - \)\(42\!\cdots\!96\)\( T^{10} + \)\(25\!\cdots\!56\)\( T^{12} - \)\(12\!\cdots\!16\)\( T^{14} + \)\(52\!\cdots\!66\)\( T^{16} - \)\(18\!\cdots\!24\)\( T^{18} + \)\(57\!\cdots\!76\)\( T^{20} - \)\(14\!\cdots\!24\)\( T^{22} + \)\(31\!\cdots\!84\)\( T^{24} - \)\(53\!\cdots\!60\)\( T^{26} + \)\(69\!\cdots\!36\)\( T^{28} - \)\(61\!\cdots\!12\)\( T^{30} + \)\(27\!\cdots\!81\)\( T^{32} \))(\( 1 - 3366328 T^{2} + 5803283641176 T^{4} - 6783928049764768040 T^{6} + \)\(60\!\cdots\!24\)\( T^{8} - \)\(42\!\cdots\!96\)\( T^{10} + \)\(25\!\cdots\!56\)\( T^{12} - \)\(12\!\cdots\!16\)\( T^{14} + \)\(52\!\cdots\!66\)\( T^{16} - \)\(18\!\cdots\!24\)\( T^{18} + \)\(57\!\cdots\!76\)\( T^{20} - \)\(14\!\cdots\!24\)\( T^{22} + \)\(31\!\cdots\!84\)\( T^{24} - \)\(53\!\cdots\!60\)\( T^{26} + \)\(69\!\cdots\!36\)\( T^{28} - \)\(61\!\cdots\!12\)\( T^{30} + \)\(27\!\cdots\!81\)\( T^{32} \))(\( 1 - 596010 T^{2} + 300446924511 T^{4} - 131249091840782924 T^{6} + \)\(45\!\cdots\!79\)\( T^{8} - \)\(13\!\cdots\!10\)\( T^{10} + \)\(34\!\cdots\!69\)\( T^{12} \))(\( 1 - 2398886 T^{2} + 2442762516189 T^{4} - 1366613667006822216 T^{6} + \)\(48\!\cdots\!38\)\( T^{8} - \)\(16\!\cdots\!36\)\( T^{10} + \)\(73\!\cdots\!82\)\( T^{12} - \)\(31\!\cdots\!36\)\( T^{14} + \)\(84\!\cdots\!41\)\( T^{16} - \)\(12\!\cdots\!26\)\( T^{18} + \)\(79\!\cdots\!49\)\( T^{20} \))(\( ( 1 - 504254 T^{2} + 151334226289 T^{4} )^{2} \))(\( 1 + 578 T - 54933 T^{2} + 224851826 T^{3} + 151334226289 T^{4} \))(\( 1 + 1654 T + 1273953 T^{2} + 1130887766 T^{3} + 921176810708 T^{4} + 439934566066022 T^{5} + 192792691583550417 T^{6} + 97373604415475128102 T^{7} + \)\(22\!\cdots\!21\)\( T^{8} \))(\( 1 - 1192 T - 104132 T^{2} + 45350124 T^{3} + 621928798908 T^{4} - 186728509861888 T^{5} - 134157440913090458 T^{6} - 72640564720942084096 T^{7} + \)\(94\!\cdots\!12\)\( T^{8} + \)\(26\!\cdots\!12\)\( T^{9} - \)\(23\!\cdots\!72\)\( T^{10} - \)\(10\!\cdots\!44\)\( T^{11} + \)\(34\!\cdots\!69\)\( T^{12} \))(\( 1 + 2006 T + 2213445 T^{2} + 2068190842 T^{3} + 1617233236496 T^{4} + 980484252789530 T^{5} + 644957368099789599 T^{6} + \)\(49\!\cdots\!02\)\( T^{7} + \)\(36\!\cdots\!03\)\( T^{8} + \)\(27\!\cdots\!32\)\( T^{9} + \)\(19\!\cdots\!20\)\( T^{10} + \)\(10\!\cdots\!44\)\( T^{11} + \)\(54\!\cdots\!67\)\( T^{12} + \)\(29\!\cdots\!26\)\( T^{13} + \)\(14\!\cdots\!79\)\( T^{14} + \)\(87\!\cdots\!10\)\( T^{15} + \)\(56\!\cdots\!24\)\( T^{16} + \)\(27\!\cdots\!66\)\( T^{17} + \)\(11\!\cdots\!45\)\( T^{18} + \)\(40\!\cdots\!82\)\( T^{19} + \)\(79\!\cdots\!49\)\( T^{20} \))(\( 1 - 2074 T + 1006865 T^{2} - 22856718 T^{3} + 797613942736 T^{4} - 798346226345510 T^{5} - 93874831999907421 T^{6} + 62628506747320190882 T^{7} + \)\(25\!\cdots\!63\)\( T^{8} - \)\(66\!\cdots\!88\)\( T^{9} - \)\(65\!\cdots\!20\)\( T^{10} - \)\(25\!\cdots\!96\)\( T^{11} + \)\(38\!\cdots\!07\)\( T^{12} + \)\(36\!\cdots\!66\)\( T^{13} - \)\(21\!\cdots\!41\)\( T^{14} - \)\(71\!\cdots\!70\)\( T^{15} + \)\(27\!\cdots\!84\)\( T^{16} - \)\(30\!\cdots\!14\)\( T^{17} + \)\(52\!\cdots\!65\)\( T^{18} - \)\(42\!\cdots\!78\)\( T^{19} + \)\(79\!\cdots\!49\)\( T^{20} \))(\( 1 + 766370 T^{2} + 435988750611 T^{4} + 115978011001100930 T^{6} + \)\(22\!\cdots\!21\)\( T^{8} \))
$79$ (\( 1 - 1136 T + 493039 T^{2} \))(\( 1 - 896 T + 493039 T^{2} \))(\( 1 - 408 T + 994782 T^{2} - 201159912 T^{3} + 243087455521 T^{4} \))(\( 1 + 408 T - 143586 T^{2} + 201159912 T^{3} + 243087455521 T^{4} \))(\( 1 + 432 T + 602142 T^{2} + 212992848 T^{3} + 243087455521 T^{4} \))(\( 1 + 888 T + 1007454 T^{2} + 437818632 T^{3} + 243087455521 T^{4} \))(\( 1 - 1832 T + 1824478 T^{2} - 903247448 T^{3} + 243087455521 T^{4} \))(\( ( 1 - 646 T + 1982385 T^{2} - 740011226 T^{3} + 1873229675366 T^{4} - 390365701033098 T^{5} + 1212389938855610239 T^{6} - \)\(11\!\cdots\!74\)\( T^{7} + \)\(62\!\cdots\!18\)\( T^{8} - \)\(57\!\cdots\!86\)\( T^{9} + \)\(29\!\cdots\!19\)\( T^{10} - \)\(46\!\cdots\!62\)\( T^{11} + \)\(11\!\cdots\!06\)\( T^{12} - \)\(21\!\cdots\!74\)\( T^{13} + \)\(28\!\cdots\!85\)\( T^{14} - \)\(45\!\cdots\!34\)\( T^{15} + \)\(34\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 - 646 T + 1982385 T^{2} - 740011226 T^{3} + 1873229675366 T^{4} - 390365701033098 T^{5} + 1212389938855610239 T^{6} - \)\(11\!\cdots\!74\)\( T^{7} + \)\(62\!\cdots\!18\)\( T^{8} - \)\(57\!\cdots\!86\)\( T^{9} + \)\(29\!\cdots\!19\)\( T^{10} - \)\(46\!\cdots\!62\)\( T^{11} + \)\(11\!\cdots\!06\)\( T^{12} - \)\(21\!\cdots\!74\)\( T^{13} + \)\(28\!\cdots\!85\)\( T^{14} - \)\(45\!\cdots\!34\)\( T^{15} + \)\(34\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 - 1620 T + 1787517 T^{2} - 1338821912 T^{3} + 881315594163 T^{4} - 393801677944020 T^{5} + 119851595982618319 T^{6} )^{2} \))(\( ( 1 - 820 T + 1736795 T^{2} - 1027136240 T^{3} + 1389341527610 T^{4} - 657402503393464 T^{5} + 684999557431306790 T^{6} - \)\(24\!\cdots\!40\)\( T^{7} + \)\(20\!\cdots\!05\)\( T^{8} - \)\(48\!\cdots\!20\)\( T^{9} + \)\(29\!\cdots\!99\)\( T^{10} )^{2} \))(\( ( 1 - 236 T + 493039 T^{2} )^{4} \))(\( 1 + 152 T - 469935 T^{2} + 74941928 T^{3} + 243087455521 T^{4} \))(\( 1 + 1134 T - 19563 T^{2} + 362246094 T^{3} + 827265943556 T^{4} + 178601451939666 T^{5} - 4755519892357323 T^{6} + \)\(13\!\cdots\!46\)\( T^{7} + \)\(59\!\cdots\!41\)\( T^{8} \))(\( 1 - 2590 T + 3397518 T^{2} - 3071564116 T^{3} + 2201525113146 T^{4} - 1283368958653574 T^{5} + 775684873337457726 T^{6} - \)\(63\!\cdots\!86\)\( T^{7} + \)\(53\!\cdots\!66\)\( T^{8} - \)\(36\!\cdots\!04\)\( T^{9} + \)\(20\!\cdots\!38\)\( T^{10} - \)\(75\!\cdots\!10\)\( T^{11} + \)\(14\!\cdots\!61\)\( T^{12} \))(\( 1 + 200 T - 1905761 T^{2} - 521788304 T^{3} + 2022855950280 T^{4} + 568166623235112 T^{5} - 1467320191398068699 T^{6} - \)\(32\!\cdots\!56\)\( T^{7} + \)\(84\!\cdots\!03\)\( T^{8} + \)\(73\!\cdots\!56\)\( T^{9} - \)\(42\!\cdots\!44\)\( T^{10} + \)\(36\!\cdots\!84\)\( T^{11} + \)\(20\!\cdots\!63\)\( T^{12} - \)\(39\!\cdots\!64\)\( T^{13} - \)\(86\!\cdots\!59\)\( T^{14} + \)\(16\!\cdots\!88\)\( T^{15} + \)\(29\!\cdots\!80\)\( T^{16} - \)\(36\!\cdots\!16\)\( T^{17} - \)\(66\!\cdots\!41\)\( T^{18} + \)\(34\!\cdots\!00\)\( T^{19} + \)\(84\!\cdots\!01\)\( T^{20} \))(\( 1 + 28 T - 1713233 T^{2} + 137836596 T^{3} + 1524513275000 T^{4} - 195374153482332 T^{5} - 1026627193743889947 T^{6} + 79301893796380256380 T^{7} + \)\(59\!\cdots\!51\)\( T^{8} - \)\(90\!\cdots\!64\)\( T^{9} - \)\(31\!\cdots\!36\)\( T^{10} - \)\(44\!\cdots\!96\)\( T^{11} + \)\(14\!\cdots\!71\)\( T^{12} + \)\(95\!\cdots\!20\)\( T^{13} - \)\(60\!\cdots\!27\)\( T^{14} - \)\(56\!\cdots\!68\)\( T^{15} + \)\(21\!\cdots\!00\)\( T^{16} + \)\(97\!\cdots\!84\)\( T^{17} - \)\(59\!\cdots\!73\)\( T^{18} + \)\(48\!\cdots\!52\)\( T^{19} + \)\(84\!\cdots\!01\)\( T^{20} \))(\( ( 1 + 62 T - 489195 T^{2} + 30568418 T^{3} + 243087455521 T^{4} )^{2} \))
$83$ (\( 1 - 156 T + 571787 T^{2} \))(\( 1 - 436 T + 571787 T^{2} \))(\( 1 - 1136 T + 1169990 T^{2} - 649550032 T^{3} + 326940373369 T^{4} \))(\( 1 - 608 T + 1200710 T^{2} - 347646496 T^{3} + 326940373369 T^{4} \))(\( 1 + 584 T + 1172390 T^{2} + 333923608 T^{3} + 326940373369 T^{4} \))(\( 1 - 928 T + 600710 T^{2} - 530618336 T^{3} + 326940373369 T^{4} \))(\( 1 + 680 T + 744870 T^{2} + 388815160 T^{3} + 326940373369 T^{4} \))(\( ( 1 + 876 T + 2629756 T^{2} + 2450428188 T^{3} + 3804910083124 T^{4} + 3209938165536732 T^{5} + 3638619575768964772 T^{6} + \)\(27\!\cdots\!08\)\( T^{7} + \)\(24\!\cdots\!30\)\( T^{8} + \)\(15\!\cdots\!96\)\( T^{9} + \)\(11\!\cdots\!68\)\( T^{10} + \)\(60\!\cdots\!96\)\( T^{11} + \)\(40\!\cdots\!64\)\( T^{12} + \)\(14\!\cdots\!16\)\( T^{13} + \)\(91\!\cdots\!04\)\( T^{14} + \)\(17\!\cdots\!08\)\( T^{15} + \)\(11\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 - 876 T + 2629756 T^{2} - 2450428188 T^{3} + 3804910083124 T^{4} - 3209938165536732 T^{5} + 3638619575768964772 T^{6} - \)\(27\!\cdots\!08\)\( T^{7} + \)\(24\!\cdots\!30\)\( T^{8} - \)\(15\!\cdots\!96\)\( T^{9} + \)\(11\!\cdots\!68\)\( T^{10} - \)\(60\!\cdots\!96\)\( T^{11} + \)\(40\!\cdots\!64\)\( T^{12} - \)\(14\!\cdots\!16\)\( T^{13} + \)\(91\!\cdots\!04\)\( T^{14} - \)\(17\!\cdots\!08\)\( T^{15} + \)\(11\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 - 1086594 T^{2} + 1370317231383 T^{4} - 756582920323766652 T^{6} + \)\(44\!\cdots\!27\)\( T^{8} - \)\(11\!\cdots\!34\)\( T^{10} + \)\(34\!\cdots\!09\)\( T^{12} \))(\( 1 - 4743150 T^{2} + 10500593430085 T^{4} - 14340896860193237480 T^{6} + \)\(13\!\cdots\!10\)\( T^{8} - \)\(90\!\cdots\!28\)\( T^{10} + \)\(43\!\cdots\!90\)\( T^{12} - \)\(15\!\cdots\!80\)\( T^{14} + \)\(36\!\cdots\!65\)\( T^{16} - \)\(54\!\cdots\!50\)\( T^{18} + \)\(37\!\cdots\!49\)\( T^{20} \))(\( ( 1 + 1141306 T^{2} + 326940373369 T^{4} )^{2} \))(\( ( 1 + 432 T + 571787 T^{2} )^{2} \))(\( ( 1 - 968 T + 1357022 T^{2} - 553489816 T^{3} + 326940373369 T^{4} )^{2} \))(\( ( 1 + 508 T + 1655669 T^{2} + 550491384 T^{3} + 946690010503 T^{4} + 166085709671452 T^{5} + 186940255267540403 T^{6} )^{2} \))(\( ( 1 + 332 T + 1330763 T^{2} + 251179960 T^{3} + 1196075575498 T^{4} + 287374399354632 T^{5} + 683900465087274926 T^{6} + 82120869905210485240 T^{7} + \)\(24\!\cdots\!89\)\( T^{8} + \)\(35\!\cdots\!52\)\( T^{9} + \)\(61\!\cdots\!07\)\( T^{10} )^{2} \))(\( ( 1 + 840 T + 1394751 T^{2} + 1097470000 T^{3} + 1235101554942 T^{4} + 765253616219632 T^{5} + 706215012795621354 T^{6} + \)\(35\!\cdots\!00\)\( T^{7} + \)\(26\!\cdots\!53\)\( T^{8} + \)\(89\!\cdots\!40\)\( T^{9} + \)\(61\!\cdots\!07\)\( T^{10} )^{2} \))(\( ( 1 - 937458 T^{2} + 326940373369 T^{4} )^{2} \))
$89$ (\( 1 + 1038 T + 704969 T^{2} \))(\( 1 + 1038 T + 704969 T^{2} \))(\( 1 - 36 T - 842170 T^{2} - 25378884 T^{3} + 496981290961 T^{4} \))(\( 1 + 1332 T + 1790774 T^{2} + 939018708 T^{3} + 496981290961 T^{4} \))(\( 1 + 1404 T + 1802390 T^{2} + 989776476 T^{3} + 496981290961 T^{4} \))(\( 1 - 588 T + 1495334 T^{2} - 414521772 T^{3} + 496981290961 T^{4} \))(\( 1 - 796 T + 411158 T^{2} - 561155324 T^{3} + 496981290961 T^{4} \))(\( ( 1 - 3048 T + 7221784 T^{2} - 12982684008 T^{3} + 19357170780076 T^{4} - 24946439819701464 T^{5} + 28081097144520074344 T^{6} - \)\(27\!\cdots\!32\)\( T^{7} + \)\(24\!\cdots\!70\)\( T^{8} - \)\(19\!\cdots\!08\)\( T^{9} + \)\(13\!\cdots\!84\)\( T^{10} - \)\(87\!\cdots\!76\)\( T^{11} + \)\(47\!\cdots\!96\)\( T^{12} - \)\(22\!\cdots\!92\)\( T^{13} + \)\(88\!\cdots\!04\)\( T^{14} - \)\(26\!\cdots\!72\)\( T^{15} + \)\(61\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 + 3048 T + 7221784 T^{2} + 12982684008 T^{3} + 19357170780076 T^{4} + 24946439819701464 T^{5} + 28081097144520074344 T^{6} + \)\(27\!\cdots\!32\)\( T^{7} + \)\(24\!\cdots\!70\)\( T^{8} + \)\(19\!\cdots\!08\)\( T^{9} + \)\(13\!\cdots\!84\)\( T^{10} + \)\(87\!\cdots\!76\)\( T^{11} + \)\(47\!\cdots\!96\)\( T^{12} + \)\(22\!\cdots\!92\)\( T^{13} + \)\(88\!\cdots\!04\)\( T^{14} + \)\(26\!\cdots\!72\)\( T^{15} + \)\(61\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 - 1938 T + 3246255 T^{2} - 2913932892 T^{3} + 2288509141095 T^{4} - 963149741882418 T^{5} + 350356403707485209 T^{6} )^{2} \))(\( ( 1 + 286 T + 2177465 T^{2} + 600135040 T^{3} + 2162009088238 T^{4} + 560754412921604 T^{5} + 1524149384926054622 T^{6} + \)\(29\!\cdots\!40\)\( T^{7} + \)\(76\!\cdots\!85\)\( T^{8} + \)\(70\!\cdots\!06\)\( T^{9} + \)\(17\!\cdots\!49\)\( T^{10} )^{2} \))(\( ( 1 + 704969 T^{2} )^{4} \))(\( 1 - 234 T - 650213 T^{2} - 164962746 T^{3} + 496981290961 T^{4} \))(\( 1 + 204 T + 809506 T^{2} - 444276912 T^{3} + 63335771235 T^{4} - 313201450375728 T^{5} + 402309336920675266 T^{6} + 71472706356326982636 T^{7} + \)\(24\!\cdots\!21\)\( T^{8} \))(\( 1 + 42 T - 564775 T^{2} + 1322241414 T^{3} - 51158611474 T^{4} - 380486119106214 T^{5} + 895055750746202909 T^{6} - \)\(26\!\cdots\!66\)\( T^{7} - \)\(25\!\cdots\!14\)\( T^{8} + \)\(46\!\cdots\!26\)\( T^{9} - \)\(13\!\cdots\!75\)\( T^{10} + \)\(73\!\cdots\!58\)\( T^{11} + \)\(12\!\cdots\!81\)\( T^{12} \))(\( 1 + 894 T - 1501253 T^{2} - 1203783426 T^{3} + 1217576227911 T^{4} + 488918737763772 T^{5} - 941190453323848894 T^{6} + \)\(20\!\cdots\!20\)\( T^{7} + \)\(93\!\cdots\!81\)\( T^{8} - \)\(16\!\cdots\!42\)\( T^{9} - \)\(80\!\cdots\!11\)\( T^{10} - \)\(11\!\cdots\!98\)\( T^{11} + \)\(46\!\cdots\!41\)\( T^{12} + \)\(70\!\cdots\!80\)\( T^{13} - \)\(23\!\cdots\!74\)\( T^{14} + \)\(85\!\cdots\!28\)\( T^{15} + \)\(14\!\cdots\!91\)\( T^{16} - \)\(10\!\cdots\!14\)\( T^{17} - \)\(91\!\cdots\!73\)\( T^{18} + \)\(38\!\cdots\!26\)\( T^{19} + \)\(30\!\cdots\!01\)\( T^{20} \))(\( 1 - 2978 T + 2191615 T^{2} - 357555834 T^{3} + 3692071571515 T^{4} - 5614366883406660 T^{5} + 955110819277629838 T^{6} - \)\(88\!\cdots\!84\)\( T^{7} + \)\(51\!\cdots\!73\)\( T^{8} - \)\(27\!\cdots\!42\)\( T^{9} - \)\(42\!\cdots\!91\)\( T^{10} - \)\(19\!\cdots\!98\)\( T^{11} + \)\(25\!\cdots\!53\)\( T^{12} - \)\(30\!\cdots\!56\)\( T^{13} + \)\(23\!\cdots\!98\)\( T^{14} - \)\(97\!\cdots\!40\)\( T^{15} + \)\(45\!\cdots\!15\)\( T^{16} - \)\(30\!\cdots\!26\)\( T^{17} + \)\(13\!\cdots\!15\)\( T^{18} - \)\(12\!\cdots\!62\)\( T^{19} + \)\(30\!\cdots\!01\)\( T^{20} \))(\( ( 1 + 1206 T + 749467 T^{2} + 850192614 T^{3} + 496981290961 T^{4} )^{2} \))
$97$ (\( 1 - 1208 T + 912673 T^{2} \))(\( 1 + 702 T + 912673 T^{2} \))(\( 1 + 498 T + 1796754 T^{2} + 454511154 T^{3} + 832972004929 T^{4} \))(\( 1 + 2448 T + 3286542 T^{2} + 2234223504 T^{3} + 832972004929 T^{4} \))(\( 1 + 1188 T + 2161254 T^{2} + 1084255524 T^{3} + 832972004929 T^{4} \))(\( 1 - 522 T + 291282 T^{2} - 476415306 T^{3} + 832972004929 T^{4} \))(\( 1 + 670 T + 1145410 T^{2} + 611490910 T^{3} + 832972004929 T^{4} \))(\( 1 - 8280178 T^{2} + 33803316226221 T^{4} - 90984674983855181258 T^{6} + \)\(18\!\cdots\!82\)\( T^{8} - \)\(29\!\cdots\!98\)\( T^{10} + \)\(38\!\cdots\!87\)\( T^{12} - \)\(44\!\cdots\!30\)\( T^{14} + \)\(43\!\cdots\!98\)\( T^{16} - \)\(36\!\cdots\!70\)\( T^{18} + \)\(26\!\cdots\!67\)\( T^{20} - \)\(16\!\cdots\!22\)\( T^{22} + \)\(87\!\cdots\!42\)\( T^{24} - \)\(36\!\cdots\!42\)\( T^{26} + \)\(11\!\cdots\!41\)\( T^{28} - \)\(23\!\cdots\!02\)\( T^{30} + \)\(23\!\cdots\!61\)\( T^{32} \))(\( 1 - 8280178 T^{2} + 33803316226221 T^{4} - 90984674983855181258 T^{6} + \)\(18\!\cdots\!82\)\( T^{8} - \)\(29\!\cdots\!98\)\( T^{10} + \)\(38\!\cdots\!87\)\( T^{12} - \)\(44\!\cdots\!30\)\( T^{14} + \)\(43\!\cdots\!98\)\( T^{16} - \)\(36\!\cdots\!70\)\( T^{18} + \)\(26\!\cdots\!67\)\( T^{20} - \)\(16\!\cdots\!22\)\( T^{22} + \)\(87\!\cdots\!42\)\( T^{24} - \)\(36\!\cdots\!42\)\( T^{26} + \)\(11\!\cdots\!41\)\( T^{28} - \)\(23\!\cdots\!02\)\( T^{30} + \)\(23\!\cdots\!61\)\( T^{32} \))(\( 1 - 3336954 T^{2} + 5694689958159 T^{4} - 6336320517980710252 T^{6} + \)\(47\!\cdots\!11\)\( T^{8} - \)\(23\!\cdots\!14\)\( T^{10} + \)\(57\!\cdots\!89\)\( T^{12} \))(\( 1 - 6782134 T^{2} + 21944276999789 T^{4} - 44851979434890226824 T^{6} + \)\(64\!\cdots\!18\)\( T^{8} - \)\(68\!\cdots\!04\)\( T^{10} + \)\(53\!\cdots\!22\)\( T^{12} - \)\(31\!\cdots\!84\)\( T^{14} + \)\(12\!\cdots\!21\)\( T^{16} - \)\(32\!\cdots\!54\)\( T^{18} + \)\(40\!\cdots\!49\)\( T^{20} \))(\( ( 1 + 897874 T^{2} + 832972004929 T^{4} )^{2} \))(\( ( 1 - 1352 T + 912673 T^{2} )^{2} \))(\( ( 1 - 1692 T + 1457670 T^{2} - 1544242716 T^{3} + 832972004929 T^{4} )^{2} \))(\( ( 1 + 1020 T + 828679 T^{2} - 17707848 T^{3} + 756312948967 T^{4} + 849631445027580 T^{5} + 760231058654565217 T^{6} )^{2} \))(\( ( 1 + 576 T + 2417013 T^{2} + 1510894720 T^{3} + 3259586132218 T^{4} + 2005403804499072 T^{5} + 2974936254049798714 T^{6} + \)\(12\!\cdots\!80\)\( T^{7} + \)\(18\!\cdots\!21\)\( T^{8} + \)\(39\!\cdots\!16\)\( T^{9} + \)\(63\!\cdots\!93\)\( T^{10} )^{2} \))(\( ( 1 + 2168 T + 2916885 T^{2} + 2446774560 T^{3} + 2052444429082 T^{4} + 1555642076834128 T^{5} + 1873210614423556186 T^{6} + \)\(20\!\cdots\!40\)\( T^{7} + \)\(22\!\cdots\!45\)\( T^{8} + \)\(15\!\cdots\!88\)\( T^{9} + \)\(63\!\cdots\!93\)\( T^{10} )^{2} \))(\( ( 1 + 24254 T^{2} + 832972004929 T^{4} )^{2} \))
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