Properties

Label 2016.3
Level 2016
Weight 3
Dimension 93942
Nonzero newspaces 60
Sturm bound 663552
Trace bound 40

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Defining parameters

Level: \( N \) = \( 2016\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \) \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(663552\)
Trace bound: \(40\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(2016))\).

Total New Old
Modular forms 224256 94842 129414
Cusp forms 218112 93942 124170
Eisenstein series 6144 900 5244

Trace form

\( 93942q - 48q^{2} - 48q^{3} - 48q^{4} - 56q^{5} - 64q^{6} - 44q^{7} - 120q^{8} - 96q^{9} + O(q^{10}) \) \( 93942q - 48q^{2} - 48q^{3} - 48q^{4} - 56q^{5} - 64q^{6} - 44q^{7} - 120q^{8} - 96q^{9} - 64q^{10} + 2q^{11} - 64q^{12} + 8q^{13} - 44q^{14} - 84q^{15} - 88q^{16} + 88q^{17} - 64q^{18} - 46q^{19} - 208q^{20} - 48q^{21} - 416q^{22} + 86q^{23} - 64q^{24} - 170q^{25} - 248q^{26} - 144q^{27} - 240q^{28} - 448q^{29} - 128q^{30} - 298q^{31} - 8q^{32} - 392q^{33} + 40q^{34} - 342q^{35} - 688q^{36} - 664q^{37} - 1280q^{38} - 276q^{39} - 1032q^{40} - 696q^{41} - 480q^{42} - 364q^{43} - 736q^{44} - 256q^{45} - 336q^{46} + 222q^{47} + 144q^{48} + 218q^{49} + 504q^{50} + 40q^{51} + 384q^{52} + 1256q^{53} + 1168q^{54} + 88q^{55} + 824q^{56} - 48q^{57} + 1704q^{58} - 350q^{59} + 1392q^{60} + 680q^{61} + 1080q^{62} - 282q^{63} + 96q^{64} - 476q^{65} - 64q^{66} + 106q^{67} + 1192q^{68} - 320q^{69} + 600q^{70} + 236q^{71} - 64q^{72} - 392q^{73} + 1008q^{74} - 64q^{75} + 976q^{76} - 28q^{77} + 656q^{78} - 1818q^{79} + 3160q^{80} + 800q^{81} + 2736q^{82} - 3088q^{83} + 1152q^{84} - 912q^{85} + 2312q^{86} - 1484q^{87} + 840q^{88} - 728q^{89} + 1376q^{90} - 1392q^{91} + 8q^{92} - 64q^{93} - 2328q^{94} - 294q^{95} - 336q^{96} - 968q^{97} - 2672q^{98} + 1484q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(2016))\)

We only show spaces with odd 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
2016.3.d \(\chi_{2016}(449, \cdot)\) 2016.3.d.a 4 1
2016.3.d.b 4
2016.3.d.c 4
2016.3.d.d 12
2016.3.d.e 12
2016.3.d.f 12
2016.3.e \(\chi_{2016}(1007, \cdot)\) 2016.3.e.a 8 1
2016.3.e.b 8
2016.3.e.c 48
2016.3.f \(\chi_{2016}(1441, \cdot)\) 2016.3.f.a 8 1
2016.3.f.b 8
2016.3.f.c 8
2016.3.f.d 8
2016.3.f.e 16
2016.3.f.f 16
2016.3.f.g 16
2016.3.g \(\chi_{2016}(1135, \cdot)\) 2016.3.g.a 4 1
2016.3.g.b 8
2016.3.g.c 24
2016.3.g.d 24
2016.3.l \(\chi_{2016}(433, \cdot)\) 2016.3.l.a 2 1
2016.3.l.b 2
2016.3.l.c 2
2016.3.l.d 4
2016.3.l.e 4
2016.3.l.f 8
2016.3.l.g 24
2016.3.l.h 32
2016.3.m \(\chi_{2016}(127, \cdot)\) 2016.3.m.a 4 1
2016.3.m.b 8
2016.3.m.c 8
2016.3.m.d 12
2016.3.m.e 12
2016.3.m.f 16
2016.3.n \(\chi_{2016}(1457, \cdot)\) 2016.3.n.a 48 1
2016.3.o \(\chi_{2016}(2015, \cdot)\) 2016.3.o.a 32 1
2016.3.o.b 32
2016.3.u \(\chi_{2016}(937, \cdot)\) None 0 2
2016.3.w \(\chi_{2016}(953, \cdot)\) None 0 2
2016.3.y \(\chi_{2016}(503, \cdot)\) None 0 2
2016.3.ba \(\chi_{2016}(631, \cdot)\) None 0 2
2016.3.bc \(\chi_{2016}(47, \cdot)\) n/a 376 2
2016.3.bd \(\chi_{2016}(65, \cdot)\) n/a 384 2
2016.3.bi \(\chi_{2016}(79, \cdot)\) n/a 376 2
2016.3.bj \(\chi_{2016}(1825, \cdot)\) n/a 384 2
2016.3.bk \(\chi_{2016}(1151, \cdot)\) n/a 128 2
2016.3.bl \(\chi_{2016}(305, \cdot)\) n/a 128 2
2016.3.bo \(\chi_{2016}(113, \cdot)\) n/a 288 2
2016.3.bp \(\chi_{2016}(383, \cdot)\) n/a 384 2
2016.3.bq \(\chi_{2016}(401, \cdot)\) n/a 376 2
2016.3.br \(\chi_{2016}(671, \cdot)\) n/a 384 2
2016.3.bv \(\chi_{2016}(1105, \cdot)\) n/a 376 2
2016.3.bw \(\chi_{2016}(1663, \cdot)\) n/a 384 2
2016.3.bx \(\chi_{2016}(241, \cdot)\) n/a 376 2
2016.3.by \(\chi_{2016}(799, \cdot)\) n/a 288 2
2016.3.cd \(\chi_{2016}(415, \cdot)\) n/a 160 2
2016.3.ce \(\chi_{2016}(145, \cdot)\) n/a 156 2
2016.3.cf \(\chi_{2016}(1423, \cdot)\) n/a 156 2
2016.3.cg \(\chi_{2016}(577, \cdot)\) n/a 160 2
2016.3.cl \(\chi_{2016}(97, \cdot)\) n/a 384 2
2016.3.cm \(\chi_{2016}(655, \cdot)\) n/a 376 2
2016.3.cn \(\chi_{2016}(481, \cdot)\) n/a 384 2
2016.3.co \(\chi_{2016}(463, \cdot)\) n/a 288 2
2016.3.ct \(\chi_{2016}(1121, \cdot)\) n/a 288 2
2016.3.cu \(\chi_{2016}(1391, \cdot)\) n/a 376 2
2016.3.cv \(\chi_{2016}(641, \cdot)\) n/a 384 2
2016.3.cw \(\chi_{2016}(335, \cdot)\) n/a 376 2
2016.3.db \(\chi_{2016}(143, \cdot)\) n/a 128 2
2016.3.dc \(\chi_{2016}(737, \cdot)\) n/a 128 2
2016.3.dd \(\chi_{2016}(319, \cdot)\) n/a 384 2
2016.3.de \(\chi_{2016}(817, \cdot)\) n/a 376 2
2016.3.di \(\chi_{2016}(1055, \cdot)\) n/a 384 2
2016.3.dj \(\chi_{2016}(977, \cdot)\) n/a 376 2
2016.3.dl \(\chi_{2016}(379, \cdot)\) n/a 960 4
2016.3.dn \(\chi_{2016}(251, \cdot)\) n/a 1024 4
2016.3.dp \(\chi_{2016}(181, \cdot)\) n/a 1272 4
2016.3.dr \(\chi_{2016}(197, \cdot)\) n/a 768 4
2016.3.dt \(\chi_{2016}(281, \cdot)\) None 0 4
2016.3.dv \(\chi_{2016}(265, \cdot)\) None 0 4
2016.3.dx \(\chi_{2016}(311, \cdot)\) None 0 4
2016.3.dy \(\chi_{2016}(151, \cdot)\) None 0 4
2016.3.eb \(\chi_{2016}(487, \cdot)\) None 0 4
2016.3.ed \(\chi_{2016}(215, \cdot)\) None 0 4
2016.3.ee \(\chi_{2016}(887, \cdot)\) None 0 4
2016.3.eh \(\chi_{2016}(583, \cdot)\) None 0 4
2016.3.ej \(\chi_{2016}(313, \cdot)\) None 0 4
2016.3.el \(\chi_{2016}(233, \cdot)\) None 0 4
2016.3.em \(\chi_{2016}(137, \cdot)\) None 0 4
2016.3.eo \(\chi_{2016}(745, \cdot)\) None 0 4
2016.3.er \(\chi_{2016}(73, \cdot)\) None 0 4
2016.3.et \(\chi_{2016}(473, \cdot)\) None 0 4
2016.3.ev \(\chi_{2016}(295, \cdot)\) None 0 4
2016.3.ex \(\chi_{2016}(167, \cdot)\) None 0 4
2016.3.ey \(\chi_{2016}(83, \cdot)\) n/a 6112 8
2016.3.fa \(\chi_{2016}(43, \cdot)\) n/a 4608 8
2016.3.fd \(\chi_{2016}(229, \cdot)\) n/a 6112 8
2016.3.fe \(\chi_{2016}(221, \cdot)\) n/a 6112 8
2016.3.ff \(\chi_{2016}(53, \cdot)\) n/a 2048 8
2016.3.fi \(\chi_{2016}(325, \cdot)\) n/a 2544 8
2016.3.fj \(\chi_{2016}(61, \cdot)\) n/a 6112 8
2016.3.fn \(\chi_{2016}(149, \cdot)\) n/a 6112 8
2016.3.fp \(\chi_{2016}(403, \cdot)\) n/a 6112 8
2016.3.fq \(\chi_{2016}(395, \cdot)\) n/a 2048 8
2016.3.fr \(\chi_{2016}(59, \cdot)\) n/a 6112 8
2016.3.fu \(\chi_{2016}(67, \cdot)\) n/a 6112 8
2016.3.fv \(\chi_{2016}(163, \cdot)\) n/a 2544 8
2016.3.fz \(\chi_{2016}(131, \cdot)\) n/a 6112 8
2016.3.ga \(\chi_{2016}(29, \cdot)\) n/a 4608 8
2016.3.gc \(\chi_{2016}(13, \cdot)\) n/a 6112 8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(2016))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(2016)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 15}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(672))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1008))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ (\( ( 1 - 5 T )^{4}( 1 + 5 T )^{4} \))(\( ( 1 + 625 T^{4} )^{2} \))(\( ( 1 - 42 T^{2} + 625 T^{4} )^{2} \))(\( ( 1 - 60 T^{2} + 2823 T^{4} - 78968 T^{6} + 1764375 T^{8} - 23437500 T^{10} + 244140625 T^{12} )^{2} \))(\( 1 - 88 T^{2} + 4446 T^{4} - 172312 T^{6} + 5715615 T^{8} - 163186704 T^{10} + 4221625796 T^{12} - 101991690000 T^{14} + 2232662109375 T^{16} - 42068359375000 T^{18} + 678405761718750 T^{20} - 8392333984375000 T^{22} + 59604644775390625 T^{24} \))(\( 1 - 88 T^{2} + 4446 T^{4} - 172312 T^{6} + 5715615 T^{8} - 163186704 T^{10} + 4221625796 T^{12} - 101991690000 T^{14} + 2232662109375 T^{16} - 42068359375000 T^{18} + 678405761718750 T^{20} - 8392333984375000 T^{22} + 59604644775390625 T^{24} \))(\( ( 1 - 2 T^{2} + 625 T^{4} )^{4} \))(\( ( 1 - 5 T )^{8}( 1 + 5 T )^{8} \))(\( ( 1 - 94 T^{4} + 390625 T^{8} )^{2} \))(\( ( 1 - 36 T^{2} + 1566 T^{4} - 22500 T^{6} + 390625 T^{8} )^{2} \))(\( ( 1 - 52 T^{2} + 1742 T^{4} - 32500 T^{6} + 390625 T^{8} )^{2} \))(\( ( 1 - 34 T^{2} + 625 T^{4} )^{4} \))(\( ( 1 - 68 T^{2} + 1832 T^{4} - 19020 T^{6} + 17294 T^{8} - 11887500 T^{10} + 715625000 T^{12} - 16601562500 T^{14} + 152587890625 T^{16} )^{2} \))(\( ( 1 - 42 T^{2} + 882 T^{4} - 26250 T^{6} + 390625 T^{8} )^{4} \))(\( ( 1 - 84 T^{2} + 3240 T^{4} - 80700 T^{6} + 1841294 T^{8} - 50437500 T^{10} + 1265625000 T^{12} - 20507812500 T^{14} + 152587890625 T^{16} )^{2} \))(\( 1 - 16 T^{2} - 254 T^{4} - 10000 T^{6} + 390625 T^{8} \))(\( 1 - 92 T^{2} + 5464 T^{4} - 211956 T^{6} + 6231214 T^{8} - 132472500 T^{10} + 2134375000 T^{12} - 22460937500 T^{14} + 152587890625 T^{16} \))(\( 1 + 22 T^{2} + 625 T^{4} \))(\( ( 1 + 25 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 625 T^{4} \))(\( ( 1 - 46 T^{2} + 625 T^{4} )^{2} \))(\( ( 1 + 25 T^{2} )^{4} \))(\( ( 1 + 56 T^{2} + 1602 T^{4} + 35000 T^{6} + 390625 T^{8} )^{2} \))(\( ( 1 - 4 T + 26 T^{2} - 100 T^{3} + 625 T^{4} )^{2} \))(\( ( 1 + 8 T + 104 T^{2} + 552 T^{3} + 3902 T^{4} + 13800 T^{5} + 65000 T^{6} + 125000 T^{7} + 390625 T^{8} )^{2} \))(\( ( 1 + 24 T^{2} + 224 T^{3} + 78 T^{4} + 5600 T^{5} + 15000 T^{6} + 390625 T^{8} )^{2} \))(\( ( 1 + 8 T + 74 T^{2} + 360 T^{3} + 1935 T^{4} + 8016 T^{5} + 41452 T^{6} + 200400 T^{7} + 1209375 T^{8} + 5625000 T^{9} + 28906250 T^{10} + 78125000 T^{11} + 244140625 T^{12} )^{2} \))(\( ( 1 - 8 T + 74 T^{2} - 360 T^{3} + 1935 T^{4} - 8016 T^{5} + 41452 T^{6} - 200400 T^{7} + 1209375 T^{8} - 5625000 T^{9} + 28906250 T^{10} - 78125000 T^{11} + 244140625 T^{12} )^{2} \))(\( ( 1 + 84 T^{2} + 80 T^{3} + 4452 T^{4} + 3344 T^{5} + 172204 T^{6} + 137760 T^{7} + 4809334 T^{8} + 3444000 T^{9} + 107627500 T^{10} + 52250000 T^{11} + 1739062500 T^{12} + 781250000 T^{13} + 20507812500 T^{14} + 152587890625 T^{16} )^{2} \))
$7$ (\( ( 1 - 7 T^{2} )^{2} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( ( 1 - 7 T^{2} )^{6} \))(\( ( 1 - 7 T^{2} )^{6} \))(\( ( 1 - 7 T^{2} )^{6} \))(\( ( 1 + 2 T^{2} + 2401 T^{4} )^{2} \))(\( ( 1 + 49 T^{2} )^{4} \))(\( ( 1 + 49 T^{2} )^{4} \))(\( 1 - 68 T^{2} + 2758 T^{4} - 163268 T^{6} + 5764801 T^{8} \))(\( 1 - 4 T^{2} + 1862 T^{4} - 9604 T^{6} + 5764801 T^{8} \))(\( ( 1 - 90 T^{2} + 2401 T^{4} )^{2} \))(\( 1 - 32 T^{2} + 380 T^{4} + 130080 T^{6} - 4071802 T^{8} + 312322080 T^{10} + 2190624380 T^{12} - 442921190432 T^{14} + 33232930569601 T^{16} \))(\( ( 1 - 8 T^{2} + 1582 T^{4} - 19208 T^{6} + 5764801 T^{8} )^{2} \))(\( 1 + 128 T^{2} + 8124 T^{4} + 294784 T^{6} + 10924550 T^{8} + 707776384 T^{10} + 46833243324 T^{12} + 1771684761728 T^{14} + 33232930569601 T^{16} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 + 7 T^{2} )^{4} \))(\( ( 1 + 7 T )^{2} \))(\( ( 1 + 7 T )^{2} \))(\( ( 1 - 7 T )^{2} \))(\( ( 1 - 10 T + 49 T^{2} )^{2} \))(\( ( 1 - 7 T )^{4} \))(\( ( 1 - 8 T + 102 T^{2} - 392 T^{3} + 2401 T^{4} )^{2} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 + 7 T^{2} )^{4} \))(\( ( 1 + 7 T^{2} )^{4} \))(\( ( 1 + 7 T^{2} )^{6} \))(\( ( 1 + 7 T^{2} )^{6} \))(\( ( 1 + 7 T^{2} )^{8} \))
$11$ (\( ( 1 - 228 T^{2} + 14641 T^{4} )^{2} \))(\( ( 1 - 18 T^{2} + 14641 T^{4} )^{2} \))(\( ( 1 - 116 T^{2} + 14641 T^{4} )^{2} \))(\( ( 1 - 138 T^{2} + 21459 T^{4} - 1576308 T^{6} + 314181219 T^{8} - 29581525578 T^{10} + 3138428376721 T^{12} )^{2} \))(\( 1 - 788 T^{2} + 295946 T^{4} - 73143140 T^{6} + 13895300031 T^{8} - 2185947504008 T^{10} + 288996636615340 T^{12} - 32004457406181128 T^{14} + 2978580965804425311 T^{16} - \)\(22\!\cdots\!40\)\( T^{18} + \)\(13\!\cdots\!06\)\( T^{20} - \)\(53\!\cdots\!88\)\( T^{22} + \)\(98\!\cdots\!41\)\( T^{24} \))(\( 1 - 788 T^{2} + 295946 T^{4} - 73143140 T^{6} + 13895300031 T^{8} - 2185947504008 T^{10} + 288996636615340 T^{12} - 32004457406181128 T^{14} + 2978580965804425311 T^{16} - \)\(22\!\cdots\!40\)\( T^{18} + \)\(13\!\cdots\!06\)\( T^{20} - \)\(53\!\cdots\!88\)\( T^{22} + \)\(98\!\cdots\!41\)\( T^{24} \))(\( ( 1 - 144 T^{2} + 14641 T^{4} )^{4} \))(\( ( 1 + 13154 T^{4} + 214358881 T^{8} )^{2} \))(\( ( 1 - 4318 T^{4} + 214358881 T^{8} )^{2} \))(\( ( 1 + 12 T^{2} - 12154 T^{4} + 175692 T^{6} + 214358881 T^{8} )^{2} \))(\( ( 1 + 236 T^{2} + 31430 T^{4} + 3455276 T^{6} + 214358881 T^{8} )^{2} \))(\( ( 1 + 170 T^{2} + 14641 T^{4} )^{4} \))(\( ( 1 + 484 T^{2} + 125624 T^{4} + 21925068 T^{6} + 2967080174 T^{8} + 321004920588 T^{10} + 26928620066744 T^{12} + 1518999334332964 T^{14} + 45949729863572161 T^{16} )^{2} \))(\( ( 1 + 258 T^{2} + 38642 T^{4} + 3777378 T^{6} + 214358881 T^{8} )^{4} \))(\( ( 1 + 660 T^{2} + 207160 T^{4} + 41252508 T^{6} + 5826809070 T^{8} + 603977969628 T^{10} + 44406585787960 T^{12} + 2071362728635860 T^{14} + 45949729863572161 T^{16} )^{2} \))(\( ( 1 - 8 T + 186 T^{2} - 968 T^{3} + 14641 T^{4} )^{2} \))(\( ( 1 + 16 T + 328 T^{2} + 4944 T^{3} + 49230 T^{4} + 598224 T^{5} + 4802248 T^{6} + 28344976 T^{7} + 214358881 T^{8} )^{2} \))(\( ( 1 - 11 T )^{2}( 1 + 11 T )^{2} \))(\( ( 1 - 6 T + 121 T^{2} )( 1 + 6 T + 121 T^{2} ) \))(\( ( 1 - 11 T )^{2}( 1 + 11 T )^{2} \))(\( ( 1 - 142 T^{2} + 14641 T^{4} )^{2} \))(\( ( 1 - 206 T^{2} + 14641 T^{4} )^{2} \))(\( ( 1 - 364 T^{2} + 59334 T^{4} - 5329324 T^{6} + 214358881 T^{8} )^{2} \))(\( 1 - 228 T^{2} + 35110 T^{4} - 3338148 T^{6} + 214358881 T^{8} \))(\( 1 - 720 T^{2} + 247100 T^{4} - 52647984 T^{6} + 7630714182 T^{8} - 770819133744 T^{10} + 52968079495100 T^{12} - 2259668431239120 T^{14} + 45949729863572161 T^{16} \))(\( 1 - 296 T^{2} + 72860 T^{4} - 12907416 T^{6} + 1704788486 T^{8} - 188977477656 T^{10} + 15618188069660 T^{12} - 928974799509416 T^{14} + 45949729863572161 T^{16} \))(\( 1 - 644 T^{2} + 191202 T^{4} - 35732660 T^{6} + 5112464783 T^{8} - 660287106440 T^{10} + 81869903390940 T^{12} - 9667263525388040 T^{14} + 1095902230035787823 T^{16} - \)\(11\!\cdots\!60\)\( T^{18} + \)\(87\!\cdots\!22\)\( T^{20} - \)\(43\!\cdots\!44\)\( T^{22} + \)\(98\!\cdots\!41\)\( T^{24} \))(\( 1 - 644 T^{2} + 191202 T^{4} - 35732660 T^{6} + 5112464783 T^{8} - 660287106440 T^{10} + 81869903390940 T^{12} - 9667263525388040 T^{14} + 1095902230035787823 T^{16} - \)\(11\!\cdots\!60\)\( T^{18} + \)\(87\!\cdots\!22\)\( T^{20} - \)\(43\!\cdots\!44\)\( T^{22} + \)\(98\!\cdots\!41\)\( T^{24} \))(\( 1 - 568 T^{2} + 171608 T^{4} - 37528232 T^{6} + 6700418780 T^{8} - 1058153018936 T^{10} + 154812072039528 T^{12} - 21114927937649640 T^{14} + 2662322500884271174 T^{16} - \)\(30\!\cdots\!40\)\( T^{18} + \)\(33\!\cdots\!68\)\( T^{20} - \)\(33\!\cdots\!56\)\( T^{22} + \)\(30\!\cdots\!80\)\( T^{24} - \)\(25\!\cdots\!32\)\( T^{26} + \)\(16\!\cdots\!28\)\( T^{28} - \)\(81\!\cdots\!08\)\( T^{30} + \)\(21\!\cdots\!21\)\( T^{32} \))
$13$ (\( ( 1 + 10 T + 169 T^{2} )^{4} \))(\( ( 1 + 169 T^{2} )^{4} \))(\( ( 1 - 14 T + 169 T^{2} )^{4} \))(\( ( 1 + 12 T + 303 T^{2} + 4120 T^{3} + 51207 T^{4} + 342732 T^{5} + 4826809 T^{6} )^{4} \))(\( ( 1 - 8 T + 558 T^{2} - 5000 T^{3} + 160239 T^{4} - 1297840 T^{5} + 31879908 T^{6} - 219334960 T^{7} + 4576586079 T^{8} - 24134045000 T^{9} + 455177742318 T^{10} - 1102867934792 T^{11} + 23298085122481 T^{12} )^{2} \))(\( ( 1 - 8 T + 558 T^{2} - 5000 T^{3} + 160239 T^{4} - 1297840 T^{5} + 31879908 T^{6} - 219334960 T^{7} + 4576586079 T^{8} - 24134045000 T^{9} + 455177742318 T^{10} - 1102867934792 T^{11} + 23298085122481 T^{12} )^{2} \))(\( ( 1 - 46 T^{2} + 28561 T^{4} )^{4} \))(\( ( 1 + 169 T^{2} )^{8} \))(\( ( 1 - 13 T )^{8}( 1 + 13 T )^{8} \))(\( ( 1 - 132 T^{2} + 37278 T^{4} - 3770052 T^{6} + 815730721 T^{8} )^{2} \))(\( ( 1 - 468 T^{2} + 102862 T^{4} - 13366548 T^{6} + 815730721 T^{8} )^{2} \))(\( ( 1 + 38 T^{2} + 28561 T^{4} )^{4} \))(\( ( 1 - 552 T^{2} + 203420 T^{4} - 51966360 T^{6} + 10048633734 T^{8} - 1484211207960 T^{10} + 165935943265820 T^{12} - 12860542987609512 T^{14} + 665416609183179841 T^{16} )^{2} \))(\( ( 1 - 444 T^{2} + 93462 T^{4} - 12681084 T^{6} + 815730721 T^{8} )^{4} \))(\( ( 1 - 648 T^{2} + 224988 T^{4} - 57121080 T^{6} + 11137246982 T^{8} - 1631435165880 T^{10} + 183529623456348 T^{12} - 15097159159367688 T^{14} + 665416609183179841 T^{16} )^{2} \))(\( 1 - 592 T^{2} + 143170 T^{4} - 16908112 T^{6} + 815730721 T^{8} \))(\( 1 - 444 T^{2} + 142936 T^{4} - 35361044 T^{6} + 6575436334 T^{8} - 1009946777684 T^{10} + 116597286336856 T^{12} - 10344349794381564 T^{14} + 665416609183179841 T^{16} \))(\( 1 + 310 T^{2} + 28561 T^{4} \))(\( ( 1 + 169 T^{2} )^{2} \))(\( 1 - 310 T^{2} + 28561 T^{4} \))(\( ( 1 + 169 T^{2} )^{4} \))(\( ( 1 + 169 T^{2} )^{4} \))(\( ( 1 + 344 T^{2} + 86658 T^{4} + 9824984 T^{6} + 815730721 T^{8} )^{2} \))(\( ( 1 + 4 T + 90 T^{2} + 676 T^{3} + 28561 T^{4} )^{2} \))(\( ( 1 + 32 T + 796 T^{2} + 14048 T^{3} + 200422 T^{4} + 2374112 T^{5} + 22734556 T^{6} + 154457888 T^{7} + 815730721 T^{8} )^{2} \))(\( ( 1 - 16 T + 696 T^{2} - 7536 T^{3} + 176398 T^{4} - 1273584 T^{5} + 19878456 T^{6} - 77228944 T^{7} + 815730721 T^{8} )^{2} \))(\( ( 1 - 12 T + 386 T^{2} - 3644 T^{3} + 56479 T^{4} - 216984 T^{5} + 6711132 T^{6} - 36670296 T^{7} + 1613096719 T^{8} - 17588891996 T^{9} + 314872058306 T^{10} - 1654301902188 T^{11} + 23298085122481 T^{12} )^{2} \))(\( ( 1 - 12 T + 386 T^{2} - 3644 T^{3} + 56479 T^{4} - 216984 T^{5} + 6711132 T^{6} - 36670296 T^{7} + 1613096719 T^{8} - 17588891996 T^{9} + 314872058306 T^{10} - 1654301902188 T^{11} + 23298085122481 T^{12} )^{2} \))(\( ( 1 - 8 T + 664 T^{2} - 4824 T^{3} + 225308 T^{4} - 1395464 T^{5} + 53184936 T^{6} - 270740888 T^{7} + 9879976070 T^{8} - 45755210072 T^{9} + 1519014957096 T^{10} - 6735638194376 T^{11} + 183790657287068 T^{12} - 665029364679576 T^{13} + 15469928521327384 T^{14} - 31499011085594312 T^{15} + 665416609183179841 T^{16} )^{2} \))
$17$ (\( ( 1 - 186 T^{2} + 83521 T^{4} )^{2} \))(\( ( 1 - 336 T^{2} + 83521 T^{4} )^{2} \))(\( ( 1 - 546 T^{2} + 83521 T^{4} )^{2} \))(\( ( 1 - 492 T^{2} + 95799 T^{4} - 13204248 T^{6} + 8001228279 T^{8} - 3432072660972 T^{10} + 582622237229761 T^{12} )^{2} \))(\( 1 - 1464 T^{2} + 915518 T^{4} - 326348920 T^{6} + 86562302975 T^{8} - 25140504641744 T^{10} + 7794388955640452 T^{12} - 2099760088183100624 T^{14} + \)\(60\!\cdots\!75\)\( T^{16} - \)\(19\!\cdots\!20\)\( T^{18} + \)\(44\!\cdots\!58\)\( T^{20} - \)\(59\!\cdots\!64\)\( T^{22} + \)\(33\!\cdots\!21\)\( T^{24} \))(\( 1 - 1464 T^{2} + 915518 T^{4} - 326348920 T^{6} + 86562302975 T^{8} - 25140504641744 T^{10} + 7794388955640452 T^{12} - 2099760088183100624 T^{14} + \)\(60\!\cdots\!75\)\( T^{16} - \)\(19\!\cdots\!20\)\( T^{18} + \)\(44\!\cdots\!58\)\( T^{20} - \)\(59\!\cdots\!64\)\( T^{22} + \)\(33\!\cdots\!21\)\( T^{24} \))(\( ( 1 + 530 T^{2} + 83521 T^{4} )^{4} \))(\( ( 1 + 289 T^{2} )^{8} \))(\( ( 1 - 135358 T^{4} + 6975757441 T^{8} )^{2} \))(\( ( 1 - 644 T^{2} + 270214 T^{4} - 53787524 T^{6} + 6975757441 T^{8} )^{2} \))(\( ( 1 - 4 T^{2} + 155270 T^{4} - 334084 T^{6} + 6975757441 T^{8} )^{2} \))(\( ( 1 - 30 T + 289 T^{2} )^{4}( 1 + 30 T + 289 T^{2} )^{4} \))(\( ( 1 - 1796 T^{2} + 1503272 T^{4} - 771720396 T^{6} + 267719274830 T^{8} - 64454859194316 T^{10} + 10486460839846952 T^{12} - 1046389538064650756 T^{14} + 48661191875666868481 T^{16} )^{2} \))(\( ( 1 - 698 T^{2} + 249202 T^{4} - 58297658 T^{6} + 6975757441 T^{8} )^{4} \))(\( ( 1 - 1012 T^{2} + 611880 T^{4} - 255929564 T^{6} + 83376383822 T^{8} - 21375493114844 T^{10} + 4268326462999080 T^{12} - 589613704076518132 T^{14} + 48661191875666868481 T^{16} )^{2} \))(\( ( 1 + 36 T + 870 T^{2} + 10404 T^{3} + 83521 T^{4} )^{2} \))(\( ( 1 - 40 T + 1308 T^{2} - 31512 T^{3} + 588230 T^{4} - 9106968 T^{5} + 109245468 T^{6} - 965502760 T^{7} + 6975757441 T^{8} )^{2} \))(\( ( 1 - 17 T )^{2}( 1 + 17 T )^{2} \))(\( ( 1 - 17 T )^{2}( 1 + 17 T )^{2} \))(\( ( 1 - 17 T )^{2}( 1 + 17 T )^{2} \))(\( ( 1 - 17 T )^{4}( 1 + 17 T )^{4} \))(\( ( 1 - 17 T )^{4}( 1 + 17 T )^{4} \))(\( ( 1 - 148 T^{2} + 165606 T^{4} - 12361108 T^{6} + 6975757441 T^{8} )^{2} \))(\( ( 1 - 28 T + 662 T^{2} - 8092 T^{3} + 83521 T^{4} )^{2} \))(\( ( 1 + 32 T + 968 T^{2} + 15600 T^{3} + 314654 T^{4} + 4508400 T^{5} + 80848328 T^{6} + 772402208 T^{7} + 6975757441 T^{8} )^{2} \))(\( ( 1 - 8 T + 428 T^{2} + 1416 T^{3} + 75814 T^{4} + 409224 T^{5} + 35746988 T^{6} - 193100552 T^{7} + 6975757441 T^{8} )^{2} \))(\( ( 1 + 40 T + 1610 T^{2} + 37864 T^{3} + 872767 T^{4} + 15204848 T^{5} + 282802860 T^{6} + 4394201072 T^{7} + 72894372607 T^{8} + 913944912616 T^{9} + 11230969480010 T^{10} + 80639756017960 T^{11} + 582622237229761 T^{12} )^{2} \))(\( ( 1 - 40 T + 1610 T^{2} - 37864 T^{3} + 872767 T^{4} - 15204848 T^{5} + 282802860 T^{6} - 4394201072 T^{7} + 72894372607 T^{8} - 913944912616 T^{9} + 11230969480010 T^{10} - 80639756017960 T^{11} + 582622237229761 T^{12} )^{2} \))(\( ( 1 - 8 T + 1460 T^{2} - 16744 T^{3} + 1091556 T^{4} - 13257752 T^{5} + 536903180 T^{6} - 6028156536 T^{7} + 184043682742 T^{8} - 1742137238904 T^{9} + 44842690496780 T^{10} - 320009903684888 T^{11} + 7614429889268196 T^{12} - 33755801869118056 T^{13} + 850628466355451060 T^{14} - 1347022612475207432 T^{15} + 48661191875666868481 T^{16} )^{2} \))
$19$ (\( ( 1 - 286 T^{2} + 130321 T^{4} )^{2} \))(\( ( 1 + 274 T^{2} + 130321 T^{4} )^{2} \))(\( ( 1 + 274 T^{2} + 130321 T^{4} )^{2} \))(\( ( 1 + 1158 T^{2} + 628287 T^{4} + 241762772 T^{6} + 81878990127 T^{8} + 19666966001478 T^{10} + 2213314919066161 T^{12} )^{2} \))(\( ( 1 + 32 T + 2086 T^{2} + 47776 T^{3} + 1756607 T^{4} + 30861376 T^{5} + 819613076 T^{6} + 11140956736 T^{7} + 228922780847 T^{8} + 2247664010656 T^{9} + 35427712503526 T^{10} + 196194120249632 T^{11} + 2213314919066161 T^{12} )^{2} \))(\( ( 1 - 32 T + 2086 T^{2} - 47776 T^{3} + 1756607 T^{4} - 30861376 T^{5} + 819613076 T^{6} - 11140956736 T^{7} + 228922780847 T^{8} - 2247664010656 T^{9} + 35427712503526 T^{10} - 196194120249632 T^{11} + 2213314919066161 T^{12} )^{2} \))(\( ( 1 - 626 T^{2} + 130321 T^{4} )^{4} \))(\( ( 1 - 19 T )^{8}( 1 + 19 T )^{8} \))(\( ( 1 - 622 T^{2} + 130321 T^{4} )^{4} \))(\( ( 1 - 372 T^{2} + 131646 T^{4} - 48479412 T^{6} + 16983563041 T^{8} )^{2} \))(\( ( 1 - 1188 T^{2} + 613294 T^{4} - 154821348 T^{6} + 16983563041 T^{8} )^{2} \))(\( ( 1 - 34 T + 361 T^{2} )^{4}( 1 + 34 T + 361 T^{2} )^{4} \))(\( ( 1 - 720 T^{2} + 107804 T^{4} - 48051504 T^{6} + 40419036678 T^{8} - 6262120052784 T^{10} + 1830896030071964 T^{12} - 1593586741727635920 T^{14} + \)\(28\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 - 480 T^{2} + 237342 T^{4} - 62554080 T^{6} + 16983563041 T^{8} )^{4} \))(\( ( 1 - 1680 T^{2} + 1396380 T^{4} - 772431216 T^{6} + 317847296774 T^{8} - 100664008500336 T^{10} + 23715507759191580 T^{12} - 3718369064031150480 T^{14} + \)\(28\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 + 4 T + 4 T^{2} + 1444 T^{3} + 130321 T^{4} )^{2} \))(\( ( 1 + 28 T + 1710 T^{2} + 31332 T^{3} + 975266 T^{4} + 11310852 T^{5} + 222848910 T^{6} + 1317284668 T^{7} + 16983563041 T^{8} )^{2} \))(\( 1 - 650 T^{2} + 130321 T^{4} \))(\( ( 1 + 361 T^{2} )^{2} \))(\( 1 + 650 T^{2} + 130321 T^{4} \))(\( ( 1 + 361 T^{2} )^{4} \))(\( ( 1 + 361 T^{2} )^{4} \))(\( ( 1 + 656 T^{2} + 327858 T^{4} + 85490576 T^{6} + 16983563041 T^{8} )^{2} \))(\( 1 - 348 T^{2} + 111718 T^{4} - 45351708 T^{6} + 16983563041 T^{8} \))(\( 1 - 2376 T^{2} + 2620892 T^{4} - 1746585720 T^{6} + 767524694790 T^{8} - 227616797616120 T^{10} + 44512084505652572 T^{12} - 5258836247701198536 T^{14} + \)\(28\!\cdots\!81\)\( T^{16} \))(\( 1 - 1936 T^{2} + 1795420 T^{4} - 1065665392 T^{6} + 449725089670 T^{8} - 138878579550832 T^{10} + 30492628755072220 T^{12} - 4284977683312087696 T^{14} + \)\(28\!\cdots\!81\)\( T^{16} \))(\( 1 - 2572 T^{2} + 3295394 T^{4} - 2806678172 T^{6} + 1778495598543 T^{8} - 885164316367896 T^{10} + 354799999408803420 T^{12} - \)\(11\!\cdots\!16\)\( T^{14} + \)\(30\!\cdots\!63\)\( T^{16} - \)\(62\!\cdots\!92\)\( T^{18} + \)\(95\!\cdots\!14\)\( T^{20} - \)\(96\!\cdots\!72\)\( T^{22} + \)\(48\!\cdots\!21\)\( T^{24} \))(\( 1 - 2572 T^{2} + 3295394 T^{4} - 2806678172 T^{6} + 1778495598543 T^{8} - 885164316367896 T^{10} + 354799999408803420 T^{12} - \)\(11\!\cdots\!16\)\( T^{14} + \)\(30\!\cdots\!63\)\( T^{16} - \)\(62\!\cdots\!92\)\( T^{18} + \)\(95\!\cdots\!14\)\( T^{20} - \)\(96\!\cdots\!72\)\( T^{22} + \)\(48\!\cdots\!21\)\( T^{24} \))(\( 1 - 1616 T^{2} + 1503864 T^{4} - 958989808 T^{6} + 454590996380 T^{8} - 158491050727248 T^{10} + 38845189362274888 T^{12} - 5743391356121447024 T^{14} + \)\(76\!\cdots\!10\)\( T^{16} - \)\(74\!\cdots\!04\)\( T^{18} + \)\(65\!\cdots\!08\)\( T^{20} - \)\(35\!\cdots\!28\)\( T^{22} + \)\(13\!\cdots\!80\)\( T^{24} - \)\(36\!\cdots\!08\)\( T^{26} + \)\(73\!\cdots\!44\)\( T^{28} - \)\(10\!\cdots\!56\)\( T^{30} + \)\(83\!\cdots\!61\)\( T^{32} \))
$23$ (\( ( 1 - 1044 T^{2} + 279841 T^{4} )^{2} \))(\( ( 1 - 834 T^{2} + 279841 T^{4} )^{2} \))(\( ( 1 - 932 T^{2} + 279841 T^{4} )^{2} \))(\( ( 1 - 570 T^{2} + 382755 T^{4} - 274121364 T^{6} + 107110541955 T^{8} - 44637261610170 T^{10} + 21914624432020321 T^{12} )^{2} \))(\( 1 - 3412 T^{2} + 5510506 T^{4} - 5616049124 T^{6} + 4124050945759 T^{8} - 2441569189763464 T^{10} + 1313577222733938284 T^{12} - \)\(68\!\cdots\!24\)\( T^{14} + \)\(32\!\cdots\!79\)\( T^{16} - \)\(12\!\cdots\!04\)\( T^{18} + \)\(33\!\cdots\!66\)\( T^{20} - \)\(58\!\cdots\!12\)\( T^{22} + \)\(48\!\cdots\!41\)\( T^{24} \))(\( 1 - 3412 T^{2} + 5510506 T^{4} - 5616049124 T^{6} + 4124050945759 T^{8} - 2441569189763464 T^{10} + 1313577222733938284 T^{12} - \)\(68\!\cdots\!24\)\( T^{14} + \)\(32\!\cdots\!79\)\( T^{16} - \)\(12\!\cdots\!04\)\( T^{18} + \)\(33\!\cdots\!66\)\( T^{20} - \)\(58\!\cdots\!12\)\( T^{22} + \)\(48\!\cdots\!41\)\( T^{24} \))(\( ( 1 - 624 T^{2} + 279841 T^{4} )^{4} \))(\( ( 1 - 20926 T^{4} + 78310985281 T^{8} )^{2} \))(\( ( 1 + 526082 T^{4} + 78310985281 T^{8} )^{2} \))(\( ( 1 + 1004 T^{2} + 516774 T^{4} + 280960364 T^{6} + 78310985281 T^{8} )^{2} \))(\( ( 1 + 1676 T^{2} + 1214822 T^{4} + 469013516 T^{6} + 78310985281 T^{8} )^{2} \))(\( ( 1 + 770 T^{2} + 279841 T^{4} )^{4} \))(\( ( 1 + 1780 T^{2} + 1176536 T^{4} + 252329916 T^{6} - 17847759250 T^{8} + 70612256023356 T^{10} + 92135693378566616 T^{12} + 39008031488996171380 T^{14} + \)\(61\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 + 1562 T^{2} + 1104114 T^{4} + 437111642 T^{6} + 78310985281 T^{8} )^{4} \))(\( ( 1 + 1444 T^{2} + 1005208 T^{4} + 384373516 T^{6} + 140491622638 T^{8} + 107563469090956 T^{10} + 78718828892343448 T^{12} + 31644717679837343524 T^{14} + \)\(61\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 - 268 T^{2} + 477286 T^{4} - 74997388 T^{6} + 78310985281 T^{8} \))(\( 1 - 1744 T^{2} + 1272156 T^{4} - 412076080 T^{6} + 99307893702 T^{8} - 115315782303280 T^{10} + 99623789791135836 T^{12} - 38219105009443439824 T^{14} + \)\(61\!\cdots\!61\)\( T^{16} \))(\( ( 1 + 10 T + 529 T^{2} )^{2} \))(\( ( 1 - 18 T + 529 T^{2} )^{2} \))(\( ( 1 + 10 T + 529 T^{2} )^{2} \))(\( ( 1 + 529 T^{2} )^{4} \))(\( ( 1 - 734 T^{2} + 279841 T^{4} )^{2} \))(\( ( 1 + 8 T + 642 T^{2} + 4232 T^{3} + 279841 T^{4} )^{4} \))(\( 1 - 1604 T^{2} + 1138374 T^{4} - 448864964 T^{6} + 78310985281 T^{8} \))(\( 1 - 2896 T^{2} + 3902332 T^{4} - 3323362480 T^{6} + 2032863959686 T^{8} - 930013079765680 T^{10} + 305595463813575292 T^{12} - 63464752355130849616 T^{14} + \)\(61\!\cdots\!61\)\( T^{16} \))(\( 1 - 1928 T^{2} + 2366876 T^{4} - 1917103032 T^{6} + 1186521008582 T^{8} - 536484029577912 T^{10} + 185352391597952156 T^{12} - 42251395904935178888 T^{14} + \)\(61\!\cdots\!61\)\( T^{16} \))(\( 1 - 3268 T^{2} + 5271042 T^{4} - 5712064692 T^{6} + 4715761171375 T^{8} - 3168464485539592 T^{10} + 1805463479913892636 T^{12} - \)\(88\!\cdots\!72\)\( T^{14} + \)\(36\!\cdots\!75\)\( T^{16} - \)\(12\!\cdots\!32\)\( T^{18} + \)\(32\!\cdots\!62\)\( T^{20} - \)\(56\!\cdots\!68\)\( T^{22} + \)\(48\!\cdots\!41\)\( T^{24} \))(\( 1 - 3268 T^{2} + 5271042 T^{4} - 5712064692 T^{6} + 4715761171375 T^{8} - 3168464485539592 T^{10} + 1805463479913892636 T^{12} - \)\(88\!\cdots\!72\)\( T^{14} + \)\(36\!\cdots\!75\)\( T^{16} - \)\(12\!\cdots\!32\)\( T^{18} + \)\(32\!\cdots\!62\)\( T^{20} - \)\(56\!\cdots\!68\)\( T^{22} + \)\(48\!\cdots\!41\)\( T^{24} \))(\( 1 - 2680 T^{2} + 3819992 T^{4} - 4018450664 T^{6} + 3538843517276 T^{8} - 2722647796005752 T^{10} + 1862831153417521128 T^{12} - \)\(11\!\cdots\!56\)\( T^{14} + \)\(63\!\cdots\!26\)\( T^{16} - \)\(32\!\cdots\!96\)\( T^{18} + \)\(14\!\cdots\!68\)\( T^{20} - \)\(59\!\cdots\!92\)\( T^{22} + \)\(21\!\cdots\!36\)\( T^{24} - \)\(68\!\cdots\!64\)\( T^{26} + \)\(18\!\cdots\!72\)\( T^{28} - \)\(36\!\cdots\!80\)\( T^{30} + \)\(37\!\cdots\!21\)\( T^{32} \))
$29$ (\( ( 1 + 707281 T^{4} )^{2} \))(\( ( 1 - 1680 T^{2} + 707281 T^{4} )^{2} \))(\( ( 1 - 1232 T^{2} + 707281 T^{4} )^{2} \))(\( ( 1 - 4704 T^{2} + 9492339 T^{4} - 10500907200 T^{6} + 6713751020259 T^{8} - 2353159126568544 T^{10} + 353814783205469041 T^{12} )^{2} \))(\( 1 - 4576 T^{2} + 10941414 T^{4} - 18431088480 T^{6} + 24224689239919 T^{8} - 26134795608984256 T^{10} + 23813832473001809620 T^{12} - \)\(18\!\cdots\!36\)\( T^{14} + \)\(12\!\cdots\!59\)\( T^{16} - \)\(65\!\cdots\!80\)\( T^{18} + \)\(27\!\cdots\!94\)\( T^{20} - \)\(80\!\cdots\!76\)\( T^{22} + \)\(12\!\cdots\!81\)\( T^{24} \))(\( 1 - 4576 T^{2} + 10941414 T^{4} - 18431088480 T^{6} + 24224689239919 T^{8} - 26134795608984256 T^{10} + 23813832473001809620 T^{12} - \)\(18\!\cdots\!36\)\( T^{14} + \)\(12\!\cdots\!59\)\( T^{16} - \)\(65\!\cdots\!80\)\( T^{18} + \)\(27\!\cdots\!94\)\( T^{20} - \)\(80\!\cdots\!76\)\( T^{22} + \)\(12\!\cdots\!81\)\( T^{24} \))(\( ( 1 + 1344 T^{2} + 707281 T^{4} )^{4} \))(\( ( 1 + 108194 T^{4} + 500246412961 T^{8} )^{2} \))(\( ( 1 + 841 T^{2} )^{8} \))(\( ( 1 + 4 T + 1398 T^{2} + 3364 T^{3} + 707281 T^{4} )^{4} \))(\( ( 1 - 28 T + 1142 T^{2} - 23548 T^{3} + 707281 T^{4} )^{4} \))(\( ( 1 + 1306 T^{2} + 707281 T^{4} )^{4} \))(\( ( 1 + 32 T + 1508 T^{2} + 2112 T^{3} + 496790 T^{4} + 1776192 T^{5} + 1066579748 T^{6} + 19034346272 T^{7} + 500246412961 T^{8} )^{4} \))(\( ( 1 + 92 T^{2} + 1300182 T^{4} + 65069852 T^{6} + 500246412961 T^{8} )^{4} \))(\( ( 1 - 32 T + 2260 T^{2} - 62144 T^{3} + 2787382 T^{4} - 52263104 T^{5} + 1598455060 T^{6} - 19034346272 T^{7} + 500246412961 T^{8} )^{4} \))(\( ( 1 - 1178 T^{2} + 707281 T^{4} )^{2} \))(\( 1 - 3384 T^{2} + 6555580 T^{4} - 8754768776 T^{6} + 8490907402822 T^{8} - 6192081614658056 T^{10} + 3279405379878872380 T^{12} - \)\(11\!\cdots\!44\)\( T^{14} + \)\(25\!\cdots\!21\)\( T^{16} \))(\( ( 1 - 29 T )^{2}( 1 + 29 T )^{2} \))(\( ( 1 - 54 T + 841 T^{2} )( 1 + 54 T + 841 T^{2} ) \))(\( ( 1 - 29 T )^{2}( 1 + 29 T )^{2} \))(\( ( 1 + 818 T^{2} + 707281 T^{4} )^{2} \))(\( ( 1 + 1234 T^{2} + 707281 T^{4} )^{2} \))(\( ( 1 - 1444 T^{2} + 1048038 T^{4} - 1021313764 T^{6} + 500246412961 T^{8} )^{2} \))(\( ( 1 + 20 T + 774 T^{2} + 16820 T^{3} + 707281 T^{4} )^{2} \))(\( ( 1 + 32 T + 1708 T^{2} + 38048 T^{3} + 1465030 T^{4} + 31998368 T^{5} + 1208035948 T^{6} + 19034346272 T^{7} + 500246412961 T^{8} )^{2} \))(\( ( 1 - 40 T + 3660 T^{2} - 100632 T^{3} + 4741126 T^{4} - 84631512 T^{5} + 2588648460 T^{6} - 23792932840 T^{7} + 500246412961 T^{8} )^{2} \))(\( ( 1 + 3110 T^{2} + 21248 T^{3} + 4689919 T^{4} + 44939520 T^{5} + 4702874772 T^{6} + 37794136320 T^{7} + 3317090600239 T^{8} + 12638805924608 T^{9} + 1555766344308710 T^{10} + 353814783205469041 T^{12} )^{2} \))(\( ( 1 + 3110 T^{2} - 21248 T^{3} + 4689919 T^{4} - 44939520 T^{5} + 4702874772 T^{6} - 37794136320 T^{7} + 3317090600239 T^{8} - 12638805924608 T^{9} + 1555766344308710 T^{10} + 353814783205469041 T^{12} )^{2} \))(\( ( 1 + 8 T + 2152 T^{2} + 6936 T^{3} + 2840252 T^{4} + 35865416 T^{5} + 3038036952 T^{6} + 47174886680 T^{7} + 2401820829254 T^{8} + 39674079697880 T^{9} + 2148745813447512 T^{10} + 21333585854166536 T^{11} + 1420825874905306172 T^{12} + 2918025370170194136 T^{13} + \)\(76\!\cdots\!32\)\( T^{14} + \)\(23\!\cdots\!48\)\( T^{15} + \)\(25\!\cdots\!21\)\( T^{16} )^{2} \))
$31$ (\( ( 1 + 130 T^{2} + 923521 T^{4} )^{2} \))(\( ( 1 + 130 T^{2} + 923521 T^{4} )^{2} \))(\( ( 1 + 914 T^{2} + 923521 T^{4} )^{2} \))(\( ( 1 + 4758 T^{2} + 10150095 T^{4} + 12487924084 T^{6} + 9373825884495 T^{8} + 4058055556144278 T^{10} + 787662783788549761 T^{12} )^{2} \))(\( ( 1 + 80 T + 4854 T^{2} + 204688 T^{3} + 7908175 T^{4} + 253266208 T^{5} + 8282803636 T^{6} + 243388825888 T^{7} + 7303365684175 T^{8} + 181661353456528 T^{9} + 4139933095738614 T^{10} + 65570262958464080 T^{11} + 787662783788549761 T^{12} )^{2} \))(\( ( 1 - 80 T + 4854 T^{2} - 204688 T^{3} + 7908175 T^{4} - 253266208 T^{5} + 8282803636 T^{6} - 243388825888 T^{7} + 7303365684175 T^{8} - 181661353456528 T^{9} + 4139933095738614 T^{10} - 65570262958464080 T^{11} + 787662783788549761 T^{12} )^{2} \))(\( ( 1 + 386 T^{2} + 923521 T^{4} )^{4} \))(\( ( 1 + 961 T^{2} )^{8} \))(\( ( 1 - 50 T + 961 T^{2} )^{4}( 1 + 50 T + 961 T^{2} )^{4} \))(\( ( 1 + 252 T^{2} - 435450 T^{4} + 232727292 T^{6} + 852891037441 T^{8} )^{2} \))(\( ( 1 - 2180 T^{2} + 2458118 T^{4} - 2013275780 T^{6} + 852891037441 T^{8} )^{2} \))(\( ( 1 - 954 T^{2} + 923521 T^{4} )^{4} \))(\( ( 1 - 2776 T^{2} + 4152380 T^{4} - 5486185320 T^{6} + 6167691221510 T^{8} - 5066607352911720 T^{10} + 3541527686049259580 T^{12} - \)\(21\!\cdots\!36\)\( T^{14} + \)\(72\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 - 2700 T^{2} + 3345942 T^{4} - 2493506700 T^{6} + 852891037441 T^{8} )^{4} \))(\( ( 1 - 5496 T^{2} + 14304252 T^{4} - 23493810888 T^{6} + 26784209493638 T^{8} - 21697027725096648 T^{10} + 12199968328097499132 T^{12} - \)\(43\!\cdots\!56\)\( T^{14} + \)\(72\!\cdots\!81\)\( T^{16} )^{2} \))(\( 1 - 1380 T^{2} + 1419974 T^{4} - 1274458980 T^{6} + 852891037441 T^{8} \))(\( 1 - 3944 T^{2} + 8438620 T^{4} - 12447428312 T^{6} + 13694235978694 T^{8} - 11495461442126552 T^{10} + 7197223366370371420 T^{12} - \)\(31\!\cdots\!84\)\( T^{14} + \)\(72\!\cdots\!81\)\( T^{16} \))(\( ( 1 - 31 T )^{2}( 1 + 31 T )^{2} \))(\( ( 1 - 31 T )^{2}( 1 + 31 T )^{2} \))(\( ( 1 - 31 T )^{2}( 1 + 31 T )^{2} \))(\( ( 1 - 38 T + 961 T^{2} )^{2}( 1 + 38 T + 961 T^{2} )^{2} \))(\( ( 1 - 31 T )^{4}( 1 + 31 T )^{4} \))(\( ( 1 + 140 T^{2} + 1206054 T^{4} + 129292940 T^{6} + 852891037441 T^{8} )^{2} \))(\( ( 1 - 1906 T^{2} + 923521 T^{4} )^{2} \))(\( 1 - 5896 T^{2} + 16111132 T^{4} - 27072775480 T^{6} + 31035743101510 T^{8} - 25002276684065080 T^{10} + 13741040085828893212 T^{12} - \)\(46\!\cdots\!56\)\( T^{14} + \)\(72\!\cdots\!81\)\( T^{16} \))(\( 1 - 3624 T^{2} + 5953500 T^{4} - 5905968152 T^{6} + 5172694104774 T^{8} - 5454285613703192 T^{10} + 5077686791404993500 T^{12} - \)\(28\!\cdots\!64\)\( T^{14} + \)\(72\!\cdots\!81\)\( T^{16} \))(\( 1 - 7340 T^{2} + 24952962 T^{4} - 52480410364 T^{6} + 78028577767919 T^{8} - 91071297834552920 T^{10} + 91962598141207812380 T^{12} - \)\(84\!\cdots\!20\)\( T^{14} + \)\(66\!\cdots\!79\)\( T^{16} - \)\(41\!\cdots\!04\)\( T^{18} + \)\(18\!\cdots\!22\)\( T^{20} - \)\(49\!\cdots\!40\)\( T^{22} + \)\(62\!\cdots\!21\)\( T^{24} \))(\( 1 - 7340 T^{2} + 24952962 T^{4} - 52480410364 T^{6} + 78028577767919 T^{8} - 91071297834552920 T^{10} + 91962598141207812380 T^{12} - \)\(84\!\cdots\!20\)\( T^{14} + \)\(66\!\cdots\!79\)\( T^{16} - \)\(41\!\cdots\!04\)\( T^{18} + \)\(18\!\cdots\!22\)\( T^{20} - \)\(49\!\cdots\!40\)\( T^{22} + \)\(62\!\cdots\!21\)\( T^{24} \))(\( 1 - 2448 T^{2} + 4544376 T^{4} - 6660944560 T^{6} + 9940033472796 T^{8} - 12711964760567440 T^{10} + 15108037137965584456 T^{12} - \)\(15\!\cdots\!88\)\( T^{14} + \)\(16\!\cdots\!18\)\( T^{16} - \)\(14\!\cdots\!48\)\( T^{18} + \)\(12\!\cdots\!96\)\( T^{20} - \)\(10\!\cdots\!40\)\( T^{22} + \)\(72\!\cdots\!76\)\( T^{24} - \)\(44\!\cdots\!60\)\( T^{26} + \)\(28\!\cdots\!96\)\( T^{28} - \)\(14\!\cdots\!68\)\( T^{30} + \)\(52\!\cdots\!61\)\( T^{32} \))
$37$ (\( ( 1 - 28 T + 1369 T^{2} )^{4} \))(\( ( 1 - 38 T + 1369 T^{2} )^{4} \))(\( ( 1 + 60 T + 1369 T^{2} )^{4} \))(\( ( 1 + 42 T + 4443 T^{2} + 115220 T^{3} + 6082467 T^{4} + 78714762 T^{5} + 2565726409 T^{6} )^{4} \))(\( ( 1 - 28 T + 5978 T^{2} - 158572 T^{3} + 16822575 T^{4} - 392980952 T^{5} + 28773500620 T^{6} - 537990923288 T^{7} + 31528213984575 T^{8} - 406852368127948 T^{9} + 20997602175539738 T^{10} - 134640362427699772 T^{11} + 6582952005840035281 T^{12} )^{2} \))(\( ( 1 - 28 T + 5978 T^{2} - 158572 T^{3} + 16822575 T^{4} - 392980952 T^{5} + 28773500620 T^{6} - 537990923288 T^{7} + 31528213984575 T^{8} - 406852368127948 T^{9} + 20997602175539738 T^{10} - 134640362427699772 T^{11} + 6582952005840035281 T^{12} )^{2} \))(\( ( 1 - 2062 T^{2} + 1874161 T^{4} )^{4} \))(\( ( 1 - 1294 T^{2} + 1874161 T^{4} )^{4} \))(\( ( 1 - 2638 T^{2} + 1874161 T^{4} )^{4} \))(\( ( 1 + 12 T + 1206 T^{2} + 16428 T^{3} + 1874161 T^{4} )^{4} \))(\( ( 1 - 52 T + 2678 T^{2} - 71188 T^{3} + 1874161 T^{4} )^{4} \))(\( ( 1 + 26 T + 1369 T^{2} )^{8} \))(\( ( 1 + 52 T + 5240 T^{2} + 204636 T^{3} + 10582478 T^{4} + 280146684 T^{5} + 9820603640 T^{6} + 133417773268 T^{7} + 3512479453921 T^{8} )^{4} \))(\( ( 1 - 6 T + 1938 T^{2} - 8214 T^{3} + 1874161 T^{4} )^{8} \))(\( ( 1 - 12 T + 2424 T^{2} - 104676 T^{3} + 2704334 T^{4} - 143301444 T^{5} + 4542966264 T^{6} - 30788716908 T^{7} + 3512479453921 T^{8} )^{4} \))(\( 1 - 1780 T^{2} + 2031622 T^{4} - 3336006580 T^{6} + 3512479453921 T^{8} \))(\( 1 - 3512 T^{2} + 9188668 T^{4} - 18622781448 T^{6} + 27544347275206 T^{8} - 34902090701365128 T^{10} + 32275007558901367228 T^{12} - \)\(23\!\cdots\!72\)\( T^{14} + \)\(12\!\cdots\!41\)\( T^{16} \))(\( ( 1 - 37 T )^{2}( 1 + 37 T )^{2} \))(\( ( 1 - 38 T + 1369 T^{2} )( 1 + 38 T + 1369 T^{2} ) \))(\( ( 1 - 37 T )^{2}( 1 + 37 T )^{2} \))(\( ( 1 - 37 T )^{4}( 1 + 37 T )^{4} \))(\( ( 1 - 38 T + 1369 T^{2} )^{2}( 1 + 38 T + 1369 T^{2} )^{2} \))(\( ( 1 - 4612 T^{2} + 8955366 T^{4} - 8643630532 T^{6} + 3512479453921 T^{8} )^{2} \))(\( ( 1 - 68 T + 3782 T^{2} - 93092 T^{3} + 1874161 T^{4} )^{2} \))(\( ( 1 - 64 T + 4220 T^{2} - 216768 T^{3} + 8557286 T^{4} - 296755392 T^{5} + 7908959420 T^{6} - 164206490176 T^{7} + 3512479453921 T^{8} )^{2} \))(\( ( 1 + 88 T + 3692 T^{2} + 66024 T^{3} + 510982 T^{4} + 90386856 T^{5} + 6919402412 T^{6} + 225783923992 T^{7} + 3512479453921 T^{8} )^{2} \))(\( ( 1 - 4 T + 4562 T^{2} - 79444 T^{3} + 11000959 T^{4} - 208839944 T^{5} + 18676988604 T^{6} - 285901883336 T^{7} + 20617568320399 T^{8} - 203831568836596 T^{9} + 16023931268787602 T^{10} - 19234337489671396 T^{11} + 6582952005840035281 T^{12} )^{2} \))(\( ( 1 - 4 T + 4562 T^{2} - 79444 T^{3} + 11000959 T^{4} - 208839944 T^{5} + 18676988604 T^{6} - 285901883336 T^{7} + 20617568320399 T^{8} - 203831568836596 T^{9} + 16023931268787602 T^{10} - 19234337489671396 T^{11} + 6582952005840035281 T^{12} )^{2} \))(\( ( 1 + 56 T + 8696 T^{2} + 389992 T^{3} + 34664796 T^{4} + 1289117240 T^{5} + 84548927816 T^{6} + 2643048584616 T^{7} + 139161224552326 T^{8} + 3618333512339304 T^{9} + 158458303104562376 T^{10} + 3307522146965191160 T^{11} + \)\(12\!\cdots\!16\)\( T^{12} + \)\(18\!\cdots\!08\)\( T^{13} + \)\(57\!\cdots\!76\)\( T^{14} + \)\(50\!\cdots\!84\)\( T^{15} + \)\(12\!\cdots\!41\)\( T^{16} )^{2} \))
$41$ (\( ( 1 - 1314 T^{2} + 2825761 T^{4} )^{2} \))(\( ( 1 + 336 T^{2} + 2825761 T^{4} )^{2} \))(\( ( 1 - 3290 T^{2} + 2825761 T^{4} )^{2} \))(\( ( 1 - 9708 T^{2} + 39870615 T^{4} - 88679839128 T^{6} + 112664828913015 T^{8} - 77517654124306668 T^{10} + 22563490300366186081 T^{12} )^{2} \))(\( 1 - 7352 T^{2} + 32864510 T^{4} - 105328464248 T^{6} + 273805951205439 T^{8} - 590413137426539984 T^{10} + \)\(10\!\cdots\!84\)\( T^{12} - \)\(16\!\cdots\!24\)\( T^{14} + \)\(21\!\cdots\!19\)\( T^{16} - \)\(23\!\cdots\!88\)\( T^{18} + \)\(20\!\cdots\!10\)\( T^{20} - \)\(13\!\cdots\!52\)\( T^{22} + \)\(50\!\cdots\!61\)\( T^{24} \))(\( 1 - 7352 T^{2} + 32864510 T^{4} - 105328464248 T^{6} + 273805951205439 T^{8} - 590413137426539984 T^{10} + \)\(10\!\cdots\!84\)\( T^{12} - \)\(16\!\cdots\!24\)\( T^{14} + \)\(21\!\cdots\!19\)\( T^{16} - \)\(23\!\cdots\!88\)\( T^{18} + \)\(20\!\cdots\!10\)\( T^{20} - \)\(13\!\cdots\!52\)\( T^{22} + \)\(50\!\cdots\!61\)\( T^{24} \))(\( ( 1 - 526 T^{2} + 2825761 T^{4} )^{4} \))(\( ( 1 + 1681 T^{2} )^{8} \))(\( ( 1 - 4058878 T^{4} + 7984925229121 T^{8} )^{2} \))(\( ( 1 - 1988 T^{2} + 1048390 T^{4} - 5617612868 T^{6} + 7984925229121 T^{8} )^{2} \))(\( ( 1 - 4868 T^{2} + 10725062 T^{4} - 13755804548 T^{6} + 7984925229121 T^{8} )^{2} \))(\( ( 1 - 1058 T^{2} + 2825761 T^{4} )^{4} \))(\( ( 1 - 9508 T^{2} + 43997096 T^{4} - 128346111276 T^{6} + 257361029033678 T^{8} - 362675435745381036 T^{10} + \)\(35\!\cdots\!16\)\( T^{12} - \)\(21\!\cdots\!48\)\( T^{14} + \)\(63\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 - 6266 T^{2} + 15427570 T^{4} - 17706218426 T^{6} + 7984925229121 T^{8} )^{4} \))(\( ( 1 - 6100 T^{2} + 16559016 T^{4} - 28948198268 T^{6} + 45761601438926 T^{8} - 81800689685981948 T^{10} + \)\(13\!\cdots\!36\)\( T^{12} - \)\(13\!\cdots\!00\)\( T^{14} + \)\(63\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 - 20 T + 3174 T^{2} - 33620 T^{3} + 2825761 T^{4} )^{2} \))(\( ( 1 + 64 T + 4956 T^{2} + 221760 T^{3} + 11848326 T^{4} + 372778560 T^{5} + 14004471516 T^{6} + 304006671424 T^{7} + 7984925229121 T^{8} )^{2} \))(\( ( 1 - 41 T )^{2}( 1 + 41 T )^{2} \))(\( ( 1 - 41 T )^{2}( 1 + 41 T )^{2} \))(\( ( 1 - 41 T )^{2}( 1 + 41 T )^{2} \))(\( ( 1 - 41 T )^{4}( 1 + 41 T )^{4} \))(\( ( 1 - 41 T )^{4}( 1 + 41 T )^{4} \))(\( ( 1 - 5380 T^{2} + 12875334 T^{4} - 15202594180 T^{6} + 7984925229121 T^{8} )^{2} \))(\( ( 1 - 60 T + 4150 T^{2} - 100860 T^{3} + 2825761 T^{4} )^{2} \))(\( ( 1 + 5384 T^{2} - 21168 T^{3} + 12368094 T^{4} - 35583408 T^{5} + 15213897224 T^{6} + 7984925229121 T^{8} )^{2} \))(\( ( 1 + 72 T + 4364 T^{2} + 180408 T^{3} + 8880422 T^{4} + 303265848 T^{5} + 12331621004 T^{6} + 342007505352 T^{7} + 7984925229121 T^{8} )^{2} \))(\( ( 1 + 24 T + 5610 T^{2} + 109272 T^{3} + 12333791 T^{4} + 221579664 T^{5} + 19306356972 T^{6} + 372475415184 T^{7} + 34852345589951 T^{8} + 519053390622552 T^{9} + 44795430535368810 T^{10} + 322143823443657624 T^{11} + 22563490300366186081 T^{12} )^{2} \))(\( ( 1 - 24 T + 5610 T^{2} - 109272 T^{3} + 12333791 T^{4} - 221579664 T^{5} + 19306356972 T^{6} - 372475415184 T^{7} + 34852345589951 T^{8} - 519053390622552 T^{9} + 44795430535368810 T^{10} - 322143823443657624 T^{11} + 22563490300366186081 T^{12} )^{2} \))(\( ( 1 + 120 T + 10612 T^{2} + 619224 T^{3} + 32879204 T^{4} + 1430831784 T^{5} + 62637551820 T^{6} + 2429685088776 T^{7} + 102774652510262 T^{8} + 4084300634232456 T^{9} + 176998751068435020 T^{10} + 6796600125335995944 T^{11} + \)\(26\!\cdots\!84\)\( T^{12} + \)\(83\!\cdots\!24\)\( T^{13} + \)\(23\!\cdots\!72\)\( T^{14} + \)\(45\!\cdots\!20\)\( T^{15} + \)\(63\!\cdots\!41\)\( T^{16} )^{2} \))
$43$ (\( ( 1 - 3470 T^{2} + 3418801 T^{4} )^{2} \))(\( ( 1 + 3250 T^{2} + 3418801 T^{4} )^{2} \))(\( ( 1 + 3250 T^{2} + 3418801 T^{4} )^{2} \))(\( ( 1 - 2346 T^{2} + 2543199 T^{4} + 1087388980 T^{6} + 8694691284399 T^{8} - 27420517851251946 T^{10} + 39959630797262576401 T^{12} )^{2} \))(\( ( 1 - 32 T + 7126 T^{2} - 257440 T^{3} + 24503903 T^{4} - 910093120 T^{5} + 54452273972 T^{6} - 1682762178880 T^{7} + 83773968080303 T^{8} - 1627371703334560 T^{9} + 83290115178184726 T^{10} - 691567434025095968 T^{11} + 39959630797262576401 T^{12} )^{2} \))(\( ( 1 + 32 T + 7126 T^{2} + 257440 T^{3} + 24503903 T^{4} + 910093120 T^{5} + 54452273972 T^{6} + 1682762178880 T^{7} + 83773968080303 T^{8} + 1627371703334560 T^{9} + 83290115178184726 T^{10} + 691567434025095968 T^{11} + 39959630797262576401 T^{12} )^{2} \))(\( ( 1 + 48 T + 1849 T^{2} )^{8} \))(\( ( 1 - 334 T^{2} + 3418801 T^{4} )^{4} \))(\( ( 1 + 1849 T^{2} )^{8} \))(\( ( 1 + 6284 T^{2} + 16414854 T^{4} + 21483745484 T^{6} + 11688200277601 T^{8} )^{2} \))(\( ( 1 + 2540 T^{2} + 7272902 T^{4} + 8683754540 T^{6} + 11688200277601 T^{8} )^{2} \))(\( ( 1 + 3510 T^{2} + 3418801 T^{4} )^{4} \))(\( ( 1 + 3616 T^{2} + 12466364 T^{4} + 23501904864 T^{6} + 51294198367046 T^{8} + 80348335850948064 T^{10} + \)\(14\!\cdots\!64\)\( T^{12} + \)\(14\!\cdots\!16\)\( T^{14} + \)\(13\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 - 712 T^{2} + 6702222 T^{4} - 2434186312 T^{6} + 11688200277601 T^{8} )^{4} \))(\( ( 1 + 7936 T^{2} + 34459516 T^{4} + 101370636544 T^{6} + 218058648174022 T^{8} + 346566033587263744 T^{10} + \)\(40\!\cdots\!16\)\( T^{12} + \)\(31\!\cdots\!36\)\( T^{14} + \)\(13\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 - 40 T + 4090 T^{2} - 73960 T^{3} + 3418801 T^{4} )^{2} \))(\( ( 1 + 4680 T^{2} + 58016 T^{3} + 10251086 T^{4} + 107271584 T^{5} + 15999988680 T^{6} + 11688200277601 T^{8} )^{2} \))(\( ( 1 - 43 T )^{2}( 1 + 43 T )^{2} \))(\( ( 1 - 58 T + 1849 T^{2} )( 1 + 58 T + 1849 T^{2} ) \))(\( ( 1 - 43 T )^{2}( 1 + 43 T )^{2} \))(\( ( 1 - 43 T )^{4}( 1 + 43 T )^{4} \))(\( ( 1 - 58 T + 1849 T^{2} )^{2}( 1 + 58 T + 1849 T^{2} )^{2} \))(\( ( 1 - 1324 T^{2} + 5788998 T^{4} - 4526492524 T^{6} + 11688200277601 T^{8} )^{2} \))(\( 1 - 1508 T^{2} + 5793318 T^{4} - 5155551908 T^{6} + 11688200277601 T^{8} \))(\( 1 - 8200 T^{2} + 33845980 T^{4} - 91985805496 T^{6} + 190535158400902 T^{8} - 314481163815530296 T^{10} + \)\(39\!\cdots\!80\)\( T^{12} - \)\(32\!\cdots\!00\)\( T^{14} + \)\(13\!\cdots\!01\)\( T^{16} \))(\( 1 - 4392 T^{2} + 15655580 T^{4} - 32786290584 T^{6} + 70340912004102 T^{8} - 112089803034869784 T^{10} + \)\(18\!\cdots\!80\)\( T^{12} - \)\(17\!\cdots\!92\)\( T^{14} + \)\(13\!\cdots\!01\)\( T^{16} \))(\( 1 - 14156 T^{2} + 94495970 T^{4} - 406877897820 T^{6} + 1300026263155855 T^{8} - 3294725001750613144 T^{10} + \)\(67\!\cdots\!44\)\( T^{12} - \)\(11\!\cdots\!44\)\( T^{14} + \)\(15\!\cdots\!55\)\( T^{16} - \)\(16\!\cdots\!20\)\( T^{18} + \)\(12\!\cdots\!70\)\( T^{20} - \)\(66\!\cdots\!56\)\( T^{22} + \)\(15\!\cdots\!01\)\( T^{24} \))(\( 1 - 14156 T^{2} + 94495970 T^{4} - 406877897820 T^{6} + 1300026263155855 T^{8} - 3294725001750613144 T^{10} + \)\(67\!\cdots\!44\)\( T^{12} - \)\(11\!\cdots\!44\)\( T^{14} + \)\(15\!\cdots\!55\)\( T^{16} - \)\(16\!\cdots\!20\)\( T^{18} + \)\(12\!\cdots\!70\)\( T^{20} - \)\(66\!\cdots\!56\)\( T^{22} + \)\(15\!\cdots\!01\)\( T^{24} \))(\( 1 - 16272 T^{2} + 136621816 T^{4} - 780160752048 T^{6} + 3370386034053532 T^{8} - 11622652546480860816 T^{10} + \)\(32\!\cdots\!76\)\( T^{12} - \)\(78\!\cdots\!56\)\( T^{14} + \)\(15\!\cdots\!30\)\( T^{16} - \)\(26\!\cdots\!56\)\( T^{18} + \)\(38\!\cdots\!76\)\( T^{20} - \)\(46\!\cdots\!16\)\( T^{22} + \)\(46\!\cdots\!32\)\( T^{24} - \)\(36\!\cdots\!48\)\( T^{26} + \)\(21\!\cdots\!16\)\( T^{28} - \)\(88\!\cdots\!72\)\( T^{30} + \)\(18\!\cdots\!01\)\( T^{32} \))
$47$ (\( ( 1 - 3018 T^{2} + 4879681 T^{4} )^{2} \))(\( ( 1 - 47 T )^{4}( 1 + 47 T )^{4} \))(\( ( 1 - 1674 T^{2} + 4879681 T^{4} )^{2} \))(\( ( 1 - 8214 T^{2} + 36280911 T^{4} - 98157210612 T^{6} + 177039272069391 T^{8} - 195585908639704854 T^{10} + \)\(11\!\cdots\!41\)\( T^{12} )^{2} \))(\( 1 - 10156 T^{2} + 38899074 T^{4} - 59018079996 T^{6} + 10144766384239 T^{8} - 44523315051525208 T^{10} + \)\(35\!\cdots\!76\)\( T^{12} - \)\(21\!\cdots\!48\)\( T^{14} + \)\(24\!\cdots\!79\)\( T^{16} - \)\(68\!\cdots\!36\)\( T^{18} + \)\(22\!\cdots\!54\)\( T^{20} - \)\(28\!\cdots\!56\)\( T^{22} + \)\(13\!\cdots\!81\)\( T^{24} \))(\( 1 - 10156 T^{2} + 38899074 T^{4} - 59018079996 T^{6} + 10144766384239 T^{8} - 44523315051525208 T^{10} + \)\(35\!\cdots\!76\)\( T^{12} - \)\(21\!\cdots\!48\)\( T^{14} + \)\(24\!\cdots\!79\)\( T^{16} - \)\(68\!\cdots\!36\)\( T^{18} + \)\(22\!\cdots\!54\)\( T^{20} - \)\(28\!\cdots\!56\)\( T^{22} + \)\(13\!\cdots\!81\)\( T^{24} \))(\( ( 1 - 3650 T^{2} + 4879681 T^{4} )^{4} \))(\( ( 1 - 47 T )^{8}( 1 + 47 T )^{8} \))(\( ( 1 - 47 T )^{8}( 1 + 47 T )^{8} \))(\( ( 1 - 5892 T^{2} + 16275078 T^{4} - 28751080452 T^{6} + 23811286661761 T^{8} )^{2} \))(\( ( 1 - 6788 T^{2} + 21266822 T^{4} - 33123274628 T^{6} + 23811286661761 T^{8} )^{2} \))(\( ( 1 - 1410 T^{2} + 4879681 T^{4} )^{4} \))(\( ( 1 - 6952 T^{2} + 23013596 T^{4} - 51270422808 T^{6} + 106001703272390 T^{8} - 250183308038164248 T^{10} + \)\(54\!\cdots\!56\)\( T^{12} - \)\(80\!\cdots\!32\)\( T^{14} + \)\(56\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 + 444 T^{2} + 8980230 T^{4} + 2166578364 T^{6} + 23811286661761 T^{8} )^{4} \))(\( ( 1 - 11304 T^{2} + 55926492 T^{4} - 169651114008 T^{6} + 399786222400454 T^{8} - 827843317653671448 T^{10} + \)\(13\!\cdots\!12\)\( T^{12} - \)\(13\!\cdots\!64\)\( T^{14} + \)\(56\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 - 7492 T^{2} + 23390470 T^{4} - 36558570052 T^{6} + 23811286661761 T^{8} \))(\( 1 - 8392 T^{2} + 39566748 T^{4} - 127207295352 T^{6} + 316693927920198 T^{8} - 620731022190542712 T^{10} + \)\(94\!\cdots\!28\)\( T^{12} - \)\(97\!\cdots\!72\)\( T^{14} + \)\(56\!\cdots\!21\)\( T^{16} \))(\( ( 1 - 47 T )^{2}( 1 + 47 T )^{2} \))(\( ( 1 - 47 T )^{2}( 1 + 47 T )^{2} \))(\( ( 1 - 47 T )^{2}( 1 + 47 T )^{2} \))(\( ( 1 - 47 T )^{4}( 1 + 47 T )^{4} \))(\( ( 1 - 47 T )^{4}( 1 + 47 T )^{4} \))(\( ( 1 - 4852 T^{2} + 14998950 T^{4} - 23676212212 T^{6} + 23811286661761 T^{8} )^{2} \))(\( 1 - 5348 T^{2} + 14587206 T^{4} - 26096533988 T^{6} + 23811286661761 T^{8} \))(\( 1 - 11176 T^{2} + 64536028 T^{4} - 240115798168 T^{6} + 627402380719558 T^{8} - 1171688498120224408 T^{10} + \)\(15\!\cdots\!08\)\( T^{12} - \)\(12\!\cdots\!16\)\( T^{14} + \)\(56\!\cdots\!21\)\( T^{16} \))(\( 1 - 6696 T^{2} + 34041564 T^{4} - 108976927256 T^{6} + 286725887177670 T^{8} - 531772641369485336 T^{10} + \)\(81\!\cdots\!04\)\( T^{12} - \)\(77\!\cdots\!36\)\( T^{14} + \)\(56\!\cdots\!21\)\( T^{16} \))(\( 1 - 14828 T^{2} + 113393538 T^{4} - 585955403836 T^{6} + 2269661951584367 T^{8} - 6918101399845148888 T^{10} + \)\(16\!\cdots\!88\)\( T^{12} - \)\(33\!\cdots\!28\)\( T^{14} + \)\(54\!\cdots\!87\)\( T^{16} - \)\(68\!\cdots\!76\)\( T^{18} + \)\(64\!\cdots\!98\)\( T^{20} - \)\(41\!\cdots\!28\)\( T^{22} + \)\(13\!\cdots\!81\)\( T^{24} \))(\( 1 - 14828 T^{2} + 113393538 T^{4} - 585955403836 T^{6} + 2269661951584367 T^{8} - 6918101399845148888 T^{10} + \)\(16\!\cdots\!88\)\( T^{12} - \)\(33\!\cdots\!28\)\( T^{14} + \)\(54\!\cdots\!87\)\( T^{16} - \)\(68\!\cdots\!76\)\( T^{18} + \)\(64\!\cdots\!98\)\( T^{20} - \)\(41\!\cdots\!28\)\( T^{22} + \)\(13\!\cdots\!81\)\( T^{24} \))(\( 1 - 9264 T^{2} + 59936568 T^{4} - 267369406864 T^{6} + 980248186718364 T^{8} - 2939328460179000880 T^{10} + \)\(78\!\cdots\!52\)\( T^{12} - \)\(18\!\cdots\!48\)\( T^{14} + \)\(42\!\cdots\!42\)\( T^{16} - \)\(91\!\cdots\!88\)\( T^{18} + \)\(18\!\cdots\!72\)\( T^{20} - \)\(34\!\cdots\!80\)\( T^{22} + \)\(55\!\cdots\!44\)\( T^{24} - \)\(73\!\cdots\!64\)\( T^{26} + \)\(80\!\cdots\!08\)\( T^{28} - \)\(61\!\cdots\!04\)\( T^{30} + \)\(32\!\cdots\!41\)\( T^{32} \))
$53$ (\( ( 1 + 1344 T^{2} + 7890481 T^{4} )^{2} \))(\( ( 1 - 3696 T^{2} + 7890481 T^{4} )^{2} \))(\( ( 1 - 1568 T^{2} + 7890481 T^{4} )^{2} \))(\( ( 1 - 7056 T^{2} + 36202899 T^{4} - 115694189856 T^{6} + 285658286704419 T^{8} - 439304375542563216 T^{10} + \)\(49\!\cdots\!41\)\( T^{12} )^{2} \))(\( 1 - 18560 T^{2} + 172143654 T^{4} - 1049067123328 T^{6} + 4738424436817071 T^{8} - 17106375657857312000 T^{10} + \)\(51\!\cdots\!88\)\( T^{12} - \)\(13\!\cdots\!00\)\( T^{14} + \)\(29\!\cdots\!31\)\( T^{16} - \)\(51\!\cdots\!48\)\( T^{18} + \)\(66\!\cdots\!34\)\( T^{20} - \)\(56\!\cdots\!60\)\( T^{22} + \)\(24\!\cdots\!81\)\( T^{24} \))(\( 1 - 18560 T^{2} + 172143654 T^{4} - 1049067123328 T^{6} + 4738424436817071 T^{8} - 17106375657857312000 T^{10} + \)\(51\!\cdots\!88\)\( T^{12} - \)\(13\!\cdots\!00\)\( T^{14} + \)\(29\!\cdots\!31\)\( T^{16} - \)\(51\!\cdots\!48\)\( T^{18} + \)\(66\!\cdots\!34\)\( T^{20} - \)\(56\!\cdots\!60\)\( T^{22} + \)\(24\!\cdots\!81\)\( T^{24} \))(\( ( 1 + 2880 T^{2} + 7890481 T^{4} )^{4} \))(\( ( 1 + 15377762 T^{4} + 62259690411361 T^{8} )^{2} \))(\( ( 1 + 2809 T^{2} )^{8} \))(\( ( 1 + 68 T + 6262 T^{2} + 191012 T^{3} + 7890481 T^{4} )^{4} \))(\( ( 1 - 30 T + 2809 T^{2} )^{8} \))(\( ( 1 + 2234 T^{2} + 7890481 T^{4} )^{4} \))(\( ( 1 + 24 T - 284 T^{2} + 5256 T^{3} + 11958486 T^{4} + 14764104 T^{5} - 2240896604 T^{6} + 531944667096 T^{7} + 62259690411361 T^{8} )^{4} \))(\( ( 1 + 7516 T^{2} + 28337302 T^{4} + 59304855196 T^{6} + 62259690411361 T^{8} )^{4} \))(\( ( 1 - 40 T + 6420 T^{2} - 247544 T^{3} + 20384246 T^{4} - 695351096 T^{5} + 50656888020 T^{6} - 886574445160 T^{7} + 62259690411361 T^{8} )^{4} \))(\( 1 - 1604 T^{2} - 6155034 T^{4} - 12656331524 T^{6} + 62259690411361 T^{8} \))(\( 1 - 18920 T^{2} + 162796828 T^{4} - 840091728600 T^{6} + 2864724835962118 T^{8} - 6628727822775456600 T^{10} + \)\(10\!\cdots\!08\)\( T^{12} - \)\(92\!\cdots\!20\)\( T^{14} + \)\(38\!\cdots\!21\)\( T^{16} \))(\( ( 1 - 53 T )^{2}( 1 + 53 T )^{2} \))(\( ( 1 - 6 T + 2809 T^{2} )( 1 + 6 T + 2809 T^{2} ) \))(\( ( 1 - 53 T )^{2}( 1 + 53 T )^{2} \))(\( ( 1 + 3218 T^{2} + 7890481 T^{4} )^{2} \))(\( ( 1 - 5582 T^{2} + 7890481 T^{4} )^{2} \))(\( ( 1 - 7780 T^{2} + 30664230 T^{4} - 61387942180 T^{6} + 62259690411361 T^{8} )^{2} \))(\( ( 1 - 140 T + 10070 T^{2} - 393260 T^{3} + 7890481 T^{4} )^{2} \))(\( ( 1 - 80 T + 7772 T^{2} - 498480 T^{3} + 33336230 T^{4} - 1400230320 T^{5} + 61324818332 T^{6} - 1773148890320 T^{7} + 62259690411361 T^{8} )^{2} \))(\( ( 1 + 24 T + 6108 T^{2} + 242920 T^{3} + 18930726 T^{4} + 682362280 T^{5} + 48195057948 T^{6} + 531944667096 T^{7} + 62259690411361 T^{8} )^{2} \))(\( ( 1 - 128 T + 17654 T^{2} - 1495296 T^{3} + 124154463 T^{4} - 7734950016 T^{5} + 461963749876 T^{6} - 21727474594944 T^{7} + 979638431366703 T^{8} - 33142280538749184 T^{9} + 1099132574522167094 T^{10} - 22385596206785670272 T^{11} + \)\(49\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 + 128 T + 17654 T^{2} + 1495296 T^{3} + 124154463 T^{4} + 7734950016 T^{5} + 461963749876 T^{6} + 21727474594944 T^{7} + 979638431366703 T^{8} + 33142280538749184 T^{9} + 1099132574522167094 T^{10} + 22385596206785670272 T^{11} + \)\(49\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 + 24 T + 10392 T^{2} + 420232 T^{3} + 58443420 T^{4} + 3234882712 T^{5} + 221678878888 T^{6} + 14475939716424 T^{7} + 680170196938246 T^{8} + 40662914663435016 T^{9} + 1749152981967065128 T^{10} + 71699108638726901848 T^{11} + \)\(36\!\cdots\!20\)\( T^{12} + \)\(73\!\cdots\!68\)\( T^{13} + \)\(51\!\cdots\!72\)\( T^{14} + \)\(33\!\cdots\!56\)\( T^{15} + \)\(38\!\cdots\!21\)\( T^{16} )^{2} \))
$59$ (\( ( 1 + 2502 T^{2} + 12117361 T^{4} )^{2} \))(\( ( 1 + 1102 T^{2} + 12117361 T^{4} )^{2} \))(\( ( 1 - 2426 T^{2} + 12117361 T^{4} )^{2} \))(\( ( 1 - 7782 T^{2} + 21241119 T^{4} - 34054569492 T^{6} + 257386306966959 T^{8} - 1142634465436826022 T^{10} + \)\(17\!\cdots\!81\)\( T^{12} )^{2} \))(\( 1 - 14284 T^{2} + 117930210 T^{4} - 654122951644 T^{6} + 2810159914812687 T^{8} - 10069521608166307224 T^{10} + \)\(34\!\cdots\!52\)\( T^{12} - \)\(12\!\cdots\!64\)\( T^{14} + \)\(41\!\cdots\!27\)\( T^{16} - \)\(11\!\cdots\!64\)\( T^{18} + \)\(25\!\cdots\!10\)\( T^{20} - \)\(37\!\cdots\!84\)\( T^{22} + \)\(31\!\cdots\!61\)\( T^{24} \))(\( 1 - 14284 T^{2} + 117930210 T^{4} - 654122951644 T^{6} + 2810159914812687 T^{8} - 10069521608166307224 T^{10} + \)\(34\!\cdots\!52\)\( T^{12} - \)\(12\!\cdots\!64\)\( T^{14} + \)\(41\!\cdots\!27\)\( T^{16} - \)\(11\!\cdots\!64\)\( T^{18} + \)\(25\!\cdots\!10\)\( T^{20} - \)\(37\!\cdots\!84\)\( T^{22} + \)\(31\!\cdots\!61\)\( T^{24} \))(\( ( 1 + 2162 T^{2} + 12117361 T^{4} )^{4} \))(\( ( 1 + 3481 T^{2} )^{8} \))(\( ( 1 - 59 T )^{8}( 1 + 59 T )^{8} \))(\( ( 1 - 7860 T^{2} + 33271422 T^{4} - 95242457460 T^{6} + 146830437604321 T^{8} )^{2} \))(\( ( 1 - 4580 T^{2} + 29037038 T^{4} - 55497513380 T^{6} + 146830437604321 T^{8} )^{2} \))(\( ( 1 + 5070 T^{2} + 12117361 T^{4} )^{4} \))(\( ( 1 - 13000 T^{2} + 57070172 T^{4} - 37155276792 T^{6} - 319963791795322 T^{8} - 450223901943585912 T^{10} + \)\(83\!\cdots\!12\)\( T^{12} - \)\(23\!\cdots\!00\)\( T^{14} + \)\(21\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 - 7908 T^{2} + 36555174 T^{4} - 95824090788 T^{6} + 146830437604321 T^{8} )^{4} \))(\( ( 1 - 21576 T^{2} + 218270556 T^{4} - 1360034575992 T^{6} + 5705353383213446 T^{8} - 16480029929776997112 T^{10} + \)\(32\!\cdots\!76\)\( T^{12} - \)\(38\!\cdots\!56\)\( T^{14} + \)\(21\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 - 92 T + 8836 T^{2} - 320252 T^{3} + 12117361 T^{4} )^{2} \))(\( ( 1 - 52 T + 2254 T^{2} + 207508 T^{3} - 19795230 T^{4} + 722335348 T^{5} + 27312531694 T^{6} - 2193387749332 T^{7} + 146830437604321 T^{8} )^{2} \))(\( 1 - 1130 T^{2} + 12117361 T^{4} \))(\( ( 1 + 3481 T^{2} )^{2} \))(\( 1 + 1130 T^{2} + 12117361 T^{4} \))(\( ( 1 - 6862 T^{2} + 12117361 T^{4} )^{2} \))(\( ( 1 + 3481 T^{2} )^{4} \))(\( ( 1 + 9200 T^{2} + 44845170 T^{4} + 111479721200 T^{6} + 146830437604321 T^{8} )^{2} \))(\( 1 - 9692 T^{2} + 45396006 T^{4} - 117441462812 T^{6} + 146830437604321 T^{8} \))(\( 1 - 10792 T^{2} + 87239068 T^{4} - 443336106136 T^{6} + 1836453342677254 T^{8} - 5372063642384227096 T^{10} + \)\(12\!\cdots\!28\)\( T^{12} - \)\(19\!\cdots\!52\)\( T^{14} + \)\(21\!\cdots\!41\)\( T^{16} \))(\( 1 - 21392 T^{2} + 213726428 T^{4} - 1316320178544 T^{6} + 5495654048256518 T^{8} - 15950326795002102384 T^{10} + \)\(31\!\cdots\!88\)\( T^{12} - \)\(38\!\cdots\!52\)\( T^{14} + \)\(21\!\cdots\!41\)\( T^{16} \))(\( 1 - 15628 T^{2} + 144668898 T^{4} - 990246600732 T^{6} + 5397356836371727 T^{8} - 24345088021389180952 T^{10} + \)\(92\!\cdots\!36\)\( T^{12} - \)\(29\!\cdots\!72\)\( T^{14} + \)\(79\!\cdots\!67\)\( T^{16} - \)\(17\!\cdots\!92\)\( T^{18} + \)\(31\!\cdots\!18\)\( T^{20} - \)\(40\!\cdots\!28\)\( T^{22} + \)\(31\!\cdots\!61\)\( T^{24} \))(\( 1 - 15628 T^{2} + 144668898 T^{4} - 990246600732 T^{6} + 5397356836371727 T^{8} - 24345088021389180952 T^{10} + \)\(92\!\cdots\!36\)\( T^{12} - \)\(29\!\cdots\!72\)\( T^{14} + \)\(79\!\cdots\!67\)\( T^{16} - \)\(17\!\cdots\!92\)\( T^{18} + \)\(31\!\cdots\!18\)\( T^{20} - \)\(40\!\cdots\!28\)\( T^{22} + \)\(31\!\cdots\!61\)\( T^{24} \))(\( 1 - 32944 T^{2} + 529003448 T^{4} - 5524852963856 T^{6} + 42286305386402588 T^{8} - \)\(25\!\cdots\!04\)\( T^{10} + \)\(12\!\cdots\!40\)\( T^{12} - \)\(53\!\cdots\!68\)\( T^{14} + \)\(19\!\cdots\!66\)\( T^{16} - \)\(64\!\cdots\!48\)\( T^{18} + \)\(18\!\cdots\!40\)\( T^{20} - \)\(45\!\cdots\!24\)\( T^{22} + \)\(91\!\cdots\!08\)\( T^{24} - \)\(14\!\cdots\!56\)\( T^{26} + \)\(16\!\cdots\!28\)\( T^{28} - \)\(12\!\cdots\!24\)\( T^{30} + \)\(46\!\cdots\!81\)\( T^{32} \))
$61$ (\( ( 1 + 50 T + 3721 T^{2} )^{4} \))(\( ( 1 - 10 T + 3721 T^{2} )^{4} \))(\( ( 1 - 10 T + 3721 T^{2} )^{4} \))(\( ( 1 - 18 T + 2871 T^{2} + 140228 T^{3} + 10682991 T^{4} - 249225138 T^{5} + 51520374361 T^{6} )^{4} \))(\( ( 1 - 52 T + 14546 T^{2} - 759172 T^{3} + 109319583 T^{4} - 5061800936 T^{5} + 502112234044 T^{6} - 18834961282856 T^{7} + 1513621564404303 T^{8} - 39112825644389092 T^{9} + 2788574574858449426 T^{10} - 37093831406469895252 T^{11} + \)\(26\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 - 52 T + 14546 T^{2} - 759172 T^{3} + 109319583 T^{4} - 5061800936 T^{5} + 502112234044 T^{6} - 18834961282856 T^{7} + 1513621564404303 T^{8} - 39112825644389092 T^{9} + 2788574574858449426 T^{10} - 37093831406469895252 T^{11} + \)\(26\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 + 6578 T^{2} + 13845841 T^{4} )^{4} \))(\( ( 1 + 3721 T^{2} )^{8} \))(\( ( 1 - 61 T )^{8}( 1 + 61 T )^{8} \))(\( ( 1 - 7140 T^{2} + 40319454 T^{4} - 98859304740 T^{6} + 191707312997281 T^{8} )^{2} \))(\( ( 1 - 4212 T^{2} + 3996814 T^{4} - 58318682292 T^{6} + 191707312997281 T^{8} )^{2} \))(\( ( 1 - 7066 T^{2} + 13845841 T^{4} )^{4} \))(\( ( 1 - 11448 T^{2} + 96722108 T^{4} - 516118988808 T^{6} + 2273573262533190 T^{8} - 7146101456116347528 T^{10} + \)\(18\!\cdots\!48\)\( T^{12} - \)\(30\!\cdots\!08\)\( T^{14} + \)\(36\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 - 7740 T^{2} + 30229398 T^{4} - 107166809340 T^{6} + 191707312997281 T^{8} )^{4} \))(\( ( 1 - 11736 T^{2} + 92284284 T^{4} - 513094045416 T^{6} + 2170460315172038 T^{8} - 7104218570876714856 T^{10} + \)\(17\!\cdots\!04\)\( T^{12} - \)\(31\!\cdots\!56\)\( T^{14} + \)\(36\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 - 13232 T^{2} + 71110338 T^{4} - 183208168112 T^{6} + 191707312997281 T^{8} \))(\( 1 - 16316 T^{2} + 140172120 T^{4} - 816942037524 T^{6} + 3499102878259502 T^{8} - 11311249557773337684 T^{10} + \)\(26\!\cdots\!20\)\( T^{12} - \)\(43\!\cdots\!36\)\( T^{14} + \)\(36\!\cdots\!61\)\( T^{16} \))(\( 1 - 7370 T^{2} + 13845841 T^{4} \))(\( ( 1 + 3721 T^{2} )^{2} \))(\( 1 + 7370 T^{2} + 13845841 T^{4} \))(\( ( 1 + 3721 T^{2} )^{4} \))(\( ( 1 + 3721 T^{2} )^{4} \))(\( ( 1 + 14840 T^{2} + 82747650 T^{4} + 205472280440 T^{6} + 191707312997281 T^{8} )^{2} \))(\( ( 1 + 4 T + 7194 T^{2} + 14884 T^{3} + 13845841 T^{4} )^{2} \))(\( ( 1 - 16 T + 5644 T^{2} - 245296 T^{3} + 27126022 T^{4} - 912746416 T^{5} + 78145926604 T^{6} - 824325989776 T^{7} + 191707312997281 T^{8} )^{2} \))(\( ( 1 + 96 T + 12728 T^{2} + 895872 T^{3} + 70065870 T^{4} + 3333539712 T^{5} + 176229864248 T^{6} + 4945955938656 T^{7} + 191707312997281 T^{8} )^{2} \))(\( ( 1 - 20 T + 15746 T^{2} - 308196 T^{3} + 121552351 T^{4} - 2024507560 T^{5} + 567759898204 T^{6} - 7533192630760 T^{7} + 1682994525122191 T^{8} - 15878373296562756 T^{9} + 3018623350455186626 T^{10} - 14266858233257652020 T^{11} + \)\(26\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 - 20 T + 15746 T^{2} - 308196 T^{3} + 121552351 T^{4} - 2024507560 T^{5} + 567759898204 T^{6} - 7533192630760 T^{7} + 1682994525122191 T^{8} - 15878373296562756 T^{9} + 3018623350455186626 T^{10} - 14266858233257652020 T^{11} + \)\(26\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 - 24 T + 4552 T^{2} - 539976 T^{3} + 38633596 T^{4} - 1157398488 T^{5} + 249536906872 T^{6} - 11308110799176 T^{7} + 545612994218182 T^{8} - 42077480283733896 T^{9} + 3455048336181519352 T^{10} - 59629603386615366168 T^{11} + \)\(74\!\cdots\!76\)\( T^{12} - \)\(38\!\cdots\!76\)\( T^{13} + \)\(12\!\cdots\!92\)\( T^{14} - \)\(23\!\cdots\!84\)\( T^{15} + \)\(36\!\cdots\!61\)\( T^{16} )^{2} \))
$67$ (\( ( 1 + 7606 T^{2} + 20151121 T^{4} )^{2} \))(\( ( 1 + 7186 T^{2} + 20151121 T^{4} )^{2} \))(\( ( 1 + 4246 T^{2} + 20151121 T^{4} )^{2} \))(\( ( 1 + 13662 T^{2} + 111168495 T^{4} + 578344466692 T^{6} + 2240169794132895 T^{8} + 5547696610778829342 T^{10} + \)\(81\!\cdots\!61\)\( T^{12} )^{2} \))(\( ( 1 - 32 T + 15614 T^{2} - 337440 T^{3} + 123909103 T^{4} - 2460293824 T^{5} + 674310911428 T^{6} - 11044258975936 T^{7} + 2496907327554463 T^{8} - 30524276479107360 T^{9} + 6340340717369392574 T^{10} - 58330809745656366368 T^{11} + \)\(81\!\cdots\!61\)\( T^{12} )^{2} \))(\( ( 1 + 32 T + 15614 T^{2} + 337440 T^{3} + 123909103 T^{4} + 2460293824 T^{5} + 674310911428 T^{6} + 11044258975936 T^{7} + 2496907327554463 T^{8} + 30524276479107360 T^{9} + 6340340717369392574 T^{10} + 58330809745656366368 T^{11} + \)\(81\!\cdots\!61\)\( T^{12} )^{2} \))(\( ( 1 - 14 T + 4489 T^{2} )^{8} \))(\( ( 1 + 118 T + 4489 T^{2} )^{8} \))(\( ( 1 + 4489 T^{2} )^{8} \))(\( ( 1 + 2892 T^{2} + 19813958 T^{4} + 58277041932 T^{6} + 406067677556641 T^{8} )^{2} \))(\( ( 1 + 8150 T^{2} + 20151121 T^{4} )^{4} \))(\( ( 1 + 7286 T^{2} + 20151121 T^{4} )^{4} \))(\( ( 1 + 11984 T^{2} + 95316124 T^{4} + 585750526256 T^{6} + 2792378180945926 T^{8} + 11803529730398332976 T^{10} + \)\(38\!\cdots\!84\)\( T^{12} + \)\(98\!\cdots\!24\)\( T^{14} + \)\(16\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 + 10200 T^{2} + 53468558 T^{4} + 205541434200 T^{6} + 406067677556641 T^{8} )^{4} \))(\( ( 1 + 7152 T^{2} + 52159708 T^{4} + 263818906128 T^{6} + 1563765552355206 T^{8} + 5316246699472969488 T^{10} + \)\(21\!\cdots\!28\)\( T^{12} + \)\(58\!\cdots\!72\)\( T^{14} + \)\(16\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 - 112 T + 11602 T^{2} - 502768 T^{3} + 20151121 T^{4} )^{2} \))(\( ( 1 + 152 T + 22224 T^{2} + 2037320 T^{3} + 158433022 T^{4} + 9145529480 T^{5} + 447838513104 T^{6} + 13749674089688 T^{7} + 406067677556641 T^{8} )^{2} \))(\( ( 1 - 67 T )^{2}( 1 + 67 T )^{2} \))(\( ( 1 - 118 T + 4489 T^{2} )( 1 + 118 T + 4489 T^{2} ) \))(\( ( 1 - 67 T )^{2}( 1 + 67 T )^{2} \))(\( ( 1 - 67 T )^{4}( 1 + 67 T )^{4} \))(\( ( 1 - 118 T + 4489 T^{2} )^{2}( 1 + 118 T + 4489 T^{2} )^{2} \))(\( ( 1 - 11884 T^{2} + 74122758 T^{4} - 239475921964 T^{6} + 406067677556641 T^{8} )^{2} \))(\( 1 - 11204 T^{2} + 65233446 T^{4} - 225773159684 T^{6} + 406067677556641 T^{8} \))(\( 1 - 7912 T^{2} + 95063452 T^{4} - 484990938328 T^{6} + 3019816096004230 T^{8} - 9773111082151065688 T^{10} + \)\(38\!\cdots\!32\)\( T^{12} - \)\(64\!\cdots\!32\)\( T^{14} + \)\(16\!\cdots\!81\)\( T^{16} \))(\( 1 - 16200 T^{2} + 120433884 T^{4} - 596093100152 T^{6} + 2634880977729030 T^{8} - 12011944188428070392 T^{10} + \)\(48\!\cdots\!44\)\( T^{12} - \)\(13\!\cdots\!00\)\( T^{14} + \)\(16\!\cdots\!81\)\( T^{16} \))(\( 1 - 18572 T^{2} + 219805986 T^{4} - 1924138298908 T^{6} + 13416169674171215 T^{8} - 77308694226120992024 T^{10} + \)\(37\!\cdots\!12\)\( T^{12} - \)\(15\!\cdots\!04\)\( T^{14} + \)\(54\!\cdots\!15\)\( T^{16} - \)\(15\!\cdots\!88\)\( T^{18} + \)\(36\!\cdots\!66\)\( T^{20} - \)\(61\!\cdots\!72\)\( T^{22} + \)\(66\!\cdots\!21\)\( T^{24} \))(\( 1 - 18572 T^{2} + 219805986 T^{4} - 1924138298908 T^{6} + 13416169674171215 T^{8} - 77308694226120992024 T^{10} + \)\(37\!\cdots\!12\)\( T^{12} - \)\(15\!\cdots\!04\)\( T^{14} + \)\(54\!\cdots\!15\)\( T^{16} - \)\(15\!\cdots\!88\)\( T^{18} + \)\(36\!\cdots\!66\)\( T^{20} - \)\(61\!\cdots\!72\)\( T^{22} + \)\(66\!\cdots\!21\)\( T^{24} \))(\( 1 - 51696 T^{2} + 1310952504 T^{4} - 21631496299984 T^{6} + 259796851945905948 T^{8} - \)\(24\!\cdots\!00\)\( T^{10} + \)\(17\!\cdots\!80\)\( T^{12} - \)\(10\!\cdots\!88\)\( T^{14} + \)\(52\!\cdots\!62\)\( T^{16} - \)\(21\!\cdots\!48\)\( T^{18} + \)\(72\!\cdots\!80\)\( T^{20} - \)\(19\!\cdots\!00\)\( T^{22} + \)\(42\!\cdots\!88\)\( T^{24} - \)\(71\!\cdots\!84\)\( T^{26} + \)\(87\!\cdots\!84\)\( T^{28} - \)\(69\!\cdots\!36\)\( T^{30} + \)\(27\!\cdots\!61\)\( T^{32} \))
$71$ (\( ( 1 + 124 T^{2} + 25411681 T^{4} )^{2} \))(\( ( 1 - 8066 T^{2} + 25411681 T^{4} )^{2} \))(\( ( 1 - 2676 T^{2} + 25411681 T^{4} )^{2} \))(\( ( 1 - 8826 T^{2} + 68062947 T^{4} - 431835844628 T^{6} + 1729593897083907 T^{8} - 5699420666775086586 T^{10} + \)\(16\!\cdots\!41\)\( T^{12} )^{2} \))(\( 1 - 28436 T^{2} + 438962666 T^{4} - 4707270790820 T^{6} + 38898275137186911 T^{8} - \)\(25\!\cdots\!72\)\( T^{10} + \)\(14\!\cdots\!04\)\( T^{12} - \)\(65\!\cdots\!32\)\( T^{14} + \)\(25\!\cdots\!71\)\( T^{16} - \)\(77\!\cdots\!20\)\( T^{18} + \)\(18\!\cdots\!86\)\( T^{20} - \)\(30\!\cdots\!36\)\( T^{22} + \)\(26\!\cdots\!81\)\( T^{24} \))(\( 1 - 28436 T^{2} + 438962666 T^{4} - 4707270790820 T^{6} + 38898275137186911 T^{8} - \)\(25\!\cdots\!72\)\( T^{10} + \)\(14\!\cdots\!04\)\( T^{12} - \)\(65\!\cdots\!32\)\( T^{14} + \)\(25\!\cdots\!71\)\( T^{16} - \)\(77\!\cdots\!20\)\( T^{18} + \)\(18\!\cdots\!86\)\( T^{20} - \)\(30\!\cdots\!36\)\( T^{22} + \)\(26\!\cdots\!81\)\( T^{24} \))(\( ( 1 + 8400 T^{2} + 25411681 T^{4} )^{4} \))(\( ( 1 - 42331966 T^{4} + 645753531245761 T^{8} )^{2} \))(\( ( 1 - 50816638 T^{4} + 645753531245761 T^{8} )^{2} \))(\( ( 1 + 11516 T^{2} + 65977926 T^{4} + 292640918396 T^{6} + 645753531245761 T^{8} )^{2} \))(\( ( 1 + 11964 T^{2} + 70047686 T^{4} + 304025351484 T^{6} + 645753531245761 T^{8} )^{2} \))(\( ( 1 + 8034 T^{2} + 25411681 T^{4} )^{4} \))(\( ( 1 + 22068 T^{2} + 246893656 T^{4} + 1926204686460 T^{6} + 11241400142198382 T^{8} + 48948099033026539260 T^{10} + \)\(15\!\cdots\!16\)\( T^{12} + \)\(36\!\cdots\!88\)\( T^{14} + \)\(41\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 + 9338 T^{2} + 69994482 T^{4} + 237294277178 T^{6} + 645753531245761 T^{8} )^{4} \))(\( ( 1 + 9700 T^{2} + 102431512 T^{4} + 737392508620 T^{6} + 3914393781676270 T^{8} + 18738383200841190220 T^{10} + \)\(66\!\cdots\!32\)\( T^{12} + \)\(15\!\cdots\!00\)\( T^{14} + \)\(41\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 - 9412 T^{2} + 47279686 T^{4} - 239174741572 T^{6} + 645753531245761 T^{8} \))(\( 1 - 9864 T^{2} + 51888284 T^{4} - 294531431096 T^{6} + 1789421441990854 T^{8} - 7484538771485032376 T^{10} + \)\(33\!\cdots\!24\)\( T^{12} - \)\(16\!\cdots\!24\)\( T^{14} + \)\(41\!\cdots\!21\)\( T^{16} \))(\( ( 1 - 110 T + 5041 T^{2} )^{2} \))(\( ( 1 + 114 T + 5041 T^{2} )^{2} \))(\( ( 1 + 110 T + 5041 T^{2} )^{2} \))(\( ( 1 + 5041 T^{2} )^{4} \))(\( ( 1 + 2914 T^{2} + 25411681 T^{4} )^{2} \))(\( ( 1 - 136 T + 12678 T^{2} - 685576 T^{3} + 25411681 T^{4} )^{4} \))(\( 1 - 8388 T^{2} + 39052870 T^{4} - 213153180228 T^{6} + 645753531245761 T^{8} \))(\( 1 - 35856 T^{2} + 578979068 T^{4} - 5523144764400 T^{6} + 34153538131631238 T^{8} - \)\(14\!\cdots\!00\)\( T^{10} + \)\(37\!\cdots\!48\)\( T^{12} - \)\(58\!\cdots\!96\)\( T^{14} + \)\(41\!\cdots\!21\)\( T^{16} \))(\( 1 - 21000 T^{2} + 247457180 T^{4} - 1991232124728 T^{6} + 11615880585488070 T^{8} - 50600555550540147768 T^{10} + \)\(15\!\cdots\!80\)\( T^{12} - \)\(34\!\cdots\!00\)\( T^{14} + \)\(41\!\cdots\!21\)\( T^{16} \))(\( 1 - 35076 T^{2} + 589219074 T^{4} - 6491139790068 T^{6} + 54120580943264559 T^{8} - \)\(36\!\cdots\!52\)\( T^{10} + \)\(20\!\cdots\!88\)\( T^{12} - \)\(92\!\cdots\!12\)\( T^{14} + \)\(34\!\cdots\!99\)\( T^{16} - \)\(10\!\cdots\!88\)\( T^{18} + \)\(24\!\cdots\!54\)\( T^{20} - \)\(37\!\cdots\!76\)\( T^{22} + \)\(26\!\cdots\!81\)\( T^{24} \))(\( 1 - 35076 T^{2} + 589219074 T^{4} - 6491139790068 T^{6} + 54120580943264559 T^{8} - \)\(36\!\cdots\!52\)\( T^{10} + \)\(20\!\cdots\!88\)\( T^{12} - \)\(92\!\cdots\!12\)\( T^{14} + \)\(34\!\cdots\!99\)\( T^{16} - \)\(10\!\cdots\!88\)\( T^{18} + \)\(24\!\cdots\!54\)\( T^{20} - \)\(37\!\cdots\!76\)\( T^{22} + \)\(26\!\cdots\!81\)\( T^{24} \))(\( 1 - 26808 T^{2} + 407905624 T^{4} - 4599225914280 T^{6} + 41967348192175708 T^{8} - \)\(32\!\cdots\!32\)\( T^{10} + \)\(22\!\cdots\!28\)\( T^{12} - \)\(13\!\cdots\!32\)\( T^{14} + \)\(70\!\cdots\!38\)\( T^{16} - \)\(33\!\cdots\!92\)\( T^{18} + \)\(14\!\cdots\!08\)\( T^{20} - \)\(53\!\cdots\!12\)\( T^{22} + \)\(17\!\cdots\!68\)\( T^{24} - \)\(48\!\cdots\!80\)\( T^{26} + \)\(10\!\cdots\!44\)\( T^{28} - \)\(18\!\cdots\!88\)\( T^{30} + \)\(17\!\cdots\!41\)\( T^{32} \))
$73$ (\( ( 1 + 114 T + 5329 T^{2} )^{4} \))(\( ( 1 - 56 T + 5329 T^{2} )^{4} \))(\( ( 1 - 42 T + 5329 T^{2} )^{4} \))(\( ( 1 - 48 T + 10623 T^{2} - 514560 T^{3} + 56609967 T^{4} - 1363115568 T^{5} + 151334226289 T^{6} )^{4} \))(\( ( 1 + 32 T + 14174 T^{2} + 972512 T^{3} + 92720223 T^{4} + 9711613696 T^{5} + 495039728068 T^{6} + 51753189385984 T^{7} + 2633091238327743 T^{8} + 147174351076767968 T^{9} + 11430765342506704094 T^{10} + \)\(13\!\cdots\!68\)\( T^{11} + \)\(22\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 + 32 T + 14174 T^{2} + 972512 T^{3} + 92720223 T^{4} + 9711613696 T^{5} + 495039728068 T^{6} + 51753189385984 T^{7} + 2633091238327743 T^{8} + 147174351076767968 T^{9} + 11430765342506704094 T^{10} + \)\(13\!\cdots\!68\)\( T^{11} + \)\(22\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 - 9794 T^{2} + 28398241 T^{4} )^{4} \))(\( ( 1 - 73 T )^{8}( 1 + 73 T )^{8} \))(\( ( 1 - 73 T )^{8}( 1 + 73 T )^{8} \))(\( ( 1 - 14980 T^{2} + 104177094 T^{4} - 425405650180 T^{6} + 806460091894081 T^{8} )^{2} \))(\( ( 1 - 8388 T^{2} + 67882822 T^{4} - 238204445508 T^{6} + 806460091894081 T^{8} )^{2} \))(\( ( 1 - 9154 T^{2} + 28398241 T^{4} )^{4} \))(\( ( 1 - 26808 T^{2} + 371491580 T^{4} - 3347620662408 T^{6} + 21080873652245766 T^{8} - 95066538347642024328 T^{10} + \)\(29\!\cdots\!80\)\( T^{12} - \)\(61\!\cdots\!68\)\( T^{14} + \)\(65\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 - 12964 T^{2} + 82037382 T^{4} - 368154796324 T^{6} + 806460091894081 T^{8} )^{4} \))(\( ( 1 - 5624 T^{2} + 75565180 T^{4} - 514924569416 T^{6} + 2672129507262982 T^{8} - 14622952019096797256 T^{10} + \)\(60\!\cdots\!80\)\( T^{12} - \)\(12\!\cdots\!04\)\( T^{14} + \)\(65\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 - 116 T + 13894 T^{2} - 618164 T^{3} + 28398241 T^{4} )^{2} \))(\( ( 1 + 56 T + 18460 T^{2} + 736008 T^{3} + 138223494 T^{4} + 3922186632 T^{5} + 524231528860 T^{6} + 8474716672184 T^{7} + 806460091894081 T^{8} )^{2} \))(\( ( 1 - 73 T )^{2}( 1 + 73 T )^{2} \))(\( ( 1 - 73 T )^{2}( 1 + 73 T )^{2} \))(\( ( 1 - 73 T )^{2}( 1 + 73 T )^{2} \))(\( ( 1 - 50 T + 5329 T^{2} )^{2}( 1 + 50 T + 5329 T^{2} )^{2} \))(\( ( 1 - 73 T )^{4}( 1 + 73 T )^{4} \))(\( ( 1 - 9364 T^{2} + 72904614 T^{4} - 265921128724 T^{6} + 806460091894081 T^{8} )^{2} \))(\( ( 1 + 76 T + 4934 T^{2} + 405004 T^{3} + 28398241 T^{4} )^{2} \))(\( ( 1 + 56 T + 19724 T^{2} + 823368 T^{3} + 154541606 T^{4} + 4387728072 T^{5} + 560126905484 T^{6} + 8474716672184 T^{7} + 806460091894081 T^{8} )^{2} \))(\( ( 1 - 136 T + 21660 T^{2} - 1811512 T^{3} + 170528390 T^{4} - 9653547448 T^{5} + 615105900060 T^{6} - 20581454775304 T^{7} + 806460091894081 T^{8} )^{2} \))(\( ( 1 - 36 T + 12418 T^{2} - 695252 T^{3} + 107776207 T^{4} - 4912411976 T^{5} + 749125005212 T^{6} - 26178243420104 T^{7} + 3060654700451887 T^{8} - 105215423495879828 T^{9} + 10014621421140697858 T^{10} - \)\(15\!\cdots\!64\)\( T^{11} + \)\(22\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 - 36 T + 12418 T^{2} - 695252 T^{3} + 107776207 T^{4} - 4912411976 T^{5} + 749125005212 T^{6} - 26178243420104 T^{7} + 3060654700451887 T^{8} - 105215423495879828 T^{9} + 10014621421140697858 T^{10} - \)\(15\!\cdots\!64\)\( T^{11} + \)\(22\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 + 16 T + 17704 T^{2} - 586256 T^{3} + 135622140 T^{4} - 9840320304 T^{5} + 1112431939224 T^{6} - 54182229509328 T^{7} + 7900193312584966 T^{8} - 288737101055208912 T^{9} + 31591110306180504984 T^{10} - \)\(14\!\cdots\!56\)\( T^{11} + \)\(10\!\cdots\!40\)\( T^{12} - \)\(25\!\cdots\!44\)\( T^{13} + \)\(40\!\cdots\!84\)\( T^{14} + \)\(19\!\cdots\!44\)\( T^{15} + \)\(65\!\cdots\!61\)\( T^{16} )^{2} \))
$79$ (\( ( 1 + 12454 T^{2} + 38950081 T^{4} )^{2} \))(\( ( 1 - 3646 T^{2} + 38950081 T^{4} )^{2} \))(\( ( 1 + 4390 T^{2} + 38950081 T^{4} )^{2} \))(\( ( 1 + 16782 T^{2} + 128030079 T^{4} + 730898992228 T^{6} + 4986781947486399 T^{8} + 25460120047851906702 T^{10} + \)\(59\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 + 16 T + 10414 T^{2} - 107440 T^{3} + 39411839 T^{4} - 5975985760 T^{5} + 161763756068 T^{6} - 37296127128160 T^{7} + 1535094321408959 T^{8} - 26117316221176240 T^{9} + 15799171146366926254 T^{10} + \)\(15\!\cdots\!16\)\( T^{11} + \)\(59\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 - 16 T + 10414 T^{2} + 107440 T^{3} + 39411839 T^{4} + 5975985760 T^{5} + 161763756068 T^{6} + 37296127128160 T^{7} + 1535094321408959 T^{8} + 26117316221176240 T^{9} + 15799171146366926254 T^{10} - \)\(15\!\cdots\!16\)\( T^{11} + \)\(59\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 - 10178 T^{2} + 38950081 T^{4} )^{4} \))(\( ( 1 - 94 T + 6241 T^{2} )^{4}( 1 + 94 T + 6241 T^{2} )^{4} \))(\( ( 1 + 6241 T^{2} )^{8} \))(\( ( 1 + 7612 T^{2} + 88816006 T^{4} + 296488016572 T^{6} + 1517108809906561 T^{8} )^{2} \))(\( ( 1 - 1028 T^{2} + 37863942 T^{4} - 40040683268 T^{6} + 1517108809906561 T^{8} )^{2} \))(\( ( 1 + 10790 T^{2} + 38950081 T^{4} )^{4} \))(\( ( 1 + 26576 T^{2} + 378923740 T^{4} + 3598913791280 T^{6} + 25659018087079750 T^{8} + \)\(14\!\cdots\!80\)\( T^{10} + \)\(57\!\cdots\!40\)\( T^{12} + \)\(15\!\cdots\!16\)\( T^{14} + \)\(23\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 + 19864 T^{2} + 174522286 T^{4} + 773704408984 T^{6} + 1517108809906561 T^{8} )^{4} \))(\( ( 1 + 14768 T^{2} + 126589596 T^{4} + 850288941904 T^{6} + 5408824791957446 T^{8} + 33118823160565094224 T^{10} + \)\(19\!\cdots\!56\)\( T^{12} + \)\(87\!\cdots\!88\)\( T^{14} + \)\(23\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 - 16900 T^{2} + 142880134 T^{4} - 658256368900 T^{6} + 1517108809906561 T^{8} \))(\( 1 - 24968 T^{2} + 330869788 T^{4} - 3106127956152 T^{6} + 22189846569597766 T^{8} - \)\(12\!\cdots\!12\)\( T^{10} + \)\(50\!\cdots\!68\)\( T^{12} - \)\(14\!\cdots\!88\)\( T^{14} + \)\(23\!\cdots\!21\)\( T^{16} \))(\( ( 1 - 130 T + 6241 T^{2} )^{2} \))(\( ( 1 + 94 T + 6241 T^{2} )^{2} \))(\( ( 1 + 130 T + 6241 T^{2} )^{2} \))(\( ( 1 + 58 T + 6241 T^{2} )^{4} \))(\( ( 1 + 94 T + 6241 T^{2} )^{4} \))(\( ( 1 - 8 T + 11526 T^{2} - 49928 T^{3} + 38950081 T^{4} )^{4} \))(\( ( 1 - 1282 T^{2} + 38950081 T^{4} )^{2} \))(\( 1 - 14632 T^{2} + 199664860 T^{4} - 1702783803160 T^{6} + 12474458954560966 T^{8} - 66323567058570055960 T^{10} + \)\(30\!\cdots\!60\)\( T^{12} - \)\(86\!\cdots\!12\)\( T^{14} + \)\(23\!\cdots\!21\)\( T^{16} \))(\( 1 - 26248 T^{2} + 289540636 T^{4} - 1851543245752 T^{6} + 10296312398061382 T^{8} - 72117759397043305912 T^{10} + \)\(43\!\cdots\!96\)\( T^{12} - \)\(15\!\cdots\!68\)\( T^{14} + \)\(23\!\cdots\!21\)\( T^{16} \))(\( 1 - 43020 T^{2} + 906603714 T^{4} - 12711826056668 T^{6} + 134359925922862191 T^{8} - \)\(11\!\cdots\!40\)\( T^{10} + \)\(78\!\cdots\!80\)\( T^{12} - \)\(44\!\cdots\!40\)\( T^{14} + \)\(20\!\cdots\!51\)\( T^{16} - \)\(75\!\cdots\!88\)\( T^{18} + \)\(20\!\cdots\!94\)\( T^{20} - \)\(38\!\cdots\!20\)\( T^{22} + \)\(34\!\cdots\!81\)\( T^{24} \))(\( 1 - 43020 T^{2} + 906603714 T^{4} - 12711826056668 T^{6} + 134359925922862191 T^{8} - \)\(11\!\cdots\!40\)\( T^{10} + \)\(78\!\cdots\!80\)\( T^{12} - \)\(44\!\cdots\!40\)\( T^{14} + \)\(20\!\cdots\!51\)\( T^{16} - \)\(75\!\cdots\!88\)\( T^{18} + \)\(20\!\cdots\!94\)\( T^{20} - \)\(38\!\cdots\!20\)\( T^{22} + \)\(34\!\cdots\!81\)\( T^{24} \))(\( 1 - 54704 T^{2} + 1486108728 T^{4} - 26654340076048 T^{6} + 355897016960757404 T^{8} - \)\(37\!\cdots\!80\)\( T^{10} + \)\(33\!\cdots\!36\)\( T^{12} - \)\(25\!\cdots\!84\)\( T^{14} + \)\(17\!\cdots\!50\)\( T^{16} - \)\(10\!\cdots\!04\)\( T^{18} + \)\(51\!\cdots\!96\)\( T^{20} - \)\(22\!\cdots\!80\)\( T^{22} + \)\(81\!\cdots\!84\)\( T^{24} - \)\(23\!\cdots\!48\)\( T^{26} + \)\(51\!\cdots\!68\)\( T^{28} - \)\(74\!\cdots\!44\)\( T^{30} + \)\(52\!\cdots\!41\)\( T^{32} \))
$83$ (\( ( 1 - 13554 T^{2} + 47458321 T^{4} )^{2} \))(\( ( 1 - 5714 T^{2} + 47458321 T^{4} )^{2} \))(\( ( 1 - 5714 T^{2} + 47458321 T^{4} )^{2} \))(\( ( 1 - 12438 T^{2} + 90917247 T^{4} - 722438497332 T^{6} + 4314779892562287 T^{8} - 28014010783345391958 T^{10} + \)\(10\!\cdots\!61\)\( T^{12} )^{2} \))(\( 1 - 45228 T^{2} + 1051862498 T^{4} - 16711593024188 T^{6} + 200629425132245199 T^{8} - \)\(19\!\cdots\!24\)\( T^{10} + \)\(14\!\cdots\!20\)\( T^{12} - \)\(90\!\cdots\!04\)\( T^{14} + \)\(45\!\cdots\!59\)\( T^{16} - \)\(17\!\cdots\!68\)\( T^{18} + \)\(53\!\cdots\!38\)\( T^{20} - \)\(10\!\cdots\!28\)\( T^{22} + \)\(11\!\cdots\!21\)\( T^{24} \))(\( 1 - 45228 T^{2} + 1051862498 T^{4} - 16711593024188 T^{6} + 200629425132245199 T^{8} - \)\(19\!\cdots\!24\)\( T^{10} + \)\(14\!\cdots\!20\)\( T^{12} - \)\(90\!\cdots\!04\)\( T^{14} + \)\(45\!\cdots\!59\)\( T^{16} - \)\(17\!\cdots\!68\)\( T^{18} + \)\(53\!\cdots\!38\)\( T^{20} - \)\(10\!\cdots\!28\)\( T^{22} + \)\(11\!\cdots\!21\)\( T^{24} \))(\( ( 1 + 1490 T^{2} + 47458321 T^{4} )^{4} \))(\( ( 1 + 6889 T^{2} )^{8} \))(\( ( 1 - 83 T )^{8}( 1 + 83 T )^{8} \))(\( ( 1 - 18644 T^{2} + 171328126 T^{4} - 884812936724 T^{6} + 2252292232139041 T^{8} )^{2} \))(\( ( 1 - 8132 T^{2} + 106317422 T^{4} - 385931066372 T^{6} + 2252292232139041 T^{8} )^{2} \))(\( ( 1 - 10770 T^{2} + 47458321 T^{4} )^{4} \))(\( ( 1 - 28264 T^{2} + 453878684 T^{4} - 5003169128280 T^{6} + 39830061755957126 T^{8} - \)\(23\!\cdots\!80\)\( T^{10} + \)\(10\!\cdots\!44\)\( T^{12} - \)\(30\!\cdots\!04\)\( T^{14} + \)\(50\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 - 6500 T^{2} + 64886758 T^{4} - 308479086500 T^{6} + 2252292232139041 T^{8} )^{4} \))(\( ( 1 - 35944 T^{2} + 663512988 T^{4} - 7834996506968 T^{6} + 64212702138578822 T^{8} - \)\(37\!\cdots\!28\)\( T^{10} + \)\(14\!\cdots\!08\)\( T^{12} - \)\(38\!\cdots\!84\)\( T^{14} + \)\(50\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 - 44 T + 13924 T^{2} - 303116 T^{3} + 47458321 T^{4} )^{2} \))(\( ( 1 - 36 T + 16478 T^{2} - 177884 T^{3} + 135298114 T^{4} - 1225442876 T^{5} + 782018213438 T^{6} - 11769853441284 T^{7} + 2252292232139041 T^{8} )^{2} \))(\( 1 - 13130 T^{2} + 47458321 T^{4} \))(\( ( 1 + 6889 T^{2} )^{2} \))(\( 1 + 13130 T^{2} + 47458321 T^{4} \))(\( ( 1 + 4178 T^{2} + 47458321 T^{4} )^{2} \))(\( ( 1 + 6889 T^{2} )^{4} \))(\( ( 1 + 6608 T^{2} - 3756750 T^{4} + 313604585168 T^{6} + 2252292232139041 T^{8} )^{2} \))(\( 1 - 11804 T^{2} + 67754214 T^{4} - 560198021084 T^{6} + 2252292232139041 T^{8} \))(\( 1 - 1672 T^{2} + 123445084 T^{4} - 156070492984 T^{6} + 7827929741188102 T^{8} - 7406843554662919864 T^{10} + \)\(27\!\cdots\!44\)\( T^{12} - \)\(17\!\cdots\!92\)\( T^{14} + \)\(50\!\cdots\!81\)\( T^{16} \))(\( 1 - 19280 T^{2} + 168996572 T^{4} - 1078781742000 T^{6} + 6945567152070790 T^{8} - 51197170200775182000 T^{10} + \)\(38\!\cdots\!52\)\( T^{12} - \)\(20\!\cdots\!80\)\( T^{14} + \)\(50\!\cdots\!81\)\( T^{16} \))(\( 1 - 48364 T^{2} + 1138161762 T^{4} - 17767706400252 T^{6} + 208480181069188815 T^{8} - \)\(19\!\cdots\!92\)\( T^{10} + \)\(14\!\cdots\!12\)\( T^{12} - \)\(92\!\cdots\!32\)\( T^{14} + \)\(46\!\cdots\!15\)\( T^{16} - \)\(18\!\cdots\!72\)\( T^{18} + \)\(57\!\cdots\!22\)\( T^{20} - \)\(11\!\cdots\!64\)\( T^{22} + \)\(11\!\cdots\!21\)\( T^{24} \))(\( 1 - 48364 T^{2} + 1138161762 T^{4} - 17767706400252 T^{6} + 208480181069188815 T^{8} - \)\(19\!\cdots\!92\)\( T^{10} + \)\(14\!\cdots\!12\)\( T^{12} - \)\(92\!\cdots\!32\)\( T^{14} + \)\(46\!\cdots\!15\)\( T^{16} - \)\(18\!\cdots\!72\)\( T^{18} + \)\(57\!\cdots\!22\)\( T^{20} - \)\(11\!\cdots\!64\)\( T^{22} + \)\(11\!\cdots\!21\)\( T^{24} \))(\( 1 - 85264 T^{2} + 3543197432 T^{4} - 95028175099952 T^{6} + 1837921879888014492 T^{8} - \)\(27\!\cdots\!04\)\( T^{10} + \)\(31\!\cdots\!40\)\( T^{12} - \)\(29\!\cdots\!96\)\( T^{14} + \)\(22\!\cdots\!62\)\( T^{16} - \)\(14\!\cdots\!16\)\( T^{18} + \)\(71\!\cdots\!40\)\( T^{20} - \)\(29\!\cdots\!44\)\( T^{22} + \)\(93\!\cdots\!52\)\( T^{24} - \)\(22\!\cdots\!52\)\( T^{26} + \)\(40\!\cdots\!72\)\( T^{28} - \)\(46\!\cdots\!24\)\( T^{30} + \)\(25\!\cdots\!61\)\( T^{32} \))
$89$ (\( ( 1 - 13250 T^{2} + 62742241 T^{4} )^{2} \))(\( ( 1 - 10640 T^{2} + 62742241 T^{4} )^{2} \))(\( ( 1 - 14490 T^{2} + 62742241 T^{4} )^{2} \))(\( ( 1 - 18924 T^{2} + 226809879 T^{4} - 2101461933080 T^{6} + 14230560089398839 T^{8} - 74496006559106180844 T^{10} + \)\(24\!\cdots\!21\)\( T^{12} )^{2} \))(\( 1 - 64696 T^{2} + 2018996734 T^{4} - 40646358567544 T^{6} + 593437857442633407 T^{8} - \)\(66\!\cdots\!08\)\( T^{10} + \)\(59\!\cdots\!36\)\( T^{12} - \)\(41\!\cdots\!28\)\( T^{14} + \)\(23\!\cdots\!67\)\( T^{16} - \)\(10\!\cdots\!24\)\( T^{18} + \)\(31\!\cdots\!74\)\( T^{20} - \)\(62\!\cdots\!96\)\( T^{22} + \)\(61\!\cdots\!41\)\( T^{24} \))(\( 1 - 64696 T^{2} + 2018996734 T^{4} - 40646358567544 T^{6} + 593437857442633407 T^{8} - \)\(66\!\cdots\!08\)\( T^{10} + \)\(59\!\cdots\!36\)\( T^{12} - \)\(41\!\cdots\!28\)\( T^{14} + \)\(23\!\cdots\!67\)\( T^{16} - \)\(10\!\cdots\!24\)\( T^{18} + \)\(31\!\cdots\!74\)\( T^{20} - \)\(62\!\cdots\!96\)\( T^{22} + \)\(61\!\cdots\!41\)\( T^{24} \))(\( ( 1 - 5326 T^{2} + 62742241 T^{4} )^{4} \))(\( ( 1 + 7921 T^{2} )^{8} \))(\( ( 1 + 63358082 T^{4} + 3936588805702081 T^{8} )^{2} \))(\( ( 1 - 18308 T^{2} + 203581510 T^{4} - 1148684948228 T^{6} + 3936588805702081 T^{8} )^{2} \))(\( ( 1 - 30916 T^{2} + 364289990 T^{4} - 1939739122756 T^{6} + 3936588805702081 T^{8} )^{2} \))(\( ( 1 + 2654 T^{2} + 62742241 T^{4} )^{4} \))(\( ( 1 - 38276 T^{2} + 689965352 T^{4} - 8000293612236 T^{6} + 70413234996490958 T^{8} - \)\(50\!\cdots\!76\)\( T^{10} + \)\(27\!\cdots\!12\)\( T^{12} - \)\(94\!\cdots\!96\)\( T^{14} + \)\(15\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 - 8282 T^{2} + 64385074 T^{4} - 519631239962 T^{6} + 3936588805702081 T^{8} )^{4} \))(\( ( 1 - 19060 T^{2} + 167995176 T^{4} - 770659944668 T^{6} + 3349863709286606 T^{8} - 48352931977406320988 T^{10} + \)\(66\!\cdots\!56\)\( T^{12} - \)\(47\!\cdots\!60\)\( T^{14} + \)\(15\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 + 156 T + 20774 T^{2} + 1235676 T^{3} + 62742241 T^{4} )^{2} \))(\( ( 1 - 256 T + 48252 T^{2} - 6269952 T^{3} + 638304966 T^{4} - 49664289792 T^{5} + 3027438612732 T^{6} - 127227210486016 T^{7} + 3936588805702081 T^{8} )^{2} \))(\( ( 1 - 89 T )^{2}( 1 + 89 T )^{2} \))(\( ( 1 - 89 T )^{2}( 1 + 89 T )^{2} \))(\( ( 1 - 89 T )^{2}( 1 + 89 T )^{2} \))(\( ( 1 - 89 T )^{4}( 1 + 89 T )^{4} \))(\( ( 1 - 89 T )^{4}( 1 + 89 T )^{4} \))(\( ( 1 - 17428 T^{2} + 180509478 T^{4} - 1093471776148 T^{6} + 3936588805702081 T^{8} )^{2} \))(\( ( 1 + 68 T + 15206 T^{2} + 538628 T^{3} + 62742241 T^{4} )^{2} \))(\( ( 1 + 176 T + 28520 T^{2} + 3175008 T^{3} + 333744158 T^{4} + 25149238368 T^{5} + 1789408713320 T^{6} + 87468707209136 T^{7} + 3936588805702081 T^{8} )^{2} \))(\( ( 1 - 40 T + 25916 T^{2} - 837912 T^{3} + 285914566 T^{4} - 6637100952 T^{5} + 1626027917756 T^{6} - 19879251638440 T^{7} + 3936588805702081 T^{8} )^{2} \))(\( ( 1 + 24 T + 25962 T^{2} + 191768 T^{3} + 253674143 T^{4} - 2941553072 T^{5} + 1755043758060 T^{6} - 23300041883312 T^{7} + 15916084215574463 T^{8} + 95305108205009048 T^{9} + \)\(10\!\cdots\!22\)\( T^{10} + \)\(74\!\cdots\!24\)\( T^{11} + \)\(24\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 - 24 T + 25962 T^{2} - 191768 T^{3} + 253674143 T^{4} + 2941553072 T^{5} + 1755043758060 T^{6} + 23300041883312 T^{7} + 15916084215574463 T^{8} - 95305108205009048 T^{9} + \)\(10\!\cdots\!22\)\( T^{10} - \)\(74\!\cdots\!24\)\( T^{11} + \)\(24\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 - 88 T + 33428 T^{2} - 2848088 T^{3} + 652685604 T^{4} - 50244275176 T^{5} + 8431061696684 T^{6} - 571359294604392 T^{7} + 78644602485944758 T^{8} - 4525736972561389032 T^{9} + \)\(52\!\cdots\!44\)\( T^{10} - \)\(24\!\cdots\!36\)\( T^{11} + \)\(25\!\cdots\!24\)\( T^{12} - \)\(88\!\cdots\!88\)\( T^{13} + \)\(82\!\cdots\!88\)\( T^{14} - \)\(17\!\cdots\!08\)\( T^{15} + \)\(15\!\cdots\!61\)\( T^{16} )^{2} \))
$97$ (\( ( 1 - 46 T + 9409 T^{2} )^{4} \))(\( ( 1 - 56 T + 9409 T^{2} )^{4} \))(\( ( 1 + 126 T + 9409 T^{2} )^{4} \))(\( ( 1 - 72 T + 18783 T^{2} - 699184 T^{3} + 176729247 T^{4} - 6374108232 T^{5} + 832972004929 T^{6} )^{4} \))(\( ( 1 + 48 T + 30238 T^{2} + 1616880 T^{3} + 464601471 T^{4} + 24248528864 T^{5} + 5040207919044 T^{6} + 228154408081376 T^{7} + 41130834179172351 T^{8} + 1346815775329601520 T^{9} + \)\(23\!\cdots\!18\)\( T^{10} + \)\(35\!\cdots\!52\)\( T^{11} + \)\(69\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 + 48 T + 30238 T^{2} + 1616880 T^{3} + 464601471 T^{4} + 24248528864 T^{5} + 5040207919044 T^{6} + 228154408081376 T^{7} + 41130834179172351 T^{8} + 1346815775329601520 T^{9} + \)\(23\!\cdots\!18\)\( T^{10} + \)\(35\!\cdots\!52\)\( T^{11} + \)\(69\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 + 8926 T^{2} + 88529281 T^{4} )^{4} \))(\( ( 1 - 97 T )^{8}( 1 + 97 T )^{8} \))(\( ( 1 - 97 T )^{8}( 1 + 97 T )^{8} \))(\( ( 1 - 10628 T^{2} + 166577158 T^{4} - 940889198468 T^{6} + 7837433594376961 T^{8} )^{2} \))(\( ( 1 - 19204 T^{2} + 268303110 T^{4} - 1700116312324 T^{6} + 7837433594376961 T^{8} )^{2} \))(\( ( 1 - 5282 T^{2} + 88529281 T^{4} )^{4} \))(\( ( 1 - 26552 T^{2} + 423728764 T^{4} - 5160251054216 T^{6} + 51404488771355014 T^{8} - \)\(45\!\cdots\!96\)\( T^{10} + \)\(33\!\cdots\!04\)\( T^{12} - \)\(18\!\cdots\!32\)\( T^{14} + \)\(61\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 - 1892 T^{2} + 118100422 T^{4} - 167497399652 T^{6} + 7837433594376961 T^{8} )^{4} \))(\( ( 1 - 57592 T^{2} + 1564478460 T^{4} - 26199743105864 T^{6} + 296300534876302982 T^{8} - \)\(23\!\cdots\!84\)\( T^{10} + \)\(12\!\cdots\!60\)\( T^{12} - \)\(39\!\cdots\!72\)\( T^{14} + \)\(61\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 + 68 T + 3046 T^{2} + 639812 T^{3} + 88529281 T^{4} )^{2} \))(\( ( 1 - 32 T + 19484 T^{2} - 1437536 T^{3} + 199130566 T^{4} - 13525776224 T^{5} + 1724904511004 T^{6} - 26655104157728 T^{7} + 7837433594376961 T^{8} )^{2} \))(\( ( 1 - 97 T )^{2}( 1 + 97 T )^{2} \))(\( ( 1 - 97 T )^{2}( 1 + 97 T )^{2} \))(\( ( 1 - 97 T )^{2}( 1 + 97 T )^{2} \))(\( ( 1 - 190 T + 9409 T^{2} )^{2}( 1 + 190 T + 9409 T^{2} )^{2} \))(\( ( 1 - 97 T )^{4}( 1 + 97 T )^{4} \))(\( ( 1 - 13588 T^{2} + 180804198 T^{4} - 1202935870228 T^{6} + 7837433594376961 T^{8} )^{2} \))(\( ( 1 + 300 T + 41206 T^{2} + 2822700 T^{3} + 88529281 T^{4} )^{2} \))(\( ( 1 + 120 T + 34316 T^{2} + 2972040 T^{3} + 480186342 T^{4} + 27963924360 T^{5} + 3037970806796 T^{6} + 99956640591480 T^{7} + 7837433594376961 T^{8} )^{2} \))(\( ( 1 - 264 T + 52364 T^{2} - 7260024 T^{3} + 808802534 T^{4} - 68309565816 T^{5} + 4635747270284 T^{6} - 219904609301256 T^{7} + 7837433594376961 T^{8} )^{2} \))(\( ( 1 + 156 T + 46434 T^{2} + 6606636 T^{3} + 998831087 T^{4} + 116839901496 T^{5} + 12239702422620 T^{6} + 1099346633175864 T^{7} + 88425797972558447 T^{8} + 5503142834756108844 T^{9} + \)\(36\!\cdots\!74\)\( T^{10} + \)\(11\!\cdots\!44\)\( T^{11} + \)\(69\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 + 156 T + 46434 T^{2} + 6606636 T^{3} + 998831087 T^{4} + 116839901496 T^{5} + 12239702422620 T^{6} + 1099346633175864 T^{7} + 88425797972558447 T^{8} + 5503142834756108844 T^{9} + \)\(36\!\cdots\!74\)\( T^{10} + \)\(11\!\cdots\!44\)\( T^{11} + \)\(69\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 - 432 T + 114280 T^{2} - 21434448 T^{3} + 3301939196 T^{4} - 437740327152 T^{5} + 53096494516824 T^{6} - 5875910744827152 T^{7} + 598998309831134342 T^{8} - 55286444198078673168 T^{9} + \)\(47\!\cdots\!44\)\( T^{10} - \)\(36\!\cdots\!08\)\( T^{11} + \)\(25\!\cdots\!56\)\( T^{12} - \)\(15\!\cdots\!52\)\( T^{13} + \)\(79\!\cdots\!80\)\( T^{14} - \)\(28\!\cdots\!08\)\( T^{15} + \)\(61\!\cdots\!21\)\( T^{16} )^{2} \))
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