Properties

Label 1584.2
Level 1584
Weight 2
Dimension 29903
Nonzero newspaces 32
Sturm bound 276480
Trace bound 25

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Defining parameters

Level: \( N \) = \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(276480\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1584))\).

Total New Old
Modular forms 71360 30631 40729
Cusp forms 66881 29903 36978
Eisenstein series 4479 728 3751

Trace form

\( 29903q - 48q^{2} - 48q^{3} - 52q^{4} - 65q^{5} - 64q^{6} - 47q^{7} - 60q^{8} - 24q^{9} + O(q^{10}) \) \( 29903q - 48q^{2} - 48q^{3} - 52q^{4} - 65q^{5} - 64q^{6} - 47q^{7} - 60q^{8} - 24q^{9} - 148q^{10} - 54q^{11} - 144q^{12} - 77q^{13} - 12q^{14} - 54q^{15} - 4q^{16} - 91q^{17} - 24q^{18} - 115q^{19} + 52q^{20} - 54q^{21} - 8q^{22} - 40q^{23} + 41q^{25} + 68q^{26} - 12q^{27} - 68q^{28} - q^{29} - 24q^{30} - 11q^{31} + 12q^{32} - 141q^{33} - 88q^{34} + 81q^{35} - 56q^{36} - 217q^{37} - 140q^{38} + 66q^{39} - 164q^{40} - 25q^{41} - 144q^{42} + 56q^{43} - 140q^{44} - 134q^{45} - 268q^{46} + 75q^{47} - 168q^{48} - 215q^{49} - 216q^{50} + 16q^{51} - 172q^{52} - 63q^{53} - 152q^{54} - 87q^{55} - 312q^{56} - 60q^{57} - 124q^{58} + 13q^{59} - 280q^{60} - 13q^{61} - 252q^{62} - 54q^{63} - 4q^{64} - 282q^{65} - 192q^{66} - 104q^{67} - 220q^{68} - 230q^{69} + 168q^{70} - 163q^{71} - 288q^{72} + 75q^{73} - 64q^{74} - 152q^{75} + 180q^{76} - 32q^{77} - 360q^{78} - 77q^{79} - 96q^{80} - 296q^{81} + 36q^{82} - 193q^{83} - 352q^{84} + 161q^{85} - 180q^{86} - 186q^{87} + 192q^{88} + 14q^{89} - 352q^{90} - 215q^{91} - 84q^{92} + 2q^{93} - 4q^{94} - 195q^{95} - 200q^{96} + 35q^{97} - 12q^{98} - 69q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1584))\)

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
1584.2.a \(\chi_{1584}(1, \cdot)\) 1584.2.a.a 1 1
1584.2.a.b 1
1584.2.a.c 1
1584.2.a.d 1
1584.2.a.e 1
1584.2.a.f 1
1584.2.a.g 1
1584.2.a.h 1
1584.2.a.i 1
1584.2.a.j 1
1584.2.a.k 1
1584.2.a.l 1
1584.2.a.m 1
1584.2.a.n 1
1584.2.a.o 1
1584.2.a.p 1
1584.2.a.q 1
1584.2.a.r 1
1584.2.a.s 1
1584.2.a.t 2
1584.2.a.u 2
1584.2.a.v 2
1584.2.b \(\chi_{1584}(593, \cdot)\) 1584.2.b.a 2 1
1584.2.b.b 2
1584.2.b.c 2
1584.2.b.d 2
1584.2.b.e 4
1584.2.b.f 6
1584.2.b.g 6
1584.2.d \(\chi_{1584}(287, \cdot)\) 1584.2.d.a 2 1
1584.2.d.b 2
1584.2.d.c 8
1584.2.d.d 8
1584.2.f \(\chi_{1584}(793, \cdot)\) None 0 1
1584.2.h \(\chi_{1584}(1495, \cdot)\) None 0 1
1584.2.k \(\chi_{1584}(1079, \cdot)\) None 0 1
1584.2.m \(\chi_{1584}(1385, \cdot)\) None 0 1
1584.2.o \(\chi_{1584}(703, \cdot)\) 1584.2.o.a 2 1
1584.2.o.b 4
1584.2.o.c 4
1584.2.o.d 4
1584.2.o.e 4
1584.2.o.f 4
1584.2.o.g 8
1584.2.q \(\chi_{1584}(529, \cdot)\) n/a 120 2
1584.2.r \(\chi_{1584}(307, \cdot)\) n/a 236 2
1584.2.u \(\chi_{1584}(397, \cdot)\) n/a 200 2
1584.2.v \(\chi_{1584}(683, \cdot)\) n/a 160 2
1584.2.y \(\chi_{1584}(197, \cdot)\) n/a 192 2
1584.2.z \(\chi_{1584}(289, \cdot)\) n/a 116 4
1584.2.bc \(\chi_{1584}(175, \cdot)\) n/a 144 2
1584.2.be \(\chi_{1584}(329, \cdot)\) None 0 2
1584.2.bg \(\chi_{1584}(23, \cdot)\) None 0 2
1584.2.bh \(\chi_{1584}(439, \cdot)\) None 0 2
1584.2.bj \(\chi_{1584}(265, \cdot)\) None 0 2
1584.2.bl \(\chi_{1584}(815, \cdot)\) n/a 120 2
1584.2.bn \(\chi_{1584}(65, \cdot)\) n/a 140 2
1584.2.bq \(\chi_{1584}(127, \cdot)\) n/a 120 4
1584.2.bs \(\chi_{1584}(233, \cdot)\) None 0 4
1584.2.bu \(\chi_{1584}(71, \cdot)\) None 0 4
1584.2.bx \(\chi_{1584}(343, \cdot)\) None 0 4
1584.2.bz \(\chi_{1584}(361, \cdot)\) None 0 4
1584.2.cb \(\chi_{1584}(575, \cdot)\) 1584.2.cb.a 32 4
1584.2.cb.b 64
1584.2.cd \(\chi_{1584}(17, \cdot)\) 1584.2.cd.a 8 4
1584.2.cd.b 8
1584.2.cd.c 16
1584.2.cd.d 16
1584.2.cd.e 24
1584.2.cd.f 24
1584.2.cf \(\chi_{1584}(155, \cdot)\) n/a 960 4
1584.2.cg \(\chi_{1584}(461, \cdot)\) n/a 1136 4
1584.2.cj \(\chi_{1584}(43, \cdot)\) n/a 1136 4
1584.2.ck \(\chi_{1584}(133, \cdot)\) n/a 960 4
1584.2.cm \(\chi_{1584}(49, \cdot)\) n/a 560 8
1584.2.cn \(\chi_{1584}(413, \cdot)\) n/a 768 8
1584.2.cq \(\chi_{1584}(179, \cdot)\) n/a 768 8
1584.2.cr \(\chi_{1584}(37, \cdot)\) n/a 944 8
1584.2.cu \(\chi_{1584}(19, \cdot)\) n/a 944 8
1584.2.cw \(\chi_{1584}(497, \cdot)\) n/a 560 8
1584.2.cy \(\chi_{1584}(47, \cdot)\) n/a 576 8
1584.2.da \(\chi_{1584}(25, \cdot)\) None 0 8
1584.2.dc \(\chi_{1584}(7, \cdot)\) None 0 8
1584.2.dd \(\chi_{1584}(119, \cdot)\) None 0 8
1584.2.df \(\chi_{1584}(41, \cdot)\) None 0 8
1584.2.dh \(\chi_{1584}(79, \cdot)\) n/a 576 8
1584.2.dl \(\chi_{1584}(157, \cdot)\) n/a 4544 16
1584.2.dm \(\chi_{1584}(139, \cdot)\) n/a 4544 16
1584.2.dp \(\chi_{1584}(29, \cdot)\) n/a 4544 16
1584.2.dq \(\chi_{1584}(59, \cdot)\) n/a 4544 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1584))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1584)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(528))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(792))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ (\( 1 + 4 T + 5 T^{2} \))(\( 1 + 4 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4} \))(\( 1 + 2 T^{2} + 25 T^{4} \))(\( 1 + 2 T^{2} + 25 T^{4} \))(\( 1 - 2 T^{2} + 25 T^{4} \))(\( 1 - 8 T^{2} + 25 T^{4} \))(\( 1 - 8 T^{2} + 25 T^{4} \))(\( 1 - 2 T^{2} + 25 T^{4} \))(\( ( 1 - 8 T^{2} + 25 T^{4} )^{2} \))(\( 1 - 2 T^{2} + 11 T^{4} - 228 T^{6} + 275 T^{8} - 1250 T^{10} + 15625 T^{12} \))(\( 1 - 2 T^{2} + 11 T^{4} - 228 T^{6} + 275 T^{8} - 1250 T^{10} + 15625 T^{12} \))(\( 1 - 8 T^{2} + 25 T^{4} \))(\( 1 - 8 T^{2} + 25 T^{4} \))(\( 1 - 12 T^{2} + 80 T^{4} - 372 T^{6} + 1614 T^{8} - 9300 T^{10} + 50000 T^{12} - 187500 T^{14} + 390625 T^{16} \))(\( 1 - 12 T^{2} + 80 T^{4} - 372 T^{6} + 1614 T^{8} - 9300 T^{10} + 50000 T^{12} - 187500 T^{14} + 390625 T^{16} \))(\( ( 1 + 3 T + 5 T^{2} )^{2} \))(\( ( 1 + 4 T^{2} + 25 T^{4} )^{2} \))(\( ( 1 + 5 T^{2} )^{4} \))(\( ( 1 + 4 T^{2} + 25 T^{4} )^{2} \))(\( ( 1 - 3 T + 4 T^{2} - 15 T^{3} + 25 T^{4} )^{2} \))(\( ( 1 - 2 T + 5 T^{2} )^{4} \))(\( ( 1 + 2 T + 8 T^{2} + 10 T^{3} + 25 T^{4} )^{4} \))(\( 1 + 2 T^{2} + 20 T^{3} - T^{4} + 40 T^{5} + 148 T^{6} + 80 T^{7} + 341 T^{8} + 400 T^{9} + 3700 T^{10} + 5000 T^{11} - 625 T^{12} + 62500 T^{13} + 31250 T^{14} + 390625 T^{16} \))(\( 1 + 2 T^{2} - 20 T^{3} - T^{4} - 40 T^{5} + 148 T^{6} - 80 T^{7} + 341 T^{8} - 400 T^{9} + 3700 T^{10} - 5000 T^{11} - 625 T^{12} - 62500 T^{13} + 31250 T^{14} + 390625 T^{16} \))(\( 1 + 26 T^{2} + 267 T^{4} + 1158 T^{6} - 345 T^{8} - 23178 T^{10} - 84123 T^{12} - 137046 T^{14} - 351264 T^{16} - 3426150 T^{18} - 52576875 T^{20} - 362156250 T^{22} - 134765625 T^{24} + 11308593750 T^{26} + 65185546875 T^{28} + 158691406250 T^{30} + 152587890625 T^{32} \))(\( 1 - 14 T^{2} + 107 T^{4} - 642 T^{6} + 2975 T^{8} - 10018 T^{10} + 21477 T^{12} - 8526 T^{14} - 100944 T^{16} - 213150 T^{18} + 13423125 T^{20} - 156531250 T^{22} + 1162109375 T^{24} - 6269531250 T^{26} + 26123046875 T^{28} - 85449218750 T^{30} + 152587890625 T^{32} \))
$7$ (\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T - 2 T^{2} - 14 T^{3} + 49 T^{4} \))(\( 1 + 4 T + 10 T^{2} + 28 T^{3} + 49 T^{4} \))(\( 1 + 4 T + 10 T^{2} + 28 T^{3} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 + 4 T^{2} + 49 T^{4} \))(\( 1 + 4 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( ( 1 - 8 T^{2} + 49 T^{4} )^{2} \))(\( 1 - 14 T^{2} + 83 T^{4} - 348 T^{6} + 4067 T^{8} - 33614 T^{10} + 117649 T^{12} \))(\( 1 - 14 T^{2} + 83 T^{4} - 348 T^{6} + 4067 T^{8} - 33614 T^{10} + 117649 T^{12} \))(\( 1 - 6 T^{2} + 49 T^{4} \))(\( 1 - 6 T^{2} + 49 T^{4} \))(\( 1 - 28 T^{2} + 416 T^{4} - 4260 T^{6} + 33422 T^{8} - 208740 T^{10} + 998816 T^{12} - 3294172 T^{14} + 5764801 T^{16} \))(\( 1 - 28 T^{2} + 416 T^{4} - 4260 T^{6} + 33422 T^{8} - 208740 T^{10} + 998816 T^{12} - 3294172 T^{14} + 5764801 T^{16} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 + 8 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 + 8 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 + 8 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 + 7 T^{2} )^{4} \))(\( ( 1 + 4 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 - 4 T^{2} - 6 T^{4} - 196 T^{6} + 2401 T^{8} )^{2} \))(\( 1 + 4 T^{2} - 40 T^{3} + 57 T^{4} - 160 T^{5} + 1052 T^{6} - 2020 T^{7} + 4565 T^{8} - 14140 T^{9} + 51548 T^{10} - 54880 T^{11} + 136857 T^{12} - 672280 T^{13} + 470596 T^{14} + 5764801 T^{16} \))(\( 1 + 4 T^{2} - 40 T^{3} + 57 T^{4} - 160 T^{5} + 1052 T^{6} - 2020 T^{7} + 4565 T^{8} - 14140 T^{9} + 51548 T^{10} - 54880 T^{11} + 136857 T^{12} - 672280 T^{13} + 470596 T^{14} + 5764801 T^{16} \))(\( ( 1 + 13 T^{2} - 20 T^{3} + 80 T^{4} - 260 T^{5} + 783 T^{6} - 2170 T^{7} + 6819 T^{8} - 15190 T^{9} + 38367 T^{10} - 89180 T^{11} + 192080 T^{12} - 336140 T^{13} + 1529437 T^{14} + 5764801 T^{16} )^{2} \))(\( ( 1 + T^{2} + 20 T^{3} + 12 T^{4} + 20 T^{5} + 263 T^{6} + 650 T^{7} - 565 T^{8} + 4550 T^{9} + 12887 T^{10} + 6860 T^{11} + 28812 T^{12} + 336140 T^{13} + 117649 T^{14} + 5764801 T^{16} )^{2} \))
$11$ (\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 + 10 T^{2} + 121 T^{4} \))(\( 1 + 2 T + 5 T^{2} + 52 T^{3} + 55 T^{4} + 242 T^{5} + 1331 T^{6} \))(\( 1 - 2 T + 5 T^{2} - 52 T^{3} + 55 T^{4} - 242 T^{5} + 1331 T^{6} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{8} \))(\( ( 1 - T )^{8} \))(\( 1 + 11 T^{2} \))(\( ( 1 + 6 T + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 - 6 T + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 12 T^{2} + 86 T^{4} - 1452 T^{6} + 14641 T^{8} \))(\( 1 + 4 T - 44 T^{3} - 226 T^{4} - 484 T^{5} + 5324 T^{7} + 14641 T^{8} \))(\( 1 - 4 T + 44 T^{3} - 226 T^{4} + 484 T^{5} - 5324 T^{7} + 14641 T^{8} \))(\( 1 - 60 T^{2} + 1779 T^{4} - 33610 T^{6} + 439341 T^{8} - 4066810 T^{10} + 26046339 T^{12} - 106293660 T^{14} + 214358881 T^{16} \))(\( 1 + 44 T^{2} + 995 T^{4} + 15646 T^{6} + 192109 T^{8} + 1893166 T^{10} + 14567795 T^{12} + 77948684 T^{14} + 214358881 T^{16} \))
$13$ (\( 1 + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 2 T + 10 T^{2} + 26 T^{3} + 169 T^{4} \))(\( 1 - 4 T + 22 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 - 4 T + 22 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 - 8 T^{2} + 169 T^{4} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( 1 - 8 T^{2} + 169 T^{4} \))(\( ( 1 - 2 T^{2} + 169 T^{4} )^{2} \))(\( 1 - 44 T^{2} + 927 T^{4} - 13496 T^{6} + 156663 T^{8} - 1256684 T^{10} + 4826809 T^{12} \))(\( 1 - 44 T^{2} + 927 T^{4} - 13496 T^{6} + 156663 T^{8} - 1256684 T^{10} + 4826809 T^{12} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( ( 1 + 4 T + 14 T^{2} - 36 T^{3} - 154 T^{4} - 468 T^{5} + 2366 T^{6} + 8788 T^{7} + 28561 T^{8} )^{2} \))(\( ( 1 + 4 T + 14 T^{2} - 36 T^{3} - 154 T^{4} - 468 T^{5} + 2366 T^{6} + 8788 T^{7} + 28561 T^{8} )^{2} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 8 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 13 T^{2} )^{4} \))(\( ( 1 - 8 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 13 T^{2} )^{4} \))(\( ( 1 + 14 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 20 T^{2} + 330 T^{4} - 3380 T^{6} + 28561 T^{8} )^{2} \))(\( 1 + 18 T^{2} - 140 T^{3} + 15 T^{4} - 2520 T^{5} + 6398 T^{6} - 7840 T^{7} + 157849 T^{8} - 101920 T^{9} + 1081262 T^{10} - 5536440 T^{11} + 428415 T^{12} - 51981020 T^{13} + 86882562 T^{14} + 815730721 T^{16} \))(\( 1 + 18 T^{2} - 140 T^{3} + 15 T^{4} - 2520 T^{5} + 6398 T^{6} - 7840 T^{7} + 157849 T^{8} - 101920 T^{9} + 1081262 T^{10} - 5536440 T^{11} + 428415 T^{12} - 51981020 T^{13} + 86882562 T^{14} + 815730721 T^{16} \))(\( ( 1 + 7 T^{2} + 80 T^{3} + 170 T^{4} + 560 T^{5} + 4587 T^{6} + 13570 T^{7} + 40179 T^{8} + 176410 T^{9} + 775203 T^{10} + 1230320 T^{11} + 4855370 T^{12} + 29703440 T^{13} + 33787663 T^{14} + 815730721 T^{16} )^{2} \))(\( ( 1 - 9 T^{2} - 80 T^{3} + 42 T^{4} + 720 T^{5} + 3803 T^{6} - 7390 T^{7} - 39725 T^{8} - 96070 T^{9} + 642707 T^{10} + 1581840 T^{11} + 1199562 T^{12} - 29703440 T^{13} - 43441281 T^{14} + 815730721 T^{16} )^{2} \))
$17$ (\( 1 - 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 - 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 - 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 - 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{4} \))(\( ( 1 - 2 T + 35 T^{2} - 52 T^{3} + 595 T^{4} - 578 T^{5} + 4913 T^{6} )^{2} \))(\( ( 1 + 2 T + 35 T^{2} + 52 T^{3} + 595 T^{4} + 578 T^{5} + 4913 T^{6} )^{2} \))(\( 1 - 32 T^{2} + 289 T^{4} \))(\( 1 - 32 T^{2} + 289 T^{4} \))(\( 1 - 48 T^{2} + 1724 T^{4} - 42960 T^{6} + 826374 T^{8} - 12415440 T^{10} + 143990204 T^{12} - 1158603312 T^{14} + 6975757441 T^{16} \))(\( 1 - 48 T^{2} + 1724 T^{4} - 42960 T^{6} + 826374 T^{8} - 12415440 T^{10} + 143990204 T^{12} - 1158603312 T^{14} + 6975757441 T^{16} \))(\( ( 1 - 17 T^{2} )^{2} \))(\( ( 1 - 22 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 + 32 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 22 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 17 T^{2} )^{4} \))(\( ( 1 - 24 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 12 T^{2} + 422 T^{4} - 3468 T^{6} + 83521 T^{8} )^{2} \))(\( 1 + 8 T + 14 T^{2} + 68 T^{3} + 863 T^{4} + 3448 T^{5} + 11526 T^{6} + 56904 T^{7} + 246073 T^{8} + 967368 T^{9} + 3331014 T^{10} + 16940024 T^{11} + 72078623 T^{12} + 96550276 T^{13} + 337925966 T^{14} + 3282709384 T^{15} + 6975757441 T^{16} \))(\( 1 - 8 T + 14 T^{2} - 68 T^{3} + 863 T^{4} - 3448 T^{5} + 11526 T^{6} - 56904 T^{7} + 246073 T^{8} - 967368 T^{9} + 3331014 T^{10} - 16940024 T^{11} + 72078623 T^{12} - 96550276 T^{13} + 337925966 T^{14} - 3282709384 T^{15} + 6975757441 T^{16} \))(\( 1 - 58 T^{2} + 1230 T^{4} + 3270 T^{6} - 669405 T^{8} + 13275246 T^{10} - 49036968 T^{12} - 2836388280 T^{14} + 74928517905 T^{16} - 819716212920 T^{18} - 4095616604328 T^{20} + 320432166316974 T^{22} - 4669606909792605 T^{24} + 6592300054468230 T^{26} + 716625351792606030 T^{28} - 9765913940445253882 T^{30} + 48661191875666868481 T^{32} \))(\( 1 - 66 T^{2} + 2454 T^{4} - 79026 T^{6} + 2169131 T^{8} - 50747418 T^{10} + 1093727256 T^{12} - 21317253528 T^{14} + 375077707057 T^{16} - 6160686269592 T^{18} + 91349194148376 T^{20} - 1224919303546842 T^{22} + 15131331713753771 T^{24} - 159315933976882674 T^{26} + 1429754970161833494 T^{28} - 11112936552920461314 T^{30} + 48661191875666868481 T^{32} \))
$19$ (\( 1 + 4 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( ( 1 - 4 T + 19 T^{2} )^{2} \))(\( ( 1 + 2 T + 19 T^{2} )^{2} \))(\( ( 1 + 2 T + 19 T^{2} )^{2} \))(\( 1 - 20 T^{2} + 361 T^{4} \))(\( 1 - 20 T^{2} + 361 T^{4} \))(\( 1 - 20 T^{2} + 361 T^{4} \))(\( 1 - 20 T^{2} + 361 T^{4} \))(\( ( 1 + 16 T^{2} + 361 T^{4} )^{2} \))(\( 1 - 84 T^{2} + 3323 T^{4} - 79336 T^{6} + 1199603 T^{8} - 10946964 T^{10} + 47045881 T^{12} \))(\( 1 - 84 T^{2} + 3323 T^{4} - 79336 T^{6} + 1199603 T^{8} - 10946964 T^{10} + 47045881 T^{12} \))(\( 1 - 30 T^{2} + 361 T^{4} \))(\( 1 - 30 T^{2} + 361 T^{4} \))(\( 1 - 40 T^{2} + 1652 T^{4} - 39864 T^{6} + 928262 T^{8} - 14390904 T^{10} + 215290292 T^{12} - 1881835240 T^{14} + 16983563041 T^{16} \))(\( 1 - 40 T^{2} + 1652 T^{4} - 39864 T^{6} + 928262 T^{8} - 14390904 T^{10} + 215290292 T^{12} - 1881835240 T^{14} + 16983563041 T^{16} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{4} \))(\( ( 1 - 16 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 + 19 T^{2} )^{4} \))(\( ( 1 + 19 T^{2} )^{4} \))(\( ( 1 + 28 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 + 20 T^{2} + 630 T^{4} + 7220 T^{6} + 130321 T^{8} )^{2} \))(\( 1 + 30 T^{2} + 260 T^{3} + 279 T^{4} + 7800 T^{5} + 27830 T^{6} + 80080 T^{7} + 888361 T^{8} + 1521520 T^{9} + 10046630 T^{10} + 53500200 T^{11} + 36359559 T^{12} + 643785740 T^{13} + 1411376430 T^{14} + 16983563041 T^{16} \))(\( 1 + 30 T^{2} + 260 T^{3} + 279 T^{4} + 7800 T^{5} + 27830 T^{6} + 80080 T^{7} + 888361 T^{8} + 1521520 T^{9} + 10046630 T^{10} + 53500200 T^{11} + 36359559 T^{12} + 643785740 T^{13} + 1411376430 T^{14} + 16983563041 T^{16} \))(\( ( 1 + 34 T^{2} - 20 T^{3} + 395 T^{4} - 680 T^{5} + 1356 T^{6} - 48280 T^{7} - 47451 T^{8} - 917320 T^{9} + 489516 T^{10} - 4664120 T^{11} + 51476795 T^{12} - 49521980 T^{13} + 1599559954 T^{14} + 16983563041 T^{16} )^{2} \))(\( ( 1 + 30 T^{2} + 20 T^{3} + 279 T^{4} + 600 T^{5} + 1340 T^{6} - 27200 T^{7} - 3419 T^{8} - 516800 T^{9} + 483740 T^{10} + 4115400 T^{11} + 36359559 T^{12} + 49521980 T^{13} + 1411376430 T^{14} + 16983563041 T^{16} )^{2} \))
$23$ (\( 1 + 6 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 9 T + 62 T^{2} - 207 T^{3} + 529 T^{4} \))(\( 1 + 38 T^{2} + 529 T^{4} \))(\( 1 + 38 T^{2} + 529 T^{4} \))(\( 1 - 44 T^{2} + 529 T^{4} \))(\( 1 - 14 T^{2} + 529 T^{4} \))(\( 1 - 14 T^{2} + 529 T^{4} \))(\( 1 - 44 T^{2} + 529 T^{4} \))(\( ( 1 - 38 T^{2} + 529 T^{4} )^{2} \))(\( 1 - 56 T^{2} + 2407 T^{4} - 60320 T^{6} + 1273303 T^{8} - 15671096 T^{10} + 148035889 T^{12} \))(\( 1 - 56 T^{2} + 2407 T^{4} - 60320 T^{6} + 1273303 T^{8} - 15671096 T^{10} + 148035889 T^{12} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( ( 1 + 4 T + 23 T^{2} )^{2} \))(\( ( 1 - 8 T + 66 T^{2} - 336 T^{3} + 2086 T^{4} - 7728 T^{5} + 34914 T^{6} - 97336 T^{7} + 279841 T^{8} )^{2} \))(\( ( 1 + 8 T + 66 T^{2} + 336 T^{3} + 2086 T^{4} + 7728 T^{5} + 34914 T^{6} + 97336 T^{7} + 279841 T^{8} )^{2} \))(\( ( 1 - 9 T + 23 T^{2} )( 1 + 9 T + 23 T^{2} ) \))(\( ( 1 - 44 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 - 2 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 - 44 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 - 9 T + 58 T^{2} - 207 T^{3} + 529 T^{4} )( 1 + 9 T + 58 T^{2} + 207 T^{3} + 529 T^{4} ) \))(\( ( 1 - 10 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 - 68 T^{2} + 2106 T^{4} - 35972 T^{6} + 279841 T^{8} )^{2} \))(\( 1 - 96 T^{2} + 4612 T^{4} - 151328 T^{6} + 3857990 T^{8} - 80052512 T^{10} + 1290626692 T^{12} - 14211445344 T^{14} + 78310985281 T^{16} \))(\( 1 - 96 T^{2} + 4612 T^{4} - 151328 T^{6} + 3857990 T^{8} - 80052512 T^{10} + 1290626692 T^{12} - 14211445344 T^{14} + 78310985281 T^{16} \))(\( ( 1 - 102 T^{2} + 5430 T^{4} - 195472 T^{6} + 5177079 T^{8} - 103404688 T^{10} + 1519536630 T^{12} - 15099660678 T^{14} + 78310985281 T^{16} )^{2} \))(\( ( 1 - 126 T^{2} + 7702 T^{4} - 299408 T^{6} + 8135495 T^{8} - 158386832 T^{10} + 2155335382 T^{12} - 18652522014 T^{14} + 78310985281 T^{16} )^{2} \))
$29$ (\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 8 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 - 2 T + 42 T^{2} - 58 T^{3} + 841 T^{4} \))(\( 1 + 4 T + 30 T^{2} + 116 T^{3} + 841 T^{4} \))(\( 1 - 4 T + 30 T^{2} - 116 T^{3} + 841 T^{4} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 + 10 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 + 4 T + 31 T^{2} - 24 T^{3} + 899 T^{4} + 3364 T^{5} + 24389 T^{6} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} + 24 T^{3} + 899 T^{4} - 3364 T^{5} + 24389 T^{6} )^{2} \))(\( 1 - 40 T^{2} + 841 T^{4} \))(\( 1 - 40 T^{2} + 841 T^{4} \))(\( ( 1 - 46 T^{2} + 841 T^{4} )^{4} \))(\( ( 1 - 46 T^{2} + 841 T^{4} )^{4} \))(\( ( 1 - 29 T^{2} )^{2} \))(\( ( 1 - 10 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 + 8 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 10 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 29 T^{2} )^{4} \))(\( ( 1 + 32 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 29 T^{2} )^{8} \))(\( 1 - 10 T + 57 T^{2} - 460 T^{3} + 4203 T^{4} - 24760 T^{5} + 119139 T^{6} - 824650 T^{7} + 5236800 T^{8} - 23914850 T^{9} + 100195899 T^{10} - 603871640 T^{11} + 2972702043 T^{12} - 9435128540 T^{13} + 33904929297 T^{14} - 172498763090 T^{15} + 500246412961 T^{16} \))(\( 1 + 10 T + 57 T^{2} + 460 T^{3} + 4203 T^{4} + 24760 T^{5} + 119139 T^{6} + 824650 T^{7} + 5236800 T^{8} + 23914850 T^{9} + 100195899 T^{10} + 603871640 T^{11} + 2972702043 T^{12} + 9435128540 T^{13} + 33904929297 T^{14} + 172498763090 T^{15} + 500246412961 T^{16} \))(\( 1 + 20 T^{2} + 338 T^{4} + 28080 T^{6} - 44437 T^{8} - 6939980 T^{10} + 33962216 T^{12} - 13624904800 T^{14} - 492015847995 T^{16} - 11458544936800 T^{18} + 24020830094696 T^{20} - 4128061951273580 T^{22} - 22229449852747957 T^{24} + 11813459111069644080 T^{26} + \)\(11\!\cdots\!58\)\( T^{28} + \)\(59\!\cdots\!20\)\( T^{30} + \)\(25\!\cdots\!21\)\( T^{32} \))(\( 1 - 124 T^{2} + 6130 T^{4} - 99600 T^{6} - 4158805 T^{8} + 266456228 T^{10} - 4329267832 T^{12} - 127695800800 T^{14} + 7658149257925 T^{16} - 107392168472800 T^{18} - 3062008881484792 T^{20} + 158494378440093188 T^{22} - 2080427283454271605 T^{24} - 41902440436700019600 T^{26} + \)\(21\!\cdots\!30\)\( T^{28} - \)\(36\!\cdots\!44\)\( T^{30} + \)\(25\!\cdots\!21\)\( T^{32} \))
$31$ (\( 1 + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 - 7 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 - 7 T + 70 T^{2} - 217 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 46 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 46 T^{2} + 248 T^{3} + 961 T^{4} \))(\( ( 1 + 2 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 8 T + 31 T^{2} )^{2} \))(\( ( 1 + 2 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{4} \))(\( ( 1 - 6 T + 77 T^{2} - 340 T^{3} + 2387 T^{4} - 5766 T^{5} + 29791 T^{6} )^{2} \))(\( ( 1 - 6 T + 77 T^{2} - 340 T^{3} + 2387 T^{4} - 5766 T^{5} + 29791 T^{6} )^{2} \))(\( 1 - 30 T^{2} + 961 T^{4} \))(\( 1 - 30 T^{2} + 961 T^{4} \))(\( 1 - 160 T^{2} + 11420 T^{4} - 506208 T^{6} + 17124038 T^{8} - 486465888 T^{10} + 10546609820 T^{12} - 142000588960 T^{14} + 852891037441 T^{16} \))(\( 1 - 160 T^{2} + 11420 T^{4} - 506208 T^{6} + 17124038 T^{8} - 486465888 T^{10} + 10546609820 T^{12} - 142000588960 T^{14} + 852891037441 T^{16} \))(\( ( 1 - 5 T + 31 T^{2} )( 1 + 5 T + 31 T^{2} ) \))(\( ( 1 - 50 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 31 T^{2} )^{4} \))(\( ( 1 - 50 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 5 T - 6 T^{2} - 155 T^{3} + 961 T^{4} )( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} ) \))(\( ( 1 + 2 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 58 T^{2} + 961 T^{4} )^{4} \))(\( 1 - 14 T + 85 T^{2} + 20 T^{3} - 3875 T^{4} + 29468 T^{5} - 66917 T^{6} - 526790 T^{7} + 5550740 T^{8} - 16330490 T^{9} - 64307237 T^{10} + 877881188 T^{11} - 3578643875 T^{12} + 572583020 T^{13} + 75437812885 T^{14} - 385176597554 T^{15} + 852891037441 T^{16} \))(\( 1 - 14 T + 85 T^{2} + 20 T^{3} - 3875 T^{4} + 29468 T^{5} - 66917 T^{6} - 526790 T^{7} + 5550740 T^{8} - 16330490 T^{9} - 64307237 T^{10} + 877881188 T^{11} - 3578643875 T^{12} + 572583020 T^{13} + 75437812885 T^{14} - 385176597554 T^{15} + 852891037441 T^{16} \))(\( ( 1 + 8 T - 24 T^{2} - 88 T^{3} + 1681 T^{4} + 7064 T^{5} + 54924 T^{6} + 168376 T^{7} - 1019363 T^{8} + 5219656 T^{9} + 52781964 T^{10} + 210443624 T^{11} + 1552438801 T^{12} - 2519365288 T^{13} - 21300088344 T^{14} + 220100912888 T^{15} + 852891037441 T^{16} )^{2} \))(\( ( 1 + 4 T - 20 T^{2} - 100 T^{3} + 1045 T^{4} + 4772 T^{5} - 26972 T^{6} + 24400 T^{7} + 1354325 T^{8} + 756400 T^{9} - 25920092 T^{10} + 142162652 T^{11} + 965079445 T^{12} - 2862915100 T^{13} - 17750073620 T^{14} + 110050456444 T^{15} + 852891037441 T^{16} )^{2} \))
$37$ (\( 1 - 6 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 3 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 11 T + 100 T^{2} + 407 T^{3} + 1369 T^{4} \))(\( 1 - 4 T + 46 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 - 4 T + 46 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( ( 1 + 10 T + 37 T^{2} )^{2} \))(\( ( 1 + 4 T + 37 T^{2} )^{2} \))(\( ( 1 + 4 T + 37 T^{2} )^{2} \))(\( ( 1 + 10 T + 37 T^{2} )^{2} \))(\( ( 1 - 8 T + 37 T^{2} )^{4} \))(\( ( 1 - 6 T + 95 T^{2} - 380 T^{3} + 3515 T^{4} - 8214 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 - 6 T + 95 T^{2} - 380 T^{3} + 3515 T^{4} - 8214 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 + 6 T + 37 T^{2} )^{2} \))(\( ( 1 + 6 T + 37 T^{2} )^{2} \))(\( ( 1 - 4 T + 56 T^{2} - 204 T^{3} + 2606 T^{4} - 7548 T^{5} + 76664 T^{6} - 202612 T^{7} + 1874161 T^{8} )^{2} \))(\( ( 1 - 4 T + 56 T^{2} - 204 T^{3} + 2606 T^{4} - 7548 T^{5} + 76664 T^{6} - 202612 T^{7} + 1874161 T^{8} )^{2} \))(\( ( 1 - 7 T + 37 T^{2} )^{2} \))(\( ( 1 + 2 T + 37 T^{2} )^{4} \))(\( ( 1 - 4 T + 37 T^{2} )^{4} \))(\( ( 1 + 2 T + 37 T^{2} )^{4} \))(\( ( 1 + 7 T + 12 T^{2} + 259 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 + 8 T + 37 T^{2} )^{4} \))(\( ( 1 - 8 T + 78 T^{2} - 296 T^{3} + 1369 T^{4} )^{4} \))(\( 1 + 6 T^{2} + 2847 T^{4} - 52622 T^{6} + 3446025 T^{8} - 72039518 T^{10} + 5335736367 T^{12} + 15394358454 T^{14} + 3512479453921 T^{16} \))(\( 1 + 6 T^{2} + 2847 T^{4} - 52622 T^{6} + 3446025 T^{8} - 72039518 T^{10} + 5335736367 T^{12} + 15394358454 T^{14} + 3512479453921 T^{16} \))(\( ( 1 + 6 T - 7 T^{2} - 118 T^{3} - 254 T^{4} + 3396 T^{5} + 36665 T^{6} - 93294 T^{7} - 1522501 T^{8} - 3451878 T^{9} + 50194385 T^{10} + 172017588 T^{11} - 476036894 T^{12} - 8182586926 T^{13} - 17960084863 T^{14} + 569591262798 T^{15} + 3512479453921 T^{16} )^{2} \))(\( ( 1 - 18 T + 129 T^{2} - 558 T^{3} + 2898 T^{4} - 2028 T^{5} - 195599 T^{6} + 1766106 T^{7} - 10077237 T^{8} + 65345922 T^{9} - 267775031 T^{10} - 102724284 T^{11} + 5431318578 T^{12} - 38693928006 T^{13} + 330978706761 T^{14} - 1708773788394 T^{15} + 3512479453921 T^{16} )^{2} \))
$41$ (\( 1 - 10 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 8 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 6 T + 74 T^{2} + 246 T^{3} + 1681 T^{4} \))(\( 1 + 12 T + 86 T^{2} + 492 T^{3} + 1681 T^{4} \))(\( 1 - 12 T + 86 T^{2} - 492 T^{3} + 1681 T^{4} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 34 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 2 T + 27 T^{2} - 468 T^{3} + 1107 T^{4} - 3362 T^{5} + 68921 T^{6} )^{2} \))(\( ( 1 + 2 T + 27 T^{2} + 468 T^{3} + 1107 T^{4} + 3362 T^{5} + 68921 T^{6} )^{2} \))(\( 1 - 80 T^{2} + 1681 T^{4} \))(\( 1 - 80 T^{2} + 1681 T^{4} \))(\( 1 - 240 T^{2} + 26300 T^{4} - 1782288 T^{6} + 85159878 T^{8} - 2996026128 T^{10} + 74317514300 T^{12} - 1140025017840 T^{14} + 7984925229121 T^{16} \))(\( 1 - 240 T^{2} + 26300 T^{4} - 1782288 T^{6} + 85159878 T^{8} - 2996026128 T^{10} + 74317514300 T^{12} - 1140025017840 T^{14} + 7984925229121 T^{16} \))(\( ( 1 - 41 T^{2} )^{2} \))(\( ( 1 - 34 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 16 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 34 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 41 T^{2} )^{4} \))(\( ( 1 - 72 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 36 T^{2} + 1958 T^{4} - 60516 T^{6} + 2825761 T^{8} )^{2} \))(\( 1 + 8 T - 84 T^{2} - 588 T^{3} + 2751 T^{4} + 16704 T^{5} + 47004 T^{6} - 114664 T^{7} - 5467983 T^{8} - 4701224 T^{9} + 79013724 T^{10} + 1151256384 T^{11} + 7773668511 T^{12} - 68123446188 T^{13} - 399008756244 T^{14} + 1558034191048 T^{15} + 7984925229121 T^{16} \))(\( 1 - 8 T - 84 T^{2} + 588 T^{3} + 2751 T^{4} - 16704 T^{5} + 47004 T^{6} + 114664 T^{7} - 5467983 T^{8} + 4701224 T^{9} + 79013724 T^{10} - 1151256384 T^{11} + 7773668511 T^{12} + 68123446188 T^{13} - 399008756244 T^{14} - 1558034191048 T^{15} + 7984925229121 T^{16} \))(\( 1 - 138 T^{2} + 4581 T^{4} + 242158 T^{6} - 19370244 T^{8} + 47020276 T^{10} + 27362707279 T^{12} - 302286948126 T^{14} - 26002484153453 T^{16} - 508144359799806 T^{18} + 77320471083414319 T^{20} + 223351212440590516 T^{22} - \)\(15\!\cdots\!24\)\( T^{24} + \)\(32\!\cdots\!58\)\( T^{26} + \)\(10\!\cdots\!61\)\( T^{28} - \)\(52\!\cdots\!18\)\( T^{30} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( 1 - 82 T^{2} + 6981 T^{4} - 469098 T^{6} + 24332836 T^{8} - 1280804476 T^{10} + 56395203159 T^{12} - 2392721860294 T^{14} + 104000445893427 T^{16} - 4022165447154214 T^{18} + 159359365673778999 T^{20} - 6083954773339382716 T^{22} + \)\(19\!\cdots\!56\)\( T^{24} - \)\(62\!\cdots\!98\)\( T^{26} + \)\(15\!\cdots\!61\)\( T^{28} - \)\(31\!\cdots\!02\)\( T^{30} + \)\(63\!\cdots\!41\)\( T^{32} \))
$43$ (\( 1 - 8 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 6 T + 78 T^{2} - 258 T^{3} + 1849 T^{4} \))(\( 1 + 12 T + 90 T^{2} + 516 T^{3} + 1849 T^{4} \))(\( 1 + 12 T + 90 T^{2} + 516 T^{3} + 1849 T^{4} \))(\( 1 + 76 T^{2} + 1849 T^{4} \))(\( 1 - 68 T^{2} + 1849 T^{4} \))(\( 1 - 68 T^{2} + 1849 T^{4} \))(\( 1 + 76 T^{2} + 1849 T^{4} \))(\( ( 1 - 80 T^{2} + 1849 T^{4} )^{2} \))(\( 1 - 148 T^{2} + 11499 T^{4} - 597736 T^{6} + 21261651 T^{8} - 505982548 T^{10} + 6321363049 T^{12} \))(\( 1 - 148 T^{2} + 11499 T^{4} - 597736 T^{6} + 21261651 T^{8} - 505982548 T^{10} + 6321363049 T^{12} \))(\( ( 1 - 10 T + 43 T^{2} )( 1 + 10 T + 43 T^{2} ) \))(\( ( 1 - 10 T + 43 T^{2} )( 1 + 10 T + 43 T^{2} ) \))(\( 1 - 104 T^{2} + 7924 T^{4} - 453368 T^{6} + 22010950 T^{8} - 838277432 T^{10} + 27090579124 T^{12} - 657421757096 T^{14} + 11688200277601 T^{16} \))(\( 1 - 104 T^{2} + 7924 T^{4} - 453368 T^{6} + 22010950 T^{8} - 838277432 T^{10} + 27090579124 T^{12} - 657421757096 T^{14} + 11688200277601 T^{16} \))(\( ( 1 + 43 T^{2} )^{2} \))(\( ( 1 - 10 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 64 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 10 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 + 43 T^{2} )^{4} \))(\( ( 1 + 76 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 + 116 T^{2} + 6870 T^{4} + 214484 T^{6} + 3418801 T^{8} )^{2} \))(\( 1 - 156 T^{2} + 14432 T^{4} - 933508 T^{6} + 46038510 T^{8} - 1726056292 T^{10} + 49340136032 T^{12} - 986132635644 T^{14} + 11688200277601 T^{16} \))(\( 1 - 156 T^{2} + 14432 T^{4} - 933508 T^{6} + 46038510 T^{8} - 1726056292 T^{10} + 49340136032 T^{12} - 986132635644 T^{14} + 11688200277601 T^{16} \))(\( ( 1 - 180 T^{2} + 12786 T^{4} - 463360 T^{6} + 14361051 T^{8} - 856752640 T^{10} + 43712789586 T^{12} - 1137845348820 T^{14} + 11688200277601 T^{16} )^{2} \))(\( ( 1 - 252 T^{2} + 30170 T^{4} - 2252272 T^{6} + 115389219 T^{8} - 4164450928 T^{10} + 103145226170 T^{12} - 1592983488348 T^{14} + 11688200277601 T^{16} )^{2} \))
$47$ (\( 1 - 6 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( 1 + 8 T + 38 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 38 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 + 4 T^{2} + 2209 T^{4} \))(\( 1 - 86 T^{2} + 2209 T^{4} \))(\( 1 - 86 T^{2} + 2209 T^{4} \))(\( 1 + 4 T^{2} + 2209 T^{4} \))(\( ( 1 - 86 T^{2} + 2209 T^{4} )^{2} \))(\( 1 - 200 T^{2} + 19031 T^{4} - 1112832 T^{6} + 42039479 T^{8} - 975936200 T^{10} + 10779215329 T^{12} \))(\( 1 - 200 T^{2} + 19031 T^{4} - 1112832 T^{6} + 42039479 T^{8} - 975936200 T^{10} + 10779215329 T^{12} \))(\( ( 1 - 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 8 T + 47 T^{2} )^{2} \))(\( ( 1 + 8 T + 42 T^{2} + 576 T^{3} + 5398 T^{4} + 27072 T^{5} + 92778 T^{6} + 830584 T^{7} + 4879681 T^{8} )^{2} \))(\( ( 1 - 8 T + 42 T^{2} - 576 T^{3} + 5398 T^{4} - 27072 T^{5} + 92778 T^{6} - 830584 T^{7} + 4879681 T^{8} )^{2} \))(\( ( 1 - 12 T + 47 T^{2} )( 1 + 12 T + 47 T^{2} ) \))(\( ( 1 - 44 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 + 82 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 44 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 12 T + 47 T^{2} )^{2}( 1 + 12 T + 47 T^{2} )^{2} \))(\( ( 1 - 30 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 132 T^{2} + 8666 T^{4} - 291588 T^{6} + 4879681 T^{8} )^{2} \))(\( 1 + 20 T + 236 T^{2} + 1340 T^{3} + 3167 T^{4} - 22340 T^{5} + 28938 T^{6} + 2709720 T^{7} + 32145805 T^{8} + 127356840 T^{9} + 63924042 T^{10} - 2319405820 T^{11} + 15453949727 T^{12} + 307322309380 T^{13} + 2543894817644 T^{14} + 10132462409260 T^{15} + 23811286661761 T^{16} \))(\( 1 - 20 T + 236 T^{2} - 1340 T^{3} + 3167 T^{4} + 22340 T^{5} + 28938 T^{6} - 2709720 T^{7} + 32145805 T^{8} - 127356840 T^{9} + 63924042 T^{10} + 2319405820 T^{11} + 15453949727 T^{12} - 307322309380 T^{13} + 2543894817644 T^{14} - 10132462409260 T^{15} + 23811286661761 T^{16} \))(\( 1 + 192 T^{2} + 14115 T^{4} + 332470 T^{6} - 12112005 T^{8} - 594955574 T^{10} + 21788151037 T^{12} + 2123156175840 T^{14} + 93108257741080 T^{16} + 4690051992430560 T^{18} + 106319226640379197 T^{20} - 6413154243334793846 T^{22} - \)\(28\!\cdots\!05\)\( T^{24} + \)\(17\!\cdots\!30\)\( T^{26} + \)\(16\!\cdots\!15\)\( T^{28} + \)\(49\!\cdots\!48\)\( T^{30} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 - 168 T^{2} + 14835 T^{4} - 971970 T^{6} + 54248555 T^{8} - 3047297454 T^{10} + 175115747757 T^{12} - 9519113612040 T^{14} + 473222443124920 T^{16} - 21027721968996360 T^{18} + 854508987130625517 T^{20} - 32847475428179472366 T^{22} + \)\(12\!\cdots\!55\)\( T^{24} - \)\(51\!\cdots\!30\)\( T^{26} + \)\(17\!\cdots\!35\)\( T^{28} - \)\(43\!\cdots\!92\)\( T^{30} + \)\(56\!\cdots\!21\)\( T^{32} \))
$53$ (\( 1 - 12 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 14 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 - 8 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 - 4 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 + 8 T + 54 T^{2} + 424 T^{3} + 2809 T^{4} \))(\( 1 + 8 T + 114 T^{2} + 424 T^{3} + 2809 T^{4} \))(\( 1 - 8 T + 114 T^{2} - 424 T^{3} + 2809 T^{4} \))(\( 1 - 74 T^{2} + 2809 T^{4} \))(\( 1 - 56 T^{2} + 2809 T^{4} \))(\( 1 - 56 T^{2} + 2809 T^{4} \))(\( 1 - 74 T^{2} + 2809 T^{4} \))(\( ( 1 - 8 T^{2} + 2809 T^{4} )^{2} \))(\( 1 - 266 T^{2} + 31595 T^{4} - 2151924 T^{6} + 88750355 T^{8} - 2098867946 T^{10} + 22164361129 T^{12} \))(\( 1 - 266 T^{2} + 31595 T^{4} - 2151924 T^{6} + 88750355 T^{8} - 2098867946 T^{10} + 22164361129 T^{12} \))(\( 1 - 104 T^{2} + 2809 T^{4} \))(\( 1 - 104 T^{2} + 2809 T^{4} \))(\( 1 - 204 T^{2} + 23504 T^{4} - 1838388 T^{6} + 110812110 T^{8} - 5164031892 T^{10} + 185457865424 T^{12} - 4521529670316 T^{14} + 62259690411361 T^{16} \))(\( 1 - 204 T^{2} + 23504 T^{4} - 1838388 T^{6} + 110812110 T^{8} - 5164031892 T^{10} + 185457865424 T^{12} - 4521529670316 T^{14} + 62259690411361 T^{16} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 52 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 + 53 T^{2} )^{4} \))(\( ( 1 + 52 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{4} \))(\( ( 1 + 6 T + 53 T^{2} )^{4} \))(\( ( 1 - 18 T + 184 T^{2} - 954 T^{3} + 2809 T^{4} )^{4} \))(\( 1 - 30 T + 569 T^{2} - 6900 T^{3} + 58587 T^{4} - 263880 T^{5} - 611693 T^{6} + 24924930 T^{7} - 240874240 T^{8} + 1321021290 T^{9} - 1718245637 T^{10} - 39285662760 T^{11} + 462279610347 T^{12} - 2885548901700 T^{13} + 12611521482401 T^{14} - 35241334195110 T^{15} + 62259690411361 T^{16} \))(\( 1 + 30 T + 569 T^{2} + 6900 T^{3} + 58587 T^{4} + 263880 T^{5} - 611693 T^{6} - 24924930 T^{7} - 240874240 T^{8} - 1321021290 T^{9} - 1718245637 T^{10} + 39285662760 T^{11} + 462279610347 T^{12} + 2885548901700 T^{13} + 12611521482401 T^{14} + 35241334195110 T^{15} + 62259690411361 T^{16} \))(\( 1 + 166 T^{2} + 9174 T^{4} - 111674 T^{6} - 30841109 T^{8} - 525703922 T^{10} + 67446933816 T^{12} + 3591171944168 T^{14} + 110175435537457 T^{16} + 10087601991167912 T^{18} + 532188749783405496 T^{20} - 11651891574139647938 T^{22} - \)\(19\!\cdots\!49\)\( T^{24} - \)\(19\!\cdots\!26\)\( T^{26} + \)\(45\!\cdots\!34\)\( T^{28} + \)\(22\!\cdots\!54\)\( T^{30} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( 1 + 142 T^{2} + 8110 T^{4} + 245630 T^{6} + 11914115 T^{8} + 1358312566 T^{10} + 93726771992 T^{12} + 3786766264040 T^{14} + 151743077440945 T^{16} + 10637026435688360 T^{18} + 739549313594208152 T^{20} + 30106130238882647014 T^{22} + \)\(74\!\cdots\!15\)\( T^{24} + \)\(42\!\cdots\!70\)\( T^{26} + \)\(39\!\cdots\!10\)\( T^{28} + \)\(19\!\cdots\!98\)\( T^{30} + \)\(38\!\cdots\!21\)\( T^{32} \))
$59$ (\( 1 + 8 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 - 5 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 3 T + 59 T^{2} \))(\( 1 + T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 5 T + 18 T^{2} + 295 T^{3} + 3481 T^{4} \))(\( 1 + 8 T + 102 T^{2} + 472 T^{3} + 3481 T^{4} \))(\( 1 - 8 T + 102 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 - 86 T^{2} + 3481 T^{4} \))(\( 1 - 110 T^{2} + 3481 T^{4} \))(\( 1 - 110 T^{2} + 3481 T^{4} \))(\( 1 - 86 T^{2} + 3481 T^{4} \))(\( ( 1 + 10 T^{2} + 3481 T^{4} )^{2} \))(\( 1 - 194 T^{2} + 16759 T^{4} - 1029500 T^{6} + 58338079 T^{8} - 2350768034 T^{10} + 42180533641 T^{12} \))(\( 1 - 194 T^{2} + 16759 T^{4} - 1029500 T^{6} + 58338079 T^{8} - 2350768034 T^{10} + 42180533641 T^{12} \))(\( ( 1 + 4 T + 59 T^{2} )^{2} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))(\( ( 1 + 8 T + 108 T^{2} + 72 T^{3} + 2902 T^{4} + 4248 T^{5} + 375948 T^{6} + 1643032 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 - 8 T + 108 T^{2} - 72 T^{3} + 2902 T^{4} - 4248 T^{5} + 375948 T^{6} - 1643032 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 - 15 T + 59 T^{2} )( 1 + 15 T + 59 T^{2} ) \))(\( ( 1 - 6 T + 59 T^{2} )^{2}( 1 + 6 T + 59 T^{2} )^{2} \))(\( ( 1 - 74 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 6 T + 59 T^{2} )^{2}( 1 + 6 T + 59 T^{2} )^{2} \))(\( ( 1 - 15 T + 166 T^{2} - 885 T^{3} + 3481 T^{4} )( 1 + 15 T + 166 T^{2} + 885 T^{3} + 3481 T^{4} ) \))(\( ( 1 - 82 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 140 T^{2} + 10134 T^{4} - 487340 T^{6} + 12117361 T^{8} )^{2} \))(\( 1 - 20 T + 336 T^{2} - 3400 T^{3} + 24405 T^{4} - 60580 T^{5} - 1156836 T^{6} + 19551820 T^{7} - 192630411 T^{8} + 1153557380 T^{9} - 4026946116 T^{10} - 12441859820 T^{11} + 295724195205 T^{12} - 2430742616600 T^{13} + 14172659303376 T^{14} - 49773029696380 T^{15} + 146830437604321 T^{16} \))(\( 1 + 20 T + 336 T^{2} + 3400 T^{3} + 24405 T^{4} + 60580 T^{5} - 1156836 T^{6} - 19551820 T^{7} - 192630411 T^{8} - 1153557380 T^{9} - 4026946116 T^{10} + 12441859820 T^{11} + 295724195205 T^{12} + 2430742616600 T^{13} + 14172659303376 T^{14} + 49773029696380 T^{15} + 146830437604321 T^{16} \))(\( 1 + 170 T^{2} + 22518 T^{4} + 2498730 T^{6} + 233218683 T^{8} + 18919071570 T^{10} + 1419551700816 T^{12} + 95367637994400 T^{14} + 5833449282172425 T^{16} + 331974747858506400 T^{18} + 17201220416951466576 T^{20} + \)\(79\!\cdots\!70\)\( T^{22} + \)\(34\!\cdots\!43\)\( T^{24} + \)\(12\!\cdots\!30\)\( T^{26} + \)\(40\!\cdots\!58\)\( T^{28} + \)\(10\!\cdots\!70\)\( T^{30} + \)\(21\!\cdots\!41\)\( T^{32} \))(\( 1 + 290 T^{2} + 38918 T^{4} + 3391810 T^{6} + 227971163 T^{8} + 13745434890 T^{10} + 860139078736 T^{12} + 55417843857600 T^{14} + 3388651967440105 T^{16} + 192909514468305600 T^{18} + 10422615727251535696 T^{20} + \)\(57\!\cdots\!90\)\( T^{22} + \)\(33\!\cdots\!23\)\( T^{24} + \)\(17\!\cdots\!10\)\( T^{26} + \)\(69\!\cdots\!58\)\( T^{28} + \)\(17\!\cdots\!90\)\( T^{30} + \)\(21\!\cdots\!41\)\( T^{32} \))
$61$ (\( 1 - 4 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 - 12 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 + 6 T + 114 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( 1 - 12 T + 150 T^{2} - 732 T^{3} + 3721 T^{4} \))(\( 1 - 12 T + 150 T^{2} - 732 T^{3} + 3721 T^{4} \))(\( 1 + 40 T^{2} + 3721 T^{4} \))(\( 1 - 50 T^{2} + 3721 T^{4} \))(\( 1 - 50 T^{2} + 3721 T^{4} \))(\( 1 + 40 T^{2} + 3721 T^{4} \))(\( ( 1 - 98 T^{2} + 3721 T^{4} )^{2} \))(\( 1 - 156 T^{2} + 5183 T^{4} + 74792 T^{6} + 19285943 T^{8} - 2159951196 T^{10} + 51520374361 T^{12} \))(\( 1 - 156 T^{2} + 5183 T^{4} + 74792 T^{6} + 19285943 T^{8} - 2159951196 T^{10} + 51520374361 T^{12} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( ( 1 - 12 T + 254 T^{2} - 2148 T^{3} + 23526 T^{4} - 131028 T^{5} + 945134 T^{6} - 2723772 T^{7} + 13845841 T^{8} )^{2} \))(\( ( 1 - 12 T + 254 T^{2} - 2148 T^{3} + 23526 T^{4} - 131028 T^{5} + 945134 T^{6} - 2723772 T^{7} + 13845841 T^{8} )^{2} \))(\( ( 1 - 61 T^{2} )^{2} \))(\( ( 1 + 40 T^{2} + 3721 T^{4} )^{2} \))(\( ( 1 - 61 T^{2} )^{4} \))(\( ( 1 + 40 T^{2} + 3721 T^{4} )^{2} \))(\( ( 1 - 61 T^{2} )^{4} \))(\( ( 1 - 61 T^{2} )^{4} \))(\( ( 1 - 4 T^{2} - 5622 T^{4} - 14884 T^{6} + 13845841 T^{8} )^{2} \))(\( 1 - 20 T + 150 T^{2} - 1200 T^{3} + 11779 T^{4} - 45580 T^{5} - 36400 T^{6} + 518400 T^{7} - 3011179 T^{8} + 31622400 T^{9} - 135444400 T^{10} - 10345793980 T^{11} + 163090161139 T^{12} - 1013515561200 T^{13} + 7728056154150 T^{14} - 62854856720420 T^{15} + 191707312997281 T^{16} \))(\( 1 - 20 T + 150 T^{2} - 1200 T^{3} + 11779 T^{4} - 45580 T^{5} - 36400 T^{6} + 518400 T^{7} - 3011179 T^{8} + 31622400 T^{9} - 135444400 T^{10} - 10345793980 T^{11} + 163090161139 T^{12} - 1013515561200 T^{13} + 7728056154150 T^{14} - 62854856720420 T^{15} + 191707312997281 T^{16} \))(\( ( 1 + 83 T^{2} + 420 T^{3} + 3413 T^{4} + 34860 T^{5} + 227941 T^{6} + 4235840 T^{7} + 8009300 T^{8} + 258386240 T^{9} + 848168461 T^{10} + 7912557660 T^{11} + 47255855333 T^{12} + 354730446420 T^{13} + 4276191071963 T^{14} + 191707312997281 T^{16} )^{2} \))(\( ( 1 + 40 T + 915 T^{2} + 15780 T^{3} + 221989 T^{4} + 2661260 T^{5} + 27843365 T^{6} + 257770200 T^{7} + 2129363636 T^{8} + 15723982200 T^{9} + 103605161165 T^{10} + 604055456060 T^{11} + 3073624397749 T^{12} + 13327729629780 T^{13} + 47141142540315 T^{14} + 125709713440840 T^{15} + 191707312997281 T^{16} )^{2} \))
$67$ (\( 1 - 12 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 7 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 15 T + 186 T^{2} + 1005 T^{3} + 4489 T^{4} \))(\( 1 + 6 T^{2} + 4489 T^{4} \))(\( 1 + 6 T^{2} + 4489 T^{4} \))(\( ( 1 + 8 T + 67 T^{2} )^{2} \))(\( ( 1 - 4 T + 67 T^{2} )^{2} \))(\( ( 1 - 4 T + 67 T^{2} )^{2} \))(\( ( 1 + 8 T + 67 T^{2} )^{2} \))(\( ( 1 - 4 T + 67 T^{2} )^{4} \))(\( ( 1 + 16 T + 217 T^{2} + 1888 T^{3} + 14539 T^{4} + 71824 T^{5} + 300763 T^{6} )^{2} \))(\( ( 1 + 16 T + 217 T^{2} + 1888 T^{3} + 14539 T^{4} + 71824 T^{5} + 300763 T^{6} )^{2} \))(\( ( 1 - 67 T^{2} )^{2} \))(\( ( 1 - 67 T^{2} )^{2} \))(\( ( 1 - 100 T^{2} + 8022 T^{4} - 448900 T^{6} + 20151121 T^{8} )^{2} \))(\( ( 1 - 100 T^{2} + 8022 T^{4} - 448900 T^{6} + 20151121 T^{8} )^{2} \))(\( ( 1 - 13 T + 67 T^{2} )( 1 + 13 T + 67 T^{2} ) \))(\( ( 1 - 16 T + 67 T^{2} )^{2}( 1 + 16 T + 67 T^{2} )^{2} \))(\( ( 1 - 67 T^{2} )^{4} \))(\( ( 1 - 16 T + 67 T^{2} )^{2}( 1 + 16 T + 67 T^{2} )^{2} \))(\( ( 1 - 13 T + 102 T^{2} - 871 T^{3} + 4489 T^{4} )( 1 + 13 T + 102 T^{2} + 871 T^{3} + 4489 T^{4} ) \))(\( ( 1 + 10 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 - 26 T^{2} + 4489 T^{4} )^{4} \))(\( ( 1 - 28 T + 452 T^{2} - 5380 T^{3} + 49986 T^{4} - 360460 T^{5} + 2029028 T^{6} - 8421364 T^{7} + 20151121 T^{8} )^{2} \))(\( ( 1 - 28 T + 452 T^{2} - 5380 T^{3} + 49986 T^{4} - 360460 T^{5} + 2029028 T^{6} - 8421364 T^{7} + 20151121 T^{8} )^{2} \))(\( ( 1 + 24 T + 429 T^{2} + 5008 T^{3} + 47859 T^{4} + 335536 T^{5} + 1925781 T^{6} + 7218312 T^{7} + 20151121 T^{8} )^{4} \))(\( ( 1 - 16 T + 269 T^{2} - 3172 T^{3} + 27039 T^{4} - 212524 T^{5} + 1207541 T^{6} - 4812208 T^{7} + 20151121 T^{8} )^{4} \))
$71$ (\( 1 - 10 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 3 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 15 T + 71 T^{2} \))(\( 1 - 3 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 2 T + 71 T^{2} \))(\( 1 + 5 T + 110 T^{2} + 355 T^{3} + 5041 T^{4} \))(\( 1 + 8 T + 86 T^{2} + 568 T^{3} + 5041 T^{4} \))(\( 1 - 8 T + 86 T^{2} - 568 T^{3} + 5041 T^{4} \))(\( 1 + 100 T^{2} + 5041 T^{4} \))(\( 1 + 58 T^{2} + 5041 T^{4} \))(\( 1 + 58 T^{2} + 5041 T^{4} \))(\( 1 + 100 T^{2} + 5041 T^{4} \))(\( ( 1 - 134 T^{2} + 5041 T^{4} )^{2} \))(\( 1 - 392 T^{2} + 66119 T^{4} - 6152448 T^{6} + 333305879 T^{8} - 9961378952 T^{10} + 128100283921 T^{12} \))(\( 1 - 392 T^{2} + 66119 T^{4} - 6152448 T^{6} + 333305879 T^{8} - 9961378952 T^{10} + 128100283921 T^{12} \))(\( ( 1 - 16 T + 71 T^{2} )^{2} \))(\( ( 1 + 16 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 258 T^{2} - 1488 T^{3} + 26662 T^{4} - 105648 T^{5} + 1300578 T^{6} - 2863288 T^{7} + 25411681 T^{8} )^{2} \))(\( ( 1 + 8 T + 258 T^{2} + 1488 T^{3} + 26662 T^{4} + 105648 T^{5} + 1300578 T^{6} + 2863288 T^{7} + 25411681 T^{8} )^{2} \))(\( ( 1 - 3 T + 71 T^{2} )( 1 + 3 T + 71 T^{2} ) \))(\( ( 1 - 44 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 + 34 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 - 44 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 - 3 T - 62 T^{2} - 213 T^{3} + 5041 T^{4} )( 1 + 3 T - 62 T^{2} + 213 T^{3} + 5041 T^{4} ) \))(\( ( 1 - 71 T^{2} )^{4} \))(\( ( 1 - 116 T^{2} + 12474 T^{4} - 584756 T^{6} + 25411681 T^{8} )^{2} \))(\( 1 + 20 T + 260 T^{2} + 1440 T^{3} - 401 T^{4} - 121620 T^{5} - 777730 T^{6} - 1388800 T^{7} + 34077661 T^{8} - 98604800 T^{9} - 3920536930 T^{10} - 43529135820 T^{11} - 10190084081 T^{12} + 2598090265440 T^{13} + 33306073819460 T^{14} + 181902403167820 T^{15} + 645753531245761 T^{16} \))(\( 1 - 20 T + 260 T^{2} - 1440 T^{3} - 401 T^{4} + 121620 T^{5} - 777730 T^{6} + 1388800 T^{7} + 34077661 T^{8} + 98604800 T^{9} - 3920536930 T^{10} + 43529135820 T^{11} - 10190084081 T^{12} - 2598090265440 T^{13} + 33306073819460 T^{14} - 181902403167820 T^{15} + 645753531245761 T^{16} \))(\( 1 + 338 T^{2} + 50091 T^{4} + 3709542 T^{6} + 63034791 T^{8} - 13931687706 T^{10} - 1397230758891 T^{12} - 60140798780574 T^{14} - 2187888491323968 T^{16} - 303169766652873534 T^{18} - 35505982328326005771 T^{20} - \)\(17\!\cdots\!26\)\( T^{22} + \)\(40\!\cdots\!51\)\( T^{24} + \)\(12\!\cdots\!42\)\( T^{26} + \)\(82\!\cdots\!31\)\( T^{28} + \)\(27\!\cdots\!78\)\( T^{30} + \)\(41\!\cdots\!21\)\( T^{32} \))(\( 1 + 114 T^{2} - 1845 T^{4} - 1094530 T^{6} - 33581145 T^{8} + 7884147182 T^{10} + 680809643893 T^{12} - 13277490209310 T^{14} - 3871800182997440 T^{16} - 66931828145131710 T^{18} + 17300517492332514133 T^{20} + \)\(10\!\cdots\!22\)\( T^{22} - \)\(21\!\cdots\!45\)\( T^{24} - \)\(35\!\cdots\!30\)\( T^{26} - \)\(30\!\cdots\!45\)\( T^{28} + \)\(94\!\cdots\!34\)\( T^{30} + \)\(41\!\cdots\!21\)\( T^{32} \))
$73$ (\( 1 - 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 2 T + 130 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( 1 + 4 T + 22 T^{2} + 292 T^{3} + 5329 T^{4} \))(\( 1 + 4 T + 22 T^{2} + 292 T^{3} + 5329 T^{4} \))(\( 1 - 74 T^{2} + 5329 T^{4} \))(\( 1 - 74 T^{2} + 5329 T^{4} \))(\( 1 - 74 T^{2} + 5329 T^{4} \))(\( 1 - 74 T^{2} + 5329 T^{4} \))(\( ( 1 - 73 T^{2} )^{4} \))(\( 1 + 18 T^{2} + 15647 T^{4} + 188348 T^{6} + 83382863 T^{8} + 511168338 T^{10} + 151334226289 T^{12} \))(\( 1 + 18 T^{2} + 15647 T^{4} + 188348 T^{6} + 83382863 T^{8} + 511168338 T^{10} + 151334226289 T^{12} \))(\( ( 1 + 4 T + 73 T^{2} )^{2} \))(\( ( 1 + 4 T + 73 T^{2} )^{2} \))(\( ( 1 + 140 T^{2} + 768 T^{3} + 9030 T^{4} + 56064 T^{5} + 746060 T^{6} + 28398241 T^{8} )^{2} \))(\( ( 1 + 140 T^{2} + 768 T^{3} + 9030 T^{4} + 56064 T^{5} + 746060 T^{6} + 28398241 T^{8} )^{2} \))(\( ( 1 - 73 T^{2} )^{2} \))(\( ( 1 - 74 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 73 T^{2} )^{4} \))(\( ( 1 - 74 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 73 T^{2} )^{4} \))(\( ( 1 - 106 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 164 T^{2} + 15654 T^{4} - 873956 T^{6} + 28398241 T^{8} )^{2} \))(\( 1 + 10 T - 141 T^{2} - 760 T^{3} + 23247 T^{4} + 55820 T^{5} - 2381703 T^{6} - 2640110 T^{7} + 176215880 T^{8} - 192728030 T^{9} - 12692095287 T^{10} + 21714928940 T^{11} + 660173908527 T^{12} - 1575534410680 T^{13} - 21338125906749 T^{14} + 110473985190970 T^{15} + 806460091894081 T^{16} \))(\( 1 + 10 T - 141 T^{2} - 760 T^{3} + 23247 T^{4} + 55820 T^{5} - 2381703 T^{6} - 2640110 T^{7} + 176215880 T^{8} - 192728030 T^{9} - 12692095287 T^{10} + 21714928940 T^{11} + 660173908527 T^{12} - 1575534410680 T^{13} - 21338125906749 T^{14} + 110473985190970 T^{15} + 806460091894081 T^{16} \))(\( ( 1 + 10 T + 276 T^{2} + 2170 T^{3} + 24127 T^{4} + 117430 T^{5} - 172242 T^{6} - 4912540 T^{7} - 124201175 T^{8} - 358615420 T^{9} - 917877618 T^{10} + 45682266310 T^{11} + 685164360607 T^{12} + 4498565356810 T^{13} + 41768246455764 T^{14} + 110473985190970 T^{15} + 806460091894081 T^{16} )^{2} \))(\( ( 1 + 10 T + 84 T^{2} + 410 T^{3} + 4767 T^{4} + 34550 T^{5} + 133782 T^{6} - 2699180 T^{7} - 18887095 T^{8} - 197040140 T^{9} + 712924278 T^{10} + 13440537350 T^{11} + 135374414847 T^{12} + 849959353130 T^{13} + 12712075008276 T^{14} + 110473985190970 T^{15} + 806460091894081 T^{16} )^{2} \))
$79$ (\( 1 + 2 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 2 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 14 T + 79 T^{2} \))(\( 1 + 2 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 2 T + 79 T^{2} \))(\( 1 + 14 T + 79 T^{2} \))(\( 1 + 14 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 2 T + 79 T^{2} \))(\( 1 + 2 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 14 T + 190 T^{2} - 1106 T^{3} + 6241 T^{4} \))(\( 1 + 4 T + 154 T^{2} + 316 T^{3} + 6241 T^{4} \))(\( 1 + 4 T + 154 T^{2} + 316 T^{3} + 6241 T^{4} \))(\( 1 - 86 T^{2} + 6241 T^{4} \))(\( 1 - 140 T^{2} + 6241 T^{4} \))(\( 1 - 140 T^{2} + 6241 T^{4} \))(\( 1 - 86 T^{2} + 6241 T^{4} \))(\( ( 1 - 8 T^{2} + 6241 T^{4} )^{2} \))(\( 1 - 86 T^{2} + 20259 T^{4} - 1065260 T^{6} + 126436419 T^{8} - 3349706966 T^{10} + 243087455521 T^{12} \))(\( 1 - 86 T^{2} + 20259 T^{4} - 1065260 T^{6} + 126436419 T^{8} - 3349706966 T^{10} + 243087455521 T^{12} \))(\( 1 - 86 T^{2} + 6241 T^{4} \))(\( 1 - 86 T^{2} + 6241 T^{4} \))(\( 1 - 284 T^{2} + 48928 T^{4} - 5986532 T^{6} + 538243534 T^{8} - 37361946212 T^{10} + 1905749563168 T^{12} - 69036837367964 T^{14} + 1517108809906561 T^{16} \))(\( 1 - 284 T^{2} + 48928 T^{4} - 5986532 T^{6} + 538243534 T^{8} - 37361946212 T^{10} + 1905749563168 T^{12} - 69036837367964 T^{14} + 1517108809906561 T^{16} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 152 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 - 136 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 + 152 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 + 79 T^{2} )^{4} \))(\( ( 1 - 92 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 + 284 T^{2} + 32538 T^{4} + 1772444 T^{6} + 38950081 T^{8} )^{2} \))(\( 1 - 20 T + 56 T^{2} - 40 T^{3} + 24325 T^{4} - 218020 T^{5} - 253116 T^{6} - 10753340 T^{7} + 280334669 T^{8} - 849513860 T^{9} - 1579696956 T^{10} - 107492362780 T^{11} + 947460720325 T^{12} - 123082255960 T^{13} + 13612897509176 T^{14} - 384078179723180 T^{15} + 1517108809906561 T^{16} \))(\( 1 - 20 T + 56 T^{2} - 40 T^{3} + 24325 T^{4} - 218020 T^{5} - 253116 T^{6} - 10753340 T^{7} + 280334669 T^{8} - 849513860 T^{9} - 1579696956 T^{10} - 107492362780 T^{11} + 947460720325 T^{12} - 123082255960 T^{13} + 13612897509176 T^{14} - 384078179723180 T^{15} + 1517108809906561 T^{16} \))(\( ( 1 + 203 T^{2} + 180 T^{3} + 12338 T^{4} + 36540 T^{5} - 807689 T^{6} + 4199410 T^{7} - 150806725 T^{8} + 331753390 T^{9} - 5040787049 T^{10} + 18015645060 T^{11} + 480566099378 T^{12} + 553870151820 T^{13} + 49346753470763 T^{14} + 1517108809906561 T^{16} )^{2} \))(\( ( 1 - 20 T + 395 T^{2} - 4960 T^{3} + 54574 T^{4} - 466180 T^{5} + 3107595 T^{6} - 20610350 T^{7} + 127628411 T^{8} - 1628217650 T^{9} + 19394500395 T^{10} - 229844921020 T^{11} + 2125661720494 T^{12} - 15262199739040 T^{13} + 96019544930795 T^{14} - 384078179723180 T^{15} + 1517108809906561 T^{16} )^{2} \))
$83$ (\( 1 - 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 2 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 - 10 T + 174 T^{2} - 830 T^{3} + 6889 T^{4} \))(\( 1 + 8 T + 150 T^{2} + 664 T^{3} + 6889 T^{4} \))(\( 1 - 8 T + 150 T^{2} - 664 T^{3} + 6889 T^{4} \))(\( ( 1 + 6 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 6 T + 83 T^{2} )^{2} \))(\( ( 1 - 26 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 22 T + 345 T^{2} - 3396 T^{3} + 28635 T^{4} - 151558 T^{5} + 571787 T^{6} )^{2} \))(\( ( 1 + 22 T + 345 T^{2} + 3396 T^{3} + 28635 T^{4} + 151558 T^{5} + 571787 T^{6} )^{2} \))(\( ( 1 - 8 T + 83 T^{2} )^{2} \))(\( ( 1 + 8 T + 83 T^{2} )^{2} \))(\( ( 1 + 20 T + 408 T^{2} + 4548 T^{3} + 51790 T^{4} + 377484 T^{5} + 2810712 T^{6} + 11435740 T^{7} + 47458321 T^{8} )^{2} \))(\( ( 1 - 20 T + 408 T^{2} - 4548 T^{3} + 51790 T^{4} - 377484 T^{5} + 2810712 T^{6} - 11435740 T^{7} + 47458321 T^{8} )^{2} \))(\( ( 1 + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{4} \))(\( ( 1 + 83 T^{2} )^{4} \))(\( ( 1 - 12 T + 83 T^{2} )^{4} \))(\( ( 1 + 83 T^{2} )^{4} \))(\( ( 1 + 6 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 + 204 T^{2} + 22454 T^{4} + 1405356 T^{6} + 47458321 T^{8} )^{2} \))(\( 1 - 12 T - 28 T^{2} + 324 T^{3} + 3801 T^{4} + 5388 T^{5} + 255940 T^{6} - 1400868 T^{7} - 37244131 T^{8} - 116272044 T^{9} + 1763170660 T^{10} + 3080788356 T^{11} + 180389078121 T^{12} + 1276249168332 T^{13} - 9154330454332 T^{14} - 325632611875524 T^{15} + 2252292232139041 T^{16} \))(\( 1 + 12 T - 28 T^{2} - 324 T^{3} + 3801 T^{4} - 5388 T^{5} + 255940 T^{6} + 1400868 T^{7} - 37244131 T^{8} + 116272044 T^{9} + 1763170660 T^{10} - 3080788356 T^{11} + 180389078121 T^{12} - 1276249168332 T^{13} - 9154330454332 T^{14} + 325632611875524 T^{15} + 2252292232139041 T^{16} \))(\( 1 - 208 T^{2} + 15045 T^{4} + 774660 T^{6} - 236047260 T^{8} + 17546406456 T^{10} - 74692835973 T^{12} - 112052982977490 T^{14} + 12843285776364315 T^{16} - 771932999731928610 T^{18} - 3544796586006981333 T^{20} + \)\(57\!\cdots\!64\)\( T^{22} - \)\(53\!\cdots\!60\)\( T^{24} + \)\(12\!\cdots\!40\)\( T^{26} + \)\(16\!\cdots\!45\)\( T^{28} - \)\(15\!\cdots\!32\)\( T^{30} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 - 344 T^{2} + 52069 T^{4} - 4251844 T^{6} + 103540436 T^{8} + 17634676168 T^{10} - 2100449059189 T^{12} + 96934226938118 T^{14} - 3530823620235653 T^{16} + 667779889376694902 T^{18} - 99683785695139561669 T^{20} + \)\(57\!\cdots\!92\)\( T^{22} + \)\(23\!\cdots\!76\)\( T^{24} - \)\(65\!\cdots\!56\)\( T^{26} + \)\(55\!\cdots\!09\)\( T^{28} - \)\(25\!\cdots\!76\)\( T^{30} + \)\(50\!\cdots\!81\)\( T^{32} \))
$89$ (\( 1 - 6 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 9 T + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 7 T + 152 T^{2} - 623 T^{3} + 7921 T^{4} \))(\( ( 1 + 16 T + 89 T^{2} )^{2} \))(\( ( 1 - 16 T + 89 T^{2} )^{2} \))(\( 1 - 128 T^{2} + 7921 T^{4} \))(\( 1 - 80 T^{2} + 7921 T^{4} \))(\( 1 - 80 T^{2} + 7921 T^{4} \))(\( 1 - 128 T^{2} + 7921 T^{4} \))(\( ( 1 - 128 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 - 160 T^{2} + 7921 T^{4} )^{3} \))(\( ( 1 - 160 T^{2} + 7921 T^{4} )^{3} \))(\( 1 - 128 T^{2} + 7921 T^{4} \))(\( 1 - 128 T^{2} + 7921 T^{4} \))(\( 1 - 384 T^{2} + 62276 T^{4} - 5930112 T^{6} + 485181510 T^{8} - 46972417152 T^{10} + 3907335800516 T^{12} - 190840815729024 T^{14} + 3936588805702081 T^{16} \))(\( 1 - 384 T^{2} + 62276 T^{4} - 5930112 T^{6} + 485181510 T^{8} - 46972417152 T^{10} + 3907335800516 T^{12} - 190840815729024 T^{14} + 3936588805702081 T^{16} \))(\( ( 1 - 9 T + 89 T^{2} )^{2} \))(\( ( 1 + 154 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 89 T^{2} )^{4} \))(\( ( 1 + 154 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 9 T - 8 T^{2} + 801 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{4} \))(\( ( 1 + 70 T^{2} + 7921 T^{4} )^{4} \))(\( ( 1 - 176 T^{2} + 21966 T^{4} - 1394096 T^{6} + 62742241 T^{8} )^{2} \))(\( ( 1 - 176 T^{2} + 21966 T^{4} - 1394096 T^{6} + 62742241 T^{8} )^{2} \))(\( ( 1 - 582 T^{2} + 157158 T^{4} - 25689904 T^{6} + 2778331335 T^{8} - 203489729584 T^{10} + 9860445111078 T^{12} - 289243111339302 T^{14} + 3936588805702081 T^{16} )^{2} \))(\( ( 1 - 190 T^{2} + 15454 T^{4} - 347920 T^{6} - 7414769 T^{8} - 2755874320 T^{10} + 969618592414 T^{12} - 94426445282590 T^{14} + 3936588805702081 T^{16} )^{2} \))
$97$ (\( 1 - 14 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 27 T + 372 T^{2} - 2619 T^{3} + 9409 T^{4} \))(\( 1 + 12 T + 102 T^{2} + 1164 T^{3} + 9409 T^{4} \))(\( 1 + 12 T + 102 T^{2} + 1164 T^{3} + 9409 T^{4} \))(\( ( 1 + 4 T + 97 T^{2} )^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 4 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{4} \))(\( ( 1 - 8 T + 183 T^{2} - 704 T^{3} + 17751 T^{4} - 75272 T^{5} + 912673 T^{6} )^{2} \))(\( ( 1 - 8 T + 183 T^{2} - 704 T^{3} + 17751 T^{4} - 75272 T^{5} + 912673 T^{6} )^{2} \))(\( ( 1 - 8 T + 97 T^{2} )^{2} \))(\( ( 1 - 8 T + 97 T^{2} )^{2} \))(\( ( 1 + 12 T + 368 T^{2} + 3348 T^{3} + 52590 T^{4} + 324756 T^{5} + 3462512 T^{6} + 10952076 T^{7} + 88529281 T^{8} )^{2} \))(\( ( 1 + 12 T + 368 T^{2} + 3348 T^{3} + 52590 T^{4} + 324756 T^{5} + 3462512 T^{6} + 10952076 T^{7} + 88529281 T^{8} )^{2} \))(\( ( 1 + 17 T + 97 T^{2} )^{2} \))(\( ( 1 + 8 T + 97 T^{2} )^{4} \))(\( ( 1 - 16 T + 97 T^{2} )^{4} \))(\( ( 1 + 8 T + 97 T^{2} )^{4} \))(\( ( 1 - 17 T + 192 T^{2} - 1649 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 - 8 T + 97 T^{2} )^{4} \))(\( ( 1 - 4 T + 186 T^{2} - 388 T^{3} + 9409 T^{4} )^{4} \))(\( 1 + 12 T + 34 T^{2} - 708 T^{3} - 6677 T^{4} - 87428 T^{5} - 231884 T^{6} + 1503776 T^{7} + 61442213 T^{8} + 145866272 T^{9} - 2181796556 T^{10} - 79793175044 T^{11} - 591110009237 T^{12} - 6079836901956 T^{13} + 28321048167586 T^{14} + 969579413737356 T^{15} + 7837433594376961 T^{16} \))(\( 1 + 12 T + 34 T^{2} - 708 T^{3} - 6677 T^{4} - 87428 T^{5} - 231884 T^{6} + 1503776 T^{7} + 61442213 T^{8} + 145866272 T^{9} - 2181796556 T^{10} - 79793175044 T^{11} - 591110009237 T^{12} - 6079836901956 T^{13} + 28321048167586 T^{14} + 969579413737356 T^{15} + 7837433594376961 T^{16} \))(\( ( 1 - 30 T + 411 T^{2} - 3150 T^{3} + 11217 T^{4} + 58230 T^{5} - 1794727 T^{6} + 27808950 T^{7} - 324085500 T^{8} + 2697468150 T^{9} - 16886586343 T^{10} + 53144948790 T^{11} + 993032944977 T^{12} - 27050121809550 T^{13} + 342351494025819 T^{14} - 2423948534343390 T^{15} + 7837433594376961 T^{16} )^{2} \))(\( ( 1 - 6 T - 77 T^{2} + 2538 T^{3} - 7319 T^{4} - 258146 T^{5} + 2476225 T^{6} + 6339134 T^{7} - 346276396 T^{8} + 614895998 T^{9} + 23298801025 T^{10} - 235602884258 T^{11} - 647945807639 T^{12} + 21794669572266 T^{13} - 64138844379533 T^{14} - 484789706868678 T^{15} + 7837433594376961 T^{16} )^{2} \))
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