Properties

Label 3234.2
Level 3234
Weight 2
Dimension 66584
Nonzero newspaces 32
Sturm bound 1128960
Trace bound 4

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Defining parameters

Level: \( N \) = \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(1128960\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3234))\).

Total New Old
Modular forms 287040 66584 220456
Cusp forms 277441 66584 210857
Eisenstein series 9599 0 9599

Trace form

\( 66584q + 2q^{2} - 6q^{3} - 14q^{4} - 36q^{5} - 27q^{6} - 32q^{7} + 2q^{8} - 50q^{9} + O(q^{10}) \) \( 66584q + 2q^{2} - 6q^{3} - 14q^{4} - 36q^{5} - 27q^{6} - 32q^{7} + 2q^{8} - 50q^{9} - 56q^{10} - 56q^{11} - 16q^{12} - 56q^{13} - 18q^{15} + 2q^{16} - 52q^{17} + 45q^{18} - 54q^{19} + 12q^{20} + 20q^{21} + 12q^{22} - 20q^{23} + 31q^{24} - 74q^{25} - 20q^{26} + 24q^{27} - 24q^{28} - 56q^{29} - 6q^{30} - 116q^{31} + 2q^{32} + 9q^{33} - 60q^{34} - 96q^{35} - 25q^{36} + 76q^{37} + 64q^{38} + 122q^{39} + 132q^{40} + 208q^{41} + 108q^{42} + 44q^{43} + 28q^{44} + 132q^{45} + 320q^{46} + 208q^{47} + 22q^{48} + 576q^{49} + 166q^{50} + 365q^{51} + 76q^{52} + 240q^{53} + 64q^{54} + 320q^{55} + 144q^{56} + 91q^{57} + 364q^{58} + 204q^{59} + 124q^{60} + 496q^{61} + 316q^{62} + 240q^{63} - 14q^{64} + 432q^{65} + 432q^{66} + 420q^{67} + 188q^{68} + 522q^{69} + 360q^{70} + 736q^{71} + 174q^{72} + 580q^{73} + 372q^{74} + 825q^{75} + 196q^{76} + 252q^{77} + 372q^{78} + 340q^{79} + 184q^{80} + 866q^{81} + 266q^{82} + 684q^{83} + 68q^{84} + 684q^{85} + 508q^{86} + 756q^{87} + 208q^{88} + 552q^{89} + 454q^{90} + 472q^{91} - 48q^{92} + 786q^{93} + 88q^{94} + 660q^{95} + 26q^{96} + 102q^{97} - 48q^{98} + 210q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3234))\)

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
3234.2.a \(\chi_{3234}(1, \cdot)\) 3234.2.a.a 1 1
3234.2.a.b 1
3234.2.a.c 1
3234.2.a.d 1
3234.2.a.e 1
3234.2.a.f 1
3234.2.a.g 1
3234.2.a.h 1
3234.2.a.i 1
3234.2.a.j 1
3234.2.a.k 1
3234.2.a.l 1
3234.2.a.m 1
3234.2.a.n 1
3234.2.a.o 1
3234.2.a.p 1
3234.2.a.q 1
3234.2.a.r 1
3234.2.a.s 1
3234.2.a.t 1
3234.2.a.u 1
3234.2.a.v 1
3234.2.a.w 2
3234.2.a.x 2
3234.2.a.y 2
3234.2.a.z 2
3234.2.a.ba 2
3234.2.a.bb 2
3234.2.a.bc 2
3234.2.a.bd 2
3234.2.a.be 2
3234.2.a.bf 3
3234.2.a.bg 3
3234.2.a.bh 3
3234.2.a.bi 3
3234.2.a.bj 4
3234.2.a.bk 4
3234.2.a.bl 4
3234.2.a.bm 4
3234.2.c \(\chi_{3234}(197, \cdot)\) n/a 164 1
3234.2.e \(\chi_{3234}(2155, \cdot)\) 3234.2.e.a 16 1
3234.2.e.b 16
3234.2.e.c 24
3234.2.e.d 24
3234.2.g \(\chi_{3234}(881, \cdot)\) n/a 136 1
3234.2.i \(\chi_{3234}(67, \cdot)\) n/a 136 2
3234.2.j \(\chi_{3234}(295, \cdot)\) n/a 328 4
3234.2.k \(\chi_{3234}(815, \cdot)\) n/a 264 2
3234.2.n \(\chi_{3234}(263, \cdot)\) n/a 320 2
3234.2.p \(\chi_{3234}(901, \cdot)\) n/a 160 2
3234.2.r \(\chi_{3234}(463, \cdot)\) n/a 576 6
3234.2.t \(\chi_{3234}(587, \cdot)\) n/a 640 4
3234.2.v \(\chi_{3234}(391, \cdot)\) n/a 320 4
3234.2.x \(\chi_{3234}(491, \cdot)\) n/a 656 4
3234.2.ba \(\chi_{3234}(419, \cdot)\) n/a 1104 6
3234.2.bc \(\chi_{3234}(307, \cdot)\) n/a 672 6
3234.2.be \(\chi_{3234}(659, \cdot)\) n/a 1344 6
3234.2.bg \(\chi_{3234}(361, \cdot)\) n/a 640 8
3234.2.bh \(\chi_{3234}(331, \cdot)\) n/a 1104 12
3234.2.bj \(\chi_{3234}(19, \cdot)\) n/a 640 8
3234.2.bl \(\chi_{3234}(557, \cdot)\) n/a 1280 8
3234.2.bo \(\chi_{3234}(509, \cdot)\) n/a 1280 8
3234.2.bp \(\chi_{3234}(169, \cdot)\) n/a 2688 24
3234.2.br \(\chi_{3234}(241, \cdot)\) n/a 1344 12
3234.2.bt \(\chi_{3234}(65, \cdot)\) n/a 2688 12
3234.2.bw \(\chi_{3234}(89, \cdot)\) n/a 2256 12
3234.2.by \(\chi_{3234}(29, \cdot)\) n/a 5376 24
3234.2.ca \(\chi_{3234}(13, \cdot)\) n/a 2688 24
3234.2.cc \(\chi_{3234}(125, \cdot)\) n/a 5376 24
3234.2.ce \(\chi_{3234}(25, \cdot)\) n/a 5376 48
3234.2.cf \(\chi_{3234}(5, \cdot)\) n/a 10752 48
3234.2.ci \(\chi_{3234}(95, \cdot)\) n/a 10752 48
3234.2.ck \(\chi_{3234}(61, \cdot)\) n/a 5376 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3234))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3234)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(462))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(539))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1078))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1617))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T^{2} )^{8} \))(\( ( 1 + T^{2} )^{8} \))
$3$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T^{2} )^{8} \))(\( ( 1 + T^{2} )^{8} \))
$5$ (\( 1 + 3 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + 3 T^{2} + 25 T^{4} \))(\( 1 - 2 T^{2} + 25 T^{4} \))(\( ( 1 + 5 T^{2} )^{2} \))(\( ( 1 + 5 T^{2} )^{2} \))(\( 1 + 3 T^{2} + 25 T^{4} \))(\( 1 + 2 T + 6 T^{2} + 10 T^{3} + 25 T^{4} \))(\( ( 1 - 2 T + 5 T^{2} )^{2} \))(\( ( 1 + 2 T + 5 T^{2} )^{2} \))(\( 1 - 2 T + 6 T^{2} - 10 T^{3} + 25 T^{4} \))(\( 1 - 20 T^{3} + 125 T^{6} \))(\( 1 + 6 T^{2} - 4 T^{3} + 30 T^{4} + 125 T^{6} \))(\( 1 + 20 T^{3} + 125 T^{6} \))(\( 1 + 6 T^{2} + 4 T^{3} + 30 T^{4} + 125 T^{6} \))(\( 1 + 4 T^{2} + 46 T^{4} + 100 T^{6} + 625 T^{8} \))(\( 1 + 4 T^{2} + 46 T^{4} + 100 T^{6} + 625 T^{8} \))(\( 1 + 4 T + 16 T^{2} + 44 T^{3} + 118 T^{4} + 220 T^{5} + 400 T^{6} + 500 T^{7} + 625 T^{8} \))(\( 1 - 4 T + 16 T^{2} - 44 T^{3} + 118 T^{4} - 220 T^{5} + 400 T^{6} - 500 T^{7} + 625 T^{8} \))(\( 1 - 30 T^{2} + 471 T^{4} - 4930 T^{6} + 37781 T^{8} - 222460 T^{10} + 1052266 T^{12} - 4383184 T^{14} + 19642634 T^{16} - 109579600 T^{18} + 657666250 T^{20} - 3475937500 T^{22} + 14758203125 T^{24} - 48144531250 T^{26} + 114990234375 T^{28} - 183105468750 T^{30} + 152587890625 T^{32} \))(\( 1 - 30 T^{2} + 471 T^{4} - 4930 T^{6} + 37781 T^{8} - 222460 T^{10} + 1052266 T^{12} - 4383184 T^{14} + 19642634 T^{16} - 109579600 T^{18} + 657666250 T^{20} - 3475937500 T^{22} + 14758203125 T^{24} - 48144531250 T^{26} + 114990234375 T^{28} - 183105468750 T^{30} + 152587890625 T^{32} \))
$7$ 1
$11$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( 1 - 8 T + 33 T^{2} - 56 T^{3} - 206 T^{4} + 1320 T^{5} - 1177 T^{6} - 15528 T^{7} + 86618 T^{8} - 170808 T^{9} - 142417 T^{10} + 1756920 T^{11} - 3016046 T^{12} - 9018856 T^{13} + 58461513 T^{14} - 155897368 T^{15} + 214358881 T^{16} \))(\( 1 - 8 T + 33 T^{2} - 56 T^{3} - 206 T^{4} + 1320 T^{5} - 1177 T^{6} - 15528 T^{7} + 86618 T^{8} - 170808 T^{9} - 142417 T^{10} + 1756920 T^{11} - 3016046 T^{12} - 9018856 T^{13} + 58461513 T^{14} - 155897368 T^{15} + 214358881 T^{16} \))
$13$ (\( 1 + 6 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( ( 1 + 4 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( 1 + 24 T^{2} + 169 T^{4} \))(\( 1 + 24 T^{2} + 169 T^{4} \))(\( ( 1 - 4 T + 13 T^{2} )^{2} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( 1 - 8 T + 40 T^{2} - 104 T^{3} + 169 T^{4} \))(\( 1 + 8 T + 40 T^{2} + 104 T^{3} + 169 T^{4} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( ( 1 + 13 T^{2} )^{3} \))(\( 1 + 3 T^{2} - 32 T^{3} + 39 T^{4} + 2197 T^{6} \))(\( ( 1 + 13 T^{2} )^{3} \))(\( 1 + 3 T^{2} + 32 T^{3} + 39 T^{4} + 2197 T^{6} \))(\( 1 + 16 T^{2} + 32 T^{3} + 242 T^{4} + 416 T^{5} + 2704 T^{6} + 28561 T^{8} \))(\( 1 + 16 T^{2} - 32 T^{3} + 242 T^{4} - 416 T^{5} + 2704 T^{6} + 28561 T^{8} \))(\( 1 + 8 T + 48 T^{2} + 232 T^{3} + 882 T^{4} + 3016 T^{5} + 8112 T^{6} + 17576 T^{7} + 28561 T^{8} \))(\( 1 - 8 T + 48 T^{2} - 232 T^{3} + 882 T^{4} - 3016 T^{5} + 8112 T^{6} - 17576 T^{7} + 28561 T^{8} \))(\( ( 1 + 40 T^{2} - 8 T^{3} + 576 T^{4} + 648 T^{5} + 3672 T^{6} + 30816 T^{7} + 19294 T^{8} + 400608 T^{9} + 620568 T^{10} + 1423656 T^{11} + 16451136 T^{12} - 2970344 T^{13} + 193072360 T^{14} + 815730721 T^{16} )^{2} \))(\( ( 1 + 40 T^{2} + 8 T^{3} + 576 T^{4} - 648 T^{5} + 3672 T^{6} - 30816 T^{7} + 19294 T^{8} - 400608 T^{9} + 620568 T^{10} - 1423656 T^{11} + 16451136 T^{12} + 2970344 T^{13} + 193072360 T^{14} + 815730721 T^{16} )^{2} \))
$17$ (\( 1 - 5 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 + T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 5 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( ( 1 + 3 T + 17 T^{2} )^{2} \))(\( 1 + 22 T^{2} + 289 T^{4} \))(\( ( 1 - 4 T + 17 T^{2} )^{2} \))(\( ( 1 + 4 T + 17 T^{2} )^{2} \))(\( ( 1 - 3 T + 17 T^{2} )^{2} \))(\( 1 + 6 T + 38 T^{2} + 102 T^{3} + 289 T^{4} \))(\( ( 1 - 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( 1 - 6 T + 38 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 - 3 T - 6 T^{2} + 37 T^{3} - 102 T^{4} - 867 T^{5} + 4913 T^{6} \))(\( ( 1 + T + 17 T^{2} )^{3} \))(\( 1 + 3 T - 6 T^{2} - 37 T^{3} - 102 T^{4} + 867 T^{5} + 4913 T^{6} \))(\( ( 1 - T + 17 T^{2} )^{3} \))(\( 1 + 36 T^{2} - 32 T^{3} + 638 T^{4} - 544 T^{5} + 10404 T^{6} + 83521 T^{8} \))(\( 1 + 36 T^{2} + 32 T^{3} + 638 T^{4} + 544 T^{5} + 10404 T^{6} + 83521 T^{8} \))(\( 1 + 4 T + 16 T^{2} + 92 T^{3} + 742 T^{4} + 1564 T^{5} + 4624 T^{6} + 19652 T^{7} + 83521 T^{8} \))(\( 1 - 4 T + 16 T^{2} - 92 T^{3} + 742 T^{4} - 1564 T^{5} + 4624 T^{6} - 19652 T^{7} + 83521 T^{8} \))(\( ( 1 + 83 T^{2} + 68 T^{3} + 3413 T^{4} + 4044 T^{5} + 95086 T^{6} + 108260 T^{7} + 1908750 T^{8} + 1840420 T^{9} + 27479854 T^{10} + 19868172 T^{11} + 285057173 T^{12} + 96550276 T^{13} + 2003418227 T^{14} + 6975757441 T^{16} )^{2} \))(\( ( 1 + 83 T^{2} - 68 T^{3} + 3413 T^{4} - 4044 T^{5} + 95086 T^{6} - 108260 T^{7} + 1908750 T^{8} - 1840420 T^{9} + 27479854 T^{10} - 19868172 T^{11} + 285057173 T^{12} - 96550276 T^{13} + 2003418227 T^{14} + 6975757441 T^{16} )^{2} \))
$19$ (\( 1 + 6 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 3 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 - 3 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 10 T^{2} + 361 T^{4} \))(\( 1 + 4 T + 30 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 8 T + 52 T^{2} - 152 T^{3} + 361 T^{4} \))(\( 1 + 8 T + 52 T^{2} + 152 T^{3} + 361 T^{4} \))(\( 1 + 10 T^{2} + 361 T^{4} \))(\( 1 + 2 T - 6 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 - 4 T + 24 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 4 T + 24 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 2 T - 6 T^{2} - 38 T^{3} + 361 T^{4} \))(\( 1 + 9 T + 69 T^{2} + 314 T^{3} + 1311 T^{4} + 3249 T^{5} + 6859 T^{6} \))(\( 1 - 3 T + 21 T^{2} - 150 T^{3} + 399 T^{4} - 1083 T^{5} + 6859 T^{6} \))(\( 1 - 9 T + 69 T^{2} - 314 T^{3} + 1311 T^{4} - 3249 T^{5} + 6859 T^{6} \))(\( 1 + 3 T + 21 T^{2} + 150 T^{3} + 399 T^{4} + 1083 T^{5} + 6859 T^{6} \))(\( 1 + 40 T^{2} - 80 T^{3} + 794 T^{4} - 1520 T^{5} + 14440 T^{6} + 130321 T^{8} \))(\( 1 + 40 T^{2} + 80 T^{3} + 794 T^{4} + 1520 T^{5} + 14440 T^{6} + 130321 T^{8} \))(\( 1 + 12 T + 116 T^{2} + 708 T^{3} + 3658 T^{4} + 13452 T^{5} + 41876 T^{6} + 82308 T^{7} + 130321 T^{8} \))(\( 1 - 12 T + 116 T^{2} - 708 T^{3} + 3658 T^{4} - 13452 T^{5} + 41876 T^{6} - 82308 T^{7} + 130321 T^{8} \))(\( ( 1 - 10 T + 145 T^{2} - 1030 T^{3} + 8870 T^{4} - 49582 T^{5} + 317127 T^{6} - 1444786 T^{7} + 7373490 T^{8} - 27450934 T^{9} + 114482847 T^{10} - 340082938 T^{11} + 1155947270 T^{12} - 2550381970 T^{13} + 6821652745 T^{14} - 8938717390 T^{15} + 16983563041 T^{16} )^{2} \))(\( ( 1 + 10 T + 145 T^{2} + 1030 T^{3} + 8870 T^{4} + 49582 T^{5} + 317127 T^{6} + 1444786 T^{7} + 7373490 T^{8} + 27450934 T^{9} + 114482847 T^{10} + 340082938 T^{11} + 1155947270 T^{12} + 2550381970 T^{13} + 6821652745 T^{14} + 8938717390 T^{15} + 16983563041 T^{16} )^{2} \))
$23$ (\( 1 - 5 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - 5 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 + 39 T^{2} + 529 T^{4} \))(\( 1 - 2 T^{2} + 529 T^{4} \))(\( 1 - 4 T + 18 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 - 4 T + 18 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 + 39 T^{2} + 529 T^{4} \))(\( 1 - 4 T + 30 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 + 4 T + 42 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 + 4 T + 42 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 - 4 T + 30 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 - 3 T + 42 T^{2} - 49 T^{3} + 966 T^{4} - 1587 T^{5} + 12167 T^{6} \))(\( 1 - 9 T + 72 T^{2} - 393 T^{3} + 1656 T^{4} - 4761 T^{5} + 12167 T^{6} \))(\( 1 - 3 T + 42 T^{2} - 49 T^{3} + 966 T^{4} - 1587 T^{5} + 12167 T^{6} \))(\( 1 - 9 T + 72 T^{2} - 393 T^{3} + 1656 T^{4} - 4761 T^{5} + 12167 T^{6} \))(\( 1 + 8 T + 36 T^{2} - 56 T^{3} - 570 T^{4} - 1288 T^{5} + 19044 T^{6} + 97336 T^{7} + 279841 T^{8} \))(\( 1 + 8 T + 36 T^{2} - 56 T^{3} - 570 T^{4} - 1288 T^{5} + 19044 T^{6} + 97336 T^{7} + 279841 T^{8} \))(\( 1 + 8 T + 92 T^{2} + 520 T^{3} + 3190 T^{4} + 11960 T^{5} + 48668 T^{6} + 97336 T^{7} + 279841 T^{8} \))(\( 1 + 8 T + 92 T^{2} + 520 T^{3} + 3190 T^{4} + 11960 T^{5} + 48668 T^{6} + 97336 T^{7} + 279841 T^{8} \))(\( ( 1 - 4 T + 57 T^{2} - 124 T^{3} + 2103 T^{4} - 4828 T^{5} + 65020 T^{6} - 100872 T^{7} + 1438254 T^{8} - 2320056 T^{9} + 34395580 T^{10} - 58742276 T^{11} + 588505623 T^{12} - 798106532 T^{13} + 8438045673 T^{14} - 13619301788 T^{15} + 78310985281 T^{16} )^{2} \))(\( ( 1 - 4 T + 57 T^{2} - 124 T^{3} + 2103 T^{4} - 4828 T^{5} + 65020 T^{6} - 100872 T^{7} + 1438254 T^{8} - 2320056 T^{9} + 34395580 T^{10} - 58742276 T^{11} + 588505623 T^{12} - 798106532 T^{13} + 8438045673 T^{14} - 13619301788 T^{15} + 78310985281 T^{16} )^{2} \))
$29$ (\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 10 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( 1 + 26 T^{2} + 841 T^{4} \))(\( 1 + 26 T^{2} + 841 T^{4} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( 1 + 38 T^{2} + 841 T^{4} \))(\( 1 - 8 T + 42 T^{2} - 232 T^{3} + 841 T^{4} \))(\( 1 - 8 T + 42 T^{2} - 232 T^{3} + 841 T^{4} \))(\( 1 + 38 T^{2} + 841 T^{4} \))(\( 1 - 9 T + 39 T^{2} - 174 T^{3} + 1131 T^{4} - 7569 T^{5} + 24389 T^{6} \))(\( 1 - 9 T + 87 T^{2} - 430 T^{3} + 2523 T^{4} - 7569 T^{5} + 24389 T^{6} \))(\( 1 - 9 T + 39 T^{2} - 174 T^{3} + 1131 T^{4} - 7569 T^{5} + 24389 T^{6} \))(\( 1 - 9 T + 87 T^{2} - 430 T^{3} + 2523 T^{4} - 7569 T^{5} + 24389 T^{6} \))(\( ( 1 + 50 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 + 50 T^{2} + 841 T^{4} )^{2} \))(\( 1 + 8 T + 84 T^{2} + 632 T^{3} + 3254 T^{4} + 18328 T^{5} + 70644 T^{6} + 195112 T^{7} + 707281 T^{8} \))(\( 1 + 8 T + 84 T^{2} + 632 T^{3} + 3254 T^{4} + 18328 T^{5} + 70644 T^{6} + 195112 T^{7} + 707281 T^{8} \))(\( 1 - 220 T^{2} + 25766 T^{4} - 2101752 T^{6} + 132425201 T^{8} - 6784185928 T^{10} + 290786240918 T^{12} - 10599475438788 T^{14} + 331431007100868 T^{16} - 8914158844020708 T^{18} + 205667583262723958 T^{20} - 4035392003974426888 T^{22} + 66245231785889430161 T^{24} - \)\(88\!\cdots\!52\)\( T^{26} + \)\(91\!\cdots\!06\)\( T^{28} - \)\(65\!\cdots\!20\)\( T^{30} + \)\(25\!\cdots\!21\)\( T^{32} \))(\( 1 - 220 T^{2} + 25766 T^{4} - 2101752 T^{6} + 132425201 T^{8} - 6784185928 T^{10} + 290786240918 T^{12} - 10599475438788 T^{14} + 331431007100868 T^{16} - 8914158844020708 T^{18} + 205667583262723958 T^{20} - 4035392003974426888 T^{22} + 66245231785889430161 T^{24} - \)\(88\!\cdots\!52\)\( T^{26} + \)\(91\!\cdots\!06\)\( T^{28} - \)\(65\!\cdots\!20\)\( T^{30} + \)\(25\!\cdots\!21\)\( T^{32} \))
$31$ (\( 1 + 4 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{2} \))(\( 1 + 4 T + 54 T^{2} + 124 T^{3} + 961 T^{4} \))(\( 1 - 8 T + 28 T^{2} - 248 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 28 T^{2} + 248 T^{3} + 961 T^{4} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( 1 + 10 T + 82 T^{2} + 310 T^{3} + 961 T^{4} \))(\( 1 - 4 T + 48 T^{2} - 124 T^{3} + 961 T^{4} \))(\( 1 + 4 T + 48 T^{2} + 124 T^{3} + 961 T^{4} \))(\( 1 - 10 T + 82 T^{2} - 310 T^{3} + 961 T^{4} \))(\( 1 + 6 T + 45 T^{2} + 180 T^{3} + 1395 T^{4} + 5766 T^{5} + 29791 T^{6} \))(\( 1 + 6 T - 3 T^{2} - 140 T^{3} - 93 T^{4} + 5766 T^{5} + 29791 T^{6} \))(\( 1 - 6 T + 45 T^{2} - 180 T^{3} + 1395 T^{4} - 5766 T^{5} + 29791 T^{6} \))(\( 1 - 6 T - 3 T^{2} + 140 T^{3} - 93 T^{4} - 5766 T^{5} + 29791 T^{6} \))(\( 1 + 16 T + 200 T^{2} + 1568 T^{3} + 10378 T^{4} + 48608 T^{5} + 192200 T^{6} + 476656 T^{7} + 923521 T^{8} \))(\( 1 - 16 T + 200 T^{2} - 1568 T^{3} + 10378 T^{4} - 48608 T^{5} + 192200 T^{6} - 476656 T^{7} + 923521 T^{8} \))(\( 1 + 4 T + 36 T^{2} + 44 T^{3} + 1274 T^{4} + 1364 T^{5} + 34596 T^{6} + 119164 T^{7} + 923521 T^{8} \))(\( 1 - 4 T + 36 T^{2} - 44 T^{3} + 1274 T^{4} - 1364 T^{5} + 34596 T^{6} - 119164 T^{7} + 923521 T^{8} \))(\( 1 - 386 T^{2} + 71901 T^{4} - 8595466 T^{6} + 739336166 T^{8} - 48582533718 T^{10} + 2525237875987 T^{12} - 105975133331486 T^{14} + 3630081582174546 T^{16} - 101842103131558046 T^{18} + 2332110208469390227 T^{20} - 43117177507031615958 T^{22} + \)\(63\!\cdots\!06\)\( T^{24} - \)\(70\!\cdots\!66\)\( T^{26} + \)\(56\!\cdots\!61\)\( T^{28} - \)\(29\!\cdots\!06\)\( T^{30} + \)\(72\!\cdots\!81\)\( T^{32} \))(\( 1 - 386 T^{2} + 71901 T^{4} - 8595466 T^{6} + 739336166 T^{8} - 48582533718 T^{10} + 2525237875987 T^{12} - 105975133331486 T^{14} + 3630081582174546 T^{16} - 101842103131558046 T^{18} + 2332110208469390227 T^{20} - 43117177507031615958 T^{22} + \)\(63\!\cdots\!06\)\( T^{24} - \)\(70\!\cdots\!66\)\( T^{26} + \)\(56\!\cdots\!61\)\( T^{28} - \)\(29\!\cdots\!06\)\( T^{30} + \)\(72\!\cdots\!81\)\( T^{32} \))
$37$ (\( 1 + 2 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 8 T + 62 T^{2} + 296 T^{3} + 1369 T^{4} \))(\( 1 - 4 T + 30 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 46 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 46 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 8 T + 62 T^{2} + 296 T^{3} + 1369 T^{4} \))(\( 1 + 4 T - 2 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 70 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 70 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T - 2 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 - 21 T + 243 T^{2} - 1782 T^{3} + 8991 T^{4} - 28749 T^{5} + 50653 T^{6} \))(\( 1 - 9 T + 99 T^{2} - 502 T^{3} + 3663 T^{4} - 12321 T^{5} + 50653 T^{6} \))(\( 1 - 21 T + 243 T^{2} - 1782 T^{3} + 8991 T^{4} - 28749 T^{5} + 50653 T^{6} \))(\( 1 - 9 T + 99 T^{2} - 502 T^{3} + 3663 T^{4} - 12321 T^{5} + 50653 T^{6} \))(\( 1 - 8 T + 76 T^{2} - 408 T^{3} + 2486 T^{4} - 15096 T^{5} + 104044 T^{6} - 405224 T^{7} + 1874161 T^{8} \))(\( 1 - 8 T + 76 T^{2} - 408 T^{3} + 2486 T^{4} - 15096 T^{5} + 104044 T^{6} - 405224 T^{7} + 1874161 T^{8} \))(\( 1 - 8 T + 116 T^{2} - 792 T^{3} + 5862 T^{4} - 29304 T^{5} + 158804 T^{6} - 405224 T^{7} + 1874161 T^{8} \))(\( 1 - 8 T + 116 T^{2} - 792 T^{3} + 5862 T^{4} - 29304 T^{5} + 158804 T^{6} - 405224 T^{7} + 1874161 T^{8} \))(\( ( 1 + 14 T + 229 T^{2} + 2126 T^{3} + 20986 T^{4} + 154618 T^{5} + 1182051 T^{6} + 7476394 T^{7} + 49108426 T^{8} + 276626578 T^{9} + 1618227819 T^{10} + 7831865554 T^{11} + 39331142746 T^{12} + 147425252582 T^{13} + 587551347661 T^{14} + 1329046279862 T^{15} + 3512479453921 T^{16} )^{2} \))(\( ( 1 + 14 T + 229 T^{2} + 2126 T^{3} + 20986 T^{4} + 154618 T^{5} + 1182051 T^{6} + 7476394 T^{7} + 49108426 T^{8} + 276626578 T^{9} + 1618227819 T^{10} + 7831865554 T^{11} + 39331142746 T^{12} + 147425252582 T^{13} + 587551347661 T^{14} + 1329046279862 T^{15} + 3512479453921 T^{16} )^{2} \))
$41$ (\( 1 + 5 T + 41 T^{2} \))(\( 1 - 4 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 12 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 12 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 5 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))(\( ( 1 - 9 T + 41 T^{2} )^{2} \))(\( 1 + 70 T^{2} + 1681 T^{4} \))(\( 1 - 8 T + 66 T^{2} - 328 T^{3} + 1681 T^{4} \))(\( 1 + 8 T + 66 T^{2} + 328 T^{3} + 1681 T^{4} \))(\( ( 1 + 9 T + 41 T^{2} )^{2} \))(\( 1 + 6 T + 86 T^{2} + 246 T^{3} + 1681 T^{4} \))(\( 1 - 12 T + 86 T^{2} - 492 T^{3} + 1681 T^{4} \))(\( 1 + 12 T + 86 T^{2} + 492 T^{3} + 1681 T^{4} \))(\( 1 - 6 T + 86 T^{2} - 246 T^{3} + 1681 T^{4} \))(\( 1 - 12 T + 96 T^{2} - 678 T^{3} + 3936 T^{4} - 20172 T^{5} + 68921 T^{6} \))(\( 1 + 12 T + 144 T^{2} + 902 T^{3} + 5904 T^{4} + 20172 T^{5} + 68921 T^{6} \))(\( 1 + 12 T + 96 T^{2} + 678 T^{3} + 3936 T^{4} + 20172 T^{5} + 68921 T^{6} \))(\( 1 - 12 T + 144 T^{2} - 902 T^{3} + 5904 T^{4} - 20172 T^{5} + 68921 T^{6} \))(\( 1 + 132 T^{2} + 32 T^{3} + 7454 T^{4} + 1312 T^{5} + 221892 T^{6} + 2825761 T^{8} \))(\( 1 + 132 T^{2} - 32 T^{3} + 7454 T^{4} - 1312 T^{5} + 221892 T^{6} + 2825761 T^{8} \))(\( 1 + 12 T + 80 T^{2} - 76 T^{3} - 1786 T^{4} - 3116 T^{5} + 134480 T^{6} + 827052 T^{7} + 2825761 T^{8} \))(\( 1 - 12 T + 80 T^{2} + 76 T^{3} - 1786 T^{4} + 3116 T^{5} + 134480 T^{6} - 827052 T^{7} + 2825761 T^{8} \))(\( ( 1 - 16 T + 330 T^{2} - 3640 T^{3} + 42745 T^{4} - 362832 T^{5} + 3123194 T^{6} - 21761352 T^{7} + 152229812 T^{8} - 892215432 T^{9} + 5250089114 T^{10} - 25006744272 T^{11} + 120787153945 T^{12} - 421716571640 T^{13} + 1567534399530 T^{14} - 3116068382096 T^{15} + 7984925229121 T^{16} )^{2} \))(\( ( 1 + 16 T + 330 T^{2} + 3640 T^{3} + 42745 T^{4} + 362832 T^{5} + 3123194 T^{6} + 21761352 T^{7} + 152229812 T^{8} + 892215432 T^{9} + 5250089114 T^{10} + 25006744272 T^{11} + 120787153945 T^{12} + 421716571640 T^{13} + 1567534399530 T^{14} + 3116068382096 T^{15} + 7984925229121 T^{16} )^{2} \))
$43$ (\( 1 + 10 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 11 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 11 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 12 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 12 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 8 T + 74 T^{2} - 344 T^{3} + 1849 T^{4} \))(\( 1 + 8 T + 54 T^{2} + 344 T^{3} + 1849 T^{4} \))(\( ( 1 + 10 T + 43 T^{2} )^{2} \))(\( ( 1 + 10 T + 43 T^{2} )^{2} \))(\( 1 - 8 T + 74 T^{2} - 344 T^{3} + 1849 T^{4} \))(\( 1 - 4 T + 70 T^{2} - 172 T^{3} + 1849 T^{4} \))(\( 1 + 4 T + 82 T^{2} + 172 T^{3} + 1849 T^{4} \))(\( 1 + 4 T + 82 T^{2} + 172 T^{3} + 1849 T^{4} \))(\( 1 - 4 T + 70 T^{2} - 172 T^{3} + 1849 T^{4} \))(\( 1 - 3 T - 3 T^{2} + 146 T^{3} - 129 T^{4} - 5547 T^{5} + 79507 T^{6} \))(\( 1 - 9 T + 117 T^{2} - 610 T^{3} + 5031 T^{4} - 16641 T^{5} + 79507 T^{6} \))(\( 1 - 3 T - 3 T^{2} + 146 T^{3} - 129 T^{4} - 5547 T^{5} + 79507 T^{6} \))(\( 1 - 9 T + 117 T^{2} - 610 T^{3} + 5031 T^{4} - 16641 T^{5} + 79507 T^{6} \))(\( 1 - 8 T + 116 T^{2} - 424 T^{3} + 5110 T^{4} - 18232 T^{5} + 214484 T^{6} - 636056 T^{7} + 3418801 T^{8} \))(\( 1 - 8 T + 116 T^{2} - 424 T^{3} + 5110 T^{4} - 18232 T^{5} + 214484 T^{6} - 636056 T^{7} + 3418801 T^{8} \))(\( 1 + 8 T + 140 T^{2} + 936 T^{3} + 8358 T^{4} + 40248 T^{5} + 258860 T^{6} + 636056 T^{7} + 3418801 T^{8} \))(\( 1 + 8 T + 140 T^{2} + 936 T^{3} + 8358 T^{4} + 40248 T^{5} + 258860 T^{6} + 636056 T^{7} + 3418801 T^{8} \))(\( 1 - 370 T^{2} + 69205 T^{4} - 8714850 T^{6} + 829915302 T^{8} - 63533346462 T^{10} + 4048663635627 T^{12} - 219017168933710 T^{14} + 10156745084830162 T^{16} - 404962745358429790 T^{18} + 13841575286145223227 T^{20} - \)\(40\!\cdots\!38\)\( T^{22} + \)\(97\!\cdots\!02\)\( T^{24} - \)\(18\!\cdots\!50\)\( T^{26} + \)\(27\!\cdots\!05\)\( T^{28} - \)\(27\!\cdots\!30\)\( T^{30} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( 1 - 370 T^{2} + 69205 T^{4} - 8714850 T^{6} + 829915302 T^{8} - 63533346462 T^{10} + 4048663635627 T^{12} - 219017168933710 T^{14} + 10156745084830162 T^{16} - 404962745358429790 T^{18} + 13841575286145223227 T^{20} - \)\(40\!\cdots\!38\)\( T^{22} + \)\(97\!\cdots\!02\)\( T^{24} - \)\(18\!\cdots\!50\)\( T^{26} + \)\(27\!\cdots\!05\)\( T^{28} - \)\(27\!\cdots\!30\)\( T^{30} + \)\(13\!\cdots\!01\)\( T^{32} \))
$47$ (\( 1 + 9 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 - 9 T + 47 T^{2} \))(\( 1 + 9 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 9 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 118 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 + 92 T^{2} + 2209 T^{4} \))(\( 1 + 92 T^{2} + 2209 T^{4} \))(\( 1 + 8 T + 47 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 + 6 T + 58 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 - 4 T - 188 T^{3} + 2209 T^{4} \))(\( 1 + 4 T + 188 T^{3} + 2209 T^{4} \))(\( 1 - 6 T + 58 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 - 3 T + 114 T^{2} - 273 T^{3} + 5358 T^{4} - 6627 T^{5} + 103823 T^{6} \))(\( 1 - 15 T + 192 T^{2} - 1391 T^{3} + 9024 T^{4} - 33135 T^{5} + 103823 T^{6} \))(\( 1 + 3 T + 114 T^{2} + 273 T^{3} + 5358 T^{4} + 6627 T^{5} + 103823 T^{6} \))(\( 1 + 15 T + 192 T^{2} + 1391 T^{3} + 9024 T^{4} + 33135 T^{5} + 103823 T^{6} \))(\( 1 + 16 T + 248 T^{2} + 2304 T^{3} + 18890 T^{4} + 108288 T^{5} + 547832 T^{6} + 1661168 T^{7} + 4879681 T^{8} \))(\( 1 - 16 T + 248 T^{2} - 2304 T^{3} + 18890 T^{4} - 108288 T^{5} + 547832 T^{6} - 1661168 T^{7} + 4879681 T^{8} \))(\( 1 + 4 T + 164 T^{2} + 572 T^{3} + 11002 T^{4} + 26884 T^{5} + 362276 T^{6} + 415292 T^{7} + 4879681 T^{8} \))(\( 1 - 4 T + 164 T^{2} - 572 T^{3} + 11002 T^{4} - 26884 T^{5} + 362276 T^{6} - 415292 T^{7} + 4879681 T^{8} \))(\( 1 - 62 T^{2} + 2031 T^{4} - 368922 T^{6} + 20631365 T^{8} - 625319636 T^{10} + 67952187226 T^{12} - 3345437111480 T^{14} + 84733582253162 T^{16} - 7390070579259320 T^{18} + 331584996915154906 T^{20} - 6740455005895900244 T^{22} + \)\(49\!\cdots\!65\)\( T^{24} - \)\(19\!\cdots\!78\)\( T^{26} + \)\(23\!\cdots\!71\)\( T^{28} - \)\(15\!\cdots\!78\)\( T^{30} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 - 62 T^{2} + 2031 T^{4} - 368922 T^{6} + 20631365 T^{8} - 625319636 T^{10} + 67952187226 T^{12} - 3345437111480 T^{14} + 84733582253162 T^{16} - 7390070579259320 T^{18} + 331584996915154906 T^{20} - 6740455005895900244 T^{22} + \)\(49\!\cdots\!65\)\( T^{24} - \)\(19\!\cdots\!78\)\( T^{26} + \)\(23\!\cdots\!71\)\( T^{28} - \)\(15\!\cdots\!78\)\( T^{30} + \)\(56\!\cdots\!21\)\( T^{32} \))
$53$ (\( 1 - 2 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 14 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 - 4 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 10 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( ( 1 - 4 T + 53 T^{2} )^{2} \))(\( 1 - 12 T + 94 T^{2} - 636 T^{3} + 2809 T^{4} \))(\( 1 - 4 T + 78 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( 1 - 4 T + 78 T^{2} - 212 T^{3} + 2809 T^{4} \))(\( ( 1 - 4 T + 53 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( 1 + 4 T + 38 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( 1 + 4 T + 38 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 8 T + 53 T^{2} )^{3} \))(\( 1 + 123 T^{2} + 32 T^{3} + 6519 T^{4} + 148877 T^{6} \))(\( ( 1 - 8 T + 53 T^{2} )^{3} \))(\( 1 + 123 T^{2} + 32 T^{3} + 6519 T^{4} + 148877 T^{6} \))(\( 1 - 8 T + 140 T^{2} - 1048 T^{3} + 9334 T^{4} - 55544 T^{5} + 393260 T^{6} - 1191016 T^{7} + 7890481 T^{8} \))(\( 1 - 8 T + 140 T^{2} - 1048 T^{3} + 9334 T^{4} - 55544 T^{5} + 393260 T^{6} - 1191016 T^{7} + 7890481 T^{8} \))(\( 1 + 8 T + 52 T^{2} + 280 T^{3} + 3750 T^{4} + 14840 T^{5} + 146068 T^{6} + 1191016 T^{7} + 7890481 T^{8} \))(\( 1 + 8 T + 52 T^{2} + 280 T^{3} + 3750 T^{4} + 14840 T^{5} + 146068 T^{6} + 1191016 T^{7} + 7890481 T^{8} \))(\( ( 1 + 189 T^{2} - 116 T^{3} + 18282 T^{4} - 21964 T^{5} + 1293871 T^{6} - 2238960 T^{7} + 74773842 T^{8} - 118664880 T^{9} + 3634483639 T^{10} - 3269934428 T^{11} + 144253773642 T^{12} - 48510677188 T^{13} + 4189064253381 T^{14} + 62259690411361 T^{16} )^{2} \))(\( ( 1 + 189 T^{2} - 116 T^{3} + 18282 T^{4} - 21964 T^{5} + 1293871 T^{6} - 2238960 T^{7} + 74773842 T^{8} - 118664880 T^{9} + 3634483639 T^{10} - 3269934428 T^{11} + 144253773642 T^{12} - 48510677188 T^{13} + 4189064253381 T^{14} + 62259690411361 T^{16} )^{2} \))
$59$ (\( 1 - 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 7 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 9 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 7 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 - 9 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 8 T + 22 T^{2} + 472 T^{3} + 3481 T^{4} \))(\( 1 + 70 T^{2} + 3481 T^{4} \))(\( 1 - 8 T + 126 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 + 8 T + 126 T^{2} + 472 T^{3} + 3481 T^{4} \))(\( 1 - 8 T + 22 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 + 12 T + 134 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 - 8 T + 126 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 + 8 T + 126 T^{2} + 472 T^{3} + 3481 T^{4} \))(\( 1 - 12 T + 134 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 + 9 T + 129 T^{2} + 1014 T^{3} + 7611 T^{4} + 31329 T^{5} + 205379 T^{6} \))(\( 1 + 9 T + 81 T^{2} + 294 T^{3} + 4779 T^{4} + 31329 T^{5} + 205379 T^{6} \))(\( 1 - 9 T + 129 T^{2} - 1014 T^{3} + 7611 T^{4} - 31329 T^{5} + 205379 T^{6} \))(\( 1 - 9 T + 81 T^{2} - 294 T^{3} + 4779 T^{4} - 31329 T^{5} + 205379 T^{6} \))(\( ( 1 + 16 T + 174 T^{2} + 944 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 - 16 T + 174 T^{2} - 944 T^{3} + 3481 T^{4} )^{2} \))(\( 1 + 92 T^{2} - 512 T^{3} + 3446 T^{4} - 30208 T^{5} + 320252 T^{6} + 12117361 T^{8} \))(\( 1 + 92 T^{2} + 512 T^{3} + 3446 T^{4} + 30208 T^{5} + 320252 T^{6} + 12117361 T^{8} \))(\( 1 - 412 T^{2} + 84726 T^{4} - 11812648 T^{6} + 1278873825 T^{8} - 115825341832 T^{10} + 9135071092582 T^{12} - 639128365018580 T^{14} + 39901635887620324 T^{16} - 2224805838629676980 T^{18} + \)\(11\!\cdots\!02\)\( T^{20} - \)\(48\!\cdots\!12\)\( T^{22} + \)\(18\!\cdots\!25\)\( T^{24} - \)\(60\!\cdots\!48\)\( T^{26} + \)\(15\!\cdots\!06\)\( T^{28} - \)\(25\!\cdots\!32\)\( T^{30} + \)\(21\!\cdots\!41\)\( T^{32} \))(\( 1 - 412 T^{2} + 84726 T^{4} - 11812648 T^{6} + 1278873825 T^{8} - 115825341832 T^{10} + 9135071092582 T^{12} - 639128365018580 T^{14} + 39901635887620324 T^{16} - 2224805838629676980 T^{18} + \)\(11\!\cdots\!02\)\( T^{20} - \)\(48\!\cdots\!12\)\( T^{22} + \)\(18\!\cdots\!25\)\( T^{24} - \)\(60\!\cdots\!48\)\( T^{26} + \)\(15\!\cdots\!06\)\( T^{28} - \)\(25\!\cdots\!32\)\( T^{30} + \)\(21\!\cdots\!41\)\( T^{32} \))
$61$ (\( 1 - 5 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 5 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 5 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - 8 T + 75 T^{2} - 488 T^{3} + 3721 T^{4} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( 1 + 120 T^{2} + 3721 T^{4} \))(\( 1 + 120 T^{2} + 3721 T^{4} \))(\( 1 + 8 T + 75 T^{2} + 488 T^{3} + 3721 T^{4} \))(\( ( 1 + 61 T^{2} )^{2} \))(\( 1 - 8 T + 136 T^{2} - 488 T^{3} + 3721 T^{4} \))(\( 1 + 8 T + 136 T^{2} + 488 T^{3} + 3721 T^{4} \))(\( ( 1 + 61 T^{2} )^{2} \))(\( 1 + 6 T + 120 T^{2} + 830 T^{3} + 7320 T^{4} + 22326 T^{5} + 226981 T^{6} \))(\( 1 - 6 T + 54 T^{2} - 506 T^{3} + 3294 T^{4} - 22326 T^{5} + 226981 T^{6} \))(\( 1 - 6 T + 120 T^{2} - 830 T^{3} + 7320 T^{4} - 22326 T^{5} + 226981 T^{6} \))(\( 1 + 6 T + 54 T^{2} + 506 T^{3} + 3294 T^{4} + 22326 T^{5} + 226981 T^{6} \))(\( 1 + 16 T + 304 T^{2} + 2864 T^{3} + 29362 T^{4} + 174704 T^{5} + 1131184 T^{6} + 3631696 T^{7} + 13845841 T^{8} \))(\( 1 - 16 T + 304 T^{2} - 2864 T^{3} + 29362 T^{4} - 174704 T^{5} + 1131184 T^{6} - 3631696 T^{7} + 13845841 T^{8} \))(\( 1 + 24 T + 336 T^{2} + 3768 T^{3} + 33714 T^{4} + 229848 T^{5} + 1250256 T^{6} + 5447544 T^{7} + 13845841 T^{8} \))(\( 1 - 24 T + 336 T^{2} - 3768 T^{3} + 33714 T^{4} - 229848 T^{5} + 1250256 T^{6} - 5447544 T^{7} + 13845841 T^{8} \))(\( ( 1 + 28 T + 652 T^{2} + 10788 T^{3} + 153837 T^{4} + 1841484 T^{5} + 19466748 T^{6} + 180831988 T^{7} + 1498320772 T^{8} + 11030751268 T^{9} + 72435769308 T^{10} + 417981879804 T^{11} + 2130002641917 T^{12} + 9111504895188 T^{13} + 33591284083372 T^{14} + 87996799408588 T^{15} + 191707312997281 T^{16} )^{2} \))(\( ( 1 - 28 T + 652 T^{2} - 10788 T^{3} + 153837 T^{4} - 1841484 T^{5} + 19466748 T^{6} - 180831988 T^{7} + 1498320772 T^{8} - 11030751268 T^{9} + 72435769308 T^{10} - 417981879804 T^{11} + 2130002641917 T^{12} - 9111504895188 T^{13} + 33591284083372 T^{14} - 87996799408588 T^{15} + 191707312997281 T^{16} )^{2} \))
$67$ (\( 1 - 5 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 5 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 6 T + 31 T^{2} + 402 T^{3} + 4489 T^{4} \))(\( 1 - 16 T + 150 T^{2} - 1072 T^{3} + 4489 T^{4} \))(\( 1 + 6 T^{2} + 4489 T^{4} \))(\( 1 + 6 T^{2} + 4489 T^{4} \))(\( 1 + 6 T + 31 T^{2} + 402 T^{3} + 4489 T^{4} \))(\( 1 - 4 T - 42 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 142 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 + 8 T + 142 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 - 4 T - 42 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 - 6 T + 138 T^{2} - 592 T^{3} + 9246 T^{4} - 26934 T^{5} + 300763 T^{6} \))(\( 1 - 6 T + 186 T^{2} - 720 T^{3} + 12462 T^{4} - 26934 T^{5} + 300763 T^{6} \))(\( 1 - 6 T + 138 T^{2} - 592 T^{3} + 9246 T^{4} - 26934 T^{5} + 300763 T^{6} \))(\( 1 - 6 T + 186 T^{2} - 720 T^{3} + 12462 T^{4} - 26934 T^{5} + 300763 T^{6} \))(\( 1 - 16 T + 124 T^{2} - 1104 T^{3} + 11510 T^{4} - 73968 T^{5} + 556636 T^{6} - 4812208 T^{7} + 20151121 T^{8} \))(\( 1 - 16 T + 124 T^{2} - 1104 T^{3} + 11510 T^{4} - 73968 T^{5} + 556636 T^{6} - 4812208 T^{7} + 20151121 T^{8} \))(\( 1 + 8 T + 228 T^{2} + 1576 T^{3} + 21606 T^{4} + 105592 T^{5} + 1023492 T^{6} + 2406104 T^{7} + 20151121 T^{8} \))(\( 1 + 8 T + 228 T^{2} + 1576 T^{3} + 21606 T^{4} + 105592 T^{5} + 1023492 T^{6} + 2406104 T^{7} + 20151121 T^{8} \))(\( ( 1 - 16 T + 442 T^{2} - 5580 T^{3} + 88929 T^{4} - 911040 T^{5} + 10786038 T^{6} - 91408468 T^{7} + 872545804 T^{8} - 6124367356 T^{9} + 48418524582 T^{10} - 274007123520 T^{11} + 1792019039409 T^{12} - 7533698097060 T^{13} + 39982604918698 T^{14} - 96971385685168 T^{15} + 406067677556641 T^{16} )^{2} \))(\( ( 1 - 16 T + 442 T^{2} - 5580 T^{3} + 88929 T^{4} - 911040 T^{5} + 10786038 T^{6} - 91408468 T^{7} + 872545804 T^{8} - 6124367356 T^{9} + 48418524582 T^{10} - 274007123520 T^{11} + 1792019039409 T^{12} - 7533698097060 T^{13} + 39982604918698 T^{14} - 96971385685168 T^{15} + 406067677556641 T^{16} )^{2} \))
$71$ (\( 1 - 4 T + 71 T^{2} \))(\( 1 - 16 T + 71 T^{2} \))(\( 1 + 15 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 3 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 + 15 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 3 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 4 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 2 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 16 T + 178 T^{2} + 1136 T^{3} + 5041 T^{4} \))(\( ( 1 + 12 T + 71 T^{2} )^{2} \))(\( 1 - 16 T + 174 T^{2} - 1136 T^{3} + 5041 T^{4} \))(\( 1 - 16 T + 174 T^{2} - 1136 T^{3} + 5041 T^{4} \))(\( 1 + 16 T + 178 T^{2} + 1136 T^{3} + 5041 T^{4} \))(\( 1 - 4 T + 126 T^{2} - 284 T^{3} + 5041 T^{4} \))(\( 1 + 110 T^{2} + 5041 T^{4} \))(\( 1 + 110 T^{2} + 5041 T^{4} \))(\( 1 - 4 T + 126 T^{2} - 284 T^{3} + 5041 T^{4} \))(\( 1 - 9 T + 105 T^{2} - 1170 T^{3} + 7455 T^{4} - 45369 T^{5} + 357911 T^{6} \))(\( 1 - 3 T + 189 T^{2} - 362 T^{3} + 13419 T^{4} - 15123 T^{5} + 357911 T^{6} \))(\( 1 - 9 T + 105 T^{2} - 1170 T^{3} + 7455 T^{4} - 45369 T^{5} + 357911 T^{6} \))(\( 1 - 3 T + 189 T^{2} - 362 T^{3} + 13419 T^{4} - 15123 T^{5} + 357911 T^{6} \))(\( 1 + 140 T^{2} - 256 T^{3} + 12422 T^{4} - 18176 T^{5} + 705740 T^{6} + 25411681 T^{8} \))(\( 1 + 140 T^{2} - 256 T^{3} + 12422 T^{4} - 18176 T^{5} + 705740 T^{6} + 25411681 T^{8} \))(\( 1 - 8 T + 60 T^{2} - 744 T^{3} + 10790 T^{4} - 52824 T^{5} + 302460 T^{6} - 2863288 T^{7} + 25411681 T^{8} \))(\( 1 - 8 T + 60 T^{2} - 744 T^{3} + 10790 T^{4} - 52824 T^{5} + 302460 T^{6} - 2863288 T^{7} + 25411681 T^{8} \))(\( ( 1 + 28 T + 665 T^{2} + 9556 T^{3} + 124346 T^{4} + 1164764 T^{5} + 10825387 T^{6} + 79684020 T^{7} + 712940082 T^{8} + 5657565420 T^{9} + 54570775867 T^{10} + 416881848004 T^{11} + 3159840885626 T^{12} + 17241215678156 T^{13} + 85186688807465 T^{14} + 254663364434948 T^{15} + 645753531245761 T^{16} )^{2} \))(\( ( 1 + 28 T + 665 T^{2} + 9556 T^{3} + 124346 T^{4} + 1164764 T^{5} + 10825387 T^{6} + 79684020 T^{7} + 712940082 T^{8} + 5657565420 T^{9} + 54570775867 T^{10} + 416881848004 T^{11} + 3159840885626 T^{12} + 17241215678156 T^{13} + 85186688807465 T^{14} + 254663364434948 T^{15} + 645753531245761 T^{16} )^{2} \))
$73$ (\( 1 + 12 T + 73 T^{2} \))(\( 1 + 12 T + 73 T^{2} \))(\( 1 - 12 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 12 T + 73 T^{2} \))(\( 1 - 12 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 12 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 73 T^{2} \))(\( 1 + 20 T + 218 T^{2} + 1460 T^{3} + 5329 T^{4} \))(\( 1 - 8 T + 150 T^{2} - 584 T^{3} + 5329 T^{4} \))(\( ( 1 - 4 T + 73 T^{2} )^{2} \))(\( ( 1 + 4 T + 73 T^{2} )^{2} \))(\( 1 - 20 T + 218 T^{2} - 1460 T^{3} + 5329 T^{4} \))(\( 1 + 18 T + 182 T^{2} + 1314 T^{3} + 5329 T^{4} \))(\( 1 - 12 T + 150 T^{2} - 876 T^{3} + 5329 T^{4} \))(\( 1 + 12 T + 150 T^{2} + 876 T^{3} + 5329 T^{4} \))(\( 1 - 18 T + 182 T^{2} - 1314 T^{3} + 5329 T^{4} \))(\( 1 + 99 T^{2} - 480 T^{3} + 7227 T^{4} + 389017 T^{6} \))(\( 1 + 123 T^{2} + 192 T^{3} + 8979 T^{4} + 389017 T^{6} \))(\( 1 + 99 T^{2} + 480 T^{3} + 7227 T^{4} + 389017 T^{6} \))(\( 1 + 123 T^{2} - 192 T^{3} + 8979 T^{4} + 389017 T^{6} \))(\( 1 + 116 T^{2} + 448 T^{3} + 6462 T^{4} + 32704 T^{5} + 618164 T^{6} + 28398241 T^{8} \))(\( 1 + 116 T^{2} - 448 T^{3} + 6462 T^{4} - 32704 T^{5} + 618164 T^{6} + 28398241 T^{8} \))(\( 1 + 4 T + 224 T^{2} + 796 T^{3} + 22758 T^{4} + 58108 T^{5} + 1193696 T^{6} + 1556068 T^{7} + 28398241 T^{8} \))(\( 1 - 4 T + 224 T^{2} - 796 T^{3} + 22758 T^{4} - 58108 T^{5} + 1193696 T^{6} - 1556068 T^{7} + 28398241 T^{8} \))(\( ( 1 - 44 T + 1204 T^{2} - 23988 T^{3} + 389092 T^{4} - 5297980 T^{5} + 62491788 T^{6} - 643636388 T^{7} + 5856468854 T^{8} - 46985456324 T^{9} + 333018738252 T^{10} - 2061004285660 T^{11} + 11049528387172 T^{12} - 49728841372884 T^{13} + 182206408451956 T^{14} - 486085534840268 T^{15} + 806460091894081 T^{16} )^{2} \))(\( ( 1 + 44 T + 1204 T^{2} + 23988 T^{3} + 389092 T^{4} + 5297980 T^{5} + 62491788 T^{6} + 643636388 T^{7} + 5856468854 T^{8} + 46985456324 T^{9} + 333018738252 T^{10} + 2061004285660 T^{11} + 11049528387172 T^{12} + 49728841372884 T^{13} + 182206408451956 T^{14} + 486085534840268 T^{15} + 806460091894081 T^{16} )^{2} \))
$79$ (\( 1 + T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 17 T + 79 T^{2} \))(\( 1 - 17 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 16 T + 215 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 + 8 T + 126 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + 8 T + 142 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + 8 T + 142 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 - 16 T + 215 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 + 4 T - 18 T^{2} + 316 T^{3} + 6241 T^{4} \))(\( 1 + 16 T + 150 T^{2} + 1264 T^{3} + 6241 T^{4} \))(\( 1 + 16 T + 150 T^{2} + 1264 T^{3} + 6241 T^{4} \))(\( 1 + 4 T - 18 T^{2} + 316 T^{3} + 6241 T^{4} \))(\( 1 - 12 T + 270 T^{2} - 1880 T^{3} + 21330 T^{4} - 74892 T^{5} + 493039 T^{6} \))(\( 1 - 12 T + 204 T^{2} - 1528 T^{3} + 16116 T^{4} - 74892 T^{5} + 493039 T^{6} \))(\( 1 - 12 T + 270 T^{2} - 1880 T^{3} + 21330 T^{4} - 74892 T^{5} + 493039 T^{6} \))(\( 1 - 12 T + 204 T^{2} - 1528 T^{3} + 16116 T^{4} - 74892 T^{5} + 493039 T^{6} \))(\( 1 - 16 T + 236 T^{2} - 2448 T^{3} + 24582 T^{4} - 193392 T^{5} + 1472876 T^{6} - 7888624 T^{7} + 38950081 T^{8} \))(\( 1 - 16 T + 236 T^{2} - 2448 T^{3} + 24582 T^{4} - 193392 T^{5} + 1472876 T^{6} - 7888624 T^{7} + 38950081 T^{8} \))(\( 1 + 8 T + 180 T^{2} + 904 T^{3} + 15990 T^{4} + 71416 T^{5} + 1123380 T^{6} + 3944312 T^{7} + 38950081 T^{8} \))(\( 1 + 8 T + 180 T^{2} + 904 T^{3} + 15990 T^{4} + 71416 T^{5} + 1123380 T^{6} + 3944312 T^{7} + 38950081 T^{8} \))(\( 1 - 538 T^{2} + 147807 T^{4} - 27647974 T^{6} + 3965128581 T^{8} - 467618207428 T^{10} + 47603630292250 T^{12} - 4323347326389920 T^{14} + 357043246909249546 T^{16} - 26982010663999490720 T^{18} + \)\(18\!\cdots\!50\)\( T^{20} - \)\(11\!\cdots\!88\)\( T^{22} + \)\(60\!\cdots\!41\)\( T^{24} - \)\(26\!\cdots\!74\)\( T^{26} + \)\(87\!\cdots\!87\)\( T^{28} - \)\(19\!\cdots\!78\)\( T^{30} + \)\(23\!\cdots\!21\)\( T^{32} \))(\( 1 - 538 T^{2} + 147807 T^{4} - 27647974 T^{6} + 3965128581 T^{8} - 467618207428 T^{10} + 47603630292250 T^{12} - 4323347326389920 T^{14} + 357043246909249546 T^{16} - 26982010663999490720 T^{18} + \)\(18\!\cdots\!50\)\( T^{20} - \)\(11\!\cdots\!88\)\( T^{22} + \)\(60\!\cdots\!41\)\( T^{24} - \)\(26\!\cdots\!74\)\( T^{26} + \)\(87\!\cdots\!87\)\( T^{28} - \)\(19\!\cdots\!78\)\( T^{30} + \)\(23\!\cdots\!21\)\( T^{32} \))
$83$ (\( 1 + T + 83 T^{2} \))(\( 1 - 2 T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 + 14 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 - T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 14 T + 83 T^{2} \))(\( 1 - 10 T + 79 T^{2} - 830 T^{3} + 6889 T^{4} \))(\( 1 - 12 T + 94 T^{2} - 996 T^{3} + 6889 T^{4} \))(\( 1 + 16 T + 180 T^{2} + 1328 T^{3} + 6889 T^{4} \))(\( 1 - 16 T + 180 T^{2} - 1328 T^{3} + 6889 T^{4} \))(\( 1 + 10 T + 79 T^{2} + 830 T^{3} + 6889 T^{4} \))(\( 1 + 2 T + 162 T^{2} + 166 T^{3} + 6889 T^{4} \))(\( 1 + 4 T + 120 T^{2} + 332 T^{3} + 6889 T^{4} \))(\( 1 - 4 T + 120 T^{2} - 332 T^{3} + 6889 T^{4} \))(\( 1 - 2 T + 162 T^{2} - 166 T^{3} + 6889 T^{4} \))(\( 1 - 18 T + 282 T^{2} - 2824 T^{3} + 23406 T^{4} - 124002 T^{5} + 571787 T^{6} \))(\( 1 - 6 T + 138 T^{2} - 1184 T^{3} + 11454 T^{4} - 41334 T^{5} + 571787 T^{6} \))(\( 1 + 18 T + 282 T^{2} + 2824 T^{3} + 23406 T^{4} + 124002 T^{5} + 571787 T^{6} \))(\( 1 + 6 T + 138 T^{2} + 1184 T^{3} + 11454 T^{4} + 41334 T^{5} + 571787 T^{6} \))(\( 1 + 280 T^{2} + 48 T^{3} + 32794 T^{4} + 3984 T^{5} + 1928920 T^{6} + 47458321 T^{8} \))(\( 1 + 280 T^{2} - 48 T^{3} + 32794 T^{4} - 3984 T^{5} + 1928920 T^{6} + 47458321 T^{8} \))(\( 1 + 4 T + 228 T^{2} + 860 T^{3} + 26058 T^{4} + 71380 T^{5} + 1570692 T^{6} + 2287148 T^{7} + 47458321 T^{8} \))(\( 1 - 4 T + 228 T^{2} - 860 T^{3} + 26058 T^{4} - 71380 T^{5} + 1570692 T^{6} - 2287148 T^{7} + 47458321 T^{8} \))(\( ( 1 - 4 T + 523 T^{2} - 1544 T^{3} + 123705 T^{4} - 263372 T^{5} + 17791866 T^{6} - 28394068 T^{7} + 1752220430 T^{8} - 2356707644 T^{9} + 122568164874 T^{10} - 150592685764 T^{11} + 5870831599305 T^{12} - 6081878752792 T^{13} + 170989815271987 T^{14} - 108544203958508 T^{15} + 2252292232139041 T^{16} )^{2} \))(\( ( 1 + 4 T + 523 T^{2} + 1544 T^{3} + 123705 T^{4} + 263372 T^{5} + 17791866 T^{6} + 28394068 T^{7} + 1752220430 T^{8} + 2356707644 T^{9} + 122568164874 T^{10} + 150592685764 T^{11} + 5870831599305 T^{12} + 6081878752792 T^{13} + 170989815271987 T^{14} + 108544203958508 T^{15} + 2252292232139041 T^{16} )^{2} \))
$89$ (\( 1 + 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 8 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 - 8 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 8 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 + 10 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 - 16 T + 214 T^{2} - 1424 T^{3} + 7921 T^{4} \))(\( 1 + 12 T + 166 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 - 8 T + 192 T^{2} - 712 T^{3} + 7921 T^{4} \))(\( 1 + 8 T + 192 T^{2} + 712 T^{3} + 7921 T^{4} \))(\( 1 + 16 T + 214 T^{2} + 1424 T^{3} + 7921 T^{4} \))(\( 1 + 4 T + 162 T^{2} + 356 T^{3} + 7921 T^{4} \))(\( 1 - 16 T + 224 T^{2} - 1424 T^{3} + 7921 T^{4} \))(\( 1 + 16 T + 224 T^{2} + 1424 T^{3} + 7921 T^{4} \))(\( 1 - 4 T + 162 T^{2} - 356 T^{3} + 7921 T^{4} \))(\( 1 + 12 T + 255 T^{2} + 2120 T^{3} + 22695 T^{4} + 95052 T^{5} + 704969 T^{6} \))(\( 1 - 36 T + 663 T^{2} - 7736 T^{3} + 59007 T^{4} - 285156 T^{5} + 704969 T^{6} \))(\( 1 - 12 T + 255 T^{2} - 2120 T^{3} + 22695 T^{4} - 95052 T^{5} + 704969 T^{6} \))(\( 1 + 36 T + 663 T^{2} + 7736 T^{3} + 59007 T^{4} + 285156 T^{5} + 704969 T^{6} \))(\( 1 + 16 T + 160 T^{2} + 1904 T^{3} + 24642 T^{4} + 169456 T^{5} + 1267360 T^{6} + 11279504 T^{7} + 62742241 T^{8} \))(\( 1 - 16 T + 160 T^{2} - 1904 T^{3} + 24642 T^{4} - 169456 T^{5} + 1267360 T^{6} - 11279504 T^{7} + 62742241 T^{8} \))(\( 1 + 24 T + 480 T^{2} + 6424 T^{3} + 69314 T^{4} + 571736 T^{5} + 3802080 T^{6} + 16919256 T^{7} + 62742241 T^{8} \))(\( 1 - 24 T + 480 T^{2} - 6424 T^{3} + 69314 T^{4} - 571736 T^{5} + 3802080 T^{6} - 16919256 T^{7} + 62742241 T^{8} \))(\( 1 - 640 T^{2} + 210552 T^{4} - 47499904 T^{6} + 8295415452 T^{8} - 1194559990144 T^{10} + 146915919459400 T^{12} - 15750756401654144 T^{14} + 1489545499043303110 T^{16} - \)\(12\!\cdots\!24\)\( T^{18} + \)\(92\!\cdots\!00\)\( T^{20} - \)\(59\!\cdots\!84\)\( T^{22} + \)\(32\!\cdots\!12\)\( T^{24} - \)\(14\!\cdots\!04\)\( T^{26} + \)\(52\!\cdots\!92\)\( T^{28} - \)\(12\!\cdots\!40\)\( T^{30} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( 1 - 640 T^{2} + 210552 T^{4} - 47499904 T^{6} + 8295415452 T^{8} - 1194559990144 T^{10} + 146915919459400 T^{12} - 15750756401654144 T^{14} + 1489545499043303110 T^{16} - \)\(12\!\cdots\!24\)\( T^{18} + \)\(92\!\cdots\!00\)\( T^{20} - \)\(59\!\cdots\!84\)\( T^{22} + \)\(32\!\cdots\!12\)\( T^{24} - \)\(14\!\cdots\!04\)\( T^{26} + \)\(52\!\cdots\!92\)\( T^{28} - \)\(12\!\cdots\!40\)\( T^{30} + \)\(15\!\cdots\!61\)\( T^{32} \))
$97$ (\( 1 + 9 T + 97 T^{2} \))(\( 1 - 6 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 - T + 97 T^{2} \))(\( 1 + 17 T + 97 T^{2} \))(\( 1 - 17 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 + T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 9 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 2 T + 83 T^{2} + 194 T^{3} + 9409 T^{4} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( 1 + 32 T^{2} + 9409 T^{4} \))(\( 1 + 32 T^{2} + 9409 T^{4} \))(\( 1 - 2 T + 83 T^{2} - 194 T^{3} + 9409 T^{4} \))(\( ( 1 + 97 T^{2} )^{2} \))(\( 1 + 96 T^{2} + 9409 T^{4} \))(\( 1 + 96 T^{2} + 9409 T^{4} \))(\( ( 1 + 97 T^{2} )^{2} \))(\( ( 1 - 7 T + 97 T^{2} )^{3} \))(\( 1 + 9 T + 210 T^{2} + 1753 T^{3} + 20370 T^{4} + 84681 T^{5} + 912673 T^{6} \))(\( ( 1 + 7 T + 97 T^{2} )^{3} \))(\( 1 - 9 T + 210 T^{2} - 1753 T^{3} + 20370 T^{4} - 84681 T^{5} + 912673 T^{6} \))(\( 1 - 16 T + 352 T^{2} - 3984 T^{3} + 51458 T^{4} - 386448 T^{5} + 3311968 T^{6} - 14602768 T^{7} + 88529281 T^{8} \))(\( 1 + 16 T + 352 T^{2} + 3984 T^{3} + 51458 T^{4} + 386448 T^{5} + 3311968 T^{6} + 14602768 T^{7} + 88529281 T^{8} \))(\( 1 + 128 T^{2} - 1280 T^{3} + 4866 T^{4} - 124160 T^{5} + 1204352 T^{6} + 88529281 T^{8} \))(\( 1 + 128 T^{2} + 1280 T^{3} + 4866 T^{4} + 124160 T^{5} + 1204352 T^{6} + 88529281 T^{8} \))(\( 1 - 608 T^{2} + 187588 T^{4} - 40328000 T^{6} + 6818823050 T^{8} - 967972100768 T^{10} + 120672937256208 T^{12} - 13517338511335328 T^{14} + 1373778662576096019 T^{16} - \)\(12\!\cdots\!52\)\( T^{18} + \)\(10\!\cdots\!48\)\( T^{20} - \)\(80\!\cdots\!72\)\( T^{22} + \)\(53\!\cdots\!50\)\( T^{24} - \)\(29\!\cdots\!00\)\( T^{26} + \)\(13\!\cdots\!08\)\( T^{28} - \)\(39\!\cdots\!52\)\( T^{30} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( 1 - 608 T^{2} + 187588 T^{4} - 40328000 T^{6} + 6818823050 T^{8} - 967972100768 T^{10} + 120672937256208 T^{12} - 13517338511335328 T^{14} + 1373778662576096019 T^{16} - \)\(12\!\cdots\!52\)\( T^{18} + \)\(10\!\cdots\!48\)\( T^{20} - \)\(80\!\cdots\!72\)\( T^{22} + \)\(53\!\cdots\!50\)\( T^{24} - \)\(29\!\cdots\!00\)\( T^{26} + \)\(13\!\cdots\!08\)\( T^{28} - \)\(39\!\cdots\!52\)\( T^{30} + \)\(61\!\cdots\!21\)\( T^{32} \))
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