Properties

Label 3630.2
Level 3630
Weight 2
Dimension 78548
Nonzero newspaces 24
Sturm bound 1393920
Trace bound 4

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Defining parameters

Level: \( N \) = \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(1393920\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3630))\).

Total New Old
Modular forms 353600 78548 275052
Cusp forms 343361 78548 264813
Eisenstein series 10239 0 10239

Trace form

\( 78548q - 2q^{3} - 4q^{5} - 22q^{6} - 80q^{7} - 80q^{9} + O(q^{10}) \) \( 78548q - 2q^{3} - 4q^{5} - 22q^{6} - 80q^{7} - 80q^{9} - 36q^{10} - 40q^{11} - 34q^{12} - 64q^{13} - 64q^{14} - 50q^{15} - 136q^{17} - 12q^{18} - 104q^{19} + 4q^{20} - 72q^{21} - 56q^{23} + 18q^{24} - 88q^{25} + 118q^{27} - 56q^{29} + 46q^{30} - 64q^{31} + 90q^{33} + 16q^{34} - 24q^{35} + 20q^{36} + 64q^{37} + 24q^{38} + 68q^{39} + 12q^{40} - 40q^{41} + 136q^{42} + 144q^{43} + 40q^{44} - 4q^{45} + 208q^{46} + 208q^{47} + 6q^{48} + 392q^{49} + 248q^{50} + 112q^{51} + 176q^{52} + 288q^{53} + 38q^{54} + 220q^{55} + 8q^{56} + 300q^{57} + 336q^{58} + 280q^{59} + 114q^{60} + 272q^{61} + 104q^{62} + 120q^{63} + 240q^{65} - 40q^{66} + 128q^{67} + 24q^{68} + 56q^{69} - 224q^{71} - 88q^{72} - 264q^{73} - 120q^{74} - 118q^{75} - 48q^{76} - 160q^{77} - 148q^{78} - 152q^{79} - 44q^{80} - 128q^{81} - 8q^{82} - 144q^{83} + 8q^{84} - 96q^{85} - 184q^{86} + 44q^{87} - 40q^{88} - 112q^{89} + 32q^{90} + 448q^{91} + 24q^{92} + 168q^{93} + 192q^{94} + 224q^{95} + 6q^{96} + 472q^{97} + 48q^{98} + 260q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3630))\)

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
3630.2.a \(\chi_{3630}(1, \cdot)\) 3630.2.a.a 1 1
3630.2.a.b 1
3630.2.a.c 1
3630.2.a.d 1
3630.2.a.e 1
3630.2.a.f 1
3630.2.a.g 1
3630.2.a.h 1
3630.2.a.i 1
3630.2.a.j 1
3630.2.a.k 1
3630.2.a.l 1
3630.2.a.m 1
3630.2.a.n 1
3630.2.a.o 1
3630.2.a.p 1
3630.2.a.q 1
3630.2.a.r 1
3630.2.a.s 1
3630.2.a.t 1
3630.2.a.u 1
3630.2.a.v 1
3630.2.a.w 1
3630.2.a.x 1
3630.2.a.y 1
3630.2.a.z 1
3630.2.a.ba 2
3630.2.a.bb 2
3630.2.a.bc 2
3630.2.a.bd 2
3630.2.a.be 2
3630.2.a.bf 2
3630.2.a.bg 2
3630.2.a.bh 2
3630.2.a.bi 2
3630.2.a.bj 2
3630.2.a.bk 2
3630.2.a.bl 2
3630.2.a.bm 2
3630.2.a.bn 2
3630.2.a.bo 2
3630.2.a.bp 2
3630.2.a.bq 4
3630.2.a.br 4
3630.2.a.bs 4
3630.2.a.bt 4
3630.2.c \(\chi_{3630}(2179, \cdot)\) n/a 110 1
3630.2.d \(\chi_{3630}(1451, \cdot)\) n/a 144 1
3630.2.f \(\chi_{3630}(3629, \cdot)\) n/a 216 1
3630.2.j \(\chi_{3630}(1937, \cdot)\) n/a 436 2
3630.2.l \(\chi_{3630}(967, \cdot)\) n/a 216 2
3630.2.m \(\chi_{3630}(511, \cdot)\) n/a 288 4
3630.2.p \(\chi_{3630}(239, \cdot)\) n/a 864 4
3630.2.r \(\chi_{3630}(161, \cdot)\) n/a 576 4
3630.2.s \(\chi_{3630}(1219, \cdot)\) n/a 432 4
3630.2.u \(\chi_{3630}(331, \cdot)\) n/a 880 10
3630.2.v \(\chi_{3630}(403, \cdot)\) n/a 864 8
3630.2.x \(\chi_{3630}(323, \cdot)\) n/a 1728 8
3630.2.bb \(\chi_{3630}(329, \cdot)\) n/a 2640 10
3630.2.bd \(\chi_{3630}(131, \cdot)\) n/a 1760 10
3630.2.be \(\chi_{3630}(199, \cdot)\) n/a 1320 10
3630.2.bg \(\chi_{3630}(43, \cdot)\) n/a 2640 20
3630.2.bi \(\chi_{3630}(23, \cdot)\) n/a 5280 20
3630.2.bk \(\chi_{3630}(31, \cdot)\) n/a 3520 40
3630.2.bm \(\chi_{3630}(49, \cdot)\) n/a 5280 40
3630.2.bn \(\chi_{3630}(41, \cdot)\) n/a 7040 40
3630.2.bp \(\chi_{3630}(29, \cdot)\) n/a 10560 40
3630.2.bt \(\chi_{3630}(47, \cdot)\) n/a 21120 80
3630.2.bv \(\chi_{3630}(7, \cdot)\) n/a 10560 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3630))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3630)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(726))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1815))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))
$3$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))
$5$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))
$7$ (\( 1 + 4 T + 7 T^{2} \))(\( 1 + 3 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 + 3 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 - 3 T + 7 T^{2} \))(\( 1 - 5 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - 3 T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - 3 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 + 5 T + 7 T^{2} \))(\( 1 + 3 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 11 T^{2} + 49 T^{4} \))(\( 1 - 2 T + 10 T^{2} - 14 T^{3} + 49 T^{4} \))(\( 1 - 5 T + 19 T^{2} - 35 T^{3} + 49 T^{4} \))(\( 1 + 11 T^{2} + 49 T^{4} \))(\( 1 - 2 T + 10 T^{2} - 14 T^{3} + 49 T^{4} \))(\( 1 - 5 T + 19 T^{2} - 35 T^{3} + 49 T^{4} \))(\( 1 - 4 T + 15 T^{2} - 28 T^{3} + 49 T^{4} \))(\( 1 + 4 T + 15 T^{2} + 28 T^{3} + 49 T^{4} \))(\( 1 + 5 T + 19 T^{2} + 35 T^{3} + 49 T^{4} \))(\( 1 + 2 T + 10 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 + 11 T^{2} + 49 T^{4} \))(\( 1 + 5 T + 19 T^{2} + 35 T^{3} + 49 T^{4} \))(\( 1 + 2 T + 10 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 + 11 T^{2} + 49 T^{4} \))(\( 1 + 4 T + 15 T^{2} + 28 T^{3} + 49 T^{4} \))(\( 1 - 4 T + 15 T^{2} - 28 T^{3} + 49 T^{4} \))(\( 1 + T - T^{2} - 13 T^{3} + 4 T^{4} - 91 T^{5} - 49 T^{6} + 343 T^{7} + 2401 T^{8} \))(\( 1 + T + 7 T^{2} + 11 T^{3} + 100 T^{4} + 77 T^{5} + 343 T^{6} + 343 T^{7} + 2401 T^{8} \))(\( 1 - T - T^{2} + 13 T^{3} + 4 T^{4} + 91 T^{5} - 49 T^{6} - 343 T^{7} + 2401 T^{8} \))(\( 1 - T + 7 T^{2} - 11 T^{3} + 100 T^{4} - 77 T^{5} + 343 T^{6} - 343 T^{7} + 2401 T^{8} \))
$11$ 1
$13$ (\( 1 + 2 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 - 7 T + 13 T^{2} \))(\( 1 + 3 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 7 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 - 3 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( ( 1 - 3 T + 13 T^{2} )^{2} \))(\( 1 + 9 T + 45 T^{2} + 117 T^{3} + 169 T^{4} \))(\( 1 + T + 25 T^{2} + 13 T^{3} + 169 T^{4} \))(\( 1 - 6 T + 23 T^{2} - 78 T^{3} + 169 T^{4} \))(\( 1 - T + 25 T^{2} - 13 T^{3} + 169 T^{4} \))(\( 1 - 3 T + 17 T^{2} - 39 T^{3} + 169 T^{4} \))(\( 1 - 2 T + 15 T^{2} - 26 T^{3} + 169 T^{4} \))(\( ( 1 + 3 T + 13 T^{2} )^{2} \))(\( 1 - T + 25 T^{2} - 13 T^{3} + 169 T^{4} \))(\( 1 - 9 T + 45 T^{2} - 117 T^{3} + 169 T^{4} \))(\( ( 1 + 3 T + 13 T^{2} )^{2} \))(\( 1 + 3 T + 17 T^{2} + 39 T^{3} + 169 T^{4} \))(\( 1 + T + 25 T^{2} + 13 T^{3} + 169 T^{4} \))(\( 1 + 6 T + 23 T^{2} + 78 T^{3} + 169 T^{4} \))(\( 1 + 2 T + 15 T^{2} + 26 T^{3} + 169 T^{4} \))(\( ( 1 - 3 T + 13 T^{2} )^{2} \))(\( 1 + 2 T + 11 T^{2} + 36 T^{3} + 69 T^{4} + 468 T^{5} + 1859 T^{6} + 4394 T^{7} + 28561 T^{8} \))(\( 1 + 4 T + 25 T^{2} + 44 T^{3} + 301 T^{4} + 572 T^{5} + 4225 T^{6} + 8788 T^{7} + 28561 T^{8} \))(\( 1 - 2 T + 11 T^{2} - 36 T^{3} + 69 T^{4} - 468 T^{5} + 1859 T^{6} - 4394 T^{7} + 28561 T^{8} \))(\( 1 - 4 T + 25 T^{2} - 44 T^{3} + 301 T^{4} - 572 T^{5} + 4225 T^{6} - 8788 T^{7} + 28561 T^{8} \))
$17$ (\( 1 + 2 T + 17 T^{2} \))(\( 1 - 7 T + 17 T^{2} \))(\( 1 - T + 17 T^{2} \))(\( 1 - T + 17 T^{2} \))(\( 1 + 5 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 7 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + T + 17 T^{2} \))(\( 1 + 7 T + 17 T^{2} \))(\( 1 - 5 T + 17 T^{2} \))(\( 1 + T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 3 T + 17 T^{2} \))(\( 1 + 7 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 31 T^{2} + 289 T^{4} \))(\( 1 - T + 3 T^{2} - 17 T^{3} + 289 T^{4} \))(\( 1 + 4 T + 18 T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 - 12 T + 67 T^{2} - 204 T^{3} + 289 T^{4} \))(\( 1 - T + 23 T^{2} - 17 T^{3} + 289 T^{4} \))(\( 1 + 4 T + 18 T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 + 31 T^{2} + 289 T^{4} \))(\( 1 + 4 T + 35 T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 - 4 T + 18 T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 + T + 3 T^{2} + 17 T^{3} + 289 T^{4} \))(\( 1 + 31 T^{2} + 289 T^{4} \))(\( 1 - 4 T + 18 T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 + T + 23 T^{2} + 17 T^{3} + 289 T^{4} \))(\( 1 + 12 T + 67 T^{2} + 204 T^{3} + 289 T^{4} \))(\( 1 + 31 T^{2} + 289 T^{4} \))(\( 1 - 4 T + 35 T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 + 11 T + 89 T^{2} + 517 T^{3} + 2464 T^{4} + 8789 T^{5} + 25721 T^{6} + 54043 T^{7} + 83521 T^{8} \))(\( 1 - 5 T + 45 T^{2} - 155 T^{3} + 968 T^{4} - 2635 T^{5} + 13005 T^{6} - 24565 T^{7} + 83521 T^{8} \))(\( 1 - 11 T + 89 T^{2} - 517 T^{3} + 2464 T^{4} - 8789 T^{5} + 25721 T^{6} - 54043 T^{7} + 83521 T^{8} \))(\( 1 + 5 T + 45 T^{2} + 155 T^{3} + 968 T^{4} + 2635 T^{5} + 13005 T^{6} + 24565 T^{7} + 83521 T^{8} \))
$19$ (\( 1 + 4 T + 19 T^{2} \))(\( 1 - 5 T + 19 T^{2} \))(\( 1 + 7 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 7 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 - 7 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 + T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 - 5 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 + 7 T + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( ( 1 + 3 T + 19 T^{2} )^{2} \))(\( 1 - 2 T + 34 T^{2} - 38 T^{3} + 361 T^{4} \))(\( 1 - T + 37 T^{2} - 19 T^{3} + 361 T^{4} \))(\( 1 - 6 T + 35 T^{2} - 114 T^{3} + 361 T^{4} \))(\( 1 + 6 T + 42 T^{2} + 114 T^{3} + 361 T^{4} \))(\( 1 - 3 T + 29 T^{2} - 57 T^{3} + 361 T^{4} \))(\( ( 1 - 7 T + 19 T^{2} )^{2} \))(\( 1 - 2 T + 27 T^{2} - 38 T^{3} + 361 T^{4} \))(\( 1 + T + 37 T^{2} + 19 T^{3} + 361 T^{4} \))(\( 1 + 2 T + 34 T^{2} + 38 T^{3} + 361 T^{4} \))(\( ( 1 - 3 T + 19 T^{2} )^{2} \))(\( 1 + 3 T + 29 T^{2} + 57 T^{3} + 361 T^{4} \))(\( 1 - 6 T + 42 T^{2} - 114 T^{3} + 361 T^{4} \))(\( 1 + 6 T + 35 T^{2} + 114 T^{3} + 361 T^{4} \))(\( ( 1 + 7 T + 19 T^{2} )^{2} \))(\( 1 + 2 T + 27 T^{2} + 38 T^{3} + 361 T^{4} \))(\( 1 + T + 37 T^{2} + 3 T^{3} + 680 T^{4} + 57 T^{5} + 13357 T^{6} + 6859 T^{7} + 130321 T^{8} \))(\( 1 + 7 T + 57 T^{2} + 209 T^{3} + 1224 T^{4} + 3971 T^{5} + 20577 T^{6} + 48013 T^{7} + 130321 T^{8} \))(\( 1 - T + 37 T^{2} - 3 T^{3} + 680 T^{4} - 57 T^{5} + 13357 T^{6} - 6859 T^{7} + 130321 T^{8} \))(\( 1 - 7 T + 57 T^{2} - 209 T^{3} + 1224 T^{4} - 3971 T^{5} + 20577 T^{6} - 48013 T^{7} + 130321 T^{8} \))
$23$ (\( 1 + 4 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 6 T + 28 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 - 7 T + 47 T^{2} - 161 T^{3} + 529 T^{4} \))(\( 1 - 3 T + 37 T^{2} - 69 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 28 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 5 T + 51 T^{2} - 115 T^{3} + 529 T^{4} \))(\( 1 + 15 T + 101 T^{2} + 345 T^{3} + 529 T^{4} \))(\( 1 + 10 T + 68 T^{2} + 230 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 52 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 - 3 T + 37 T^{2} - 69 T^{3} + 529 T^{4} \))(\( 1 - 7 T + 47 T^{2} - 161 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 28 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 + 15 T + 101 T^{2} + 345 T^{3} + 529 T^{4} \))(\( 1 - 5 T + 51 T^{2} - 115 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 28 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 + 10 T + 68 T^{2} + 230 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 52 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 + 27 T^{2} + 130 T^{3} + 239 T^{4} + 2990 T^{5} + 14283 T^{6} + 279841 T^{8} \))(\( 1 - 8 T + 63 T^{2} - 222 T^{3} + 1235 T^{4} - 5106 T^{5} + 33327 T^{6} - 97336 T^{7} + 279841 T^{8} \))(\( 1 + 27 T^{2} + 130 T^{3} + 239 T^{4} + 2990 T^{5} + 14283 T^{6} + 279841 T^{8} \))(\( 1 - 8 T + 63 T^{2} - 222 T^{3} + 1235 T^{4} - 5106 T^{5} + 33327 T^{6} - 97336 T^{7} + 279841 T^{8} \))
$29$ (\( 1 + 6 T + 29 T^{2} \))(\( 1 - 5 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 + T + 29 T^{2} \))(\( 1 - 10 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 7 T + 29 T^{2} \))(\( 1 - 9 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 - T + 29 T^{2} \))(\( 1 - 5 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 9 T + 29 T^{2} \))(\( 1 - 7 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 55 T^{2} + 174 T^{3} + 841 T^{4} \))(\( 1 - 3 T + 59 T^{2} - 87 T^{3} + 841 T^{4} \))(\( 1 + 6 T + 22 T^{2} + 174 T^{3} + 841 T^{4} \))(\( 1 - 6 T + 55 T^{2} - 174 T^{3} + 841 T^{4} \))(\( 1 + T + 27 T^{2} + 29 T^{3} + 841 T^{4} \))(\( 1 + 10 T + 78 T^{2} + 290 T^{3} + 841 T^{4} \))(\( ( 1 - 5 T + 29 T^{2} )^{2} \))(\( ( 1 - 3 T + 29 T^{2} )^{2} \))(\( 1 - 6 T + 22 T^{2} - 174 T^{3} + 841 T^{4} \))(\( 1 + 3 T + 59 T^{2} + 87 T^{3} + 841 T^{4} \))(\( 1 - 6 T + 55 T^{2} - 174 T^{3} + 841 T^{4} \))(\( 1 - 10 T + 78 T^{2} - 290 T^{3} + 841 T^{4} \))(\( 1 - T + 27 T^{2} - 29 T^{3} + 841 T^{4} \))(\( 1 + 6 T + 55 T^{2} + 174 T^{3} + 841 T^{4} \))(\( ( 1 + 5 T + 29 T^{2} )^{2} \))(\( ( 1 + 3 T + 29 T^{2} )^{2} \))(\( 1 + 9 T + 67 T^{2} + 297 T^{3} + 1480 T^{4} + 8613 T^{5} + 56347 T^{6} + 219501 T^{7} + 707281 T^{8} \))(\( 1 + T + 95 T^{2} + 77 T^{3} + 3928 T^{4} + 2233 T^{5} + 79895 T^{6} + 24389 T^{7} + 707281 T^{8} \))(\( 1 - 9 T + 67 T^{2} - 297 T^{3} + 1480 T^{4} - 8613 T^{5} + 56347 T^{6} - 219501 T^{7} + 707281 T^{8} \))(\( 1 - T + 95 T^{2} - 77 T^{3} + 3928 T^{4} - 2233 T^{5} + 79895 T^{6} - 24389 T^{7} + 707281 T^{8} \))
$31$ (\( 1 + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 2 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 2 T + 36 T^{2} - 62 T^{3} + 961 T^{4} \))(\( 1 + 5 T + 67 T^{2} + 155 T^{3} + 961 T^{4} \))(\( 1 + 14 T + 106 T^{2} + 434 T^{3} + 961 T^{4} \))(\( 1 + 10 T + 60 T^{2} + 310 T^{3} + 961 T^{4} \))(\( 1 + T + 51 T^{2} + 31 T^{3} + 961 T^{4} \))(\( 1 + 10 T + 82 T^{2} + 310 T^{3} + 961 T^{4} \))(\( 1 - 2 T + 36 T^{2} - 62 T^{3} + 961 T^{4} \))(\( 1 - 6 T + 44 T^{2} - 186 T^{3} + 961 T^{4} \))(\( 1 + 14 T + 106 T^{2} + 434 T^{3} + 961 T^{4} \))(\( 1 + 5 T + 67 T^{2} + 155 T^{3} + 961 T^{4} \))(\( 1 - 2 T + 36 T^{2} - 62 T^{3} + 961 T^{4} \))(\( 1 + 10 T + 82 T^{2} + 310 T^{3} + 961 T^{4} \))(\( 1 + T + 51 T^{2} + 31 T^{3} + 961 T^{4} \))(\( 1 + 10 T + 60 T^{2} + 310 T^{3} + 961 T^{4} \))(\( 1 - 2 T + 36 T^{2} - 62 T^{3} + 961 T^{4} \))(\( 1 - 6 T + 44 T^{2} - 186 T^{3} + 961 T^{4} \))(\( 1 - 17 T + 203 T^{2} - 1619 T^{3} + 10500 T^{4} - 50189 T^{5} + 195083 T^{6} - 506447 T^{7} + 923521 T^{8} \))(\( 1 - 9 T + 103 T^{2} - 647 T^{3} + 4244 T^{4} - 20057 T^{5} + 98983 T^{6} - 268119 T^{7} + 923521 T^{8} \))(\( 1 - 17 T + 203 T^{2} - 1619 T^{3} + 10500 T^{4} - 50189 T^{5} + 195083 T^{6} - 506447 T^{7} + 923521 T^{8} \))(\( 1 - 9 T + 103 T^{2} - 647 T^{3} + 4244 T^{4} - 20057 T^{5} + 98983 T^{6} - 268119 T^{7} + 923521 T^{8} \))
$37$ (\( 1 + 10 T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 - 3 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 - 5 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 5 T + 37 T^{2} \))(\( 1 - 5 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 - 3 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 - 5 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 5 T + 37 T^{2} \))(\( 1 + 5 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 8 T + 63 T^{2} - 296 T^{3} + 1369 T^{4} \))(\( 1 + 15 T + 129 T^{2} + 555 T^{3} + 1369 T^{4} \))(\( 1 - T + 73 T^{2} - 37 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 51 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 - 5 T + 69 T^{2} - 185 T^{3} + 1369 T^{4} \))(\( 1 + 13 T + 105 T^{2} + 481 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 51 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 71 T^{2} + 1369 T^{4} \))(\( 1 - T + 73 T^{2} - 37 T^{3} + 1369 T^{4} \))(\( 1 + 15 T + 129 T^{2} + 555 T^{3} + 1369 T^{4} \))(\( 1 - 8 T + 63 T^{2} - 296 T^{3} + 1369 T^{4} \))(\( 1 + 13 T + 105 T^{2} + 481 T^{3} + 1369 T^{4} \))(\( 1 - 5 T + 69 T^{2} - 185 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 51 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T + 51 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 71 T^{2} + 1369 T^{4} \))(\( 1 - 8 T + 77 T^{2} - 540 T^{3} + 4701 T^{4} - 19980 T^{5} + 105413 T^{6} - 405224 T^{7} + 1874161 T^{8} \))(\( ( 1 - 11 T + 93 T^{2} - 407 T^{3} + 1369 T^{4} )^{2} \))(\( 1 - 8 T + 77 T^{2} - 540 T^{3} + 4701 T^{4} - 19980 T^{5} + 105413 T^{6} - 405224 T^{7} + 1874161 T^{8} \))(\( ( 1 - 11 T + 93 T^{2} - 407 T^{3} + 1369 T^{4} )^{2} \))
$41$ (\( 1 - 6 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 12 T + 41 T^{2} \))(\( 1 - 4 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 4 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 18 T + 160 T^{2} + 738 T^{3} + 1681 T^{4} \))(\( 1 - 2 T + 78 T^{2} - 82 T^{3} + 1681 T^{4} \))(\( 1 + 3 T + 23 T^{2} + 123 T^{3} + 1681 T^{4} \))(\( 1 - 6 T + 16 T^{2} - 246 T^{3} + 1681 T^{4} \))(\( 1 - 10 T + 62 T^{2} - 410 T^{3} + 1681 T^{4} \))(\( 1 + 9 T + 71 T^{2} + 369 T^{3} + 1681 T^{4} \))(\( 1 - 2 T + 56 T^{2} - 82 T^{3} + 1681 T^{4} \))(\( 1 + 6 T + 88 T^{2} + 246 T^{3} + 1681 T^{4} \))(\( 1 - 3 T + 23 T^{2} - 123 T^{3} + 1681 T^{4} \))(\( 1 + 2 T + 78 T^{2} + 82 T^{3} + 1681 T^{4} \))(\( 1 - 18 T + 160 T^{2} - 738 T^{3} + 1681 T^{4} \))(\( 1 - 9 T + 71 T^{2} - 369 T^{3} + 1681 T^{4} \))(\( 1 + 10 T + 62 T^{2} + 410 T^{3} + 1681 T^{4} \))(\( 1 + 6 T + 16 T^{2} + 246 T^{3} + 1681 T^{4} \))(\( 1 + 2 T + 56 T^{2} + 82 T^{3} + 1681 T^{4} \))(\( 1 - 6 T + 88 T^{2} - 246 T^{3} + 1681 T^{4} \))(\( 1 - 11 T + 35 T^{2} + 201 T^{3} - 2296 T^{4} + 8241 T^{5} + 58835 T^{6} - 758131 T^{7} + 2825761 T^{8} \))(\( 1 + 3 T + 63 T^{2} + 211 T^{3} + 4400 T^{4} + 8651 T^{5} + 105903 T^{6} + 206763 T^{7} + 2825761 T^{8} \))(\( 1 + 11 T + 35 T^{2} - 201 T^{3} - 2296 T^{4} - 8241 T^{5} + 58835 T^{6} + 758131 T^{7} + 2825761 T^{8} \))(\( 1 - 3 T + 63 T^{2} - 211 T^{3} + 4400 T^{4} - 8651 T^{5} + 105903 T^{6} - 206763 T^{7} + 2825761 T^{8} \))
$43$ (\( 1 - 12 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 + 12 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 - 12 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 12 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 6 T + 68 T^{2} - 258 T^{3} + 1849 T^{4} \))(\( 1 + 11 T + 85 T^{2} + 473 T^{3} + 1849 T^{4} \))(\( 1 - 6 T + 90 T^{2} - 258 T^{3} + 1849 T^{4} \))(\( 1 - 6 T + 92 T^{2} - 258 T^{3} + 1849 T^{4} \))(\( 1 + 5 T + 81 T^{2} + 215 T^{3} + 1849 T^{4} \))(\( 1 - 2 T + 82 T^{2} - 86 T^{3} + 1849 T^{4} \))(\( 1 - 6 T + 68 T^{2} - 258 T^{3} + 1849 T^{4} \))(\( 1 + 10 T + 108 T^{2} + 430 T^{3} + 1849 T^{4} \))(\( 1 + 6 T + 90 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 - 11 T + 85 T^{2} - 473 T^{3} + 1849 T^{4} \))(\( 1 + 6 T + 68 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 + 2 T + 82 T^{2} + 86 T^{3} + 1849 T^{4} \))(\( 1 - 5 T + 81 T^{2} - 215 T^{3} + 1849 T^{4} \))(\( 1 + 6 T + 92 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 + 6 T + 68 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 - 10 T + 108 T^{2} - 430 T^{3} + 1849 T^{4} \))(\( 1 + T + 133 T^{2} + 75 T^{3} + 7736 T^{4} + 3225 T^{5} + 245917 T^{6} + 79507 T^{7} + 3418801 T^{8} \))(\( 1 - T + 65 T^{2} - 371 T^{3} + 2296 T^{4} - 15953 T^{5} + 120185 T^{6} - 79507 T^{7} + 3418801 T^{8} \))(\( 1 - T + 133 T^{2} - 75 T^{3} + 7736 T^{4} - 3225 T^{5} + 245917 T^{6} - 79507 T^{7} + 3418801 T^{8} \))(\( 1 + T + 65 T^{2} + 371 T^{3} + 2296 T^{4} + 15953 T^{5} + 120185 T^{6} + 79507 T^{7} + 3418801 T^{8} \))
$47$ (\( 1 + 4 T + 47 T^{2} \))(\( 1 + 10 T + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 10 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 + 10 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 10 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( ( 1 - 6 T + 47 T^{2} )^{2} \))(\( 1 - 7 T + 45 T^{2} - 329 T^{3} + 2209 T^{4} \))(\( 1 + 3 T + 95 T^{2} + 141 T^{3} + 2209 T^{4} \))(\( ( 1 + 6 T + 47 T^{2} )^{2} \))(\( 1 - 25 T + 249 T^{2} - 1175 T^{3} + 2209 T^{4} \))(\( 1 + T - 57 T^{2} + 47 T^{3} + 2209 T^{4} \))(\( 1 + 4 T + 50 T^{2} + 188 T^{3} + 2209 T^{4} \))(\( 1 - 4 T + 50 T^{2} - 188 T^{3} + 2209 T^{4} \))(\( 1 + 3 T + 95 T^{2} + 141 T^{3} + 2209 T^{4} \))(\( 1 - 7 T + 45 T^{2} - 329 T^{3} + 2209 T^{4} \))(\( ( 1 - 6 T + 47 T^{2} )^{2} \))(\( 1 + T - 57 T^{2} + 47 T^{3} + 2209 T^{4} \))(\( 1 - 25 T + 249 T^{2} - 1175 T^{3} + 2209 T^{4} \))(\( ( 1 + 6 T + 47 T^{2} )^{2} \))(\( 1 + 4 T + 50 T^{2} + 188 T^{3} + 2209 T^{4} \))(\( 1 - 4 T + 50 T^{2} - 188 T^{3} + 2209 T^{4} \))(\( 1 - 10 T + 173 T^{2} - 1050 T^{3} + 11099 T^{4} - 49350 T^{5} + 382157 T^{6} - 1038230 T^{7} + 4879681 T^{8} \))(\( 1 - 2 T + 37 T^{2} - 130 T^{3} + 1711 T^{4} - 6110 T^{5} + 81733 T^{6} - 207646 T^{7} + 4879681 T^{8} \))(\( 1 - 10 T + 173 T^{2} - 1050 T^{3} + 11099 T^{4} - 49350 T^{5} + 382157 T^{6} - 1038230 T^{7} + 4879681 T^{8} \))(\( 1 - 2 T + 37 T^{2} - 130 T^{3} + 1711 T^{4} - 6110 T^{5} + 81733 T^{6} - 207646 T^{7} + 4879681 T^{8} \))
$53$ (\( 1 + 6 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 8 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 - 8 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 - 14 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 6 T + 88 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 - 8 T + 102 T^{2} - 424 T^{3} + 2809 T^{4} \))(\( 1 + T + 75 T^{2} + 53 T^{3} + 2809 T^{4} \))(\( 1 - 6 T + 88 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 - 8 T + 102 T^{2} - 424 T^{3} + 2809 T^{4} \))(\( 1 + 15 T + 131 T^{2} + 795 T^{3} + 2809 T^{4} \))(\( 1 + 2 T + 104 T^{2} + 106 T^{3} + 2809 T^{4} \))(\( 1 + 14 T + 152 T^{2} + 742 T^{3} + 2809 T^{4} \))(\( 1 + T + 75 T^{2} + 53 T^{3} + 2809 T^{4} \))(\( 1 - 8 T + 102 T^{2} - 424 T^{3} + 2809 T^{4} \))(\( 1 + 6 T + 88 T^{2} + 318 T^{3} + 2809 T^{4} \))(\( 1 + 15 T + 131 T^{2} + 795 T^{3} + 2809 T^{4} \))(\( 1 - 8 T + 102 T^{2} - 424 T^{3} + 2809 T^{4} \))(\( 1 - 6 T + 88 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 + 2 T + 104 T^{2} + 106 T^{3} + 2809 T^{4} \))(\( 1 + 14 T + 152 T^{2} + 742 T^{3} + 2809 T^{4} \))(\( 1 - 11 T + 213 T^{2} - 1685 T^{3} + 16916 T^{4} - 89305 T^{5} + 598317 T^{6} - 1637647 T^{7} + 7890481 T^{8} \))(\( 1 - 5 T + 125 T^{2} - 555 T^{3} + 8228 T^{4} - 29415 T^{5} + 351125 T^{6} - 744385 T^{7} + 7890481 T^{8} \))(\( 1 - 11 T + 213 T^{2} - 1685 T^{3} + 16916 T^{4} - 89305 T^{5} + 598317 T^{6} - 1637647 T^{7} + 7890481 T^{8} \))(\( 1 - 5 T + 125 T^{2} - 555 T^{3} + 8228 T^{4} - 29415 T^{5} + 351125 T^{6} - 744385 T^{7} + 7890481 T^{8} \))
$59$ (\( 1 + 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 14 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 - 18 T + 172 T^{2} - 1062 T^{3} + 3481 T^{4} \))(\( 1 - 17 T + 159 T^{2} - 1003 T^{3} + 3481 T^{4} \))(\( 1 + 27 T + 299 T^{2} + 1593 T^{3} + 3481 T^{4} \))(\( 1 + 6 T + 100 T^{2} + 354 T^{3} + 3481 T^{4} \))(\( 1 - 7 T + 119 T^{2} - 413 T^{3} + 3481 T^{4} \))(\( 1 + 3 T + 59 T^{2} + 177 T^{3} + 3481 T^{4} \))(\( 1 + 6 T + 52 T^{2} + 354 T^{3} + 3481 T^{4} \))(\( 1 - 2 T + 92 T^{2} - 118 T^{3} + 3481 T^{4} \))(\( 1 + 27 T + 299 T^{2} + 1593 T^{3} + 3481 T^{4} \))(\( 1 - 17 T + 159 T^{2} - 1003 T^{3} + 3481 T^{4} \))(\( 1 - 18 T + 172 T^{2} - 1062 T^{3} + 3481 T^{4} \))(\( 1 + 3 T + 59 T^{2} + 177 T^{3} + 3481 T^{4} \))(\( 1 - 7 T + 119 T^{2} - 413 T^{3} + 3481 T^{4} \))(\( 1 + 6 T + 100 T^{2} + 354 T^{3} + 3481 T^{4} \))(\( 1 + 6 T + 52 T^{2} + 354 T^{3} + 3481 T^{4} \))(\( 1 - 2 T + 92 T^{2} - 118 T^{3} + 3481 T^{4} \))(\( ( 1 - 5 T + 63 T^{2} - 295 T^{3} + 3481 T^{4} )^{2} \))(\( 1 - 16 T + 205 T^{2} - 2072 T^{3} + 17173 T^{4} - 122248 T^{5} + 713605 T^{6} - 3286064 T^{7} + 12117361 T^{8} \))(\( ( 1 - 5 T + 63 T^{2} - 295 T^{3} + 3481 T^{4} )^{2} \))(\( 1 - 16 T + 205 T^{2} - 2072 T^{3} + 17173 T^{4} - 122248 T^{5} + 713605 T^{6} - 3286064 T^{7} + 12117361 T^{8} \))
$61$ (\( 1 + 10 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 12 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 12 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 + 12 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 - 12 T + 61 T^{2} \))(\( 1 + 61 T^{2} \))(\( 1 + 6 T + 56 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( ( 1 + 61 T^{2} )^{2} \))(\( 1 - 18 T + 198 T^{2} - 1098 T^{3} + 3721 T^{4} \))(\( 1 - 6 T + 128 T^{2} - 366 T^{3} + 3721 T^{4} \))(\( 1 + 12 T + 138 T^{2} + 732 T^{3} + 3721 T^{4} \))(\( 1 + 6 T + 86 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( 1 - 6 T - 16 T^{2} - 366 T^{3} + 3721 T^{4} \))(\( 1 + 6 T + 104 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( 1 + 18 T + 198 T^{2} + 1098 T^{3} + 3721 T^{4} \))(\( ( 1 + 61 T^{2} )^{2} \))(\( 1 - 6 T + 56 T^{2} - 366 T^{3} + 3721 T^{4} \))(\( 1 - 6 T + 86 T^{2} - 366 T^{3} + 3721 T^{4} \))(\( 1 - 12 T + 138 T^{2} - 732 T^{3} + 3721 T^{4} \))(\( 1 + 6 T + 128 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( 1 + 6 T - 16 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( 1 - 6 T + 104 T^{2} - 366 T^{3} + 3721 T^{4} \))(\( 1 - 10 T + 144 T^{2} - 1670 T^{3} + 11406 T^{4} - 101870 T^{5} + 535824 T^{6} - 2269810 T^{7} + 13845841 T^{8} \))(\( 1 - 14 T + 232 T^{2} - 2130 T^{3} + 21566 T^{4} - 129930 T^{5} + 863272 T^{6} - 3177734 T^{7} + 13845841 T^{8} \))(\( 1 + 10 T + 144 T^{2} + 1670 T^{3} + 11406 T^{4} + 101870 T^{5} + 535824 T^{6} + 2269810 T^{7} + 13845841 T^{8} \))(\( 1 + 14 T + 232 T^{2} + 2130 T^{3} + 21566 T^{4} + 129930 T^{5} + 863272 T^{6} + 3177734 T^{7} + 13845841 T^{8} \))
$67$ (\( 1 + 12 T + 67 T^{2} \))(\( 1 + 6 T + 67 T^{2} \))(\( 1 + 6 T + 67 T^{2} \))(\( 1 + 10 T + 67 T^{2} \))(\( 1 - 14 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 10 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 + 6 T + 67 T^{2} \))(\( 1 + 6 T + 67 T^{2} \))(\( 1 - 14 T + 67 T^{2} \))(\( 1 + 10 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 10 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 - 8 T + 42 T^{2} - 536 T^{3} + 4489 T^{4} \))(\( 1 - T + 103 T^{2} - 67 T^{3} + 4489 T^{4} \))(\( 1 - 6 T + 18 T^{2} - 402 T^{3} + 4489 T^{4} \))(\( 1 - 8 T + 42 T^{2} - 536 T^{3} + 4489 T^{4} \))(\( 1 + 3 T + 75 T^{2} + 201 T^{3} + 4489 T^{4} \))(\( 1 + 18 T + 170 T^{2} + 1206 T^{3} + 4489 T^{4} \))(\( 1 - 16 T + 186 T^{2} - 1072 T^{3} + 4489 T^{4} \))(\( 1 + 16 T + 186 T^{2} + 1072 T^{3} + 4489 T^{4} \))(\( 1 - 6 T + 18 T^{2} - 402 T^{3} + 4489 T^{4} \))(\( 1 - T + 103 T^{2} - 67 T^{3} + 4489 T^{4} \))(\( 1 - 8 T + 42 T^{2} - 536 T^{3} + 4489 T^{4} \))(\( 1 + 18 T + 170 T^{2} + 1206 T^{3} + 4489 T^{4} \))(\( 1 + 3 T + 75 T^{2} + 201 T^{3} + 4489 T^{4} \))(\( 1 - 8 T + 42 T^{2} - 536 T^{3} + 4489 T^{4} \))(\( 1 - 16 T + 186 T^{2} - 1072 T^{3} + 4489 T^{4} \))(\( 1 + 16 T + 186 T^{2} + 1072 T^{3} + 4489 T^{4} \))(\( 1 - 9 T + 179 T^{2} - 1883 T^{3} + 15084 T^{4} - 126161 T^{5} + 803531 T^{6} - 2706867 T^{7} + 20151121 T^{8} \))(\( 1 - 29 T + 351 T^{2} - 2167 T^{3} + 11580 T^{4} - 145189 T^{5} + 1575639 T^{6} - 8722127 T^{7} + 20151121 T^{8} \))(\( 1 - 9 T + 179 T^{2} - 1883 T^{3} + 15084 T^{4} - 126161 T^{5} + 803531 T^{6} - 2706867 T^{7} + 20151121 T^{8} \))(\( 1 - 29 T + 351 T^{2} - 2167 T^{3} + 11580 T^{4} - 145189 T^{5} + 1575639 T^{6} - 8722127 T^{7} + 20151121 T^{8} \))
$71$ (\( 1 + 4 T + 71 T^{2} \))(\( 1 - 9 T + 71 T^{2} \))(\( 1 - 5 T + 71 T^{2} \))(\( 1 - 7 T + 71 T^{2} \))(\( 1 + T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 15 T + 71 T^{2} \))(\( 1 - 9 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 - 3 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 5 T + 71 T^{2} \))(\( 1 - 9 T + 71 T^{2} \))(\( 1 + T + 71 T^{2} \))(\( 1 - 7 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 - 9 T + 71 T^{2} \))(\( 1 + 15 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 3 T + 71 T^{2} \))(\( 1 + 9 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( ( 1 - 3 T + 71 T^{2} )^{2} \))(\( 1 - 12 T + 158 T^{2} - 852 T^{3} + 5041 T^{4} \))(\( 1 + 14 T + 146 T^{2} + 994 T^{3} + 5041 T^{4} \))(\( 1 - 6 T + 43 T^{2} - 426 T^{3} + 5041 T^{4} \))(\( 1 + 4 T - 34 T^{2} + 284 T^{3} + 5041 T^{4} \))(\( 1 + 6 T + 26 T^{2} + 426 T^{3} + 5041 T^{4} \))(\( 1 - 2 T + 131 T^{2} - 142 T^{3} + 5041 T^{4} \))(\( 1 + 6 T + 103 T^{2} + 426 T^{3} + 5041 T^{4} \))(\( 1 + 14 T + 146 T^{2} + 994 T^{3} + 5041 T^{4} \))(\( 1 - 12 T + 158 T^{2} - 852 T^{3} + 5041 T^{4} \))(\( ( 1 - 3 T + 71 T^{2} )^{2} \))(\( 1 + 6 T + 26 T^{2} + 426 T^{3} + 5041 T^{4} \))(\( 1 + 4 T - 34 T^{2} + 284 T^{3} + 5041 T^{4} \))(\( 1 - 6 T + 43 T^{2} - 426 T^{3} + 5041 T^{4} \))(\( 1 - 2 T + 131 T^{2} - 142 T^{3} + 5041 T^{4} \))(\( 1 + 6 T + 103 T^{2} + 426 T^{3} + 5041 T^{4} \))(\( 1 - 10 T + 224 T^{2} - 1650 T^{3} + 23006 T^{4} - 117150 T^{5} + 1129184 T^{6} - 3579110 T^{7} + 25411681 T^{8} \))(\( 1 + 6 T + 168 T^{2} + 1118 T^{3} + 15374 T^{4} + 79378 T^{5} + 846888 T^{6} + 2147466 T^{7} + 25411681 T^{8} \))(\( 1 - 10 T + 224 T^{2} - 1650 T^{3} + 23006 T^{4} - 117150 T^{5} + 1129184 T^{6} - 3579110 T^{7} + 25411681 T^{8} \))(\( 1 + 6 T + 168 T^{2} + 1118 T^{3} + 15374 T^{4} + 79378 T^{5} + 846888 T^{6} + 2147466 T^{7} + 25411681 T^{8} \))
$73$ (\( 1 + 10 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 8 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 - 8 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 16 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 8 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))(\( 1 + 8 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 16 T + 73 T^{2} \))(\( 1 - 6 T + 152 T^{2} - 438 T^{3} + 5329 T^{4} \))(\( 1 - 34 T^{2} + 5329 T^{4} \))(\( 1 - 4 T + 70 T^{2} - 292 T^{3} + 5329 T^{4} \))(\( 1 - 6 T + 152 T^{2} - 438 T^{3} + 5329 T^{4} \))(\( 1 + 126 T^{2} + 5329 T^{4} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( 1 + 2 T + 72 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 + 2 T + 120 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 + 4 T + 70 T^{2} + 292 T^{3} + 5329 T^{4} \))(\( 1 - 34 T^{2} + 5329 T^{4} \))(\( 1 + 6 T + 152 T^{2} + 438 T^{3} + 5329 T^{4} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( 1 + 126 T^{2} + 5329 T^{4} \))(\( 1 + 6 T + 152 T^{2} + 438 T^{3} + 5329 T^{4} \))(\( 1 - 2 T + 72 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( 1 - 2 T + 120 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( ( 1 - 4 T + 70 T^{2} - 292 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 6 T + 73 T^{2} )^{4} \))(\( ( 1 + 4 T + 70 T^{2} + 292 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 + 6 T + 73 T^{2} )^{4} \))
$79$ (\( 1 + 4 T + 79 T^{2} \))(\( 1 + 6 T + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 6 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 14 T + 79 T^{2} \))(\( 1 - 6 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))(\( 1 - 16 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 14 T + 79 T^{2} \))(\( 1 - 6 T + 79 T^{2} \))(\( 1 - 6 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 12 T + 79 T^{2} \))(\( 1 + 6 T + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 2 T + 79 T^{2} \))(\( 1 + 50 T^{2} + 6241 T^{4} \))(\( 1 + 3 T + 129 T^{2} + 237 T^{3} + 6241 T^{4} \))(\( 1 + 138 T^{2} + 6241 T^{4} \))(\( 1 + 24 T + 290 T^{2} + 1896 T^{3} + 6241 T^{4} \))(\( 1 + T + 57 T^{2} + 79 T^{3} + 6241 T^{4} \))(\( 1 - 16 T + 202 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 + 50 T^{2} + 6241 T^{4} \))(\( 1 + 8 T + 162 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + 138 T^{2} + 6241 T^{4} \))(\( 1 - 3 T + 129 T^{2} - 237 T^{3} + 6241 T^{4} \))(\( 1 + 50 T^{2} + 6241 T^{4} \))(\( 1 + 16 T + 202 T^{2} + 1264 T^{3} + 6241 T^{4} \))(\( 1 - T + 57 T^{2} - 79 T^{3} + 6241 T^{4} \))(\( 1 - 24 T + 290 T^{2} - 1896 T^{3} + 6241 T^{4} \))(\( 1 + 50 T^{2} + 6241 T^{4} \))(\( 1 - 8 T + 162 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( 1 - 7 T + 115 T^{2} - 727 T^{3} + 14764 T^{4} - 57433 T^{5} + 717715 T^{6} - 3451273 T^{7} + 38950081 T^{8} \))(\( 1 + 3 T + 107 T^{2} + 851 T^{3} + 10044 T^{4} + 67229 T^{5} + 667787 T^{6} + 1479117 T^{7} + 38950081 T^{8} \))(\( 1 + 7 T + 115 T^{2} + 727 T^{3} + 14764 T^{4} + 57433 T^{5} + 717715 T^{6} + 3451273 T^{7} + 38950081 T^{8} \))(\( 1 - 3 T + 107 T^{2} - 851 T^{3} + 10044 T^{4} - 67229 T^{5} + 667787 T^{6} - 1479117 T^{7} + 38950081 T^{8} \))
$83$ (\( 1 + 4 T + 83 T^{2} \))(\( 1 - 7 T + 83 T^{2} \))(\( 1 + T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 + 17 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 3 T + 83 T^{2} \))(\( 1 - 3 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 13 T + 83 T^{2} \))(\( 1 - 3 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - T + 83 T^{2} \))(\( 1 + 7 T + 83 T^{2} \))(\( 1 - 17 T + 83 T^{2} \))(\( 1 - 9 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 3 T + 83 T^{2} \))(\( 1 + 3 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 3 T + 83 T^{2} \))(\( 1 - 13 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 + 6 T + 163 T^{2} + 498 T^{3} + 6889 T^{4} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( 1 - 8 T + 102 T^{2} - 664 T^{3} + 6889 T^{4} \))(\( 1 - 18 T + 235 T^{2} - 1494 T^{3} + 6889 T^{4} \))(\( 1 + 12 T + 182 T^{2} + 996 T^{3} + 6889 T^{4} \))(\( 1 - 4 T + 150 T^{2} - 332 T^{3} + 6889 T^{4} \))(\( 1 - 26 T + 323 T^{2} - 2158 T^{3} + 6889 T^{4} \))(\( 1 - 2 T + 59 T^{2} - 166 T^{3} + 6889 T^{4} \))(\( 1 + 8 T + 102 T^{2} + 664 T^{3} + 6889 T^{4} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( 1 - 6 T + 163 T^{2} - 498 T^{3} + 6889 T^{4} \))(\( 1 + 4 T + 150 T^{2} + 332 T^{3} + 6889 T^{4} \))(\( 1 - 12 T + 182 T^{2} - 996 T^{3} + 6889 T^{4} \))(\( 1 + 18 T + 235 T^{2} + 1494 T^{3} + 6889 T^{4} \))(\( 1 + 26 T + 323 T^{2} + 2158 T^{3} + 6889 T^{4} \))(\( 1 + 2 T + 59 T^{2} + 166 T^{3} + 6889 T^{4} \))(\( ( 1 + 8 T + 83 T^{2} )^{4} \))(\( ( 1 - 12 T + 182 T^{2} - 996 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 - 8 T + 83 T^{2} )^{4} \))(\( ( 1 + 12 T + 182 T^{2} + 996 T^{3} + 6889 T^{4} )^{2} \))
$89$ (\( 1 - 10 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 8 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 4 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 8 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 - 18 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 - 4 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 12 T + 106 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 - 30 T + 398 T^{2} - 2670 T^{3} + 7921 T^{4} \))(\( 1 + 17 T + 239 T^{2} + 1513 T^{3} + 7921 T^{4} \))(\( 1 - 12 T + 106 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 + 2 T + 134 T^{2} + 178 T^{3} + 7921 T^{4} \))(\( 1 - 3 T + 79 T^{2} - 267 T^{3} + 7921 T^{4} \))(\( 1 - 12 T + 202 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 + 12 T + 106 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 + 17 T + 239 T^{2} + 1513 T^{3} + 7921 T^{4} \))(\( 1 - 30 T + 398 T^{2} - 2670 T^{3} + 7921 T^{4} \))(\( 1 + 12 T + 106 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 - 3 T + 79 T^{2} - 267 T^{3} + 7921 T^{4} \))(\( 1 + 2 T + 134 T^{2} + 178 T^{3} + 7921 T^{4} \))(\( 1 - 12 T + 106 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 - 12 T + 202 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 + 12 T + 106 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 + 23 T + 435 T^{2} + 4963 T^{3} + 54864 T^{4} + 441707 T^{5} + 3445635 T^{6} + 16214287 T^{7} + 62742241 T^{8} \))(\( 1 - 5 T + 211 T^{2} - 985 T^{3} + 22216 T^{4} - 87665 T^{5} + 1671331 T^{6} - 3524845 T^{7} + 62742241 T^{8} \))(\( 1 + 23 T + 435 T^{2} + 4963 T^{3} + 54864 T^{4} + 441707 T^{5} + 3445635 T^{6} + 16214287 T^{7} + 62742241 T^{8} \))(\( 1 - 5 T + 211 T^{2} - 985 T^{3} + 22216 T^{4} - 87665 T^{5} + 1671331 T^{6} - 3524845 T^{7} + 62742241 T^{8} \))
$97$ (\( 1 - 18 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 + 12 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 18 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 4 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 12 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 8 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 4 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 - 10 T + 192 T^{2} - 970 T^{3} + 9409 T^{4} \))(\( 1 - 6 T - 42 T^{2} - 582 T^{3} + 9409 T^{4} \))(\( 1 - 12 T + 150 T^{2} - 1164 T^{3} + 9409 T^{4} \))(\( 1 - 10 T + 192 T^{2} - 970 T^{3} + 9409 T^{4} \))(\( 1 - 22 T + 270 T^{2} - 2134 T^{3} + 9409 T^{4} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( 1 - 14 T + 240 T^{2} - 1358 T^{3} + 9409 T^{4} \))(\( 1 + 34 T + 480 T^{2} + 3298 T^{3} + 9409 T^{4} \))(\( 1 - 12 T + 150 T^{2} - 1164 T^{3} + 9409 T^{4} \))(\( 1 - 6 T - 42 T^{2} - 582 T^{3} + 9409 T^{4} \))(\( 1 - 10 T + 192 T^{2} - 970 T^{3} + 9409 T^{4} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( 1 - 22 T + 270 T^{2} - 2134 T^{3} + 9409 T^{4} \))(\( 1 - 10 T + 192 T^{2} - 970 T^{3} + 9409 T^{4} \))(\( 1 - 14 T + 240 T^{2} - 1358 T^{3} + 9409 T^{4} \))(\( 1 + 34 T + 480 T^{2} + 3298 T^{3} + 9409 T^{4} \))(\( 1 + 2 T + 252 T^{2} + 910 T^{3} + 31206 T^{4} + 88270 T^{5} + 2371068 T^{6} + 1825346 T^{7} + 88529281 T^{8} \))(\( 1 - 30 T + 580 T^{2} - 8210 T^{3} + 88598 T^{4} - 796370 T^{5} + 5457220 T^{6} - 27380190 T^{7} + 88529281 T^{8} \))(\( 1 + 2 T + 252 T^{2} + 910 T^{3} + 31206 T^{4} + 88270 T^{5} + 2371068 T^{6} + 1825346 T^{7} + 88529281 T^{8} \))(\( 1 - 30 T + 580 T^{2} - 8210 T^{3} + 88598 T^{4} - 796370 T^{5} + 5457220 T^{6} - 27380190 T^{7} + 88529281 T^{8} \))
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