Properties

Label 2366.2
Level 2366
Weight 2
Dimension 53774
Nonzero newspaces 30
Sturm bound 681408
Trace bound 7

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Defining parameters

Level: \( N \) = \( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(681408\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2366))\).

Total New Old
Modular forms 173088 53774 119314
Cusp forms 167617 53774 113843
Eisenstein series 5471 0 5471

Trace form

\( 53774q - 2q^{2} - 6q^{3} - 6q^{5} - 2q^{6} + 8q^{7} + 10q^{8} + 52q^{9} + O(q^{10}) \) \( 53774q - 2q^{2} - 6q^{3} - 6q^{5} - 2q^{6} + 8q^{7} + 10q^{8} + 52q^{9} + 54q^{10} + 36q^{11} + 10q^{12} + 48q^{13} + 22q^{14} + 72q^{15} + 16q^{16} + 48q^{17} + 46q^{18} + 94q^{19} + 6q^{20} + 50q^{21} - 12q^{22} + 24q^{23} - 2q^{24} + 24q^{25} + 108q^{27} + 8q^{28} + 120q^{29} + 72q^{30} + 124q^{31} - 2q^{32} + 192q^{33} + 72q^{34} + 138q^{35} + 84q^{36} + 88q^{37} + 122q^{38} + 104q^{39} - 6q^{40} + 168q^{41} + 70q^{42} + 140q^{43} + 84q^{44} + 222q^{45} + 72q^{46} + 132q^{47} - 6q^{48} + 64q^{49} + 82q^{50} + 204q^{51} + 14q^{52} + 96q^{53} + 100q^{54} + 168q^{55} + 22q^{56} + 172q^{57} + 84q^{58} + 126q^{59} + 72q^{60} + 102q^{61} + 116q^{62} + 236q^{63} + 12q^{64} + 174q^{65} + 144q^{66} + 232q^{67} + 384q^{69} + 66q^{70} + 216q^{71} + 82q^{72} + 232q^{73} - 28q^{74} + 142q^{75} - 98q^{76} - 204q^{77} - 24q^{78} - 264q^{79} + 6q^{80} - 260q^{81} - 420q^{82} - 138q^{83} - 286q^{84} - 480q^{85} - 244q^{86} - 492q^{87} - 12q^{88} - 288q^{89} - 558q^{90} - 236q^{91} - 216q^{92} - 296q^{93} - 516q^{94} - 408q^{95} - 2q^{96} - 572q^{97} - 194q^{98} - 588q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2366))\)

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
2366.2.a \(\chi_{2366}(1, \cdot)\) 2366.2.a.a 1 1
2366.2.a.b 1
2366.2.a.c 1
2366.2.a.d 1
2366.2.a.e 1
2366.2.a.f 1
2366.2.a.g 1
2366.2.a.h 1
2366.2.a.i 1
2366.2.a.j 1
2366.2.a.k 1
2366.2.a.l 1
2366.2.a.m 1
2366.2.a.n 1
2366.2.a.o 1
2366.2.a.p 1
2366.2.a.q 2
2366.2.a.r 2
2366.2.a.s 2
2366.2.a.t 2
2366.2.a.u 3
2366.2.a.v 3
2366.2.a.w 3
2366.2.a.x 3
2366.2.a.y 3
2366.2.a.z 3
2366.2.a.ba 3
2366.2.a.bb 3
2366.2.a.bc 3
2366.2.a.bd 3
2366.2.a.be 6
2366.2.a.bf 6
2366.2.a.bg 6
2366.2.a.bh 6
2366.2.d \(\chi_{2366}(337, \cdot)\) 2366.2.d.a 2 1
2366.2.d.b 2
2366.2.d.c 2
2366.2.d.d 2
2366.2.d.e 2
2366.2.d.f 2
2366.2.d.g 2
2366.2.d.h 2
2366.2.d.i 2
2366.2.d.j 2
2366.2.d.k 4
2366.2.d.l 4
2366.2.d.m 6
2366.2.d.n 6
2366.2.d.o 6
2366.2.d.p 6
2366.2.d.q 12
2366.2.d.r 12
2366.2.e \(\chi_{2366}(529, \cdot)\) n/a 204 2
2366.2.f \(\chi_{2366}(1353, \cdot)\) n/a 208 2
2366.2.g \(\chi_{2366}(1205, \cdot)\) n/a 156 2
2366.2.h \(\chi_{2366}(191, \cdot)\) n/a 204 2
2366.2.i \(\chi_{2366}(2127, \cdot)\) n/a 200 2
2366.2.m \(\chi_{2366}(1037, \cdot)\) n/a 152 2
2366.2.n \(\chi_{2366}(1689, \cdot)\) n/a 208 2
2366.2.o \(\chi_{2366}(23, \cdot)\) n/a 204 2
2366.2.v \(\chi_{2366}(361, \cdot)\) n/a 204 2
2366.2.w \(\chi_{2366}(19, \cdot)\) n/a 408 4
2366.2.ba \(\chi_{2366}(587, \cdot)\) n/a 416 4
2366.2.bb \(\chi_{2366}(437, \cdot)\) n/a 416 4
2366.2.bc \(\chi_{2366}(89, \cdot)\) n/a 408 4
2366.2.be \(\chi_{2366}(183, \cdot)\) n/a 1080 12
2366.2.bf \(\chi_{2366}(155, \cdot)\) n/a 1104 12
2366.2.bi \(\chi_{2366}(9, \cdot)\) n/a 2928 24
2366.2.bj \(\chi_{2366}(29, \cdot)\) n/a 2160 24
2366.2.bk \(\chi_{2366}(53, \cdot)\) n/a 2880 24
2366.2.bl \(\chi_{2366}(107, \cdot)\) n/a 2928 24
2366.2.bn \(\chi_{2366}(83, \cdot)\) n/a 2976 24
2366.2.bo \(\chi_{2366}(121, \cdot)\) n/a 2928 24
2366.2.bv \(\chi_{2366}(95, \cdot)\) n/a 2928 24
2366.2.bw \(\chi_{2366}(25, \cdot)\) n/a 2880 24
2366.2.bx \(\chi_{2366}(43, \cdot)\) n/a 2208 24
2366.2.cb \(\chi_{2366}(45, \cdot)\) n/a 5856 48
2366.2.cc \(\chi_{2366}(5, \cdot)\) n/a 5760 48
2366.2.cd \(\chi_{2366}(41, \cdot)\) n/a 5760 48
2366.2.ch \(\chi_{2366}(33, \cdot)\) n/a 5856 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2366))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2366)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1183))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{6} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 - T )^{6} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{3} \))(\( ( 1 + T^{2} )^{3} \))(\( ( 1 + T^{2} )^{3} \))(\( ( 1 + T^{2} )^{3} \))(\( ( 1 + T^{2} )^{6} \))(\( ( 1 + T^{2} )^{6} \))
$3$ (\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 + 2 T + 4 T^{2} + 6 T^{3} + 9 T^{4} \))(\( 1 + 3 T^{2} + 9 T^{4} \))(\( 1 + 2 T + 4 T^{2} + 6 T^{3} + 9 T^{4} \))(\( 1 + 3 T^{2} + 9 T^{4} \))(\( 1 + 5 T + 15 T^{2} + 31 T^{3} + 45 T^{4} + 45 T^{5} + 27 T^{6} \))(\( 1 + 4 T + 12 T^{2} + 23 T^{3} + 36 T^{4} + 36 T^{5} + 27 T^{6} \))(\( 1 + 2 T^{2} + 7 T^{3} + 6 T^{4} + 27 T^{6} \))(\( 1 - T - T^{2} + 8 T^{3} - 3 T^{4} - 9 T^{5} + 27 T^{6} \))(\( 1 - 2 T + 8 T^{2} - 11 T^{3} + 24 T^{4} - 18 T^{5} + 27 T^{6} \))(\( 1 + 5 T + 15 T^{2} + 31 T^{3} + 45 T^{4} + 45 T^{5} + 27 T^{6} \))(\( 1 + 4 T + 12 T^{2} + 23 T^{3} + 36 T^{4} + 36 T^{5} + 27 T^{6} \))(\( 1 + 2 T^{2} + 7 T^{3} + 6 T^{4} + 27 T^{6} \))(\( 1 - T - T^{2} + 8 T^{3} - 3 T^{4} - 9 T^{5} + 27 T^{6} \))(\( 1 - 2 T + 8 T^{2} - 11 T^{3} + 24 T^{4} - 18 T^{5} + 27 T^{6} \))(\( 1 - T + 7 T^{2} - 8 T^{3} + 36 T^{4} - 36 T^{5} + 117 T^{6} - 108 T^{7} + 324 T^{8} - 216 T^{9} + 567 T^{10} - 243 T^{11} + 729 T^{12} \))(\( 1 - 2 T + 8 T^{2} - 18 T^{3} + 36 T^{4} - 70 T^{5} + 124 T^{6} - 210 T^{7} + 324 T^{8} - 486 T^{9} + 648 T^{10} - 486 T^{11} + 729 T^{12} \))(\( 1 - T + 7 T^{2} - 8 T^{3} + 36 T^{4} - 36 T^{5} + 117 T^{6} - 108 T^{7} + 324 T^{8} - 216 T^{9} + 567 T^{10} - 243 T^{11} + 729 T^{12} \))(\( 1 - 2 T + 8 T^{2} - 18 T^{3} + 36 T^{4} - 70 T^{5} + 124 T^{6} - 210 T^{7} + 324 T^{8} - 486 T^{9} + 648 T^{10} - 486 T^{11} + 729 T^{12} \))(\( ( 1 + 2 T + 3 T^{2} )^{2} \))(\( ( 1 + 2 T + 3 T^{2} )^{2} \))(\( ( 1 + 2 T + 3 T^{2} )^{2} \))(\( ( 1 + 3 T^{2} )^{2} \))(\( ( 1 - T + 3 T^{2} )^{2} \))(\( ( 1 - T + 3 T^{2} )^{2} \))(\( ( 1 - T + 3 T^{2} )^{2} \))(\( ( 1 - 3 T + 3 T^{2} )^{2} \))(\( ( 1 - 3 T + 3 T^{2} )^{2} \))(\( ( 1 - 3 T + 3 T^{2} )^{2} \))(\( ( 1 + 2 T + 4 T^{2} + 6 T^{3} + 9 T^{4} )^{2} \))(\( ( 1 + 3 T^{2} + 9 T^{4} )^{2} \))(\( ( 1 + 5 T + 15 T^{2} + 31 T^{3} + 45 T^{4} + 45 T^{5} + 27 T^{6} )^{2} \))(\( ( 1 + 4 T + 12 T^{2} + 23 T^{3} + 36 T^{4} + 36 T^{5} + 27 T^{6} )^{2} \))(\( ( 1 + 2 T^{2} + 7 T^{3} + 6 T^{4} + 27 T^{6} )^{2} \))(\( ( 1 - 2 T + 8 T^{2} - 11 T^{3} + 24 T^{4} - 18 T^{5} + 27 T^{6} )^{2} \))(\( ( 1 - T + 7 T^{2} - 8 T^{3} + 36 T^{4} - 36 T^{5} + 117 T^{6} - 108 T^{7} + 324 T^{8} - 216 T^{9} + 567 T^{10} - 243 T^{11} + 729 T^{12} )^{2} \))(\( ( 1 - 2 T + 8 T^{2} - 18 T^{3} + 36 T^{4} - 70 T^{5} + 124 T^{6} - 210 T^{7} + 324 T^{8} - 486 T^{9} + 648 T^{10} - 486 T^{11} + 729 T^{12} )^{2} \))
$5$ (\( 1 + 3 T + 5 T^{2} \))(\( 1 - T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 + 4 T + 5 T^{2} \))(\( 1 + 3 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 3 T + 5 T^{2} \))(\( ( 1 - T + 5 T^{2} )^{2} \))(\( 1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4} \))(\( ( 1 + T + 5 T^{2} )^{2} \))(\( 1 - 4 T + 11 T^{2} - 20 T^{3} + 25 T^{4} \))(\( 1 + 2 T + 7 T^{2} + 12 T^{3} + 35 T^{4} + 50 T^{5} + 125 T^{6} \))(\( 1 + 2 T + 14 T^{2} + 19 T^{3} + 70 T^{4} + 50 T^{5} + 125 T^{6} \))(\( 1 - 8 T + 34 T^{2} - 93 T^{3} + 170 T^{4} - 200 T^{5} + 125 T^{6} \))(\( 1 + 2 T + 5 T^{2} + 16 T^{3} + 25 T^{4} + 50 T^{5} + 125 T^{6} \))(\( 1 + 8 T^{2} - 7 T^{3} + 40 T^{4} + 125 T^{6} \))(\( 1 - 2 T + 7 T^{2} - 12 T^{3} + 35 T^{4} - 50 T^{5} + 125 T^{6} \))(\( 1 - 2 T + 14 T^{2} - 19 T^{3} + 70 T^{4} - 50 T^{5} + 125 T^{6} \))(\( 1 + 8 T + 34 T^{2} + 93 T^{3} + 170 T^{4} + 200 T^{5} + 125 T^{6} \))(\( 1 - 2 T + 5 T^{2} - 16 T^{3} + 25 T^{4} - 50 T^{5} + 125 T^{6} \))(\( 1 + 8 T^{2} + 7 T^{3} + 40 T^{4} + 125 T^{6} \))(\( 1 + 4 T + 19 T^{2} + 43 T^{3} + 141 T^{4} + 257 T^{5} + 766 T^{6} + 1285 T^{7} + 3525 T^{8} + 5375 T^{9} + 11875 T^{10} + 12500 T^{11} + 15625 T^{12} \))(\( 1 - 2 T + 11 T^{2} - 26 T^{3} + 88 T^{4} - 150 T^{5} + 509 T^{6} - 750 T^{7} + 2200 T^{8} - 3250 T^{9} + 6875 T^{10} - 6250 T^{11} + 15625 T^{12} \))(\( 1 - 4 T + 19 T^{2} - 43 T^{3} + 141 T^{4} - 257 T^{5} + 766 T^{6} - 1285 T^{7} + 3525 T^{8} - 5375 T^{9} + 11875 T^{10} - 12500 T^{11} + 15625 T^{12} \))(\( 1 + 2 T + 11 T^{2} + 26 T^{3} + 88 T^{4} + 150 T^{5} + 509 T^{6} + 750 T^{7} + 2200 T^{8} + 3250 T^{9} + 6875 T^{10} + 6250 T^{11} + 15625 T^{12} \))(\( 1 - T^{2} + 25 T^{4} \))(\( ( 1 - 5 T^{2} )^{2} \))(\( 1 - 9 T^{2} + 25 T^{4} \))(\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))(\( ( 1 - 5 T^{2} )^{2} \))(\( 1 - T^{2} + 25 T^{4} \))(\( ( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} ) \))(\( 1 - T^{2} + 25 T^{4} \))(\( ( 1 - 5 T^{2} )^{2} \))(\( ( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} ) \))(\( ( 1 - 9 T^{2} + 25 T^{4} )^{2} \))(\( ( 1 - 2 T - T^{2} - 10 T^{3} + 25 T^{4} )( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} ) \))(\( 1 - 10 T^{2} + 71 T^{4} - 396 T^{6} + 1775 T^{8} - 6250 T^{10} + 15625 T^{12} \))(\( 1 - 24 T^{2} + 260 T^{4} - 1649 T^{6} + 6500 T^{8} - 15000 T^{10} + 15625 T^{12} \))(\( 1 - 4 T^{2} + 8 T^{4} + 39 T^{6} + 200 T^{8} - 2500 T^{10} + 15625 T^{12} \))(\( 1 - 16 T^{2} + 144 T^{4} - 841 T^{6} + 3600 T^{8} - 10000 T^{10} + 15625 T^{12} \))(\( 1 - 22 T^{2} + 299 T^{4} - 2985 T^{6} + 23657 T^{8} - 154153 T^{10} + 840566 T^{12} - 3853825 T^{14} + 14785625 T^{16} - 46640625 T^{18} + 116796875 T^{20} - 214843750 T^{22} + 244140625 T^{24} \))(\( 1 - 18 T^{2} + 193 T^{4} - 1678 T^{6} + 12542 T^{8} - 77234 T^{10} + 409781 T^{12} - 1930850 T^{14} + 7838750 T^{16} - 26218750 T^{18} + 75390625 T^{20} - 175781250 T^{22} + 244140625 T^{24} \))
$7$ (\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 + T )^{6} \))(\( ( 1 + T )^{6} \))(\( ( 1 - T )^{6} \))(\( ( 1 - T )^{6} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{3} \))(\( ( 1 + T^{2} )^{3} \))(\( ( 1 + T^{2} )^{3} \))(\( ( 1 + T^{2} )^{3} \))(\( ( 1 + T^{2} )^{6} \))(\( ( 1 + T^{2} )^{6} \))
$11$ (\( 1 + 6 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( 1 + 5 T + 11 T^{2} \))(\( 1 - T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 5 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 2 T + 20 T^{2} + 22 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 14 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 - 2 T + 20 T^{2} - 22 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 14 T^{2} + 44 T^{3} + 121 T^{4} \))(\( 1 + 3 T + 15 T^{2} + 53 T^{3} + 165 T^{4} + 363 T^{5} + 1331 T^{6} \))(\( 1 - 11 T + 71 T^{2} - 283 T^{3} + 781 T^{4} - 1331 T^{5} + 1331 T^{6} \))(\( 1 - 9 T + 53 T^{2} - 211 T^{3} + 583 T^{4} - 1089 T^{5} + 1331 T^{6} \))(\( 1 + 7 T + 25 T^{2} + 66 T^{3} + 275 T^{4} + 847 T^{5} + 1331 T^{6} \))(\( 1 + T + 31 T^{2} + 21 T^{3} + 341 T^{4} + 121 T^{5} + 1331 T^{6} \))(\( 1 - 3 T + 15 T^{2} - 53 T^{3} + 165 T^{4} - 363 T^{5} + 1331 T^{6} \))(\( 1 + 11 T + 71 T^{2} + 283 T^{3} + 781 T^{4} + 1331 T^{5} + 1331 T^{6} \))(\( 1 + 9 T + 53 T^{2} + 211 T^{3} + 583 T^{4} + 1089 T^{5} + 1331 T^{6} \))(\( 1 - 7 T + 25 T^{2} - 66 T^{3} + 275 T^{4} - 847 T^{5} + 1331 T^{6} \))(\( 1 - T + 31 T^{2} - 21 T^{3} + 341 T^{4} - 121 T^{5} + 1331 T^{6} \))(\( 1 + 6 T + 61 T^{2} + 270 T^{3} + 1565 T^{4} + 5398 T^{5} + 22427 T^{6} + 59378 T^{7} + 189365 T^{8} + 359370 T^{9} + 893101 T^{10} + 966306 T^{11} + 1771561 T^{12} \))(\( 1 + 2 T + 24 T^{2} + 14 T^{3} + 335 T^{4} - 108 T^{5} + 3520 T^{6} - 1188 T^{7} + 40535 T^{8} + 18634 T^{9} + 351384 T^{10} + 322102 T^{11} + 1771561 T^{12} \))(\( 1 - 6 T + 61 T^{2} - 270 T^{3} + 1565 T^{4} - 5398 T^{5} + 22427 T^{6} - 59378 T^{7} + 189365 T^{8} - 359370 T^{9} + 893101 T^{10} - 966306 T^{11} + 1771561 T^{12} \))(\( 1 - 2 T + 24 T^{2} - 14 T^{3} + 335 T^{4} + 108 T^{5} + 3520 T^{6} + 1188 T^{7} + 40535 T^{8} - 18634 T^{9} + 351384 T^{10} - 322102 T^{11} + 1771561 T^{12} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( 1 - 13 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 - 21 T^{2} + 121 T^{4} \))(\( 1 - 6 T^{2} + 121 T^{4} \))(\( 1 + 3 T^{2} + 121 T^{4} \))(\( 1 - 21 T^{2} + 121 T^{4} \))(\( 1 - 36 T^{2} + 554 T^{4} - 4356 T^{6} + 14641 T^{8} \))(\( 1 - 12 T^{2} + 86 T^{4} - 1452 T^{6} + 14641 T^{8} \))(\( 1 - 21 T^{2} + 237 T^{4} - 2625 T^{6} + 28677 T^{8} - 307461 T^{10} + 1771561 T^{12} \))(\( 1 - 21 T^{2} + 377 T^{4} - 4193 T^{6} + 45617 T^{8} - 307461 T^{10} + 1771561 T^{12} \))(\( 1 - 25 T^{2} + 177 T^{4} - 337 T^{6} + 21417 T^{8} - 366025 T^{10} + 1771561 T^{12} \))(\( 1 - 61 T^{2} + 1601 T^{4} - 23121 T^{6} + 193721 T^{8} - 893101 T^{10} + 1771561 T^{12} \))(\( 1 - 86 T^{2} + 3611 T^{4} - 98108 T^{6} + 1936593 T^{8} - 29570278 T^{10} + 361483863 T^{12} - 3578003638 T^{14} + 28353658113 T^{16} - 173804306588 T^{18} + 774049919291 T^{20} - 2230618515686 T^{22} + 3138428376721 T^{24} \))(\( 1 - 44 T^{2} + 1190 T^{4} - 23356 T^{6} + 370031 T^{8} - 4953912 T^{10} + 57891636 T^{12} - 599423352 T^{14} + 5417623871 T^{16} - 41376578716 T^{18} + 255087068390 T^{20} - 1141246682444 T^{22} + 3138428376721 T^{24} \))
$13$ 1
$17$ (\( 1 + 3 T + 17 T^{2} \))(\( 1 - T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 8 T + 47 T^{2} + 136 T^{3} + 289 T^{4} \))(\( 1 + 22 T^{2} + 289 T^{4} \))(\( 1 + 8 T + 47 T^{2} + 136 T^{3} + 289 T^{4} \))(\( 1 + 22 T^{2} + 289 T^{4} \))(\( 1 + 7 T + 65 T^{2} + 245 T^{3} + 1105 T^{4} + 2023 T^{5} + 4913 T^{6} \))(\( 1 + 2 T - 6 T^{2} - 3 T^{3} - 102 T^{4} + 578 T^{5} + 4913 T^{6} \))(\( 1 - 10 T + 40 T^{2} - 117 T^{3} + 680 T^{4} - 2890 T^{5} + 4913 T^{6} \))(\( 1 - 2 T + 7 T^{2} - 12 T^{3} + 119 T^{4} - 578 T^{5} + 4913 T^{6} \))(\( 1 - 2 T + 36 T^{2} - 81 T^{3} + 612 T^{4} - 578 T^{5} + 4913 T^{6} \))(\( 1 + 7 T + 65 T^{2} + 245 T^{3} + 1105 T^{4} + 2023 T^{5} + 4913 T^{6} \))(\( 1 + 2 T - 6 T^{2} - 3 T^{3} - 102 T^{4} + 578 T^{5} + 4913 T^{6} \))(\( 1 - 10 T + 40 T^{2} - 117 T^{3} + 680 T^{4} - 2890 T^{5} + 4913 T^{6} \))(\( 1 - 2 T + 7 T^{2} - 12 T^{3} + 119 T^{4} - 578 T^{5} + 4913 T^{6} \))(\( 1 - 2 T + 36 T^{2} - 81 T^{3} + 612 T^{4} - 578 T^{5} + 4913 T^{6} \))(\( 1 + 9 T + 101 T^{2} + 638 T^{3} + 4134 T^{4} + 19764 T^{5} + 92011 T^{6} + 335988 T^{7} + 1194726 T^{8} + 3134494 T^{9} + 8435621 T^{10} + 12778713 T^{11} + 24137569 T^{12} \))(\( 1 - 4 T + 63 T^{2} - 172 T^{3} + 1859 T^{4} - 3792 T^{5} + 36442 T^{6} - 64464 T^{7} + 537251 T^{8} - 845036 T^{9} + 5261823 T^{10} - 5679428 T^{11} + 24137569 T^{12} \))(\( 1 + 9 T + 101 T^{2} + 638 T^{3} + 4134 T^{4} + 19764 T^{5} + 92011 T^{6} + 335988 T^{7} + 1194726 T^{8} + 3134494 T^{9} + 8435621 T^{10} + 12778713 T^{11} + 24137569 T^{12} \))(\( 1 - 4 T + 63 T^{2} - 172 T^{3} + 1859 T^{4} - 3792 T^{5} + 36442 T^{6} - 64464 T^{7} + 537251 T^{8} - 845036 T^{9} + 5261823 T^{10} - 5679428 T^{11} + 24137569 T^{12} \))(\( ( 1 - 3 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 + T + 17 T^{2} )^{2} \))(\( ( 1 - 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 4 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 - 4 T + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 - 8 T + 47 T^{2} - 136 T^{3} + 289 T^{4} )^{2} \))(\( ( 1 + 22 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 7 T + 65 T^{2} - 245 T^{3} + 1105 T^{4} - 2023 T^{5} + 4913 T^{6} )^{2} \))(\( ( 1 - 2 T - 6 T^{2} + 3 T^{3} - 102 T^{4} - 578 T^{5} + 4913 T^{6} )^{2} \))(\( ( 1 + 10 T + 40 T^{2} + 117 T^{3} + 680 T^{4} + 2890 T^{5} + 4913 T^{6} )^{2} \))(\( ( 1 + 2 T + 36 T^{2} + 81 T^{3} + 612 T^{4} + 578 T^{5} + 4913 T^{6} )^{2} \))(\( ( 1 - 9 T + 101 T^{2} - 638 T^{3} + 4134 T^{4} - 19764 T^{5} + 92011 T^{6} - 335988 T^{7} + 1194726 T^{8} - 3134494 T^{9} + 8435621 T^{10} - 12778713 T^{11} + 24137569 T^{12} )^{2} \))(\( ( 1 + 4 T + 63 T^{2} + 172 T^{3} + 1859 T^{4} + 3792 T^{5} + 36442 T^{6} + 64464 T^{7} + 537251 T^{8} + 845036 T^{9} + 5261823 T^{10} + 5679428 T^{11} + 24137569 T^{12} )^{2} \))
$19$ (\( 1 + 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 30 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 26 T^{2} + 361 T^{4} \))(\( 1 + 4 T + 30 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 + 26 T^{2} + 361 T^{4} \))(\( 1 - 11 T + 53 T^{2} - 207 T^{3} + 1007 T^{4} - 3971 T^{5} + 6859 T^{6} \))(\( 1 - 13 T + 111 T^{2} - 565 T^{3} + 2109 T^{4} - 4693 T^{5} + 6859 T^{6} \))(\( 1 - 7 T + 57 T^{2} - 259 T^{3} + 1083 T^{4} - 2527 T^{5} + 6859 T^{6} \))(\( 1 + 4 T + 51 T^{2} + 136 T^{3} + 969 T^{4} + 1444 T^{5} + 6859 T^{6} \))(\( 1 + 15 T + 125 T^{2} + 653 T^{3} + 2375 T^{4} + 5415 T^{5} + 6859 T^{6} \))(\( 1 + 11 T + 53 T^{2} + 207 T^{3} + 1007 T^{4} + 3971 T^{5} + 6859 T^{6} \))(\( 1 + 13 T + 111 T^{2} + 565 T^{3} + 2109 T^{4} + 4693 T^{5} + 6859 T^{6} \))(\( 1 + 7 T + 57 T^{2} + 259 T^{3} + 1083 T^{4} + 2527 T^{5} + 6859 T^{6} \))(\( 1 - 4 T + 51 T^{2} - 136 T^{3} + 969 T^{4} - 1444 T^{5} + 6859 T^{6} \))(\( 1 - 15 T + 125 T^{2} - 653 T^{3} + 2375 T^{4} - 5415 T^{5} + 6859 T^{6} \))(\( 1 + 10 T + 97 T^{2} + 568 T^{3} + 3695 T^{4} + 17488 T^{5} + 89105 T^{6} + 332272 T^{7} + 1333895 T^{8} + 3895912 T^{9} + 12641137 T^{10} + 24760990 T^{11} + 47045881 T^{12} \))(\( 1 - 4 T + 22 T^{2} - 76 T^{3} + 971 T^{4} - 2824 T^{5} + 15500 T^{6} - 53656 T^{7} + 350531 T^{8} - 521284 T^{9} + 2867062 T^{10} - 9904396 T^{11} + 47045881 T^{12} \))(\( 1 - 10 T + 97 T^{2} - 568 T^{3} + 3695 T^{4} - 17488 T^{5} + 89105 T^{6} - 332272 T^{7} + 1333895 T^{8} - 3895912 T^{9} + 12641137 T^{10} - 24760990 T^{11} + 47045881 T^{12} \))(\( 1 + 4 T + 22 T^{2} + 76 T^{3} + 971 T^{4} + 2824 T^{5} + 15500 T^{6} + 53656 T^{7} + 350531 T^{8} + 521284 T^{9} + 2867062 T^{10} + 9904396 T^{11} + 47045881 T^{12} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 34 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 - 34 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 34 T^{2} + 361 T^{4} \))(\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 34 T^{2} + 361 T^{4} \))(\( 1 - 2 T^{2} + 361 T^{4} \))(\( 1 - 44 T^{2} + 1014 T^{4} - 15884 T^{6} + 130321 T^{8} \))(\( ( 1 - 8 T + 19 T^{2} )^{2}( 1 + 8 T + 19 T^{2} )^{2} \))(\( 1 + 15 T^{2} + 269 T^{4} + 9751 T^{6} + 97109 T^{8} + 1954815 T^{10} + 47045881 T^{12} \))(\( 1 - 53 T^{2} + 1849 T^{4} - 40673 T^{6} + 667489 T^{8} - 6907013 T^{10} + 47045881 T^{12} \))(\( 1 - 65 T^{2} + 1789 T^{4} - 34721 T^{6} + 645829 T^{8} - 8470865 T^{10} + 47045881 T^{12} \))(\( 1 - 25 T^{2} + 785 T^{4} - 18609 T^{6} + 283385 T^{8} - 3258025 T^{10} + 47045881 T^{12} \))(\( 1 - 94 T^{2} + 5439 T^{4} - 222656 T^{6} + 7095377 T^{8} - 181334478 T^{10} + 3801136111 T^{12} - 65461746558 T^{14} + 924676626017 T^{16} - 10475047679936 T^{18} + 92373599379999 T^{20} - 576320228233294 T^{22} + 2213314919066161 T^{24} \))(\( 1 - 28 T^{2} + 1818 T^{4} - 45356 T^{6} + 1467407 T^{8} - 30957528 T^{10} + 679704268 T^{12} - 11175667608 T^{14} + 191233947647 T^{16} - 2133812978636 T^{18} + 30876117608538 T^{20} - 171669855218428 T^{22} + 2213314919066161 T^{24} \))
$23$ (\( 1 + 6 T + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 3 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 + 7 T + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 9 T + 23 T^{2} \))(\( 1 + 7 T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - 5 T + 23 T^{2} \))(\( 1 + T + 23 T^{2} \))(\( 1 - 6 T + 52 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 10 T + 59 T^{2} - 230 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 52 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 10 T + 59 T^{2} - 230 T^{3} + 529 T^{4} \))(\( 1 + 14 T + 125 T^{2} + 700 T^{3} + 2875 T^{4} + 7406 T^{5} + 12167 T^{6} \))(\( 1 + 7 T + 69 T^{2} + 273 T^{3} + 1587 T^{4} + 3703 T^{5} + 12167 T^{6} \))(\( 1 - 3 T + 65 T^{2} - 125 T^{3} + 1495 T^{4} - 1587 T^{5} + 12167 T^{6} \))(\( 1 - 3 T + 53 T^{2} - 106 T^{3} + 1219 T^{4} - 1587 T^{5} + 12167 T^{6} \))(\( 1 - T + 53 T^{2} - 59 T^{3} + 1219 T^{4} - 529 T^{5} + 12167 T^{6} \))(\( 1 + 14 T + 125 T^{2} + 700 T^{3} + 2875 T^{4} + 7406 T^{5} + 12167 T^{6} \))(\( 1 + 7 T + 69 T^{2} + 273 T^{3} + 1587 T^{4} + 3703 T^{5} + 12167 T^{6} \))(\( 1 - 3 T + 65 T^{2} - 125 T^{3} + 1495 T^{4} - 1587 T^{5} + 12167 T^{6} \))(\( 1 - 3 T + 53 T^{2} - 106 T^{3} + 1219 T^{4} - 1587 T^{5} + 12167 T^{6} \))(\( 1 - T + 53 T^{2} - 59 T^{3} + 1219 T^{4} - 529 T^{5} + 12167 T^{6} \))(\( 1 - 21 T + 244 T^{2} - 1974 T^{3} + 13037 T^{4} - 74557 T^{5} + 380660 T^{6} - 1714811 T^{7} + 6896573 T^{8} - 24017658 T^{9} + 68281204 T^{10} - 135163203 T^{11} + 148035889 T^{12} \))(\( 1 + 6 T + 70 T^{2} + 202 T^{3} + 1572 T^{4} + 782 T^{5} + 25728 T^{6} + 17986 T^{7} + 831588 T^{8} + 2457734 T^{9} + 19588870 T^{10} + 38618058 T^{11} + 148035889 T^{12} \))(\( 1 - 21 T + 244 T^{2} - 1974 T^{3} + 13037 T^{4} - 74557 T^{5} + 380660 T^{6} - 1714811 T^{7} + 6896573 T^{8} - 24017658 T^{9} + 68281204 T^{10} - 135163203 T^{11} + 148035889 T^{12} \))(\( 1 + 6 T + 70 T^{2} + 202 T^{3} + 1572 T^{4} + 782 T^{5} + 25728 T^{6} + 17986 T^{7} + 831588 T^{8} + 2457734 T^{9} + 19588870 T^{10} + 38618058 T^{11} + 148035889 T^{12} \))(\( ( 1 - 6 T + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 + 2 T + 23 T^{2} )^{2} \))(\( ( 1 + 8 T + 23 T^{2} )^{2} \))(\( ( 1 - 3 T + 23 T^{2} )^{2} \))(\( ( 1 + 3 T + 23 T^{2} )^{2} \))(\( ( 1 - 7 T + 23 T^{2} )^{2} \))(\( ( 1 - T + 23 T^{2} )^{2} \))(\( ( 1 + 5 T + 23 T^{2} )^{2} \))(\( ( 1 - 7 T + 23 T^{2} )^{2} \))(\( ( 1 + 6 T + 52 T^{2} + 138 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 + 10 T + 59 T^{2} + 230 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 - 14 T + 125 T^{2} - 700 T^{3} + 2875 T^{4} - 7406 T^{5} + 12167 T^{6} )^{2} \))(\( ( 1 - 7 T + 69 T^{2} - 273 T^{3} + 1587 T^{4} - 3703 T^{5} + 12167 T^{6} )^{2} \))(\( ( 1 + 3 T + 65 T^{2} + 125 T^{3} + 1495 T^{4} + 1587 T^{5} + 12167 T^{6} )^{2} \))(\( ( 1 + T + 53 T^{2} + 59 T^{3} + 1219 T^{4} + 529 T^{5} + 12167 T^{6} )^{2} \))(\( ( 1 + 21 T + 244 T^{2} + 1974 T^{3} + 13037 T^{4} + 74557 T^{5} + 380660 T^{6} + 1714811 T^{7} + 6896573 T^{8} + 24017658 T^{9} + 68281204 T^{10} + 135163203 T^{11} + 148035889 T^{12} )^{2} \))(\( ( 1 - 6 T + 70 T^{2} - 202 T^{3} + 1572 T^{4} - 782 T^{5} + 25728 T^{6} - 17986 T^{7} + 831588 T^{8} - 2457734 T^{9} + 19588870 T^{10} - 38618058 T^{11} + 148035889 T^{12} )^{2} \))
$29$ (\( 1 - 3 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 3 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 8 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 4 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( ( 1 + 3 T + 29 T^{2} )^{2} \))(\( 1 - 4 T + 14 T^{2} - 116 T^{3} + 841 T^{4} \))(\( ( 1 + 3 T + 29 T^{2} )^{2} \))(\( 1 - 4 T + 14 T^{2} - 116 T^{3} + 841 T^{4} \))(\( 1 - 2 T + 79 T^{2} - 108 T^{3} + 2291 T^{4} - 1682 T^{5} + 24389 T^{6} \))(\( 1 + 3 T + 41 T^{2} + 175 T^{3} + 1189 T^{4} + 2523 T^{5} + 24389 T^{6} \))(\( 1 - 5 T - 5 T^{2} + 87 T^{3} - 145 T^{4} - 4205 T^{5} + 24389 T^{6} \))(\( 1 - 8 T + 67 T^{2} - 288 T^{3} + 1943 T^{4} - 6728 T^{5} + 24389 T^{6} \))(\( 1 - 5 T + 65 T^{2} - 193 T^{3} + 1885 T^{4} - 4205 T^{5} + 24389 T^{6} \))(\( 1 - 2 T + 79 T^{2} - 108 T^{3} + 2291 T^{4} - 1682 T^{5} + 24389 T^{6} \))(\( 1 + 3 T + 41 T^{2} + 175 T^{3} + 1189 T^{4} + 2523 T^{5} + 24389 T^{6} \))(\( 1 - 5 T - 5 T^{2} + 87 T^{3} - 145 T^{4} - 4205 T^{5} + 24389 T^{6} \))(\( 1 - 8 T + 67 T^{2} - 288 T^{3} + 1943 T^{4} - 6728 T^{5} + 24389 T^{6} \))(\( 1 - 5 T + 65 T^{2} - 193 T^{3} + 1885 T^{4} - 4205 T^{5} + 24389 T^{6} \))(\( 1 + T + 60 T^{2} - 38 T^{3} + 1813 T^{4} - 5663 T^{5} + 52956 T^{6} - 164227 T^{7} + 1524733 T^{8} - 926782 T^{9} + 42436860 T^{10} + 20511149 T^{11} + 594823321 T^{12} \))(\( 1 - 10 T + 135 T^{2} - 898 T^{3} + 7715 T^{4} - 39852 T^{5} + 268810 T^{6} - 1155708 T^{7} + 6488315 T^{8} - 21901322 T^{9} + 95482935 T^{10} - 205111490 T^{11} + 594823321 T^{12} \))(\( 1 + T + 60 T^{2} - 38 T^{3} + 1813 T^{4} - 5663 T^{5} + 52956 T^{6} - 164227 T^{7} + 1524733 T^{8} - 926782 T^{9} + 42436860 T^{10} + 20511149 T^{11} + 594823321 T^{12} \))(\( 1 - 10 T + 135 T^{2} - 898 T^{3} + 7715 T^{4} - 39852 T^{5} + 268810 T^{6} - 1155708 T^{7} + 6488315 T^{8} - 21901322 T^{9} + 95482935 T^{10} - 205111490 T^{11} + 594823321 T^{12} \))(\( ( 1 - 3 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 5 T + 29 T^{2} )^{2} \))(\( ( 1 + 10 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 8 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 4 T + 29 T^{2} )^{2} \))(\( ( 1 + 4 T + 29 T^{2} )^{2} \))(\( ( 1 + 3 T + 29 T^{2} )^{4} \))(\( ( 1 - 4 T + 14 T^{2} - 116 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 - 2 T + 79 T^{2} - 108 T^{3} + 2291 T^{4} - 1682 T^{5} + 24389 T^{6} )^{2} \))(\( ( 1 + 3 T + 41 T^{2} + 175 T^{3} + 1189 T^{4} + 2523 T^{5} + 24389 T^{6} )^{2} \))(\( ( 1 - 5 T - 5 T^{2} + 87 T^{3} - 145 T^{4} - 4205 T^{5} + 24389 T^{6} )^{2} \))(\( ( 1 - 5 T + 65 T^{2} - 193 T^{3} + 1885 T^{4} - 4205 T^{5} + 24389 T^{6} )^{2} \))(\( ( 1 + T + 60 T^{2} - 38 T^{3} + 1813 T^{4} - 5663 T^{5} + 52956 T^{6} - 164227 T^{7} + 1524733 T^{8} - 926782 T^{9} + 42436860 T^{10} + 20511149 T^{11} + 594823321 T^{12} )^{2} \))(\( ( 1 - 10 T + 135 T^{2} - 898 T^{3} + 7715 T^{4} - 39852 T^{5} + 268810 T^{6} - 1155708 T^{7} + 6488315 T^{8} - 21901322 T^{9} + 95482935 T^{10} - 205111490 T^{11} + 594823321 T^{12} )^{2} \))
$31$ (\( 1 + 10 T + 31 T^{2} \))(\( 1 - 6 T + 31 T^{2} \))(\( 1 - 5 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 + 7 T + 31 T^{2} \))(\( 1 + 6 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 + 3 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))(\( 1 + T + 31 T^{2} \))(\( 1 + 10 T + 31 T^{2} \))(\( 1 + 14 T + 108 T^{2} + 434 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 66 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 - 14 T + 108 T^{2} - 434 T^{3} + 961 T^{4} \))(\( 1 - 8 T + 66 T^{2} - 248 T^{3} + 961 T^{4} \))(\( 1 - 14 T + 149 T^{2} - 924 T^{3} + 4619 T^{4} - 13454 T^{5} + 29791 T^{6} \))(\( 1 - 2 T + 64 T^{2} - 53 T^{3} + 1984 T^{4} - 1922 T^{5} + 29791 T^{6} \))(\( 1 - 24 T + 278 T^{2} - 1951 T^{3} + 8618 T^{4} - 23064 T^{5} + 29791 T^{6} \))(\( 1 - 7 T + 85 T^{2} - 346 T^{3} + 2635 T^{4} - 6727 T^{5} + 29791 T^{6} \))(\( 1 + 4 T + 54 T^{2} + 289 T^{3} + 1674 T^{4} + 3844 T^{5} + 29791 T^{6} \))(\( 1 + 14 T + 149 T^{2} + 924 T^{3} + 4619 T^{4} + 13454 T^{5} + 29791 T^{6} \))(\( 1 + 2 T + 64 T^{2} + 53 T^{3} + 1984 T^{4} + 1922 T^{5} + 29791 T^{6} \))(\( 1 + 24 T + 278 T^{2} + 1951 T^{3} + 8618 T^{4} + 23064 T^{5} + 29791 T^{6} \))(\( 1 + 7 T + 85 T^{2} + 346 T^{3} + 2635 T^{4} + 6727 T^{5} + 29791 T^{6} \))(\( 1 - 4 T + 54 T^{2} - 289 T^{3} + 1674 T^{4} - 3844 T^{5} + 29791 T^{6} \))(\( 1 + 20 T + 321 T^{2} + 3425 T^{3} + 31041 T^{4} + 220905 T^{5} + 1365586 T^{6} + 6848055 T^{7} + 29830401 T^{8} + 102034175 T^{9} + 296450241 T^{10} + 572583020 T^{11} + 887503681 T^{12} \))(\( 1 - 2 T + 144 T^{2} - 358 T^{3} + 9287 T^{4} - 23652 T^{5} + 358576 T^{6} - 733212 T^{7} + 8924807 T^{8} - 10665178 T^{9} + 132987024 T^{10} - 57258302 T^{11} + 887503681 T^{12} \))(\( 1 - 20 T + 321 T^{2} - 3425 T^{3} + 31041 T^{4} - 220905 T^{5} + 1365586 T^{6} - 6848055 T^{7} + 29830401 T^{8} - 102034175 T^{9} + 296450241 T^{10} - 572583020 T^{11} + 887503681 T^{12} \))(\( 1 + 2 T + 144 T^{2} + 358 T^{3} + 9287 T^{4} + 23652 T^{5} + 358576 T^{6} + 733212 T^{7} + 8924807 T^{8} + 10665178 T^{9} + 132987024 T^{10} + 57258302 T^{11} + 887503681 T^{12} \))(\( 1 + 38 T^{2} + 961 T^{4} \))(\( 1 - 46 T^{2} + 961 T^{4} \))(\( 1 - 26 T^{2} + 961 T^{4} \))(\( 1 + 2 T^{2} + 961 T^{4} \))(\( 1 - 37 T^{2} + 961 T^{4} \))(\( 1 + 38 T^{2} + 961 T^{4} \))(\( 1 - 53 T^{2} + 961 T^{4} \))(\( 1 + 38 T^{2} + 961 T^{4} \))(\( 1 - 61 T^{2} + 961 T^{4} \))(\( 1 - 13 T^{2} + 961 T^{4} \))(\( 1 - 20 T^{2} + 1434 T^{4} - 19220 T^{6} + 923521 T^{8} \))(\( 1 - 68 T^{2} + 2310 T^{4} - 65348 T^{6} + 923521 T^{8} \))(\( 1 - 102 T^{2} + 5567 T^{4} - 205556 T^{6} + 5349887 T^{8} - 94199142 T^{10} + 887503681 T^{12} \))(\( 1 - 124 T^{2} + 7852 T^{4} - 303037 T^{6} + 7545772 T^{8} - 114516604 T^{10} + 887503681 T^{12} \))(\( 1 + 20 T^{2} + 872 T^{4} + 62283 T^{6} + 837992 T^{8} + 18470420 T^{10} + 887503681 T^{12} \))(\( 1 - 92 T^{2} + 3952 T^{4} - 126101 T^{6} + 3797872 T^{8} - 84963932 T^{10} + 887503681 T^{12} \))(\( 1 - 242 T^{2} + 28123 T^{4} - 2092669 T^{6} + 112789245 T^{8} - 4732765201 T^{10} + 161475541262 T^{12} - 4548187358161 T^{14} + 104163236331645 T^{16} - 1857251440614589 T^{18} + 23985854645953243 T^{20} - 198350045449353842 T^{22} + 787662783788549761 T^{24} \))(\( 1 - 284 T^{2} + 37878 T^{4} - 3169036 T^{6} + 187500191 T^{8} - 8369451480 T^{10} + 291872222164 T^{12} - 8043042872280 T^{14} + 173160363892511 T^{16} - 2812531115221516 T^{18} + 32305806716190198 T^{20} - 232774433502547484 T^{22} + 787662783788549761 T^{24} \))
$37$ (\( 1 + T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 - 3 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 - 8 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 + 9 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - T + 37 T^{2} \))(\( 1 + 3 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 + 8 T + 37 T^{2} \))(\( 1 + 7 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 47 T^{2} + 1369 T^{4} \))(\( 1 - 12 T + 98 T^{2} - 444 T^{3} + 1369 T^{4} \))(\( 1 + 47 T^{2} + 1369 T^{4} \))(\( 1 + 12 T + 98 T^{2} + 444 T^{3} + 1369 T^{4} \))(\( 1 - 8 T + 123 T^{2} - 584 T^{3} + 4551 T^{4} - 10952 T^{5} + 50653 T^{6} \))(\( 1 + 90 T^{2} + 7 T^{3} + 3330 T^{4} + 50653 T^{6} \))(\( 1 + 4 T + 72 T^{2} + 337 T^{3} + 2664 T^{4} + 5476 T^{5} + 50653 T^{6} \))(\( 1 + 9 T + 119 T^{2} + 622 T^{3} + 4403 T^{4} + 12321 T^{5} + 50653 T^{6} \))(\( 1 + 28 T + 370 T^{2} + 2863 T^{3} + 13690 T^{4} + 38332 T^{5} + 50653 T^{6} \))(\( 1 + 8 T + 123 T^{2} + 584 T^{3} + 4551 T^{4} + 10952 T^{5} + 50653 T^{6} \))(\( 1 + 90 T^{2} - 7 T^{3} + 3330 T^{4} + 50653 T^{6} \))(\( 1 - 4 T + 72 T^{2} - 337 T^{3} + 2664 T^{4} - 5476 T^{5} + 50653 T^{6} \))(\( 1 - 9 T + 119 T^{2} - 622 T^{3} + 4403 T^{4} - 12321 T^{5} + 50653 T^{6} \))(\( 1 - 28 T + 370 T^{2} - 2863 T^{3} + 13690 T^{4} - 38332 T^{5} + 50653 T^{6} \))(\( 1 + 16 T + 179 T^{2} + 1601 T^{3} + 12575 T^{4} + 87987 T^{5} + 557826 T^{6} + 3255519 T^{7} + 17215175 T^{8} + 81095453 T^{9} + 335474819 T^{10} + 1109503312 T^{11} + 2565726409 T^{12} \))(\( 1 + 67 T^{2} + 8 T^{3} + 3347 T^{4} + 280 T^{5} + 165506 T^{6} + 10360 T^{7} + 4582043 T^{8} + 405224 T^{9} + 125568787 T^{10} + 2565726409 T^{12} \))(\( 1 - 16 T + 179 T^{2} - 1601 T^{3} + 12575 T^{4} - 87987 T^{5} + 557826 T^{6} - 3255519 T^{7} + 17215175 T^{8} - 81095453 T^{9} + 335474819 T^{10} - 1109503312 T^{11} + 2565726409 T^{12} \))(\( 1 + 67 T^{2} - 8 T^{3} + 3347 T^{4} - 280 T^{5} + 165506 T^{6} - 10360 T^{7} + 4582043 T^{8} - 405224 T^{9} + 125568787 T^{10} + 2565726409 T^{12} \))(\( 1 - 73 T^{2} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( 1 - 25 T^{2} + 1369 T^{4} \))(\( 1 - 38 T^{2} + 1369 T^{4} \))(\( 1 - 25 T^{2} + 1369 T^{4} \))(\( 1 - 10 T^{2} + 1369 T^{4} \))(\( 1 - 25 T^{2} + 1369 T^{4} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 - 25 T^{2} + 1369 T^{4} \))(\( 1 + 7 T^{2} + 1369 T^{4} \))(\( ( 1 - 11 T + 37 T^{2} )^{2}( 1 + 11 T + 37 T^{2} )^{2} \))(\( 1 - 52 T^{2} + 1686 T^{4} - 71188 T^{6} + 1874161 T^{8} \))(\( 1 - 182 T^{2} + 14887 T^{4} - 704564 T^{6} + 20380303 T^{8} - 341097302 T^{10} + 2565726409 T^{12} \))(\( 1 - 180 T^{2} + 14760 T^{4} - 700657 T^{6} + 20206440 T^{8} - 337348980 T^{10} + 2565726409 T^{12} \))(\( 1 - 128 T^{2} + 7816 T^{4} - 327545 T^{6} + 10700104 T^{8} - 239892608 T^{10} + 2565726409 T^{12} \))(\( 1 + 44 T^{2} + 3952 T^{4} + 111455 T^{6} + 5410288 T^{8} + 82463084 T^{10} + 2565726409 T^{12} \))(\( 1 - 102 T^{2} + 5959 T^{4} - 238717 T^{6} + 6351701 T^{8} - 102367685 T^{10} + 1304488550 T^{12} - 140141360765 T^{14} + 11904110297861 T^{16} - 612482511177253 T^{18} + 20930865065915239 T^{20} - 490475605986620598 T^{22} + 6582952005840035281 T^{24} \))(\( 1 - 134 T^{2} + 11183 T^{4} - 779446 T^{6} + 42539819 T^{8} - 1972784340 T^{10} + 80009816970 T^{12} - 2700741761460 T^{14} + 79726469716859 T^{16} - 1999845186589414 T^{18} + 39280057733198543 T^{20} - 644350305903991766 T^{22} + 6582952005840035281 T^{24} \))
$41$ (\( 1 + 3 T + 41 T^{2} \))(\( 1 + 7 T + 41 T^{2} \))(\( 1 - 5 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 3 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 12 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 3 T + 41 T^{2} \))(\( 1 + 5 T + 41 T^{2} \))(\( 1 - 7 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 9 T + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))(\( 1 + 2 T + 71 T^{2} + 82 T^{3} + 1681 T^{4} \))(\( 1 + 12 T + 106 T^{2} + 492 T^{3} + 1681 T^{4} \))(\( 1 - 2 T + 71 T^{2} - 82 T^{3} + 1681 T^{4} \))(\( 1 - 12 T + 106 T^{2} - 492 T^{3} + 1681 T^{4} \))(\( 1 - 9 T + 59 T^{2} - 205 T^{3} + 2419 T^{4} - 15129 T^{5} + 68921 T^{6} \))(\( 1 - 7 T + 25 T^{2} - 231 T^{3} + 1025 T^{4} - 11767 T^{5} + 68921 T^{6} \))(\( 1 + 3 T + 77 T^{2} + 289 T^{3} + 3157 T^{4} + 5043 T^{5} + 68921 T^{6} \))(\( 1 - 15 T + 179 T^{2} - 1274 T^{3} + 7339 T^{4} - 25215 T^{5} + 68921 T^{6} \))(\( 1 + 13 T + 149 T^{2} + 1067 T^{3} + 6109 T^{4} + 21853 T^{5} + 68921 T^{6} \))(\( 1 + 9 T + 59 T^{2} + 205 T^{3} + 2419 T^{4} + 15129 T^{5} + 68921 T^{6} \))(\( 1 + 7 T + 25 T^{2} + 231 T^{3} + 1025 T^{4} + 11767 T^{5} + 68921 T^{6} \))(\( 1 - 3 T + 77 T^{2} - 289 T^{3} + 3157 T^{4} - 5043 T^{5} + 68921 T^{6} \))(\( 1 + 15 T + 179 T^{2} + 1274 T^{3} + 7339 T^{4} + 25215 T^{5} + 68921 T^{6} \))(\( 1 - 13 T + 149 T^{2} - 1067 T^{3} + 6109 T^{4} - 21853 T^{5} + 68921 T^{6} \))(\( 1 + 2 T + 77 T^{2} - 18 T^{3} + 4625 T^{4} + 618 T^{5} + 215007 T^{6} + 25338 T^{7} + 7774625 T^{8} - 1240578 T^{9} + 217583597 T^{10} + 231712402 T^{11} + 4750104241 T^{12} \))(\( 1 + 6 T + 151 T^{2} + 878 T^{3} + 11883 T^{4} + 57724 T^{5} + 604554 T^{6} + 2366684 T^{7} + 19975323 T^{8} + 60512638 T^{9} + 426689911 T^{10} + 695137206 T^{11} + 4750104241 T^{12} \))(\( 1 - 2 T + 77 T^{2} + 18 T^{3} + 4625 T^{4} - 618 T^{5} + 215007 T^{6} - 25338 T^{7} + 7774625 T^{8} + 1240578 T^{9} + 217583597 T^{10} - 231712402 T^{11} + 4750104241 T^{12} \))(\( 1 - 6 T + 151 T^{2} - 878 T^{3} + 11883 T^{4} - 57724 T^{5} + 604554 T^{6} - 2366684 T^{7} + 19975323 T^{8} - 60512638 T^{9} + 426689911 T^{10} - 695137206 T^{11} + 4750104241 T^{12} \))(\( 1 - 73 T^{2} + 1681 T^{4} \))(\( 1 - 46 T^{2} + 1681 T^{4} \))(\( 1 - 33 T^{2} + 1681 T^{4} \))(\( 1 - 46 T^{2} + 1681 T^{4} \))(\( 1 - 73 T^{2} + 1681 T^{4} \))(\( ( 1 - 41 T^{2} )^{2} \))(\( 1 - 33 T^{2} + 1681 T^{4} \))(\( 1 + 62 T^{2} + 1681 T^{4} \))(\( 1 - T^{2} + 1681 T^{4} \))(\( 1 - 73 T^{2} + 1681 T^{4} \))(\( 1 - 138 T^{2} + 8075 T^{4} - 231978 T^{6} + 2825761 T^{8} \))(\( 1 - 68 T^{2} + 2790 T^{4} - 114308 T^{6} + 2825761 T^{8} \))(\( 1 - 37 T^{2} + 4629 T^{4} - 108937 T^{6} + 7781349 T^{8} - 104553157 T^{10} + 4750104241 T^{12} \))(\( 1 - T^{2} - 559 T^{4} + 29007 T^{6} - 939679 T^{8} - 2825761 T^{10} + 4750104241 T^{12} \))(\( 1 - 145 T^{2} + 10509 T^{4} - 510241 T^{6} + 17665629 T^{8} - 409735345 T^{10} + 4750104241 T^{12} \))(\( 1 - 129 T^{2} + 6677 T^{4} - 251657 T^{6} + 11224037 T^{8} - 364523169 T^{10} + 4750104241 T^{12} \))(\( 1 - 150 T^{2} + 15251 T^{4} - 1139468 T^{6} + 69971849 T^{8} - 3626766750 T^{10} + 160148545535 T^{12} - 6096594906750 T^{14} + 197723722002089 T^{16} - 5412591779283788 T^{18} + 121778094669324371 T^{20} - 2013398896522860150 T^{22} + 22563490300366186081 T^{24} \))(\( 1 - 266 T^{2} + 36031 T^{4} - 3334202 T^{6} + 233968091 T^{8} - 13039648796 T^{10} + 590748853706 T^{12} - 21919649626076 T^{14} + 661137906792251 T^{16} - 15837807060550682 T^{18} + 287704840930458751 T^{20} - 3570427376500538666 T^{22} + 22563490300366186081 T^{24} \))
$43$ (\( 1 + 10 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 12 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 14 T + 108 T^{2} + 602 T^{3} + 1849 T^{4} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( 1 + 14 T + 108 T^{2} + 602 T^{3} + 1849 T^{4} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( 1 - 19 T + 219 T^{2} - 1663 T^{3} + 9417 T^{4} - 35131 T^{5} + 79507 T^{6} \))(\( 1 + 17 T + 209 T^{2} + 1533 T^{3} + 8987 T^{4} + 31433 T^{5} + 79507 T^{6} \))(\( 1 + 9 T + 149 T^{2} + 787 T^{3} + 6407 T^{4} + 16641 T^{5} + 79507 T^{6} \))(\( 1 + 8 T + 105 T^{2} + 560 T^{3} + 4515 T^{4} + 14792 T^{5} + 79507 T^{6} \))(\( 1 + T + 85 T^{2} + 169 T^{3} + 3655 T^{4} + 1849 T^{5} + 79507 T^{6} \))(\( 1 - 19 T + 219 T^{2} - 1663 T^{3} + 9417 T^{4} - 35131 T^{5} + 79507 T^{6} \))(\( 1 + 17 T + 209 T^{2} + 1533 T^{3} + 8987 T^{4} + 31433 T^{5} + 79507 T^{6} \))(\( 1 + 9 T + 149 T^{2} + 787 T^{3} + 6407 T^{4} + 16641 T^{5} + 79507 T^{6} \))(\( 1 + 8 T + 105 T^{2} + 560 T^{3} + 4515 T^{4} + 14792 T^{5} + 79507 T^{6} \))(\( 1 + T + 85 T^{2} + 169 T^{3} + 3655 T^{4} + 1849 T^{5} + 79507 T^{6} \))(\( 1 - 2 T + 25 T^{2} - 136 T^{3} + 5603 T^{4} - 9604 T^{5} + 92961 T^{6} - 412972 T^{7} + 10359947 T^{8} - 10812952 T^{9} + 85470025 T^{10} - 294016886 T^{11} + 6321363049 T^{12} \))(\( 1 - 26 T + 472 T^{2} - 5942 T^{3} + 61823 T^{4} - 518084 T^{5} + 3733280 T^{6} - 22277612 T^{7} + 114310727 T^{8} - 472430594 T^{9} + 1613674072 T^{10} - 3822219518 T^{11} + 6321363049 T^{12} \))(\( 1 - 2 T + 25 T^{2} - 136 T^{3} + 5603 T^{4} - 9604 T^{5} + 92961 T^{6} - 412972 T^{7} + 10359947 T^{8} - 10812952 T^{9} + 85470025 T^{10} - 294016886 T^{11} + 6321363049 T^{12} \))(\( 1 - 26 T + 472 T^{2} - 5942 T^{3} + 61823 T^{4} - 518084 T^{5} + 3733280 T^{6} - 22277612 T^{7} + 114310727 T^{8} - 472430594 T^{9} + 1613674072 T^{10} - 3822219518 T^{11} + 6321363049 T^{12} \))(\( ( 1 - 10 T + 43 T^{2} )^{2} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( ( 1 - 2 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( ( 1 - 8 T + 43 T^{2} )^{2} \))(\( ( 1 + 43 T^{2} )^{2} \))(\( ( 1 - 12 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 14 T + 108 T^{2} - 602 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{4} \))(\( ( 1 + 19 T + 219 T^{2} + 1663 T^{3} + 9417 T^{4} + 35131 T^{5} + 79507 T^{6} )^{2} \))(\( ( 1 - 17 T + 209 T^{2} - 1533 T^{3} + 8987 T^{4} - 31433 T^{5} + 79507 T^{6} )^{2} \))(\( ( 1 - 9 T + 149 T^{2} - 787 T^{3} + 6407 T^{4} - 16641 T^{5} + 79507 T^{6} )^{2} \))(\( ( 1 - T + 85 T^{2} - 169 T^{3} + 3655 T^{4} - 1849 T^{5} + 79507 T^{6} )^{2} \))(\( ( 1 + 2 T + 25 T^{2} + 136 T^{3} + 5603 T^{4} + 9604 T^{5} + 92961 T^{6} + 412972 T^{7} + 10359947 T^{8} + 10812952 T^{9} + 85470025 T^{10} + 294016886 T^{11} + 6321363049 T^{12} )^{2} \))(\( ( 1 + 26 T + 472 T^{2} + 5942 T^{3} + 61823 T^{4} + 518084 T^{5} + 3733280 T^{6} + 22277612 T^{7} + 114310727 T^{8} + 472430594 T^{9} + 1613674072 T^{10} + 3822219518 T^{11} + 6321363049 T^{12} )^{2} \))
$47$ (\( 1 + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 13 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 10 T + 47 T^{2} \))(\( 1 + 7 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 13 T + 47 T^{2} \))(\( 1 + 3 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 7 T + 47 T^{2} \))(\( 1 - 10 T + 47 T^{2} \))(\( 1 - 8 T + 62 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 - 4 T + 50 T^{2} - 188 T^{3} + 2209 T^{4} \))(\( 1 + 8 T + 62 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 + 4 T + 50 T^{2} + 188 T^{3} + 2209 T^{4} \))(\( 1 + 14 T + 169 T^{2} + 1260 T^{3} + 7943 T^{4} + 30926 T^{5} + 103823 T^{6} \))(\( 1 + 5 T + 77 T^{2} + 499 T^{3} + 3619 T^{4} + 11045 T^{5} + 103823 T^{6} \))(\( 1 - 17 T + 235 T^{2} - 1767 T^{3} + 11045 T^{4} - 37553 T^{5} + 103823 T^{6} \))(\( 1 + 17 T + 213 T^{2} + 1686 T^{3} + 10011 T^{4} + 37553 T^{5} + 103823 T^{6} \))(\( 1 + 7 T + 43 T^{2} + 21 T^{3} + 2021 T^{4} + 15463 T^{5} + 103823 T^{6} \))(\( 1 - 14 T + 169 T^{2} - 1260 T^{3} + 7943 T^{4} - 30926 T^{5} + 103823 T^{6} \))(\( 1 - 5 T + 77 T^{2} - 499 T^{3} + 3619 T^{4} - 11045 T^{5} + 103823 T^{6} \))(\( 1 + 17 T + 235 T^{2} + 1767 T^{3} + 11045 T^{4} + 37553 T^{5} + 103823 T^{6} \))(\( 1 - 17 T + 213 T^{2} - 1686 T^{3} + 10011 T^{4} - 37553 T^{5} + 103823 T^{6} \))(\( 1 - 7 T + 43 T^{2} - 21 T^{3} + 2021 T^{4} - 15463 T^{5} + 103823 T^{6} \))(\( 1 - 5 T + 164 T^{2} - 954 T^{3} + 15413 T^{4} - 75645 T^{5} + 908724 T^{6} - 3555315 T^{7} + 34047317 T^{8} - 99047142 T^{9} + 800267684 T^{10} - 1146725035 T^{11} + 10779215329 T^{12} \))(\( 1 - 8 T + 178 T^{2} - 792 T^{3} + 11679 T^{4} - 26000 T^{5} + 524700 T^{6} - 1222000 T^{7} + 25798911 T^{8} - 82227816 T^{9} + 868583218 T^{10} - 1834760056 T^{11} + 10779215329 T^{12} \))(\( 1 + 5 T + 164 T^{2} + 954 T^{3} + 15413 T^{4} + 75645 T^{5} + 908724 T^{6} + 3555315 T^{7} + 34047317 T^{8} + 99047142 T^{9} + 800267684 T^{10} + 1146725035 T^{11} + 10779215329 T^{12} \))(\( 1 + 8 T + 178 T^{2} + 792 T^{3} + 11679 T^{4} + 26000 T^{5} + 524700 T^{6} + 1222000 T^{7} + 25798911 T^{8} + 82227816 T^{9} + 868583218 T^{10} + 1834760056 T^{11} + 10779215329 T^{12} \))(\( ( 1 - 47 T^{2} )^{2} \))(\( 1 + 50 T^{2} + 2209 T^{4} \))(\( ( 1 - 47 T^{2} )^{2} \))(\( 1 - 30 T^{2} + 2209 T^{4} \))(\( 1 - 85 T^{2} + 2209 T^{4} \))(\( 1 - 58 T^{2} + 2209 T^{4} \))(\( 1 - 85 T^{2} + 2209 T^{4} \))(\( 1 + 6 T^{2} + 2209 T^{4} \))(\( 1 - 45 T^{2} + 2209 T^{4} \))(\( 1 - 45 T^{2} + 2209 T^{4} \))(\( 1 - 60 T^{2} + 2246 T^{4} - 132540 T^{6} + 4879681 T^{8} \))(\( 1 - 84 T^{2} + 5414 T^{4} - 185556 T^{6} + 4879681 T^{8} \))(\( 1 - 142 T^{2} + 9167 T^{4} - 438852 T^{6} + 20249903 T^{8} - 692914702 T^{10} + 10779215329 T^{12} \))(\( 1 - 129 T^{2} + 8177 T^{4} - 405521 T^{6} + 18062993 T^{8} - 629478849 T^{10} + 10779215329 T^{12} \))(\( 1 - 181 T^{2} + 17237 T^{4} - 999705 T^{6} + 38076533 T^{8} - 883222261 T^{10} + 10779215329 T^{12} \))(\( 1 - 37 T^{2} + 5597 T^{4} - 164529 T^{6} + 12363773 T^{8} - 180548197 T^{10} + 10779215329 T^{12} \))(\( 1 - 303 T^{2} + 48182 T^{4} - 5206346 T^{6} + 423832865 T^{8} - 27284202903 T^{10} + 1421035329392 T^{12} - 60270804212727 T^{14} + 2068169178516065 T^{16} - 56120324611277834 T^{18} + 1147275413936968502 T^{20} - 15937537067456504847 T^{22} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 - 292 T^{2} + 42370 T^{4} - 4163860 T^{6} + 314054063 T^{8} - 19250228296 T^{10} + 985546087964 T^{12} - 42523754305864 T^{14} + 1532483644193903 T^{16} - 44883143539809940 T^{18} + 1008884215858813570 T^{20} - 15358946612862374308 T^{22} + \)\(11\!\cdots\!41\)\( T^{24} \))
$53$ (\( 1 + 9 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - 14 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 9 T + 53 T^{2} \))(\( 1 - 14 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))(\( 1 - 10 T + 119 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 + 58 T^{2} + 2809 T^{4} \))(\( 1 - 10 T + 119 T^{2} - 530 T^{3} + 2809 T^{4} \))(\( 1 + 58 T^{2} + 2809 T^{4} \))(\( 1 + 14 T + 215 T^{2} + 1540 T^{3} + 11395 T^{4} + 39326 T^{5} + 148877 T^{6} \))(\( 1 + 110 T^{2} + 91 T^{3} + 5830 T^{4} + 148877 T^{6} \))(\( 1 + 10 T + 176 T^{2} + 1019 T^{3} + 9328 T^{4} + 28090 T^{5} + 148877 T^{6} \))(\( ( 1 + 6 T + 53 T^{2} )^{3} \))(\( 1 + 12 T + 186 T^{2} + 1259 T^{3} + 9858 T^{4} + 33708 T^{5} + 148877 T^{6} \))(\( 1 + 14 T + 215 T^{2} + 1540 T^{3} + 11395 T^{4} + 39326 T^{5} + 148877 T^{6} \))(\( 1 + 110 T^{2} + 91 T^{3} + 5830 T^{4} + 148877 T^{6} \))(\( 1 + 10 T + 176 T^{2} + 1019 T^{3} + 9328 T^{4} + 28090 T^{5} + 148877 T^{6} \))(\( ( 1 + 6 T + 53 T^{2} )^{3} \))(\( 1 + 12 T + 186 T^{2} + 1259 T^{3} + 9858 T^{4} + 33708 T^{5} + 148877 T^{6} \))(\( 1 - 28 T + 551 T^{2} - 7735 T^{3} + 88485 T^{4} - 826301 T^{5} + 6574358 T^{6} - 43793953 T^{7} + 248554365 T^{8} - 1151563595 T^{9} + 4347655031 T^{10} - 11709473804 T^{11} + 22164361129 T^{12} \))(\( 1 - 18 T + 267 T^{2} - 3114 T^{3} + 31467 T^{4} - 273420 T^{5} + 2178178 T^{6} - 14491260 T^{7} + 88390803 T^{8} - 463602978 T^{9} + 2106758427 T^{10} - 7527518874 T^{11} + 22164361129 T^{12} \))(\( 1 - 28 T + 551 T^{2} - 7735 T^{3} + 88485 T^{4} - 826301 T^{5} + 6574358 T^{6} - 43793953 T^{7} + 248554365 T^{8} - 1151563595 T^{9} + 4347655031 T^{10} - 11709473804 T^{11} + 22164361129 T^{12} \))(\( 1 - 18 T + 267 T^{2} - 3114 T^{3} + 31467 T^{4} - 273420 T^{5} + 2178178 T^{6} - 14491260 T^{7} + 88390803 T^{8} - 463602978 T^{9} + 2106758427 T^{10} - 7527518874 T^{11} + 22164361129 T^{12} \))(\( ( 1 + 9 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 9 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 + 12 T + 53 T^{2} )^{2} \))(\( ( 1 - 12 T + 53 T^{2} )^{2} \))(\( ( 1 + 53 T^{2} )^{2} \))(\( ( 1 + 4 T + 53 T^{2} )^{2} \))(\( ( 1 + 4 T + 53 T^{2} )^{2} \))(\( ( 1 + 53 T^{2} )^{2} \))(\( ( 1 - 10 T + 119 T^{2} - 530 T^{3} + 2809 T^{4} )^{2} \))(\( ( 1 + 58 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 + 14 T + 215 T^{2} + 1540 T^{3} + 11395 T^{4} + 39326 T^{5} + 148877 T^{6} )^{2} \))(\( ( 1 + 110 T^{2} + 91 T^{3} + 5830 T^{4} + 148877 T^{6} )^{2} \))(\( ( 1 + 10 T + 176 T^{2} + 1019 T^{3} + 9328 T^{4} + 28090 T^{5} + 148877 T^{6} )^{2} \))(\( ( 1 + 12 T + 186 T^{2} + 1259 T^{3} + 9858 T^{4} + 33708 T^{5} + 148877 T^{6} )^{2} \))(\( ( 1 - 28 T + 551 T^{2} - 7735 T^{3} + 88485 T^{4} - 826301 T^{5} + 6574358 T^{6} - 43793953 T^{7} + 248554365 T^{8} - 1151563595 T^{9} + 4347655031 T^{10} - 11709473804 T^{11} + 22164361129 T^{12} )^{2} \))(\( ( 1 - 18 T + 267 T^{2} - 3114 T^{3} + 31467 T^{4} - 273420 T^{5} + 2178178 T^{6} - 14491260 T^{7} + 88390803 T^{8} - 463602978 T^{9} + 2106758427 T^{10} - 7527518874 T^{11} + 22164361129 T^{12} )^{2} \))
$59$ (\( 1 + 6 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 + 6 T + 59 T^{2} \))(\( 1 - 3 T + 59 T^{2} \))(\( 1 - 9 T + 59 T^{2} \))(\( 1 - 10 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 3 T + 59 T^{2} \))(\( 1 - 6 T + 59 T^{2} \))(\( 1 + 9 T + 59 T^{2} \))(\( 1 - 18 T + 196 T^{2} - 1062 T^{3} + 3481 T^{4} \))(\( 1 + 16 T + 155 T^{2} + 944 T^{3} + 3481 T^{4} \))(\( 1 + 18 T + 196 T^{2} + 1062 T^{3} + 3481 T^{4} \))(\( 1 - 16 T + 155 T^{2} - 944 T^{3} + 3481 T^{4} \))(\( 1 - 9 T - 13 T^{2} + 745 T^{3} - 767 T^{4} - 31329 T^{5} + 205379 T^{6} \))(\( 1 - 17 T + 271 T^{2} - 2175 T^{3} + 15989 T^{4} - 59177 T^{5} + 205379 T^{6} \))(\( 1 + 3 T + 131 T^{2} + 355 T^{3} + 7729 T^{4} + 10443 T^{5} + 205379 T^{6} \))(\( 1 + 10 T + 83 T^{2} + 296 T^{3} + 4897 T^{4} + 34810 T^{5} + 205379 T^{6} \))(\( 1 - 3 T + 117 T^{2} - 481 T^{3} + 6903 T^{4} - 10443 T^{5} + 205379 T^{6} \))(\( 1 + 9 T - 13 T^{2} - 745 T^{3} - 767 T^{4} + 31329 T^{5} + 205379 T^{6} \))(\( 1 + 17 T + 271 T^{2} + 2175 T^{3} + 15989 T^{4} + 59177 T^{5} + 205379 T^{6} \))(\( 1 - 3 T + 131 T^{2} - 355 T^{3} + 7729 T^{4} - 10443 T^{5} + 205379 T^{6} \))(\( 1 - 10 T + 83 T^{2} - 296 T^{3} + 4897 T^{4} - 34810 T^{5} + 205379 T^{6} \))(\( 1 + 3 T + 117 T^{2} + 481 T^{3} + 6903 T^{4} + 10443 T^{5} + 205379 T^{6} \))(\( 1 - 12 T + 243 T^{2} - 1492 T^{3} + 18371 T^{4} - 52238 T^{5} + 891263 T^{6} - 3082042 T^{7} + 63949451 T^{8} - 306425468 T^{9} + 2944518723 T^{10} - 8579091588 T^{11} + 42180533641 T^{12} \))(\( 1 + 2 T + 272 T^{2} + 506 T^{3} + 32980 T^{4} + 54774 T^{5} + 2408732 T^{6} + 3231666 T^{7} + 114803380 T^{8} + 103921774 T^{9} + 3295922192 T^{10} + 1429848598 T^{11} + 42180533641 T^{12} \))(\( 1 + 12 T + 243 T^{2} + 1492 T^{3} + 18371 T^{4} + 52238 T^{5} + 891263 T^{6} + 3082042 T^{7} + 63949451 T^{8} + 306425468 T^{9} + 2944518723 T^{10} + 8579091588 T^{11} + 42180533641 T^{12} \))(\( 1 - 2 T + 272 T^{2} - 506 T^{3} + 32980 T^{4} - 54774 T^{5} + 2408732 T^{6} - 3231666 T^{7} + 114803380 T^{8} - 103921774 T^{9} + 3295922192 T^{10} - 1429848598 T^{11} + 42180533641 T^{12} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 54 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 109 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 37 T^{2} + 3481 T^{4} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 18 T^{2} + 3481 T^{4} \))(\( 1 - 68 T^{2} + 7146 T^{4} - 236708 T^{6} + 12117361 T^{8} \))(\( 1 - 54 T^{2} + 779 T^{4} - 187974 T^{6} + 12117361 T^{8} \))(\( 1 + 107 T^{2} + 12045 T^{4} + 688247 T^{6} + 41928645 T^{8} + 1296557627 T^{10} + 42180533641 T^{12} \))(\( 1 - 253 T^{2} + 31469 T^{4} - 2334153 T^{6} + 109543589 T^{8} - 3065692333 T^{10} + 42180533641 T^{12} \))(\( 1 - 253 T^{2} + 30489 T^{4} - 2247073 T^{6} + 106132209 T^{8} - 3065692333 T^{10} + 42180533641 T^{12} \))(\( 1 - 225 T^{2} + 24609 T^{4} - 1732041 T^{6} + 85663929 T^{8} - 2726406225 T^{10} + 42180533641 T^{12} \))(\( 1 - 342 T^{2} + 59983 T^{4} - 7231056 T^{6} + 668699161 T^{8} - 50435422574 T^{10} + 3217106415855 T^{12} - 175565705980094 T^{14} + 8102869134234121 T^{16} - 305009800867954896 T^{18} + 8807330138819986543 T^{20} - \)\(17\!\cdots\!42\)\( T^{22} + \)\(17\!\cdots\!81\)\( T^{24} \))(\( 1 - 540 T^{2} + 137920 T^{4} - 22283452 T^{6} + 2559279416 T^{8} - 221238521660 T^{10} + 14786852755706 T^{12} - 770131293898460 T^{14} + 31011712583541176 T^{16} - 939927896723608732 T^{18} + 20250853954387952320 T^{20} - \)\(27\!\cdots\!40\)\( T^{22} + \)\(17\!\cdots\!81\)\( T^{24} \))
$61$ (\( 1 + 7 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 + 13 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + T + 61 T^{2} \))(\( 1 - 11 T + 61 T^{2} \))(\( 1 - 13 T + 61 T^{2} \))(\( 1 - T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 + 7 T + 61 T^{2} \))(\( 1 + 13 T + 61 T^{2} \))(\( 1 + 13 T + 61 T^{2} \))(\( 1 - 11 T + 61 T^{2} \))(\( 1 - 13 T + 61 T^{2} \))(\( 1 - 13 T + 61 T^{2} \))(\( 1 + 20 T + 219 T^{2} + 1220 T^{3} + 3721 T^{4} \))(\( 1 + 4 T + 99 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( 1 + 20 T + 219 T^{2} + 1220 T^{3} + 3721 T^{4} \))(\( 1 + 4 T + 99 T^{2} + 244 T^{3} + 3721 T^{4} \))(\( 1 + 4 T + 123 T^{2} + 256 T^{3} + 7503 T^{4} + 14884 T^{5} + 226981 T^{6} \))(\( 1 - 3 T + 137 T^{2} - 367 T^{3} + 8357 T^{4} - 11163 T^{5} + 226981 T^{6} \))(\( 1 + 5 T + 105 T^{2} + 779 T^{3} + 6405 T^{4} + 18605 T^{5} + 226981 T^{6} \))(\( 1 - 5 T + 181 T^{2} - 608 T^{3} + 11041 T^{4} - 18605 T^{5} + 226981 T^{6} \))(\( 1 + 3 T + 95 T^{2} + 479 T^{3} + 5795 T^{4} + 11163 T^{5} + 226981 T^{6} \))(\( 1 + 4 T + 123 T^{2} + 256 T^{3} + 7503 T^{4} + 14884 T^{5} + 226981 T^{6} \))(\( 1 - 3 T + 137 T^{2} - 367 T^{3} + 8357 T^{4} - 11163 T^{5} + 226981 T^{6} \))(\( 1 + 5 T + 105 T^{2} + 779 T^{3} + 6405 T^{4} + 18605 T^{5} + 226981 T^{6} \))(\( 1 - 5 T + 181 T^{2} - 608 T^{3} + 11041 T^{4} - 18605 T^{5} + 226981 T^{6} \))(\( 1 + 3 T + 95 T^{2} + 479 T^{3} + 5795 T^{4} + 11163 T^{5} + 226981 T^{6} \))(\( 1 + 27 T + 598 T^{2} + 8766 T^{3} + 111115 T^{4} + 1098335 T^{5} + 9564612 T^{6} + 66998435 T^{7} + 413458915 T^{8} + 1989715446 T^{9} + 8279812918 T^{10} + 22804100127 T^{11} + 51520374361 T^{12} \))(\( 1 - 28 T + 435 T^{2} - 3956 T^{3} + 18488 T^{4} + 18948 T^{5} - 811259 T^{6} + 1155828 T^{7} + 68793848 T^{8} - 897936836 T^{9} + 6022940835 T^{10} - 23648696428 T^{11} + 51520374361 T^{12} \))(\( 1 + 27 T + 598 T^{2} + 8766 T^{3} + 111115 T^{4} + 1098335 T^{5} + 9564612 T^{6} + 66998435 T^{7} + 413458915 T^{8} + 1989715446 T^{9} + 8279812918 T^{10} + 22804100127 T^{11} + 51520374361 T^{12} \))(\( 1 - 28 T + 435 T^{2} - 3956 T^{3} + 18488 T^{4} + 18948 T^{5} - 811259 T^{6} + 1155828 T^{7} + 68793848 T^{8} - 897936836 T^{9} + 6022940835 T^{10} - 23648696428 T^{11} + 51520374361 T^{12} \))(\( ( 1 + 7 T + 61 T^{2} )^{2} \))(\( ( 1 - 8 T + 61 T^{2} )^{2} \))(\( ( 1 - 5 T + 61 T^{2} )^{2} \))(\( ( 1 - 10 T + 61 T^{2} )^{2} \))(\( ( 1 + T + 61 T^{2} )^{2} \))(\( ( 1 - 11 T + 61 T^{2} )^{2} \))(\( ( 1 + 13 T + 61 T^{2} )^{2} \))(\( ( 1 - 13 T + 61 T^{2} )^{2} \))(\( ( 1 - 13 T + 61 T^{2} )^{2} \))(\( ( 1 - T + 61 T^{2} )^{2} \))(\( ( 1 + 20 T + 219 T^{2} + 1220 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 + 4 T + 99 T^{2} + 244 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 + 4 T + 123 T^{2} + 256 T^{3} + 7503 T^{4} + 14884 T^{5} + 226981 T^{6} )^{2} \))(\( ( 1 - 3 T + 137 T^{2} - 367 T^{3} + 8357 T^{4} - 11163 T^{5} + 226981 T^{6} )^{2} \))(\( ( 1 + 5 T + 105 T^{2} + 779 T^{3} + 6405 T^{4} + 18605 T^{5} + 226981 T^{6} )^{2} \))(\( ( 1 + 3 T + 95 T^{2} + 479 T^{3} + 5795 T^{4} + 11163 T^{5} + 226981 T^{6} )^{2} \))(\( ( 1 + 27 T + 598 T^{2} + 8766 T^{3} + 111115 T^{4} + 1098335 T^{5} + 9564612 T^{6} + 66998435 T^{7} + 413458915 T^{8} + 1989715446 T^{9} + 8279812918 T^{10} + 22804100127 T^{11} + 51520374361 T^{12} )^{2} \))(\( ( 1 - 28 T + 435 T^{2} - 3956 T^{3} + 18488 T^{4} + 18948 T^{5} - 811259 T^{6} + 1155828 T^{7} + 68793848 T^{8} - 897936836 T^{9} + 6022940835 T^{10} - 23648696428 T^{11} + 51520374361 T^{12} )^{2} \))
$67$ (\( 1 - 2 T + 67 T^{2} \))(\( 1 - 10 T + 67 T^{2} \))(\( 1 + 3 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 5 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))(\( 1 + T + 67 T^{2} \))(\( 1 + 10 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 - 3 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 11 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 6 T + 68 T^{2} + 402 T^{3} + 4489 T^{4} \))(\( 1 - 4 T + 90 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 - 6 T + 68 T^{2} - 402 T^{3} + 4489 T^{4} \))(\( 1 + 4 T + 90 T^{2} + 268 T^{3} + 4489 T^{4} \))(\( 1 + 3 T + 141 T^{2} + 151 T^{3} + 9447 T^{4} + 13467 T^{5} + 300763 T^{6} \))(\( 1 - 21 T + 327 T^{2} - 3017 T^{3} + 21909 T^{4} - 94269 T^{5} + 300763 T^{6} \))(\( 1 + 5 T + 95 T^{2} + 867 T^{3} + 6365 T^{4} + 22445 T^{5} + 300763 T^{6} \))(\( 1 + 15 T + 257 T^{2} + 2026 T^{3} + 17219 T^{4} + 67335 T^{5} + 300763 T^{6} \))(\( 1 - 5 T + 151 T^{2} - 545 T^{3} + 10117 T^{4} - 22445 T^{5} + 300763 T^{6} \))(\( 1 - 3 T + 141 T^{2} - 151 T^{3} + 9447 T^{4} - 13467 T^{5} + 300763 T^{6} \))(\( 1 + 21 T + 327 T^{2} + 3017 T^{3} + 21909 T^{4} + 94269 T^{5} + 300763 T^{6} \))(\( 1 - 5 T + 95 T^{2} - 867 T^{3} + 6365 T^{4} - 22445 T^{5} + 300763 T^{6} \))(\( 1 - 15 T + 257 T^{2} - 2026 T^{3} + 17219 T^{4} - 67335 T^{5} + 300763 T^{6} \))(\( 1 + 5 T + 151 T^{2} + 545 T^{3} + 10117 T^{4} + 22445 T^{5} + 300763 T^{6} \))(\( 1 + 16 T + 259 T^{2} + 2960 T^{3} + 34347 T^{4} + 316274 T^{5} + 2882699 T^{6} + 21190358 T^{7} + 154183683 T^{8} + 890258480 T^{9} + 5219140339 T^{10} + 21602001712 T^{11} + 90458382169 T^{12} \))(\( 1 + 6 T + 280 T^{2} + 1562 T^{3} + 34127 T^{4} + 179068 T^{5} + 2660672 T^{6} + 11997556 T^{7} + 153196103 T^{8} + 469791806 T^{9} + 5642313880 T^{10} + 8100750642 T^{11} + 90458382169 T^{12} \))(\( 1 - 16 T + 259 T^{2} - 2960 T^{3} + 34347 T^{4} - 316274 T^{5} + 2882699 T^{6} - 21190358 T^{7} + 154183683 T^{8} - 890258480 T^{9} + 5219140339 T^{10} - 21602001712 T^{11} + 90458382169 T^{12} \))(\( 1 - 6 T + 280 T^{2} - 1562 T^{3} + 34127 T^{4} - 179068 T^{5} + 2660672 T^{6} - 11997556 T^{7} + 153196103 T^{8} - 469791806 T^{9} + 5642313880 T^{10} - 8100750642 T^{11} + 90458382169 T^{12} \))(\( 1 - 130 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 34 T^{2} + 4489 T^{4} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 109 T^{2} + 4489 T^{4} \))(\( 1 - 130 T^{2} + 4489 T^{4} \))(\( 1 - 85 T^{2} + 4489 T^{4} \))(\( 1 - 130 T^{2} + 4489 T^{4} \))(\( 1 - 13 T^{2} + 4489 T^{4} \))(\( 1 - 133 T^{2} + 4489 T^{4} \))(\( 1 - 100 T^{2} + 8778 T^{4} - 448900 T^{6} + 20151121 T^{8} \))(\( 1 - 164 T^{2} + 14934 T^{4} - 736196 T^{6} + 20151121 T^{8} \))(\( 1 - 273 T^{2} + 37869 T^{4} - 3161977 T^{6} + 169993941 T^{8} - 5501256033 T^{10} + 90458382169 T^{12} \))(\( 1 - 213 T^{2} + 24033 T^{4} - 1868425 T^{6} + 107884137 T^{8} - 4292188773 T^{10} + 90458382169 T^{12} \))(\( 1 - 165 T^{2} + 13085 T^{4} - 834737 T^{6} + 58738565 T^{8} - 3324934965 T^{10} + 90458382169 T^{12} \))(\( 1 - 277 T^{2} + 37585 T^{4} - 3135385 T^{6} + 168719065 T^{8} - 5581860517 T^{10} + 90458382169 T^{12} \))(\( 1 - 262 T^{2} + 41055 T^{4} - 4674776 T^{6} + 430888321 T^{8} - 34365119782 T^{10} + 2420366075975 T^{12} - 154265022701398 T^{14} + 8682882693957841 T^{16} - 422872673962469144 T^{18} + 16671108502087896255 T^{20} - \)\(47\!\cdots\!38\)\( T^{22} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( 1 - 524 T^{2} + 127910 T^{4} - 19843804 T^{6} + 2257641551 T^{8} - 203492736888 T^{10} + 15014439517620 T^{12} - 913478895890232 T^{14} + 45494008068828671 T^{16} - 1795038405918730876 T^{18} + 51940116636269950310 T^{20} - \)\(95\!\cdots\!76\)\( T^{22} + \)\(81\!\cdots\!61\)\( T^{24} \))
$71$ (\( 1 + 71 T^{2} \))(\( 1 - 16 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 3 T + 71 T^{2} \))(\( 1 + 15 T + 71 T^{2} \))(\( 1 + 16 T + 71 T^{2} \))(\( 1 + 16 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 4 T + 71 T^{2} \))(\( 1 - 3 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 15 T + 71 T^{2} \))(\( 1 - 50 T^{2} + 5041 T^{4} \))(\( 1 + 2 T + 131 T^{2} + 142 T^{3} + 5041 T^{4} \))(\( 1 - 50 T^{2} + 5041 T^{4} \))(\( 1 - 2 T + 131 T^{2} - 142 T^{3} + 5041 T^{4} \))(\( 1 - 8 T + 169 T^{2} - 792 T^{3} + 11999 T^{4} - 40328 T^{5} + 357911 T^{6} \))(\( 1 + 16 T + 184 T^{2} + 1431 T^{3} + 13064 T^{4} + 80656 T^{5} + 357911 T^{6} \))(\( 1 - 24 T + 356 T^{2} - 3577 T^{3} + 25276 T^{4} - 120984 T^{5} + 357911 T^{6} \))(\( 1 - 4 T + 53 T^{2} + 328 T^{3} + 3763 T^{4} - 20164 T^{5} + 357911 T^{6} \))(\( 1 + 164 T^{2} + 91 T^{3} + 11644 T^{4} + 357911 T^{6} \))(\( 1 + 8 T + 169 T^{2} + 792 T^{3} + 11999 T^{4} + 40328 T^{5} + 357911 T^{6} \))(\( 1 - 16 T + 184 T^{2} - 1431 T^{3} + 13064 T^{4} - 80656 T^{5} + 357911 T^{6} \))(\( 1 + 24 T + 356 T^{2} + 3577 T^{3} + 25276 T^{4} + 120984 T^{5} + 357911 T^{6} \))(\( 1 + 4 T + 53 T^{2} - 328 T^{3} + 3763 T^{4} + 20164 T^{5} + 357911 T^{6} \))(\( 1 + 164 T^{2} - 91 T^{3} + 11644 T^{4} + 357911 T^{6} \))(\( 1 + 169 T^{2} + 35 T^{3} + 11271 T^{4} - 4445 T^{5} + 581862 T^{6} - 315595 T^{7} + 56817111 T^{8} + 12526885 T^{9} + 4294574089 T^{10} + 128100283921 T^{12} \))(\( 1 + 4 T + 272 T^{2} + 880 T^{3} + 36280 T^{4} + 92988 T^{5} + 3097886 T^{6} + 6602148 T^{7} + 182887480 T^{8} + 314961680 T^{9} + 6911977232 T^{10} + 7216917404 T^{11} + 128100283921 T^{12} \))(\( 1 + 169 T^{2} - 35 T^{3} + 11271 T^{4} + 4445 T^{5} + 581862 T^{6} + 315595 T^{7} + 56817111 T^{8} - 12526885 T^{9} + 4294574089 T^{10} + 128100283921 T^{12} \))(\( 1 - 4 T + 272 T^{2} - 880 T^{3} + 36280 T^{4} - 92988 T^{5} + 3097886 T^{6} - 6602148 T^{7} + 182887480 T^{8} - 314961680 T^{9} + 6911977232 T^{10} - 7216917404 T^{11} + 128100283921 T^{12} \))(\( ( 1 - 71 T^{2} )^{2} \))(\( ( 1 - 71 T^{2} )^{2} \))(\( 1 + 114 T^{2} + 5041 T^{4} \))(\( 1 - 78 T^{2} + 5041 T^{4} \))(\( 1 + 2 T^{2} + 5041 T^{4} \))(\( 1 - 133 T^{2} + 5041 T^{4} \))(\( 1 - 126 T^{2} + 5041 T^{4} \))(\( 1 + 83 T^{2} + 5041 T^{4} \))(\( ( 1 - 71 T^{2} )^{2} \))(\( 1 + 114 T^{2} + 5041 T^{4} \))(\( ( 1 + 50 T^{2} + 5041 T^{4} )^{2} \))(\( 1 - 258 T^{2} + 26675 T^{4} - 1300578 T^{6} + 25411681 T^{8} \))(\( 1 - 274 T^{2} + 39887 T^{4} - 3498972 T^{6} + 201070367 T^{8} - 6962800594 T^{10} + 128100283921 T^{12} \))(\( 1 - 112 T^{2} + 14192 T^{4} - 894621 T^{6} + 71541872 T^{8} - 2846108272 T^{10} + 128100283921 T^{12} \))(\( 1 - 136 T^{2} + 5592 T^{4} - 110173 T^{6} + 28189272 T^{8} - 3455988616 T^{10} + 128100283921 T^{12} \))(\( 1 - 328 T^{2} + 50184 T^{4} - 4526773 T^{6} + 252977544 T^{8} - 8335031368 T^{10} + 128100283921 T^{12} \))(\( 1 - 338 T^{2} + 51103 T^{4} - 4972097 T^{6} + 437650169 T^{8} - 40911998525 T^{10} + 3323418791630 T^{12} - 206237384564525 T^{14} + 11121426484224089 T^{16} - 636927037382752337 T^{18} + 32999942707252124383 T^{20} - \)\(11\!\cdots\!38\)\( T^{22} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 - 528 T^{2} + 139504 T^{4} - 24413788 T^{6} + 3150787280 T^{8} - 315311109680 T^{10} + 25043620427366 T^{12} - 1589483303896880 T^{14} + 80066801258217680 T^{16} - 3127413174387102748 T^{18} + 90085200622908642544 T^{20} - \)\(17\!\cdots\!28\)\( T^{22} + \)\(16\!\cdots\!41\)\( T^{24} \))
$73$ (\( 1 + 7 T + 73 T^{2} \))(\( 1 + 3 T + 73 T^{2} \))(\( 1 - T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 11 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 5 T + 73 T^{2} \))(\( 1 - 3 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 7 T + 73 T^{2} \))(\( 1 + T + 73 T^{2} \))(\( 1 + 9 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 7 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 2 T + 39 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( 1 - 8 T + 150 T^{2} - 584 T^{3} + 5329 T^{4} \))(\( 1 + 2 T + 39 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 + 8 T + 150 T^{2} + 584 T^{3} + 5329 T^{4} \))(\( 1 - 13 T + 203 T^{2} - 1731 T^{3} + 14819 T^{4} - 69277 T^{5} + 389017 T^{6} \))(\( 1 + T + 203 T^{2} + 117 T^{3} + 14819 T^{4} + 5329 T^{5} + 389017 T^{6} \))(\( 1 - T + 189 T^{2} - 103 T^{3} + 13797 T^{4} - 5329 T^{5} + 389017 T^{6} \))(\( 1 - 11 T + 235 T^{2} - 1610 T^{3} + 17155 T^{4} - 58619 T^{5} + 389017 T^{6} \))(\( 1 + 21 T + 149 T^{2} + 707 T^{3} + 10877 T^{4} + 111909 T^{5} + 389017 T^{6} \))(\( 1 + 13 T + 203 T^{2} + 1731 T^{3} + 14819 T^{4} + 69277 T^{5} + 389017 T^{6} \))(\( 1 - T + 203 T^{2} - 117 T^{3} + 14819 T^{4} - 5329 T^{5} + 389017 T^{6} \))(\( 1 + T + 189 T^{2} + 103 T^{3} + 13797 T^{4} + 5329 T^{5} + 389017 T^{6} \))(\( 1 + 11 T + 235 T^{2} + 1610 T^{3} + 17155 T^{4} + 58619 T^{5} + 389017 T^{6} \))(\( 1 - 21 T + 149 T^{2} - 707 T^{3} + 10877 T^{4} - 111909 T^{5} + 389017 T^{6} \))(\( 1 + 38 T + 811 T^{2} + 12294 T^{3} + 150495 T^{4} + 1568896 T^{5} + 14314189 T^{6} + 114529408 T^{7} + 801987855 T^{8} + 4782574998 T^{9} + 23030973451 T^{10} + 78776720534 T^{11} + 151334226289 T^{12} \))(\( 1 - 22 T + 375 T^{2} - 3350 T^{3} + 25043 T^{4} - 71940 T^{5} + 489610 T^{6} - 5251620 T^{7} + 133454147 T^{8} - 1303206950 T^{9} + 10649340375 T^{10} - 45607575046 T^{11} + 151334226289 T^{12} \))(\( 1 - 38 T + 811 T^{2} - 12294 T^{3} + 150495 T^{4} - 1568896 T^{5} + 14314189 T^{6} - 114529408 T^{7} + 801987855 T^{8} - 4782574998 T^{9} + 23030973451 T^{10} - 78776720534 T^{11} + 151334226289 T^{12} \))(\( 1 + 22 T + 375 T^{2} + 3350 T^{3} + 25043 T^{4} + 71940 T^{5} + 489610 T^{6} + 5251620 T^{7} + 133454147 T^{8} + 1303206950 T^{9} + 10649340375 T^{10} + 45607575046 T^{11} + 151334226289 T^{12} \))(\( 1 - 97 T^{2} + 5329 T^{4} \))(\( 1 - 142 T^{2} + 5329 T^{4} \))(\( 1 - 137 T^{2} + 5329 T^{4} \))(\( 1 - 142 T^{2} + 5329 T^{4} \))(\( 1 - 25 T^{2} + 5329 T^{4} \))(\( 1 - 142 T^{2} + 5329 T^{4} \))(\( 1 - 65 T^{2} + 5329 T^{4} \))(\( 1 - 142 T^{2} + 5329 T^{4} \))(\( 1 - 97 T^{2} + 5329 T^{4} \))(\( 1 - 121 T^{2} + 5329 T^{4} \))(\( 1 - 74 T^{2} + 11595 T^{4} - 394346 T^{6} + 28398241 T^{8} \))(\( 1 - 236 T^{2} + 23814 T^{4} - 1257644 T^{6} + 28398241 T^{8} \))(\( 1 - 237 T^{2} + 25841 T^{4} - 1996985 T^{6} + 137706689 T^{8} - 6730383117 T^{10} + 151334226289 T^{12} \))(\( 1 - 405 T^{2} + 70613 T^{4} - 6770201 T^{6} + 376296677 T^{8} - 11501287605 T^{10} + 151334226289 T^{12} \))(\( 1 - 377 T^{2} + 63109 T^{4} - 5972033 T^{6} + 336307861 T^{8} - 10706136857 T^{10} + 151334226289 T^{12} \))(\( 1 + 143 T^{2} + 14261 T^{4} + 1180647 T^{6} + 75996869 T^{8} + 4060948463 T^{10} + 151334226289 T^{12} \))(\( 1 - 178 T^{2} + 24367 T^{4} - 2352736 T^{6} + 190085437 T^{8} - 14354552254 T^{10} + 994793595727 T^{12} - 76495408961566 T^{14} + 5398092050516317 T^{16} - 356049482222276704 T^{18} + 19651013059183071727 T^{20} - \)\(76\!\cdots\!22\)\( T^{22} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 - 266 T^{2} + 43311 T^{4} - 5373610 T^{6} + 548198363 T^{8} - 48209574060 T^{10} + 3719753139946 T^{12} - 256908820165740 T^{14} + 15567869228279483 T^{16} - 813211111728833290 T^{18} + 34928593040024542191 T^{20} - \)\(11\!\cdots\!34\)\( T^{22} + \)\(22\!\cdots\!21\)\( T^{24} \))
$79$ (\( 1 - 14 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 15 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 11 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 - 14 T + 79 T^{2} \))(\( 1 + 15 T + 79 T^{2} \))(\( 1 + 13 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 17 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 18 T + 212 T^{2} + 1422 T^{3} + 6241 T^{4} \))(\( 1 - 16 T + 174 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 + 18 T + 212 T^{2} + 1422 T^{3} + 6241 T^{4} \))(\( 1 - 16 T + 174 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 + 16 T + 201 T^{2} + 2296 T^{3} + 15879 T^{4} + 99856 T^{5} + 493039 T^{6} \))(\( 1 - 10 T + 212 T^{2} - 1455 T^{3} + 16748 T^{4} - 62410 T^{5} + 493039 T^{6} \))(\( 1 - 10 T + 128 T^{2} - 489 T^{3} + 10112 T^{4} - 62410 T^{5} + 493039 T^{6} \))(\( 1 + 7 T + 149 T^{2} + 1254 T^{3} + 11771 T^{4} + 43687 T^{5} + 493039 T^{6} \))(\( 1 + 2 T + 12 T^{2} - 931 T^{3} + 948 T^{4} + 12482 T^{5} + 493039 T^{6} \))(\( 1 + 16 T + 201 T^{2} + 2296 T^{3} + 15879 T^{4} + 99856 T^{5} + 493039 T^{6} \))(\( 1 - 10 T + 212 T^{2} - 1455 T^{3} + 16748 T^{4} - 62410 T^{5} + 493039 T^{6} \))(\( 1 - 10 T + 128 T^{2} - 489 T^{3} + 10112 T^{4} - 62410 T^{5} + 493039 T^{6} \))(\( 1 + 7 T + 149 T^{2} + 1254 T^{3} + 11771 T^{4} + 43687 T^{5} + 493039 T^{6} \))(\( 1 + 2 T + 12 T^{2} - 931 T^{3} + 948 T^{4} + 12482 T^{5} + 493039 T^{6} \))(\( 1 - 6 T + 337 T^{2} - 1579 T^{3} + 54647 T^{4} - 210917 T^{5} + 5415446 T^{6} - 16662443 T^{7} + 341051927 T^{8} - 778508581 T^{9} + 13126177297 T^{10} - 18462338394 T^{11} + 243087455521 T^{12} \))(\( 1 - 22 T + 536 T^{2} - 7106 T^{3} + 100727 T^{4} - 974028 T^{5} + 10218624 T^{6} - 76948212 T^{7} + 628637207 T^{8} - 3503535134 T^{9} + 20877243416 T^{10} - 67695240778 T^{11} + 243087455521 T^{12} \))(\( 1 - 6 T + 337 T^{2} - 1579 T^{3} + 54647 T^{4} - 210917 T^{5} + 5415446 T^{6} - 16662443 T^{7} + 341051927 T^{8} - 778508581 T^{9} + 13126177297 T^{10} - 18462338394 T^{11} + 243087455521 T^{12} \))(\( 1 - 22 T + 536 T^{2} - 7106 T^{3} + 100727 T^{4} - 974028 T^{5} + 10218624 T^{6} - 76948212 T^{7} + 628637207 T^{8} - 3503535134 T^{9} + 20877243416 T^{10} - 67695240778 T^{11} + 243087455521 T^{12} \))(\( ( 1 - 14 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 10 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 + T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 13 T + 79 T^{2} )^{2} \))(\( ( 1 - 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 17 T + 79 T^{2} )^{2} \))(\( ( 1 - 11 T + 79 T^{2} )^{2} \))(\( ( 1 + 18 T + 212 T^{2} + 1422 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - 16 T + 174 T^{2} - 1264 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 + 16 T + 201 T^{2} + 2296 T^{3} + 15879 T^{4} + 99856 T^{5} + 493039 T^{6} )^{2} \))(\( ( 1 - 10 T + 212 T^{2} - 1455 T^{3} + 16748 T^{4} - 62410 T^{5} + 493039 T^{6} )^{2} \))(\( ( 1 - 10 T + 128 T^{2} - 489 T^{3} + 10112 T^{4} - 62410 T^{5} + 493039 T^{6} )^{2} \))(\( ( 1 + 2 T + 12 T^{2} - 931 T^{3} + 948 T^{4} + 12482 T^{5} + 493039 T^{6} )^{2} \))(\( ( 1 - 6 T + 337 T^{2} - 1579 T^{3} + 54647 T^{4} - 210917 T^{5} + 5415446 T^{6} - 16662443 T^{7} + 341051927 T^{8} - 778508581 T^{9} + 13126177297 T^{10} - 18462338394 T^{11} + 243087455521 T^{12} )^{2} \))(\( ( 1 - 22 T + 536 T^{2} - 7106 T^{3} + 100727 T^{4} - 974028 T^{5} + 10218624 T^{6} - 76948212 T^{7} + 628637207 T^{8} - 3503535134 T^{9} + 20877243416 T^{10} - 67695240778 T^{11} + 243087455521 T^{12} )^{2} \))
$83$ (\( 1 + 18 T + 83 T^{2} \))(\( 1 - 14 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 8 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 14 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 18 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 8 T + 83 T^{2} \))(\( 1 - 18 T + 220 T^{2} - 1494 T^{3} + 6889 T^{4} \))(\( 1 + 58 T^{2} + 6889 T^{4} \))(\( 1 + 18 T + 220 T^{2} + 1494 T^{3} + 6889 T^{4} \))(\( 1 + 58 T^{2} + 6889 T^{4} \))(\( 1 - 21 T + 333 T^{2} - 3577 T^{3} + 27639 T^{4} - 144669 T^{5} + 571787 T^{6} \))(\( 1 - T + 149 T^{2} - 347 T^{3} + 12367 T^{4} - 6889 T^{5} + 571787 T^{6} \))(\( 1 + 7 T + 95 T^{2} + 371 T^{3} + 7885 T^{4} + 48223 T^{5} + 571787 T^{6} \))(\( 1 + 10 T + 123 T^{2} + 408 T^{3} + 10209 T^{4} + 68890 T^{5} + 571787 T^{6} \))(\( 1 - 5 T + 241 T^{2} - 789 T^{3} + 20003 T^{4} - 34445 T^{5} + 571787 T^{6} \))(\( 1 + 21 T + 333 T^{2} + 3577 T^{3} + 27639 T^{4} + 144669 T^{5} + 571787 T^{6} \))(\( 1 + T + 149 T^{2} + 347 T^{3} + 12367 T^{4} + 6889 T^{5} + 571787 T^{6} \))(\( 1 - 7 T + 95 T^{2} - 371 T^{3} + 7885 T^{4} - 48223 T^{5} + 571787 T^{6} \))(\( 1 - 10 T + 123 T^{2} - 408 T^{3} + 10209 T^{4} - 68890 T^{5} + 571787 T^{6} \))(\( 1 + 5 T + 241 T^{2} + 789 T^{3} + 20003 T^{4} + 34445 T^{5} + 571787 T^{6} \))(\( 1 - 6 T + 265 T^{2} - 1224 T^{3} + 35891 T^{4} - 128808 T^{5} + 3418761 T^{6} - 10691064 T^{7} + 247253099 T^{8} - 699867288 T^{9} + 12576455065 T^{10} - 23634243858 T^{11} + 326940373369 T^{12} \))(\( 1 - 10 T + 316 T^{2} - 2478 T^{3} + 41691 T^{4} - 288388 T^{5} + 3740088 T^{6} - 23936204 T^{7} + 287209299 T^{8} - 1416888186 T^{9} + 14996829436 T^{10} - 39390406430 T^{11} + 326940373369 T^{12} \))(\( 1 + 6 T + 265 T^{2} + 1224 T^{3} + 35891 T^{4} + 128808 T^{5} + 3418761 T^{6} + 10691064 T^{7} + 247253099 T^{8} + 699867288 T^{9} + 12576455065 T^{10} + 23634243858 T^{11} + 326940373369 T^{12} \))(\( 1 + 10 T + 316 T^{2} + 2478 T^{3} + 41691 T^{4} + 288388 T^{5} + 3740088 T^{6} + 23936204 T^{7} + 287209299 T^{8} + 1416888186 T^{9} + 14996829436 T^{10} + 39390406430 T^{11} + 326940373369 T^{12} \))(\( 1 + 158 T^{2} + 6889 T^{4} \))(\( 1 - 130 T^{2} + 6889 T^{4} \))(\( 1 + 30 T^{2} + 6889 T^{4} \))(\( ( 1 - 83 T^{2} )^{2} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( ( 1 - 83 T^{2} )^{2} \))(\( 1 + 90 T^{2} + 6889 T^{4} \))(\( 1 - 102 T^{2} + 6889 T^{4} \))(\( 1 - 150 T^{2} + 6889 T^{4} \))(\( ( 1 - 83 T^{2} )^{2} \))(\( 1 - 116 T^{2} + 8394 T^{4} - 799124 T^{6} + 47458321 T^{8} \))(\( ( 1 - 58 T^{2} + 6889 T^{4} )^{2} \))(\( 1 - 225 T^{2} + 15933 T^{4} - 680121 T^{6} + 109762437 T^{8} - 10678122225 T^{10} + 326940373369 T^{12} \))(\( 1 - 297 T^{2} + 46241 T^{4} - 4694753 T^{6} + 318554249 T^{8} - 14095121337 T^{10} + 326940373369 T^{12} \))(\( 1 - 141 T^{2} + 19601 T^{4} - 1828961 T^{6} + 135031289 T^{8} - 6691623261 T^{10} + 326940373369 T^{12} \))(\( 1 - 457 T^{2} + 90197 T^{4} - 9818049 T^{6} + 621367133 T^{8} - 21688452697 T^{10} + 326940373369 T^{12} \))(\( 1 - 494 T^{2} + 127319 T^{4} - 22815880 T^{6} + 3150998657 T^{8} - 350440921710 T^{10} + 32004575467983 T^{12} - 2414187509660190 T^{14} + 149541105734474897 T^{16} - 7459432325942299720 T^{18} + \)\(28\!\cdots\!79\)\( T^{20} - \)\(76\!\cdots\!06\)\( T^{22} + \)\(10\!\cdots\!61\)\( T^{24} \))(\( 1 - 532 T^{2} + 133678 T^{4} - 21920644 T^{6} + 2768318687 T^{8} - 293232724168 T^{10} + 26452486990532 T^{12} - 2020080236793352 T^{14} + 131379756877944527 T^{16} - 7166743533848929636 T^{18} + \)\(30\!\cdots\!98\)\( T^{20} - \)\(82\!\cdots\!68\)\( T^{22} + \)\(10\!\cdots\!61\)\( T^{24} \))
$89$ (\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 18 T + 89 T^{2} \))(\( 1 - 18 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 - 12 T + 202 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 - 24 T + 310 T^{2} - 2136 T^{3} + 7921 T^{4} \))(\( 1 + 12 T + 202 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 + 24 T + 310 T^{2} + 2136 T^{3} + 7921 T^{4} \))(\( 1 - 25 T + 431 T^{2} - 4547 T^{3} + 38359 T^{4} - 198025 T^{5} + 704969 T^{6} \))(\( 1 + 4 T + 158 T^{2} + 473 T^{3} + 14062 T^{4} + 31684 T^{5} + 704969 T^{6} \))(\( 1 - 2 T + 252 T^{2} - 327 T^{3} + 22428 T^{4} - 15842 T^{5} + 704969 T^{6} \))(\( 1 - 26 T + 447 T^{2} - 4860 T^{3} + 39783 T^{4} - 205946 T^{5} + 704969 T^{6} \))(\( 1 + 14 T + 176 T^{2} + 2191 T^{3} + 15664 T^{4} + 110894 T^{5} + 704969 T^{6} \))(\( 1 + 25 T + 431 T^{2} + 4547 T^{3} + 38359 T^{4} + 198025 T^{5} + 704969 T^{6} \))(\( 1 - 4 T + 158 T^{2} - 473 T^{3} + 14062 T^{4} - 31684 T^{5} + 704969 T^{6} \))(\( 1 + 2 T + 252 T^{2} + 327 T^{3} + 22428 T^{4} + 15842 T^{5} + 704969 T^{6} \))(\( 1 + 26 T + 447 T^{2} + 4860 T^{3} + 39783 T^{4} + 205946 T^{5} + 704969 T^{6} \))(\( 1 - 14 T + 176 T^{2} - 2191 T^{3} + 15664 T^{4} - 110894 T^{5} + 704969 T^{6} \))(\( 1 - T + 229 T^{2} + 94 T^{3} + 31324 T^{4} - 21644 T^{5} + 3356869 T^{6} - 1926316 T^{7} + 248117404 T^{8} + 66267086 T^{9} + 14367973189 T^{10} - 5584059449 T^{11} + 496981290961 T^{12} \))(\( 1 - 4 T + 334 T^{2} - 1140 T^{3} + 57807 T^{4} - 169576 T^{5} + 6306852 T^{6} - 15092264 T^{7} + 457889247 T^{8} - 803664660 T^{9} + 20955908494 T^{10} - 22336237796 T^{11} + 496981290961 T^{12} \))(\( 1 + T + 229 T^{2} - 94 T^{3} + 31324 T^{4} + 21644 T^{5} + 3356869 T^{6} + 1926316 T^{7} + 248117404 T^{8} - 66267086 T^{9} + 14367973189 T^{10} + 5584059449 T^{11} + 496981290961 T^{12} \))(\( 1 + 4 T + 334 T^{2} + 1140 T^{3} + 57807 T^{4} + 169576 T^{5} + 6306852 T^{6} + 15092264 T^{7} + 457889247 T^{8} + 803664660 T^{9} + 20955908494 T^{10} + 22336237796 T^{11} + 496981290961 T^{12} \))(\( 1 - 142 T^{2} + 7921 T^{4} \))(\( 1 - 142 T^{2} + 7921 T^{4} \))(\( 1 - 142 T^{2} + 7921 T^{4} \))(\( 1 + 146 T^{2} + 7921 T^{4} \))(\( 1 + 146 T^{2} + 7921 T^{4} \))(\( 1 - 142 T^{2} + 7921 T^{4} \))(\( 1 - 142 T^{2} + 7921 T^{4} \))(\( 1 + 18 T^{2} + 7921 T^{4} \))(\( 1 + 18 T^{2} + 7921 T^{4} \))(\( 1 - 142 T^{2} + 7921 T^{4} \))(\( 1 - 260 T^{2} + 31014 T^{4} - 2059460 T^{6} + 62742241 T^{8} \))(\( 1 - 44 T^{2} + 9414 T^{4} - 348524 T^{6} + 62742241 T^{8} \))(\( 1 - 237 T^{2} + 35129 T^{4} - 3898937 T^{6} + 278256809 T^{8} - 14869911117 T^{10} + 496981290961 T^{12} \))(\( 1 - 300 T^{2} + 49304 T^{4} - 5376329 T^{6} + 390536984 T^{8} - 18822672300 T^{10} + 496981290961 T^{12} \))(\( 1 - 500 T^{2} + 107052 T^{4} - 12543353 T^{6} + 847958892 T^{8} - 31371120500 T^{10} + 496981290961 T^{12} \))(\( 1 - 156 T^{2} + 956 T^{4} + 981847 T^{6} + 7572476 T^{8} - 9787789596 T^{10} + 496981290961 T^{12} \))(\( 1 - 457 T^{2} + 115277 T^{4} - 21008006 T^{6} + 3015090226 T^{8} - 352701065366 T^{10} + 34280110213363 T^{12} - 2793745138764086 T^{14} + 189173517596436466 T^{16} - 10440585942396433766 T^{18} + \)\(45\!\cdots\!37\)\( T^{20} - \)\(14\!\cdots\!57\)\( T^{22} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 - 652 T^{2} + 218050 T^{4} - 48572572 T^{6} + 7963033487 T^{8} - 1007346522136 T^{10} + 100577682161180 T^{12} - 7979191801839256 T^{14} + 499618566132424367 T^{16} - 24139659537856121692 T^{18} + \)\(85\!\cdots\!50\)\( T^{20} - \)\(20\!\cdots\!52\)\( T^{22} + \)\(24\!\cdots\!21\)\( T^{24} \))
$97$ (\( 1 - 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 17 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( 1 + 11 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 5 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 4 T + 186 T^{2} + 388 T^{3} + 9409 T^{4} \))(\( 1 - 20 T + 246 T^{2} - 1940 T^{3} + 9409 T^{4} \))(\( 1 - 4 T + 186 T^{2} - 388 T^{3} + 9409 T^{4} \))(\( 1 + 20 T + 246 T^{2} + 1940 T^{3} + 9409 T^{4} \))(\( 1 - 31 T + 609 T^{2} - 7093 T^{3} + 59073 T^{4} - 291679 T^{5} + 912673 T^{6} \))(\( 1 - 19 T + 311 T^{2} - 3225 T^{3} + 30167 T^{4} - 178771 T^{5} + 912673 T^{6} \))(\( 1 + 27 T + 527 T^{2} + 5911 T^{3} + 51119 T^{4} + 254043 T^{5} + 912673 T^{6} \))(\( 1 - 21 T + 419 T^{2} - 4270 T^{3} + 40643 T^{4} - 197589 T^{5} + 912673 T^{6} \))(\( 1 - 15 T + 359 T^{2} - 3007 T^{3} + 34823 T^{4} - 141135 T^{5} + 912673 T^{6} \))(\( 1 + 31 T + 609 T^{2} + 7093 T^{3} + 59073 T^{4} + 291679 T^{5} + 912673 T^{6} \))(\( 1 + 19 T + 311 T^{2} + 3225 T^{3} + 30167 T^{4} + 178771 T^{5} + 912673 T^{6} \))(\( 1 - 27 T + 527 T^{2} - 5911 T^{3} + 51119 T^{4} - 254043 T^{5} + 912673 T^{6} \))(\( 1 + 21 T + 419 T^{2} + 4270 T^{3} + 40643 T^{4} + 197589 T^{5} + 912673 T^{6} \))(\( 1 + 15 T + 359 T^{2} + 3007 T^{3} + 34823 T^{4} + 141135 T^{5} + 912673 T^{6} \))(\( 1 + 16 T + 511 T^{2} + 6198 T^{3} + 113769 T^{4} + 1087256 T^{5} + 14310613 T^{6} + 105463832 T^{7} + 1070452521 T^{8} + 5656747254 T^{9} + 45238462591 T^{10} + 137397444112 T^{11} + 832972004929 T^{12} \))(\( 1 - 12 T + 358 T^{2} - 3260 T^{3} + 59423 T^{4} - 424120 T^{5} + 6536564 T^{6} - 41139640 T^{7} + 559111007 T^{8} - 2975313980 T^{9} + 31693482598 T^{10} - 103048083084 T^{11} + 832972004929 T^{12} \))(\( 1 - 16 T + 511 T^{2} - 6198 T^{3} + 113769 T^{4} - 1087256 T^{5} + 14310613 T^{6} - 105463832 T^{7} + 1070452521 T^{8} - 5656747254 T^{9} + 45238462591 T^{10} - 137397444112 T^{11} + 832972004929 T^{12} \))(\( 1 + 12 T + 358 T^{2} + 3260 T^{3} + 59423 T^{4} + 424120 T^{5} + 6536564 T^{6} + 41139640 T^{7} + 559111007 T^{8} + 2975313980 T^{9} + 31693482598 T^{10} + 103048083084 T^{11} + 832972004929 T^{12} \))(\( 1 - 190 T^{2} + 9409 T^{4} \))(\( 1 - 94 T^{2} + 9409 T^{4} \))(\( 1 - 190 T^{2} + 9409 T^{4} \))(\( 1 - 190 T^{2} + 9409 T^{4} \))(\( 1 + 95 T^{2} + 9409 T^{4} \))(\( 1 - 190 T^{2} + 9409 T^{4} \))(\( 1 - 73 T^{2} + 9409 T^{4} \))(\( 1 - 190 T^{2} + 9409 T^{4} \))(\( 1 - 169 T^{2} + 9409 T^{4} \))(\( 1 - 193 T^{2} + 9409 T^{4} \))(\( 1 - 356 T^{2} + 50310 T^{4} - 3349604 T^{6} + 88529281 T^{8} \))(\( 1 - 92 T^{2} + 1734 T^{4} - 865628 T^{6} + 88529281 T^{8} \))(\( 1 - 257 T^{2} + 49261 T^{4} - 5381513 T^{6} + 463496749 T^{8} - 22752025217 T^{10} + 832972004929 T^{12} \))(\( 1 - 261 T^{2} + 34505 T^{4} - 3395297 T^{6} + 324657545 T^{8} - 23106142341 T^{10} + 832972004929 T^{12} \))(\( 1 - 325 T^{2} + 60773 T^{4} - 7046529 T^{6} + 571813157 T^{8} - 28772016325 T^{10} + 832972004929 T^{12} \))(\( 1 - 493 T^{2} + 108317 T^{4} - 13552161 T^{6} + 1019154653 T^{8} - 43644935533 T^{10} + 832972004929 T^{12} \))(\( 1 - 766 T^{2} + 290323 T^{4} - 71685748 T^{6} + 12857268889 T^{8} - 1770216479302 T^{10} + 192411797514775 T^{12} - 16655966853752518 T^{14} + 1138244770366838809 T^{16} - 59712221236395051892 T^{18} + \)\(22\!\cdots\!03\)\( T^{20} - \)\(56\!\cdots\!34\)\( T^{22} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( 1 - 572 T^{2} + 168770 T^{4} - 34813516 T^{6} + 5576881007 T^{8} - 721039168632 T^{10} + 76764763836828 T^{12} - 6784257537658488 T^{14} + 493717265772265967 T^{16} - 28998684221147820364 T^{18} + \)\(13\!\cdots\!70\)\( T^{20} - \)\(42\!\cdots\!28\)\( T^{22} + \)\(69\!\cdots\!41\)\( T^{24} \))
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