Properties

Label 588.2
Level 588
Weight 2
Dimension 3852
Nonzero newspaces 16
Newform subspaces 61
Sturm bound 37632
Trace bound 3

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Defining parameters

Level: \( N \) = \( 588\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 61 \)
Sturm bound: \(37632\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(588))\).

Total New Old
Modular forms 10008 4048 5960
Cusp forms 8809 3852 4957
Eisenstein series 1199 196 1003

Trace form

\( 3852q - 2q^{3} - 30q^{4} - 12q^{5} - 9q^{6} - 8q^{7} + 12q^{8} - 20q^{9} + O(q^{10}) \) \( 3852q - 2q^{3} - 30q^{4} - 12q^{5} - 9q^{6} - 8q^{7} + 12q^{8} - 20q^{9} + 6q^{10} + 12q^{11} + 15q^{12} - 16q^{13} + 24q^{14} + 36q^{15} + 18q^{16} + 24q^{17} + 15q^{18} + 32q^{19} - 7q^{21} - 102q^{22} + 24q^{23} - 33q^{24} - 60q^{26} + 4q^{27} - 84q^{28} + 72q^{29} - 81q^{30} + 8q^{31} - 60q^{32} - 48q^{33} - 90q^{34} - 6q^{35} - 99q^{36} - 36q^{38} - 27q^{39} - 90q^{40} + 36q^{41} - 69q^{42} + 4q^{43} - 48q^{44} - 78q^{45} - 90q^{46} + 48q^{47} - 150q^{48} + 66q^{49} - 84q^{50} + 42q^{51} - 90q^{52} + 36q^{53} - 117q^{54} + 210q^{55} - 18q^{56} - 16q^{57} - 42q^{58} + 108q^{59} - 45q^{60} + 94q^{61} + 24q^{63} + 6q^{64} + 12q^{65} + 15q^{66} + 120q^{67} + 72q^{68} - 18q^{69} + 30q^{70} + 39q^{72} + 32q^{73} + 132q^{74} - 20q^{75} + 126q^{76} + 93q^{78} + 24q^{79} + 18q^{80} - 272q^{81} - 84q^{82} - 144q^{83} - 138q^{84} - 252q^{85} - 162q^{86} - 192q^{87} - 264q^{88} - 192q^{89} - 180q^{90} - 188q^{91} - 126q^{92} - 304q^{93} - 372q^{94} - 300q^{95} - 246q^{96} - 448q^{97} - 546q^{98} - 60q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(588))\)

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
588.2.a \(\chi_{588}(1, \cdot)\) 588.2.a.a 1 1
588.2.a.b 1
588.2.a.c 1
588.2.a.d 1
588.2.a.e 1
588.2.a.f 1
588.2.b \(\chi_{588}(391, \cdot)\) 588.2.b.a 8 1
588.2.b.b 8
588.2.b.c 12
588.2.b.d 12
588.2.e \(\chi_{588}(491, \cdot)\) 588.2.e.a 4 1
588.2.e.b 8
588.2.e.c 12
588.2.e.d 12
588.2.e.e 12
588.2.e.f 24
588.2.f \(\chi_{588}(293, \cdot)\) 588.2.f.a 2 1
588.2.f.b 2
588.2.f.c 2
588.2.f.d 8
588.2.i \(\chi_{588}(361, \cdot)\) 588.2.i.a 2 2
588.2.i.b 2
588.2.i.c 2
588.2.i.d 2
588.2.i.e 2
588.2.i.f 2
588.2.i.g 2
588.2.k \(\chi_{588}(509, \cdot)\) 588.2.k.a 2 2
588.2.k.b 2
588.2.k.c 2
588.2.k.d 2
588.2.k.e 2
588.2.k.f 16
588.2.n \(\chi_{588}(263, \cdot)\) 588.2.n.a 4 2
588.2.n.b 4
588.2.n.c 16
588.2.n.d 24
588.2.n.e 24
588.2.n.f 24
588.2.n.g 24
588.2.n.h 24
588.2.o \(\chi_{588}(19, \cdot)\) 588.2.o.a 8 2
588.2.o.b 8
588.2.o.c 8
588.2.o.d 8
588.2.o.e 24
588.2.o.f 24
588.2.q \(\chi_{588}(85, \cdot)\) 588.2.q.a 30 6
588.2.q.b 30
588.2.t \(\chi_{588}(41, \cdot)\) 588.2.t.a 12 6
588.2.t.b 96
588.2.u \(\chi_{588}(71, \cdot)\) 588.2.u.a 648 6
588.2.x \(\chi_{588}(55, \cdot)\) 588.2.x.a 168 6
588.2.x.b 168
588.2.y \(\chi_{588}(25, \cdot)\) 588.2.y.a 48 12
588.2.y.b 60
588.2.ba \(\chi_{588}(103, \cdot)\) 588.2.ba.a 336 12
588.2.ba.b 336
588.2.bb \(\chi_{588}(11, \cdot)\) 588.2.bb.a 1296 12
588.2.be \(\chi_{588}(5, \cdot)\) 588.2.be.a 12 12
588.2.be.b 216

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(588))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(588)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T + T^{2} - 2 T^{3} - 6 T^{4} - 4 T^{5} + 4 T^{6} + 16 T^{7} + 16 T^{8} \))(\( 1 + 2 T + T^{2} - 2 T^{3} - 6 T^{4} - 4 T^{5} + 4 T^{6} + 16 T^{7} + 16 T^{8} \))(\( 1 - 4 T + 10 T^{2} - 20 T^{3} + 35 T^{4} - 56 T^{5} + 84 T^{6} - 112 T^{7} + 140 T^{8} - 160 T^{9} + 160 T^{10} - 128 T^{11} + 64 T^{12} \))(\( 1 - 4 T + 10 T^{2} - 20 T^{3} + 35 T^{4} - 56 T^{5} + 84 T^{6} - 112 T^{7} + 140 T^{8} - 160 T^{9} + 160 T^{10} - 128 T^{11} + 64 T^{12} \))(\( ( 1 - 2 T^{2} )^{2} \))(\( ( 1 + T^{2} + 4 T^{4} )^{2} \))(\( 1 + 2 T^{2} + T^{4} - 4 T^{6} + 4 T^{8} + 32 T^{10} + 64 T^{12} \))(\( 1 - T^{2} - 2 T^{4} + 8 T^{6} - 8 T^{8} - 16 T^{10} + 64 T^{12} \))(\( 1 - T^{2} - 2 T^{4} + 8 T^{6} - 8 T^{8} - 16 T^{10} + 64 T^{12} \))(\( 1 + 2 T^{2} + 4 T^{4} \))(\( 1 + 2 T^{2} + 4 T^{4} \))(\( ( 1 - T^{2} - 3 T^{4} - 4 T^{6} + 16 T^{8} )^{2} \))(\( 1 - T + T^{2} + 4 T^{3} - 6 T^{4} + 8 T^{5} + 4 T^{6} - 8 T^{7} + 16 T^{8} \))(\( 1 - T + T^{2} - 2 T^{3} - 4 T^{5} + 4 T^{6} - 8 T^{7} + 16 T^{8} \))(\( 1 - T + T^{2} + 4 T^{3} - 6 T^{4} + 8 T^{5} + 4 T^{6} - 8 T^{7} + 16 T^{8} \))(\( 1 - T + T^{2} - 2 T^{3} + 6 T^{4} - 4 T^{5} + 4 T^{6} - 8 T^{7} + 16 T^{8} \))
$3$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{8} \))(\( ( 1 - T )^{8} \))(\( ( 1 + T )^{12} \))(\( ( 1 - T )^{12} \))(\( ( 1 + 3 T^{2} )^{2} \))(\( ( 1 - 4 T^{2} + 9 T^{4} )^{2} \))(\( 1 + 2 T^{2} - 5 T^{4} - 44 T^{6} - 45 T^{8} + 162 T^{10} + 729 T^{12} \))(\( 1 - T^{2} + 7 T^{4} - 14 T^{6} + 63 T^{8} - 81 T^{10} + 729 T^{12} \))(\( 1 - T^{2} + 7 T^{4} - 14 T^{6} + 63 T^{8} - 81 T^{10} + 729 T^{12} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 - 4 T^{2} + 14 T^{4} - 36 T^{6} + 81 T^{8} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 - T + T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 + 4 T^{2} + 2 T^{4} - 16 T^{6} - 29 T^{8} - 144 T^{10} + 162 T^{12} + 2916 T^{14} + 6561 T^{16} \))(\( ( 1 + 3 T + 3 T^{2} )^{2} \))(\( ( 1 - 3 T + 3 T^{2} )^{2} \))(\( ( 1 + 4 T^{2} + 7 T^{4} + 36 T^{6} + 81 T^{8} )^{2} \))(\( ( 1 + T + T^{2} )^{4} \))(\( ( 1 + T + T^{2} )^{4} \))(\( ( 1 - T + T^{2} )^{4} \))(\( ( 1 - T + T^{2} )^{4} \))(\( 1 - 3 T^{2} + 9 T^{4} - 27 T^{6} + 81 T^{8} - 243 T^{10} + 729 T^{12} \))(\( 1 + 3 T + 6 T^{2} + 9 T^{3} + 9 T^{4} - 27 T^{6} + 81 T^{8} + 243 T^{9} + 486 T^{10} + 729 T^{11} + 729 T^{12} \))
$5$ (\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 4 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 18 T^{2} + 153 T^{4} - 906 T^{6} + 4676 T^{8} - 22650 T^{10} + 95625 T^{12} - 281250 T^{14} + 390625 T^{16} \))(\( 1 - 18 T^{2} + 153 T^{4} - 906 T^{6} + 4676 T^{8} - 22650 T^{10} + 95625 T^{12} - 281250 T^{14} + 390625 T^{16} \))(\( 1 - 24 T^{2} + 296 T^{4} - 2744 T^{6} + 21123 T^{8} - 134032 T^{10} + 718928 T^{12} - 3350800 T^{14} + 13201875 T^{16} - 42875000 T^{18} + 115625000 T^{20} - 234375000 T^{22} + 244140625 T^{24} \))(\( 1 - 24 T^{2} + 296 T^{4} - 2744 T^{6} + 21123 T^{8} - 134032 T^{10} + 718928 T^{12} - 3350800 T^{14} + 13201875 T^{16} - 42875000 T^{18} + 115625000 T^{20} - 234375000 T^{22} + 244140625 T^{24} \))(\( ( 1 - 4 T^{2} + 25 T^{4} )^{2} \))(\( ( 1 - 4 T^{2} + 25 T^{4} )^{4} \))(\( ( 1 - 12 T^{2} + 83 T^{4} - 472 T^{6} + 2075 T^{8} - 7500 T^{10} + 15625 T^{12} )^{2} \))(\( ( 1 - 18 T^{2} + 170 T^{4} - 1042 T^{6} + 4250 T^{8} - 11250 T^{10} + 15625 T^{12} )^{2} \))(\( ( 1 - 18 T^{2} + 170 T^{4} - 1042 T^{6} + 4250 T^{8} - 11250 T^{10} + 15625 T^{12} )^{2} \))(\( ( 1 - 3 T + 5 T^{2} )^{2} \))(\( ( 1 + 5 T^{2} )^{2} \))(\( ( 1 + 3 T + 5 T^{2} )^{2} \))(\( ( 1 + 4 T^{2} + 4 T^{4} + 100 T^{6} + 625 T^{8} )^{2} \))(\( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 + 2 T - T^{2} + 10 T^{3} + 25 T^{4} \))(\( 1 - 5 T^{2} + 25 T^{4} \))(\( 1 - 4 T + 11 T^{2} - 20 T^{3} + 25 T^{4} \))(\( 1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4} \))(\( 1 - 5 T^{2} + 25 T^{4} \))(\( 1 - 2 T - T^{2} - 10 T^{3} + 25 T^{4} \))(\( 1 - 5 T^{2} + 25 T^{4} \))(\( 1 - 5 T^{2} + 25 T^{4} \))(\( 1 - 3 T + 4 T^{2} - 15 T^{3} + 25 T^{4} \))(\( 1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4} \))(\( 1 - 5 T^{2} + 25 T^{4} \))(\( ( 1 - 4 T^{2} + 12 T^{4} + 184 T^{6} - 1009 T^{8} + 4600 T^{10} + 7500 T^{12} - 62500 T^{14} + 390625 T^{16} )^{2} \))(\( 1 + 4 T^{2} - 9 T^{4} + 100 T^{6} + 625 T^{8} \))(\( 1 + 4 T^{2} - 9 T^{4} + 100 T^{6} + 625 T^{8} \))(\( ( 1 + 4 T^{2} - 9 T^{4} + 100 T^{6} + 625 T^{8} )^{4} \))(\( 1 + 6 T^{2} - 6 T^{4} - 48 T^{6} + 239 T^{8} - 1200 T^{10} - 3750 T^{12} + 93750 T^{14} + 390625 T^{16} \))(\( 1 + 9 T^{2} + 45 T^{4} - 96 T^{5} + 66 T^{6} - 864 T^{7} - 394 T^{8} - 4320 T^{9} + 1650 T^{10} - 12000 T^{11} + 28125 T^{12} + 140625 T^{14} + 390625 T^{16} \))(\( 1 + 6 T^{2} - 6 T^{4} - 48 T^{6} + 239 T^{8} - 1200 T^{10} - 3750 T^{12} + 93750 T^{14} + 390625 T^{16} \))(\( 1 + 9 T^{2} + 45 T^{4} - 96 T^{5} + 66 T^{6} - 864 T^{7} - 394 T^{8} - 4320 T^{9} + 1650 T^{10} - 12000 T^{11} + 28125 T^{12} + 140625 T^{14} + 390625 T^{16} \))(\( ( 1 - 5 T^{2} + 25 T^{4} - 125 T^{6} + 625 T^{8} - 3125 T^{10} + 15625 T^{12} )^{2} \))(\( 1 + 5 T^{2} - 125 T^{6} - 625 T^{8} + 15625 T^{12} - 390625 T^{16} - 1953125 T^{18} + 48828125 T^{22} + 244140625 T^{24} \))
$7$ (\( 1 + 4 T + 9 T^{2} + 8 T^{3} - 31 T^{4} - 180 T^{5} - 503 T^{6} - 1260 T^{7} - 1519 T^{8} + 2744 T^{9} + 21609 T^{10} + 67228 T^{11} + 117649 T^{12} \))(\( 1 - 5 T + 18 T^{2} - 55 T^{3} + 149 T^{4} - 360 T^{5} + 757 T^{6} - 2520 T^{7} + 7301 T^{8} - 18865 T^{9} + 43218 T^{10} - 84035 T^{11} + 117649 T^{12} \))
$11$ (\( 1 - 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( ( 1 - 10 T + 25 T^{2} + 94 T^{3} - 684 T^{4} + 1034 T^{5} + 3025 T^{6} - 13310 T^{7} + 14641 T^{8} )( 1 + 10 T + 25 T^{2} - 94 T^{3} - 684 T^{4} - 1034 T^{5} + 3025 T^{6} + 13310 T^{7} + 14641 T^{8} ) \))(\( ( 1 - 10 T + 25 T^{2} + 94 T^{3} - 684 T^{4} + 1034 T^{5} + 3025 T^{6} - 13310 T^{7} + 14641 T^{8} )( 1 + 10 T + 25 T^{2} - 94 T^{3} - 684 T^{4} - 1034 T^{5} + 3025 T^{6} + 13310 T^{7} + 14641 T^{8} ) \))(\( 1 - 28 T^{2} + 586 T^{4} - 9388 T^{6} + 131503 T^{8} - 1628696 T^{10} + 19283052 T^{12} - 197072216 T^{14} + 1925335423 T^{16} - 16631414668 T^{18} + 125614304266 T^{20} - 726247888828 T^{22} + 3138428376721 T^{24} \))(\( 1 - 28 T^{2} + 586 T^{4} - 9388 T^{6} + 131503 T^{8} - 1628696 T^{10} + 19283052 T^{12} - 197072216 T^{14} + 1925335423 T^{16} - 16631414668 T^{18} + 125614304266 T^{20} - 726247888828 T^{22} + 3138428376721 T^{24} \))(\( ( 1 + 20 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 + 10 T^{2} + 121 T^{4} )^{4} \))(\( ( 1 + 32 T^{2} + 607 T^{4} + 8240 T^{6} + 73447 T^{8} + 468512 T^{10} + 1771561 T^{12} )^{2} \))(\( ( 1 + 44 T^{2} + 952 T^{4} + 12830 T^{6} + 115192 T^{8} + 644204 T^{10} + 1771561 T^{12} )^{2} \))(\( ( 1 + 44 T^{2} + 952 T^{4} + 12830 T^{6} + 115192 T^{8} + 644204 T^{10} + 1771561 T^{12} )^{2} \))(\( 1 + 5 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 + 5 T^{2} + 121 T^{4} \))(\( ( 1 - 24 T^{2} + 314 T^{4} - 2904 T^{6} + 14641 T^{8} )^{2} \))(\( 1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4} \))(\( 1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4} \))(\( 1 - 6 T + 25 T^{2} - 66 T^{3} + 121 T^{4} \))(\( 1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4} \))(\( 1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4} \))(\( 1 - 6 T + 25 T^{2} - 66 T^{3} + 121 T^{4} \))(\( 1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4} \))(\( 1 + 11 T^{2} + 121 T^{4} \))(\( 1 + 11 T^{2} + 121 T^{4} \))(\( 1 - 9 T + 38 T^{2} - 99 T^{3} + 121 T^{4} \))(\( 1 + 9 T + 38 T^{2} + 99 T^{3} + 121 T^{4} \))(\( 1 + 11 T^{2} + 121 T^{4} \))(\( ( 1 + 24 T^{2} + 262 T^{4} + 1728 T^{6} + 14259 T^{8} + 209088 T^{10} + 3835942 T^{12} + 42517464 T^{14} + 214358881 T^{16} )^{2} \))(\( 1 - 20 T^{2} + 279 T^{4} - 2420 T^{6} + 14641 T^{8} \))(\( 1 - 20 T^{2} + 279 T^{4} - 2420 T^{6} + 14641 T^{8} \))(\( ( 1 - 10 T^{2} - 21 T^{4} - 1210 T^{6} + 14641 T^{8} )^{4} \))(\( 1 + 34 T^{2} + 642 T^{4} + 9248 T^{6} + 109679 T^{8} + 1119008 T^{10} + 9399522 T^{12} + 60233074 T^{14} + 214358881 T^{16} \))(\( ( 1 - 2 T + 25 T^{2} - 58 T^{3} + 372 T^{4} - 638 T^{5} + 3025 T^{6} - 2662 T^{7} + 14641 T^{8} )( 1 + 8 T + 34 T^{2} + 112 T^{3} + 339 T^{4} + 1232 T^{5} + 4114 T^{6} + 10648 T^{7} + 14641 T^{8} ) \))(\( 1 + 34 T^{2} + 642 T^{4} + 9248 T^{6} + 109679 T^{8} + 1119008 T^{10} + 9399522 T^{12} + 60233074 T^{14} + 214358881 T^{16} \))(\( ( 1 - 8 T + 34 T^{2} - 112 T^{3} + 339 T^{4} - 1232 T^{5} + 4114 T^{6} - 10648 T^{7} + 14641 T^{8} )( 1 + 2 T + 25 T^{2} + 58 T^{3} + 372 T^{4} + 638 T^{5} + 3025 T^{6} + 2662 T^{7} + 14641 T^{8} ) \))(\( ( 1 + 11 T^{2} + 121 T^{4} + 1331 T^{6} + 14641 T^{8} + 161051 T^{10} + 1771561 T^{12} )^{2} \))(\( 1 - 11 T^{2} + 1331 T^{6} - 14641 T^{8} + 1771561 T^{12} - 214358881 T^{16} + 2357947691 T^{18} - 285311670611 T^{22} + 3138428376721 T^{24} \))
$13$ (\( 1 + 3 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 - 3 T + 13 T^{2} \))(\( 1 - 66 T^{2} + 2241 T^{4} - 49362 T^{6} + 759092 T^{8} - 8342178 T^{10} + 64005201 T^{12} - 318569394 T^{14} + 815730721 T^{16} \))(\( 1 - 66 T^{2} + 2241 T^{4} - 49362 T^{6} + 759092 T^{8} - 8342178 T^{10} + 64005201 T^{12} - 318569394 T^{14} + 815730721 T^{16} \))(\( 1 - 64 T^{2} + 2288 T^{4} - 59968 T^{6} + 1236915 T^{8} - 20973696 T^{10} + 297955296 T^{12} - 3544554624 T^{14} + 35327529315 T^{16} - 289454082112 T^{18} + 1866391889648 T^{20} - 8822943478336 T^{22} + 23298085122481 T^{24} \))(\( 1 - 64 T^{2} + 2288 T^{4} - 59968 T^{6} + 1236915 T^{8} - 20973696 T^{10} + 297955296 T^{12} - 3544554624 T^{14} + 35327529315 T^{16} - 289454082112 T^{18} + 1866391889648 T^{20} - 8822943478336 T^{22} + 23298085122481 T^{24} \))(\( ( 1 + 13 T^{2} )^{4} \))(\( ( 1 - 4 T^{2} + 169 T^{4} )^{4} \))(\( ( 1 + 29 T^{2} + 4 T^{3} + 377 T^{4} + 2197 T^{6} )^{4} \))(\( ( 1 - 3 T + 29 T^{2} - 62 T^{3} + 377 T^{4} - 507 T^{5} + 2197 T^{6} )^{4} \))(\( ( 1 + 3 T + 29 T^{2} + 62 T^{3} + 377 T^{4} + 507 T^{5} + 2197 T^{6} )^{4} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 5 T + 13 T^{2} )( 1 + 5 T + 13 T^{2} ) \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 32 T^{2} + 592 T^{4} - 5408 T^{6} + 28561 T^{8} )^{2} \))(\( ( 1 + 4 T + 13 T^{2} )^{2} \))(\( ( 1 - 3 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )^{2} \))(\( ( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 4 T + 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )( 1 + 2 T + 13 T^{2} ) \))(\( ( 1 - 5 T + 13 T^{2} )( 1 + 5 T + 13 T^{2} ) \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 2 T + 13 T^{2} )( 1 + 2 T + 13 T^{2} ) \))(\( ( 1 - 32 T^{2} + 592 T^{4} - 5408 T^{6} + 28561 T^{8} )^{4} \))(\( ( 1 + 13 T^{2} )^{4} \))(\( ( 1 + 13 T^{2} )^{4} \))(\( ( 1 - 4 T^{2} + 169 T^{4} )^{8} \))(\( ( 1 - 12 T^{2} + 102 T^{4} - 2028 T^{6} + 28561 T^{8} )^{2} \))(\( 1 - 66 T^{2} + 2241 T^{4} - 49362 T^{6} + 759092 T^{8} - 8342178 T^{10} + 64005201 T^{12} - 318569394 T^{14} + 815730721 T^{16} \))(\( ( 1 - 12 T^{2} + 102 T^{4} - 2028 T^{6} + 28561 T^{8} )^{2} \))(\( 1 - 66 T^{2} + 2241 T^{4} - 49362 T^{6} + 759092 T^{8} - 8342178 T^{10} + 64005201 T^{12} - 318569394 T^{14} + 815730721 T^{16} \))(\( ( 1 - 2 T - 9 T^{2} + 44 T^{3} + 29 T^{4} - 630 T^{5} + 883 T^{6} - 8190 T^{7} + 4901 T^{8} + 96668 T^{9} - 257049 T^{10} - 742586 T^{11} + 4826809 T^{12} )( 1 + 2 T - 9 T^{2} - 44 T^{3} + 29 T^{4} + 630 T^{5} + 883 T^{6} + 8190 T^{7} + 4901 T^{8} - 96668 T^{9} - 257049 T^{10} + 742586 T^{11} + 4826809 T^{12} ) \))(\( ( 1 - 5 T + 12 T^{2} + 5 T^{3} - 181 T^{4} + 840 T^{5} - 1847 T^{6} + 10920 T^{7} - 30589 T^{8} + 10985 T^{9} + 342732 T^{10} - 1856465 T^{11} + 4826809 T^{12} )( 1 + 5 T + 12 T^{2} - 5 T^{3} - 181 T^{4} - 840 T^{5} - 1847 T^{6} - 10920 T^{7} - 30589 T^{8} - 10985 T^{9} + 342732 T^{10} + 1856465 T^{11} + 4826809 T^{12} ) \))
$17$ (\( 1 - 8 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 8 T + 17 T^{2} \))(\( 1 - 80 T^{2} + 3228 T^{4} - 87472 T^{6} + 1728326 T^{8} - 25279408 T^{10} + 269605788 T^{12} - 1931005520 T^{14} + 6975757441 T^{16} \))(\( 1 - 80 T^{2} + 3228 T^{4} - 87472 T^{6} + 1728326 T^{8} - 25279408 T^{10} + 269605788 T^{12} - 1931005520 T^{14} + 6975757441 T^{16} \))(\( 1 - 88 T^{2} + 4536 T^{4} - 165688 T^{6} + 4700147 T^{8} - 107164048 T^{10} + 2007265136 T^{12} - 30970409872 T^{14} + 392560977587 T^{16} - 3999305532472 T^{18} + 31642035752376 T^{20} - 177407463239512 T^{22} + 582622237229761 T^{24} \))(\( 1 - 88 T^{2} + 4536 T^{4} - 165688 T^{6} + 4700147 T^{8} - 107164048 T^{10} + 2007265136 T^{12} - 30970409872 T^{14} + 392560977587 T^{16} - 3999305532472 T^{18} + 31642035752376 T^{20} - 177407463239512 T^{22} + 582622237229761 T^{24} \))(\( ( 1 + 20 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 10 T^{2} + 289 T^{4} )^{4} \))(\( ( 1 - 68 T^{2} + 2311 T^{4} - 49064 T^{6} + 667879 T^{8} - 5679428 T^{10} + 24137569 T^{12} )^{2} \))(\( ( 1 - 59 T^{2} + 1723 T^{4} - 34178 T^{6} + 497947 T^{8} - 4927739 T^{10} + 24137569 T^{12} )^{2} \))(\( ( 1 - 59 T^{2} + 1723 T^{4} - 34178 T^{6} + 497947 T^{8} - 4927739 T^{10} + 24137569 T^{12} )^{2} \))(\( ( 1 - 3 T + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 + 3 T + 17 T^{2} )^{2} \))(\( ( 1 - 4 T^{2} + 420 T^{4} - 1156 T^{6} + 83521 T^{8} )^{2} \))(\( 1 + 6 T + 19 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 - 8 T + 47 T^{2} - 136 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 + 4 T - T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 - 4 T - T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 - 6 T + 19 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( 1 - 3 T - 8 T^{2} - 51 T^{3} + 289 T^{4} \))(\( 1 + 3 T - 8 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 - 17 T^{2} + 289 T^{4} \))(\( ( 1 + 4 T^{2} - 404 T^{4} - 632 T^{6} + 88255 T^{8} - 182648 T^{10} - 33742484 T^{12} + 96550276 T^{14} + 6975757441 T^{16} )^{2} \))(\( 1 - 20 T^{2} + 111 T^{4} - 5780 T^{6} + 83521 T^{8} \))(\( 1 - 20 T^{2} + 111 T^{4} - 5780 T^{6} + 83521 T^{8} \))(\( ( 1 + 10 T^{2} - 189 T^{4} + 2890 T^{6} + 83521 T^{8} )^{4} \))(\( 1 + 22 T^{2} - 198 T^{4} + 2288 T^{6} + 241727 T^{8} + 661232 T^{10} - 16537158 T^{12} + 531026518 T^{14} + 6975757441 T^{16} \))(\( 1 + 40 T^{2} + 786 T^{4} - 1104 T^{5} + 10208 T^{6} - 39072 T^{7} + 129731 T^{8} - 664224 T^{9} + 2950112 T^{10} - 5423952 T^{11} + 65647506 T^{12} + 965502760 T^{14} + 6975757441 T^{16} \))(\( 1 + 22 T^{2} - 198 T^{4} + 2288 T^{6} + 241727 T^{8} + 661232 T^{10} - 16537158 T^{12} + 531026518 T^{14} + 6975757441 T^{16} \))(\( 1 + 40 T^{2} + 786 T^{4} - 1104 T^{5} + 10208 T^{6} - 39072 T^{7} + 129731 T^{8} - 664224 T^{9} + 2950112 T^{10} - 5423952 T^{11} + 65647506 T^{12} + 965502760 T^{14} + 6975757441 T^{16} \))(\( ( 1 - 17 T^{2} + 289 T^{4} - 4913 T^{6} + 83521 T^{8} - 1419857 T^{10} + 24137569 T^{12} )^{2} \))(\( 1 + 17 T^{2} - 4913 T^{6} - 83521 T^{8} + 24137569 T^{12} - 6975757441 T^{16} - 118587876497 T^{18} + 34271896307633 T^{22} + 582622237229761 T^{24} \))
$19$ (\( 1 + T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( ( 1 + 6 T + 69 T^{2} + 282 T^{3} + 1904 T^{4} + 5358 T^{5} + 24909 T^{6} + 41154 T^{7} + 130321 T^{8} )^{2} \))(\( ( 1 - 6 T + 69 T^{2} - 282 T^{3} + 1904 T^{4} - 5358 T^{5} + 24909 T^{6} - 41154 T^{7} + 130321 T^{8} )^{2} \))(\( ( 1 + 42 T^{2} + 32 T^{3} + 1231 T^{4} + 544 T^{5} + 29916 T^{6} + 10336 T^{7} + 444391 T^{8} + 219488 T^{9} + 5473482 T^{10} + 47045881 T^{12} )^{2} \))(\( ( 1 + 42 T^{2} - 32 T^{3} + 1231 T^{4} - 544 T^{5} + 29916 T^{6} - 10336 T^{7} + 444391 T^{8} - 219488 T^{9} + 5473482 T^{10} + 47045881 T^{12} )^{2} \))(\( ( 1 + 10 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 - 20 T^{2} + 361 T^{4} )^{4} \))(\( ( 1 - 50 T^{2} + 1675 T^{4} - 38132 T^{6} + 604675 T^{8} - 6516050 T^{10} + 47045881 T^{12} )^{2} \))(\( ( 1 - 98 T^{2} + 4270 T^{4} - 105158 T^{6} + 1541470 T^{8} - 12771458 T^{10} + 47045881 T^{12} )^{2} \))(\( ( 1 - 98 T^{2} + 4270 T^{4} - 105158 T^{6} + 1541470 T^{8} - 12771458 T^{10} + 47045881 T^{12} )^{2} \))(\( 1 - 35 T^{2} + 361 T^{4} \))(\( ( 1 - T + 19 T^{2} )( 1 + T + 19 T^{2} ) \))(\( 1 - 35 T^{2} + 361 T^{4} \))(\( ( 1 - 12 T^{2} + 246 T^{4} - 4332 T^{6} + 130321 T^{8} )^{2} \))(\( ( 1 + T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( ( 1 - 7 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 4 T - 3 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( ( 1 - 7 T + 19 T^{2} )( 1 - T + 19 T^{2} ) \))(\( ( 1 - T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( ( 1 - 8 T + 19 T^{2} )( 1 - 7 T + 19 T^{2} ) \))(\( 1 + 3 T + 22 T^{2} + 57 T^{3} + 361 T^{4} \))(\( 1 + 3 T + 22 T^{2} + 57 T^{3} + 361 T^{4} \))(\( ( 1 - 7 T + 19 T^{2} )( 1 + T + 19 T^{2} ) \))(\( ( 1 + 12 T^{2} - 102 T^{4} - 5712 T^{6} - 121789 T^{8} - 2062032 T^{10} - 13292742 T^{12} + 564550572 T^{14} + 16983563041 T^{16} )^{2} \))(\( ( 1 - 12 T + 67 T^{2} - 228 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 + 12 T + 67 T^{2} + 228 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 + 20 T^{2} + 39 T^{4} + 7220 T^{6} + 130321 T^{8} )^{4} \))(\( ( 1 - 6 T + 6 T^{2} + 48 T^{3} - 145 T^{4} + 912 T^{5} + 2166 T^{6} - 41154 T^{7} + 130321 T^{8} )^{2} \))(\( 1 + 6 T - 33 T^{2} - 150 T^{3} + 1165 T^{4} + 1968 T^{5} - 34182 T^{6} - 11868 T^{7} + 759066 T^{8} - 225492 T^{9} - 12339702 T^{10} + 13498512 T^{11} + 151823965 T^{12} - 371414850 T^{13} - 1552514073 T^{14} + 5363230434 T^{15} + 16983563041 T^{16} \))(\( ( 1 + 6 T + 6 T^{2} - 48 T^{3} - 145 T^{4} - 912 T^{5} + 2166 T^{6} + 41154 T^{7} + 130321 T^{8} )^{2} \))(\( 1 - 6 T - 33 T^{2} + 150 T^{3} + 1165 T^{4} - 1968 T^{5} - 34182 T^{6} + 11868 T^{7} + 759066 T^{8} + 225492 T^{9} - 12339702 T^{10} - 13498512 T^{11} + 151823965 T^{12} + 371414850 T^{13} - 1552514073 T^{14} - 5363230434 T^{15} + 16983563041 T^{16} \))(\( ( 1 - 8 T + 45 T^{2} - 208 T^{3} + 809 T^{4} - 2520 T^{5} + 4789 T^{6} - 47880 T^{7} + 292049 T^{8} - 1426672 T^{9} + 5864445 T^{10} - 19808792 T^{11} + 47045881 T^{12} )( 1 + 8 T + 45 T^{2} + 208 T^{3} + 809 T^{4} + 2520 T^{5} + 4789 T^{6} + 47880 T^{7} + 292049 T^{8} + 1426672 T^{9} + 5864445 T^{10} + 19808792 T^{11} + 47045881 T^{12} ) \))(\( ( 1 - 8 T + 45 T^{2} - 208 T^{3} + 809 T^{4} - 2520 T^{5} + 4789 T^{6} - 47880 T^{7} + 292049 T^{8} - 1426672 T^{9} + 5864445 T^{10} - 19808792 T^{11} + 47045881 T^{12} )( 1 - 7 T + 30 T^{2} - 77 T^{3} - 31 T^{4} + 1680 T^{5} - 11171 T^{6} + 31920 T^{7} - 11191 T^{8} - 528143 T^{9} + 3909630 T^{10} - 17332693 T^{11} + 47045881 T^{12} ) \))
$23$ (\( 1 - 8 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 - 104 T^{2} + 5628 T^{4} - 203992 T^{6} + 5416646 T^{8} - 107911768 T^{10} + 1574945148 T^{12} - 15395732456 T^{14} + 78310985281 T^{16} \))(\( 1 - 104 T^{2} + 5628 T^{4} - 203992 T^{6} + 5416646 T^{8} - 107911768 T^{10} + 1574945148 T^{12} - 15395732456 T^{14} + 78310985281 T^{16} \))(\( 1 - 60 T^{2} + 3354 T^{4} - 123436 T^{6} + 4153279 T^{8} - 110540568 T^{10} + 2811666956 T^{12} - 58475960472 T^{14} + 1162257748639 T^{16} - 18272957994604 T^{18} + 262655044632474 T^{20} - 2485590672818940 T^{22} + 21914624432020321 T^{24} \))(\( 1 - 60 T^{2} + 3354 T^{4} - 123436 T^{6} + 4153279 T^{8} - 110540568 T^{10} + 2811666956 T^{12} - 58475960472 T^{14} + 1162257748639 T^{16} - 18272957994604 T^{18} + 262655044632474 T^{20} - 2485590672818940 T^{22} + 21914624432020321 T^{24} \))(\( ( 1 - 4 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 + 23 T^{2} )^{8} \))(\( ( 1 + 112 T^{2} + 5671 T^{4} + 166576 T^{6} + 2999959 T^{8} + 31342192 T^{10} + 148035889 T^{12} )^{2} \))(\( ( 1 + 55 T^{2} + 1831 T^{4} + 48802 T^{6} + 968599 T^{8} + 15391255 T^{10} + 148035889 T^{12} )^{2} \))(\( ( 1 + 55 T^{2} + 1831 T^{4} + 48802 T^{6} + 968599 T^{8} + 15391255 T^{10} + 148035889 T^{12} )^{2} \))(\( 1 - 19 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 19 T^{2} + 529 T^{4} \))(\( ( 1 - 16 T^{2} + 1050 T^{4} - 8464 T^{6} + 279841 T^{8} )^{2} \))(\( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 + 8 T + 41 T^{2} + 184 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 + 2 T - 19 T^{2} + 46 T^{3} + 529 T^{4} \))(\( 1 + 2 T - 19 T^{2} + 46 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 + 23 T^{2} + 529 T^{4} \))(\( 1 + 23 T^{2} + 529 T^{4} \))(\( 1 + 9 T + 50 T^{2} + 207 T^{3} + 529 T^{4} \))(\( 1 - 9 T + 50 T^{2} - 207 T^{3} + 529 T^{4} \))(\( 1 + 23 T^{2} + 529 T^{4} \))(\( ( 1 + 16 T^{2} - 794 T^{4} - 128 T^{6} + 687235 T^{8} - 67712 T^{10} - 222193754 T^{12} + 2368574224 T^{14} + 78310985281 T^{16} )^{2} \))(\( 1 + 4 T^{2} - 513 T^{4} + 2116 T^{6} + 279841 T^{8} \))(\( 1 + 4 T^{2} - 513 T^{4} + 2116 T^{6} + 279841 T^{8} \))(\( ( 1 - 23 T^{2} + 529 T^{4} )^{8} \))(\( 1 + 82 T^{2} + 4002 T^{4} + 136448 T^{6} + 3572447 T^{8} + 72180992 T^{10} + 1119923682 T^{12} + 12138942898 T^{14} + 78310985281 T^{16} \))(\( 1 + 52 T^{2} + 1242 T^{4} - 2784 T^{5} + 24080 T^{6} - 140352 T^{7} + 497843 T^{8} - 3228096 T^{9} + 12738320 T^{10} - 33872928 T^{11} + 347562522 T^{12} + 7697866228 T^{14} + 78310985281 T^{16} \))(\( 1 + 82 T^{2} + 4002 T^{4} + 136448 T^{6} + 3572447 T^{8} + 72180992 T^{10} + 1119923682 T^{12} + 12138942898 T^{14} + 78310985281 T^{16} \))(\( 1 + 52 T^{2} + 1242 T^{4} + 2784 T^{5} + 24080 T^{6} + 140352 T^{7} + 497843 T^{8} + 3228096 T^{9} + 12738320 T^{10} + 33872928 T^{11} + 347562522 T^{12} + 7697866228 T^{14} + 78310985281 T^{16} \))(\( ( 1 + 23 T^{2} + 529 T^{4} + 12167 T^{6} + 279841 T^{8} + 6436343 T^{10} + 148035889 T^{12} )^{2} \))(\( 1 - 23 T^{2} + 12167 T^{6} - 279841 T^{8} + 148035889 T^{12} - 78310985281 T^{16} + 1801152661463 T^{18} - 952809757913927 T^{22} + 21914624432020321 T^{24} \))
$29$ (\( 1 - 4 T + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 - 4 T + 29 T^{2} \))(\( ( 1 + 8 T + 71 T^{2} + 344 T^{3} + 1924 T^{4} + 9976 T^{5} + 59711 T^{6} + 195112 T^{7} + 707281 T^{8} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} + 344 T^{3} + 1924 T^{4} + 9976 T^{5} + 59711 T^{6} + 195112 T^{7} + 707281 T^{8} )^{2} \))(\( ( 1 - 16 T + 200 T^{2} - 1728 T^{3} + 13363 T^{4} - 84496 T^{5} + 496976 T^{6} - 2450384 T^{7} + 11238283 T^{8} - 42144192 T^{9} + 141456200 T^{10} - 328178384 T^{11} + 594823321 T^{12} )^{2} \))(\( ( 1 - 16 T + 200 T^{2} - 1728 T^{3} + 13363 T^{4} - 84496 T^{5} + 496976 T^{6} - 2450384 T^{7} + 11238283 T^{8} - 42144192 T^{9} + 141456200 T^{10} - 328178384 T^{11} + 594823321 T^{12} )^{2} \))(\( ( 1 - 29 T^{2} )^{4} \))(\( ( 1 - 38 T^{2} + 841 T^{4} )^{4} \))(\( ( 1 - 30 T^{2} + 1047 T^{4} - 12836 T^{6} + 880527 T^{8} - 21218430 T^{10} + 594823321 T^{12} )^{2} \))(\( ( 1 - 129 T^{2} + 7599 T^{4} - 272414 T^{6} + 6390759 T^{8} - 91239249 T^{10} + 594823321 T^{12} )^{2} \))(\( ( 1 - 129 T^{2} + 7599 T^{4} - 272414 T^{6} + 6390759 T^{8} - 91239249 T^{10} + 594823321 T^{12} )^{2} \))(\( ( 1 - 29 T^{2} )^{2} \))(\( ( 1 - 29 T^{2} )^{2} \))(\( ( 1 - 29 T^{2} )^{2} \))(\( ( 1 - 32 T^{2} + 1546 T^{4} - 26912 T^{6} + 707281 T^{8} )^{2} \))(\( ( 1 + 10 T + 29 T^{2} )^{2} \))(\( ( 1 - 4 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 10 T + 29 T^{2} )^{2} \))(\( ( 1 - 29 T^{2} )^{2} \))(\( ( 1 - 29 T^{2} )^{2} \))(\( ( 1 - 29 T^{2} )^{2} \))(\( ( 1 - 29 T^{2} )^{2} \))(\( ( 1 - 29 T^{2} )^{2} \))(\( ( 1 - 32 T^{2} + 1546 T^{4} - 26912 T^{6} + 707281 T^{8} )^{4} \))(\( ( 1 - 29 T^{2} )^{4} \))(\( ( 1 - 29 T^{2} )^{4} \))(\( ( 1 - 38 T^{2} + 841 T^{4} )^{8} \))(\( ( 1 + 2 T + 29 T^{2} )^{8} \))(\( ( 1 + 8 T + 71 T^{2} + 344 T^{3} + 1924 T^{4} + 9976 T^{5} + 59711 T^{6} + 195112 T^{7} + 707281 T^{8} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{8} \))(\( ( 1 + 8 T + 71 T^{2} + 344 T^{3} + 1924 T^{4} + 9976 T^{5} + 59711 T^{6} + 195112 T^{7} + 707281 T^{8} )^{2} \))(\( ( 1 + 29 T^{2} + 841 T^{4} + 24389 T^{6} + 707281 T^{8} + 20511149 T^{10} + 594823321 T^{12} )^{2} \))(\( ( 1 + 29 T^{2} + 841 T^{4} + 24389 T^{6} + 707281 T^{8} + 20511149 T^{10} + 594823321 T^{12} )^{2} \))
$31$ (\( 1 - 3 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 3 T + 31 T^{2} \))(\( ( 1 - 6 T + 40 T^{2} - 288 T^{3} + 2601 T^{4} - 8928 T^{5} + 38440 T^{6} - 178746 T^{7} + 923521 T^{8} )^{2} \))(\( ( 1 + 6 T + 40 T^{2} + 288 T^{3} + 2601 T^{4} + 8928 T^{5} + 38440 T^{6} + 178746 T^{7} + 923521 T^{8} )^{2} \))(\( ( 1 + 8 T + 130 T^{2} + 824 T^{3} + 8247 T^{4} + 42224 T^{5} + 314764 T^{6} + 1308944 T^{7} + 7925367 T^{8} + 24547784 T^{9} + 120057730 T^{10} + 229033208 T^{11} + 887503681 T^{12} )^{2} \))(\( ( 1 - 8 T + 130 T^{2} - 824 T^{3} + 8247 T^{4} - 42224 T^{5} + 314764 T^{6} - 1308944 T^{7} + 7925367 T^{8} - 24547784 T^{9} + 120057730 T^{10} - 229033208 T^{11} + 887503681 T^{12} )^{2} \))(\( ( 1 - 50 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 + 10 T^{2} + 961 T^{4} )^{4} \))(\( ( 1 - 118 T^{2} + 7327 T^{4} - 280660 T^{6} + 7041247 T^{8} - 108975478 T^{10} + 887503681 T^{12} )^{2} \))(\( ( 1 - 115 T^{2} + 6850 T^{4} - 257011 T^{6} + 6582850 T^{8} - 106204915 T^{10} + 887503681 T^{12} )^{2} \))(\( ( 1 - 115 T^{2} + 6850 T^{4} - 257011 T^{6} + 6582850 T^{8} - 106204915 T^{10} + 887503681 T^{12} )^{2} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) \))(\( ( 1 - 20 T^{2} + 1630 T^{4} - 19220 T^{6} + 923521 T^{8} )^{2} \))(\( ( 1 - 7 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) \))(\( 1 - 3 T - 22 T^{2} - 93 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 33 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 - 31 T^{2} + 961 T^{4} \))(\( 1 - 31 T^{2} + 961 T^{4} \))(\( 1 - 8 T + 33 T^{2} - 248 T^{3} + 961 T^{4} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} ) \))(\( ( 1 + 7 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) \))(\( ( 1 - 7 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))(\( ( 1 - 7 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))(\( ( 1 - 7 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))(\( ( 1 - 11 T + 31 T^{2} )( 1 - 7 T + 31 T^{2} ) \))(\( ( 1 + 20 T^{2} - 1230 T^{4} - 5840 T^{6} + 1348979 T^{8} - 5612240 T^{10} - 1135930830 T^{12} + 17750073620 T^{14} + 852891037441 T^{16} )^{2} \))(\( ( 1 + 6 T + 43 T^{2} + 186 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 - 6 T + 43 T^{2} - 186 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 - 10 T^{2} - 861 T^{4} - 9610 T^{6} + 923521 T^{8} )^{4} \))(\( ( 1 - 31 T^{2} + 961 T^{4} )^{4} \))(\( 1 - 6 T - 4 T^{2} + 336 T^{3} - 2729 T^{4} + 10764 T^{5} + 2216 T^{6} - 444234 T^{7} + 3877768 T^{8} - 13771254 T^{9} + 2129576 T^{10} + 320670324 T^{11} - 2520288809 T^{12} + 9619394736 T^{13} - 3550014724 T^{14} - 165075684666 T^{15} + 852891037441 T^{16} \))(\( ( 1 - 31 T^{2} + 961 T^{4} )^{4} \))(\( 1 + 6 T - 4 T^{2} - 336 T^{3} - 2729 T^{4} - 10764 T^{5} + 2216 T^{6} + 444234 T^{7} + 3877768 T^{8} + 13771254 T^{9} + 2129576 T^{10} - 320670324 T^{11} - 2520288809 T^{12} - 9619394736 T^{13} - 3550014724 T^{14} + 165075684666 T^{15} + 852891037441 T^{16} \))(\( ( 1 - 4 T - 15 T^{2} + 184 T^{3} - 271 T^{4} - 4620 T^{5} + 26881 T^{6} - 143220 T^{7} - 260431 T^{8} + 5481544 T^{9} - 13852815 T^{10} - 114516604 T^{11} + 887503681 T^{12} )( 1 + 4 T - 15 T^{2} - 184 T^{3} - 271 T^{4} + 4620 T^{5} + 26881 T^{6} + 143220 T^{7} - 260431 T^{8} - 5481544 T^{9} - 13852815 T^{10} + 114516604 T^{11} + 887503681 T^{12} ) \))(\( ( 1 - 7 T + 18 T^{2} + 91 T^{3} - 1195 T^{4} + 5544 T^{5} - 1763 T^{6} + 171864 T^{7} - 1148395 T^{8} + 2710981 T^{9} + 16623378 T^{10} - 200404057 T^{11} + 887503681 T^{12} )( 1 + 4 T - 15 T^{2} - 184 T^{3} - 271 T^{4} + 4620 T^{5} + 26881 T^{6} + 143220 T^{7} - 260431 T^{8} - 5481544 T^{9} - 13852815 T^{10} + 114516604 T^{11} + 887503681 T^{12} ) \))
$37$ (\( 1 + T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( ( 1 + 6 T + 105 T^{2} + 306 T^{3} + 4436 T^{4} + 11322 T^{5} + 143745 T^{6} + 303918 T^{7} + 1874161 T^{8} )^{2} \))(\( ( 1 + 6 T + 105 T^{2} + 306 T^{3} + 4436 T^{4} + 11322 T^{5} + 143745 T^{6} + 303918 T^{7} + 1874161 T^{8} )^{2} \))(\( ( 1 - 16 T + 200 T^{2} - 1680 T^{3} + 13131 T^{4} - 82528 T^{5} + 535824 T^{6} - 3053536 T^{7} + 17976339 T^{8} - 85097040 T^{9} + 374832200 T^{10} - 1109503312 T^{11} + 2565726409 T^{12} )^{2} \))(\( ( 1 - 16 T + 200 T^{2} - 1680 T^{3} + 13131 T^{4} - 82528 T^{5} + 535824 T^{6} - 3053536 T^{7} + 17976339 T^{8} - 85097040 T^{9} + 374832200 T^{10} - 1109503312 T^{11} + 2565726409 T^{12} )^{2} \))(\( ( 1 - 8 T + 37 T^{2} )^{4} \))(\( ( 1 + 2 T + 37 T^{2} )^{8} \))(\( ( 1 + 4 T + 83 T^{2} + 312 T^{3} + 3071 T^{4} + 5476 T^{5} + 50653 T^{6} )^{4} \))(\( ( 1 - 2 T + 32 T^{2} + 144 T^{3} + 1184 T^{4} - 2738 T^{5} + 50653 T^{6} )^{4} \))(\( ( 1 - 2 T + 32 T^{2} + 144 T^{3} + 1184 T^{4} - 2738 T^{5} + 50653 T^{6} )^{4} \))(\( ( 1 - 7 T + 37 T^{2} )^{2} \))(\( ( 1 + 11 T + 37 T^{2} )^{2} \))(\( ( 1 - 7 T + 37 T^{2} )^{2} \))(\( ( 1 + 4 T + 60 T^{2} + 148 T^{3} + 1369 T^{4} )^{4} \))(\( 1 + 6 T - T^{2} + 222 T^{3} + 1369 T^{4} \))(\( ( 1 - 11 T + 37 T^{2} )( 1 + 10 T + 37 T^{2} ) \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 + 6 T - T^{2} + 222 T^{3} + 1369 T^{4} \))(\( ( 1 - T + 37 T^{2} )( 1 + 11 T + 37 T^{2} ) \))(\( ( 1 - 10 T + 37 T^{2} )( 1 - T + 37 T^{2} ) \))(\( 1 + 7 T + 12 T^{2} + 259 T^{3} + 1369 T^{4} \))(\( 1 + 7 T + 12 T^{2} + 259 T^{3} + 1369 T^{4} \))(\( ( 1 - T + 37 T^{2} )( 1 + 11 T + 37 T^{2} ) \))(\( ( 1 - 4 T - 44 T^{2} + 56 T^{3} + 1639 T^{4} + 2072 T^{5} - 60236 T^{6} - 202612 T^{7} + 1874161 T^{8} )^{4} \))(\( ( 1 + 8 T + 27 T^{2} + 296 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 + 8 T + 27 T^{2} + 296 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 - 2 T - 33 T^{2} - 74 T^{3} + 1369 T^{4} )^{8} \))(\( ( 1 - 6 T - 30 T^{2} + 48 T^{3} + 1655 T^{4} + 1776 T^{5} - 41070 T^{6} - 303918 T^{7} + 1874161 T^{8} )^{2} \))(\( 1 - 6 T - 69 T^{2} - 18 T^{3} + 4753 T^{4} + 9780 T^{5} - 152586 T^{6} - 146184 T^{7} + 2893194 T^{8} - 5408808 T^{9} - 208890234 T^{10} + 495386340 T^{11} + 8907887233 T^{12} - 1248191226 T^{13} - 177035122221 T^{14} - 569591262798 T^{15} + 3512479453921 T^{16} \))(\( ( 1 - 6 T - 30 T^{2} + 48 T^{3} + 1655 T^{4} + 1776 T^{5} - 41070 T^{6} - 303918 T^{7} + 1874161 T^{8} )^{2} \))(\( 1 - 6 T - 69 T^{2} - 18 T^{3} + 4753 T^{4} + 9780 T^{5} - 152586 T^{6} - 146184 T^{7} + 2893194 T^{8} - 5408808 T^{9} - 208890234 T^{10} + 495386340 T^{11} + 8907887233 T^{12} - 1248191226 T^{13} - 177035122221 T^{14} - 569591262798 T^{15} + 3512479453921 T^{16} \))(\( ( 1 - 10 T + 37 T^{2} )^{6}( 1 + 10 T + 63 T^{2} + 260 T^{3} + 269 T^{4} - 6930 T^{5} - 79253 T^{6} - 256410 T^{7} + 368261 T^{8} + 13169780 T^{9} + 118072143 T^{10} + 693439570 T^{11} + 2565726409 T^{12} ) \))(\( ( 1 - T + 37 T^{2} )^{6}( 1 + 10 T + 63 T^{2} + 260 T^{3} + 269 T^{4} - 6930 T^{5} - 79253 T^{6} - 256410 T^{7} + 368261 T^{8} + 13169780 T^{9} + 118072143 T^{10} + 693439570 T^{11} + 2565726409 T^{12} ) \))
$41$ (\( 1 - 6 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 12 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - 120 T^{2} + 9948 T^{4} - 607176 T^{6} + 27583238 T^{8} - 1020662856 T^{10} + 28110670428 T^{12} - 570012508920 T^{14} + 7984925229121 T^{16} \))(\( 1 - 120 T^{2} + 9948 T^{4} - 607176 T^{6} + 27583238 T^{8} - 1020662856 T^{10} + 28110670428 T^{12} - 570012508920 T^{14} + 7984925229121 T^{16} \))(\( 1 - 264 T^{2} + 32344 T^{4} - 2436136 T^{6} + 127693075 T^{8} - 5269183920 T^{10} + 207449944752 T^{12} - 8857498169520 T^{14} + 360830111305075 T^{16} - 11571899945252776 T^{18} + 258264421610689624 T^{20} - 3543582057880233864 T^{22} + 22563490300366186081 T^{24} \))(\( 1 - 264 T^{2} + 32344 T^{4} - 2436136 T^{6} + 127693075 T^{8} - 5269183920 T^{10} + 207449944752 T^{12} - 8857498169520 T^{14} + 360830111305075 T^{16} - 11571899945252776 T^{18} + 258264421610689624 T^{20} - 3543582057880233864 T^{22} + 22563490300366186081 T^{24} \))(\( ( 1 + 68 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 41 T^{2} )^{8} \))(\( ( 1 - 180 T^{2} + 14903 T^{4} - 753928 T^{6} + 25051943 T^{8} - 508636980 T^{10} + 4750104241 T^{12} )^{2} \))(\( ( 1 - 102 T^{2} + 8303 T^{4} - 375412 T^{6} + 13957343 T^{8} - 288227622 T^{10} + 4750104241 T^{12} )^{2} \))(\( ( 1 - 102 T^{2} + 8303 T^{4} - 375412 T^{6} + 13957343 T^{8} - 288227622 T^{10} + 4750104241 T^{12} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 100 T^{2} + 5524 T^{4} + 168100 T^{6} + 2825761 T^{8} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 12 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 12 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 100 T^{2} + 5524 T^{4} + 168100 T^{6} + 2825761 T^{8} )^{4} \))(\( ( 1 + 68 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 + 68 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 41 T^{2} )^{16} \))(\( ( 1 - 102 T^{2} + 5130 T^{4} - 171462 T^{6} + 2825761 T^{8} )^{2} \))(\( 1 - 120 T^{2} + 9948 T^{4} - 607176 T^{6} + 27583238 T^{8} - 1020662856 T^{10} + 28110670428 T^{12} - 570012508920 T^{14} + 7984925229121 T^{16} \))(\( ( 1 - 102 T^{2} + 5130 T^{4} - 171462 T^{6} + 2825761 T^{8} )^{2} \))(\( 1 - 120 T^{2} + 9948 T^{4} - 607176 T^{6} + 27583238 T^{8} - 1020662856 T^{10} + 28110670428 T^{12} - 570012508920 T^{14} + 7984925229121 T^{16} \))(\( ( 1 - 41 T^{2} + 1681 T^{4} - 68921 T^{6} + 2825761 T^{8} - 115856201 T^{10} + 4750104241 T^{12} )^{2} \))(\( ( 1 - 41 T^{2} + 1681 T^{4} - 68921 T^{6} + 2825761 T^{8} - 115856201 T^{10} + 4750104241 T^{12} )^{2} \))
$43$ (\( 1 - 11 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 - 11 T + 43 T^{2} \))(\( 1 - 210 T^{2} + 23793 T^{4} - 1729746 T^{6} + 88400276 T^{8} - 3198300354 T^{10} + 81343532193 T^{12} - 1327486240290 T^{14} + 11688200277601 T^{16} \))(\( 1 - 210 T^{2} + 23793 T^{4} - 1729746 T^{6} + 88400276 T^{8} - 3198300354 T^{10} + 81343532193 T^{12} - 1327486240290 T^{14} + 11688200277601 T^{16} \))(\( 1 - 276 T^{2} + 36338 T^{4} - 3157924 T^{6} + 212530239 T^{8} - 11922137512 T^{10} + 561568704636 T^{12} - 22044032259688 T^{14} + 726598593623439 T^{16} - 19962384085150276 T^{18} + 424725821687465138 T^{20} - 5964769118466452724 T^{22} + 39959630797262576401 T^{24} \))(\( 1 - 276 T^{2} + 36338 T^{4} - 3157924 T^{6} + 212530239 T^{8} - 11922137512 T^{10} + 561568704636 T^{12} - 22044032259688 T^{14} + 726598593623439 T^{16} - 19962384085150276 T^{18} + 424725821687465138 T^{20} - 5964769118466452724 T^{22} + 39959630797262576401 T^{24} \))(\( ( 1 - 43 T^{2} )^{4} \))(\( ( 1 - 26 T^{2} + 1849 T^{4} )^{4} \))(\( ( 1 - 74 T^{2} + 4039 T^{4} - 189452 T^{6} + 7468111 T^{8} - 252991274 T^{10} + 6321363049 T^{12} )^{2} \))(\( ( 1 - 227 T^{2} + 22639 T^{4} - 1266458 T^{6} + 41859511 T^{8} - 776067827 T^{10} + 6321363049 T^{12} )^{2} \))(\( ( 1 - 227 T^{2} + 22639 T^{4} - 1266458 T^{6} + 41859511 T^{8} - 776067827 T^{10} + 6321363049 T^{12} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 13 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 82 T^{2} + 172 T^{3} + 1849 T^{4} )^{4} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 11 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( ( 1 - 13 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( ( 1 + 4 T + 82 T^{2} + 172 T^{3} + 1849 T^{4} )^{8} \))(\( ( 1 - 43 T^{2} )^{4} \))(\( ( 1 - 43 T^{2} )^{4} \))(\( ( 1 - 26 T^{2} + 1849 T^{4} )^{8} \))(\( ( 1 - 24 T^{2} + 3774 T^{4} - 44376 T^{6} + 3418801 T^{8} )^{2} \))(\( 1 - 210 T^{2} + 23793 T^{4} - 1729746 T^{6} + 88400276 T^{8} - 3198300354 T^{10} + 81343532193 T^{12} - 1327486240290 T^{14} + 11688200277601 T^{16} \))(\( ( 1 - 24 T^{2} + 3774 T^{4} - 44376 T^{6} + 3418801 T^{8} )^{2} \))(\( 1 - 210 T^{2} + 23793 T^{4} - 1729746 T^{6} + 88400276 T^{8} - 3198300354 T^{10} + 81343532193 T^{12} - 1327486240290 T^{14} + 11688200277601 T^{16} \))(\( ( 1 - 8 T + 21 T^{2} + 176 T^{3} - 2311 T^{4} + 10920 T^{5} + 12013 T^{6} + 469560 T^{7} - 4273039 T^{8} + 13993232 T^{9} + 71794821 T^{10} - 1176067544 T^{11} + 6321363049 T^{12} )^{2} \))(\( ( 1 + 13 T + 126 T^{2} + 1079 T^{3} + 8609 T^{4} + 65520 T^{5} + 481573 T^{6} + 2817360 T^{7} + 15918041 T^{8} + 85788053 T^{9} + 430768926 T^{10} + 1911109759 T^{11} + 6321363049 T^{12} )^{2} \))
$47$ (\( 1 - 6 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 + 12 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( ( 1 - 4 T + 160 T^{2} - 548 T^{3} + 10686 T^{4} - 25756 T^{5} + 353440 T^{6} - 415292 T^{7} + 4879681 T^{8} )^{2} \))(\( ( 1 + 4 T + 160 T^{2} + 548 T^{3} + 10686 T^{4} + 25756 T^{5} + 353440 T^{6} + 415292 T^{7} + 4879681 T^{8} )^{2} \))(\( ( 1 + 90 T^{2} + 160 T^{3} + 6183 T^{4} + 13280 T^{5} + 328892 T^{6} + 624160 T^{7} + 13658247 T^{8} + 16611680 T^{9} + 439171290 T^{10} + 10779215329 T^{12} )^{2} \))(\( ( 1 + 90 T^{2} - 160 T^{3} + 6183 T^{4} - 13280 T^{5} + 328892 T^{6} - 624160 T^{7} + 13658247 T^{8} - 16611680 T^{9} + 439171290 T^{10} + 10779215329 T^{12} )^{2} \))(\( ( 1 + 47 T^{2} )^{4} \))(\( ( 1 + 47 T^{2} )^{8} \))(\( ( 1 + 178 T^{2} + 15631 T^{4} + 882364 T^{6} + 34528879 T^{8} + 868583218 T^{10} + 10779215329 T^{12} )^{2} \))(\( ( 1 + 199 T^{2} + 19063 T^{4} + 1118818 T^{6} + 42110167 T^{8} + 971056519 T^{10} + 10779215329 T^{12} )^{2} \))(\( ( 1 + 199 T^{2} + 19063 T^{4} + 1118818 T^{6} + 42110167 T^{8} + 971056519 T^{10} + 10779215329 T^{12} )^{2} \))(\( ( 1 - 3 T + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 + 3 T + 47 T^{2} )^{2} \))(\( ( 1 + 172 T^{2} + 11806 T^{4} + 379948 T^{6} + 4879681 T^{8} )^{2} \))(\( 1 + 8 T + 17 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 97 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 - 12 T + 97 T^{2} - 564 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 97 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 - 12 T + 97 T^{2} - 564 T^{3} + 2209 T^{4} \))(\( 1 - 8 T + 17 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 - 3 T - 38 T^{2} - 141 T^{3} + 2209 T^{4} \))(\( 1 + 3 T - 38 T^{2} + 141 T^{3} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( ( 1 - 172 T^{2} + 17778 T^{4} - 1270736 T^{6} + 69150899 T^{8} - 2807055824 T^{10} + 86750968818 T^{12} - 1854025036588 T^{14} + 23811286661761 T^{16} )^{2} \))(\( ( 1 - 47 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 47 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 47 T^{2} + 2209 T^{4} )^{8} \))(\( ( 1 + 4 T - 14 T^{2} - 256 T^{3} - 2061 T^{4} - 12032 T^{5} - 30926 T^{6} + 415292 T^{7} + 4879681 T^{8} )^{2} \))(\( 1 - 4 T - 144 T^{2} + 456 T^{3} + 12722 T^{4} - 27948 T^{5} - 805600 T^{6} + 556940 T^{7} + 41968563 T^{8} + 26176180 T^{9} - 1779570400 T^{10} - 2901645204 T^{11} + 62079301682 T^{12} + 104581323192 T^{13} - 1552207007376 T^{14} - 2026492481852 T^{15} + 23811286661761 T^{16} \))(\( ( 1 - 4 T - 14 T^{2} + 256 T^{3} - 2061 T^{4} + 12032 T^{5} - 30926 T^{6} - 415292 T^{7} + 4879681 T^{8} )^{2} \))(\( 1 + 4 T - 144 T^{2} - 456 T^{3} + 12722 T^{4} + 27948 T^{5} - 805600 T^{6} - 556940 T^{7} + 41968563 T^{8} - 26176180 T^{9} - 1779570400 T^{10} + 2901645204 T^{11} + 62079301682 T^{12} - 104581323192 T^{13} - 1552207007376 T^{14} + 2026492481852 T^{15} + 23811286661761 T^{16} \))(\( ( 1 - 47 T^{2} + 2209 T^{4} - 103823 T^{6} + 4879681 T^{8} - 229345007 T^{10} + 10779215329 T^{12} )^{2} \))(\( 1 + 47 T^{2} - 103823 T^{6} - 4879681 T^{8} + 10779215329 T^{12} - 23811286661761 T^{16} - 1119130473102767 T^{18} + 2472159215084012303 T^{22} + \)\(11\!\cdots\!41\)\( T^{24} \))
$53$ (\( 1 + 12 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( ( 1 - 4 T + 151 T^{2} - 752 T^{3} + 10380 T^{4} - 39856 T^{5} + 424159 T^{6} - 595508 T^{7} + 7890481 T^{8} )^{2} \))(\( ( 1 - 4 T + 151 T^{2} - 752 T^{3} + 10380 T^{4} - 39856 T^{5} + 424159 T^{6} - 595508 T^{7} + 7890481 T^{8} )^{2} \))(\( ( 1 + 16 T + 342 T^{2} + 3952 T^{3} + 47367 T^{4} + 404032 T^{5} + 3397044 T^{6} + 21413696 T^{7} + 133053903 T^{8} + 588361904 T^{9} + 2698544502 T^{10} + 6691127888 T^{11} + 22164361129 T^{12} )^{2} \))(\( ( 1 + 16 T + 342 T^{2} + 3952 T^{3} + 47367 T^{4} + 404032 T^{5} + 3397044 T^{6} + 21413696 T^{7} + 133053903 T^{8} + 588361904 T^{9} + 2698544502 T^{10} + 6691127888 T^{11} + 22164361129 T^{12} )^{2} \))(\( ( 1 - 53 T^{2} )^{4} \))(\( ( 1 - 86 T^{2} + 2809 T^{4} )^{4} \))(\( ( 1 - 262 T^{2} + 31111 T^{4} - 2121556 T^{6} + 87390799 T^{8} - 2067306022 T^{10} + 22164361129 T^{12} )^{2} \))(\( ( 1 - 154 T^{2} + 13858 T^{4} - 826258 T^{6} + 38927122 T^{8} - 1215134074 T^{10} + 22164361129 T^{12} )^{2} \))(\( ( 1 - 154 T^{2} + 13858 T^{4} - 826258 T^{6} + 38927122 T^{8} - 1215134074 T^{10} + 22164361129 T^{12} )^{2} \))(\( 1 - 79 T^{2} + 2809 T^{4} \))(\( ( 1 - 53 T^{2} )^{2} \))(\( 1 - 79 T^{2} + 2809 T^{4} \))(\( ( 1 - 108 T^{2} + 5942 T^{4} - 303372 T^{6} + 7890481 T^{8} )^{2} \))(\( 1 + 2 T - 49 T^{2} + 106 T^{3} + 2809 T^{4} \))(\( 1 - 12 T + 91 T^{2} - 636 T^{3} + 2809 T^{4} \))(\( 1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4} \))(\( 1 + 2 T - 49 T^{2} + 106 T^{3} + 2809 T^{4} \))(\( 1 + 53 T^{2} + 2809 T^{4} \))(\( 1 + 53 T^{2} + 2809 T^{4} \))(\( 1 + 9 T + 80 T^{2} + 477 T^{3} + 2809 T^{4} \))(\( 1 - 9 T + 80 T^{2} - 477 T^{3} + 2809 T^{4} \))(\( 1 + 53 T^{2} + 2809 T^{4} \))(\( ( 1 + 108 T^{2} + 5722 T^{4} + 34992 T^{6} - 5347293 T^{8} + 98292528 T^{10} + 45149332282 T^{12} + 2393751001932 T^{14} + 62259690411361 T^{16} )^{2} \))(\( ( 1 + 53 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 + 53 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 + 86 T^{2} + 4587 T^{4} + 241574 T^{6} + 7890481 T^{8} )^{4} \))(\( ( 1 + 8 T + 10 T^{2} - 416 T^{3} - 3285 T^{4} - 22048 T^{5} + 28090 T^{6} + 1191016 T^{7} + 7890481 T^{8} )^{2} \))(\( 1 + 4 T - 135 T^{2} - 900 T^{3} + 9413 T^{4} + 70368 T^{5} - 312982 T^{6} - 1938608 T^{7} + 10598262 T^{8} - 102746224 T^{9} - 879166438 T^{10} + 10476176736 T^{11} + 74273097653 T^{12} - 376375943700 T^{13} - 2992188752415 T^{14} + 4698844559348 T^{15} + 62259690411361 T^{16} \))(\( ( 1 + 8 T + 10 T^{2} - 416 T^{3} - 3285 T^{4} - 22048 T^{5} + 28090 T^{6} + 1191016 T^{7} + 7890481 T^{8} )^{2} \))(\( 1 + 4 T - 135 T^{2} - 900 T^{3} + 9413 T^{4} + 70368 T^{5} - 312982 T^{6} - 1938608 T^{7} + 10598262 T^{8} - 102746224 T^{9} - 879166438 T^{10} + 10476176736 T^{11} + 74273097653 T^{12} - 376375943700 T^{13} - 2992188752415 T^{14} + 4698844559348 T^{15} + 62259690411361 T^{16} \))(\( ( 1 + 53 T^{2} + 2809 T^{4} + 148877 T^{6} + 7890481 T^{8} + 418195493 T^{10} + 22164361129 T^{12} )^{2} \))(\( 1 - 53 T^{2} + 148877 T^{6} - 7890481 T^{8} + 22164361129 T^{12} - 62259690411361 T^{16} + 3299763591802133 T^{18} - 9269035929372191597 T^{22} + \)\(49\!\cdots\!41\)\( T^{24} \))
$59$ (\( 1 - 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( ( 1 + 14 T + 209 T^{2} + 2018 T^{3} + 18892 T^{4} + 119062 T^{5} + 727529 T^{6} + 2875306 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 - 14 T + 209 T^{2} - 2018 T^{3} + 18892 T^{4} - 119062 T^{5} + 727529 T^{6} - 2875306 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 - 8 T + 210 T^{2} - 1624 T^{3} + 18415 T^{4} - 148976 T^{5} + 1121964 T^{6} - 8789584 T^{7} + 64102615 T^{8} - 333535496 T^{9} + 2544645810 T^{10} - 5719394392 T^{11} + 42180533641 T^{12} )^{2} \))(\( ( 1 + 8 T + 210 T^{2} + 1624 T^{3} + 18415 T^{4} + 148976 T^{5} + 1121964 T^{6} + 8789584 T^{7} + 64102615 T^{8} + 333535496 T^{9} + 2544645810 T^{10} + 5719394392 T^{11} + 42180533641 T^{12} )^{2} \))(\( ( 1 + 59 T^{2} )^{4} \))(\( ( 1 + 28 T^{2} + 3481 T^{4} )^{4} \))(\( ( 1 + 74 T^{2} + 3563 T^{4} + 111204 T^{6} + 12402803 T^{8} + 896684714 T^{10} + 42180533641 T^{12} )^{2} \))(\( ( 1 + 308 T^{2} + 42008 T^{4} + 3220518 T^{6} + 146229848 T^{8} + 3732147188 T^{10} + 42180533641 T^{12} )^{2} \))(\( ( 1 + 308 T^{2} + 42008 T^{4} + 3220518 T^{6} + 146229848 T^{8} + 3732147188 T^{10} + 42180533641 T^{12} )^{2} \))(\( ( 1 + 3 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 - 3 T + 59 T^{2} )^{2} \))(\( ( 1 + 108 T^{2} + 6678 T^{4} + 375948 T^{6} + 12117361 T^{8} )^{2} \))(\( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 + 8 T + 5 T^{2} + 472 T^{3} + 3481 T^{4} \))(\( 1 - 8 T + 5 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 + 4 T - 43 T^{2} + 236 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 + 3 T - 50 T^{2} + 177 T^{3} + 3481 T^{4} \))(\( 1 - 3 T - 50 T^{2} - 177 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( ( 1 - 108 T^{2} + 4986 T^{4} + 30672 T^{6} - 8124061 T^{8} + 106769232 T^{10} + 60417161946 T^{12} - 4555497633228 T^{14} + 146830437604321 T^{16} )^{2} \))(\( ( 1 - 59 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 59 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 28 T^{2} - 2697 T^{4} - 97468 T^{6} + 12117361 T^{8} )^{4} \))(\( ( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} )^{4} \))(\( 1 + 14 T - 13 T^{2} - 1110 T^{3} - 3463 T^{4} + 11848 T^{5} - 87914 T^{6} + 1416852 T^{7} + 32978194 T^{8} + 83594268 T^{9} - 306028634 T^{10} + 2433330392 T^{11} - 41962421143 T^{12} - 793565971890 T^{13} - 548346937333 T^{14} + 34841120787466 T^{15} + 146830437604321 T^{16} \))(\( ( 1 + 4 T - 43 T^{2} + 236 T^{3} + 3481 T^{4} )^{4} \))(\( 1 - 14 T - 13 T^{2} + 1110 T^{3} - 3463 T^{4} - 11848 T^{5} - 87914 T^{6} - 1416852 T^{7} + 32978194 T^{8} - 83594268 T^{9} - 306028634 T^{10} - 2433330392 T^{11} - 41962421143 T^{12} + 793565971890 T^{13} - 548346937333 T^{14} - 34841120787466 T^{15} + 146830437604321 T^{16} \))(\( ( 1 - 59 T^{2} + 3481 T^{4} - 205379 T^{6} + 12117361 T^{8} - 714924299 T^{10} + 42180533641 T^{12} )^{2} \))(\( 1 + 59 T^{2} - 205379 T^{6} - 12117361 T^{8} + 42180533641 T^{12} - 146830437604321 T^{16} - 8662995818654939 T^{18} + 30155888444737842659 T^{22} + \)\(17\!\cdots\!81\)\( T^{24} \))
$61$ (\( 1 + 6 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 - 216 T^{2} + 27420 T^{4} - 2531496 T^{6} + 176195558 T^{8} - 9419696616 T^{10} + 379652960220 T^{12} - 11128400861976 T^{14} + 191707312997281 T^{16} \))(\( 1 - 216 T^{2} + 27420 T^{4} - 2531496 T^{6} + 176195558 T^{8} - 9419696616 T^{10} + 379652960220 T^{12} - 11128400861976 T^{14} + 191707312997281 T^{16} \))(\( 1 - 544 T^{2} + 142480 T^{4} - 23858720 T^{6} + 2849681139 T^{8} - 255863393088 T^{10} + 17709328352032 T^{12} - 952067685680448 T^{14} + 39456231951292899 T^{16} - 1229210186174277920 T^{18} + 27314457955852596880 T^{20} - \)\(38\!\cdots\!44\)\( T^{22} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( 1 - 544 T^{2} + 142480 T^{4} - 23858720 T^{6} + 2849681139 T^{8} - 255863393088 T^{10} + 17709328352032 T^{12} - 952067685680448 T^{14} + 39456231951292899 T^{16} - 1229210186174277920 T^{18} + 27314457955852596880 T^{20} - \)\(38\!\cdots\!44\)\( T^{22} + \)\(26\!\cdots\!21\)\( T^{24} \))(\( ( 1 + 61 T^{2} )^{4} \))(\( ( 1 + 92 T^{2} + 3721 T^{4} )^{4} \))(\( ( 1 - 4 T + 37 T^{2} - 436 T^{3} + 2257 T^{4} - 14884 T^{5} + 226981 T^{6} )^{4} \))(\( ( 1 - T + 163 T^{2} - 118 T^{3} + 9943 T^{4} - 3721 T^{5} + 226981 T^{6} )^{4} \))(\( ( 1 + T + 163 T^{2} + 118 T^{3} + 9943 T^{4} + 3721 T^{5} + 226981 T^{6} )^{4} \))(\( 1 + 25 T^{2} + 3721 T^{4} \))(\( ( 1 - 14 T + 61 T^{2} )( 1 + 14 T + 61 T^{2} ) \))(\( 1 + 25 T^{2} + 3721 T^{4} \))(\( ( 1 - 224 T^{2} + 19984 T^{4} - 833504 T^{6} + 13845841 T^{8} )^{2} \))(\( 1 - 8 T + 3 T^{2} - 488 T^{3} + 3721 T^{4} \))(\( 1 + 6 T - 25 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( 1 - 6 T - 25 T^{2} - 366 T^{3} + 3721 T^{4} \))(\( 1 + 6 T - 25 T^{2} + 366 T^{3} + 3721 T^{4} \))(\( 1 + 10 T + 39 T^{2} + 610 T^{3} + 3721 T^{4} \))(\( 1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4} \))(\( ( 1 - 13 T + 61 T^{2} )( 1 + T + 61 T^{2} ) \))(\( ( 1 - 13 T + 61 T^{2} )( 1 + T + 61 T^{2} ) \))(\( 1 - 21 T + 208 T^{2} - 1281 T^{3} + 3721 T^{4} \))(\( 1 - 21 T + 208 T^{2} - 1281 T^{3} + 3721 T^{4} \))(\( ( 1 - T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) \))(\( ( 1 + 224 T^{2} + 30192 T^{4} + 2809408 T^{6} + 198809519 T^{8} + 10453807168 T^{10} + 418033631472 T^{12} + 11540563856864 T^{14} + 191707312997281 T^{16} )^{2} \))(\( ( 1 - 61 T^{2} + 3721 T^{4} )^{2} \))(\( ( 1 - 61 T^{2} + 3721 T^{4} )^{2} \))(\( ( 1 - 92 T^{2} + 4743 T^{4} - 342332 T^{6} + 13845841 T^{8} )^{4} \))(\( 1 + 132 T^{2} + 6714 T^{4} + 431376 T^{6} + 36023555 T^{8} + 1605150096 T^{10} + 92960976474 T^{12} + 6800689415652 T^{14} + 191707312997281 T^{16} \))(\( 1 + 12 T + 180 T^{2} + 1584 T^{3} + 12426 T^{4} + 46860 T^{5} + 10032 T^{6} - 3576756 T^{7} - 33274477 T^{8} - 218182116 T^{9} + 37329072 T^{10} + 10636329660 T^{11} + 172048420266 T^{12} + 1337840540784 T^{13} + 9273667384980 T^{14} + 37712914032252 T^{15} + 191707312997281 T^{16} \))(\( 1 + 132 T^{2} + 6714 T^{4} + 431376 T^{6} + 36023555 T^{8} + 1605150096 T^{10} + 92960976474 T^{12} + 6800689415652 T^{14} + 191707312997281 T^{16} \))(\( 1 + 12 T + 180 T^{2} + 1584 T^{3} + 12426 T^{4} + 46860 T^{5} + 10032 T^{6} - 3576756 T^{7} - 33274477 T^{8} - 218182116 T^{9} + 37329072 T^{10} + 10636329660 T^{11} + 172048420266 T^{12} + 1337840540784 T^{13} + 9273667384980 T^{14} + 37712914032252 T^{15} + 191707312997281 T^{16} \))(\( ( 1 + 14 T + 61 T^{2} )^{6}( 1 + 14 T + 135 T^{2} + 1036 T^{3} + 6269 T^{4} + 24570 T^{5} - 38429 T^{6} + 1498770 T^{7} + 23326949 T^{8} + 235152316 T^{9} + 1869188535 T^{10} + 11824348214 T^{11} + 51520374361 T^{12} ) \))(\( ( 1 - T + 61 T^{2} )^{6}( 1 - 13 T + 108 T^{2} - 611 T^{3} + 1355 T^{4} + 19656 T^{5} - 338183 T^{6} + 1199016 T^{7} + 5041955 T^{8} - 138685391 T^{9} + 1495350828 T^{10} - 10979751913 T^{11} + 51520374361 T^{12} ) \))
$67$ (\( 1 - 13 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 - 13 T + 67 T^{2} \))(\( 1 - 282 T^{2} + 45393 T^{4} - 4904034 T^{6} + 383059316 T^{8} - 22014208626 T^{10} + 914719835553 T^{12} - 25509263771658 T^{14} + 406067677556641 T^{16} \))(\( 1 - 282 T^{2} + 45393 T^{4} - 4904034 T^{6} + 383059316 T^{8} - 22014208626 T^{10} + 914719835553 T^{12} - 25509263771658 T^{14} + 406067677556641 T^{16} \))(\( 1 - 356 T^{2} + 55762 T^{4} - 4560756 T^{6} + 122644383 T^{8} + 13948776888 T^{10} - 1693776977860 T^{12} + 62616059450232 T^{14} + 2471421801803343 T^{16} - 412558609227559764 T^{18} + 22643145835913415442 T^{20} - \)\(64\!\cdots\!44\)\( T^{22} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( 1 - 356 T^{2} + 55762 T^{4} - 4560756 T^{6} + 122644383 T^{8} + 13948776888 T^{10} - 1693776977860 T^{12} + 62616059450232 T^{14} + 2471421801803343 T^{16} - 412558609227559764 T^{18} + 22643145835913415442 T^{20} - \)\(64\!\cdots\!44\)\( T^{22} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( ( 1 - 67 T^{2} )^{4} \))(\( ( 1 - 74 T^{2} + 4489 T^{4} )^{4} \))(\( ( 1 - 330 T^{2} + 48695 T^{4} - 4163660 T^{6} + 218591855 T^{8} - 6649869930 T^{10} + 90458382169 T^{12} )^{2} \))(\( ( 1 - 258 T^{2} + 32174 T^{4} - 2581142 T^{6} + 144429086 T^{8} - 5198989218 T^{10} + 90458382169 T^{12} )^{2} \))(\( ( 1 - 258 T^{2} + 32174 T^{4} - 2581142 T^{6} + 144429086 T^{8} - 5198989218 T^{10} + 90458382169 T^{12} )^{2} \))(\( ( 1 - 5 T + 67 T^{2} )^{2} \))(\( ( 1 - 5 T + 67 T^{2} )^{2} \))(\( ( 1 - 5 T + 67 T^{2} )^{2} \))(\( ( 1 + 2 T + 67 T^{2} )^{8} \))(\( 1 - 8 T - 3 T^{2} - 536 T^{3} + 4489 T^{4} \))(\( 1 + 13 T + 102 T^{2} + 871 T^{3} + 4489 T^{4} \))(\( 1 + 8 T - 3 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 - 8 T - 3 T^{2} - 536 T^{3} + 4489 T^{4} \))(\( 1 - 8 T - 3 T^{2} - 536 T^{3} + 4489 T^{4} \))(\( 1 + 8 T - 3 T^{2} + 536 T^{3} + 4489 T^{4} \))(\( 1 - 8 T - 3 T^{2} - 536 T^{3} + 4489 T^{4} \))(\( ( 1 - 11 T + 67 T^{2} )( 1 - 5 T + 67 T^{2} ) \))(\( ( 1 - 11 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} ) \))(\( ( 1 - 11 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} ) \))(\( ( 1 - 11 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} ) \))(\( ( 1 - 11 T + 67 T^{2} )( 1 - 5 T + 67 T^{2} ) \))(\( ( 1 - 2 T - 63 T^{2} - 134 T^{3} + 4489 T^{4} )^{8} \))(\( ( 1 + 67 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 + 67 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 + 74 T^{2} + 987 T^{4} + 332186 T^{6} + 20151121 T^{8} )^{4} \))(\( 1 + 144 T^{2} + 9906 T^{4} + 266688 T^{6} + 4053875 T^{8} + 1197162432 T^{10} + 199617004626 T^{12} + 13026007032336 T^{14} + 406067677556641 T^{16} \))(\( 1 + 42 T + 1023 T^{2} + 18270 T^{3} + 261141 T^{4} + 3133152 T^{5} + 32837970 T^{6} + 307895844 T^{7} + 2631022010 T^{8} + 20629021548 T^{9} + 147409647330 T^{10} + 942336194976 T^{11} + 5262283889061 T^{12} + 24666785704890 T^{13} + 92538924958887 T^{14} + 254549887423566 T^{15} + 406067677556641 T^{16} \))(\( 1 + 144 T^{2} + 9906 T^{4} + 266688 T^{6} + 4053875 T^{8} + 1197162432 T^{10} + 199617004626 T^{12} + 13026007032336 T^{14} + 406067677556641 T^{16} \))(\( 1 - 42 T + 1023 T^{2} - 18270 T^{3} + 261141 T^{4} - 3133152 T^{5} + 32837970 T^{6} - 307895844 T^{7} + 2631022010 T^{8} - 20629021548 T^{9} + 147409647330 T^{10} - 942336194976 T^{11} + 5262283889061 T^{12} - 24666785704890 T^{13} + 92538924958887 T^{14} - 254549887423566 T^{15} + 406067677556641 T^{16} \))(\( ( 1 - 16 T + 189 T^{2} - 1952 T^{3} + 18569 T^{4} - 166320 T^{5} + 1416997 T^{6} - 11143440 T^{7} + 83356241 T^{8} - 587089376 T^{9} + 3808561869 T^{10} - 21602001712 T^{11} + 90458382169 T^{12} )^{2} \))(\( ( 1 - 16 T + 189 T^{2} - 1952 T^{3} + 18569 T^{4} - 166320 T^{5} + 1416997 T^{6} - 11143440 T^{7} + 83356241 T^{8} - 587089376 T^{9} + 3808561869 T^{10} - 21602001712 T^{11} + 90458382169 T^{12} )( 1 + 11 T + 54 T^{2} - 143 T^{3} - 5191 T^{4} - 47520 T^{5} - 174923 T^{6} - 3183840 T^{7} - 23302399 T^{8} - 43009109 T^{9} + 1088160534 T^{10} + 14851376177 T^{11} + 90458382169 T^{12} ) \))
$71$ (\( 1 + 10 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 - 6 T + 71 T^{2} \))(\( 1 - 14 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 - 288 T^{2} + 41724 T^{4} - 4336608 T^{6} + 350671046 T^{8} - 21860840928 T^{10} + 1060276978044 T^{12} - 36892881769248 T^{14} + 645753531245761 T^{16} \))(\( 1 - 288 T^{2} + 41724 T^{4} - 4336608 T^{6} + 350671046 T^{8} - 21860840928 T^{10} + 1060276978044 T^{12} - 36892881769248 T^{14} + 645753531245761 T^{16} \))(\( 1 - 556 T^{2} + 151546 T^{4} - 27058972 T^{6} + 3535695487 T^{8} - 356059001528 T^{10} + 28330933942092 T^{12} - 1794893426702648 T^{14} + 89847965828783647 T^{16} - 3466261995810389212 T^{18} + 97861364646170096506 T^{20} - \)\(18\!\cdots\!56\)\( T^{22} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( 1 - 556 T^{2} + 151546 T^{4} - 27058972 T^{6} + 3535695487 T^{8} - 356059001528 T^{10} + 28330933942092 T^{12} - 1794893426702648 T^{14} + 89847965828783647 T^{16} - 3466261995810389212 T^{18} + 97861364646170096506 T^{20} - \)\(18\!\cdots\!56\)\( T^{22} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( ( 1 - 100 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 + 130 T^{2} + 5041 T^{4} )^{4} \))(\( ( 1 + 152 T^{2} + 19111 T^{4} + 1530752 T^{6} + 96338551 T^{8} + 3862575512 T^{10} + 128100283921 T^{12} )^{2} \))(\( ( 1 + 374 T^{2} + 61519 T^{4} + 5680340 T^{6} + 310117279 T^{8} + 9503968694 T^{10} + 128100283921 T^{12} )^{2} \))(\( ( 1 + 374 T^{2} + 61519 T^{4} + 5680340 T^{6} + 310117279 T^{8} + 9503968694 T^{10} + 128100283921 T^{12} )^{2} \))(\( 1 - 34 T^{2} + 5041 T^{4} \))(\( ( 1 - 71 T^{2} )^{2} \))(\( 1 - 34 T^{2} + 5041 T^{4} \))(\( ( 1 - 176 T^{2} + 14938 T^{4} - 887216 T^{6} + 25411681 T^{8} )^{2} \))(\( ( 1 + 10 T + 71 T^{2} )^{2} \))(\( ( 1 + 10 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 - 14 T + 71 T^{2} )^{2} \))(\( ( 1 - 14 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 10 T + 71 T^{2} )^{2} \))(\( ( 1 - 71 T^{2} )^{2} \))(\( ( 1 - 71 T^{2} )^{2} \))(\( 1 - 34 T^{2} + 5041 T^{4} \))(\( 1 - 34 T^{2} + 5041 T^{4} \))(\( ( 1 - 71 T^{2} )^{2} \))(\( ( 1 - 176 T^{2} + 14938 T^{4} - 887216 T^{6} + 25411681 T^{8} )^{4} \))(\( ( 1 - 100 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 - 100 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 + 130 T^{2} + 5041 T^{4} )^{8} \))(\( ( 1 - 114 T^{2} + 8418 T^{4} - 574674 T^{6} + 25411681 T^{8} )^{2} \))(\( 1 - 288 T^{2} + 41724 T^{4} - 4336608 T^{6} + 350671046 T^{8} - 21860840928 T^{10} + 1060276978044 T^{12} - 36892881769248 T^{14} + 645753531245761 T^{16} \))(\( ( 1 - 114 T^{2} + 8418 T^{4} - 574674 T^{6} + 25411681 T^{8} )^{2} \))(\( 1 - 288 T^{2} + 41724 T^{4} - 4336608 T^{6} + 350671046 T^{8} - 21860840928 T^{10} + 1060276978044 T^{12} - 36892881769248 T^{14} + 645753531245761 T^{16} \))(\( ( 1 + 71 T^{2} + 5041 T^{4} + 357911 T^{6} + 25411681 T^{8} + 1804229351 T^{10} + 128100283921 T^{12} )^{2} \))(\( ( 1 + 71 T^{2} + 5041 T^{4} + 357911 T^{6} + 25411681 T^{8} + 1804229351 T^{10} + 128100283921 T^{12} )^{2} \))
$73$ (\( 1 + 11 T + 73 T^{2} \))(\( 1 + 4 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 11 T + 73 T^{2} \))(\( 1 - 370 T^{2} + 70161 T^{4} - 8626802 T^{6} + 743765828 T^{8} - 45972227858 T^{10} + 1992448986801 T^{12} - 55993663726930 T^{14} + 806460091894081 T^{16} \))(\( 1 - 370 T^{2} + 70161 T^{4} - 8626802 T^{6} + 743765828 T^{8} - 45972227858 T^{10} + 1992448986801 T^{12} - 55993663726930 T^{14} + 806460091894081 T^{16} \))(\( 1 - 480 T^{2} + 105792 T^{4} - 14378720 T^{6} + 1390885347 T^{8} - 108814494400 T^{10} + 7928879090304 T^{12} - 579872440657600 T^{14} + 39498697287474627 T^{16} - 2175992466226170080 T^{18} + 85317026041658617152 T^{20} - \)\(20\!\cdots\!20\)\( T^{22} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( 1 - 480 T^{2} + 105792 T^{4} - 14378720 T^{6} + 1390885347 T^{8} - 108814494400 T^{10} + 7928879090304 T^{12} - 579872440657600 T^{14} + 39498697287474627 T^{16} - 2175992466226170080 T^{18} + 85317026041658617152 T^{20} - \)\(20\!\cdots\!20\)\( T^{22} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( ( 1 + 73 T^{2} )^{4} \))(\( ( 1 + 26 T^{2} + 5329 T^{4} )^{4} \))(\( ( 1 + 6 T + 191 T^{2} + 772 T^{3} + 13943 T^{4} + 31974 T^{5} + 389017 T^{6} )^{4} \))(\( ( 1 + 80 T^{2} + 394 T^{3} + 5840 T^{4} + 389017 T^{6} )^{4} \))(\( ( 1 + 80 T^{2} - 394 T^{3} + 5840 T^{4} + 389017 T^{6} )^{4} \))(\( 1 + T^{2} + 5329 T^{4} \))(\( ( 1 - 17 T + 73 T^{2} )( 1 + 17 T + 73 T^{2} ) \))(\( 1 + T^{2} + 5329 T^{4} \))(\( ( 1 - 240 T^{2} + 24480 T^{4} - 1278960 T^{6} + 28398241 T^{8} )^{2} \))(\( 1 + 4 T - 57 T^{2} + 292 T^{3} + 5329 T^{4} \))(\( 1 + 11 T + 48 T^{2} + 803 T^{3} + 5329 T^{4} \))(\( ( 1 - 17 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} ) \))(\( 1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 - 2 T - 69 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( ( 1 - 7 T + 73 T^{2} )( 1 + 17 T + 73 T^{2} ) \))(\( 1 - 4 T - 57 T^{2} - 292 T^{3} + 5329 T^{4} \))(\( ( 1 - 17 T + 73 T^{2} )( 1 - 7 T + 73 T^{2} ) \))(\( ( 1 - 10 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} ) \))(\( 1 - 21 T + 220 T^{2} - 1533 T^{3} + 5329 T^{4} \))(\( 1 - 21 T + 220 T^{2} - 1533 T^{3} + 5329 T^{4} \))(\( ( 1 + 7 T + 73 T^{2} )( 1 + 17 T + 73 T^{2} ) \))(\( ( 1 + 240 T^{2} + 33120 T^{4} + 3317280 T^{6} + 263921759 T^{8} + 17677785120 T^{10} + 940549741920 T^{12} + 36320214309360 T^{14} + 806460091894081 T^{16} )^{2} \))(\( ( 1 - 73 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 73 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 26 T^{2} - 4653 T^{4} - 138554 T^{6} + 28398241 T^{8} )^{4} \))(\( 1 + 236 T^{2} + 31386 T^{4} + 3221872 T^{6} + 265773875 T^{8} + 17169355888 T^{10} + 891307192026 T^{12} + 35714877404204 T^{14} + 806460091894081 T^{16} \))(\( 1 - 18 T + 347 T^{2} - 4302 T^{3} + 50601 T^{4} - 463140 T^{5} + 4384558 T^{6} - 34967736 T^{7} + 313616978 T^{8} - 2552644728 T^{9} + 23365309582 T^{10} - 180169333380 T^{11} + 1436979392841 T^{12} - 8918353993086 T^{13} + 52512976522283 T^{14} - 198853173343746 T^{15} + 806460091894081 T^{16} \))(\( 1 + 236 T^{2} + 31386 T^{4} + 3221872 T^{6} + 265773875 T^{8} + 17169355888 T^{10} + 891307192026 T^{12} + 35714877404204 T^{14} + 806460091894081 T^{16} \))(\( 1 - 18 T + 347 T^{2} - 4302 T^{3} + 50601 T^{4} - 463140 T^{5} + 4384558 T^{6} - 34967736 T^{7} + 313616978 T^{8} - 2552644728 T^{9} + 23365309582 T^{10} - 180169333380 T^{11} + 1436979392841 T^{12} - 8918353993086 T^{13} + 52512976522283 T^{14} - 198853173343746 T^{15} + 806460091894081 T^{16} \))(\( ( 1 - 10 T + 27 T^{2} + 460 T^{3} - 6571 T^{4} + 32130 T^{5} + 158383 T^{6} + 2345490 T^{7} - 35016859 T^{8} + 178947820 T^{9} + 766752507 T^{10} - 20730715930 T^{11} + 151334226289 T^{12} )( 1 + 10 T + 27 T^{2} - 460 T^{3} - 6571 T^{4} - 32130 T^{5} + 158383 T^{6} - 2345490 T^{7} - 35016859 T^{8} - 178947820 T^{9} + 766752507 T^{10} + 20730715930 T^{11} + 151334226289 T^{12} ) \))(\( ( 1 - 10 T + 27 T^{2} + 460 T^{3} - 6571 T^{4} + 32130 T^{5} + 158383 T^{6} + 2345490 T^{7} - 35016859 T^{8} + 178947820 T^{9} + 766752507 T^{10} - 20730715930 T^{11} + 151334226289 T^{12} )( 1 + 7 T - 24 T^{2} - 679 T^{3} - 3001 T^{4} + 28560 T^{5} + 418993 T^{6} + 2084880 T^{7} - 15992329 T^{8} - 264142543 T^{9} - 681557784 T^{10} + 14511501151 T^{11} + 151334226289 T^{12} ) \))
$79$ (\( 1 + 3 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 3 T + 79 T^{2} \))(\( 1 - 228 T^{2} + 23202 T^{4} - 2215104 T^{6} + 207545771 T^{8} - 13824464064 T^{10} + 903719779362 T^{12} - 55423939858788 T^{14} + 1517108809906561 T^{16} \))(\( 1 - 228 T^{2} + 23202 T^{4} - 2215104 T^{6} + 207545771 T^{8} - 13824464064 T^{10} + 903719779362 T^{12} - 55423939858788 T^{14} + 1517108809906561 T^{16} \))(\( 1 - 516 T^{2} + 134210 T^{4} - 23318900 T^{6} + 3036334383 T^{8} - 315920772616 T^{10} + 27245615350940 T^{12} - 1971661541896456 T^{14} + 118265470160935023 T^{16} - 5668532066548646900 T^{18} + \)\(20\!\cdots\!10\)\( T^{20} - \)\(48\!\cdots\!16\)\( T^{22} + \)\(59\!\cdots\!41\)\( T^{24} \))(\( 1 - 516 T^{2} + 134210 T^{4} - 23318900 T^{6} + 3036334383 T^{8} - 315920772616 T^{10} + 27245615350940 T^{12} - 1971661541896456 T^{14} + 118265470160935023 T^{16} - 5668532066548646900 T^{18} + \)\(20\!\cdots\!10\)\( T^{20} - \)\(48\!\cdots\!16\)\( T^{22} + \)\(59\!\cdots\!41\)\( T^{24} \))(\( ( 1 - 79 T^{2} )^{4} \))(\( ( 1 + 82 T^{2} + 6241 T^{4} )^{4} \))(\( ( 1 - 142 T^{2} + 6241 T^{4} )^{6} \))(\( ( 1 - 243 T^{2} + 34434 T^{4} - 3335443 T^{6} + 214902594 T^{8} - 9464869683 T^{10} + 243087455521 T^{12} )^{2} \))(\( ( 1 - 243 T^{2} + 34434 T^{4} - 3335443 T^{6} + 214902594 T^{8} - 9464869683 T^{10} + 243087455521 T^{12} )^{2} \))(\( ( 1 + T + 79 T^{2} )^{2} \))(\( ( 1 - 17 T + 79 T^{2} )^{2} \))(\( ( 1 + T + 79 T^{2} )^{2} \))(\( ( 1 + 12 T + 162 T^{2} + 948 T^{3} + 6241 T^{4} )^{4} \))(\( ( 1 - 13 T + 79 T^{2} )( 1 + 17 T + 79 T^{2} ) \))(\( 1 - 3 T - 70 T^{2} - 237 T^{3} + 6241 T^{4} \))(\( ( 1 - 17 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} ) \))(\( 1 + 12 T + 65 T^{2} + 948 T^{3} + 6241 T^{4} \))(\( 1 + 12 T + 65 T^{2} + 948 T^{3} + 6241 T^{4} \))(\( ( 1 - 17 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} ) \))(\( ( 1 - 13 T + 79 T^{2} )( 1 + 17 T + 79 T^{2} ) \))(\( ( 1 - 17 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} ) \))(\( ( 1 + 4 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} ) \))(\( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} \))(\( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} \))(\( ( 1 - 17 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} ) \))(\( ( 1 - 12 T - 18 T^{2} - 48 T^{3} + 8627 T^{4} - 3792 T^{5} - 112338 T^{6} - 5916468 T^{7} + 38950081 T^{8} )^{4} \))(\( ( 1 + 79 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 + 79 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 - 82 T^{2} + 483 T^{4} - 511762 T^{6} + 38950081 T^{8} )^{4} \))(\( 1 + 288 T^{2} + 49794 T^{4} + 5952384 T^{6} + 542318915 T^{8} + 37148828544 T^{10} + 1939480333314 T^{12} + 70009187190048 T^{14} + 1517108809906561 T^{16} \))(\( 1 - 6 T + 132 T^{2} - 720 T^{3} + 9999 T^{4} - 52644 T^{5} - 314880 T^{6} - 1496442 T^{7} - 48671848 T^{8} - 118218918 T^{9} - 1965166080 T^{10} - 25955545116 T^{11} + 389461859919 T^{12} - 2215480607280 T^{13} + 32087544128772 T^{14} - 115223453916954 T^{15} + 1517108809906561 T^{16} \))(\( 1 + 288 T^{2} + 49794 T^{4} + 5952384 T^{6} + 542318915 T^{8} + 37148828544 T^{10} + 1939480333314 T^{12} + 70009187190048 T^{14} + 1517108809906561 T^{16} \))(\( 1 + 6 T + 132 T^{2} + 720 T^{3} + 9999 T^{4} + 52644 T^{5} - 314880 T^{6} + 1496442 T^{7} - 48671848 T^{8} + 118218918 T^{9} - 1965166080 T^{10} + 25955545116 T^{11} + 389461859919 T^{12} + 2215480607280 T^{13} + 32087544128772 T^{14} + 115223453916954 T^{15} + 1517108809906561 T^{16} \))(\( ( 1 - 4 T - 63 T^{2} + 568 T^{3} + 2705 T^{4} - 55692 T^{5} + 9073 T^{6} - 4399668 T^{7} + 16881905 T^{8} + 280046152 T^{9} - 2453855103 T^{10} - 12308225596 T^{11} + 243087455521 T^{12} )^{2} \))(\( ( 1 - 13 T + 90 T^{2} - 143 T^{3} - 5251 T^{4} + 79560 T^{5} - 619451 T^{6} + 6285240 T^{7} - 32771491 T^{8} - 70504577 T^{9} + 3505507290 T^{10} - 40001733187 T^{11} + 243087455521 T^{12} )( 1 - 4 T - 63 T^{2} + 568 T^{3} + 2705 T^{4} - 55692 T^{5} + 9073 T^{6} - 4399668 T^{7} + 16881905 T^{8} + 280046152 T^{9} - 2453855103 T^{10} - 12308225596 T^{11} + 243087455521 T^{12} ) \))
$83$ (\( 1 - 2 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 2 T + 83 T^{2} \))(\( ( 1 + 2 T + 229 T^{2} + 802 T^{3} + 24432 T^{4} + 66566 T^{5} + 1577581 T^{6} + 1143574 T^{7} + 47458321 T^{8} )^{2} \))(\( ( 1 - 2 T + 229 T^{2} - 802 T^{3} + 24432 T^{4} - 66566 T^{5} + 1577581 T^{6} - 1143574 T^{7} + 47458321 T^{8} )^{2} \))(\( ( 1 - 8 T + 290 T^{2} - 1848 T^{3} + 43207 T^{4} - 256016 T^{5} + 4402748 T^{6} - 21249328 T^{7} + 297653023 T^{8} - 1056662376 T^{9} + 13762913090 T^{10} - 31512325144 T^{11} + 326940373369 T^{12} )^{2} \))(\( ( 1 + 8 T + 290 T^{2} + 1848 T^{3} + 43207 T^{4} + 256016 T^{5} + 4402748 T^{6} + 21249328 T^{7} + 297653023 T^{8} + 1056662376 T^{9} + 13762913090 T^{10} + 31512325144 T^{11} + 326940373369 T^{12} )^{2} \))(\( ( 1 + 83 T^{2} )^{4} \))(\( ( 1 + 76 T^{2} + 6889 T^{4} )^{4} \))(\( ( 1 + 370 T^{2} + 64699 T^{4} + 6784180 T^{6} + 445711411 T^{8} + 17559578770 T^{10} + 326940373369 T^{12} )^{2} \))(\( ( 1 + 115 T^{2} + 23611 T^{4} + 1604482 T^{6} + 162656179 T^{8} + 5457706915 T^{10} + 326940373369 T^{12} )^{2} \))(\( ( 1 + 115 T^{2} + 23611 T^{4} + 1604482 T^{6} + 162656179 T^{8} + 5457706915 T^{10} + 326940373369 T^{12} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 300 T^{2} + 36078 T^{4} + 2066700 T^{6} + 47458321 T^{8} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 2 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 83 T^{2} )^{2} \))(\( ( 1 + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 83 T^{2} )^{2} \))(\( ( 1 + 300 T^{2} + 36078 T^{4} + 2066700 T^{6} + 47458321 T^{8} )^{4} \))(\( ( 1 + 83 T^{2} )^{4} \))(\( ( 1 + 83 T^{2} )^{4} \))(\( ( 1 + 76 T^{2} + 6889 T^{4} )^{8} \))(\( ( 1 - 4 T + 102 T^{2} - 332 T^{3} + 6889 T^{4} )^{4} \))(\( ( 1 - 2 T + 229 T^{2} - 802 T^{3} + 24432 T^{4} - 66566 T^{5} + 1577581 T^{6} - 1143574 T^{7} + 47458321 T^{8} )^{2} \))(\( ( 1 + 4 T + 102 T^{2} + 332 T^{3} + 6889 T^{4} )^{4} \))(\( ( 1 + 2 T + 229 T^{2} + 802 T^{3} + 24432 T^{4} + 66566 T^{5} + 1577581 T^{6} + 1143574 T^{7} + 47458321 T^{8} )^{2} \))(\( ( 1 - 83 T^{2} + 6889 T^{4} - 571787 T^{6} + 47458321 T^{8} - 3939040643 T^{10} + 326940373369 T^{12} )^{2} \))(\( ( 1 - 83 T^{2} + 6889 T^{4} - 571787 T^{6} + 47458321 T^{8} - 3939040643 T^{10} + 326940373369 T^{12} )^{2} \))
$89$ (\( 1 + 89 T^{2} \))(\( 1 - 14 T + 89 T^{2} \))(\( 1 + 12 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 - 528 T^{2} + 131868 T^{4} - 20568048 T^{6} + 2191026566 T^{8} - 162919508208 T^{10} + 8273693836188 T^{12} - 262406121627408 T^{14} + 3936588805702081 T^{16} \))(\( 1 - 528 T^{2} + 131868 T^{4} - 20568048 T^{6} + 2191026566 T^{8} - 162919508208 T^{10} + 8273693836188 T^{12} - 262406121627408 T^{14} + 3936588805702081 T^{16} \))(\( 1 - 696 T^{2} + 241496 T^{4} - 54982424 T^{6} + 9125837523 T^{8} - 1161685318736 T^{10} + 116205471399600 T^{12} - 9201709409707856 T^{14} + 572575497194909043 T^{16} - 27325236059685069464 T^{18} + \)\(95\!\cdots\!76\)\( T^{20} - \)\(21\!\cdots\!96\)\( T^{22} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 - 696 T^{2} + 241496 T^{4} - 54982424 T^{6} + 9125837523 T^{8} - 1161685318736 T^{10} + 116205471399600 T^{12} - 9201709409707856 T^{14} + 572575497194909043 T^{16} - 27325236059685069464 T^{18} + \)\(95\!\cdots\!76\)\( T^{20} - \)\(21\!\cdots\!96\)\( T^{22} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( ( 1 - 172 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 - 82 T^{2} + 7921 T^{4} )^{4} \))(\( ( 1 - 212 T^{2} + 30551 T^{4} - 3163080 T^{6} + 241994471 T^{8} - 13301355092 T^{10} + 496981290961 T^{12} )^{2} \))(\( ( 1 - 455 T^{2} + 91151 T^{4} - 10426578 T^{6} + 722007071 T^{8} - 28547719655 T^{10} + 496981290961 T^{12} )^{2} \))(\( ( 1 - 455 T^{2} + 91151 T^{4} - 10426578 T^{6} + 722007071 T^{8} - 28547719655 T^{10} + 496981290961 T^{12} )^{2} \))(\( ( 1 + 9 T + 89 T^{2} )^{2} \))(\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 - 9 T + 89 T^{2} )^{2} \))(\( ( 1 + 156 T^{2} + 20676 T^{4} + 1235676 T^{6} + 62742241 T^{8} )^{2} \))(\( 1 - 14 T + 107 T^{2} - 1246 T^{3} + 7921 T^{4} \))(\( 1 - 89 T^{2} + 7921 T^{4} \))(\( 1 + 12 T + 55 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 - 89 T^{2} + 7921 T^{4} \))(\( 1 - 89 T^{2} + 7921 T^{4} \))(\( 1 - 12 T + 55 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 + 14 T + 107 T^{2} + 1246 T^{3} + 7921 T^{4} \))(\( 1 - 89 T^{2} + 7921 T^{4} \))(\( 1 - 89 T^{2} + 7921 T^{4} \))(\( 1 + 9 T - 8 T^{2} + 801 T^{3} + 7921 T^{4} \))(\( 1 - 9 T - 8 T^{2} - 801 T^{3} + 7921 T^{4} \))(\( 1 - 89 T^{2} + 7921 T^{4} \))(\( ( 1 - 156 T^{2} + 3660 T^{4} - 754104 T^{6} + 171989279 T^{8} - 5973257784 T^{10} + 229636602060 T^{12} - 77529081389916 T^{14} + 3936588805702081 T^{16} )^{2} \))(\( 1 + 172 T^{2} + 21663 T^{4} + 1362412 T^{6} + 62742241 T^{8} \))(\( 1 + 172 T^{2} + 21663 T^{4} + 1362412 T^{6} + 62742241 T^{8} \))(\( ( 1 + 82 T^{2} - 1197 T^{4} + 649522 T^{6} + 62742241 T^{8} )^{4} \))(\( 1 + 294 T^{2} + 49818 T^{4} + 6108144 T^{6} + 593476127 T^{8} + 48382608624 T^{10} + 3125692962138 T^{12} + 146112499542534 T^{14} + 3936588805702081 T^{16} \))(\( 1 + 264 T^{2} + 38610 T^{4} - 50400 T^{5} + 4052064 T^{6} - 8952768 T^{7} + 353995811 T^{8} - 796796352 T^{9} + 32096398944 T^{10} - 35530437600 T^{11} + 2422477925010 T^{12} + 131203060813704 T^{14} + 3936588805702081 T^{16} \))(\( 1 + 294 T^{2} + 49818 T^{4} + 6108144 T^{6} + 593476127 T^{8} + 48382608624 T^{10} + 3125692962138 T^{12} + 146112499542534 T^{14} + 3936588805702081 T^{16} \))(\( 1 + 264 T^{2} + 38610 T^{4} - 50400 T^{5} + 4052064 T^{6} - 8952768 T^{7} + 353995811 T^{8} - 796796352 T^{9} + 32096398944 T^{10} - 35530437600 T^{11} + 2422477925010 T^{12} + 131203060813704 T^{14} + 3936588805702081 T^{16} \))(\( ( 1 - 89 T^{2} + 7921 T^{4} - 704969 T^{6} + 62742241 T^{8} - 5584059449 T^{10} + 496981290961 T^{12} )^{2} \))(\( 1 + 89 T^{2} - 704969 T^{6} - 62742241 T^{8} + 496981290961 T^{12} - 3936588805702081 T^{16} - 350356403707485209 T^{18} + \)\(27\!\cdots\!89\)\( T^{22} + \)\(24\!\cdots\!21\)\( T^{24} \))
$97$ (\( 1 - 10 T + 97 T^{2} \))(\( 1 + 4 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 4 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 594 T^{2} + 165777 T^{4} - 28537554 T^{6} + 3324136868 T^{8} - 268509845586 T^{10} + 14676118616337 T^{12} - 494785370927826 T^{14} + 7837433594376961 T^{16} \))(\( 1 - 594 T^{2} + 165777 T^{4} - 28537554 T^{6} + 3324136868 T^{8} - 268509845586 T^{10} + 14676118616337 T^{12} - 494785370927826 T^{14} + 7837433594376961 T^{16} \))(\( 1 - 672 T^{2} + 218848 T^{4} - 46502304 T^{6} + 7344144003 T^{8} - 928722590784 T^{10} + 97980461927872 T^{12} - 8738350856686656 T^{14} + 650171788146051843 T^{16} - 38735117396697856416 T^{18} + \)\(17\!\cdots\!28\)\( T^{20} - \)\(49\!\cdots\!28\)\( T^{22} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( 1 - 672 T^{2} + 218848 T^{4} - 46502304 T^{6} + 7344144003 T^{8} - 928722590784 T^{10} + 97980461927872 T^{12} - 8738350856686656 T^{14} + 650171788146051843 T^{16} - 38735117396697856416 T^{18} + \)\(17\!\cdots\!28\)\( T^{20} - \)\(49\!\cdots\!28\)\( T^{22} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( ( 1 + 97 T^{2} )^{4} \))(\( ( 1 + 97 T^{2} )^{8} \))(\( ( 1 - 2 T + 97 T^{2} )^{12} \))(\( ( 1 + 9 T + 189 T^{2} + 1690 T^{3} + 18333 T^{4} + 84681 T^{5} + 912673 T^{6} )^{4} \))(\( ( 1 - 9 T + 189 T^{2} - 1690 T^{3} + 18333 T^{4} - 84681 T^{5} + 912673 T^{6} )^{4} \))(\( 1 - 146 T^{2} + 9409 T^{4} \))(\( ( 1 - 14 T + 97 T^{2} )( 1 + 14 T + 97 T^{2} ) \))(\( 1 - 146 T^{2} + 9409 T^{4} \))(\( ( 1 + 48 T^{2} + 17472 T^{4} + 451632 T^{6} + 88529281 T^{8} )^{2} \))(\( ( 1 - 4 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( ( 1 - 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 4 T + 97 T^{2} )^{2} \))(\( ( 1 - 14 T + 97 T^{2} )( 1 + 14 T + 97 T^{2} ) \))(\( ( 1 - 14 T + 97 T^{2} )( 1 + 14 T + 97 T^{2} ) \))(\( 1 - 146 T^{2} + 9409 T^{4} \))(\( 1 - 146 T^{2} + 9409 T^{4} \))(\( ( 1 - 14 T + 97 T^{2} )( 1 + 14 T + 97 T^{2} ) \))(\( ( 1 + 48 T^{2} + 17472 T^{4} + 451632 T^{6} + 88529281 T^{8} )^{4} \))(\( ( 1 + 97 T^{2} )^{4} \))(\( ( 1 + 97 T^{2} )^{4} \))(\( ( 1 + 97 T^{2} )^{16} \))(\( ( 1 - 204 T^{2} + 28950 T^{4} - 1919436 T^{6} + 88529281 T^{8} )^{2} \))(\( 1 - 594 T^{2} + 165777 T^{4} - 28537554 T^{6} + 3324136868 T^{8} - 268509845586 T^{10} + 14676118616337 T^{12} - 494785370927826 T^{14} + 7837433594376961 T^{16} \))(\( ( 1 - 204 T^{2} + 28950 T^{4} - 1919436 T^{6} + 88529281 T^{8} )^{2} \))(\( 1 - 594 T^{2} + 165777 T^{4} - 28537554 T^{6} + 3324136868 T^{8} - 268509845586 T^{10} + 14676118616337 T^{12} - 494785370927826 T^{14} + 7837433594376961 T^{16} \))(\( ( 1 - 14 T + 99 T^{2} - 28 T^{3} - 9211 T^{4} + 131670 T^{5} - 949913 T^{6} + 12771990 T^{7} - 86666299 T^{8} - 25554844 T^{9} + 8764398819 T^{10} - 120222763598 T^{11} + 832972004929 T^{12} )( 1 + 14 T + 99 T^{2} + 28 T^{3} - 9211 T^{4} - 131670 T^{5} - 949913 T^{6} - 12771990 T^{7} - 86666299 T^{8} + 25554844 T^{9} + 8764398819 T^{10} + 120222763598 T^{11} + 832972004929 T^{12} ) \))(\( ( 1 - 14 T + 99 T^{2} - 28 T^{3} - 9211 T^{4} + 131670 T^{5} - 949913 T^{6} + 12771990 T^{7} - 86666299 T^{8} - 25554844 T^{9} + 8764398819 T^{10} - 120222763598 T^{11} + 832972004929 T^{12} )( 1 + 14 T + 99 T^{2} + 28 T^{3} - 9211 T^{4} - 131670 T^{5} - 949913 T^{6} - 12771990 T^{7} - 86666299 T^{8} + 25554844 T^{9} + 8764398819 T^{10} + 120222763598 T^{11} + 832972004929 T^{12} ) \))
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