Properties

Label 528.2
Level 528
Weight 2
Dimension 3104
Nonzero newspaces 16
Newform subspaces 57
Sturm bound 30720
Trace bound 11

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Defining parameters

Level: \( N \) = \( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 57 \)
Sturm bound: \(30720\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(528))\).

Total New Old
Modular forms 8240 3268 4972
Cusp forms 7121 3104 4017
Eisenstein series 1119 164 955

Trace form

\( 3104q - 13q^{3} - 24q^{4} + 4q^{5} - 4q^{6} - 14q^{7} + 24q^{8} + 5q^{9} + O(q^{10}) \) \( 3104q - 13q^{3} - 24q^{4} + 4q^{5} - 4q^{6} - 14q^{7} + 24q^{8} + 5q^{9} - 24q^{10} + 12q^{11} - 40q^{12} - 30q^{13} - 24q^{14} + 5q^{15} - 72q^{16} - 4q^{17} - 36q^{18} + 2q^{19} - 32q^{20} - 28q^{21} - 56q^{22} - 16q^{23} - 76q^{24} - 28q^{25} - 40q^{26} - 37q^{27} - 40q^{28} + 20q^{29} - 60q^{30} - 62q^{31} - 17q^{33} - 64q^{34} + 12q^{35} - 52q^{36} + 58q^{37} + 16q^{38} + 9q^{39} + 8q^{40} + 92q^{41} + 68q^{42} + 20q^{43} + 40q^{44} + 38q^{45} + 56q^{46} + 60q^{47} + 108q^{48} + 80q^{49} + 72q^{50} - 23q^{51} + 24q^{52} + 12q^{53} + 76q^{54} - 2q^{55} + 31q^{57} - 72q^{58} - 56q^{59} - 36q^{60} - 158q^{61} + 24q^{62} - 31q^{63} - 168q^{64} + 24q^{65} - 72q^{66} - 92q^{67} - 64q^{68} - 66q^{69} - 464q^{70} - 4q^{71} - 132q^{72} - 230q^{73} - 304q^{74} - 17q^{75} - 488q^{76} - 176q^{77} - 376q^{78} - 98q^{79} - 456q^{80} - 59q^{81} - 488q^{82} - 28q^{83} - 244q^{84} - 394q^{85} - 288q^{86} + 8q^{87} - 648q^{88} - 148q^{89} - 52q^{90} - 22q^{91} - 288q^{92} - 153q^{93} - 440q^{94} + 12q^{95} - 108q^{96} - 262q^{97} - 360q^{98} + 29q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(528))\)

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
528.2.a \(\chi_{528}(1, \cdot)\) 528.2.a.a 1 1
528.2.a.b 1
528.2.a.c 1
528.2.a.d 1
528.2.a.e 1
528.2.a.f 1
528.2.a.g 1
528.2.a.h 1
528.2.a.i 1
528.2.a.j 1
528.2.b \(\chi_{528}(65, \cdot)\) 528.2.b.a 2 1
528.2.b.b 2
528.2.b.c 2
528.2.b.d 4
528.2.b.e 6
528.2.b.f 6
528.2.d \(\chi_{528}(287, \cdot)\) 528.2.d.a 2 1
528.2.d.b 2
528.2.d.c 2
528.2.d.d 2
528.2.d.e 2
528.2.d.f 2
528.2.d.g 4
528.2.d.h 4
528.2.f \(\chi_{528}(265, \cdot)\) None 0 1
528.2.h \(\chi_{528}(439, \cdot)\) None 0 1
528.2.k \(\chi_{528}(23, \cdot)\) None 0 1
528.2.m \(\chi_{528}(329, \cdot)\) None 0 1
528.2.o \(\chi_{528}(175, \cdot)\) 528.2.o.a 4 1
528.2.o.b 8
528.2.q \(\chi_{528}(43, \cdot)\) 528.2.q.a 96 2
528.2.t \(\chi_{528}(133, \cdot)\) 528.2.t.a 40 2
528.2.t.b 40
528.2.u \(\chi_{528}(155, \cdot)\) 528.2.u.a 160 2
528.2.x \(\chi_{528}(197, \cdot)\) 528.2.x.a 184 2
528.2.y \(\chi_{528}(49, \cdot)\) 528.2.y.a 4 4
528.2.y.b 4
528.2.y.c 4
528.2.y.d 4
528.2.y.e 4
528.2.y.f 4
528.2.y.g 4
528.2.y.h 4
528.2.y.i 4
528.2.y.j 4
528.2.y.k 8
528.2.ba \(\chi_{528}(79, \cdot)\) 528.2.ba.a 8 4
528.2.ba.b 8
528.2.ba.c 32
528.2.bc \(\chi_{528}(41, \cdot)\) None 0 4
528.2.be \(\chi_{528}(71, \cdot)\) None 0 4
528.2.bh \(\chi_{528}(7, \cdot)\) None 0 4
528.2.bj \(\chi_{528}(25, \cdot)\) None 0 4
528.2.bl \(\chi_{528}(47, \cdot)\) 528.2.bl.a 32 4
528.2.bl.b 64
528.2.bn \(\chi_{528}(17, \cdot)\) 528.2.bn.a 8 4
528.2.bn.b 8
528.2.bn.c 8
528.2.bn.d 16
528.2.bn.e 24
528.2.bn.f 24
528.2.bo \(\chi_{528}(29, \cdot)\) 528.2.bo.a 736 8
528.2.br \(\chi_{528}(59, \cdot)\) 528.2.br.a 736 8
528.2.bs \(\chi_{528}(37, \cdot)\) 528.2.bs.a 384 8
528.2.bv \(\chi_{528}(19, \cdot)\) 528.2.bv.a 384 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(528))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(528)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - T - 2 T^{2} - 3 T^{3} + 9 T^{4} \))(\( 1 + T - T^{2} - 2 T^{3} - 3 T^{4} + 9 T^{5} + 27 T^{6} \))(\( 1 + T - T^{2} - 2 T^{3} - 3 T^{4} + 9 T^{5} + 27 T^{6} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))(\( 1 + T - 2 T^{2} + 3 T^{3} + 9 T^{4} \))(\( 1 - T - 2 T^{2} - 3 T^{3} + 9 T^{4} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( 1 + T + T^{2} + T^{3} + T^{4} \))(\( 1 + T + T^{2} + T^{3} + T^{4} \))(\( 1 + T + T^{2} + T^{3} + T^{4} \))(\( 1 + T + T^{2} + T^{3} + T^{4} \))(\( 1 - T + T^{2} - T^{3} + T^{4} \))(\( 1 - T + T^{2} - T^{3} + T^{4} \))(\( 1 - T + T^{2} - T^{3} + T^{4} \))(\( 1 - T + T^{2} - T^{3} + T^{4} \))(\( 1 - T + T^{2} - T^{3} + T^{4} \))(\( 1 - T + T^{2} - T^{3} + T^{4} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} )^{2} \))(\( 1 - T^{2} + T^{4} - T^{6} + T^{8} \))(\( 1 - T^{2} + T^{4} - T^{6} + T^{8} \))(\( ( 1 + T + 5 T^{2} + 3 T^{3} + 9 T^{4} )^{2} \))(\( 1 + 2 T + T^{2} + 6 T^{3} + 19 T^{4} + 18 T^{5} + 9 T^{6} + 54 T^{7} + 81 T^{8} \))(\( 1 - 6 T + 13 T^{2} - 10 T^{3} + T^{4} - 30 T^{5} + 117 T^{6} - 162 T^{7} + 81 T^{8} \))(\( 1 + T - 2 T^{2} - 2 T^{3} - 12 T^{4} - 37 T^{5} + 21 T^{6} + 94 T^{7} + 88 T^{8} + 282 T^{9} + 189 T^{10} - 999 T^{11} - 972 T^{12} - 486 T^{13} - 1458 T^{14} + 2187 T^{15} + 6561 T^{16} \))
$5$ (\( 1 + 4 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( ( 1 - 3 T + 5 T^{2} )( 1 + 3 T + 5 T^{2} ) \))(\( 1 - 8 T^{2} + 25 T^{4} \))(\( 1 - 8 T^{2} + 25 T^{4} \))(\( ( 1 - 3 T + 4 T^{2} - 15 T^{3} + 25 T^{4} )( 1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4} ) \))(\( 1 - 17 T^{2} + 161 T^{4} - 978 T^{6} + 4025 T^{8} - 10625 T^{10} + 15625 T^{12} \))(\( 1 - 17 T^{2} + 161 T^{4} - 978 T^{6} + 4025 T^{8} - 10625 T^{10} + 15625 T^{12} \))(\( 1 - 7 T^{2} + 25 T^{4} \))(\( 1 - 2 T^{2} + 25 T^{4} \))(\( 1 + 2 T^{2} + 25 T^{4} \))(\( 1 + 2 T^{2} + 25 T^{4} \))(\( 1 - 2 T^{2} + 25 T^{4} \))(\( 1 - 7 T^{2} + 25 T^{4} \))(\( 1 - 13 T^{2} + 84 T^{4} - 325 T^{6} + 625 T^{8} \))(\( 1 - 13 T^{2} + 84 T^{4} - 325 T^{6} + 625 T^{8} \))(\( ( 1 + 2 T + 5 T^{2} )^{4} \))(\( ( 1 - 2 T + 8 T^{2} - 10 T^{3} + 25 T^{4} )^{4} \))(\( 1 + 7 T + 29 T^{2} + 93 T^{3} + 236 T^{4} + 465 T^{5} + 725 T^{6} + 875 T^{7} + 625 T^{8} \))(\( 1 + 3 T - T^{2} - 3 T^{3} + 16 T^{4} - 15 T^{5} - 25 T^{6} + 375 T^{7} + 625 T^{8} \))(\( 1 - 3 T - T^{2} + 3 T^{3} + 16 T^{4} + 15 T^{5} - 25 T^{6} - 375 T^{7} + 625 T^{8} \))(\( 1 - 8 T + 29 T^{2} - 72 T^{3} + 161 T^{4} - 360 T^{5} + 725 T^{6} - 1000 T^{7} + 625 T^{8} \))(\( 1 + 8 T + 29 T^{2} + 72 T^{3} + 161 T^{4} + 360 T^{5} + 725 T^{6} + 1000 T^{7} + 625 T^{8} \))(\( 1 + T + T^{2} + 11 T^{3} + 36 T^{4} + 55 T^{5} + 25 T^{6} + 125 T^{7} + 625 T^{8} \))(\( ( 1 - 5 T + 15 T^{2} - 25 T^{3} + 25 T^{4} )( 1 + 5 T + 15 T^{2} + 25 T^{3} + 25 T^{4} ) \))(\( 1 - T + T^{2} - 11 T^{3} + 36 T^{4} - 55 T^{5} + 25 T^{6} - 125 T^{7} + 625 T^{8} \))(\( 1 - 3 T - T^{2} + 3 T^{3} + 16 T^{4} + 15 T^{5} - 25 T^{6} - 375 T^{7} + 625 T^{8} \))(\( ( 1 - 5 T^{2} )^{2}( 1 - 5 T + 15 T^{2} - 25 T^{3} + 25 T^{4} ) \))(\( 1 + T - 8 T^{2} - 12 T^{3} + 127 T^{5} + 267 T^{6} - 376 T^{7} - 1544 T^{8} - 1880 T^{9} + 6675 T^{10} + 15875 T^{11} - 37500 T^{13} - 125000 T^{14} + 78125 T^{15} + 390625 T^{16} \))(\( ( 1 + 3 T - T^{2} - 3 T^{3} + 16 T^{4} - 15 T^{5} - 25 T^{6} + 375 T^{7} + 625 T^{8} )^{2} \))(\( ( 1 - 7 T + 29 T^{2} - 93 T^{3} + 236 T^{4} - 465 T^{5} + 725 T^{6} - 875 T^{7} + 625 T^{8} )^{2} \))(\( 1 + 8 T^{2} + 10 T^{3} + 29 T^{4} + 80 T^{5} + 112 T^{6} + 700 T^{7} + 221 T^{8} + 3500 T^{9} + 2800 T^{10} + 10000 T^{11} + 18125 T^{12} + 31250 T^{13} + 125000 T^{14} + 390625 T^{16} \))(\( 1 + 8 T^{2} - 10 T^{3} + 29 T^{4} - 80 T^{5} + 112 T^{6} - 700 T^{7} + 221 T^{8} - 3500 T^{9} + 2800 T^{10} - 10000 T^{11} + 18125 T^{12} - 31250 T^{13} + 125000 T^{14} + 390625 T^{16} \))(\( 1 - T^{2} + 51 T^{4} + 109 T^{6} + 1136 T^{8} + 2725 T^{10} + 31875 T^{12} - 15625 T^{14} + 390625 T^{16} \))(\( 1 + 16 T^{2} + 65 T^{4} - 396 T^{6} - 3721 T^{8} + 2804 T^{10} + 96795 T^{12} - 48024 T^{14} - 2751144 T^{16} - 1200600 T^{18} + 60496875 T^{20} + 43812500 T^{22} - 1453515625 T^{24} - 3867187500 T^{26} + 15869140625 T^{28} + 97656250000 T^{30} + 152587890625 T^{32} \))
$7$ (\( 1 - 2 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 + 4 T^{2} + 49 T^{4} \))(\( 1 + 4 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{4} \))(\( 1 - 20 T^{2} + 239 T^{4} - 1944 T^{6} + 11711 T^{8} - 48020 T^{10} + 117649 T^{12} \))(\( 1 - 20 T^{2} + 239 T^{4} - 1944 T^{6} + 11711 T^{8} - 48020 T^{10} + 117649 T^{12} \))(\( ( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} ) \))(\( 1 - 12 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 - 12 T^{2} + 49 T^{4} \))(\( ( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} ) \))(\( 1 - 34 T^{4} + 2401 T^{8} \))(\( 1 - 34 T^{4} + 2401 T^{8} \))(\( ( 1 + 4 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 - 4 T^{2} - 6 T^{4} - 196 T^{6} + 2401 T^{8} )^{2} \))(\( 1 + 3 T + 12 T^{2} + 35 T^{3} + 141 T^{4} + 245 T^{5} + 588 T^{6} + 1029 T^{7} + 2401 T^{8} \))(\( 1 + T - 6 T^{2} - 13 T^{3} + 29 T^{4} - 91 T^{5} - 294 T^{6} + 343 T^{7} + 2401 T^{8} \))(\( 1 + 5 T + 8 T^{2} + 25 T^{3} + 109 T^{4} + 175 T^{5} + 392 T^{6} + 1715 T^{7} + 2401 T^{8} \))(\( 1 - 6 T + 9 T^{2} + 38 T^{3} - 201 T^{4} + 266 T^{5} + 441 T^{6} - 2058 T^{7} + 2401 T^{8} \))(\( 1 + 6 T + 29 T^{2} + 102 T^{3} + 319 T^{4} + 714 T^{5} + 1421 T^{6} + 2058 T^{7} + 2401 T^{8} \))(\( 1 - 3 T + 2 T^{2} + 15 T^{3} - 59 T^{4} + 105 T^{5} + 98 T^{6} - 1029 T^{7} + 2401 T^{8} \))(\( 1 - 2 T - 3 T^{2} - 10 T^{3} + 71 T^{4} - 70 T^{5} - 147 T^{6} - 686 T^{7} + 2401 T^{8} \))(\( 1 - 3 T + 12 T^{2} - 35 T^{3} + 141 T^{4} - 245 T^{5} + 588 T^{6} - 1029 T^{7} + 2401 T^{8} \))(\( 1 + 7 T + 12 T^{2} - 25 T^{3} - 139 T^{4} - 175 T^{5} + 588 T^{6} + 2401 T^{7} + 2401 T^{8} \))(\( 1 - 7 T + 12 T^{2} + 25 T^{3} - 139 T^{4} + 175 T^{5} + 588 T^{6} - 2401 T^{7} + 2401 T^{8} \))(\( 1 - 5 T + 11 T^{2} - 20 T^{3} - 28 T^{4} + 155 T^{5} + 228 T^{6} - 2350 T^{7} + 8205 T^{8} - 16450 T^{9} + 11172 T^{10} + 53165 T^{11} - 67228 T^{12} - 336140 T^{13} + 1294139 T^{14} - 4117715 T^{15} + 5764801 T^{16} \))(\( 1 - 19 T^{2} + 92 T^{4} + 943 T^{6} - 13625 T^{8} + 46207 T^{10} + 220892 T^{12} - 2235331 T^{14} + 5764801 T^{16} \))(\( 1 - 19 T^{2} + 92 T^{4} + 943 T^{6} - 13625 T^{8} + 46207 T^{10} + 220892 T^{12} - 2235331 T^{14} + 5764801 T^{16} \))(\( 1 + 16 T^{2} - 10 T^{3} + 87 T^{4} - 160 T^{5} - 82 T^{6} - 1720 T^{7} - 3505 T^{8} - 12040 T^{9} - 4018 T^{10} - 54880 T^{11} + 208887 T^{12} - 168070 T^{13} + 1882384 T^{14} + 5764801 T^{16} \))(\( 1 + 16 T^{2} - 10 T^{3} + 87 T^{4} - 160 T^{5} - 82 T^{6} - 1720 T^{7} - 3505 T^{8} - 12040 T^{9} - 4018 T^{10} - 54880 T^{11} + 208887 T^{12} - 168070 T^{13} + 1882384 T^{14} + 5764801 T^{16} \))(\( ( 1 - 5 T + 12 T^{2} + 5 T^{3} - 51 T^{4} + 35 T^{5} + 588 T^{6} - 1715 T^{7} + 2401 T^{8} )^{2} \))(\( ( 1 + 4 T^{2} + 5 T^{3} - 3 T^{4} + 20 T^{5} - 43 T^{6} - 985 T^{7} + 50 T^{8} - 6895 T^{9} - 2107 T^{10} + 6860 T^{11} - 7203 T^{12} + 84035 T^{13} + 470596 T^{14} + 5764801 T^{16} )^{2} \))
$11$ (\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))(\( 1 - 6 T + 11 T^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( 1 + 2 T - 7 T^{2} - 20 T^{3} - 77 T^{4} + 242 T^{5} + 1331 T^{6} \))(\( 1 - 2 T - 7 T^{2} + 20 T^{3} - 77 T^{4} - 242 T^{5} + 1331 T^{6} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 - 12 T^{2} + 86 T^{4} - 1452 T^{6} + 14641 T^{8} \))(\( 1 + 11 T + 51 T^{2} + 121 T^{3} + 121 T^{4} \))(\( 1 - 11 T + 51 T^{2} - 121 T^{3} + 121 T^{4} \))(\( 1 + 9 T + 41 T^{2} + 99 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 6 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 6 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + 9 T + 41 T^{2} + 99 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 6 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 + T - 9 T^{2} + 11 T^{3} + 121 T^{4} \))(\( 1 - T + 21 T^{2} - 11 T^{3} + 121 T^{4} \))(\( 1 - 11 T + 51 T^{2} - 121 T^{3} + 121 T^{4} \))(\( 1 + T + 15 T^{2} - 11 T^{3} + 104 T^{4} - 121 T^{5} + 1815 T^{6} + 1331 T^{7} + 14641 T^{8} \))(\( 1 - T^{2} + 141 T^{4} - 121 T^{6} + 14641 T^{8} \))(\( 1 + 19 T^{2} + 301 T^{4} + 2299 T^{6} + 14641 T^{8} \))(\( 1 - T + 15 T^{2} + 11 T^{3} + 104 T^{4} + 121 T^{5} + 1815 T^{6} - 1331 T^{7} + 14641 T^{8} \))(\( 1 + T + 15 T^{2} - 11 T^{3} + 104 T^{4} - 121 T^{5} + 1815 T^{6} + 1331 T^{7} + 14641 T^{8} \))(\( 1 + 19 T^{2} + 301 T^{4} + 2299 T^{6} + 14641 T^{8} \))(\( 1 - 37 T^{2} + 803 T^{4} - 13079 T^{6} + 164560 T^{8} - 1582559 T^{10} + 11756723 T^{12} - 65547757 T^{14} + 214358881 T^{16} \))
$13$ (\( 1 - 4 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 6 T + 13 T^{2} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( 1 - 8 T^{2} + 169 T^{4} \))(\( 1 - 8 T^{2} + 169 T^{4} \))(\( ( 1 - 13 T^{2} )^{4} \))(\( 1 - 20 T^{2} + 351 T^{4} - 6248 T^{6} + 59319 T^{8} - 571220 T^{10} + 4826809 T^{12} \))(\( 1 - 20 T^{2} + 351 T^{4} - 6248 T^{6} + 59319 T^{8} - 571220 T^{10} + 4826809 T^{12} \))(\( ( 1 - 4 T + 13 T^{2} )^{2} \))(\( ( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 - 4 T + 13 T^{2} )^{2} \))(\( ( 1 - 4 T + 13 T^{2} )^{2} \))(\( ( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 - 4 T + 13 T^{2} )^{2} \))(\( ( 1 + 13 T^{2} )^{4} \))(\( ( 1 + 13 T^{2} )^{4} \))(\( ( 1 + 14 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 20 T^{2} + 330 T^{4} - 3380 T^{6} + 28561 T^{8} )^{2} \))(\( 1 + T + 18 T^{2} + 5 T^{3} + 251 T^{4} + 65 T^{5} + 3042 T^{6} + 2197 T^{7} + 28561 T^{8} \))(\( 1 - 7 T + 6 T^{2} + 49 T^{3} - 181 T^{4} + 637 T^{5} + 1014 T^{6} - 15379 T^{7} + 28561 T^{8} \))(\( 1 - 3 T + 6 T^{2} - 59 T^{3} + 339 T^{4} - 767 T^{5} + 1014 T^{6} - 6591 T^{7} + 28561 T^{8} \))(\( 1 + 4 T + 3 T^{2} + 50 T^{3} + 341 T^{4} + 650 T^{5} + 507 T^{6} + 8788 T^{7} + 28561 T^{8} \))(\( 1 - 4 T + 3 T^{2} - 50 T^{3} + 341 T^{4} - 650 T^{5} + 507 T^{6} - 8788 T^{7} + 28561 T^{8} \))(\( 1 + 9 T + 18 T^{2} - 115 T^{3} - 789 T^{4} - 1495 T^{5} + 3042 T^{6} + 19773 T^{7} + 28561 T^{8} \))(\( 1 - 4 T + 3 T^{2} - 50 T^{3} + 341 T^{4} - 650 T^{5} + 507 T^{6} - 8788 T^{7} + 28561 T^{8} \))(\( 1 + 5 T + 2 T^{2} + 25 T^{3} + 259 T^{4} + 325 T^{5} + 338 T^{6} + 10985 T^{7} + 28561 T^{8} \))(\( 1 - 7 T + 6 T^{2} + 49 T^{3} - 181 T^{4} + 637 T^{5} + 1014 T^{6} - 15379 T^{7} + 28561 T^{8} \))(\( 1 + 5 T + 2 T^{2} + 25 T^{3} + 259 T^{4} + 325 T^{5} + 338 T^{6} + 10985 T^{7} + 28561 T^{8} \))(\( 1 + T - 19 T^{2} - 26 T^{3} + 248 T^{4} + 131 T^{5} - 4056 T^{6} - 1558 T^{7} + 64353 T^{8} - 20254 T^{9} - 685464 T^{10} + 287807 T^{11} + 7083128 T^{12} - 9653618 T^{13} - 91709371 T^{14} + 62748517 T^{15} + 815730721 T^{16} \))(\( ( 1 - 5 T + 8 T^{2} + 75 T^{3} - 461 T^{4} + 975 T^{5} + 1352 T^{6} - 10985 T^{7} + 28561 T^{8} )^{2} \))(\( ( 1 - 5 T + 28 T^{2} - 145 T^{3} + 499 T^{4} - 1885 T^{5} + 4732 T^{6} - 10985 T^{7} + 28561 T^{8} )^{2} \))(\( 1 + 18 T^{2} + 10 T^{3} + 135 T^{4} + 180 T^{5} + 1568 T^{6} + 12740 T^{7} + 13729 T^{8} + 165620 T^{9} + 264992 T^{10} + 395460 T^{11} + 3855735 T^{12} + 3712930 T^{13} + 86882562 T^{14} + 815730721 T^{16} \))(\( 1 + 18 T^{2} + 10 T^{3} + 135 T^{4} + 180 T^{5} + 1568 T^{6} + 12740 T^{7} + 13729 T^{8} + 165620 T^{9} + 264992 T^{10} + 395460 T^{11} + 3855735 T^{12} + 3712930 T^{13} + 86882562 T^{14} + 815730721 T^{16} \))(\( ( 1 + 5 T + 18 T^{2} - 5 T^{3} - 21 T^{4} - 65 T^{5} + 3042 T^{6} + 10985 T^{7} + 28561 T^{8} )^{2} \))(\( ( 1 + 36 T^{2} + 25 T^{3} + 387 T^{4} + 900 T^{5} - 1657 T^{6} + 13775 T^{7} - 72830 T^{8} + 179075 T^{9} - 280033 T^{10} + 1977300 T^{11} + 11053107 T^{12} + 9282325 T^{13} + 173765124 T^{14} + 815730721 T^{16} )^{2} \))
$17$ (\( 1 + 2 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 4 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 4 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{4} \))(\( ( 1 - 2 T + 11 T^{2} - 4 T^{3} + 187 T^{4} - 578 T^{5} + 4913 T^{6} )^{2} \))(\( ( 1 + 2 T + 11 T^{2} + 4 T^{3} + 187 T^{4} + 578 T^{5} + 4913 T^{6} )^{2} \))(\( 1 - 22 T^{2} + 289 T^{4} \))(\( 1 - 32 T^{2} + 289 T^{4} \))(\( 1 + 14 T^{2} + 289 T^{4} \))(\( 1 + 14 T^{2} + 289 T^{4} \))(\( 1 - 32 T^{2} + 289 T^{4} \))(\( 1 - 22 T^{2} + 289 T^{4} \))(\( 1 - 40 T^{2} + 846 T^{4} - 11560 T^{6} + 83521 T^{8} \))(\( 1 - 40 T^{2} + 846 T^{4} - 11560 T^{6} + 83521 T^{8} \))(\( ( 1 - 24 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 12 T^{2} + 422 T^{4} - 3468 T^{6} + 83521 T^{8} )^{2} \))(\( 1 + 6 T - T^{2} - 108 T^{3} - 491 T^{4} - 1836 T^{5} - 289 T^{6} + 29478 T^{7} + 83521 T^{8} \))(\( 1 - 12 T + 37 T^{2} + 180 T^{3} - 1619 T^{4} + 3060 T^{5} + 10693 T^{6} - 58956 T^{7} + 83521 T^{8} \))(\( 1 - 4 T - 11 T^{2} + 52 T^{3} + 69 T^{4} + 884 T^{5} - 3179 T^{6} - 19652 T^{7} + 83521 T^{8} \))(\( 1 + 12 T + 47 T^{2} + 60 T^{3} + T^{4} + 1020 T^{5} + 13583 T^{6} + 58956 T^{7} + 83521 T^{8} \))(\( 1 - 4 T - T^{2} + 72 T^{3} - 271 T^{4} + 1224 T^{5} - 289 T^{6} - 19652 T^{7} + 83521 T^{8} \))(\( 1 - 2 T - 13 T^{2} - 20 T^{3} + 341 T^{4} - 340 T^{5} - 3757 T^{6} - 9826 T^{7} + 83521 T^{8} \))(\( 1 + 4 T - T^{2} - 72 T^{3} - 271 T^{4} - 1224 T^{5} - 289 T^{6} + 19652 T^{7} + 83521 T^{8} \))(\( 1 - 6 T + 19 T^{2} - 132 T^{3} + 829 T^{4} - 2244 T^{5} + 5491 T^{6} - 29478 T^{7} + 83521 T^{8} \))(\( 1 + 4 T + 29 T^{2} + 108 T^{3} + 749 T^{4} + 1836 T^{5} + 8381 T^{6} + 19652 T^{7} + 83521 T^{8} \))(\( 1 - 2 T + 7 T^{2} + 20 T^{3} + 21 T^{4} + 340 T^{5} + 2023 T^{6} - 9826 T^{7} + 83521 T^{8} \))(\( 1 + 4 T + 8 T^{2} + 28 T^{3} + 101 T^{4} + 44 T^{5} + 2100 T^{6} - 2736 T^{7} - 21011 T^{8} - 46512 T^{9} + 606900 T^{10} + 216172 T^{11} + 8435621 T^{12} + 39755996 T^{13} + 193100552 T^{14} + 1641354692 T^{15} + 6975757441 T^{16} \))(\( ( 1 - 20 T + 197 T^{2} - 1280 T^{3} + 6089 T^{4} - 21760 T^{5} + 56933 T^{6} - 98260 T^{7} + 83521 T^{8} )^{2} \))(\( ( 1 + 10 T + 47 T^{2} + 100 T^{3} + 209 T^{4} + 1700 T^{5} + 13583 T^{6} + 49130 T^{7} + 83521 T^{8} )^{2} \))(\( 1 + 10 T + 26 T^{2} + 40 T^{3} + 467 T^{4} + 3290 T^{5} + 19488 T^{6} + 56400 T^{7} + 71725 T^{8} + 958800 T^{9} + 5632032 T^{10} + 16163770 T^{11} + 39004307 T^{12} + 56794280 T^{13} + 627576794 T^{14} + 4103386730 T^{15} + 6975757441 T^{16} \))(\( 1 - 10 T + 26 T^{2} - 40 T^{3} + 467 T^{4} - 3290 T^{5} + 19488 T^{6} - 56400 T^{7} + 71725 T^{8} - 958800 T^{9} + 5632032 T^{10} - 16163770 T^{11} + 39004307 T^{12} - 56794280 T^{13} + 627576794 T^{14} - 4103386730 T^{15} + 6975757441 T^{16} \))(\( 1 - 34 T^{2} + 267 T^{4} + 8548 T^{6} - 277795 T^{8} + 2470372 T^{10} + 22300107 T^{12} - 820677346 T^{14} + 6975757441 T^{16} \))(\( 1 - 33 T^{2} + 540 T^{4} - 10740 T^{6} + 269660 T^{8} - 6033879 T^{10} + 97965207 T^{12} - 1568615640 T^{14} + 29047977640 T^{16} - 453329919960 T^{18} + 8182152053847 T^{20} - 145643170700151 T^{22} + 1881082751540060 T^{24} - 21651774490822260 T^{26} + 314616008104070940 T^{28} - 5556468276460230657 T^{30} + 48661191875666868481 T^{32} \))
$19$ (\( 1 + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 - 2 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( ( 1 - 19 T^{2} )^{4} \))(\( 1 - 6 T^{2} + 599 T^{4} + 620 T^{6} + 216239 T^{8} - 781926 T^{10} + 47045881 T^{12} \))(\( 1 - 6 T^{2} + 599 T^{4} + 620 T^{6} + 216239 T^{8} - 781926 T^{10} + 47045881 T^{12} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 + 12 T^{2} + 361 T^{4} \))(\( ( 1 - 8 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( ( 1 - 8 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( 1 + 12 T^{2} + 361 T^{4} \))(\( ( 1 - 19 T^{2} )^{2} \))(\( 1 - 48 T^{2} + 1166 T^{4} - 17328 T^{6} + 130321 T^{8} \))(\( 1 - 48 T^{2} + 1166 T^{4} - 17328 T^{6} + 130321 T^{8} \))(\( ( 1 + 28 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 + 20 T^{2} + 630 T^{4} + 7220 T^{6} + 130321 T^{8} )^{2} \))(\( 1 + 12 T + 75 T^{2} + 422 T^{3} + 2139 T^{4} + 8018 T^{5} + 27075 T^{6} + 82308 T^{7} + 130321 T^{8} \))(\( 1 - 10 T + 21 T^{2} + 70 T^{3} - 469 T^{4} + 1330 T^{5} + 7581 T^{6} - 68590 T^{7} + 130321 T^{8} \))(\( 1 - 9 T^{2} - 70 T^{3} + 291 T^{4} - 1330 T^{5} - 3249 T^{6} + 130321 T^{8} \))(\( 1 + 6 T - 3 T^{2} - 22 T^{3} + 225 T^{4} - 418 T^{5} - 1083 T^{6} + 41154 T^{7} + 130321 T^{8} \))(\( 1 - 2 T + 5 T^{2} - 82 T^{3} + 529 T^{4} - 1558 T^{5} + 1805 T^{6} - 13718 T^{7} + 130321 T^{8} \))(\( 1 - 10 T + 21 T^{2} + 70 T^{3} - 469 T^{4} + 1330 T^{5} + 7581 T^{6} - 68590 T^{7} + 130321 T^{8} \))(\( 1 + 14 T + 117 T^{2} + 742 T^{3} + 3665 T^{4} + 14098 T^{5} + 42237 T^{6} + 96026 T^{7} + 130321 T^{8} \))(\( 1 - 4 T - 13 T^{2} + 58 T^{3} + 115 T^{4} + 1102 T^{5} - 4693 T^{6} - 27436 T^{7} + 130321 T^{8} \))(\( 1 - 4 T + 27 T^{2} - 122 T^{3} + 875 T^{4} - 2318 T^{5} + 9747 T^{6} - 27436 T^{7} + 130321 T^{8} \))(\( 1 + 12 T + 35 T^{2} - 198 T^{3} - 1781 T^{4} - 3762 T^{5} + 12635 T^{6} + 82308 T^{7} + 130321 T^{8} \))(\( 1 - 2 T - 20 T^{2} - 130 T^{3} + 235 T^{4} + 4574 T^{5} + 11842 T^{6} - 35540 T^{7} - 520405 T^{8} - 675260 T^{9} + 4274962 T^{10} + 31373066 T^{11} + 30625435 T^{12} - 321892870 T^{13} - 940917620 T^{14} - 1787743478 T^{15} + 16983563041 T^{16} \))(\( 1 + 42 T^{2} + 1023 T^{4} + 26284 T^{6} + 626325 T^{8} + 9488524 T^{10} + 133318383 T^{12} + 1975927002 T^{14} + 16983563041 T^{16} \))(\( 1 - 38 T^{2} + 383 T^{4} + 10364 T^{6} - 409595 T^{8} + 3741404 T^{10} + 49912943 T^{12} - 1787743478 T^{14} + 16983563041 T^{16} \))(\( 1 - 15 T + 138 T^{2} - 970 T^{3} + 5778 T^{4} - 30495 T^{5} + 154091 T^{6} - 736340 T^{7} + 3317800 T^{8} - 13990460 T^{9} + 55626851 T^{10} - 209165205 T^{11} + 752994738 T^{12} - 2401816030 T^{13} + 6492331578 T^{14} - 13408076085 T^{15} + 16983563041 T^{16} \))(\( 1 - 15 T + 138 T^{2} - 970 T^{3} + 5778 T^{4} - 30495 T^{5} + 154091 T^{6} - 736340 T^{7} + 3317800 T^{8} - 13990460 T^{9} + 55626851 T^{10} - 209165205 T^{11} + 752994738 T^{12} - 2401816030 T^{13} + 6492331578 T^{14} - 13408076085 T^{15} + 16983563041 T^{16} \))(\( ( 1 + 10 T + 69 T^{2} + 410 T^{3} + 1911 T^{4} + 7790 T^{5} + 24909 T^{6} + 68590 T^{7} + 130321 T^{8} )^{2} \))(\( ( 1 - 15 T + 138 T^{2} - 850 T^{3} + 3618 T^{4} - 8535 T^{5} - 17749 T^{6} + 301900 T^{7} - 1737560 T^{8} + 5736100 T^{9} - 6407389 T^{10} - 58541565 T^{11} + 471501378 T^{12} - 2104684150 T^{13} + 6492331578 T^{14} - 13408076085 T^{15} + 16983563041 T^{16} )^{2} \))
$23$ (\( 1 - 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 2 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 - 8 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( ( 1 - 9 T + 23 T^{2} )( 1 + 9 T + 23 T^{2} ) \))(\( 1 - 44 T^{2} + 529 T^{4} \))(\( 1 - 44 T^{2} + 529 T^{4} \))(\( ( 1 - 9 T + 58 T^{2} - 207 T^{3} + 529 T^{4} )( 1 + 9 T + 58 T^{2} + 207 T^{3} + 529 T^{4} ) \))(\( 1 - 65 T^{2} + 2365 T^{4} - 60122 T^{6} + 1251085 T^{8} - 18189665 T^{10} + 148035889 T^{12} \))(\( 1 - 65 T^{2} + 2365 T^{4} - 60122 T^{6} + 1251085 T^{8} - 18189665 T^{10} + 148035889 T^{12} \))(\( ( 1 - 3 T + 23 T^{2} )^{2} \))(\( ( 1 + 8 T + 23 T^{2} )^{2} \))(\( ( 1 + 6 T + 23 T^{2} )^{2} \))(\( ( 1 - 6 T + 23 T^{2} )^{2} \))(\( ( 1 - 8 T + 23 T^{2} )^{2} \))(\( ( 1 + 3 T + 23 T^{2} )^{2} \))(\( ( 1 - 11 T + 68 T^{2} - 253 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 + 11 T + 68 T^{2} + 253 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 - 10 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 - 68 T^{2} + 2106 T^{4} - 35972 T^{6} + 279841 T^{8} )^{2} \))(\( ( 1 + 4 T + 45 T^{2} + 92 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 - 4 T + 45 T^{2} - 92 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 - 2 T + 27 T^{2} - 46 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 - 2 T + 42 T^{2} - 46 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 + 10 T + 66 T^{2} + 230 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 - 2 T + 27 T^{2} - 46 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 + 2 T + 2 T^{2} + 46 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 + 8 T + 57 T^{2} + 184 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 - 5 T + 23 T^{2} )^{4} \))(\( ( 1 - 4 T + 5 T^{2} - 92 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 + 8 T + 101 T^{2} + 534 T^{3} + 3584 T^{4} + 12282 T^{5} + 53429 T^{6} + 97336 T^{7} + 279841 T^{8} )^{2} \))(\( ( 1 - 50 T^{2} + 1603 T^{4} - 26450 T^{6} + 279841 T^{8} )^{2} \))(\( ( 1 - 50 T^{2} + 1363 T^{4} - 26450 T^{6} + 279841 T^{8} )^{2} \))(\( 1 - 96 T^{2} + 5212 T^{4} - 191648 T^{6} + 5108870 T^{8} - 101381792 T^{10} + 1458531292 T^{12} - 14211445344 T^{14} + 78310985281 T^{16} \))(\( 1 - 96 T^{2} + 5212 T^{4} - 191648 T^{6} + 5108870 T^{8} - 101381792 T^{10} + 1458531292 T^{12} - 14211445344 T^{14} + 78310985281 T^{16} \))(\( ( 1 - 50 T^{2} + 1363 T^{4} - 26450 T^{6} + 279841 T^{8} )^{2} \))(\( ( 1 - 90 T^{2} + 4117 T^{4} - 140810 T^{6} + 3753788 T^{8} - 74488490 T^{10} + 1152105397 T^{12} - 13323230010 T^{14} + 78310985281 T^{16} )^{2} \))
$29$ (\( 1 - 10 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 8 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 - 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 29 T^{2} )^{4} \))(\( ( 1 - 8 T + 67 T^{2} - 336 T^{3} + 1943 T^{4} - 6728 T^{5} + 24389 T^{6} )^{2} \))(\( ( 1 + 8 T + 67 T^{2} + 336 T^{3} + 1943 T^{4} + 6728 T^{5} + 24389 T^{6} )^{2} \))(\( 1 - 10 T^{2} + 841 T^{4} \))(\( 1 - 40 T^{2} + 841 T^{4} \))(\( 1 - 10 T^{2} + 841 T^{4} \))(\( 1 - 10 T^{2} + 841 T^{4} \))(\( 1 - 40 T^{2} + 841 T^{4} \))(\( 1 - 10 T^{2} + 841 T^{4} \))(\( ( 1 - 10 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 10 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 + 32 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 29 T^{2} )^{8} \))(\( 1 + 10 T + 31 T^{2} + 200 T^{3} + 1821 T^{4} + 5800 T^{5} + 26071 T^{6} + 243890 T^{7} + 707281 T^{8} \))(\( 1 - 6 T + 7 T^{2} + 132 T^{3} - 995 T^{4} + 3828 T^{5} + 5887 T^{6} - 146334 T^{7} + 707281 T^{8} \))(\( 1 + 2 T - 25 T^{2} - 108 T^{3} + 509 T^{4} - 3132 T^{5} - 21025 T^{6} + 48778 T^{7} + 707281 T^{8} \))(\( 1 + T - 23 T^{2} + 83 T^{3} + 900 T^{4} + 2407 T^{5} - 19343 T^{6} + 24389 T^{7} + 707281 T^{8} \))(\( 1 - T - 23 T^{2} - 83 T^{3} + 900 T^{4} - 2407 T^{5} - 19343 T^{6} - 24389 T^{7} + 707281 T^{8} \))(\( 1 + 10 T + 31 T^{2} + 200 T^{3} + 1821 T^{4} + 5800 T^{5} + 26071 T^{6} + 243890 T^{7} + 707281 T^{8} \))(\( 1 + 11 T + 17 T^{2} - 207 T^{3} - 1420 T^{4} - 6003 T^{5} + 14297 T^{6} + 268279 T^{7} + 707281 T^{8} \))(\( 1 - 14 T + 47 T^{2} + 208 T^{3} - 2275 T^{4} + 6032 T^{5} + 39527 T^{6} - 341446 T^{7} + 707281 T^{8} \))(\( 1 + 2 T - 25 T^{2} - 108 T^{3} + 509 T^{4} - 3132 T^{5} - 21025 T^{6} + 48778 T^{7} + 707281 T^{8} \))(\( 1 - 6 T + 47 T^{2} - 288 T^{3} + 2365 T^{4} - 8352 T^{5} + 39527 T^{6} - 146334 T^{7} + 707281 T^{8} \))(\( 1 + 7 T + 10 T^{2} - 1310 T^{4} - 9899 T^{5} - 113 T^{6} + 219340 T^{7} + 1482000 T^{8} + 6360860 T^{9} - 95033 T^{10} - 241426711 T^{11} - 926538110 T^{12} + 5948233210 T^{14} + 120749134163 T^{15} + 500246412961 T^{16} \))(\( ( 1 + 10 T + 69 T^{2} + 370 T^{3} + 2081 T^{4} + 10730 T^{5} + 58029 T^{6} + 243890 T^{7} + 707281 T^{8} )^{2} \))(\( ( 1 - 10 T + 69 T^{2} - 370 T^{3} + 2081 T^{4} - 10730 T^{5} + 58029 T^{6} - 243890 T^{7} + 707281 T^{8} )^{2} \))(\( 1 - 23 T + 270 T^{2} - 2180 T^{3} + 12870 T^{4} - 47489 T^{5} + 12147 T^{6} + 1202500 T^{7} - 9195720 T^{8} + 34872500 T^{9} + 10215627 T^{10} - 1158209221 T^{11} + 9102706470 T^{12} - 44714304820 T^{13} + 160602296670 T^{14} - 396747155107 T^{15} + 500246412961 T^{16} \))(\( 1 + 23 T + 270 T^{2} + 2180 T^{3} + 12870 T^{4} + 47489 T^{5} + 12147 T^{6} - 1202500 T^{7} - 9195720 T^{8} - 34872500 T^{9} + 10215627 T^{10} + 1158209221 T^{11} + 9102706470 T^{12} + 44714304820 T^{13} + 160602296670 T^{14} + 396747155107 T^{15} + 500246412961 T^{16} \))(\( 1 - 58 T^{2} + 1523 T^{4} - 6056 T^{6} - 679595 T^{8} - 5093096 T^{10} + 1077188963 T^{12} - 34499752618 T^{14} + 500246412961 T^{16} \))(\( 1 - 181 T^{2} + 13060 T^{4} - 391800 T^{6} - 3565840 T^{8} + 628427837 T^{10} - 13497806017 T^{12} - 343438272820 T^{14} + 22793106751600 T^{16} - 288831587441620 T^{18} - 9546741737509777 T^{20} + 373803533013186677 T^{22} - 1783798669192852240 T^{24} - \)\(16\!\cdots\!00\)\( T^{26} + \)\(46\!\cdots\!60\)\( T^{28} - \)\(53\!\cdots\!61\)\( T^{30} + \)\(25\!\cdots\!21\)\( T^{32} \))
$31$ (\( 1 - 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( ( 1 + 5 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 31 T^{2} )^{2} \))(\( ( 1 - 5 T - 6 T^{2} - 155 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 + 3 T + 65 T^{2} + 218 T^{3} + 2015 T^{4} + 2883 T^{5} + 29791 T^{6} )^{2} \))(\( ( 1 + 3 T + 65 T^{2} + 218 T^{3} + 2015 T^{4} + 2883 T^{5} + 29791 T^{6} )^{2} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) \))(\( 1 - 54 T^{2} + 961 T^{4} \))(\( 1 - 50 T^{2} + 961 T^{4} \))(\( 1 - 50 T^{2} + 961 T^{4} \))(\( 1 - 54 T^{2} + 961 T^{4} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) \))(\( 1 - 45 T^{2} + 2024 T^{4} - 43245 T^{6} + 923521 T^{8} \))(\( 1 - 45 T^{2} + 2024 T^{4} - 43245 T^{6} + 923521 T^{8} \))(\( ( 1 + 2 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 58 T^{2} + 961 T^{4} )^{4} \))(\( 1 + 10 T + 29 T^{2} - 190 T^{3} - 2369 T^{4} - 5890 T^{5} + 27869 T^{6} + 297910 T^{7} + 923521 T^{8} \))(\( 1 - 12 T + 63 T^{2} - 434 T^{3} + 3255 T^{4} - 13454 T^{5} + 60543 T^{6} - 357492 T^{7} + 923521 T^{8} \))(\( 1 - 10 T + 69 T^{2} - 530 T^{3} + 3911 T^{4} - 16430 T^{5} + 66309 T^{6} - 297910 T^{7} + 923521 T^{8} \))(\( 1 - 5 T + 29 T^{2} - 85 T^{3} - 44 T^{4} - 2635 T^{5} + 27869 T^{6} - 148955 T^{7} + 923521 T^{8} \))(\( 1 - 5 T + 9 T^{2} - 205 T^{3} + 1916 T^{4} - 6355 T^{5} + 8649 T^{6} - 148955 T^{7} + 923521 T^{8} \))(\( 1 + 8 T + 3 T^{2} + 46 T^{3} + 1175 T^{4} + 1426 T^{5} + 2883 T^{6} + 238328 T^{7} + 923521 T^{8} \))(\( 1 + 7 T - 7 T^{2} - 241 T^{3} - 1220 T^{4} - 7471 T^{5} - 6727 T^{6} + 208537 T^{7} + 923521 T^{8} \))(\( 1 - 10 T + 29 T^{2} + 190 T^{3} - 2369 T^{4} + 5890 T^{5} + 27869 T^{6} - 297910 T^{7} + 923521 T^{8} \))(\( 1 - 2 T - 7 T^{2} + 146 T^{3} + 175 T^{4} + 4526 T^{5} - 6727 T^{6} - 59582 T^{7} + 923521 T^{8} \))(\( 1 - 10 T + 69 T^{2} - 530 T^{3} + 3911 T^{4} - 16430 T^{5} + 66309 T^{6} - 297910 T^{7} + 923521 T^{8} \))(\( 1 + 29 T + 420 T^{2} + 4350 T^{3} + 37960 T^{4} + 293597 T^{5} + 2021703 T^{6} + 12592220 T^{7} + 72565800 T^{8} + 390358820 T^{9} + 1942856583 T^{10} + 8746548227 T^{11} + 35056857160 T^{12} + 124536806850 T^{13} + 372751546020 T^{14} + 797865809219 T^{15} + 852891037441 T^{16} \))(\( ( 1 - T^{2} - 1859 T^{4} - 961 T^{6} + 923521 T^{8} )( 1 + 59 T^{2} + 2341 T^{4} + 56699 T^{6} + 923521 T^{8} ) \))(\( 1 + 18 T^{2} + 63 T^{4} - 19964 T^{6} - 187395 T^{8} - 19185404 T^{10} + 58181823 T^{12} + 15975066258 T^{14} + 852891037441 T^{16} \))(\( 1 + 13 T + 106 T^{2} + 872 T^{3} + 6586 T^{4} + 40319 T^{5} + 251629 T^{6} + 1513756 T^{7} + 8591372 T^{8} + 46926436 T^{9} + 241815469 T^{10} + 1201143329 T^{11} + 6082309306 T^{12} + 24964619672 T^{13} + 94075390186 T^{14} + 357663983443 T^{15} + 852891037441 T^{16} \))(\( 1 + 13 T + 106 T^{2} + 872 T^{3} + 6586 T^{4} + 40319 T^{5} + 251629 T^{6} + 1513756 T^{7} + 8591372 T^{8} + 46926436 T^{9} + 241815469 T^{10} + 1201143329 T^{11} + 6082309306 T^{12} + 24964619672 T^{13} + 94075390186 T^{14} + 357663983443 T^{15} + 852891037441 T^{16} \))(\( ( 1 - 10 T + 9 T^{2} + 130 T^{3} - 409 T^{4} + 4030 T^{5} + 8649 T^{6} - 297910 T^{7} + 923521 T^{8} )^{2} \))(\( ( 1 - 5 T - 44 T^{2} + 410 T^{3} + 400 T^{4} - 5365 T^{5} - 16361 T^{6} - 15620 T^{7} + 1743224 T^{8} - 484220 T^{9} - 15722921 T^{10} - 159828715 T^{11} + 369408400 T^{12} + 11737951910 T^{13} - 39050161964 T^{14} - 137563070555 T^{15} + 852891037441 T^{16} )^{2} \))
$37$ (\( 1 + 2 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 10 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( ( 1 + 7 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 - 7 T + 12 T^{2} - 259 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 + 3 T + 83 T^{2} + 130 T^{3} + 3071 T^{4} + 4107 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 + 3 T + 83 T^{2} + 130 T^{3} + 3071 T^{4} + 4107 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 - 5 T + 37 T^{2} )^{2} \))(\( ( 1 + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 37 T^{2} )^{2} \))(\( ( 1 - 5 T + 37 T^{2} )^{2} \))(\( ( 1 - 3 T + 68 T^{2} - 111 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 - 3 T + 68 T^{2} - 111 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 + 8 T + 37 T^{2} )^{4} \))(\( ( 1 - 8 T + 78 T^{2} - 296 T^{3} + 1369 T^{4} )^{4} \))(\( 1 - T + 14 T^{2} + 103 T^{3} + 739 T^{4} + 3811 T^{5} + 19166 T^{6} - 50653 T^{7} + 1874161 T^{8} \))(\( 1 - 9 T - 6 T^{2} + 307 T^{3} - 1581 T^{4} + 11359 T^{5} - 8214 T^{6} - 455877 T^{7} + 1874161 T^{8} \))(\( 1 + 15 T + 98 T^{2} + 675 T^{3} + 5059 T^{4} + 24975 T^{5} + 134162 T^{6} + 759795 T^{7} + 1874161 T^{8} \))(\( 1 - 4 T + 59 T^{2} - 188 T^{3} + 2809 T^{4} - 6956 T^{5} + 80771 T^{6} - 202612 T^{7} + 1874161 T^{8} \))(\( 1 - 4 T - 21 T^{2} + 232 T^{3} - 151 T^{4} + 8584 T^{5} - 28749 T^{6} - 202612 T^{7} + 1874161 T^{8} \))(\( 1 + 3 T - 18 T^{2} + 155 T^{3} + 1851 T^{4} + 5735 T^{5} - 24642 T^{6} + 151959 T^{7} + 1874161 T^{8} \))(\( 1 - 20 T + 203 T^{2} - 1600 T^{3} + 10729 T^{4} - 59200 T^{5} + 277907 T^{6} - 1013060 T^{7} + 1874161 T^{8} \))(\( 1 + 11 T + 14 T^{2} - 413 T^{3} - 3701 T^{4} - 15281 T^{5} + 19166 T^{6} + 557183 T^{7} + 1874161 T^{8} \))(\( 1 - 5 T - 22 T^{2} - 25 T^{3} + 1579 T^{4} - 925 T^{5} - 30118 T^{6} - 253265 T^{7} + 1874161 T^{8} \))(\( 1 + 3 T - 18 T^{2} + 155 T^{3} + 1851 T^{4} + 5735 T^{5} - 24642 T^{6} + 151959 T^{7} + 1874161 T^{8} \))(\( 1 - 13 T + 49 T^{2} - 308 T^{3} + 5258 T^{4} - 29513 T^{5} + 47876 T^{6} - 651424 T^{7} + 7877593 T^{8} - 24102688 T^{9} + 65542244 T^{10} - 1494921989 T^{11} + 9854338538 T^{12} - 21357938756 T^{13} + 125720594041 T^{14} - 1234114402729 T^{15} + 3512479453921 T^{16} \))(\( ( 1 + 7 T + 12 T^{2} - 175 T^{3} - 1669 T^{4} - 6475 T^{5} + 16428 T^{6} + 354571 T^{7} + 1874161 T^{8} )^{2} \))(\( ( 1 - 13 T + 32 T^{2} + 145 T^{3} - 989 T^{4} + 5365 T^{5} + 43808 T^{6} - 658489 T^{7} + 1874161 T^{8} )^{2} \))(\( 1 - 6 T - 42 T^{2} + 498 T^{3} - 789 T^{4} - 26526 T^{5} + 159760 T^{6} + 440664 T^{7} - 7027551 T^{8} + 16304568 T^{9} + 218711440 T^{10} - 1343621478 T^{11} - 1478713029 T^{12} + 34533290586 T^{13} - 107760509178 T^{14} - 569591262798 T^{15} + 3512479453921 T^{16} \))(\( 1 - 6 T - 42 T^{2} + 498 T^{3} - 789 T^{4} - 26526 T^{5} + 159760 T^{6} + 440664 T^{7} - 7027551 T^{8} + 16304568 T^{9} + 218711440 T^{10} - 1343621478 T^{11} - 1478713029 T^{12} + 34533290586 T^{13} - 107760509178 T^{14} - 569591262798 T^{15} + 3512479453921 T^{16} \))(\( ( 1 + 3 T - 28 T^{2} - 195 T^{3} + 451 T^{4} - 7215 T^{5} - 38332 T^{6} + 151959 T^{7} + 1874161 T^{8} )^{2} \))(\( ( 1 + 12 T - 18 T^{2} - 771 T^{3} - 2007 T^{4} + 14286 T^{5} + 78109 T^{6} + 20877 T^{7} - 828762 T^{8} + 772449 T^{9} + 106931221 T^{10} + 723628758 T^{11} - 3761441127 T^{12} - 53464190847 T^{13} - 46183075362 T^{14} + 1139182525596 T^{15} + 3512479453921 T^{16} )^{2} \))
$41$ (\( 1 - 2 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{4} \))(\( ( 1 + 4 T + 87 T^{2} + 312 T^{3} + 3567 T^{4} + 6724 T^{5} + 68921 T^{6} )^{2} \))(\( ( 1 - 4 T + 87 T^{2} - 312 T^{3} + 3567 T^{4} - 6724 T^{5} + 68921 T^{6} )^{2} \))(\( 1 - 34 T^{2} + 1681 T^{4} \))(\( 1 + 16 T^{2} + 1681 T^{4} \))(\( 1 - 34 T^{2} + 1681 T^{4} \))(\( 1 - 34 T^{2} + 1681 T^{4} \))(\( 1 + 16 T^{2} + 1681 T^{4} \))(\( 1 - 34 T^{2} + 1681 T^{4} \))(\( 1 - 52 T^{2} + 1926 T^{4} - 87412 T^{6} + 2825761 T^{8} \))(\( 1 - 52 T^{2} + 1926 T^{4} - 87412 T^{6} + 2825761 T^{8} \))(\( ( 1 - 72 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 36 T^{2} + 1958 T^{4} - 60516 T^{6} + 2825761 T^{8} )^{2} \))(\( 1 + 15 T + 44 T^{2} - 435 T^{3} - 4649 T^{4} - 17835 T^{5} + 73964 T^{6} + 1033815 T^{7} + 2825761 T^{8} \))(\( 1 + 3 T - 22 T^{2} + 171 T^{3} + 2215 T^{4} + 7011 T^{5} - 36982 T^{6} + 206763 T^{7} + 2825761 T^{8} \))(\( 1 + T + 10 T^{2} - 151 T^{3} + 879 T^{4} - 6191 T^{5} + 16810 T^{6} + 68921 T^{7} + 2825761 T^{8} \))(\( 1 - 6 T - 25 T^{2} + 66 T^{3} + 1369 T^{4} + 2706 T^{5} - 42025 T^{6} - 413526 T^{7} + 2825761 T^{8} \))(\( 1 + 10 T - T^{2} - 410 T^{3} - 2839 T^{4} - 16810 T^{5} - 1681 T^{6} + 689210 T^{7} + 2825761 T^{8} \))(\( 1 - 23 T + 208 T^{2} - 961 T^{3} + 3975 T^{4} - 39401 T^{5} + 349648 T^{6} - 1585183 T^{7} + 2825761 T^{8} \))(\( 1 - 14 T + 95 T^{2} - 786 T^{3} + 6569 T^{4} - 32226 T^{5} + 159695 T^{6} - 964894 T^{7} + 2825761 T^{8} \))(\( 1 - 5 T - 16 T^{2} + 285 T^{3} - 769 T^{4} + 11685 T^{5} - 26896 T^{6} - 344605 T^{7} + 2825761 T^{8} \))(\( 1 + 13 T + 98 T^{2} + 861 T^{3} + 7175 T^{4} + 35301 T^{5} + 164738 T^{6} + 895973 T^{7} + 2825761 T^{8} \))(\( 1 + 7 T + 28 T^{2} + 389 T^{3} + 3975 T^{4} + 15949 T^{5} + 47068 T^{6} + 482447 T^{7} + 2825761 T^{8} \))(\( 1 + 23 T + 231 T^{2} + 1282 T^{3} + 4366 T^{4} + 2369 T^{5} - 244206 T^{6} - 3763224 T^{7} - 31196163 T^{8} - 154292184 T^{9} - 410510286 T^{10} + 163273849 T^{11} + 12337272526 T^{12} + 148527649682 T^{13} + 1097274079671 T^{14} + 4479348299263 T^{15} + 7984925229121 T^{16} \))(\( ( 1 - 15 T + 176 T^{2} - 1635 T^{3} + 11311 T^{4} - 67035 T^{5} + 295856 T^{6} - 1033815 T^{7} + 2825761 T^{8} )^{2} \))(\( ( 1 - 5 T + 66 T^{2} - 695 T^{3} + 2831 T^{4} - 28495 T^{5} + 110946 T^{6} - 344605 T^{7} + 2825761 T^{8} )^{2} \))(\( 1 - 2 T - 114 T^{2} + 132 T^{3} + 3471 T^{4} - 3306 T^{5} + 199344 T^{6} - 1544 T^{7} - 17114163 T^{8} - 63304 T^{9} + 335097264 T^{10} - 227852826 T^{11} + 9808216431 T^{12} + 15293018532 T^{13} - 541511883474 T^{14} - 389508547762 T^{15} + 7984925229121 T^{16} \))(\( 1 + 2 T - 114 T^{2} - 132 T^{3} + 3471 T^{4} + 3306 T^{5} + 199344 T^{6} + 1544 T^{7} - 17114163 T^{8} + 63304 T^{9} + 335097264 T^{10} + 227852826 T^{11} + 9808216431 T^{12} - 15293018532 T^{13} - 541511883474 T^{14} + 389508547762 T^{15} + 7984925229121 T^{16} \))(\( 1 - 87 T^{2} + 4308 T^{4} - 137029 T^{6} + 5286975 T^{8} - 230345749 T^{10} + 12173378388 T^{12} - 413259068967 T^{14} + 7984925229121 T^{16} \))(\( 1 + 26 T^{2} + 540 T^{4} + 94185 T^{6} + 576865 T^{8} - 92511562 T^{10} + 817706943 T^{12} - 130394374045 T^{14} - 13553961986130 T^{16} - 219192942769645 T^{18} + 2310644388958623 T^{20} - 439439562997734442 T^{22} + 4606223892296885665 T^{24} + \)\(12\!\cdots\!85\)\( T^{26} + \)\(12\!\cdots\!40\)\( T^{28} + \)\(98\!\cdots\!86\)\( T^{30} + \)\(63\!\cdots\!41\)\( T^{32} \))
$43$ (\( 1 + 4 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( ( 1 - 43 T^{2} )^{2} \))(\( ( 1 - 10 T + 43 T^{2} )( 1 + 10 T + 43 T^{2} ) \))(\( ( 1 - 10 T + 43 T^{2} )( 1 + 10 T + 43 T^{2} ) \))(\( ( 1 - 43 T^{2} )^{4} \))(\( 1 - 190 T^{2} + 17415 T^{4} - 945892 T^{6} + 32200335 T^{8} - 649572190 T^{10} + 6321363049 T^{12} \))(\( 1 - 190 T^{2} + 17415 T^{4} - 945892 T^{6} + 32200335 T^{8} - 649572190 T^{10} + 6321363049 T^{12} \))(\( ( 1 - 8 T + 43 T^{2} )( 1 + 8 T + 43 T^{2} ) \))(\( 1 - 68 T^{2} + 1849 T^{4} \))(\( ( 1 - 8 T + 43 T^{2} )( 1 + 8 T + 43 T^{2} ) \))(\( ( 1 - 8 T + 43 T^{2} )( 1 + 8 T + 43 T^{2} ) \))(\( 1 - 68 T^{2} + 1849 T^{4} \))(\( ( 1 - 8 T + 43 T^{2} )( 1 + 8 T + 43 T^{2} ) \))(\( ( 1 - 74 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 74 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 + 76 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 + 116 T^{2} + 6870 T^{4} + 214484 T^{6} + 3418801 T^{8} )^{2} \))(\( ( 1 + 10 T + 91 T^{2} + 430 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 41 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 6 T + 15 T^{2} - 258 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 - 2 T + 82 T^{2} - 86 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 - 6 T + 50 T^{2} - 258 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 8 T + 97 T^{2} + 344 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 - 14 T + 130 T^{2} - 602 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 14 T + 115 T^{2} + 602 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 - 14 T + 115 T^{2} - 602 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 - 2 T + 67 T^{2} - 86 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 - 24 T + 373 T^{2} - 3770 T^{3} + 29096 T^{4} - 162110 T^{5} + 689677 T^{6} - 1908168 T^{7} + 3418801 T^{8} )^{2} \))(\( ( 1 + 82 T^{2} + 3759 T^{4} + 151618 T^{6} + 3418801 T^{8} )^{2} \))(\( ( 1 - 78 T^{2} + 4719 T^{4} - 144222 T^{6} + 3418801 T^{8} )^{2} \))(\( 1 - 231 T^{2} + 27167 T^{4} - 2024653 T^{6} + 103981560 T^{8} - 3743583397 T^{10} + 92878566767 T^{12} - 1460234864319 T^{14} + 11688200277601 T^{16} \))(\( 1 - 231 T^{2} + 27167 T^{4} - 2024653 T^{6} + 103981560 T^{8} - 3743583397 T^{10} + 92878566767 T^{12} - 1460234864319 T^{14} + 11688200277601 T^{16} \))(\( ( 1 - 122 T^{2} + 6919 T^{4} - 225578 T^{6} + 3418801 T^{8} )^{2} \))(\( ( 1 - 174 T^{2} + 12917 T^{4} - 562102 T^{6} + 21452940 T^{8} - 1039326598 T^{10} + 44160652517 T^{12} - 1099917170526 T^{14} + 11688200277601 T^{16} )^{2} \))
$47$ (\( 1 - 2 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 - 12 T + 47 T^{2} \))(\( ( 1 - 12 T + 47 T^{2} )( 1 + 12 T + 47 T^{2} ) \))(\( 1 + 4 T^{2} + 2209 T^{4} \))(\( 1 + 4 T^{2} + 2209 T^{4} \))(\( ( 1 - 12 T + 47 T^{2} )^{2}( 1 + 12 T + 47 T^{2} )^{2} \))(\( 1 - 152 T^{2} + 14039 T^{4} - 785088 T^{6} + 31012151 T^{8} - 741711512 T^{10} + 10779215329 T^{12} \))(\( 1 - 152 T^{2} + 14039 T^{4} - 785088 T^{6} + 31012151 T^{8} - 741711512 T^{10} + 10779215329 T^{12} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 + 10 T + 47 T^{2} )^{2} \))(\( ( 1 + 6 T + 47 T^{2} )^{2} \))(\( ( 1 - 6 T + 47 T^{2} )^{2} \))(\( ( 1 - 10 T + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 + 2 T + 62 T^{2} + 94 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 - 2 T + 62 T^{2} - 94 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 - 30 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 132 T^{2} + 8666 T^{4} - 291588 T^{6} + 4879681 T^{8} )^{2} \))(\( 1 - 5 T - 37 T^{2} + 235 T^{3} + 824 T^{4} + 11045 T^{5} - 81733 T^{6} - 519115 T^{7} + 4879681 T^{8} \))(\( 1 + 17 T + 67 T^{2} - 335 T^{3} - 4344 T^{4} - 15745 T^{5} + 148003 T^{6} + 1764991 T^{7} + 4879681 T^{8} \))(\( 1 - 11 T + 29 T^{2} + 373 T^{3} - 4876 T^{4} + 17531 T^{5} + 64061 T^{6} - 1142053 T^{7} + 4879681 T^{8} \))(\( 1 - 8 T + 17 T^{2} - 380 T^{3} + 4721 T^{4} - 17860 T^{5} + 37553 T^{6} - 830584 T^{7} + 4879681 T^{8} \))(\( 1 - 20 T + 193 T^{2} - 1600 T^{3} + 12369 T^{4} - 75200 T^{5} + 426337 T^{6} - 2076460 T^{7} + 4879681 T^{8} \))(\( 1 - 3 T - 43 T^{2} + 45 T^{3} + 2116 T^{4} + 2115 T^{5} - 94987 T^{6} - 311469 T^{7} + 4879681 T^{8} \))(\( 1 - 4 T - 31 T^{2} + 312 T^{3} + 209 T^{4} + 14664 T^{5} - 68479 T^{6} - 415292 T^{7} + 4879681 T^{8} \))(\( 1 - 11 T - T^{2} + 333 T^{3} - 1456 T^{4} + 15651 T^{5} - 2209 T^{6} - 1142053 T^{7} + 4879681 T^{8} \))(\( 1 + 23 T + 257 T^{2} + 2175 T^{3} + 16076 T^{4} + 102225 T^{5} + 567713 T^{6} + 2387929 T^{7} + 4879681 T^{8} \))(\( 1 + T + 59 T^{2} + 177 T^{3} + 2264 T^{4} + 8319 T^{5} + 130331 T^{6} + 103823 T^{7} + 4879681 T^{8} \))(\( 1 - 15 T + 106 T^{2} - 610 T^{3} + 5682 T^{4} - 11735 T^{5} - 270377 T^{6} + 2518900 T^{7} - 12357400 T^{8} + 118388300 T^{9} - 597262793 T^{10} - 1218362905 T^{11} + 27726347442 T^{12} - 139900454270 T^{13} + 1142596824874 T^{14} - 7599346806945 T^{15} + 23811286661761 T^{16} \))(\( 1 - 5 T^{2} + 4431 T^{4} + 113225 T^{6} + 8614376 T^{8} + 250114025 T^{10} + 21621866511 T^{12} - 53896076645 T^{14} + 23811286661761 T^{16} \))(\( 1 - 105 T^{2} + 10191 T^{4} - 606835 T^{6} + 33401256 T^{8} - 1340498515 T^{10} + 49728829071 T^{12} - 1131817609545 T^{14} + 23811286661761 T^{16} \))(\( 1 + 10 T + 86 T^{2} - 380 T^{3} - 6733 T^{4} - 69970 T^{5} - 65532 T^{6} + 2017800 T^{7} + 29345725 T^{8} + 94836600 T^{9} - 144760188 T^{10} - 7264495310 T^{11} - 32854892173 T^{12} - 87151102660 T^{13} + 927012518294 T^{14} + 5066231204630 T^{15} + 23811286661761 T^{16} \))(\( 1 - 10 T + 86 T^{2} + 380 T^{3} - 6733 T^{4} + 69970 T^{5} - 65532 T^{6} - 2017800 T^{7} + 29345725 T^{8} - 94836600 T^{9} - 144760188 T^{10} + 7264495310 T^{11} - 32854892173 T^{12} + 87151102660 T^{13} + 927012518294 T^{14} - 5066231204630 T^{15} + 23811286661761 T^{16} \))(\( 1 + 15 T^{2} - 969 T^{4} - 93835 T^{6} + 1517976 T^{8} - 207281515 T^{10} - 4728410889 T^{12} + 161688229935 T^{14} + 23811286661761 T^{16} \))(\( 1 + 120 T^{2} + 8097 T^{4} + 370980 T^{6} + 6487103 T^{8} - 163505580 T^{10} - 10395846741 T^{12} + 1822592400 T^{14} + 20419686632680 T^{16} + 4026106611600 T^{18} - 50728415820969621 T^{20} - 1762461854313035820 T^{22} + \)\(15\!\cdots\!83\)\( T^{24} + \)\(19\!\cdots\!20\)\( T^{26} + \)\(94\!\cdots\!77\)\( T^{28} + \)\(30\!\cdots\!80\)\( T^{30} + \)\(56\!\cdots\!21\)\( T^{32} \))
$53$ (\( 1 - 4 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 8 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 - 14 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( ( 1 - 6 T + 53 T^{2} )( 1 + 6 T + 53 T^{2} ) \))(\( 1 - 56 T^{2} + 2809 T^{4} \))(\( 1 - 56 T^{2} + 2809 T^{4} \))(\( ( 1 - 6 T + 53 T^{2} )^{2}( 1 + 6 T + 53 T^{2} )^{2} \))(\( 1 - 260 T^{2} + 30671 T^{4} - 2087688 T^{6} + 86154839 T^{8} - 2051525060 T^{10} + 22164361129 T^{12} \))(\( 1 - 260 T^{2} + 30671 T^{4} - 2087688 T^{6} + 86154839 T^{8} - 2051525060 T^{10} + 22164361129 T^{12} \))(\( 1 + 86 T^{2} + 2809 T^{4} \))(\( 1 - 74 T^{2} + 2809 T^{4} \))(\( 1 - 94 T^{2} + 2809 T^{4} \))(\( 1 - 94 T^{2} + 2809 T^{4} \))(\( 1 - 74 T^{2} + 2809 T^{4} \))(\( 1 + 86 T^{2} + 2809 T^{4} \))(\( 1 - 136 T^{2} + 9054 T^{4} - 382024 T^{6} + 7890481 T^{8} \))(\( 1 - 136 T^{2} + 9054 T^{4} - 382024 T^{6} + 7890481 T^{8} \))(\( ( 1 - 6 T + 53 T^{2} )^{4} \))(\( ( 1 + 18 T + 184 T^{2} + 954 T^{3} + 2809 T^{4} )^{4} \))(\( 1 - 26 T + 263 T^{2} - 1320 T^{3} + 5801 T^{4} - 69960 T^{5} + 738767 T^{6} - 3870802 T^{7} + 7890481 T^{8} \))(\( 1 - 4 T - 47 T^{2} + 160 T^{3} + 2121 T^{4} + 8480 T^{5} - 132023 T^{6} - 595508 T^{7} + 7890481 T^{8} \))(\( 1 + 24 T + 253 T^{2} + 1920 T^{3} + 14041 T^{4} + 101760 T^{5} + 710677 T^{6} + 3573048 T^{7} + 7890481 T^{8} \))(\( 1 + 7 T - 19 T^{2} + 141 T^{3} + 3884 T^{4} + 7473 T^{5} - 53371 T^{6} + 1042139 T^{7} + 7890481 T^{8} \))(\( 1 + T + 53 T^{2} + 75 T^{3} + 2396 T^{4} + 3975 T^{5} + 148877 T^{6} + 148877 T^{7} + 7890481 T^{8} \))(\( 1 - 6 T + 23 T^{2} + 120 T^{3} - 1319 T^{4} + 6360 T^{5} + 64607 T^{6} - 893262 T^{7} + 7890481 T^{8} \))(\( 1 + 5 T - 43 T^{2} - 265 T^{3} + 1244 T^{4} - 14045 T^{5} - 120787 T^{6} + 744385 T^{7} + 7890481 T^{8} \))(\( 1 - 22 T + 251 T^{2} - 2376 T^{3} + 19529 T^{4} - 125928 T^{5} + 705059 T^{6} - 3275294 T^{7} + 7890481 T^{8} \))(\( 1 + 8 T - 19 T^{2} - 496 T^{3} - 2551 T^{4} - 26288 T^{5} - 53371 T^{6} + 1191016 T^{7} + 7890481 T^{8} \))(\( 1 - 18 T + 71 T^{2} + 576 T^{3} - 7631 T^{4} + 30528 T^{5} + 199439 T^{6} - 2679786 T^{7} + 7890481 T^{8} \))(\( 1 - 9 T - 54 T^{2} + 224 T^{3} + 7158 T^{4} - 27719 T^{5} - 247621 T^{6} - 254328 T^{7} + 21780128 T^{8} - 13479384 T^{9} - 695567389 T^{10} - 4126721563 T^{11} + 56480062998 T^{12} + 93675790432 T^{13} - 1196875500966 T^{14} - 10572400258533 T^{15} + 62259690411361 T^{16} \))(\( ( 1 - 4 T - 7 T^{2} - 360 T^{3} + 4241 T^{4} - 19080 T^{5} - 19663 T^{6} - 595508 T^{7} + 7890481 T^{8} )^{2} \))(\( ( 1 - 14 T + 43 T^{2} - 160 T^{3} + 2961 T^{4} - 8480 T^{5} + 120787 T^{6} - 2084278 T^{7} + 7890481 T^{8} )^{2} \))(\( 1 - 15 T + 206 T^{2} - 2820 T^{3} + 27882 T^{4} - 271485 T^{5} + 2462023 T^{6} - 19707960 T^{7} + 150191000 T^{8} - 1044521880 T^{9} + 6915822607 T^{10} - 40417872345 T^{11} + 220002391242 T^{12} - 1179311290260 T^{13} + 4565858392574 T^{14} - 17620667097555 T^{15} + 62259690411361 T^{16} \))(\( 1 + 15 T + 206 T^{2} + 2820 T^{3} + 27882 T^{4} + 271485 T^{5} + 2462023 T^{6} + 19707960 T^{7} + 150191000 T^{8} + 1044521880 T^{9} + 6915822607 T^{10} + 40417872345 T^{11} + 220002391242 T^{12} + 1179311290260 T^{13} + 4565858392574 T^{14} + 17620667097555 T^{15} + 62259690411361 T^{16} \))(\( 1 + 70 T^{2} + 6051 T^{4} + 452660 T^{6} + 19250861 T^{8} + 1271521940 T^{10} + 47745300531 T^{12} + 1551505279030 T^{14} + 62259690411361 T^{16} \))(\( 1 + 55 T^{2} + 5692 T^{4} + 297140 T^{6} + 15710108 T^{8} + 452689705 T^{10} + 30761663159 T^{12} + 521382533000 T^{14} + 55744044557080 T^{16} + 1464563535197000 T^{18} + 242724318684489479 T^{20} + 10033578101000476945 T^{22} + \)\(97\!\cdots\!88\)\( T^{24} + \)\(51\!\cdots\!60\)\( T^{26} + \)\(27\!\cdots\!72\)\( T^{28} + \)\(75\!\cdots\!95\)\( T^{30} + \)\(38\!\cdots\!21\)\( T^{32} \))
$59$ (\( 1 + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( ( 1 - 15 T + 59 T^{2} )( 1 + 15 T + 59 T^{2} ) \))(\( 1 + 10 T^{2} + 3481 T^{4} \))(\( 1 + 10 T^{2} + 3481 T^{4} \))(\( ( 1 - 15 T + 166 T^{2} - 885 T^{3} + 3481 T^{4} )( 1 + 15 T + 166 T^{2} + 885 T^{3} + 3481 T^{4} ) \))(\( 1 - 299 T^{2} + 39799 T^{4} - 3024890 T^{6} + 138540319 T^{8} - 3623090939 T^{10} + 42180533641 T^{12} \))(\( 1 - 299 T^{2} + 39799 T^{4} - 3024890 T^{6} + 138540319 T^{8} - 3623090939 T^{10} + 42180533641 T^{12} \))(\( ( 1 - 9 T + 59 T^{2} )^{2} \))(\( ( 1 + 4 T + 59 T^{2} )^{2} \))(\( ( 1 - 12 T + 59 T^{2} )^{2} \))(\( ( 1 + 12 T + 59 T^{2} )^{2} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))(\( ( 1 + 9 T + 59 T^{2} )^{2} \))(\( ( 1 - 7 T + 122 T^{2} - 413 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 + 7 T + 122 T^{2} + 413 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 - 82 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 140 T^{2} + 10134 T^{4} - 487340 T^{6} + 12117361 T^{8} )^{2} \))(\( 1 + 2 T + 5 T^{2} + 402 T^{3} + 4019 T^{4} + 23718 T^{5} + 17405 T^{6} + 410758 T^{7} + 12117361 T^{8} \))(\( 1 - 6 T + 17 T^{2} + 222 T^{3} - 1685 T^{4} + 13098 T^{5} + 59177 T^{6} - 1232274 T^{7} + 12117361 T^{8} \))(\( 1 - 8 T - 25 T^{2} - 18 T^{3} + 3779 T^{4} - 1062 T^{5} - 87025 T^{6} - 1643032 T^{7} + 12117361 T^{8} \))(\( 1 + 8 T - 25 T^{2} + 18 T^{3} + 3779 T^{4} + 1062 T^{5} - 87025 T^{6} + 1643032 T^{7} + 12117361 T^{8} \))(\( 1 - 4 T - 13 T^{2} + 398 T^{3} - 325 T^{4} + 23482 T^{5} - 45253 T^{6} - 821516 T^{7} + 12117361 T^{8} \))(\( 1 - 20 T + 131 T^{2} - 530 T^{3} + 3851 T^{4} - 31270 T^{5} + 456011 T^{6} - 4107580 T^{7} + 12117361 T^{8} \))(\( 1 - 20 T + 131 T^{2} - 530 T^{3} + 3851 T^{4} - 31270 T^{5} + 456011 T^{6} - 4107580 T^{7} + 12117361 T^{8} \))(\( 1 + 18 T + 265 T^{2} + 2718 T^{3} + 24379 T^{4} + 160362 T^{5} + 922465 T^{6} + 3696822 T^{7} + 12117361 T^{8} \))(\( 1 + 28 T + 395 T^{2} + 4018 T^{3} + 33539 T^{4} + 237062 T^{5} + 1374995 T^{6} + 5750612 T^{7} + 12117361 T^{8} \))(\( 1 - 2 T + 5 T^{2} - 402 T^{3} + 4019 T^{4} - 23718 T^{5} + 17405 T^{6} - 410758 T^{7} + 12117361 T^{8} \))(\( 1 + 12 T - 110 T^{2} - 1900 T^{3} + 675 T^{4} + 146476 T^{5} + 980452 T^{6} - 3926720 T^{7} - 90713275 T^{8} - 231676480 T^{9} + 3412953412 T^{10} + 30083094404 T^{11} + 8179218675 T^{12} - 1358356168100 T^{13} - 4639858700510 T^{14} + 29863817817828 T^{15} + 146830437604321 T^{16} \))(\( 1 - 78 T^{2} + 7503 T^{4} - 480316 T^{6} + 40879005 T^{8} - 1671979996 T^{10} + 90916559583 T^{12} - 3290081623998 T^{14} + 146830437604321 T^{16} \))(\( 1 + 82 T^{2} - 537 T^{4} - 63796 T^{6} + 6771125 T^{8} - 222073876 T^{10} - 6507022857 T^{12} + 3458803758562 T^{14} + 146830437604321 T^{16} \))(\( 1 - 25 T + 300 T^{2} - 1010 T^{3} - 15456 T^{4} + 230275 T^{5} - 679305 T^{6} - 11567740 T^{7} + 158967216 T^{8} - 682496660 T^{9} - 2364660705 T^{10} + 47293649225 T^{11} - 187285931616 T^{12} - 722073541990 T^{13} + 12654160092300 T^{14} - 62216287120475 T^{15} + 146830437604321 T^{16} \))(\( 1 + 25 T + 300 T^{2} + 1010 T^{3} - 15456 T^{4} - 230275 T^{5} - 679305 T^{6} + 11567740 T^{7} + 158967216 T^{8} + 682496660 T^{9} - 2364660705 T^{10} - 47293649225 T^{11} - 187285931616 T^{12} + 722073541990 T^{13} + 12654160092300 T^{14} + 62216287120475 T^{15} + 146830437604321 T^{16} \))(\( 1 + 122 T^{2} + 9663 T^{4} + 604444 T^{6} + 40851365 T^{8} + 2104069564 T^{10} + 117090059343 T^{12} + 5146025104202 T^{14} + 146830437604321 T^{16} \))(\( 1 + 83 T^{2} - 2824 T^{4} - 710228 T^{6} - 14741224 T^{8} + 3387550269 T^{10} + 226729848199 T^{12} - 5011587031104 T^{14} - 993441132283448 T^{16} - 17445334455273024 T^{18} + 2747367420102482839 T^{20} + \)\(14\!\cdots\!29\)\( T^{22} - \)\(21\!\cdots\!04\)\( T^{24} - \)\(36\!\cdots\!28\)\( T^{26} - \)\(50\!\cdots\!44\)\( T^{28} + \)\(51\!\cdots\!63\)\( T^{30} + \)\(21\!\cdots\!41\)\( T^{32} \))
$61$ (\( 1 + 8 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 8 T + 61 T^{2} \))(\( 1 - 10 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( ( 1 - 61 T^{2} )^{2} \))(\( 1 - 104 T^{2} + 3721 T^{4} \))(\( 1 - 104 T^{2} + 3721 T^{4} \))(\( ( 1 - 61 T^{2} )^{4} \))(\( 1 - 132 T^{2} + 12383 T^{4} - 851272 T^{6} + 46077143 T^{8} - 1827651012 T^{10} + 51520374361 T^{12} \))(\( 1 - 132 T^{2} + 12383 T^{4} - 851272 T^{6} + 46077143 T^{8} - 1827651012 T^{10} + 51520374361 T^{12} \))(\( ( 1 - 8 T + 61 T^{2} )^{2} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( ( 1 + 4 T + 61 T^{2} )^{2} \))(\( ( 1 + 4 T + 61 T^{2} )^{2} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( ( 1 - 8 T + 61 T^{2} )^{2} \))(\( ( 1 + 8 T + 61 T^{2} )^{4} \))(\( ( 1 + 8 T + 61 T^{2} )^{4} \))(\( ( 1 - 61 T^{2} )^{4} \))(\( ( 1 - 4 T^{2} - 5622 T^{4} - 14884 T^{6} + 13845841 T^{8} )^{2} \))(\( 1 + T - 55 T^{2} + 179 T^{3} + 3844 T^{4} + 10919 T^{5} - 204655 T^{6} + 226981 T^{7} + 13845841 T^{8} \))(\( 1 + 21 T + 245 T^{2} + 2559 T^{3} + 23404 T^{4} + 156099 T^{5} + 911645 T^{6} + 4766601 T^{7} + 13845841 T^{8} \))(\( 1 - 3 T - 27 T^{2} + 439 T^{3} + 780 T^{4} + 26779 T^{5} - 100467 T^{6} - 680943 T^{7} + 13845841 T^{8} \))(\( 1 - 14 T + 35 T^{2} + 794 T^{3} - 10511 T^{4} + 48434 T^{5} + 130235 T^{6} - 3177734 T^{7} + 13845841 T^{8} \))(\( 1 - 22 T + 323 T^{2} - 3614 T^{3} + 32305 T^{4} - 220454 T^{5} + 1201883 T^{6} - 4993582 T^{7} + 13845841 T^{8} \))(\( 1 - 3 T - 7 T^{2} - 441 T^{3} + 4900 T^{4} - 26901 T^{5} - 26047 T^{6} - 680943 T^{7} + 13845841 T^{8} \))(\( 1 + 18 T + 83 T^{2} + 66 T^{3} + 625 T^{4} + 4026 T^{5} + 308843 T^{6} + 4085658 T^{7} + 13845841 T^{8} \))(\( 1 - 11 T - 15 T^{2} + 431 T^{3} - 1036 T^{4} + 26291 T^{5} - 55815 T^{6} - 2496791 T^{7} + 13845841 T^{8} \))(\( 1 - 15 T + 29 T^{2} + 915 T^{3} - 10724 T^{4} + 55815 T^{5} + 107909 T^{6} - 3404715 T^{7} + 13845841 T^{8} \))(\( 1 + 21 T + 105 T^{2} - 1201 T^{3} - 18876 T^{4} - 73261 T^{5} + 390705 T^{6} + 4766601 T^{7} + 13845841 T^{8} \))(\( 1 - 9 T + 130 T^{2} - 1350 T^{3} + 15420 T^{4} - 101367 T^{5} + 1044383 T^{6} - 7034850 T^{7} + 62117900 T^{8} - 429125850 T^{9} + 3886149143 T^{10} - 23008383027 T^{11} + 213502868220 T^{12} - 1140205006350 T^{13} + 6697648666930 T^{14} - 28284685524189 T^{15} + 191707312997281 T^{16} \))(\( ( 1 + 15 T + 181 T^{2} + 1965 T^{3} + 15916 T^{4} + 119865 T^{5} + 673501 T^{6} + 3404715 T^{7} + 13845841 T^{8} )^{2} \))(\( ( 1 - 25 T + 361 T^{2} - 3995 T^{3} + 34756 T^{4} - 243695 T^{5} + 1343281 T^{6} - 5674525 T^{7} + 13845841 T^{8} )^{2} \))(\( 1 + 10 T + 234 T^{2} + 1560 T^{3} + 20515 T^{4} + 80630 T^{5} + 839156 T^{6} + 234480 T^{7} + 25957949 T^{8} + 14303280 T^{9} + 3122499476 T^{10} + 18301478030 T^{11} + 284047428115 T^{12} + 1317570229560 T^{13} + 12055767600474 T^{14} + 31427428360210 T^{15} + 191707312997281 T^{16} \))(\( 1 + 10 T + 234 T^{2} + 1560 T^{3} + 20515 T^{4} + 80630 T^{5} + 839156 T^{6} + 234480 T^{7} + 25957949 T^{8} + 14303280 T^{9} + 3122499476 T^{10} + 18301478030 T^{11} + 284047428115 T^{12} + 1317570229560 T^{13} + 12055767600474 T^{14} + 31427428360210 T^{15} + 191707312997281 T^{16} \))(\( ( 1 + 5 T + 61 T^{2} - 305 T^{3} + 796 T^{4} - 18605 T^{5} + 226981 T^{6} + 1134905 T^{7} + 13845841 T^{8} )^{2} \))(\( ( 1 - 20 T + 207 T^{2} - 2250 T^{3} + 26173 T^{4} - 248230 T^{5} + 2138069 T^{6} - 18794100 T^{7} + 155104700 T^{8} - 1146440100 T^{9} + 7955754749 T^{10} - 56343493630 T^{11} + 362387196493 T^{12} - 1900341677250 T^{13} + 10664717492727 T^{14} - 62854856720420 T^{15} + 191707312997281 T^{16} )^{2} \))
$67$ (\( 1 - 12 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( ( 1 - 13 T + 67 T^{2} )^{2} \))(\( ( 1 - 4 T + 67 T^{2} )^{2} \))(\( ( 1 - 4 T + 67 T^{2} )^{2} \))(\( ( 1 + 13 T + 102 T^{2} + 871 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 - 11 T + 169 T^{2} - 1490 T^{3} + 11323 T^{4} - 49379 T^{5} + 300763 T^{6} )^{2} \))(\( ( 1 - 11 T + 169 T^{2} - 1490 T^{3} + 11323 T^{4} - 49379 T^{5} + 300763 T^{6} )^{2} \))(\( ( 1 - 11 T + 67 T^{2} )( 1 + 11 T + 67 T^{2} ) \))(\( ( 1 - 14 T + 67 T^{2} )( 1 + 14 T + 67 T^{2} ) \))(\( 1 - 26 T^{2} + 4489 T^{4} \))(\( 1 - 26 T^{2} + 4489 T^{4} \))(\( ( 1 - 14 T + 67 T^{2} )( 1 + 14 T + 67 T^{2} ) \))(\( ( 1 - 11 T + 67 T^{2} )( 1 + 11 T + 67 T^{2} ) \))(\( 1 - 181 T^{2} + 15312 T^{4} - 812509 T^{6} + 20151121 T^{8} \))(\( 1 - 181 T^{2} + 15312 T^{4} - 812509 T^{6} + 20151121 T^{8} \))(\( ( 1 + 10 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 - 26 T^{2} + 4489 T^{4} )^{4} \))(\( ( 1 - 7 T + 135 T^{2} - 469 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 - 3 T + 125 T^{2} - 201 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 - 17 T + 175 T^{2} - 1139 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 + 4 T + 67 T^{2} )^{4} \))(\( ( 1 + 8 T + 67 T^{2} )^{4} \))(\( ( 1 + T + 33 T^{2} + 67 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 - 8 T + 70 T^{2} - 536 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 + 11 T + 63 T^{2} + 737 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 - 11 T + 163 T^{2} - 737 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 - T + 103 T^{2} - 67 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 + 19 T + 229 T^{2} + 1563 T^{3} + 12284 T^{4} + 104721 T^{5} + 1027981 T^{6} + 5714497 T^{7} + 20151121 T^{8} )^{2} \))(\( ( 1 - 5 T^{2} - 3267 T^{4} - 22445 T^{6} + 20151121 T^{8} )^{2} \))(\( ( 1 - 45 T^{2} + 8933 T^{4} - 202005 T^{6} + 20151121 T^{8} )^{2} \))(\( ( 1 - T + 119 T^{2} + 83 T^{3} + 10044 T^{4} + 5561 T^{5} + 534191 T^{6} - 300763 T^{7} + 20151121 T^{8} )^{2} \))(\( ( 1 - T + 119 T^{2} + 83 T^{3} + 10044 T^{4} + 5561 T^{5} + 534191 T^{6} - 300763 T^{7} + 20151121 T^{8} )^{2} \))(\( ( 1 - T + 73 T^{2} - 67 T^{3} + 4489 T^{4} )^{4} \))(\( ( 1 + 11 T + 233 T^{2} + 1859 T^{3} + 23268 T^{4} + 124553 T^{5} + 1045937 T^{6} + 3308393 T^{7} + 20151121 T^{8} )^{4} \))
$71$ (\( 1 + 2 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 - 10 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( ( 1 - 3 T + 71 T^{2} )( 1 + 3 T + 71 T^{2} ) \))(\( 1 - 92 T^{2} + 5041 T^{4} \))(\( 1 - 92 T^{2} + 5041 T^{4} \))(\( ( 1 - 3 T - 62 T^{2} - 213 T^{3} + 5041 T^{4} )( 1 + 3 T - 62 T^{2} + 213 T^{3} + 5041 T^{4} ) \))(\( 1 - 281 T^{2} + 38333 T^{4} - 3308394 T^{6} + 193236653 T^{8} - 7140682361 T^{10} + 128100283921 T^{12} \))(\( 1 - 281 T^{2} + 38333 T^{4} - 3308394 T^{6} + 193236653 T^{8} - 7140682361 T^{10} + 128100283921 T^{12} \))(\( ( 1 - 15 T + 71 T^{2} )^{2} \))(\( ( 1 - 10 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 10 T + 71 T^{2} )^{2} \))(\( ( 1 + 15 T + 71 T^{2} )^{2} \))(\( ( 1 + 13 T + 176 T^{2} + 923 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 13 T + 176 T^{2} - 923 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 71 T^{2} )^{4} \))(\( ( 1 - 116 T^{2} + 12474 T^{4} - 584756 T^{6} + 25411681 T^{8} )^{2} \))(\( 1 + 5 T - 61 T^{2} - 355 T^{3} + 2936 T^{4} - 25205 T^{5} - 307501 T^{6} + 1789555 T^{7} + 25411681 T^{8} \))(\( 1 + 15 T + 119 T^{2} + 1455 T^{3} + 17296 T^{4} + 103305 T^{5} + 599879 T^{6} + 5368665 T^{7} + 25411681 T^{8} \))(\( 1 + 13 T - 7 T^{2} - 819 T^{3} - 6100 T^{4} - 58149 T^{5} - 35287 T^{6} + 4652843 T^{7} + 25411681 T^{8} \))(\( 1 + 2 T + 53 T^{2} + 344 T^{3} + 6125 T^{4} + 24424 T^{5} + 267173 T^{6} + 715822 T^{7} + 25411681 T^{8} \))(\( 1 + 18 T + 173 T^{2} + 1956 T^{3} + 21325 T^{4} + 138876 T^{5} + 872093 T^{6} + 6442398 T^{7} + 25411681 T^{8} \))(\( 1 - 27 T + 253 T^{2} - 819 T^{3} + 100 T^{4} - 58149 T^{5} + 1275373 T^{6} - 9663597 T^{7} + 25411681 T^{8} \))(\( 1 - 6 T - 35 T^{2} + 636 T^{3} - 1331 T^{4} + 45156 T^{5} - 176435 T^{6} - 2147466 T^{7} + 25411681 T^{8} \))(\( 1 - 25 T + 239 T^{2} - 1545 T^{3} + 11936 T^{4} - 109695 T^{5} + 1204799 T^{6} - 8947775 T^{7} + 25411681 T^{8} \))(\( 1 + 27 T + 253 T^{2} + 819 T^{3} + 100 T^{4} + 58149 T^{5} + 1275373 T^{6} + 9663597 T^{7} + 25411681 T^{8} \))(\( 1 + 15 T + 19 T^{2} - 1065 T^{3} - 12104 T^{4} - 75615 T^{5} + 95779 T^{6} + 5368665 T^{7} + 25411681 T^{8} \))(\( 1 - 41 T + 620 T^{2} - 3160 T^{3} - 14740 T^{4} + 144797 T^{5} + 1569213 T^{6} - 27991580 T^{7} + 245368020 T^{8} - 1987402180 T^{9} + 7910402733 T^{10} + 51824439067 T^{11} - 374568177940 T^{12} - 5701364749160 T^{13} + 79422176031020 T^{14} - 372899926494031 T^{15} + 645753531245761 T^{16} \))(\( 1 - 153 T^{2} + 6543 T^{4} - 275731 T^{6} + 31891080 T^{8} - 1389959971 T^{10} + 166268628783 T^{12} - 19599343439913 T^{14} + 645753531245761 T^{16} \))(\( 1 + 147 T^{2} + 13143 T^{4} + 847169 T^{6} + 61167480 T^{8} + 4270578929 T^{10} + 333985723383 T^{12} + 18830741736387 T^{14} + 645753531245761 T^{16} \))(\( ( 1 + 20 T + 191 T^{2} + 830 T^{3} + 3701 T^{4} + 58930 T^{5} + 962831 T^{6} + 7158220 T^{7} + 25411681 T^{8} )^{2} \))(\( ( 1 - 20 T + 191 T^{2} - 830 T^{3} + 3701 T^{4} - 58930 T^{5} + 962831 T^{6} - 7158220 T^{7} + 25411681 T^{8} )^{2} \))(\( 1 - 13 T^{2} + 5103 T^{4} - 100031 T^{6} + 31068680 T^{8} - 504256271 T^{10} + 129675808143 T^{12} - 1665303690973 T^{14} + 645753531245761 T^{16} \))(\( 1 - 132 T^{2} + 18261 T^{4} - 1280668 T^{6} + 92311071 T^{8} - 6877184836 T^{10} + 595366834039 T^{12} - 64597379926044 T^{14} + 4540669173180712 T^{16} - 325635392207187804 T^{18} + 15129272064579009559 T^{20} - \)\(88\!\cdots\!56\)\( T^{22} + \)\(59\!\cdots\!31\)\( T^{24} - \)\(41\!\cdots\!68\)\( T^{26} + \)\(29\!\cdots\!01\)\( T^{28} - \)\(10\!\cdots\!92\)\( T^{30} + \)\(41\!\cdots\!21\)\( T^{32} \))
$73$ (\( 1 + 6 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 - 6 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( ( 1 - 73 T^{2} )^{2} \))(\( ( 1 - 73 T^{2} )^{2} \))(\( ( 1 - 73 T^{2} )^{2} \))(\( ( 1 - 73 T^{2} )^{4} \))(\( 1 - 198 T^{2} + 21119 T^{4} - 1620052 T^{6} + 112543151 T^{8} - 5622851718 T^{10} + 151334226289 T^{12} \))(\( 1 - 198 T^{2} + 21119 T^{4} - 1620052 T^{6} + 112543151 T^{8} - 5622851718 T^{10} + 151334226289 T^{12} \))(\( ( 1 + 8 T + 73 T^{2} )^{2} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 2 T + 73 T^{2} )^{2} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 8 T + 73 T^{2} )^{2} \))(\( ( 1 - 10 T + 138 T^{2} - 730 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 10 T + 138 T^{2} - 730 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 106 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 164 T^{2} + 15654 T^{4} - 873956 T^{6} + 28398241 T^{8} )^{2} \))(\( 1 + 6 T - 57 T^{2} - 130 T^{3} + 4761 T^{4} - 9490 T^{5} - 303753 T^{6} + 2334102 T^{7} + 28398241 T^{8} \))(\( 1 - 14 T + 63 T^{2} - 850 T^{3} + 12521 T^{4} - 62050 T^{5} + 335727 T^{6} - 5446238 T^{7} + 28398241 T^{8} \))(\( 1 + 6 T + 63 T^{2} + 250 T^{3} + 681 T^{4} + 18250 T^{5} + 335727 T^{6} + 2334102 T^{7} + 28398241 T^{8} \))(\( 1 - 21 T + 123 T^{2} - 175 T^{3} + 576 T^{4} - 12775 T^{5} + 655467 T^{6} - 8169357 T^{7} + 28398241 T^{8} \))(\( 1 - 13 T + 171 T^{2} - 2039 T^{3} + 15584 T^{4} - 148847 T^{5} + 911259 T^{6} - 5057221 T^{7} + 28398241 T^{8} \))(\( 1 - 6 T - 57 T^{2} + 130 T^{3} + 4761 T^{4} + 9490 T^{5} - 303753 T^{6} - 2334102 T^{7} + 28398241 T^{8} \))(\( 1 + 27 T + 251 T^{2} + 801 T^{3} + 64 T^{4} + 58473 T^{5} + 1337579 T^{6} + 10503459 T^{7} + 28398241 T^{8} \))(\( 1 - 18 T + 71 T^{2} + 6 T^{3} + 1369 T^{4} + 438 T^{5} + 378359 T^{6} - 7002306 T^{7} + 28398241 T^{8} \))(\( 1 + 6 T + 143 T^{2} + 450 T^{3} + 11881 T^{4} + 32850 T^{5} + 762047 T^{6} + 2334102 T^{7} + 28398241 T^{8} \))(\( 1 + 14 T + 23 T^{2} - 1010 T^{3} - 12839 T^{4} - 73730 T^{5} + 122567 T^{6} + 5446238 T^{7} + 28398241 T^{8} \))(\( 1 + 25 T + 124 T^{2} - 2070 T^{3} - 23478 T^{4} + 77275 T^{5} + 1965307 T^{6} - 3453050 T^{7} - 174879020 T^{8} - 252072650 T^{9} + 10473121003 T^{10} + 30061288675 T^{11} - 666733902198 T^{12} - 4291258197510 T^{13} + 18765444059836 T^{14} + 276184962977425 T^{15} + 806460091894081 T^{16} \))(\( ( 1 + 73 T^{2} + 1140 T^{3} + 769 T^{4} + 83220 T^{5} + 389017 T^{6} + 28398241 T^{8} )^{2} \))(\( ( 1 + 40 T + 713 T^{2} + 8040 T^{3} + 72529 T^{4} + 586920 T^{5} + 3799577 T^{6} + 15560680 T^{7} + 28398241 T^{8} )^{2} \))(\( 1 - 5 T + 96 T^{2} - 220 T^{3} + 10752 T^{4} - 34675 T^{5} + 1158063 T^{6} - 2376560 T^{7} + 65290040 T^{8} - 173488880 T^{9} + 6171317727 T^{10} - 13489164475 T^{11} + 305337887232 T^{12} - 456075750460 T^{13} + 14528085723744 T^{14} - 55236992595485 T^{15} + 806460091894081 T^{16} \))(\( 1 - 5 T + 96 T^{2} - 220 T^{3} + 10752 T^{4} - 34675 T^{5} + 1158063 T^{6} - 2376560 T^{7} + 65290040 T^{8} - 173488880 T^{9} + 6171317727 T^{10} - 13489164475 T^{11} + 305337887232 T^{12} - 456075750460 T^{13} + 14528085723744 T^{14} - 55236992595485 T^{15} + 806460091894081 T^{16} \))(\( ( 1 + 73 T^{2} - 360 T^{3} + 2449 T^{4} - 26280 T^{5} + 389017 T^{6} + 28398241 T^{8} )^{2} \))(\( ( 1 - 5 T + 96 T^{2} - 940 T^{3} + 3792 T^{4} - 50995 T^{5} + 180783 T^{6} + 1245280 T^{7} + 3839000 T^{8} + 90905440 T^{9} + 963392607 T^{10} - 19837921915 T^{11} + 107686129872 T^{12} - 1948687297420 T^{13} + 14528085723744 T^{14} - 55236992595485 T^{15} + 806460091894081 T^{16} )^{2} \))
$79$ (\( 1 + 10 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 14 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))(\( 1 + 2 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( 1 + 2 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))(\( ( 1 - 79 T^{2} )^{2} \))(\( 1 - 140 T^{2} + 6241 T^{4} \))(\( 1 - 140 T^{2} + 6241 T^{4} \))(\( ( 1 - 79 T^{2} )^{4} \))(\( 1 - 308 T^{2} + 43359 T^{4} - 3991832 T^{6} + 270603519 T^{8} - 11996624948 T^{10} + 243087455521 T^{12} \))(\( 1 - 308 T^{2} + 43359 T^{4} - 3991832 T^{6} + 270603519 T^{8} - 11996624948 T^{10} + 243087455521 T^{12} \))(\( 1 - 146 T^{2} + 6241 T^{4} \))(\( 1 + 4 T^{2} + 6241 T^{4} \))(\( ( 1 - 79 T^{2} )^{2} \))(\( ( 1 - 79 T^{2} )^{2} \))(\( 1 + 4 T^{2} + 6241 T^{4} \))(\( 1 - 146 T^{2} + 6241 T^{4} \))(\( 1 - 64 T^{2} + 2814 T^{4} - 399424 T^{6} + 38950081 T^{8} \))(\( 1 - 64 T^{2} + 2814 T^{4} - 399424 T^{6} + 38950081 T^{8} \))(\( ( 1 - 92 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 + 284 T^{2} + 32538 T^{4} + 1772444 T^{6} + 38950081 T^{8} )^{2} \))(\( 1 - 7 T + 80 T^{2} - 467 T^{3} + 1309 T^{4} - 36893 T^{5} + 499280 T^{6} - 3451273 T^{7} + 38950081 T^{8} \))(\( 1 - 11 T + 42 T^{2} + 407 T^{3} - 7795 T^{4} + 32153 T^{5} + 262122 T^{6} - 5423429 T^{7} + 38950081 T^{8} \))(\( 1 - T - 48 T^{2} - 533 T^{3} + 6125 T^{4} - 42107 T^{5} - 299568 T^{6} - 493039 T^{7} + 38950081 T^{8} \))(\( 1 - 16 T + 107 T^{2} - 1358 T^{3} + 18175 T^{4} - 107282 T^{5} + 667787 T^{6} - 7888624 T^{7} + 38950081 T^{8} \))(\( 1 + 4 T - 73 T^{2} - 238 T^{3} + 5215 T^{4} - 18802 T^{5} - 455593 T^{6} + 1972156 T^{7} + 38950081 T^{8} \))(\( 1 + 5 T + 6 T^{2} + 715 T^{3} + 9821 T^{4} + 56485 T^{5} + 37446 T^{6} + 2465195 T^{7} + 38950081 T^{8} \))(\( 1 - 4 T - 33 T^{2} - 542 T^{3} + 8375 T^{4} - 42818 T^{5} - 205953 T^{6} - 1972156 T^{7} + 38950081 T^{8} \))(\( 1 - 17 T + 80 T^{2} + 923 T^{3} - 17651 T^{4} + 72917 T^{5} + 499280 T^{6} - 8381663 T^{7} + 38950081 T^{8} \))(\( 1 + 17 T + 60 T^{2} + 217 T^{3} + 5789 T^{4} + 17143 T^{5} + 374460 T^{6} + 8381663 T^{7} + 38950081 T^{8} \))(\( 1 + 35 T + 656 T^{2} + 8575 T^{3} + 85621 T^{4} + 677425 T^{5} + 4094096 T^{6} + 17256365 T^{7} + 38950081 T^{8} \))(\( 1 + 11 T - 61 T^{2} - 814 T^{3} + 9506 T^{4} + 28633 T^{5} - 1559934 T^{6} - 2600252 T^{7} + 110325177 T^{8} - 205419908 T^{9} - 9735548094 T^{10} + 14117185687 T^{11} + 370259469986 T^{12} - 2504723908786 T^{13} - 14828334786781 T^{14} + 211242998847749 T^{15} + 1517108809906561 T^{16} \))(\( 1 - 163 T^{2} + 17228 T^{4} - 1434881 T^{6} + 128736055 T^{8} - 8955092321 T^{10} + 671031995468 T^{12} - 39623255249923 T^{14} + 1517108809906561 T^{16} \))(\( 1 - 323 T^{2} + 51588 T^{4} - 5495881 T^{6} + 468376055 T^{8} - 34299793321 T^{10} + 2009356778628 T^{12} - 78517248133283 T^{14} + 1517108809906561 T^{16} \))(\( 1 + 10 T + 110 T^{2} - 580 T^{3} - 1331 T^{4} - 50110 T^{5} + 938610 T^{6} + 2546560 T^{7} + 94198811 T^{8} + 201178240 T^{9} + 5857865010 T^{10} - 24706184290 T^{11} - 51842557811 T^{12} - 1784692711420 T^{13} + 26739620107310 T^{14} + 192039089861590 T^{15} + 1517108809906561 T^{16} \))(\( 1 + 10 T + 110 T^{2} - 580 T^{3} - 1331 T^{4} - 50110 T^{5} + 938610 T^{6} + 2546560 T^{7} + 94198811 T^{8} + 201178240 T^{9} + 5857865010 T^{10} - 24706184290 T^{11} - 51842557811 T^{12} - 1784692711420 T^{13} + 26739620107310 T^{14} + 192039089861590 T^{15} + 1517108809906561 T^{16} \))(\( ( 1 + 25 T + 304 T^{2} + 2435 T^{3} + 19501 T^{4} + 192365 T^{5} + 1897264 T^{6} + 12325975 T^{7} + 38950081 T^{8} )^{2} \))(\( ( 1 + 10 T + 188 T^{2} + 2645 T^{3} + 19153 T^{4} + 238850 T^{5} + 1759431 T^{6} + 11107015 T^{7} + 148176230 T^{8} + 877454185 T^{9} + 10980608871 T^{10} + 117762365150 T^{11} + 746010901393 T^{12} + 8138814175355 T^{13} + 45700441637948 T^{14} + 192039089861590 T^{15} + 1517108809906561 T^{16} )^{2} \))
$83$ (\( 1 + 4 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( ( 1 + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 83 T^{2} )^{4} \))(\( ( 1 + 8 T + 105 T^{2} + 1200 T^{3} + 8715 T^{4} + 55112 T^{5} + 571787 T^{6} )^{2} \))(\( ( 1 - 8 T + 105 T^{2} - 1200 T^{3} + 8715 T^{4} - 55112 T^{5} + 571787 T^{6} )^{2} \))(\( ( 1 + 6 T + 83 T^{2} )^{2} \))(\( ( 1 + 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 4 T + 83 T^{2} )^{2} \))(\( ( 1 - 6 T + 83 T^{2} )^{2} \))(\( ( 1 - 10 T + 158 T^{2} - 830 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 + 10 T + 158 T^{2} + 830 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 + 6 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 + 204 T^{2} + 22454 T^{4} + 1405356 T^{6} + 47458321 T^{8} )^{2} \))(\( 1 - T + 98 T^{2} - 295 T^{3} + 6881 T^{4} - 24485 T^{5} + 675122 T^{6} - 571787 T^{7} + 47458321 T^{8} \))(\( 1 + 13 T - 14 T^{2} - 421 T^{3} + 1449 T^{4} - 34943 T^{5} - 96446 T^{6} + 7433231 T^{7} + 47458321 T^{8} \))(\( 1 - 23 T + 296 T^{2} - 3599 T^{3} + 39209 T^{4} - 298717 T^{5} + 2039144 T^{6} - 13151101 T^{7} + 47458321 T^{8} \))(\( 1 + 26 T + 173 T^{2} - 1510 T^{3} - 30589 T^{4} - 125330 T^{5} + 1191797 T^{6} + 14866462 T^{7} + 47458321 T^{8} \))(\( 1 + 2 T - 79 T^{2} + 86 T^{3} + 7139 T^{4} + 7138 T^{5} - 544231 T^{6} + 1143574 T^{7} + 47458321 T^{8} \))(\( 1 + 21 T + 88 T^{2} - 915 T^{3} - 13199 T^{4} - 75945 T^{5} + 606232 T^{6} + 12007527 T^{7} + 47458321 T^{8} \))(\( 1 + 2 T - 79 T^{2} + 86 T^{3} + 7139 T^{4} + 7138 T^{5} - 544231 T^{6} + 1143574 T^{7} + 47458321 T^{8} \))(\( 1 + 13 T + 206 T^{2} + 1999 T^{3} + 25529 T^{4} + 165917 T^{5} + 1419134 T^{6} + 7433231 T^{7} + 47458321 T^{8} \))(\( 1 - T - 52 T^{2} - 565 T^{3} + 6761 T^{4} - 46895 T^{5} - 358228 T^{6} - 571787 T^{7} + 47458321 T^{8} \))(\( 1 + 9 T - 22 T^{2} + 375 T^{3} + 10321 T^{4} + 31125 T^{5} - 151558 T^{6} + 5146083 T^{7} + 47458321 T^{8} \))(\( 1 + 23 T + 107 T^{2} - 116 T^{3} + 16156 T^{4} + 243703 T^{5} + 1341600 T^{6} + 12361042 T^{7} + 156273429 T^{8} + 1025966486 T^{9} + 9242282400 T^{10} + 139346207261 T^{11} + 766736634076 T^{12} - 456928714588 T^{13} + 34982619950483 T^{14} + 624129172761421 T^{15} + 2252292232139041 T^{16} \))(\( 1 + 89 T^{2} + 812 T^{4} + 548587 T^{6} + 90759175 T^{8} + 3779215843 T^{10} + 38536156652 T^{12} + 29097693229841 T^{14} + 2252292232139041 T^{16} \))(\( 1 - 91 T^{2} + 3372 T^{4} + 261487 T^{6} - 45659425 T^{8} + 1801383943 T^{10} + 160029458412 T^{12} - 29751573976579 T^{14} + 2252292232139041 T^{16} \))(\( 1 - 21 T + 86 T^{2} + 846 T^{3} - 3342 T^{4} - 29181 T^{5} - 520301 T^{6} + 8399448 T^{7} - 56629312 T^{8} + 697154184 T^{9} - 3584353589 T^{10} - 16685316447 T^{11} - 158605708782 T^{12} + 3332428383978 T^{13} + 28116872109734 T^{14} - 569857070782167 T^{15} + 2252292232139041 T^{16} \))(\( 1 + 21 T + 86 T^{2} - 846 T^{3} - 3342 T^{4} + 29181 T^{5} - 520301 T^{6} - 8399448 T^{7} - 56629312 T^{8} - 697154184 T^{9} - 3584353589 T^{10} + 16685316447 T^{11} - 158605708782 T^{12} - 3332428383978 T^{13} + 28116872109734 T^{14} + 569857070782167 T^{15} + 2252292232139041 T^{16} \))(\( 1 + 149 T^{2} + 16452 T^{4} + 1844407 T^{6} + 200466815 T^{8} + 12706119823 T^{10} + 780784297092 T^{12} + 48714115631981 T^{14} + 2252292232139041 T^{16} \))(\( 1 - 62 T^{2} + 25000 T^{4} - 2719015 T^{6} + 347393225 T^{8} - 42007700966 T^{10} + 4066308503087 T^{12} - 369641749946425 T^{14} + 34933927750382710 T^{16} - 2546462015380921825 T^{18} + \)\(19\!\cdots\!27\)\( T^{20} - \)\(13\!\cdots\!54\)\( T^{22} + \)\(78\!\cdots\!25\)\( T^{24} - \)\(42\!\cdots\!35\)\( T^{26} + \)\(26\!\cdots\!00\)\( T^{28} - \)\(45\!\cdots\!98\)\( T^{30} + \)\(50\!\cdots\!81\)\( T^{32} \))
$89$ (\( 1 - 10 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( ( 1 - 9 T + 89 T^{2} )( 1 + 9 T + 89 T^{2} ) \))(\( ( 1 - 18 T + 89 T^{2} )( 1 + 18 T + 89 T^{2} ) \))(\( ( 1 - 18 T + 89 T^{2} )( 1 + 18 T + 89 T^{2} ) \))(\( ( 1 - 9 T - 8 T^{2} - 801 T^{3} + 7921 T^{4} )( 1 + 9 T - 8 T^{2} + 801 T^{3} + 7921 T^{4} ) \))(\( 1 - 147 T^{2} + 25107 T^{4} - 2057218 T^{6} + 198872547 T^{8} - 9223109427 T^{10} + 496981290961 T^{12} \))(\( 1 - 147 T^{2} + 25107 T^{4} - 2057218 T^{6} + 198872547 T^{8} - 9223109427 T^{10} + 496981290961 T^{12} \))(\( 1 - 175 T^{2} + 7921 T^{4} \))(\( 1 - 50 T^{2} + 7921 T^{4} \))(\( 1 - 130 T^{2} + 7921 T^{4} \))(\( 1 - 130 T^{2} + 7921 T^{4} \))(\( 1 - 50 T^{2} + 7921 T^{4} \))(\( 1 - 175 T^{2} + 7921 T^{4} \))(\( 1 - 337 T^{2} + 44160 T^{4} - 2669377 T^{6} + 62742241 T^{8} \))(\( 1 - 337 T^{2} + 44160 T^{4} - 2669377 T^{6} + 62742241 T^{8} \))(\( ( 1 - 6 T + 89 T^{2} )^{4} \))(\( ( 1 + 70 T^{2} + 7921 T^{4} )^{4} \))(\( ( 1 - T + 89 T^{2} )^{4} \))(\( ( 1 + 12 T + 209 T^{2} + 1068 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 20 T + 273 T^{2} + 1780 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 10 T + 158 T^{2} + 890 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 - 18 T + 254 T^{2} - 1602 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 - 10 T + 183 T^{2} - 890 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 - 18 T + 254 T^{2} - 1602 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 2 T + 159 T^{2} + 178 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 - 12 T + 89 T^{2} - 1068 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 15 T + 89 T^{2} )^{4} \))(\( ( 1 - 6 T + 147 T^{2} - 548 T^{3} + 11480 T^{4} - 48772 T^{5} + 1164387 T^{6} - 4229814 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 + 8 T + 189 T^{2} + 712 T^{3} + 7921 T^{4} )^{4} \))(\( ( 1 + 18 T + 239 T^{2} + 1602 T^{3} + 7921 T^{4} )^{4} \))(\( 1 - 199 T^{2} + 19855 T^{4} - 1662361 T^{6} + 149152624 T^{8} - 13167561481 T^{10} + 1245747195055 T^{12} - 98899276901239 T^{14} + 3936588805702081 T^{16} \))(\( 1 - 199 T^{2} + 19855 T^{4} - 1662361 T^{6} + 149152624 T^{8} - 13167561481 T^{10} + 1245747195055 T^{12} - 98899276901239 T^{14} + 3936588805702081 T^{16} \))(\( ( 1 - 266 T^{2} + 31531 T^{4} - 2106986 T^{6} + 62742241 T^{8} )^{2} \))(\( ( 1 - 154 T^{2} + 29845 T^{4} - 2842666 T^{6} + 328069564 T^{8} - 22516757386 T^{10} + 1872542182645 T^{12} - 76535118807994 T^{14} + 3936588805702081 T^{16} )^{2} \))
$97$ (\( 1 + 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( ( 1 - 17 T + 97 T^{2} )^{2} \))(\( ( 1 - 8 T + 97 T^{2} )^{2} \))(\( ( 1 - 8 T + 97 T^{2} )^{2} \))(\( ( 1 + 17 T + 192 T^{2} + 1649 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 + 13 T + 213 T^{2} + 2554 T^{3} + 20661 T^{4} + 122317 T^{5} + 912673 T^{6} )^{2} \))(\( ( 1 + 13 T + 213 T^{2} + 2554 T^{3} + 20661 T^{4} + 122317 T^{5} + 912673 T^{6} )^{2} \))(\( ( 1 + 17 T + 97 T^{2} )^{2} \))(\( ( 1 - 8 T + 97 T^{2} )^{2} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( ( 1 - 8 T + 97 T^{2} )^{2} \))(\( ( 1 + 17 T + 97 T^{2} )^{2} \))(\( ( 1 - 13 T + 228 T^{2} - 1261 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 - 13 T + 228 T^{2} - 1261 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 - 8 T + 97 T^{2} )^{4} \))(\( ( 1 - 4 T + 186 T^{2} - 388 T^{3} + 9409 T^{4} )^{4} \))(\( 1 + 13 T - 3 T^{2} + 275 T^{3} + 12116 T^{4} + 26675 T^{5} - 28227 T^{6} + 11864749 T^{7} + 88529281 T^{8} \))(\( 1 - 3 T - 43 T^{2} - 765 T^{3} + 11236 T^{4} - 74205 T^{5} - 404587 T^{6} - 2738019 T^{7} + 88529281 T^{8} \))(\( 1 + T + 129 T^{2} - 193 T^{3} + 12044 T^{4} - 18721 T^{5} + 1213761 T^{6} + 912673 T^{7} + 88529281 T^{8} \))(\( 1 - 14 T + 99 T^{2} - 1708 T^{3} + 26069 T^{4} - 165676 T^{5} + 931491 T^{6} - 12777422 T^{7} + 88529281 T^{8} \))(\( 1 - 38 T + 747 T^{2} - 10300 T^{3} + 111941 T^{4} - 999100 T^{5} + 7028523 T^{6} - 34681574 T^{7} + 88529281 T^{8} \))(\( 1 + 33 T + 537 T^{2} + 6655 T^{3} + 71196 T^{4} + 645535 T^{5} + 5052633 T^{6} + 30118209 T^{7} + 88529281 T^{8} \))(\( 1 - 6 T - 21 T^{2} + 868 T^{3} - 2331 T^{4} + 84196 T^{5} - 197589 T^{6} - 5476038 T^{7} + 88529281 T^{8} \))(\( 1 - 11 T - 51 T^{2} + 683 T^{3} + 1844 T^{4} + 66251 T^{5} - 479859 T^{6} - 10039403 T^{7} + 88529281 T^{8} \))(\( 1 + 33 T + 537 T^{2} + 6655 T^{3} + 71196 T^{4} + 645535 T^{5} + 5052633 T^{6} + 30118209 T^{7} + 88529281 T^{8} \))(\( 1 + 13 T - 3 T^{2} + 275 T^{3} + 12116 T^{4} + 26675 T^{5} - 28227 T^{6} + 11864749 T^{7} + 88529281 T^{8} \))(\( 1 - 21 T + 118 T^{2} - 1032 T^{3} + 27526 T^{4} - 287671 T^{5} + 2296315 T^{6} - 24390956 T^{7} + 246806624 T^{8} - 2365922732 T^{9} + 21606027835 T^{10} - 262549554583 T^{11} + 2436856988806 T^{12} - 8862135145224 T^{13} + 98290696581622 T^{14} - 1696763974040373 T^{15} + 7837433594376961 T^{16} \))(\( ( 1 - 7 T - 73 T^{2} + 835 T^{3} + 1816 T^{4} + 80995 T^{5} - 686857 T^{6} - 6388711 T^{7} + 88529281 T^{8} )^{2} \))(\( ( 1 + 13 T + 147 T^{2} + 1295 T^{3} + 4256 T^{4} + 125615 T^{5} + 1383123 T^{6} + 11864749 T^{7} + 88529281 T^{8} )^{2} \))(\( 1 - 9 T + 88 T^{2} - 1068 T^{3} + 25336 T^{4} - 153839 T^{5} + 668695 T^{6} - 11831104 T^{7} + 232073144 T^{8} - 1147617088 T^{9} + 6291751255 T^{10} - 140404701647 T^{11} + 2242977863416 T^{12} - 9171279394476 T^{13} + 73301536433752 T^{14} - 727184560303017 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 9 T + 88 T^{2} - 1068 T^{3} + 25336 T^{4} - 153839 T^{5} + 668695 T^{6} - 11831104 T^{7} + 232073144 T^{8} - 1147617088 T^{9} + 6291751255 T^{10} - 140404701647 T^{11} + 2242977863416 T^{12} - 9171279394476 T^{13} + 73301536433752 T^{14} - 727184560303017 T^{15} + 7837433594376961 T^{16} \))(\( ( 1 - 3 T - 63 T^{2} + 835 T^{3} + 4236 T^{4} + 80995 T^{5} - 592767 T^{6} - 2738019 T^{7} + 88529281 T^{8} )^{2} \))(\( ( 1 + 18 T - 23 T^{2} - 2214 T^{3} - 5987 T^{4} + 15994 T^{5} - 1338701 T^{6} + 2590298 T^{7} + 243789068 T^{8} + 251258906 T^{9} - 12595837709 T^{10} + 14597291962 T^{11} - 530024805347 T^{12} - 19012371328998 T^{13} - 19158356113367 T^{14} + 1454369120606034 T^{15} + 7837433594376961 T^{16} )^{2} \))
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