Properties

Label 105.2
Level 105
Weight 2
Dimension 227
Nonzero newspaces 12
Newform subspaces 25
Sturm bound 1536
Trace bound 4

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Defining parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 25 \)
Sturm bound: \(1536\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(105))\).

Total New Old
Modular forms 480 283 197
Cusp forms 289 227 62
Eisenstein series 191 56 135

Trace form

\( 227q + 5q^{2} - 5q^{3} - 19q^{4} - 7q^{5} - 35q^{6} - 21q^{7} - 27q^{8} - 21q^{9} + O(q^{10}) \) \( 227q + 5q^{2} - 5q^{3} - 19q^{4} - 7q^{5} - 35q^{6} - 21q^{7} - 27q^{8} - 21q^{9} - 43q^{10} - 16q^{11} - 27q^{12} - 34q^{13} - 27q^{14} - 21q^{15} - 75q^{16} - 10q^{17} - 7q^{18} - 40q^{19} - 27q^{20} - 25q^{21} - 68q^{22} - 24q^{23} + 21q^{24} - 37q^{25} + 2q^{26} + 19q^{27} - 11q^{28} + 10q^{29} + 37q^{30} - 44q^{31} + 85q^{32} + 16q^{33} + 34q^{34} + 37q^{35} + 61q^{36} + 26q^{37} + 56q^{38} + 30q^{39} + 45q^{40} + 22q^{41} + 57q^{42} - 44q^{43} + 4q^{44} + 17q^{45} - 72q^{46} - 52q^{47} + 45q^{48} - 57q^{49} - 55q^{50} - 26q^{51} - 18q^{52} - 22q^{53} - 11q^{54} - 28q^{55} - 3q^{56} - 36q^{57} + 86q^{58} - 4q^{59} + 65q^{60} + 38q^{61} + 48q^{62} - 25q^{63} + 85q^{64} + 72q^{65} + 92q^{66} + 80q^{67} + 130q^{68} + 72q^{69} + 249q^{70} + 64q^{71} + 57q^{72} + 134q^{73} + 154q^{74} + 91q^{75} + 108q^{76} + 84q^{77} + 70q^{78} + 92q^{79} + 69q^{80} - 9q^{81} + 74q^{82} - 12q^{83} - 31q^{84} - 58q^{85} - 16q^{86} - 46q^{87} - 12q^{88} - 18q^{89} - 115q^{90} - 158q^{91} - 168q^{92} - 80q^{93} - 176q^{94} - 102q^{95} - 271q^{96} - 138q^{97} - 167q^{98} - 124q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)

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
105.2.a \(\chi_{105}(1, \cdot)\) 105.2.a.a 1 1
105.2.a.b 2
105.2.b \(\chi_{105}(41, \cdot)\) 105.2.b.a 2 1
105.2.b.b 2
105.2.b.c 4
105.2.b.d 4
105.2.d \(\chi_{105}(64, \cdot)\) 105.2.d.a 2 1
105.2.d.b 6
105.2.g \(\chi_{105}(104, \cdot)\) 105.2.g.a 4 1
105.2.g.b 4
105.2.g.c 4
105.2.i \(\chi_{105}(16, \cdot)\) 105.2.i.a 2 2
105.2.i.b 2
105.2.i.c 4
105.2.i.d 4
105.2.j \(\chi_{105}(8, \cdot)\) 105.2.j.a 24 2
105.2.m \(\chi_{105}(13, \cdot)\) 105.2.m.a 16 2
105.2.p \(\chi_{105}(59, \cdot)\) 105.2.p.a 24 2
105.2.q \(\chi_{105}(4, \cdot)\) 105.2.q.a 16 2
105.2.s \(\chi_{105}(26, \cdot)\) 105.2.s.a 2 2
105.2.s.b 2
105.2.s.c 8
105.2.s.d 8
105.2.u \(\chi_{105}(52, \cdot)\) 105.2.u.a 32 4
105.2.x \(\chi_{105}(2, \cdot)\) 105.2.x.a 48 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(105))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(105)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 - T + 2 T^{2} \))(\( 1 - T^{2} + 4 T^{4} \))(\( 1 - T^{2} + 4 T^{4} \))(\( 1 - T^{2} + 4 T^{4} \))(\( 1 - T^{2} - 4 T^{6} + 16 T^{8} \))(\( 1 - T^{2} - 4 T^{6} + 16 T^{8} \))(\( 1 - 3 T^{2} + 4 T^{4} \))(\( 1 - T^{2} - T^{4} - 3 T^{6} - 4 T^{8} - 16 T^{10} + 64 T^{12} \))(\( ( 1 + T^{2} + 4 T^{4} )^{2} \))(\( ( 1 + 2 T^{2} )^{4} \))(\( ( 1 + T^{2} + 4 T^{4} )^{2} \))(\( 1 - 2 T^{2} + 4 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4} \))(\( ( 1 - 2 T^{2} )^{2}( 1 + 2 T^{2} + 4 T^{4} ) \))(\( ( 1 - 2 T + 2 T^{2} )^{2}( 1 + 2 T + 2 T^{2} + 4 T^{3} + 4 T^{4} ) \))(\( ( 1 - 2 T - 2 T^{3} + 9 T^{4} - 4 T^{5} - 16 T^{7} + 16 T^{8} )^{2}( 1 + 2 T + 4 T^{2} + 6 T^{3} + 9 T^{4} + 12 T^{5} + 16 T^{6} + 16 T^{7} + 16 T^{8} )^{2} \))(\( 1 + 4 T^{2} + 4 T^{4} - 8 T^{6} - 20 T^{8} + 32 T^{10} + 96 T^{12} - 208 T^{14} - 944 T^{16} - 832 T^{18} + 1536 T^{20} + 2048 T^{22} - 5120 T^{24} - 8192 T^{26} + 16384 T^{28} + 65536 T^{30} + 65536 T^{32} \))(\( 1 + 3 T + 5 T^{2} + 6 T^{3} + 4 T^{4} \))(\( 1 - 3 T + 5 T^{2} - 6 T^{3} + 4 T^{4} \))(\( 1 + 3 T + 7 T^{2} + 12 T^{3} + 16 T^{4} + 12 T^{5} - 8 T^{6} - 36 T^{7} - 68 T^{8} - 72 T^{9} - 32 T^{10} + 96 T^{11} + 256 T^{12} + 384 T^{13} + 448 T^{14} + 384 T^{15} + 256 T^{16} \))(\( 1 - 3 T + 7 T^{2} - 12 T^{3} + 16 T^{4} - 12 T^{5} - 8 T^{6} + 36 T^{7} - 68 T^{8} + 72 T^{9} - 32 T^{10} - 96 T^{11} + 256 T^{12} - 384 T^{13} + 448 T^{14} - 384 T^{15} + 256 T^{16} \))
$3$ (\( 1 - T \))(\( ( 1 + T )^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + T - 2 T^{2} + 3 T^{3} + 9 T^{4} \))(\( 1 - T - 2 T^{2} - 3 T^{3} + 9 T^{4} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{3} \))(\( ( 1 + 2 T + 3 T^{2} )^{2} \))(\( 1 - T^{2} + 9 T^{4} \))(\( ( 1 - 2 T + 3 T^{2} )^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T^{4} )^{4} \))(\( ( 1 - T^{2} + T^{4} )^{4} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - T + 3 T^{2} - 4 T^{3} + 16 T^{4} - 12 T^{5} + 27 T^{6} - 27 T^{7} + 81 T^{8} \))(\( 1 - 2 T + 4 T^{3} - 11 T^{4} + 12 T^{5} - 54 T^{7} + 81 T^{8} \))
$5$ (\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{4} \))(\( ( 1 - T )^{4} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 3 T^{2} - 12 T^{3} + 15 T^{4} - 50 T^{5} + 125 T^{6} \))(\( 1 - 2 T^{2} + 25 T^{4} \))(\( ( 1 + 5 T^{2} )^{2} \))(\( 1 - 2 T^{2} + 25 T^{4} \))(\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( 1 + 28 T^{4} - 256 T^{6} - 26 T^{8} - 6400 T^{10} + 17500 T^{12} + 390625 T^{16} \))(\( 1 - 2 T + 4 T^{2} - 20 T^{3} + 62 T^{4} - 118 T^{5} + 200 T^{6} - 670 T^{7} + 1639 T^{8} - 3350 T^{9} + 5000 T^{10} - 14750 T^{11} + 38750 T^{12} - 62500 T^{13} + 62500 T^{14} - 156250 T^{15} + 390625 T^{16} \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))(\( ( 1 - T + T^{2} )^{4} \))(\( ( 1 + T + T^{2} )^{4} \))
$7$ (\( 1 - T \))(\( ( 1 - T )^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( ( 1 + 4 T + 7 T^{2} )^{2} \))(\( ( 1 + 4 T + 7 T^{2} )^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{3} \))(\( ( 1 - 2 T + 7 T^{2} )^{2} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( ( 1 + 2 T + 7 T^{2} )^{2} \))(\( 1 - 5 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 + 11 T^{2} + 49 T^{4} \))(\( 1 + 8 T + 32 T^{2} + 88 T^{3} + 196 T^{4} + 248 T^{5} - 416 T^{6} - 2840 T^{7} - 8634 T^{8} - 19880 T^{9} - 20384 T^{10} + 85064 T^{11} + 470596 T^{12} + 1479016 T^{13} + 3764768 T^{14} + 6588344 T^{15} + 5764801 T^{16} \))(\( 1 + 20 T^{2} + 202 T^{4} + 1244 T^{6} + 7267 T^{8} + 60956 T^{10} + 485002 T^{12} + 2352980 T^{14} + 5764801 T^{16} \))(\( 1 + 5 T + 7 T^{2} \))(\( 1 + 5 T + 7 T^{2} \))(\( 1 - 2 T + 4 T^{2} + 10 T^{3} - 41 T^{4} + 70 T^{5} + 196 T^{6} - 686 T^{7} + 2401 T^{8} \))(\( 1 - 2 T + 4 T^{2} + 10 T^{3} - 41 T^{4} + 70 T^{5} + 196 T^{6} - 686 T^{7} + 2401 T^{8} \))
$11$ (\( 1 + 11 T^{2} \))(\( 1 - 4 T + 6 T^{2} - 44 T^{3} + 121 T^{4} \))(\( 1 - 10 T^{2} + 121 T^{4} \))(\( 1 - 10 T^{2} + 121 T^{4} \))(\( 1 - 37 T^{2} + 576 T^{4} - 4477 T^{6} + 14641 T^{8} \))(\( 1 - 37 T^{2} + 576 T^{4} - 4477 T^{6} + 14641 T^{8} \))(\( ( 1 + 6 T + 11 T^{2} )^{2} \))(\( ( 1 - 2 T + 11 T^{2} )^{6} \))(\( ( 1 - 6 T + 11 T^{2} )^{2}( 1 + 6 T + 11 T^{2} )^{2} \))(\( ( 1 - 3 T + 11 T^{2} )^{2}( 1 + 3 T + 11 T^{2} )^{2} \))(\( ( 1 - 6 T + 11 T^{2} )^{2}( 1 + 6 T + 11 T^{2} )^{2} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 6 T + 25 T^{2} - 66 T^{3} + 121 T^{4} \))(\( 1 + 4 T - 8 T^{2} + 8 T^{3} + 279 T^{4} + 88 T^{5} - 968 T^{6} + 5324 T^{7} + 14641 T^{8} \))(\( 1 - 2 T - 16 T^{2} + 4 T^{3} + 235 T^{4} + 44 T^{5} - 1936 T^{6} - 2662 T^{7} + 14641 T^{8} \))(\( ( 1 + 4 T + 32 T^{2} + 68 T^{3} + 402 T^{4} + 748 T^{5} + 3872 T^{6} + 5324 T^{7} + 14641 T^{8} )^{4} \))(\( ( 1 - 26 T^{2} - 28 T^{3} + 316 T^{4} + 518 T^{5} - 2872 T^{6} - 2968 T^{7} + 31007 T^{8} - 32648 T^{9} - 347512 T^{10} + 689458 T^{11} + 4626556 T^{12} - 4509428 T^{13} - 46060586 T^{14} + 214358881 T^{16} )^{2} \))(\( 1 + 6 T + 23 T^{2} + 66 T^{3} + 121 T^{4} \))(\( 1 - 6 T + 23 T^{2} - 66 T^{3} + 121 T^{4} \))(\( 1 + 16 T^{2} - 2 T^{4} + 30 T^{5} + 268 T^{6} + 1548 T^{7} + 21079 T^{8} + 17028 T^{9} + 32428 T^{10} + 39930 T^{11} - 29282 T^{12} + 28344976 T^{14} + 214358881 T^{16} \))(\( 1 + 16 T^{2} - 2 T^{4} - 30 T^{5} + 268 T^{6} - 1548 T^{7} + 21079 T^{8} - 17028 T^{9} + 32428 T^{10} - 39930 T^{11} - 29282 T^{12} + 28344976 T^{14} + 214358881 T^{16} \))
$13$ (\( 1 + 6 T + 13 T^{2} \))(\( 1 + 6 T^{2} + 169 T^{4} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( ( 1 - 13 T^{2} )^{2} \))(\( 1 - T^{2} + 264 T^{4} - 169 T^{6} + 28561 T^{8} \))(\( 1 - T^{2} + 264 T^{4} - 169 T^{6} + 28561 T^{8} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - 34 T^{2} + 359 T^{4} - 2172 T^{6} + 60671 T^{8} - 971074 T^{10} + 4826809 T^{12} \))(\( ( 1 + 4 T + 13 T^{2} )^{4} \))(\( ( 1 + 19 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 4 T + 13 T^{2} )^{4} \))(\( ( 1 + T + 13 T^{2} )^{2} \))(\( ( 1 + 3 T + 13 T^{2} )^{2} \))(\( ( 1 + 6 T + 33 T^{2} + 78 T^{3} + 169 T^{4} )^{2} \))(\( ( 1 - 8 T + 39 T^{2} - 104 T^{3} + 169 T^{4} )^{2} \))(\( 1 + 424 T^{4} + 47004 T^{8} - 12160488 T^{12} - 4129271418 T^{16} - 347315697768 T^{20} + 38342606809884 T^{24} + 9878388091931944 T^{28} + 665416609183179841 T^{32} \))(\( ( 1 - 44 T^{2} + 1234 T^{4} - 23988 T^{6} + 358939 T^{8} - 4053972 T^{10} + 35244274 T^{12} - 212379596 T^{14} + 815730721 T^{16} )^{2} \))(\( 1 - 14 T^{2} + 169 T^{4} \))(\( 1 - 14 T^{2} + 169 T^{4} \))(\( 1 - 83 T^{2} + 3217 T^{4} - 76058 T^{6} + 1197778 T^{8} - 12853802 T^{10} + 91880737 T^{12} - 400625147 T^{14} + 815730721 T^{16} \))(\( 1 - 83 T^{2} + 3217 T^{4} - 76058 T^{6} + 1197778 T^{8} - 12853802 T^{10} + 91880737 T^{12} - 400625147 T^{14} + 815730721 T^{16} \))
$17$ (\( 1 - 2 T + 17 T^{2} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 - 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 + 3 T + 28 T^{2} + 51 T^{3} + 289 T^{4} )^{2} \))(\( ( 1 - 3 T + 28 T^{2} - 51 T^{3} + 289 T^{4} )^{2} \))(\( 1 - 18 T^{2} + 289 T^{4} \))(\( 1 - 70 T^{2} + 2415 T^{4} - 51220 T^{6} + 697935 T^{8} - 5846470 T^{10} + 24137569 T^{12} \))(\( ( 1 - 26 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 29 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 26 T^{2} + 289 T^{4} )^{2} \))(\( 1 + 6 T + 19 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 - 4 T - T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 - 4 T - 4 T^{2} + 56 T^{3} - 161 T^{4} + 952 T^{5} - 1156 T^{6} - 19652 T^{7} + 83521 T^{8} \))(\( 1 + 10 T + 44 T^{2} + 220 T^{3} + 1147 T^{4} + 3740 T^{5} + 12716 T^{6} + 49130 T^{7} + 83521 T^{8} \))(\( 1 + 120 T^{4} + 166556 T^{8} - 9625784 T^{12} + 12237871174 T^{16} - 803955105464 T^{20} + 1161854256343196 T^{24} + 69914668467571320 T^{28} + 48661191875666868481 T^{32} \))(\( 1 + 76 T^{2} + 2664 T^{4} + 67392 T^{6} + 1583990 T^{8} + 33141472 T^{10} + 603483136 T^{12} + 11039990476 T^{14} + 198790801859 T^{16} + 3190557247564 T^{18} + 50403515001856 T^{20} + 799954567161568 T^{22} + 11049530028969590 T^{24} + 135861860939059008 T^{26} + 1552105639980083304 T^{28} + 12796714818514470604 T^{30} + 48661191875666868481 T^{32} \))(\( 1 + 6 T + 19 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 - 6 T + 19 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 + 12 T + 34 T^{2} + 12 T^{3} + 1078 T^{4} + 6882 T^{5} + 8740 T^{6} + 70272 T^{7} + 637627 T^{8} + 1194624 T^{9} + 2525860 T^{10} + 33811266 T^{11} + 90035638 T^{12} + 17038284 T^{13} + 820677346 T^{14} + 4924064076 T^{15} + 6975757441 T^{16} \))(\( 1 - 12 T + 34 T^{2} - 12 T^{3} + 1078 T^{4} - 6882 T^{5} + 8740 T^{6} - 70272 T^{7} + 637627 T^{8} - 1194624 T^{9} + 2525860 T^{10} - 33811266 T^{11} + 90035638 T^{12} - 17038284 T^{13} + 820677346 T^{14} - 4924064076 T^{15} + 6975757441 T^{16} \))
$19$ (\( 1 + 8 T + 19 T^{2} \))(\( 1 - 4 T + 22 T^{2} - 76 T^{3} + 361 T^{4} \))(\( ( 1 - 8 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( ( 1 - 8 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( ( 1 - 8 T + 19 T^{2} )^{2}( 1 + 8 T + 19 T^{2} )^{2} \))(\( ( 1 - 8 T + 19 T^{2} )^{2}( 1 + 8 T + 19 T^{2} )^{2} \))(\( ( 1 - 6 T + 19 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} + 188 T^{3} + 1007 T^{4} + 2166 T^{5} + 6859 T^{6} )^{2} \))(\( ( 1 - 19 T^{2} )^{4} \))(\( ( 1 - 19 T^{2} )^{4} \))(\( ( 1 - 19 T^{2} )^{4} \))(\( 1 + 5 T + 6 T^{2} + 95 T^{3} + 361 T^{4} \))(\( ( 1 - 7 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( 1 - 2 T - 3 T^{2} + 62 T^{3} - 388 T^{4} + 1178 T^{5} - 1083 T^{6} - 13718 T^{7} + 130321 T^{8} \))(\( 1 + 2 T - 23 T^{2} - 22 T^{3} + 292 T^{4} - 418 T^{5} - 8303 T^{6} + 13718 T^{7} + 130321 T^{8} \))(\( ( 1 + 48 T^{2} + 1524 T^{4} + 40016 T^{6} + 818246 T^{8} + 14445776 T^{10} + 198609204 T^{12} + 2258202288 T^{14} + 16983563041 T^{16} )^{2} \))(\( ( 1 + 12 T + 30 T^{2} - 80 T^{3} + 689 T^{4} + 9436 T^{5} + 28846 T^{6} + 59944 T^{7} + 291332 T^{8} + 1138936 T^{9} + 10413406 T^{10} + 64721524 T^{11} + 89791169 T^{12} - 198087920 T^{13} + 1411376430 T^{14} + 10726460868 T^{15} + 16983563041 T^{16} )^{2} \))(\( 1 + 12 T + 67 T^{2} + 228 T^{3} + 361 T^{4} \))(\( 1 + 12 T + 67 T^{2} + 228 T^{3} + 361 T^{4} \))(\( 1 - 9 T + 100 T^{2} - 657 T^{3} + 4723 T^{4} - 26244 T^{5} + 148996 T^{6} - 704196 T^{7} + 3331528 T^{8} - 13379724 T^{9} + 53787556 T^{10} - 180007596 T^{11} + 615506083 T^{12} - 1626797043 T^{13} + 4704588100 T^{14} - 8044845651 T^{15} + 16983563041 T^{16} \))(\( 1 - 9 T + 100 T^{2} - 657 T^{3} + 4723 T^{4} - 26244 T^{5} + 148996 T^{6} - 704196 T^{7} + 3331528 T^{8} - 13379724 T^{9} + 53787556 T^{10} - 180007596 T^{11} + 615506083 T^{12} - 1626797043 T^{13} + 4704588100 T^{14} - 8044845651 T^{15} + 16983563041 T^{16} \))
$23$ (\( 1 - 8 T + 23 T^{2} \))(\( ( 1 - 4 T + 23 T^{2} )^{2} \))(\( 1 - 34 T^{2} + 529 T^{4} \))(\( 1 - 34 T^{2} + 529 T^{4} \))(\( 1 - 16 T^{2} - 66 T^{4} - 8464 T^{6} + 279841 T^{8} \))(\( 1 - 16 T^{2} - 66 T^{4} - 8464 T^{6} + 279841 T^{8} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 106 T^{2} + 5183 T^{4} - 150348 T^{6} + 2741807 T^{8} - 29663146 T^{10} + 148035889 T^{12} \))(\( ( 1 + 34 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 + 23 T^{2} )^{4} \))(\( ( 1 + 34 T^{2} + 529 T^{4} )^{2} \))(\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 - 4 T - 7 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 - 4 T - 16 T^{2} + 56 T^{3} + 127 T^{4} + 1288 T^{5} - 8464 T^{6} - 48668 T^{7} + 279841 T^{8} \))(\( 1 - 6 T - 16 T^{2} - 36 T^{3} + 1347 T^{4} - 828 T^{5} - 8464 T^{6} - 73002 T^{7} + 279841 T^{8} \))(\( ( 1 + 20 T + 200 T^{2} + 1516 T^{3} + 10388 T^{4} + 65340 T^{5} + 378328 T^{6} + 2076676 T^{7} + 10539814 T^{8} + 47763548 T^{9} + 200135512 T^{10} + 794991780 T^{11} + 2906988308 T^{12} + 9757495988 T^{13} + 29607177800 T^{14} + 68096508940 T^{15} + 78310985281 T^{16} )^{2} \))(\( 1 + 20 T^{2} - 1512 T^{4} - 18448 T^{6} + 1612902 T^{8} + 10149224 T^{10} - 1248424544 T^{12} - 1840459676 T^{14} + 770565238915 T^{16} - 973603168604 T^{18} - 349360372817504 T^{20} + 1502449397500136 T^{22} + 126307944781695462 T^{24} - 764236278869396752 T^{26} - 33134912141214725352 T^{28} + \)\(23\!\cdots\!80\)\( T^{30} + \)\(61\!\cdots\!61\)\( T^{32} \))(\( 1 - 3 T + 26 T^{2} - 69 T^{3} + 529 T^{4} \))(\( 1 + 3 T + 26 T^{2} + 69 T^{3} + 529 T^{4} \))(\( 1 - 27 T + 391 T^{2} - 3996 T^{3} + 31651 T^{4} - 205875 T^{5} + 1157938 T^{6} - 5917779 T^{7} + 28782226 T^{8} - 136108917 T^{9} + 612549202 T^{10} - 2504881125 T^{11} + 8857247491 T^{12} - 25719626628 T^{13} + 57882032599 T^{14} - 91930287069 T^{15} + 78310985281 T^{16} \))(\( 1 + 27 T + 391 T^{2} + 3996 T^{3} + 31651 T^{4} + 205875 T^{5} + 1157938 T^{6} + 5917779 T^{7} + 28782226 T^{8} + 136108917 T^{9} + 612549202 T^{10} + 2504881125 T^{11} + 8857247491 T^{12} + 25719626628 T^{13} + 57882032599 T^{14} + 91930287069 T^{15} + 78310985281 T^{16} \))
$29$ (\( 1 + 2 T + 29 T^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( 1 - 10 T^{2} + 841 T^{4} \))(\( 1 - 10 T^{2} + 841 T^{4} \))(\( 1 - 97 T^{2} + 3960 T^{4} - 81577 T^{6} + 707281 T^{8} \))(\( 1 - 97 T^{2} + 3960 T^{4} - 81577 T^{6} + 707281 T^{8} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 35 T^{2} + 76 T^{3} + 1015 T^{4} + 1682 T^{5} + 24389 T^{6} )^{2} \))(\( ( 1 - 26 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 9 T + 29 T^{2} )^{2}( 1 + 9 T + 29 T^{2} )^{2} \))(\( ( 1 - 26 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 8 T + 29 T^{2} )^{2} \))(\( ( 1 - 8 T + 56 T^{2} - 232 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 - 2 T + 32 T^{2} - 58 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 - 184 T^{2} + 15868 T^{4} - 835400 T^{6} + 29324070 T^{8} - 702571400 T^{10} + 11223134908 T^{12} - 109447491064 T^{14} + 500246412961 T^{16} )^{2} \))(\( ( 1 - 6 T + 78 T^{2} - 332 T^{3} + 2820 T^{4} - 9628 T^{5} + 65598 T^{6} - 146334 T^{7} + 707281 T^{8} )^{4} \))(\( 1 - 55 T^{2} + 841 T^{4} \))(\( 1 - 55 T^{2} + 841 T^{4} \))(\( 1 - 53 T^{2} + 3250 T^{4} - 128951 T^{6} + 4063174 T^{8} - 108447791 T^{10} + 2298663250 T^{12} - 31525636013 T^{14} + 500246412961 T^{16} \))(\( 1 - 53 T^{2} + 3250 T^{4} - 128951 T^{6} + 4063174 T^{8} - 108447791 T^{10} + 2298663250 T^{12} - 31525636013 T^{14} + 500246412961 T^{16} \))
$31$ (\( 1 - 4 T + 31 T^{2} \))(\( 1 - 12 T + 78 T^{2} - 372 T^{3} + 961 T^{4} \))(\( 1 - 50 T^{2} + 961 T^{4} \))(\( 1 - 50 T^{2} + 961 T^{4} \))(\( ( 1 - 50 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 50 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 + 10 T + 31 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} + 60 T^{3} + 1271 T^{4} - 1922 T^{5} + 29791 T^{6} )^{2} \))(\( ( 1 + 34 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 31 T^{2} )^{4} \))(\( ( 1 + 34 T^{2} + 961 T^{4} )^{2} \))(\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( 1 + T - 30 T^{2} + 31 T^{3} + 961 T^{4} \))(\( 1 - 6 T - 27 T^{2} - 6 T^{3} + 1892 T^{4} - 186 T^{5} - 25947 T^{6} - 178746 T^{7} + 923521 T^{8} \))(\( 1 + 6 T - 23 T^{2} - 18 T^{3} + 1404 T^{4} - 558 T^{5} - 22103 T^{6} + 178746 T^{7} + 923521 T^{8} \))(\( ( 1 - 128 T^{2} + 9396 T^{4} - 463040 T^{6} + 16703398 T^{8} - 444981440 T^{10} + 8677403316 T^{12} - 113600471168 T^{14} + 852891037441 T^{16} )^{2} \))(\( ( 1 - 8 T - 54 T^{2} + 352 T^{3} + 3285 T^{4} - 9272 T^{5} - 157694 T^{6} + 60416 T^{7} + 6248764 T^{8} + 1872896 T^{9} - 151543934 T^{10} - 276222152 T^{11} + 3033766485 T^{12} + 10077461152 T^{13} - 47925198774 T^{14} - 220100912888 T^{15} + 852891037441 T^{16} )^{2} \))(\( 1 + 6 T + 43 T^{2} + 186 T^{3} + 961 T^{4} \))(\( 1 + 6 T + 43 T^{2} + 186 T^{3} + 961 T^{4} \))(\( 1 + 21 T + 262 T^{2} + 2415 T^{3} + 17293 T^{4} + 101304 T^{5} + 505090 T^{6} + 2328618 T^{7} + 11769748 T^{8} + 72187158 T^{9} + 485391490 T^{10} + 3017947464 T^{11} + 15970448653 T^{12} + 69139399665 T^{13} + 232525964422 T^{14} + 577764896331 T^{15} + 852891037441 T^{16} \))(\( 1 + 21 T + 262 T^{2} + 2415 T^{3} + 17293 T^{4} + 101304 T^{5} + 505090 T^{6} + 2328618 T^{7} + 11769748 T^{8} + 72187158 T^{9} + 485391490 T^{10} + 3017947464 T^{11} + 15970448653 T^{12} + 69139399665 T^{13} + 232525964422 T^{14} + 577764896331 T^{15} + 852891037441 T^{16} \))
$37$ (\( 1 + 2 T + 37 T^{2} \))(\( 1 - 4 T - 2 T^{2} - 148 T^{3} + 1369 T^{4} \))(\( ( 1 + 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 2 T + 37 T^{2} )^{2} \))(\( ( 1 + 2 T + 42 T^{2} + 74 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 + 2 T + 42 T^{2} + 74 T^{3} + 1369 T^{4} )^{2} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 - 46 T^{2} + 1399 T^{4} - 74788 T^{6} + 1915231 T^{8} - 86211406 T^{10} + 2565726409 T^{12} \))(\( ( 1 - 37 T^{2} )^{4} \))(\( ( 1 - 37 T^{2} )^{4} \))(\( ( 1 - 37 T^{2} )^{4} \))(\( 1 - 7 T + 12 T^{2} - 259 T^{3} + 1369 T^{4} \))(\( 1 + 7 T + 12 T^{2} + 259 T^{3} + 1369 T^{4} \))(\( 1 - 14 T + 75 T^{2} - 658 T^{3} + 6020 T^{4} - 24346 T^{5} + 102675 T^{6} - 709142 T^{7} + 1874161 T^{8} \))(\( 1 + 4 T - 35 T^{2} - 92 T^{3} + 640 T^{4} - 3404 T^{5} - 47915 T^{6} + 202612 T^{7} + 1874161 T^{8} \))(\( ( 1 - 16 T + 128 T^{2} - 944 T^{3} + 8860 T^{4} - 73552 T^{5} + 488320 T^{6} - 3175280 T^{7} + 20212134 T^{8} - 117485360 T^{9} + 668510080 T^{10} - 3725629456 T^{11} + 16605066460 T^{12} - 65460695408 T^{13} + 328412980352 T^{14} - 1518910034128 T^{15} + 3512479453921 T^{16} )^{2} \))(\( 1 + 128 T^{2} + 6574 T^{4} + 187656 T^{6} + 5183961 T^{8} + 158877780 T^{10} + 5690568750 T^{12} + 459641012708 T^{14} + 25029766954564 T^{16} + 629248546397252 T^{18} + 10665042019068750 T^{20} + 407636915949292020 T^{22} + 18208556502427761081 T^{24} + \)\(90\!\cdots\!44\)\( T^{26} + \)\(43\!\cdots\!94\)\( T^{28} + \)\(11\!\cdots\!92\)\( T^{30} + \)\(12\!\cdots\!41\)\( T^{32} \))(\( 1 + 4 T - 21 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 4 T - 21 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 - 7 T - 24 T^{2} + 493 T^{3} - 973 T^{4} - 16188 T^{5} + 118336 T^{6} + 258098 T^{7} - 5756772 T^{8} + 9549626 T^{9} + 162001984 T^{10} - 819970764 T^{11} - 1823558653 T^{12} + 34186570801 T^{13} - 61577433816 T^{14} - 664523139931 T^{15} + 3512479453921 T^{16} \))(\( 1 - 7 T - 24 T^{2} + 493 T^{3} - 973 T^{4} - 16188 T^{5} + 118336 T^{6} + 258098 T^{7} - 5756772 T^{8} + 9549626 T^{9} + 162001984 T^{10} - 819970764 T^{11} - 1823558653 T^{12} + 34186570801 T^{13} - 61577433816 T^{14} - 664523139931 T^{15} + 3512479453921 T^{16} \))
$41$ (\( 1 + 6 T + 41 T^{2} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{4} \))(\( ( 1 + 6 T + 41 T^{2} )^{4} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 63 T^{2} + 36 T^{3} + 2583 T^{4} - 3362 T^{5} + 68921 T^{6} )^{2} \))(\( ( 1 + 70 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 + 41 T^{2} )^{4} \))(\( ( 1 + 70 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 12 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 4 T + 68 T^{2} + 164 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 - 2 T + 80 T^{2} - 82 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 - 144 T^{2} + 12956 T^{4} - 823792 T^{6} + 38320198 T^{8} - 1384794352 T^{10} + 36610559516 T^{12} - 684015010704 T^{14} + 7984925229121 T^{16} )^{2} \))(\( ( 1 - 4 T + 114 T^{2} - 346 T^{3} + 5976 T^{4} - 14186 T^{5} + 191634 T^{6} - 275684 T^{7} + 2825761 T^{8} )^{4} \))(\( ( 1 + 3 T + 41 T^{2} )^{2} \))(\( ( 1 - 3 T + 41 T^{2} )^{2} \))(\( ( 1 + 15 T + 218 T^{2} + 1791 T^{3} + 14136 T^{4} + 73431 T^{5} + 366458 T^{6} + 1033815 T^{7} + 2825761 T^{8} )^{2} \))(\( ( 1 - 15 T + 218 T^{2} - 1791 T^{3} + 14136 T^{4} - 73431 T^{5} + 366458 T^{6} - 1033815 T^{7} + 2825761 T^{8} )^{2} \))
$43$ (\( 1 - 4 T + 43 T^{2} \))(\( 1 + 6 T^{2} + 1849 T^{4} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( ( 1 + 2 T + 54 T^{2} + 86 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 2 T + 54 T^{2} + 86 T^{3} + 1849 T^{4} )^{2} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 + 46 T^{2} + 2839 T^{4} + 118948 T^{6} + 5249311 T^{8} + 157264846 T^{10} + 6321363049 T^{12} \))(\( ( 1 - 62 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 43 T^{2} )^{4} \))(\( ( 1 - 62 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 + T + 43 T^{2} )^{2} \))(\( ( 1 - T + 43 T^{2} )^{2} \))(\( ( 1 + 18 T + 165 T^{2} + 774 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 4 T + 63 T^{2} + 172 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 8 T + 32 T^{2} + 280 T^{3} + 2788 T^{4} + 14232 T^{5} + 63840 T^{6} + 569416 T^{7} + 5017638 T^{8} + 24484888 T^{9} + 118040160 T^{10} + 1131543624 T^{11} + 9531617188 T^{12} + 41162364040 T^{13} + 202283617568 T^{14} + 2174548888856 T^{15} + 11688200277601 T^{16} )^{2} \))(\( ( 1 - 216 T^{2} + 22138 T^{4} - 1464812 T^{6} + 71619331 T^{8} - 2708437388 T^{10} + 75685416538 T^{12} - 1365414418584 T^{14} + 11688200277601 T^{16} )^{2} \))(\( ( 1 - T + 43 T^{2} )^{2} \))(\( ( 1 - T + 43 T^{2} )^{2} \))(\( ( 1 - 8 T + 184 T^{2} - 1022 T^{3} + 12127 T^{4} - 43946 T^{5} + 340216 T^{6} - 636056 T^{7} + 3418801 T^{8} )^{2} \))(\( ( 1 - 8 T + 184 T^{2} - 1022 T^{3} + 12127 T^{4} - 43946 T^{5} + 340216 T^{6} - 636056 T^{7} + 3418801 T^{8} )^{2} \))
$47$ (\( 1 - 8 T + 47 T^{2} \))(\( 1 - 8 T + 30 T^{2} - 376 T^{3} + 2209 T^{4} \))(\( ( 1 + 12 T + 47 T^{2} )^{2} \))(\( ( 1 - 12 T + 47 T^{2} )^{2} \))(\( ( 1 - 9 T + 106 T^{2} - 423 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 + 9 T + 106 T^{2} + 423 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 - 47 T^{2} )^{2} \))(\( 1 - 154 T^{2} + 12143 T^{4} - 652332 T^{6} + 26823887 T^{8} - 751470874 T^{10} + 10779215329 T^{12} \))(\( ( 1 - 86 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 + 31 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 86 T^{2} + 2209 T^{4} )^{2} \))(\( 1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 + 2 T - 43 T^{2} + 94 T^{3} + 2209 T^{4} \))(\( 1 - 4 T + 46 T^{2} + 496 T^{3} - 2061 T^{4} + 23312 T^{5} + 101614 T^{6} - 415292 T^{7} + 4879681 T^{8} \))(\( ( 1 + 2 T - 43 T^{2} + 94 T^{3} + 2209 T^{4} )^{2} \))(\( 1 + 3784 T^{4} + 1124764 T^{8} + 9138019192 T^{12} + 63538455194182 T^{16} + 44590618628837752 T^{20} + 26782078030828949404 T^{24} + \)\(43\!\cdots\!44\)\( T^{28} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 + 308 T^{2} + 50892 T^{4} + 5950136 T^{6} + 547353834 T^{8} + 41768130380 T^{10} + 2726163659344 T^{12} + 155042751818668 T^{14} + 7757667166613347 T^{16} + 342489438767437612 T^{18} + 13302809011391389264 T^{20} + \)\(45\!\cdots\!20\)\( T^{22} + \)\(13\!\cdots\!74\)\( T^{24} + \)\(31\!\cdots\!64\)\( T^{26} + \)\(59\!\cdots\!72\)\( T^{28} + \)\(79\!\cdots\!52\)\( T^{30} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 + 6 T - 116 T^{2} - 252 T^{3} + 10126 T^{4} + 1986 T^{5} - 595736 T^{6} - 157218 T^{7} + 25623007 T^{8} - 7389246 T^{9} - 1315980824 T^{10} + 206192478 T^{11} + 49411649806 T^{12} - 57794941764 T^{13} - 1250388978164 T^{14} + 3039738722778 T^{15} + 23811286661761 T^{16} \))(\( 1 - 6 T - 116 T^{2} + 252 T^{3} + 10126 T^{4} - 1986 T^{5} - 595736 T^{6} + 157218 T^{7} + 25623007 T^{8} + 7389246 T^{9} - 1315980824 T^{10} - 206192478 T^{11} + 49411649806 T^{12} + 57794941764 T^{13} - 1250388978164 T^{14} - 3039738722778 T^{15} + 23811286661761 T^{16} \))
$53$ (\( 1 - 10 T + 53 T^{2} \))(\( 1 + 16 T + 150 T^{2} + 848 T^{3} + 2809 T^{4} \))(\( ( 1 - 53 T^{2} )^{2} \))(\( ( 1 - 53 T^{2} )^{2} \))(\( 1 - 136 T^{2} + 9054 T^{4} - 382024 T^{6} + 7890481 T^{8} \))(\( 1 - 136 T^{2} + 9054 T^{4} - 382024 T^{6} + 7890481 T^{8} \))(\( 1 - 70 T^{2} + 2809 T^{4} \))(\( 1 - 146 T^{2} + 14103 T^{4} - 884828 T^{6} + 39615327 T^{8} - 1152010226 T^{10} + 22164361129 T^{12} \))(\( ( 1 + 53 T^{2} )^{4} \))(\( ( 1 + 53 T^{2} )^{4} \))(\( ( 1 + 53 T^{2} )^{4} \))(\( 1 - 53 T^{2} + 2809 T^{4} \))(\( 1 + 4 T - 37 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( 1 + 8 T - 50 T^{2} + 64 T^{3} + 6795 T^{4} + 3392 T^{5} - 140450 T^{6} + 1191016 T^{7} + 7890481 T^{8} \))(\( 1 + 4 T + 14 T^{2} - 416 T^{3} - 3653 T^{4} - 22048 T^{5} + 39326 T^{6} + 595508 T^{7} + 7890481 T^{8} \))(\( ( 1 - 12 T + 72 T^{2} - 572 T^{3} + 1780 T^{4} + 1436 T^{5} + 18200 T^{6} - 441076 T^{7} + 6254598 T^{8} - 23377028 T^{9} + 51123800 T^{10} + 213787372 T^{11} + 14045056180 T^{12} - 239207821996 T^{13} + 1595834001288 T^{14} - 14096533678044 T^{15} + 62259690411361 T^{16} )^{2} \))(\( 1 + 264 T^{2} + 35652 T^{4} + 3177712 T^{6} + 212585578 T^{8} + 12279652216 T^{10} + 710817442960 T^{12} + 42611108403128 T^{14} + 2398437218467955 T^{16} + 119694603504386552 T^{18} + 5608691528144463760 T^{20} + \)\(27\!\cdots\!64\)\( T^{22} + \)\(13\!\cdots\!58\)\( T^{24} + \)\(55\!\cdots\!88\)\( T^{26} + \)\(17\!\cdots\!32\)\( T^{28} + \)\(36\!\cdots\!16\)\( T^{30} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( 1 + 53 T^{2} + 2809 T^{4} \))(\( 1 + 53 T^{2} + 2809 T^{4} \))(\( 1 - 24 T + 340 T^{2} - 3552 T^{3} + 29050 T^{4} - 180120 T^{5} + 750160 T^{6} - 1659096 T^{7} + 1273315 T^{8} - 87932088 T^{9} + 2107199440 T^{10} - 26815725240 T^{11} + 229218473050 T^{12} - 1485430391136 T^{13} + 7535882783860 T^{14} - 28193067356088 T^{15} + 62259690411361 T^{16} \))(\( 1 + 24 T + 340 T^{2} + 3552 T^{3} + 29050 T^{4} + 180120 T^{5} + 750160 T^{6} + 1659096 T^{7} + 1273315 T^{8} + 87932088 T^{9} + 2107199440 T^{10} + 26815725240 T^{11} + 229218473050 T^{12} + 1485430391136 T^{13} + 7535882783860 T^{14} + 28193067356088 T^{15} + 62259690411361 T^{16} \))
$59$ (\( 1 - 4 T + 59 T^{2} \))(\( 1 + 38 T^{2} + 3481 T^{4} \))(\( ( 1 + 12 T + 59 T^{2} )^{2} \))(\( ( 1 - 12 T + 59 T^{2} )^{2} \))(\( ( 1 - 6 T + 94 T^{2} - 354 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 + 6 T + 94 T^{2} + 354 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 - 8 T + 59 T^{2} )^{2} \))(\( ( 1 + 16 T + 113 T^{2} + 608 T^{3} + 6667 T^{4} + 55696 T^{5} + 205379 T^{6} )^{2} \))(\( ( 1 + 70 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 + 59 T^{2} )^{4} \))(\( ( 1 + 70 T^{2} + 3481 T^{4} )^{2} \))(\( 1 - 6 T - 23 T^{2} - 354 T^{3} + 3481 T^{4} \))(\( 1 - 8 T + 5 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 - 116 T^{2} + 9975 T^{4} - 403796 T^{6} + 12117361 T^{8} \))(\( 1 + 10 T - 16 T^{2} - 20 T^{3} + 4075 T^{4} - 1180 T^{5} - 55696 T^{6} + 2053790 T^{7} + 12117361 T^{8} \))(\( ( 1 + 312 T^{2} + 49660 T^{4} + 5040712 T^{6} + 354176614 T^{8} + 17546718472 T^{10} + 601748147260 T^{12} + 13160326495992 T^{14} + 146830437604321 T^{16} )^{2} \))(\( ( 1 - 2 T - 226 T^{2} + 236 T^{3} + 32016 T^{4} - 19820 T^{5} - 2961940 T^{6} + 407278 T^{7} + 205790979 T^{8} + 24029402 T^{9} - 10310513140 T^{10} - 4070611780 T^{11} + 387949429776 T^{12} + 168722134564 T^{13} - 9532800602866 T^{14} - 4977302969638 T^{15} + 146830437604321 T^{16} )^{2} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 + 12 T - 80 T^{2} - 1164 T^{3} + 7690 T^{4} + 80082 T^{5} - 434420 T^{6} - 1772232 T^{7} + 28861927 T^{8} - 104561688 T^{9} - 1512216020 T^{10} + 16447161078 T^{11} + 93182506090 T^{12} - 832171884036 T^{13} - 3374442691280 T^{14} + 29863817817828 T^{15} + 146830437604321 T^{16} \))(\( 1 - 12 T - 80 T^{2} + 1164 T^{3} + 7690 T^{4} - 80082 T^{5} - 434420 T^{6} + 1772232 T^{7} + 28861927 T^{8} + 104561688 T^{9} - 1512216020 T^{10} - 16447161078 T^{11} + 93182506090 T^{12} + 832171884036 T^{13} - 3374442691280 T^{14} - 29863817817828 T^{15} + 146830437604321 T^{16} \))
$61$ (\( 1 + 2 T + 61 T^{2} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( ( 1 - 14 T + 61 T^{2} )( 1 + 14 T + 61 T^{2} ) \))(\( ( 1 - 14 T + 61 T^{2} )( 1 + 14 T + 61 T^{2} ) \))(\( ( 1 - 14 T + 61 T^{2} )^{2}( 1 + 14 T + 61 T^{2} )^{2} \))(\( ( 1 - 14 T + 61 T^{2} )^{2}( 1 + 14 T + 61 T^{2} )^{2} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( ( 1 + 6 T + 131 T^{2} + 484 T^{3} + 7991 T^{4} + 22326 T^{5} + 226981 T^{6} )^{2} \))(\( ( 1 - 26 T^{2} + 3721 T^{4} )^{2} \))(\( ( 1 - 61 T^{2} )^{4} \))(\( ( 1 - 26 T^{2} + 3721 T^{4} )^{2} \))(\( 1 + 2 T - 57 T^{2} + 122 T^{3} + 3721 T^{4} \))(\( ( 1 - 13 T + 61 T^{2} )( 1 - T + 61 T^{2} ) \))(\( 1 + 8 T - 2 T^{2} - 448 T^{3} - 3269 T^{4} - 27328 T^{5} - 7442 T^{6} + 1815848 T^{7} + 13845841 T^{8} \))(\( ( 1 + 4 T - 45 T^{2} + 244 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 - 200 T^{2} + 17532 T^{4} - 857912 T^{6} + 37932838 T^{8} - 3192290552 T^{10} + 242745284412 T^{12} - 10304074872200 T^{14} + 191707312997281 T^{16} )^{2} \))(\( ( 1 - 8 T - 80 T^{2} + 376 T^{3} + 3998 T^{4} + 13396 T^{5} - 247632 T^{6} - 798752 T^{7} + 15355491 T^{8} - 48723872 T^{9} - 921438672 T^{10} + 3040637476 T^{11} + 55355672318 T^{12} + 317568209176 T^{13} - 4121629948880 T^{14} - 25141942688168 T^{15} + 191707312997281 T^{16} )^{2} \))(\( 1 + 9 T + 88 T^{2} + 549 T^{3} + 3721 T^{4} \))(\( 1 + 9 T + 88 T^{2} + 549 T^{3} + 3721 T^{4} \))(\( 1 - 15 T + 223 T^{2} - 2220 T^{3} + 19711 T^{4} - 141723 T^{5} + 816310 T^{6} - 5175267 T^{7} + 31433836 T^{8} - 315691287 T^{9} + 3037489510 T^{10} - 32168428263 T^{11} + 272915371951 T^{12} - 1875003788220 T^{13} + 11489043482503 T^{14} - 47141142540315 T^{15} + 191707312997281 T^{16} \))(\( 1 - 15 T + 223 T^{2} - 2220 T^{3} + 19711 T^{4} - 141723 T^{5} + 816310 T^{6} - 5175267 T^{7} + 31433836 T^{8} - 315691287 T^{9} + 3037489510 T^{10} - 32168428263 T^{11} + 272915371951 T^{12} - 1875003788220 T^{13} + 11489043482503 T^{14} - 47141142540315 T^{15} + 191707312997281 T^{16} \))
$67$ (\( 1 - 4 T + 67 T^{2} \))(\( ( 1 + 4 T + 67 T^{2} )^{2} \))(\( ( 1 - 8 T + 67 T^{2} )^{2} \))(\( ( 1 - 8 T + 67 T^{2} )^{2} \))(\( ( 1 + 2 T + 102 T^{2} + 134 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 + 2 T + 102 T^{2} + 134 T^{3} + 4489 T^{4} )^{2} \))(\( 1 + 122 T^{2} + 4489 T^{4} \))(\( 1 - 274 T^{2} + 36103 T^{4} - 2962972 T^{6} + 162066367 T^{8} - 5521407154 T^{10} + 90458382169 T^{12} \))(\( ( 1 - 110 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 - 67 T^{2} )^{4} \))(\( ( 1 - 110 T^{2} + 4489 T^{4} )^{2} \))(\( 1 - 7 T - 18 T^{2} - 469 T^{3} + 4489 T^{4} \))(\( 1 + 7 T - 18 T^{2} + 469 T^{3} + 4489 T^{4} \))(\( 1 - 2 T + 31 T^{2} + 322 T^{3} - 4028 T^{4} + 21574 T^{5} + 139159 T^{6} - 601526 T^{7} + 20151121 T^{8} \))(\( 1 - 12 T + 49 T^{2} + 468 T^{3} - 5112 T^{4} + 31356 T^{5} + 219961 T^{6} - 3609156 T^{7} + 20151121 T^{8} \))(\( ( 1 + 16 T + 128 T^{2} + 1424 T^{3} + 22436 T^{4} + 211280 T^{5} + 1522560 T^{6} + 15870032 T^{7} + 163564774 T^{8} + 1063292144 T^{9} + 6834771840 T^{10} + 63545206640 T^{11} + 452110550756 T^{12} + 1922578152368 T^{13} + 11578672917632 T^{14} + 96971385685168 T^{15} + 406067677556641 T^{16} )^{2} \))(\( 1 + 356 T^{2} + 63502 T^{4} + 8090208 T^{6} + 858425049 T^{8} + 80231005476 T^{10} + 6774300927054 T^{12} + 525083738078264 T^{14} + 37066264561921156 T^{16} + 2357100900233327096 T^{18} + \)\(13\!\cdots\!34\)\( T^{20} + \)\(72\!\cdots\!44\)\( T^{22} + \)\(34\!\cdots\!09\)\( T^{24} + \)\(14\!\cdots\!92\)\( T^{26} + \)\(51\!\cdots\!22\)\( T^{28} + \)\(13\!\cdots\!24\)\( T^{30} + \)\(16\!\cdots\!81\)\( T^{32} \))(\( 1 - 13 T + 102 T^{2} - 871 T^{3} + 4489 T^{4} \))(\( 1 - 13 T + 102 T^{2} - 871 T^{3} + 4489 T^{4} \))(\( 1 - 4 T - 234 T^{2} + 412 T^{3} + 35255 T^{4} - 28434 T^{5} - 3551522 T^{6} + 717722 T^{7} + 271900824 T^{8} + 48087374 T^{9} - 15942782258 T^{10} - 8551895142 T^{11} + 710427770855 T^{12} + 556251544084 T^{13} - 21167261427546 T^{14} - 24242846421292 T^{15} + 406067677556641 T^{16} \))(\( 1 - 4 T - 234 T^{2} + 412 T^{3} + 35255 T^{4} - 28434 T^{5} - 3551522 T^{6} + 717722 T^{7} + 271900824 T^{8} + 48087374 T^{9} - 15942782258 T^{10} - 8551895142 T^{11} + 710427770855 T^{12} + 556251544084 T^{13} - 21167261427546 T^{14} - 24242846421292 T^{15} + 406067677556641 T^{16} \))
$71$ (\( 1 + 12 T + 71 T^{2} \))(\( 1 - 20 T + 222 T^{2} - 1420 T^{3} + 5041 T^{4} \))(\( 1 - 130 T^{2} + 5041 T^{4} \))(\( 1 - 130 T^{2} + 5041 T^{4} \))(\( 1 - 100 T^{2} + 4134 T^{4} - 504100 T^{6} + 25411681 T^{8} \))(\( 1 - 100 T^{2} + 4134 T^{4} - 504100 T^{6} + 25411681 T^{8} \))(\( ( 1 - 10 T + 71 T^{2} )^{2} \))(\( ( 1 - 2 T + 71 T^{2} )^{6} \))(\( ( 1 - 134 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2}( 1 + 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 134 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 4 T + 144 T^{2} + 284 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 2 T + 116 T^{2} - 142 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 16 T + 232 T^{2} - 2376 T^{3} + 21730 T^{4} - 168696 T^{5} + 1169512 T^{6} - 5726576 T^{7} + 25411681 T^{8} )^{4} \))(\( ( 1 + 14 T + 194 T^{2} + 1648 T^{3} + 14264 T^{4} + 117008 T^{5} + 977954 T^{6} + 5010754 T^{7} + 25411681 T^{8} )^{4} \))(\( 1 - 94 T^{2} + 5041 T^{4} \))(\( 1 - 94 T^{2} + 5041 T^{4} \))(\( 1 - 464 T^{2} + 99532 T^{4} - 12936548 T^{6} + 1114829374 T^{8} - 65213138468 T^{10} + 2529275433292 T^{12} - 59438531739344 T^{14} + 645753531245761 T^{16} \))(\( 1 - 464 T^{2} + 99532 T^{4} - 12936548 T^{6} + 1114829374 T^{8} - 65213138468 T^{10} + 2529275433292 T^{12} - 59438531739344 T^{14} + 645753531245761 T^{16} \))
$73$ (\( 1 + 2 T + 73 T^{2} \))(\( 1 + 16 T + 190 T^{2} + 1168 T^{3} + 5329 T^{4} \))(\( 1 - 98 T^{2} + 5329 T^{4} \))(\( 1 - 98 T^{2} + 5329 T^{4} \))(\( ( 1 - 98 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 98 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} ) \))(\( 1 - 298 T^{2} + 43775 T^{4} - 3982284 T^{6} + 233276975 T^{8} - 8462675818 T^{10} + 151334226289 T^{12} \))(\( ( 1 - 8 T + 73 T^{2} )^{4} \))(\( ( 1 + 34 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 + 8 T + 73 T^{2} )^{4} \))(\( 1 + 11 T + 48 T^{2} + 803 T^{3} + 5329 T^{4} \))(\( 1 + T - 72 T^{2} + 73 T^{3} + 5329 T^{4} \))(\( 1 - 10 T - 21 T^{2} + 250 T^{3} + 2012 T^{4} + 18250 T^{5} - 111909 T^{6} - 3890170 T^{7} + 28398241 T^{8} \))(\( 1 + 8 T - 23 T^{2} - 472 T^{3} - 2432 T^{4} - 34456 T^{5} - 122567 T^{6} + 3112136 T^{7} + 28398241 T^{8} \))(\( 1 - 15256 T^{4} + 80862300 T^{8} + 94053698264 T^{12} - 2362018367550906 T^{16} + 2670959590242353624 T^{20} + \)\(65\!\cdots\!00\)\( T^{24} - \)\(34\!\cdots\!76\)\( T^{28} + \)\(65\!\cdots\!61\)\( T^{32} \))(\( 1 + 312 T^{2} + 46894 T^{4} + 4662008 T^{6} + 358067385 T^{8} + 22613492772 T^{10} + 1186535858958 T^{12} + 57781939528716 T^{14} + 3463839236542756 T^{16} + 307919955748527564 T^{18} + 33695531277831292878 T^{20} + \)\(34\!\cdots\!08\)\( T^{22} + \)\(28\!\cdots\!85\)\( T^{24} + \)\(20\!\cdots\!92\)\( T^{26} + \)\(10\!\cdots\!74\)\( T^{28} + \)\(38\!\cdots\!08\)\( T^{30} + \)\(65\!\cdots\!61\)\( T^{32} \))(\( 1 - 6 T + 85 T^{2} - 438 T^{3} + 5329 T^{4} \))(\( 1 - 6 T + 85 T^{2} - 438 T^{3} + 5329 T^{4} \))(\( 1 - 15 T + 280 T^{2} - 3075 T^{3} + 38779 T^{4} - 422928 T^{5} + 4017052 T^{6} - 39506334 T^{7} + 310273396 T^{8} - 2883962382 T^{9} + 21406870108 T^{10} - 164526181776 T^{11} + 1101255387739 T^{12} - 6374695148475 T^{13} + 42373583360920 T^{14} - 165710977786455 T^{15} + 806460091894081 T^{16} \))(\( 1 - 15 T + 280 T^{2} - 3075 T^{3} + 38779 T^{4} - 422928 T^{5} + 4017052 T^{6} - 39506334 T^{7} + 310273396 T^{8} - 2883962382 T^{9} + 21406870108 T^{10} - 164526181776 T^{11} + 1101255387739 T^{12} - 6374695148475 T^{13} + 42373583360920 T^{14} - 165710977786455 T^{15} + 806460091894081 T^{16} \))
$79$ (\( 1 - 8 T + 79 T^{2} \))(\( 1 - 8 T + 94 T^{2} - 632 T^{3} + 6241 T^{4} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 - T + 150 T^{2} - 79 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - T + 150 T^{2} - 79 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 + 4 T + 79 T^{2} )^{2} \))(\( ( 1 + 12 T + 221 T^{2} + 1576 T^{3} + 17459 T^{4} + 74892 T^{5} + 493039 T^{6} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{4} \))(\( ( 1 + T + 79 T^{2} )^{4} \))(\( ( 1 - 8 T + 79 T^{2} )^{4} \))(\( ( 1 - 17 T + 79 T^{2} )( 1 + 4 T + 79 T^{2} ) \))(\( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} \))(\( 1 + 2 T - 123 T^{2} - 62 T^{3} + 9572 T^{4} - 4898 T^{5} - 767643 T^{6} + 986078 T^{7} + 38950081 T^{8} \))(\( 1 + 6 T - 23 T^{2} - 594 T^{3} - 5604 T^{4} - 46926 T^{5} - 143543 T^{6} + 2958234 T^{7} + 38950081 T^{8} \))(\( ( 1 - 312 T^{2} + 58396 T^{4} - 7293320 T^{6} + 672141766 T^{8} - 45517610120 T^{10} + 2274528930076 T^{12} - 75843286122552 T^{14} + 1517108809906561 T^{16} )^{2} \))(\( ( 1 + 8 T - 98 T^{2} - 1128 T^{3} - 3647 T^{4} - 31028 T^{5} - 546546 T^{6} + 5486636 T^{7} + 152161556 T^{8} + 433444244 T^{9} - 3410993586 T^{10} - 15298014092 T^{11} - 142050945407 T^{12} - 3470919618072 T^{13} - 23822570641058 T^{14} + 153631271889272 T^{15} + 1517108809906561 T^{16} )^{2} \))(\( 1 - 16 T + 177 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 - 16 T + 177 T^{2} - 1264 T^{3} + 6241 T^{4} \))(\( 1 + 29 T + 294 T^{2} + 1975 T^{3} + 27377 T^{4} + 260496 T^{5} + 598654 T^{6} + 2403434 T^{7} + 77714340 T^{8} + 189871286 T^{9} + 3736199614 T^{10} + 128434687344 T^{11} + 1066336367537 T^{12} + 6077186388025 T^{13} + 71467711923174 T^{14} + 556913360598611 T^{15} + 1517108809906561 T^{16} \))(\( 1 + 29 T + 294 T^{2} + 1975 T^{3} + 27377 T^{4} + 260496 T^{5} + 598654 T^{6} + 2403434 T^{7} + 77714340 T^{8} + 189871286 T^{9} + 3736199614 T^{10} + 128434687344 T^{11} + 1066336367537 T^{12} + 6077186388025 T^{13} + 71467711923174 T^{14} + 556913360598611 T^{15} + 1517108809906561 T^{16} \))
$83$ (\( 1 + 4 T + 83 T^{2} \))(\( 1 + 16 T + 150 T^{2} + 1328 T^{3} + 6889 T^{4} \))(\( ( 1 + 83 T^{2} )^{2} \))(\( ( 1 + 83 T^{2} )^{2} \))(\( ( 1 - 12 T + 70 T^{2} - 996 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 + 12 T + 70 T^{2} + 996 T^{3} + 6889 T^{4} )^{2} \))(\( 1 - 102 T^{2} + 6889 T^{4} \))(\( 1 - 306 T^{2} + 47783 T^{4} - 4793948 T^{6} + 329177087 T^{8} - 14522246226 T^{10} + 326940373369 T^{12} \))(\( ( 1 - 18 T + 83 T^{2} )^{2}( 1 + 18 T + 83 T^{2} )^{2} \))(\( ( 1 - 86 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 18 T + 83 T^{2} )^{2}( 1 + 18 T + 83 T^{2} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 2 T + 83 T^{2} )^{2} \))(\( ( 1 - 8 T + 180 T^{2} - 664 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 - 6 T + 28 T^{2} - 498 T^{3} + 6889 T^{4} )^{2} \))(\( 1 + 5000 T^{4} + 95818588 T^{8} + 596752860728 T^{12} + 4571727903671302 T^{16} + 28320888822097717688 T^{20} + \)\(21\!\cdots\!08\)\( T^{24} + \)\(53\!\cdots\!00\)\( T^{28} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( ( 1 - 516 T^{2} + 125904 T^{4} - 18859016 T^{6} + 1891189930 T^{8} - 129919761224 T^{10} + 5975192447184 T^{12} - 168701232658404 T^{14} + 2252292232139041 T^{16} )^{2} \))(\( ( 1 + 9 T + 83 T^{2} )^{2} \))(\( ( 1 - 9 T + 83 T^{2} )^{2} \))(\( ( 1 - 15 T + 380 T^{2} - 3759 T^{3} + 49260 T^{4} - 311997 T^{5} + 2617820 T^{6} - 8576805 T^{7} + 47458321 T^{8} )^{2} \))(\( ( 1 + 15 T + 380 T^{2} + 3759 T^{3} + 49260 T^{4} + 311997 T^{5} + 2617820 T^{6} + 8576805 T^{7} + 47458321 T^{8} )^{2} \))
$89$ (\( 1 + 6 T + 89 T^{2} \))(\( ( 1 + 2 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 18 T + 226 T^{2} + 1602 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 - 18 T + 226 T^{2} - 1602 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 14 T + 319 T^{2} + 2532 T^{3} + 28391 T^{4} + 110894 T^{5} + 704969 T^{6} )^{2} \))(\( ( 1 + 70 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 89 T^{2} )^{4} \))(\( ( 1 + 70 T^{2} + 7921 T^{4} )^{2} \))(\( 1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 - 12 T + 55 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 - 16 T + 32 T^{2} - 736 T^{3} + 19471 T^{4} - 65504 T^{5} + 253472 T^{6} - 11279504 T^{7} + 62742241 T^{8} \))(\( 1 + 6 T - 4 T^{2} - 828 T^{3} - 9525 T^{4} - 73692 T^{5} - 31684 T^{6} + 4229814 T^{7} + 62742241 T^{8} \))(\( ( 1 + 576 T^{2} + 155068 T^{4} + 25338304 T^{6} + 2740378246 T^{8} + 200704705984 T^{10} + 9729313827388 T^{12} + 286261223593536 T^{14} + 3936588805702081 T^{16} )^{2} \))(\( ( 1 - 8 T - 98 T^{2} + 1004 T^{3} + 4584 T^{4} - 89290 T^{5} + 1051584 T^{6} + 2927032 T^{7} - 142835833 T^{8} + 260505848 T^{9} + 8329596864 T^{10} - 62946682010 T^{11} + 287610432744 T^{12} + 5606395686796 T^{13} - 48704166514178 T^{14} - 353850679164232 T^{15} + 3936588805702081 T^{16} )^{2} \))(\( 1 + 3 T - 80 T^{2} + 267 T^{3} + 7921 T^{4} \))(\( 1 - 3 T - 80 T^{2} - 267 T^{3} + 7921 T^{4} \))(\( 1 + 3 T - 53 T^{2} + 2820 T^{3} + 14227 T^{4} - 160275 T^{5} + 3467116 T^{6} + 26593569 T^{7} - 193500020 T^{8} + 2366827641 T^{9} + 27463025836 T^{10} - 112988906475 T^{11} + 892633862707 T^{12} + 15747047646180 T^{13} - 26340008420933 T^{14} + 132694004686587 T^{15} + 3936588805702081 T^{16} \))(\( 1 - 3 T - 53 T^{2} - 2820 T^{3} + 14227 T^{4} + 160275 T^{5} + 3467116 T^{6} - 26593569 T^{7} - 193500020 T^{8} - 2366827641 T^{9} + 27463025836 T^{10} + 112988906475 T^{11} + 892633862707 T^{12} - 15747047646180 T^{13} - 26340008420933 T^{14} - 132694004686587 T^{15} + 3936588805702081 T^{16} \))
$97$ (\( 1 + 18 T + 97 T^{2} \))(\( 1 - 8 T + 190 T^{2} - 776 T^{3} + 9409 T^{4} \))(\( 1 - 146 T^{2} + 9409 T^{4} \))(\( 1 - 146 T^{2} + 9409 T^{4} \))(\( 1 - 265 T^{2} + 32736 T^{4} - 2493385 T^{6} + 88529281 T^{8} \))(\( 1 - 265 T^{2} + 32736 T^{4} - 2493385 T^{6} + 88529281 T^{8} \))(\( 1 - 190 T^{2} + 9409 T^{4} \))(\( 1 - 26 T^{2} + 8719 T^{4} + 446932 T^{6} + 82037071 T^{8} - 2301761306 T^{10} + 832972004929 T^{12} \))(\( ( 1 - 8 T + 97 T^{2} )^{4} \))(\( ( 1 - 149 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 + 8 T + 97 T^{2} )^{4} \))(\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 6 T + 97 T^{2} )^{2} \))(\( ( 1 + 16 T + 250 T^{2} + 1552 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 - 16 T + 210 T^{2} - 1552 T^{3} + 9409 T^{4} )^{2} \))(\( 1 - 55064 T^{4} + 1465436892 T^{8} - 24336256217256 T^{12} + 274732504520067270 T^{16} - \)\(21\!\cdots\!36\)\( T^{20} + \)\(11\!\cdots\!12\)\( T^{24} - \)\(38\!\cdots\!24\)\( T^{28} + \)\(61\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 756 T^{2} + 251932 T^{4} - 48333356 T^{6} + 5838717718 T^{8} - 454768546604 T^{10} + 22303358820892 T^{12} - 629726835726324 T^{14} + 7837433594376961 T^{16} )^{2} \))(\( 1 - 86 T^{2} + 9409 T^{4} \))(\( 1 - 86 T^{2} + 9409 T^{4} \))(\( 1 - 368 T^{2} + 81676 T^{4} - 12257504 T^{6} + 1385094598 T^{8} - 115330855136 T^{10} + 7230717554956 T^{12} - 306533697813872 T^{14} + 7837433594376961 T^{16} \))(\( 1 - 368 T^{2} + 81676 T^{4} - 12257504 T^{6} + 1385094598 T^{8} - 115330855136 T^{10} + 7230717554956 T^{12} - 306533697813872 T^{14} + 7837433594376961 T^{16} \))
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