Properties

Label 287.2
Level 287
Weight 2
Dimension 3019
Nonzero newspaces 16
Newform subspaces 30
Sturm bound 13440
Trace bound 3

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Defining parameters

Level: \( N \) = \( 287 = 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 30 \)
Sturm bound: \(13440\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(287))\).

Total New Old
Modular forms 3600 3411 189
Cusp forms 3121 3019 102
Eisenstein series 479 392 87

Trace form

\( 3019q - 83q^{2} - 84q^{3} - 87q^{4} - 86q^{5} - 92q^{6} - 101q^{7} - 215q^{8} - 93q^{9} + O(q^{10}) \) \( 3019q - 83q^{2} - 84q^{3} - 87q^{4} - 86q^{5} - 92q^{6} - 101q^{7} - 215q^{8} - 93q^{9} - 98q^{10} - 92q^{11} - 108q^{12} - 94q^{13} - 103q^{14} - 224q^{15} - 111q^{16} - 98q^{17} - 119q^{18} - 100q^{19} - 122q^{20} - 104q^{21} - 236q^{22} - 104q^{23} - 140q^{24} - 111q^{25} - 122q^{26} - 120q^{27} - 107q^{28} - 230q^{29} - 72q^{30} - 72q^{31} - 3q^{32} - 8q^{33} - 34q^{34} - 66q^{35} - 11q^{36} + 2q^{37} - 60q^{38} + 24q^{39} + 110q^{40} - 81q^{41} - 52q^{42} - 204q^{43} + 76q^{44} + 2q^{45} - 72q^{46} - 8q^{47} + 76q^{48} - 61q^{49} - 193q^{50} - 32q^{51} - 38q^{52} - 94q^{53} - 120q^{54} - 152q^{55} - 115q^{56} - 280q^{57} - 170q^{58} - 140q^{59} - 248q^{60} - 142q^{61} - 176q^{62} - 113q^{63} - 327q^{64} - 144q^{65} - 64q^{66} - 28q^{67} - 6q^{68} - 16q^{69} + 82q^{70} - 112q^{71} + 85q^{72} + 6q^{73} + 46q^{74} + 116q^{75} + 380q^{76} - 32q^{77} + 32q^{78} + 214q^{80} + 179q^{81} + 277q^{82} - 84q^{83} + 152q^{84} + 32q^{85} + 188q^{86} - 40q^{87} + 140q^{88} - 10q^{89} + 286q^{90} + 46q^{91} - 128q^{92} - 48q^{93} + 136q^{94} - 40q^{95} + 68q^{96} - 18q^{97} - 3q^{98} - 236q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(287))\)

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
287.2.a \(\chi_{287}(1, \cdot)\) 287.2.a.a 2 1
287.2.a.b 2
287.2.a.c 3
287.2.a.d 3
287.2.a.e 5
287.2.a.f 6
287.2.c \(\chi_{287}(204, \cdot)\) 287.2.c.a 10 1
287.2.c.b 12
287.2.e \(\chi_{287}(165, \cdot)\) 287.2.e.a 4 2
287.2.e.b 4
287.2.e.c 10
287.2.e.d 34
287.2.f \(\chi_{287}(50, \cdot)\) 287.2.f.a 40 2
287.2.h \(\chi_{287}(57, \cdot)\) 287.2.h.a 4 4
287.2.h.b 4
287.2.h.c 40
287.2.h.d 40
287.2.j \(\chi_{287}(81, \cdot)\) 287.2.j.a 52 2
287.2.l \(\chi_{287}(27, \cdot)\) 287.2.l.a 104 4
287.2.n \(\chi_{287}(64, \cdot)\) 287.2.n.a 88 4
287.2.r \(\chi_{287}(9, \cdot)\) 287.2.r.a 4 4
287.2.r.b 4
287.2.r.c 96
287.2.s \(\chi_{287}(16, \cdot)\) 287.2.s.a 208 8
287.2.u \(\chi_{287}(8, \cdot)\) 287.2.u.a 160 8
287.2.w \(\chi_{287}(3, \cdot)\) 287.2.w.a 208 8
287.2.z \(\chi_{287}(4, \cdot)\) 287.2.z.a 208 8
287.2.bb \(\chi_{287}(6, \cdot)\) 287.2.bb.a 416 16
287.2.bc \(\chi_{287}(2, \cdot)\) 287.2.bc.a 416 16
287.2.be \(\chi_{287}(12, \cdot)\) 287.2.be.a 832 32

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(287))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(287)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4} \))(\( 1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4} \))(\( 1 - T + 2 T^{2} - T^{3} + 4 T^{4} - 4 T^{5} + 8 T^{6} \))(\( 1 - 4 T + 9 T^{2} - 15 T^{3} + 18 T^{4} - 16 T^{5} + 8 T^{6} \))(\( 1 + T + 4 T^{2} + 4 T^{3} + 10 T^{4} + 11 T^{5} + 20 T^{6} + 16 T^{7} + 32 T^{8} + 16 T^{9} + 32 T^{10} \))(\( 1 + T + 2 T^{2} + 3 T^{4} + 4 T^{5} + 17 T^{6} + 8 T^{7} + 12 T^{8} + 32 T^{10} + 32 T^{11} + 64 T^{12} \))(\( ( 1 - 2 T + 4 T^{2} - 6 T^{3} + 13 T^{4} - 19 T^{5} + 26 T^{6} - 24 T^{7} + 32 T^{8} - 32 T^{9} + 32 T^{10} )^{2} \))(\( ( 1 + 2 T + 5 T^{2} + 10 T^{3} + 16 T^{4} + 25 T^{5} + 39 T^{6} + 50 T^{7} + 64 T^{8} + 80 T^{9} + 80 T^{10} + 64 T^{11} + 64 T^{12} )^{2} \))(\( 1 + T - 2 T^{2} - T^{3} + 3 T^{4} - 2 T^{5} - 8 T^{6} + 8 T^{7} + 16 T^{8} \))(\( ( 1 - 2 T^{2} + 4 T^{4} )^{2} \))(\( 1 - 2 T + 2 T^{3} - 6 T^{4} + 11 T^{5} - 9 T^{6} + 8 T^{7} + 11 T^{8} - 44 T^{9} + 61 T^{10} - 88 T^{11} + 44 T^{12} + 64 T^{13} - 144 T^{14} + 352 T^{15} - 384 T^{16} + 256 T^{17} - 1024 T^{19} + 1024 T^{20} \))(\( 1 - 2 T^{2} + 4 T^{4} - 8 T^{6} + 16 T^{8} \))(\( 1 - T + 4 T^{2} - 2 T^{3} + 9 T^{4} - 4 T^{5} + 16 T^{6} - 8 T^{7} + 16 T^{8} \))(\( 1 + 3 T^{2} + 5 T^{4} + 12 T^{6} + 16 T^{8} \))(\( 1 + 3 T^{2} + 5 T^{4} + 12 T^{6} + 16 T^{8} \))
$3$ (\( 1 + 3 T + 7 T^{2} + 9 T^{3} + 9 T^{4} \))(\( 1 + T + 5 T^{2} + 3 T^{3} + 9 T^{4} \))(\( 1 + T + T^{2} + 3 T^{3} + 3 T^{4} + 9 T^{5} + 27 T^{6} \))(\( 1 - 5 T + 15 T^{2} - 31 T^{3} + 45 T^{4} - 45 T^{5} + 27 T^{6} \))(\( 1 - 4 T + 15 T^{2} - 38 T^{3} + 87 T^{4} - 157 T^{5} + 261 T^{6} - 342 T^{7} + 405 T^{8} - 324 T^{9} + 243 T^{10} \))(\( 1 + 4 T + 10 T^{2} + 14 T^{3} + 26 T^{4} + 57 T^{5} + 130 T^{6} + 171 T^{7} + 234 T^{8} + 378 T^{9} + 810 T^{10} + 972 T^{11} + 729 T^{12} \))(\( 1 - 10 T^{2} + 55 T^{4} - 224 T^{6} + 769 T^{8} - 2417 T^{10} + 6921 T^{12} - 18144 T^{14} + 40095 T^{16} - 65610 T^{18} + 59049 T^{20} \))(\( 1 - 16 T^{2} + 132 T^{4} - 728 T^{6} + 3044 T^{8} - 10563 T^{10} + 32896 T^{12} - 95067 T^{14} + 246564 T^{16} - 530712 T^{18} + 866052 T^{20} - 944784 T^{22} + 531441 T^{24} \))(\( ( 1 + T - 2 T^{2} + 3 T^{3} + 9 T^{4} )^{2} \))(\( 1 + T - 2 T^{2} - 3 T^{3} - 3 T^{4} - 9 T^{5} - 18 T^{6} + 27 T^{7} + 81 T^{8} \))(\( 1 - 2 T - 3 T^{2} - 4 T^{3} + 23 T^{4} + 28 T^{5} + 7 T^{6} - 207 T^{7} - 94 T^{8} + 95 T^{9} + 1087 T^{10} + 285 T^{11} - 846 T^{12} - 5589 T^{13} + 567 T^{14} + 6804 T^{15} + 16767 T^{16} - 8748 T^{17} - 19683 T^{18} - 39366 T^{19} + 59049 T^{20} \))(\( ( 1 + T^{2} + 9 T^{4} )^{2} \))(\( ( 1 - 3 T + 7 T^{2} - 9 T^{3} + 9 T^{4} )^{2} \))(\( 1 + 2 T + 5 T^{2} + 10 T^{3} + 16 T^{4} + 30 T^{5} + 45 T^{6} + 54 T^{7} + 81 T^{8} \))(\( 1 - 4 T + 5 T^{2} + 4 T^{3} - 20 T^{4} + 12 T^{5} + 45 T^{6} - 108 T^{7} + 81 T^{8} \))
$5$ (\( 1 + T + 9 T^{2} + 5 T^{3} + 25 T^{4} \))(\( 1 - T + 9 T^{2} - 5 T^{3} + 25 T^{4} \))(\( ( 1 - 2 T + 5 T^{2} )^{3} \))(\( 1 - 2 T + 7 T^{2} - 12 T^{3} + 35 T^{4} - 50 T^{5} + 125 T^{6} \))(\( 1 + 5 T + 14 T^{2} + 14 T^{3} - 11 T^{4} - 86 T^{5} - 55 T^{6} + 350 T^{7} + 1750 T^{8} + 3125 T^{9} + 3125 T^{10} \))(\( 1 + T + T^{2} + 9 T^{3} - 5 T^{4} - 6 T^{5} + 134 T^{6} - 30 T^{7} - 125 T^{8} + 1125 T^{9} + 625 T^{10} + 3125 T^{11} + 15625 T^{12} \))(\( ( 1 + 5 T + 26 T^{2} + 84 T^{3} + 261 T^{4} + 598 T^{5} + 1305 T^{6} + 2100 T^{7} + 3250 T^{8} + 3125 T^{9} + 3125 T^{10} )^{2} \))(\( ( 1 - T + 7 T^{2} - 5 T^{3} + 39 T^{4} + 10 T^{5} + 114 T^{6} + 50 T^{7} + 975 T^{8} - 625 T^{9} + 4375 T^{10} - 3125 T^{11} + 15625 T^{12} )^{2} \))(\( ( 1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4} )^{2} \))(\( 1 - T - 6 T^{2} + 3 T^{3} + 19 T^{4} + 15 T^{5} - 150 T^{6} - 125 T^{7} + 625 T^{8} \))(\( 1 + 2 T - 13 T^{2} - 8 T^{3} + 119 T^{4} - 38 T^{5} - 689 T^{6} + 515 T^{7} + 3022 T^{8} - 1229 T^{9} - 12631 T^{10} - 6145 T^{11} + 75550 T^{12} + 64375 T^{13} - 430625 T^{14} - 118750 T^{15} + 1859375 T^{16} - 625000 T^{17} - 5078125 T^{18} + 3906250 T^{19} + 9765625 T^{20} \))(\( 1 + T - 4 T^{2} - 9 T^{3} + 11 T^{4} - 45 T^{5} - 100 T^{6} + 125 T^{7} + 625 T^{8} \))(\( 1 + 2 T - T^{2} + 8 T^{3} + 41 T^{4} + 40 T^{5} - 25 T^{6} + 250 T^{7} + 625 T^{8} \))(\( ( 1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4} )^{2} \))(\( ( 1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4} )^{2} \))
$7$ (\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{5} \))(\( ( 1 + T )^{6} \))(\( ( 1 + T^{2} )^{5} \))(\( ( 1 + T^{2} )^{6} \))(\( ( 1 + 4 T + 7 T^{2} )^{2} \))(\( ( 1 + T + 7 T^{2} )^{2} \))(\( 1 - 8 T + 36 T^{2} - 115 T^{3} + 302 T^{4} - 783 T^{5} + 2114 T^{6} - 5635 T^{7} + 12348 T^{8} - 19208 T^{9} + 16807 T^{10} \))(\( 1 - T + T^{2} - T^{3} + T^{4} \))(\( 1 + T + T^{2} + T^{3} + T^{4} \))(\( ( 1 - 5 T + 7 T^{2} )^{2} \))(\( 1 + 11 T^{2} + 49 T^{4} \))
$11$ (\( 1 + 17 T^{2} + 121 T^{4} \))(\( ( 1 + T + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 11 T^{2} )^{3} \))(\( 1 + 4 T + 29 T^{2} + 80 T^{3} + 319 T^{4} + 484 T^{5} + 1331 T^{6} \))(\( 1 - 2 T - 8 T^{2} + 52 T^{3} + 103 T^{4} - 844 T^{5} + 1133 T^{6} + 6292 T^{7} - 10648 T^{8} - 29282 T^{9} + 161051 T^{10} \))(\( 1 - 6 T + 37 T^{2} - 112 T^{3} + 567 T^{4} - 1994 T^{5} + 8902 T^{6} - 21934 T^{7} + 68607 T^{8} - 149072 T^{9} + 541717 T^{10} - 966306 T^{11} + 1771561 T^{12} \))(\( 1 - 64 T^{2} + 2166 T^{4} - 49150 T^{6} + 814601 T^{8} - 10239268 T^{10} + 98566721 T^{12} - 719605150 T^{14} + 3837201126 T^{16} - 13718968384 T^{18} + 25937424601 T^{20} \))(\( 1 - 26 T^{2} + 543 T^{4} - 6538 T^{6} + 81003 T^{8} - 680588 T^{10} + 8259370 T^{12} - 82351148 T^{14} + 1185964923 T^{16} - 11582465818 T^{18} + 116396872383 T^{20} - 674373039626 T^{22} + 3138428376721 T^{24} \))(\( ( 1 + T - 10 T^{2} + 11 T^{3} + 121 T^{4} )^{2} \))(\( 1 - 5 T - 15 T^{3} + 229 T^{4} - 165 T^{5} - 6655 T^{7} + 14641 T^{8} \))(\( 1 - 6 T - 16 T^{2} + 126 T^{3} + 272 T^{4} - 1391 T^{5} - 6093 T^{6} + 10447 T^{7} + 110443 T^{8} - 53446 T^{9} - 1352963 T^{10} - 587906 T^{11} + 13363603 T^{12} + 13904957 T^{13} - 89207613 T^{14} - 224021941 T^{15} + 481864592 T^{16} + 2455383546 T^{17} - 3429742096 T^{18} - 14147686146 T^{19} + 25937424601 T^{20} \))(\( 1 - T^{2} + 30 T^{3} + 91 T^{4} + 330 T^{5} - 121 T^{6} + 14641 T^{8} \))(\( 1 - 7 T + 23 T^{2} - 99 T^{3} + 440 T^{4} - 1089 T^{5} + 2783 T^{6} - 9317 T^{7} + 14641 T^{8} \))(\( 1 + 8 T + 41 T^{2} + 152 T^{3} + 532 T^{4} + 1672 T^{5} + 4961 T^{6} + 10648 T^{7} + 14641 T^{8} \))(\( 1 - 10 T + 41 T^{2} - 82 T^{3} + 136 T^{4} - 902 T^{5} + 4961 T^{6} - 13310 T^{7} + 14641 T^{8} \))
$13$ (\( ( 1 + 3 T + 13 T^{2} )^{2} \))(\( 1 + 8 T + 37 T^{2} + 104 T^{3} + 169 T^{4} \))(\( 1 - 9 T + 61 T^{2} - 249 T^{3} + 793 T^{4} - 1521 T^{5} + 2197 T^{6} \))(\( 1 - 7 T + 39 T^{2} - 133 T^{3} + 507 T^{4} - 1183 T^{5} + 2197 T^{6} \))(\( 1 - 5 T + 56 T^{2} - 180 T^{3} + 1219 T^{4} - 2941 T^{5} + 15847 T^{6} - 30420 T^{7} + 123032 T^{8} - 142805 T^{9} + 371293 T^{10} \))(\( 1 - 7 T + 29 T^{2} - 125 T^{3} + 387 T^{4} - 877 T^{5} + 3108 T^{6} - 11401 T^{7} + 65403 T^{8} - 274625 T^{9} + 828269 T^{10} - 2599051 T^{11} + 4826809 T^{12} \))(\( 1 - 59 T^{2} + 1942 T^{4} - 42976 T^{6} + 737713 T^{8} - 10374425 T^{10} + 124673497 T^{12} - 1227437536 T^{14} + 9373663078 T^{16} - 48128112539 T^{18} + 137858491849 T^{20} \))(\( 1 - 101 T^{2} + 4641 T^{4} - 128343 T^{6} + 2426323 T^{8} - 35344595 T^{10} + 463046060 T^{12} - 5973236555 T^{14} + 69298211203 T^{16} - 619487147487 T^{18} + 3785806276161 T^{20} - 13923707676749 T^{22} + 23298085122481 T^{24} \))(\( ( 1 + 6 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 + T + 23 T^{2} + 13 T^{3} + 169 T^{4} )^{2} \))(\( ( 1 - 2 T + 57 T^{2} - 85 T^{3} + 1376 T^{4} - 1541 T^{5} + 17888 T^{6} - 14365 T^{7} + 125229 T^{8} - 57122 T^{9} + 371293 T^{10} )^{2} \))(\( 1 + 9 T + 18 T^{2} - 115 T^{3} - 789 T^{4} - 1495 T^{5} + 3042 T^{6} + 19773 T^{7} + 28561 T^{8} \))(\( 1 + 5 T + 2 T^{2} + 25 T^{3} + 259 T^{4} + 325 T^{5} + 338 T^{6} + 10985 T^{7} + 28561 T^{8} \))(\( 1 + 62 T^{4} + 28561 T^{8} \))(\( 1 + 62 T^{4} + 28561 T^{8} \))
$17$ (\( 1 + 6 T + 23 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 + 4 T + 33 T^{2} + 68 T^{3} + 289 T^{4} \))(\( 1 - T + 29 T^{2} - 61 T^{3} + 493 T^{4} - 289 T^{5} + 4913 T^{6} \))(\( 1 - 3 T + 5 T^{2} - 5 T^{3} + 85 T^{4} - 867 T^{5} + 4913 T^{6} \))(\( 1 - 13 T + 110 T^{2} - 580 T^{3} + 2611 T^{4} - 10157 T^{5} + 44387 T^{6} - 167620 T^{7} + 540430 T^{8} - 1085773 T^{9} + 1419857 T^{10} \))(\( 1 - 7 T + 105 T^{2} - 569 T^{3} + 4539 T^{4} - 18913 T^{5} + 103464 T^{6} - 321521 T^{7} + 1311771 T^{8} - 2795497 T^{9} + 8769705 T^{10} - 9938999 T^{11} + 24137569 T^{12} \))(\( 1 - 115 T^{2} + 6566 T^{4} - 242720 T^{6} + 6399649 T^{8} - 125429145 T^{10} + 1849498561 T^{12} - 20272217120 T^{14} + 158487278054 T^{16} - 802212105715 T^{18} + 2015993900449 T^{20} \))(\( 1 - 97 T^{2} + 4737 T^{4} - 151495 T^{6} + 3587155 T^{8} - 69463071 T^{10} + 1214041604 T^{12} - 20074827519 T^{14} + 299602772755 T^{16} - 3656721015655 T^{18} + 33044162998017 T^{20} - 195551408343553 T^{22} + 582622237229761 T^{24} \))(\( 1 + 4 T - 17 T^{2} - 4 T^{3} + 528 T^{4} - 68 T^{5} - 4913 T^{6} + 19652 T^{7} + 83521 T^{8} \))(\( 1 + 3 T + 2 T^{2} - 81 T^{3} - 393 T^{4} - 1377 T^{5} + 578 T^{6} + 14739 T^{7} + 83521 T^{8} \))(\( 1 - 3 T - 51 T^{2} + 126 T^{3} + 1418 T^{4} - 2471 T^{5} - 32276 T^{6} + 39771 T^{7} + 626554 T^{8} - 325955 T^{9} - 10861899 T^{10} - 5541235 T^{11} + 181074106 T^{12} + 195394923 T^{13} - 2695723796 T^{14} - 3508466647 T^{15} + 34227072842 T^{16} + 51702672798 T^{17} - 355763629491 T^{18} - 355763629491 T^{19} + 2015993900449 T^{20} \))(\( 1 + 12 T + 77 T^{2} + 420 T^{3} + 1981 T^{4} + 7140 T^{5} + 22253 T^{6} + 58956 T^{7} + 83521 T^{8} \))(\( 1 + 13 T + 52 T^{2} - 25 T^{3} - 729 T^{4} - 425 T^{5} + 15028 T^{6} + 63869 T^{7} + 83521 T^{8} \))(\( 1 - 12 T + 36 T^{2} + 204 T^{3} - 1777 T^{4} + 3468 T^{5} + 10404 T^{6} - 58956 T^{7} + 83521 T^{8} \))(\( 1 + 36 T^{2} + 60 T^{3} + 671 T^{4} + 1020 T^{5} + 10404 T^{6} + 83521 T^{8} \))
$19$ (\( 1 + 3 T + 29 T^{2} + 57 T^{3} + 361 T^{4} \))(\( 1 + T + 27 T^{2} + 19 T^{3} + 361 T^{4} \))(\( 1 - 13 T + 109 T^{2} - 555 T^{3} + 2071 T^{4} - 4693 T^{5} + 6859 T^{6} \))(\( 1 + 11 T + 81 T^{2} + 431 T^{3} + 1539 T^{4} + 3971 T^{5} + 6859 T^{6} \))(\( 1 + 47 T^{2} - 132 T^{3} + 851 T^{4} - 5017 T^{5} + 16169 T^{6} - 47652 T^{7} + 322373 T^{8} + 2476099 T^{10} \))(\( 1 - 2 T + 46 T^{2} - 42 T^{3} + 1172 T^{4} + 383 T^{5} + 21830 T^{6} + 7277 T^{7} + 423092 T^{8} - 288078 T^{9} + 5994766 T^{10} - 4952198 T^{11} + 47045881 T^{12} \))(\( 1 - 94 T^{2} + 4603 T^{4} - 151512 T^{6} + 3820801 T^{8} - 79003953 T^{10} + 1379309161 T^{12} - 19745195352 T^{14} + 216552190243 T^{16} - 1596454925854 T^{18} + 6131066257801 T^{20} \))(\( 1 - 108 T^{2} + 6204 T^{4} - 246096 T^{6} + 7515428 T^{8} - 186417687 T^{10} + 3860756896 T^{12} - 67296785007 T^{14} + 979418092388 T^{16} - 11577803130576 T^{18} + 105366025106364 T^{20} - 662155155842508 T^{22} + 2213314919066161 T^{24} \))(\( 1 - 6 T + 9 T^{2} + 66 T^{3} - 316 T^{4} + 1254 T^{5} + 3249 T^{6} - 41154 T^{7} + 130321 T^{8} \))(\( 1 - 25 T^{2} + 264 T^{4} - 9025 T^{6} + 130321 T^{8} \))(\( 1 + 7 T - 30 T^{2} - 229 T^{3} + 765 T^{4} + 2984 T^{5} - 32505 T^{6} - 73291 T^{7} + 742704 T^{8} + 1021299 T^{9} - 11963649 T^{10} + 19404681 T^{11} + 268116144 T^{12} - 502702969 T^{13} - 4236084105 T^{14} + 7388679416 T^{15} + 35990098965 T^{16} - 204696628231 T^{17} - 509506891230 T^{18} + 2258813884453 T^{19} + 6131066257801 T^{20} \))(\( 1 + 13 T + 50 T^{2} - 37 T^{3} - 791 T^{4} - 703 T^{5} + 18050 T^{6} + 89167 T^{7} + 130321 T^{8} \))(\( 1 - 2 T + 5 T^{2} - 82 T^{3} + 529 T^{4} - 1558 T^{5} + 1805 T^{6} - 13718 T^{7} + 130321 T^{8} \))(\( ( 1 - 8 T + 19 T^{2} )^{2}( 1 + 11 T^{2} + 361 T^{4} ) \))(\( ( 1 + 7 T + 19 T^{2} )^{2}( 1 + 26 T^{2} + 361 T^{4} ) \))
$23$ (\( 1 - 3 T + 47 T^{2} - 69 T^{3} + 529 T^{4} \))(\( 1 + 5 T + 51 T^{2} + 115 T^{3} + 529 T^{4} \))(\( 1 + 11 T + 101 T^{2} + 525 T^{3} + 2323 T^{4} + 5819 T^{5} + 12167 T^{6} \))(\( 1 + 13 T + 109 T^{2} + 627 T^{3} + 2507 T^{4} + 6877 T^{5} + 12167 T^{6} \))(\( 1 - 2 T + 49 T^{2} - 158 T^{3} + 1885 T^{4} - 3835 T^{5} + 43355 T^{6} - 83582 T^{7} + 596183 T^{8} - 559682 T^{9} + 6436343 T^{10} \))(\( 1 - 20 T + 290 T^{2} - 2858 T^{3} + 22970 T^{4} - 145271 T^{5} + 774478 T^{6} - 3341233 T^{7} + 12151130 T^{8} - 34773286 T^{9} + 81153890 T^{10} - 128726860 T^{11} + 148035889 T^{12} \))(\( ( 1 + 2 T + 59 T^{2} + 176 T^{3} + 2067 T^{4} + 5357 T^{5} + 47541 T^{6} + 93104 T^{7} + 717853 T^{8} + 559682 T^{9} + 6436343 T^{10} )^{2} \))(\( ( 1 - 8 T + 88 T^{2} - 560 T^{3} + 4126 T^{4} - 20273 T^{5} + 115538 T^{6} - 466279 T^{7} + 2182654 T^{8} - 6813520 T^{9} + 24626008 T^{10} - 51490744 T^{11} + 148035889 T^{12} )^{2} \))(\( 1 - 4 T + 11 T^{2} + 164 T^{3} - 872 T^{4} + 3772 T^{5} + 5819 T^{6} - 48668 T^{7} + 279841 T^{8} \))(\( 1 - 4 T - 21 T^{2} + 36 T^{3} + 472 T^{4} + 828 T^{5} - 11109 T^{6} - 48668 T^{7} + 279841 T^{8} \))(\( 1 - 77 T^{2} + 38 T^{3} + 3059 T^{4} - 2146 T^{5} - 88609 T^{6} + 40601 T^{7} + 2204294 T^{8} - 225757 T^{9} - 51333237 T^{10} - 5192411 T^{11} + 1166071526 T^{12} + 493992367 T^{13} - 24796431169 T^{14} - 13812392078 T^{15} + 452841784451 T^{16} + 129383366986 T^{17} - 6029945866637 T^{18} + 41426511213649 T^{20} \))(\( 1 + 4 T + 23 T^{2} + 150 T^{3} + 1151 T^{4} + 3450 T^{5} + 12167 T^{6} + 48668 T^{7} + 279841 T^{8} \))(\( 1 - 3 T - 4 T^{2} - 99 T^{3} + 829 T^{4} - 2277 T^{5} - 2116 T^{6} - 36501 T^{7} + 279841 T^{8} \))(\( 1 + 8 T + 14 T^{2} + 32 T^{3} + 499 T^{4} + 736 T^{5} + 7406 T^{6} + 97336 T^{7} + 279841 T^{8} \))(\( 1 + 8 T + 14 T^{2} + 32 T^{3} + 499 T^{4} + 736 T^{5} + 7406 T^{6} + 97336 T^{7} + 279841 T^{8} \))
$29$ (\( 1 - 9 T + 67 T^{2} - 261 T^{3} + 841 T^{4} \))(\( 1 + 5 T + 53 T^{2} + 145 T^{3} + 841 T^{4} \))(\( 1 - 10 T + 103 T^{2} - 572 T^{3} + 2987 T^{4} - 8410 T^{5} + 24389 T^{6} \))(\( 1 - 2 T + 51 T^{2} - 108 T^{3} + 1479 T^{4} - 1682 T^{5} + 24389 T^{6} \))(\( 1 + 5 T + 74 T^{2} + 230 T^{3} + 2629 T^{4} + 6442 T^{5} + 76241 T^{6} + 193430 T^{7} + 1804786 T^{8} + 3536405 T^{9} + 20511149 T^{10} \))(\( 1 + 9 T + 95 T^{2} + 533 T^{3} + 3647 T^{4} + 18534 T^{5} + 110962 T^{6} + 537486 T^{7} + 3067127 T^{8} + 12999337 T^{9} + 67191695 T^{10} + 184600341 T^{11} + 594823321 T^{12} \))(\( 1 - 91 T^{2} + 5518 T^{4} - 214978 T^{6} + 7185025 T^{8} - 204873190 T^{10} + 6042606025 T^{12} - 152049854818 T^{14} + 3282235085278 T^{16} - 45522423579451 T^{18} + 420707233300201 T^{20} \))(\( 1 - 93 T^{2} + 6353 T^{4} - 344165 T^{6} + 14894379 T^{8} - 544118406 T^{10} + 17240428422 T^{12} - 457603579446 T^{14} + 10534511273499 T^{16} - 204717368271965 T^{18} + 3178065461541233 T^{20} - 39125772696918693 T^{22} + 353814783205469041 T^{24} \))(\( ( 1 + 38 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 4 T + 49 T^{2} - 116 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 10 T + 154 T^{2} + 1024 T^{3} + 8899 T^{4} + 42621 T^{5} + 258071 T^{6} + 861184 T^{7} + 3755906 T^{8} + 7072810 T^{9} + 20511149 T^{10} )^{2} \))(\( 1 + 7 T + 5 T^{2} + 117 T^{3} + 1484 T^{4} + 3393 T^{5} + 4205 T^{6} + 170723 T^{7} + 707281 T^{8} \))(\( 1 - 4 T - 13 T^{2} + 168 T^{3} - 295 T^{4} + 4872 T^{5} - 10933 T^{6} - 97556 T^{7} + 707281 T^{8} \))(\( 1 - 20 T + 200 T^{2} - 1460 T^{3} + 8722 T^{4} - 42340 T^{5} + 168200 T^{6} - 487780 T^{7} + 707281 T^{8} \))(\( 1 - 20 T + 200 T^{2} - 1460 T^{3} + 8722 T^{4} - 42340 T^{5} + 168200 T^{6} - 487780 T^{7} + 707281 T^{8} \))
$31$ (\( 1 + 17 T + 133 T^{2} + 527 T^{3} + 961 T^{4} \))(\( 1 - 5 T + 37 T^{2} - 155 T^{3} + 961 T^{4} \))(\( 1 + 2 T + 77 T^{2} + 100 T^{3} + 2387 T^{4} + 1922 T^{5} + 29791 T^{6} \))(\( 1 + 9 T^{2} - 56 T^{3} + 279 T^{4} + 29791 T^{6} \))(\( 1 - 17 T + 226 T^{2} - 2084 T^{3} + 16065 T^{4} - 96590 T^{5} + 498015 T^{6} - 2002724 T^{7} + 6732766 T^{8} - 15699857 T^{9} + 28629151 T^{10} \))(\( 1 + 27 T + 443 T^{2} + 5167 T^{3} + 47219 T^{4} + 349172 T^{5} + 2134434 T^{6} + 10824332 T^{7} + 45377459 T^{8} + 153930097 T^{9} + 409119803 T^{10} + 772987077 T^{11} + 887503681 T^{12} \))(\( ( 1 - 7 T + 104 T^{2} - 586 T^{3} + 5279 T^{4} - 22742 T^{5} + 163649 T^{6} - 563146 T^{7} + 3098264 T^{8} - 6464647 T^{9} + 28629151 T^{10} )^{2} \))(\( ( 1 + 3 T + 135 T^{2} + 343 T^{3} + 8539 T^{4} + 18980 T^{5} + 330618 T^{6} + 588380 T^{7} + 8205979 T^{8} + 10218313 T^{9} + 124675335 T^{10} + 85887453 T^{11} + 887503681 T^{12} )^{2} \))(\( 1 + 4 T - 45 T^{2} - 4 T^{3} + 2264 T^{4} - 124 T^{5} - 43245 T^{6} + 119164 T^{7} + 923521 T^{8} \))(\( 1 - T - 58 T^{2} + 3 T^{3} + 2489 T^{4} + 93 T^{5} - 55738 T^{6} - 29791 T^{7} + 923521 T^{8} \))(\( 1 - 6 T - 57 T^{2} + 472 T^{3} + 757 T^{4} - 10368 T^{5} - 4219 T^{6} - 123075 T^{7} + 2033500 T^{8} + 5253845 T^{9} - 112378329 T^{10} + 162869195 T^{11} + 1954193500 T^{12} - 3666527325 T^{13} - 3896335099 T^{14} - 296827037568 T^{15} + 671840286517 T^{16} + 12985953860392 T^{17} - 48614789134137 T^{18} - 158637732964026 T^{19} + 819628286980801 T^{20} \))(\( 1 + 5 T + 9 T^{2} + 205 T^{3} + 1916 T^{4} + 6355 T^{5} + 8649 T^{6} + 148955 T^{7} + 923521 T^{8} \))(\( 1 - 13 T + 108 T^{2} - 821 T^{3} + 5525 T^{4} - 25451 T^{5} + 103788 T^{6} - 387283 T^{7} + 923521 T^{8} \))(\( 1 - 2 T - 56 T^{2} + 4 T^{3} + 2515 T^{4} + 124 T^{5} - 53816 T^{6} - 59582 T^{7} + 923521 T^{8} \))(\( 1 - 2 T - 56 T^{2} + 4 T^{3} + 2515 T^{4} + 124 T^{5} - 53816 T^{6} - 59582 T^{7} + 923521 T^{8} \))
$37$ (\( 1 - 2 T + 30 T^{2} - 74 T^{3} + 1369 T^{4} \))(\( 1 + 10 T + 94 T^{2} + 370 T^{3} + 1369 T^{4} \))(\( 1 - 3 T - 11 T^{2} + 277 T^{3} - 407 T^{4} - 4107 T^{5} + 50653 T^{6} \))(\( 1 - 3 T + 93 T^{2} - 195 T^{3} + 3441 T^{4} - 4107 T^{5} + 50653 T^{6} \))(\( 1 + 7 T + 149 T^{2} + 879 T^{3} + 9772 T^{4} + 45884 T^{5} + 361564 T^{6} + 1203351 T^{7} + 7547297 T^{8} + 13119127 T^{9} + 69343957 T^{10} \))(\( 1 - 19 T + 276 T^{2} - 3096 T^{3} + 28095 T^{4} - 214681 T^{5} + 1424272 T^{6} - 7943197 T^{7} + 38462055 T^{8} - 156821688 T^{9} + 517268436 T^{10} - 1317535183 T^{11} + 2565726409 T^{12} \))(\( ( 1 + 11 T + 129 T^{2} + 1051 T^{3} + 8808 T^{4} + 52380 T^{5} + 325896 T^{6} + 1438819 T^{7} + 6534237 T^{8} + 20615771 T^{9} + 69343957 T^{10} )^{2} \))(\( ( 1 + 5 T + 164 T^{2} + 740 T^{3} + 12967 T^{4} + 48803 T^{5} + 610448 T^{6} + 1805711 T^{7} + 17751823 T^{8} + 37483220 T^{9} + 307362404 T^{10} + 346719785 T^{11} + 2565726409 T^{12} )^{2} \))(\( 1 + 2 T - 51 T^{2} - 38 T^{3} + 1508 T^{4} - 1406 T^{5} - 69819 T^{6} + 101306 T^{7} + 1874161 T^{8} \))(\( 1 - 22 T^{2} - 885 T^{4} - 30118 T^{6} + 1874161 T^{8} \))(\( 1 - 18 T + 74 T^{2} + 384 T^{3} - 1647 T^{4} - 14801 T^{5} + 48562 T^{6} - 508226 T^{7} + 8263775 T^{8} + 3837217 T^{9} - 385416905 T^{10} + 141977029 T^{11} + 11313107975 T^{12} - 25743171578 T^{13} + 91013006482 T^{14} - 1026359907557 T^{15} - 4225751395623 T^{16} + 36453840819072 T^{17} + 259923479590154 T^{18} - 2339311316311386 T^{19} + 4808584372417849 T^{20} \))(\( 1 - 17 T + 72 T^{2} + 605 T^{3} - 7669 T^{4} + 22385 T^{5} + 98568 T^{6} - 861101 T^{7} + 1874161 T^{8} \))(\( 1 - 9 T + 9 T^{2} + 317 T^{3} - 2796 T^{4} + 11729 T^{5} + 12321 T^{6} - 455877 T^{7} + 1874161 T^{8} \))(\( 1 + 8 T - 14 T^{2} + 32 T^{3} + 2347 T^{4} + 1184 T^{5} - 19166 T^{6} + 405224 T^{7} + 1874161 T^{8} \))(\( 1 + 8 T - 14 T^{2} + 32 T^{3} + 2347 T^{4} + 1184 T^{5} - 19166 T^{6} + 405224 T^{7} + 1874161 T^{8} \))
$41$ (\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{5} \))(\( ( 1 - T )^{6} \))(\( 1 + 4 T - 47 T^{2} + 144 T^{3} + 1942 T^{4} - 3688 T^{5} + 79622 T^{6} + 242064 T^{7} - 3239287 T^{8} + 11303044 T^{9} + 115856201 T^{10} \))(\( 1 + 2 T + 50 T^{2} + 146 T^{3} + 1327 T^{4} + 3324 T^{5} + 25820 T^{6} + 136284 T^{7} + 2230687 T^{8} + 10062466 T^{9} + 141288050 T^{10} + 231712402 T^{11} + 4750104241 T^{12} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{10} \))(\( 1 + 11 T + 111 T^{2} + 451 T^{3} + 1681 T^{4} \))(\( 1 - T - 69 T^{2} - 41 T^{3} + 1681 T^{4} \))(\( ( 1 - 8 T + 41 T^{2} )^{2} \))(\( ( 1 - 8 T + 41 T^{2} )^{2} \))
$43$ (\( 1 + 2 T + 7 T^{2} + 86 T^{3} + 1849 T^{4} \))(\( ( 1 + T + 43 T^{2} )^{2} \))(\( 1 - 9 T + 25 T^{2} + 61 T^{3} + 1075 T^{4} - 16641 T^{5} + 79507 T^{6} \))(\( 1 - 11 T + 125 T^{2} - 945 T^{3} + 5375 T^{4} - 20339 T^{5} + 79507 T^{6} \))(\( 1 - T + 102 T^{2} - 198 T^{3} + 6135 T^{4} - 15081 T^{5} + 263805 T^{6} - 366102 T^{7} + 8109714 T^{8} - 3418801 T^{9} + 147008443 T^{10} \))(\( 1 - 19 T + 285 T^{2} - 3095 T^{3} + 29793 T^{4} - 236989 T^{5} + 1697038 T^{6} - 10190527 T^{7} + 55087257 T^{8} - 246074165 T^{9} + 974358285 T^{10} - 2793160417 T^{11} + 6321363049 T^{12} \))(\( ( 1 - 9 T + 150 T^{2} - 1070 T^{3} + 10507 T^{4} - 58949 T^{5} + 451801 T^{6} - 1978430 T^{7} + 11926050 T^{8} - 30769209 T^{9} + 147008443 T^{10} )^{2} \))(\( ( 1 + 25 T + 473 T^{2} + 6005 T^{3} + 64245 T^{4} + 540087 T^{5} + 3936326 T^{6} + 23223741 T^{7} + 118789005 T^{8} + 477439535 T^{9} + 1617092873 T^{10} + 3675211075 T^{11} + 6321363049 T^{12} )^{2} \))(\( ( 1 + 4 T + 70 T^{2} + 172 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 12 T + 109 T^{2} + 516 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 14 T + 162 T^{2} + 1230 T^{3} + 7725 T^{4} + 51435 T^{5} + 332175 T^{6} + 2274270 T^{7} + 12880134 T^{8} + 47863214 T^{9} + 147008443 T^{10} )^{2} \))(\( 1 + T + 8 T^{2} - 175 T^{3} + 961 T^{4} - 7525 T^{5} + 14792 T^{6} + 79507 T^{7} + 3418801 T^{8} \))(\( 1 + 10 T + 17 T^{2} + 200 T^{3} + 3109 T^{4} + 8600 T^{5} + 31433 T^{6} + 795070 T^{7} + 3418801 T^{8} \))(\( 1 - 140 T^{2} + 8406 T^{4} - 258860 T^{6} + 3418801 T^{8} \))(\( 1 - 140 T^{2} + 8406 T^{4} - 258860 T^{6} + 3418801 T^{8} \))
$47$ (\( 1 + 2 T + 90 T^{2} + 94 T^{3} + 2209 T^{4} \))(\( 1 - 6 T + 58 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 + 7 T + 101 T^{2} + 445 T^{3} + 4747 T^{4} + 15463 T^{5} + 103823 T^{6} \))(\( 1 - 13 T + 195 T^{2} - 1293 T^{3} + 9165 T^{4} - 28717 T^{5} + 103823 T^{6} \))(\( 1 - 9 T + 115 T^{2} - 653 T^{3} + 5488 T^{4} - 31712 T^{5} + 257936 T^{6} - 1442477 T^{7} + 11939645 T^{8} - 43917129 T^{9} + 229345007 T^{10} \))(\( 1 + 19 T + 376 T^{2} + 4402 T^{3} + 50057 T^{4} + 412039 T^{5} + 3251324 T^{6} + 19365833 T^{7} + 110575913 T^{8} + 457028846 T^{9} + 1834760056 T^{10} + 4357555133 T^{11} + 10779215329 T^{12} \))(\( 1 - 205 T^{2} + 17547 T^{4} - 626815 T^{6} - 7566568 T^{8} + 1397327840 T^{10} - 16714548712 T^{12} - 3058657246015 T^{14} + 189142891377963 T^{16} - 4881313765661005 T^{18} + 52599132235830049 T^{20} \))(\( 1 - 299 T^{2} + 43950 T^{4} - 4318630 T^{6} + 326173317 T^{8} - 20183490527 T^{10} + 1039793696824 T^{12} - 44585330574143 T^{14} + 1591621737671877 T^{16} - 46551442696279270 T^{18} + 1046506048784395950 T^{20} - 15727140538513184651 T^{22} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( 1 + 2 T - 71 T^{2} - 38 T^{3} + 3228 T^{4} - 1786 T^{5} - 156839 T^{6} + 207646 T^{7} + 4879681 T^{8} \))(\( ( 1 - 9 T + 34 T^{2} - 423 T^{3} + 2209 T^{4} )^{2} \))(\( 1 + 3 T - 139 T^{2} - 574 T^{3} + 9696 T^{4} + 47035 T^{5} - 425060 T^{6} - 2526513 T^{7} + 12950606 T^{8} + 54446897 T^{9} - 378378327 T^{10} + 2559004159 T^{11} + 28607888654 T^{12} - 262310159199 T^{13} - 2074157205860 T^{14} + 10787242404245 T^{15} + 104515271829984 T^{16} - 290801671145762 T^{17} - 3309768845984779 T^{18} + 3357391419308301 T^{19} + 52599132235830049 T^{20} \))(\( 1 - 6 T - 31 T^{2} + 318 T^{3} - 161 T^{4} + 14946 T^{5} - 68479 T^{6} - 622938 T^{7} + 4879681 T^{8} \))(\( 1 - 24 T + 259 T^{2} - 1938 T^{3} + 13279 T^{4} - 91086 T^{5} + 572131 T^{6} - 2491752 T^{7} + 4879681 T^{8} \))(\( 1 + 10 T + 74 T^{2} + 496 T^{3} + 2599 T^{4} + 23312 T^{5} + 163466 T^{6} + 1038230 T^{7} + 4879681 T^{8} \))(\( 1 - 14 T + 74 T^{2} - 32 T^{3} - 1913 T^{4} - 1504 T^{5} + 163466 T^{6} - 1453522 T^{7} + 4879681 T^{8} \))
$53$ (\( 1 + 17 T + 147 T^{2} + 901 T^{3} + 2809 T^{4} \))(\( 1 - 7 T + 117 T^{2} - 371 T^{3} + 2809 T^{4} \))(\( 1 - 2 T + 119 T^{2} - 284 T^{3} + 6307 T^{4} - 5618 T^{5} + 148877 T^{6} \))(\( 1 + 20 T + 283 T^{2} + 2352 T^{3} + 14999 T^{4} + 56180 T^{5} + 148877 T^{6} \))(\( 1 - 5 T + 156 T^{2} - 36 T^{3} + 7939 T^{4} + 26602 T^{5} + 420767 T^{6} - 101124 T^{7} + 23224812 T^{8} - 39452405 T^{9} + 418195493 T^{10} \))(\( 1 - 5 T + 191 T^{2} - 861 T^{3} + 19247 T^{4} - 75162 T^{5} + 1236466 T^{6} - 3983586 T^{7} + 54064823 T^{8} - 128183097 T^{9} + 1507081871 T^{10} - 2090977465 T^{11} + 22164361129 T^{12} \))(\( 1 - 235 T^{2} + 27554 T^{4} - 2210254 T^{6} + 143685261 T^{8} - 8113437742 T^{10} + 403611898149 T^{12} - 17439967192174 T^{14} + 610716806548466 T^{16} - 14631027246669835 T^{18} + 174887470365513049 T^{20} \))(\( 1 - 469 T^{2} + 107333 T^{4} - 15765953 T^{6} + 1650642227 T^{8} - 129539943618 T^{10} + 7806473597838 T^{12} - 363877701622962 T^{14} + 13024361129941187 T^{16} - 349442275834840937 T^{18} + 6682519350922610213 T^{20} - 82022223601425619981 T^{22} + \)\(49\!\cdots\!41\)\( T^{24} \))(\( 1 - 16 T + 91 T^{2} - 944 T^{3} + 10848 T^{4} - 50032 T^{5} + 255619 T^{6} - 2382032 T^{7} + 7890481 T^{8} \))(\( 1 + 9 T - 16 T^{2} - 81 T^{3} + 2307 T^{4} - 4293 T^{5} - 44944 T^{6} + 1339893 T^{7} + 7890481 T^{8} \))(\( 1 - 9 T - 64 T^{2} - 235 T^{3} + 10113 T^{4} + 27650 T^{5} + 7753 T^{6} - 6361889 T^{7} - 6637266 T^{8} + 48032331 T^{9} + 2449196135 T^{10} + 2545713543 T^{11} - 18644080194 T^{12} - 947138948653 T^{13} + 61174899193 T^{14} + 11563105381450 T^{15} + 224148184097577 T^{16} - 276057117861695 T^{17} - 3984620186327104 T^{18} - 29697872326219197 T^{19} + 174887470365513049 T^{20} \))(\( 1 + 12 T + 11 T^{2} - 84 T^{3} + 1369 T^{4} - 4452 T^{5} + 30899 T^{6} + 1786524 T^{7} + 7890481 T^{8} \))(\( 1 + 4 T + 43 T^{2} + 110 T^{3} + 741 T^{4} + 5830 T^{5} + 120787 T^{6} + 595508 T^{7} + 7890481 T^{8} \))(\( 1 + 2 T + 2 T^{2} - 208 T^{3} - 3017 T^{4} - 11024 T^{5} + 5618 T^{6} + 297754 T^{7} + 7890481 T^{8} \))(\( 1 + 2 T + 2 T^{2} - 208 T^{3} - 3017 T^{4} - 11024 T^{5} + 5618 T^{6} + 297754 T^{7} + 7890481 T^{8} \))
$59$ (\( 1 - 13 T + 159 T^{2} - 767 T^{3} + 3481 T^{4} \))(\( 1 - 19 T + 207 T^{2} - 1121 T^{3} + 3481 T^{4} \))(\( ( 1 + 4 T + 59 T^{2} )^{3} \))(\( 1 - 4 T + 61 T^{2} - 576 T^{3} + 3599 T^{4} - 13924 T^{5} + 205379 T^{6} \))(\( 1 - 7 T + 124 T^{2} - 772 T^{3} + 12043 T^{4} - 63362 T^{5} + 710537 T^{6} - 2687332 T^{7} + 25466996 T^{8} - 84821527 T^{9} + 714924299 T^{10} \))(\( 1 + 7 T + 171 T^{2} + 589 T^{3} + 9235 T^{4} - 15790 T^{5} + 310242 T^{6} - 931610 T^{7} + 32147035 T^{8} + 120968231 T^{9} + 2072068731 T^{10} + 5004470093 T^{11} + 42180533641 T^{12} \))(\( ( 1 - 17 T + 144 T^{2} - 1134 T^{3} + 11155 T^{4} - 94458 T^{5} + 658145 T^{6} - 3947454 T^{7} + 29574576 T^{8} - 205995137 T^{9} + 714924299 T^{10} )^{2} \))(\( ( 1 + 35 T + 841 T^{2} + 13753 T^{3} + 179943 T^{4} + 1849018 T^{5} + 15806430 T^{6} + 109092062 T^{7} + 626381583 T^{8} + 2824577387 T^{9} + 10190700601 T^{10} + 25022350465 T^{11} + 42180533641 T^{12} )^{2} \))(\( 1 + 4 T - 61 T^{2} - 164 T^{3} + 1504 T^{4} - 9676 T^{5} - 212341 T^{6} + 821516 T^{7} + 12117361 T^{8} \))(\( 1 + 8 T - 57 T^{2} + 24 T^{3} + 7384 T^{4} + 1416 T^{5} - 198417 T^{6} + 1643032 T^{7} + 12117361 T^{8} \))(\( 1 - 19 T + 69 T^{2} + 994 T^{3} - 10320 T^{4} + 43687 T^{5} - 280758 T^{6} + 446353 T^{7} + 25825034 T^{8} - 183280321 T^{9} + 559637617 T^{10} - 10813538939 T^{11} + 89896943354 T^{12} + 91671532787 T^{13} - 3402046039638 T^{14} + 31232897850413 T^{15} - 435303107175120 T^{16} + 2473719575910086 T^{17} + 10131300194698149 T^{18} - 164596920554443841 T^{19} + 511116753300641401 T^{20} \))(\( 1 + 16 T + 47 T^{2} - 942 T^{3} - 12445 T^{4} - 55578 T^{5} + 163607 T^{6} + 3286064 T^{7} + 12117361 T^{8} \))(\( 1 - 4 T - 13 T^{2} + 398 T^{3} - 325 T^{4} + 23482 T^{5} - 45253 T^{6} - 821516 T^{7} + 12117361 T^{8} \))(\( 1 + 18 T + 128 T^{2} + 1404 T^{3} + 15819 T^{4} + 82836 T^{5} + 445568 T^{6} + 3696822 T^{7} + 12117361 T^{8} \))(\( 1 + 18 T + 128 T^{2} + 1404 T^{3} + 15819 T^{4} + 82836 T^{5} + 445568 T^{6} + 3696822 T^{7} + 12117361 T^{8} \))
$61$ (\( ( 1 + 11 T + 61 T^{2} )^{2} \))(\( 1 - 10 T + 127 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( 1 + 4 T + 147 T^{2} + 336 T^{3} + 8967 T^{4} + 14884 T^{5} + 226981 T^{6} \))(\( 1 - 8 T + 139 T^{2} - 632 T^{3} + 8479 T^{4} - 29768 T^{5} + 226981 T^{6} \))(\( 1 - 22 T + 458 T^{2} - 5620 T^{3} + 64261 T^{4} - 519412 T^{5} + 3919921 T^{6} - 20912020 T^{7} + 103957298 T^{8} - 304608502 T^{9} + 844596301 T^{10} \))(\( 1 + 12 T + 183 T^{2} + 1050 T^{3} + 10135 T^{4} + 11674 T^{5} + 272594 T^{6} + 712114 T^{7} + 37712335 T^{8} + 238330050 T^{9} + 2533788903 T^{10} + 10135155612 T^{11} + 51520374361 T^{12} \))(\( ( 1 + 14 T + 314 T^{2} + 3100 T^{3} + 38149 T^{4} + 273684 T^{5} + 2327089 T^{6} + 11535100 T^{7} + 71272034 T^{8} + 193841774 T^{9} + 844596301 T^{10} )^{2} \))(\( ( 1 - 26 T + 435 T^{2} - 5262 T^{3} + 54223 T^{4} - 484904 T^{5} + 3996266 T^{6} - 29579144 T^{7} + 201763783 T^{8} - 1194374022 T^{9} + 6022940835 T^{10} - 21959503826 T^{11} + 51520374361 T^{12} )^{2} \))(\( 1 + 10 T - 27 T^{2} + 50 T^{3} + 6308 T^{4} + 3050 T^{5} - 100467 T^{6} + 2269810 T^{7} + 13845841 T^{8} \))(\( ( 1 - 24 T + 253 T^{2} - 1464 T^{3} + 3721 T^{4} )( 1 + 24 T + 253 T^{2} + 1464 T^{3} + 3721 T^{4} ) \))(\( 1 - 23 T + 208 T^{2} + 739 T^{3} - 31393 T^{4} + 246920 T^{5} + 577277 T^{6} - 22998515 T^{7} + 134106750 T^{8} + 614594089 T^{9} - 11935706585 T^{10} + 37490239429 T^{11} + 499011216750 T^{12} - 5220225933215 T^{13} + 7992885554957 T^{14} + 208547718642920 T^{15} - 1617379112314873 T^{16} + 2322486955819519 T^{17} + 39875121103434448 T^{18} - 268965360135185243 T^{19} + 713342911662882601 T^{20} \))(\( 1 + 8 T - 27 T^{2} + 16 T^{3} + 4025 T^{4} + 976 T^{5} - 100467 T^{6} + 1815848 T^{7} + 13845841 T^{8} \))(\( 1 - 3 T + 48 T^{2} - 361 T^{3} + 5355 T^{4} - 22021 T^{5} + 178608 T^{6} - 680943 T^{7} + 13845841 T^{8} \))(\( 1 + 73 T^{2} + 1608 T^{4} + 271633 T^{6} + 13845841 T^{8} \))(\( 1 + 73 T^{2} + 1608 T^{4} + 271633 T^{6} + 13845841 T^{8} \))
$67$ (\( 1 - 11 T + 163 T^{2} - 737 T^{3} + 4489 T^{4} \))(\( 1 + 13 T + 145 T^{2} + 871 T^{3} + 4489 T^{4} \))(\( 1 - 10 T + 193 T^{2} - 1140 T^{3} + 12931 T^{4} - 44890 T^{5} + 300763 T^{6} \))(\( 1 + 36 T + 605 T^{2} + 6160 T^{3} + 40535 T^{4} + 161604 T^{5} + 300763 T^{6} \))(\( 1 + 3 T + 230 T^{2} + 228 T^{3} + 22853 T^{4} + 3146 T^{5} + 1531151 T^{6} + 1023492 T^{7} + 69175490 T^{8} + 60453363 T^{9} + 1350125107 T^{10} \))(\( 1 - 27 T + 645 T^{2} - 9607 T^{3} + 129139 T^{4} - 1305704 T^{5} + 12088494 T^{6} - 87482168 T^{7} + 579704971 T^{8} - 2889430141 T^{9} + 12997473045 T^{10} - 36453377889 T^{11} + 90458382169 T^{12} \))(\( 1 - 427 T^{2} + 89738 T^{4} - 12380986 T^{6} + 1246484565 T^{8} - 95340189814 T^{10} + 5595469212285 T^{12} - 249490746985306 T^{14} + 8117554299081722 T^{16} - 173390898316685707 T^{18} + 1822837804551761449 T^{20} \))(\( 1 - 193 T^{2} + 28633 T^{4} - 3220965 T^{6} + 311546403 T^{8} - 25322448162 T^{10} + 1820948852486 T^{12} - 113672469799218 T^{14} + 6278009263967763 T^{16} - 291363282922973085 T^{18} + 11626935811479301753 T^{20} - \)\(35\!\cdots\!57\)\( T^{22} + \)\(81\!\cdots\!61\)\( T^{24} \))(\( 1 - 6 T - 27 T^{2} + 426 T^{3} - 2932 T^{4} + 28542 T^{5} - 121203 T^{6} - 1804578 T^{7} + 20151121 T^{8} \))(\( 1 - 6 T - 94 T^{2} + 24 T^{3} + 9999 T^{4} + 1608 T^{5} - 421966 T^{6} - 1804578 T^{7} + 20151121 T^{8} \))(\( 1 - 11 T - 79 T^{2} + 1010 T^{3} + 2242 T^{4} - 14343 T^{5} - 242472 T^{6} - 42471 T^{7} + 15451954 T^{8} - 61918455 T^{9} + 21903105 T^{10} - 4148536485 T^{11} + 69363821506 T^{12} - 12773705373 T^{13} - 4886082611112 T^{14} - 19364844409701 T^{15} + 202807692822898 T^{16} + 6121318721376230 T^{17} - 32079346526974639 T^{18} - 299271878359244417 T^{19} + 1822837804551761449 T^{20} \))(\( 1 - 8 T - 3 T^{2} + 560 T^{3} - 4279 T^{4} + 37520 T^{5} - 13467 T^{6} - 2406104 T^{7} + 20151121 T^{8} \))(\( 1 + 25 T + 198 T^{2} + 155 T^{3} - 5551 T^{4} + 10385 T^{5} + 888822 T^{6} + 7519075 T^{7} + 20151121 T^{8} \))(\( 1 - 6 T + 18 T^{2} - 36 T^{3} - 3649 T^{4} - 2412 T^{5} + 80802 T^{6} - 1804578 T^{7} + 20151121 T^{8} \))(\( 1 + 6 T + 18 T^{2} + 36 T^{3} - 3649 T^{4} + 2412 T^{5} + 80802 T^{6} + 1804578 T^{7} + 20151121 T^{8} \))
$71$ (\( 1 + 4 T + 141 T^{2} + 284 T^{3} + 5041 T^{4} \))(\( 1 - 6 T + 71 T^{2} - 426 T^{3} + 5041 T^{4} \))(\( 1 + 14 T + 197 T^{2} + 1964 T^{3} + 13987 T^{4} + 70574 T^{5} + 357911 T^{6} \))(\( 1 + 2 T + 177 T^{2} + 276 T^{3} + 12567 T^{4} + 10082 T^{5} + 357911 T^{6} \))(\( 1 + 24 T + 396 T^{2} + 4954 T^{3} + 55267 T^{4} + 504628 T^{5} + 3923957 T^{6} + 24973114 T^{7} + 141732756 T^{8} + 609880344 T^{9} + 1804229351 T^{10} \))(\( 1 + 6 T + 321 T^{2} + 1680 T^{3} + 48347 T^{4} + 214362 T^{5} + 4349446 T^{6} + 15219702 T^{7} + 243717227 T^{8} + 601290480 T^{9} + 8157149601 T^{10} + 10825376106 T^{11} + 128100283921 T^{12} \))(\( 1 - 264 T^{2} + 49006 T^{4} - 5988070 T^{6} + 599427089 T^{8} - 46178547364 T^{10} + 3021711955649 T^{12} - 152166924645670 T^{14} + 6277682513832526 T^{16} - 170478932248880904 T^{18} + 3255243551009881201 T^{20} \))(\( 1 - 418 T^{2} + 87967 T^{4} - 12398170 T^{6} + 1321240923 T^{8} - 115285590564 T^{10} + 8707128566282 T^{12} - 581154662033124 T^{14} + 33574952859421563 T^{16} - 1588209097100824570 T^{18} + 56805000883095857887 T^{20} - \)\(13\!\cdots\!18\)\( T^{22} + \)\(16\!\cdots\!41\)\( T^{24} \))(\( ( 1 + 20 T + 222 T^{2} + 1420 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 + 25 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 + 205 T^{2} + 61 T^{3} + 23652 T^{4} + 1421 T^{5} + 1679292 T^{6} + 307501 T^{7} + 73371755 T^{8} + 1804229351 T^{10} )^{2} \))(\( 1 + 22 T + 313 T^{2} + 3674 T^{3} + 36105 T^{4} + 260854 T^{5} + 1577833 T^{6} + 7874042 T^{7} + 25411681 T^{8} \))(\( 1 - 31 T + 395 T^{2} - 2839 T^{3} + 18824 T^{4} - 201569 T^{5} + 1991195 T^{6} - 11095241 T^{7} + 25411681 T^{8} \))(\( 1 - 30 T + 450 T^{2} - 5460 T^{3} + 53927 T^{4} - 387660 T^{5} + 2268450 T^{6} - 10737330 T^{7} + 25411681 T^{8} \))(\( 1 - 30 T + 450 T^{2} - 5460 T^{3} + 53927 T^{4} - 387660 T^{5} + 2268450 T^{6} - 10737330 T^{7} + 25411681 T^{8} \))
$73$ (\( ( 1 + 15 T + 73 T^{2} )^{2} \))(\( 1 + 2 T + 67 T^{2} + 146 T^{3} + 5329 T^{4} \))(\( 1 + 4 T + 135 T^{2} + 192 T^{3} + 9855 T^{4} + 21316 T^{5} + 389017 T^{6} \))(\( 1 + 2 T + 183 T^{2} + 284 T^{3} + 13359 T^{4} + 10658 T^{5} + 389017 T^{6} \))(\( 1 - 40 T + 950 T^{2} - 15562 T^{3} + 192937 T^{4} - 1857916 T^{5} + 14084401 T^{6} - 82929898 T^{7} + 369566150 T^{8} - 1135929640 T^{9} + 2073071593 T^{10} \))(\( 1 - 52 T + 1447 T^{2} - 27846 T^{3} + 408023 T^{4} - 4752206 T^{5} + 44927922 T^{6} - 346911038 T^{7} + 2174354567 T^{8} - 10832567382 T^{9} + 41092254727 T^{10} - 107799722836 T^{11} + 151334226289 T^{12} \))(\( ( 1 + 210 T^{2} - 834 T^{3} + 18641 T^{4} - 121708 T^{5} + 1360793 T^{6} - 4444386 T^{7} + 81693570 T^{8} + 2073071593 T^{10} )^{2} \))(\( ( 1 + 32 T + 675 T^{2} + 10622 T^{3} + 135415 T^{4} + 1460250 T^{5} + 13435226 T^{6} + 106598250 T^{7} + 721626535 T^{8} + 4132138574 T^{9} + 19168812675 T^{10} + 66338290976 T^{11} + 151334226289 T^{12} )^{2} \))(\( 1 - 14 T + 21 T^{2} - 406 T^{3} + 10988 T^{4} - 29638 T^{5} + 111909 T^{6} - 5446238 T^{7} + 28398241 T^{8} \))(\( 1 + 15 T + 26 T^{2} + 795 T^{3} + 17847 T^{4} + 58035 T^{5} + 138554 T^{6} + 5835255 T^{7} + 28398241 T^{8} \))(\( 1 + 13 T - 86 T^{2} - 905 T^{3} + 13406 T^{4} + 75611 T^{5} - 348676 T^{6} + 336091 T^{7} - 23283159 T^{8} - 6294026 T^{9} + 4995107620 T^{10} - 459463898 T^{11} - 124075954311 T^{12} + 130745112547 T^{13} - 9901785078916 T^{14} + 156747016218323 T^{15} + 2028786637630334 T^{16} - 9997895659782785 T^{17} - 69355567902890966 T^{18} + 765330627207482869 T^{19} + 4297625829703557649 T^{20} \))(\( ( 1 - 11 T + 115 T^{2} - 803 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 8 T + 117 T^{2} - 584 T^{3} + 5329 T^{4} )^{2} \))(\( 1 - 12 T + 142 T^{2} - 1128 T^{3} + 7011 T^{4} - 82344 T^{5} + 756718 T^{6} - 4668204 T^{7} + 28398241 T^{8} \))(\( 1 + 12 T + 142 T^{2} + 1128 T^{3} + 7011 T^{4} + 82344 T^{5} + 756718 T^{6} + 4668204 T^{7} + 28398241 T^{8} \))
$79$ (\( 1 + 2 T + 114 T^{2} + 158 T^{3} + 6241 T^{4} \))(\( 1 + 10 T + 138 T^{2} + 790 T^{3} + 6241 T^{4} \))(\( 1 - 14 T + 269 T^{2} - 2156 T^{3} + 21251 T^{4} - 87374 T^{5} + 493039 T^{6} \))(\( 1 - 20 T + 333 T^{2} - 3224 T^{3} + 26307 T^{4} - 124820 T^{5} + 493039 T^{6} \))(\( 1 + 42 T + 967 T^{2} + 15192 T^{3} + 184214 T^{4} + 1801084 T^{5} + 14552906 T^{6} + 94813272 T^{7} + 476768713 T^{8} + 1635903402 T^{9} + 3077056399 T^{10} \))(\( 1 + 322 T^{2} - 96 T^{3} + 49695 T^{4} - 14720 T^{5} + 4820732 T^{6} - 1162880 T^{7} + 310146495 T^{8} - 47331744 T^{9} + 12541926082 T^{10} + 243087455521 T^{12} \))(\( 1 - 18 T^{2} + 20301 T^{4} - 484504 T^{6} + 185399314 T^{8} - 4645230508 T^{10} + 1157077118674 T^{12} - 18871470044824 T^{14} + 4934918434531821 T^{16} - 27307958578318098 T^{18} + 9468276082626847201 T^{20} \))(\( 1 - 728 T^{2} + 251530 T^{4} - 54850424 T^{6} + 8462759439 T^{8} - 979440687792 T^{10} + 87606054257228 T^{12} - 6112689332509872 T^{14} + 329625165632564559 T^{16} - 13333450004407990904 T^{18} + \)\(38\!\cdots\!30\)\( T^{20} - \)\(68\!\cdots\!28\)\( T^{22} + \)\(59\!\cdots\!41\)\( T^{24} \))(\( ( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} )^{2} \))(\( 1 - 6 T + 77 T^{2} + 1194 T^{3} - 7404 T^{4} + 94326 T^{5} + 480557 T^{6} - 2958234 T^{7} + 38950081 T^{8} \))(\( 1 - 41 T + 733 T^{2} - 8706 T^{3} + 95432 T^{4} - 946091 T^{5} + 6898586 T^{6} - 40642481 T^{7} + 229690774 T^{8} - 233690255 T^{9} - 8874765303 T^{10} - 18461530145 T^{11} + 1433500120534 T^{12} - 20038328189759 T^{13} + 268700483485466 T^{14} - 2911175365586309 T^{15} + 23198322055280072 T^{16} - 167189231633500254 T^{17} + 1112040757661509213 T^{18} - 4913915435287351079 T^{19} + 9468276082626847201 T^{20} \))(\( ( 1 + 8 T + 169 T^{2} + 632 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 + 13 T + 169 T^{2} + 1027 T^{3} + 6241 T^{4} )^{2} \))(\( 1 - 24 T + 225 T^{2} - 768 T^{3} - 532 T^{4} - 60672 T^{5} + 1404225 T^{6} - 11832936 T^{7} + 38950081 T^{8} \))(\( 1 + 18 T + 225 T^{2} + 2130 T^{3} + 19376 T^{4} + 168270 T^{5} + 1404225 T^{6} + 8874702 T^{7} + 38950081 T^{8} \))
$83$ (\( 1 - 6 T + 95 T^{2} - 498 T^{3} + 6889 T^{4} \))(\( 1 + 2 T + 147 T^{2} + 166 T^{3} + 6889 T^{4} \))(\( 1 + 2 T + 181 T^{2} + 388 T^{3} + 15023 T^{4} + 13778 T^{5} + 571787 T^{6} \))(\( 1 + 6 T + 149 T^{2} + 332 T^{3} + 12367 T^{4} + 41334 T^{5} + 571787 T^{6} \))(\( 1 + 12 T + 156 T^{2} + 1442 T^{3} + 16075 T^{4} + 98732 T^{5} + 1334225 T^{6} + 9933938 T^{7} + 89198772 T^{8} + 569499852 T^{9} + 3939040643 T^{10} \))(\( 1 - 12 T + 371 T^{2} - 4410 T^{3} + 66551 T^{4} - 681302 T^{5} + 7059658 T^{6} - 56548066 T^{7} + 458469839 T^{8} - 2521580670 T^{9} + 17607037091 T^{10} - 47268487716 T^{11} + 326940373369 T^{12} \))(\( ( 1 + 10 T + 288 T^{2} + 2608 T^{3} + 42487 T^{4} + 296724 T^{5} + 3526421 T^{6} + 17966512 T^{7} + 164674656 T^{8} + 474583210 T^{9} + 3939040643 T^{10} )^{2} \))(\( ( 1 - 30 T + 735 T^{2} - 11402 T^{3} + 158167 T^{4} - 1691404 T^{5} + 17096242 T^{6} - 140386532 T^{7} + 1089612463 T^{8} - 6519515374 T^{9} + 34881865935 T^{10} - 118171219290 T^{11} + 326940373369 T^{12} )^{2} \))(\( ( 1 + 12 T + 182 T^{2} + 996 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 - 16 T + 217 T^{2} - 1328 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 + 2 T + 338 T^{2} + 520 T^{3} + 50961 T^{4} + 61081 T^{5} + 4229763 T^{6} + 3582280 T^{7} + 193264006 T^{8} + 94916642 T^{9} + 3939040643 T^{10} )^{2} \))(\( ( 1 - 7 T + 83 T^{2} )^{4} \))(\( ( 1 + 7 T + 167 T^{2} + 581 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 + 2 T + 164 T^{2} + 166 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 + 2 T + 164 T^{2} + 166 T^{3} + 6889 T^{4} )^{2} \))
$89$ (\( 1 + 9 T + 97 T^{2} + 801 T^{3} + 7921 T^{4} \))(\( 1 + 3 T + 119 T^{2} + 267 T^{3} + 7921 T^{4} \))(\( 1 - 5 T + T^{2} + 911 T^{3} + 89 T^{4} - 39605 T^{5} + 704969 T^{6} \))(\( 1 + T + 55 T^{2} + 1227 T^{3} + 4895 T^{4} + 7921 T^{5} + 704969 T^{6} \))(\( 1 - 8 T + 457 T^{2} - 2846 T^{3} + 82405 T^{4} - 379849 T^{5} + 7334045 T^{6} - 22543166 T^{7} + 322170833 T^{8} - 501937928 T^{9} + 5584059449 T^{10} \))(\( 1 + 38 T + 938 T^{2} + 15970 T^{3} + 222014 T^{4} + 2537075 T^{5} + 25723552 T^{6} + 225799675 T^{7} + 1758572894 T^{8} + 11258354930 T^{9} + 58852222058 T^{10} + 212194259062 T^{11} + 496981290961 T^{12} \))(\( 1 - 454 T^{2} + 89791 T^{4} - 10376100 T^{6} + 846113269 T^{8} - 67027887669 T^{10} + 6702063203749 T^{12} - 651019766840100 T^{14} + 44624447096679151 T^{16} - 1787211317788744774 T^{18} + 31181719929966183601 T^{20} \))(\( 1 - 492 T^{2} + 126284 T^{4} - 22065984 T^{6} + 2959726964 T^{8} - 326386132143 T^{10} + 31027309678500 T^{12} - 2585304552704703 T^{14} + 185699902469486324 T^{16} - 10966381214644770624 T^{18} + \)\(49\!\cdots\!04\)\( T^{20} - \)\(15\!\cdots\!92\)\( T^{22} + \)\(24\!\cdots\!21\)\( T^{24} \))(\( 1 - 24 T + 259 T^{2} - 3336 T^{3} + 41304 T^{4} - 296904 T^{5} + 2051539 T^{6} - 16919256 T^{7} + 62742241 T^{8} \))(\( 1 + 8 T - 117 T^{2} + 24 T^{3} + 19144 T^{4} + 2136 T^{5} - 926757 T^{6} + 5639752 T^{7} + 62742241 T^{8} \))(\( 1 + 14 T + 2 T^{2} + 32 T^{3} + 6355 T^{4} - 26749 T^{5} + 723178 T^{6} + 18631550 T^{7} + 17093627 T^{8} + 19250247 T^{9} + 10958940527 T^{10} + 1713271983 T^{11} + 135398619467 T^{12} + 13134665171950 T^{13} + 45373808361898 T^{14} - 149368006201301 T^{15} + 3158316104057155 T^{16} + 1415402716656928 T^{17} + 7873177611404162 T^{18} + 4904989651904792926 T^{19} + 31181719929966183601 T^{20} \))(\( 1 + 29 T + 367 T^{2} + 3607 T^{3} + 35640 T^{4} + 321023 T^{5} + 2907007 T^{6} + 20444101 T^{7} + 62742241 T^{8} \))(\( 1 - 12 T + 5 T^{2} - 492 T^{3} + 12709 T^{4} - 43788 T^{5} + 39605 T^{6} - 8459628 T^{7} + 62742241 T^{8} \))(\( 1 + 10 T + 50 T^{2} - 1280 T^{3} - 14321 T^{4} - 113920 T^{5} + 396050 T^{6} + 7049690 T^{7} + 62742241 T^{8} \))(\( 1 + 10 T + 50 T^{2} - 1280 T^{3} - 14321 T^{4} - 113920 T^{5} + 396050 T^{6} + 7049690 T^{7} + 62742241 T^{8} \))
$97$ (\( 1 + 17 T + 255 T^{2} + 1649 T^{3} + 9409 T^{4} \))(\( 1 + 15 T + 149 T^{2} + 1455 T^{3} + 9409 T^{4} \))(\( 1 - 27 T + 493 T^{2} - 5699 T^{3} + 47821 T^{4} - 254043 T^{5} + 912673 T^{6} \))(\( 1 - 11 T + 315 T^{2} - 2147 T^{3} + 30555 T^{4} - 103499 T^{5} + 912673 T^{6} \))(\( 1 - 16 T + 323 T^{2} - 4394 T^{3} + 51905 T^{4} - 561841 T^{5} + 5034785 T^{6} - 41343146 T^{7} + 294793379 T^{8} - 1416468496 T^{9} + 8587340257 T^{10} \))(\( 1 - 8 T + 266 T^{2} - 1362 T^{3} + 34864 T^{4} - 189883 T^{5} + 3886868 T^{6} - 18418651 T^{7} + 328035376 T^{8} - 1243060626 T^{9} + 23548788746 T^{10} - 68698722056 T^{11} + 832972004929 T^{12} \))(\( 1 - 478 T^{2} + 119351 T^{4} - 20862580 T^{6} + 2835760101 T^{8} - 307720470589 T^{10} + 26681666790309 T^{12} - 1846949207204980 T^{14} + 99416041760281079 T^{16} - 3746293258112187358 T^{18} + 73742412689492826049 T^{20} \))(\( 1 - 616 T^{2} + 180388 T^{4} - 33135268 T^{6} + 4327449448 T^{8} - 451466664719 T^{10} + 43610759665116 T^{12} - 4247849848341071 T^{14} + 383105988195286888 T^{16} - 27600750619819735972 T^{18} + \)\(14\!\cdots\!68\)\( T^{20} - \)\(45\!\cdots\!84\)\( T^{22} + \)\(69\!\cdots\!41\)\( T^{24} \))(\( ( 1 - 8 T + 190 T^{2} - 776 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 - 15 T + 247 T^{2} - 1455 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 + 27 T + 448 T^{2} + 5083 T^{3} + 45427 T^{4} + 421253 T^{5} + 4406419 T^{6} + 47825947 T^{7} + 408877504 T^{8} + 2390290587 T^{9} + 8587340257 T^{10} )^{2} \))(\( 1 + T + 44 T^{2} + 587 T^{3} + 8959 T^{4} + 56939 T^{5} + 413996 T^{6} + 912673 T^{7} + 88529281 T^{8} \))(\( 1 + 6 T - 21 T^{2} - 868 T^{3} - 2331 T^{4} - 84196 T^{5} - 197589 T^{6} + 5476038 T^{7} + 88529281 T^{8} \))(\( 1 + 8 T + 32 T^{2} + 648 T^{3} + 12866 T^{4} + 62856 T^{5} + 301088 T^{6} + 7301384 T^{7} + 88529281 T^{8} \))(\( 1 + 8 T + 32 T^{2} + 648 T^{3} + 12866 T^{4} + 62856 T^{5} + 301088 T^{6} + 7301384 T^{7} + 88529281 T^{8} \))
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