Properties

Label 575.2
Level 575
Weight 2
Dimension 11691
Nonzero newspaces 12
Newform subspaces 46
Sturm bound 52800
Trace bound 2

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Defining parameters

Level: \( N \) = \( 575 = 5^{2} \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 46 \)
Sturm bound: \(52800\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(575))\).

Total New Old
Modular forms 13816 12551 1265
Cusp forms 12585 11691 894
Eisenstein series 1231 860 371

Trace form

\( 11691q - 129q^{2} - 131q^{3} - 137q^{4} - 166q^{5} - 219q^{6} - 139q^{7} - 153q^{8} - 149q^{9} + O(q^{10}) \) \( 11691q - 129q^{2} - 131q^{3} - 137q^{4} - 166q^{5} - 219q^{6} - 139q^{7} - 153q^{8} - 149q^{9} - 186q^{10} - 219q^{11} - 179q^{12} - 151q^{13} - 171q^{14} - 196q^{15} - 247q^{16} - 150q^{17} - 195q^{18} - 134q^{19} - 156q^{20} - 252q^{21} - 148q^{22} - 159q^{23} - 312q^{24} - 146q^{25} - 461q^{26} - 176q^{27} - 159q^{28} - 154q^{29} - 196q^{30} - 230q^{31} - 201q^{32} - 190q^{33} - 203q^{34} - 216q^{35} - 320q^{36} - 233q^{37} - 238q^{38} - 199q^{39} - 206q^{40} - 261q^{41} - 225q^{42} - 175q^{43} - 250q^{44} - 126q^{45} - 313q^{46} - 326q^{47} - 181q^{48} - 193q^{49} - 126q^{50} - 463q^{51} - 209q^{52} - 163q^{53} - 213q^{54} - 196q^{55} - 372q^{56} - 200q^{57} - 262q^{58} - 209q^{59} - 156q^{60} - 283q^{61} - 161q^{62} - 206q^{63} - 245q^{64} - 186q^{65} - 388q^{66} - 201q^{67} - 278q^{68} - 214q^{69} - 412q^{70} - 314q^{71} - 338q^{72} - 213q^{73} - 230q^{74} - 196q^{75} - 594q^{76} - 254q^{77} - 375q^{78} - 291q^{79} - 186q^{80} - 461q^{81} - 245q^{82} - 148q^{83} - 391q^{84} - 106q^{85} - 351q^{86} - 235q^{87} + 137q^{88} - 119q^{89} - 126q^{90} - 318q^{91} - 260q^{92} - 394q^{93} - 212q^{94} - 152q^{95} - 204q^{96} + 126q^{97} + 75q^{98} + 78q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(575))\)

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
575.2.a \(\chi_{575}(1, \cdot)\) 575.2.a.a 1 1
575.2.a.b 1
575.2.a.c 1
575.2.a.d 1
575.2.a.e 1
575.2.a.f 2
575.2.a.g 2
575.2.a.h 4
575.2.a.i 4
575.2.a.j 4
575.2.a.k 7
575.2.a.l 7
575.2.b \(\chi_{575}(24, \cdot)\) 575.2.b.a 2 1
575.2.b.b 2
575.2.b.c 4
575.2.b.d 4
575.2.b.e 8
575.2.b.f 14
575.2.e \(\chi_{575}(68, \cdot)\) 575.2.e.a 4 2
575.2.e.b 8
575.2.e.c 12
575.2.e.d 20
575.2.e.e 24
575.2.g \(\chi_{575}(116, \cdot)\) 575.2.g.a 4 4
575.2.g.b 108
575.2.g.c 112
575.2.i \(\chi_{575}(139, \cdot)\) 575.2.i.a 216 4
575.2.k \(\chi_{575}(26, \cdot)\) 575.2.k.a 10 10
575.2.k.b 10
575.2.k.c 20
575.2.k.d 50
575.2.k.e 80
575.2.k.f 80
575.2.k.g 100
575.2.m \(\chi_{575}(22, \cdot)\) 575.2.m.a 464 8
575.2.p \(\chi_{575}(49, \cdot)\) 575.2.p.a 20 10
575.2.p.b 20
575.2.p.c 40
575.2.p.d 100
575.2.p.e 160
575.2.r \(\chi_{575}(7, \cdot)\) 575.2.r.a 160 20
575.2.r.b 200
575.2.r.c 320
575.2.s \(\chi_{575}(6, \cdot)\) 575.2.s.a 2320 40
575.2.u \(\chi_{575}(4, \cdot)\) 575.2.u.a 2320 40
575.2.w \(\chi_{575}(17, \cdot)\) 575.2.w.a 4640 80

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(575))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(575)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T + 2 T^{2} \))(\( 1 + 2 T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))(\( 1 - T + 2 T^{2} \))(\( 1 - 2 T + 2 T^{2} \))(\( 1 - T + 3 T^{2} - 2 T^{3} + 4 T^{4} \))(\( 1 - 3 T + 5 T^{2} - 6 T^{3} + 4 T^{4} \))(\( 1 + 2 T + 4 T^{2} + 7 T^{3} + 10 T^{4} + 14 T^{5} + 16 T^{6} + 16 T^{7} + 16 T^{8} \))(\( 1 + 3 T^{2} + 2 T^{3} + 5 T^{4} + 4 T^{5} + 12 T^{6} + 16 T^{8} \))(\( 1 + 3 T^{2} - 2 T^{3} + 5 T^{4} - 4 T^{5} + 12 T^{6} + 16 T^{8} \))(\( 1 + T + 2 T^{2} + 3 T^{3} + 7 T^{4} + 2 T^{5} + 9 T^{6} + 9 T^{7} + 18 T^{8} + 8 T^{9} + 56 T^{10} + 48 T^{11} + 64 T^{12} + 64 T^{13} + 128 T^{14} \))(\( 1 - T + 2 T^{2} - 3 T^{3} + 7 T^{4} - 2 T^{5} + 9 T^{6} - 9 T^{7} + 18 T^{8} - 8 T^{9} + 56 T^{10} - 48 T^{11} + 64 T^{12} - 64 T^{13} + 128 T^{14} \))(\( ( 1 - 2 T + 2 T^{2} )( 1 + 2 T + 2 T^{2} ) \))(\( 1 - 3 T^{2} + 4 T^{4} \))(\( 1 - T^{2} - 3 T^{4} - 4 T^{6} + 16 T^{8} \))(\( 1 - 5 T^{2} + 13 T^{4} - 20 T^{6} + 16 T^{8} \))(\( 1 - 4 T^{2} + 8 T^{4} - 7 T^{6} - 28 T^{10} + 128 T^{12} - 256 T^{14} + 256 T^{16} \))(\( 1 - 3 T^{2} + 12 T^{4} - 33 T^{6} + 91 T^{8} - 236 T^{10} + 505 T^{12} - 1091 T^{14} + 2020 T^{16} - 3776 T^{18} + 5824 T^{20} - 8448 T^{22} + 12288 T^{24} - 12288 T^{26} + 16384 T^{28} \))(\( ( 1 - 2 T + 2 T^{2} )^{2}( 1 + 2 T + 2 T^{2} )^{2} \))(\( ( 1 - 7 T^{4} + 16 T^{8} )^{2} \))(\( 1 - 79 T^{12} + 4096 T^{24} \))(\( ( 1 - 2 T + 2 T^{2} - 2 T^{3} - T^{4} + 6 T^{5} - 8 T^{6} + 16 T^{7} - 11 T^{8} - 4 T^{9} + 8 T^{10} - 8 T^{11} - 44 T^{12} + 128 T^{13} - 128 T^{14} + 192 T^{15} - 64 T^{16} - 256 T^{17} + 512 T^{18} - 1024 T^{19} + 1024 T^{20} )^{2} \))(\( 1 - T + 4 T^{2} - 2 T^{3} + 9 T^{4} - 4 T^{5} + 16 T^{6} - 8 T^{7} + 16 T^{8} \))(\( 1 + 5 T + 12 T^{2} + 17 T^{3} + 6 T^{4} - 37 T^{5} - 98 T^{6} - 119 T^{7} - 25 T^{8} + 212 T^{9} + 461 T^{10} + 424 T^{11} - 100 T^{12} - 952 T^{13} - 1568 T^{14} - 1184 T^{15} + 384 T^{16} + 2176 T^{17} + 3072 T^{18} + 2560 T^{19} + 1024 T^{20} \))(\( 1 - 7 T + 25 T^{2} - 62 T^{3} + 120 T^{4} - 188 T^{5} + 229 T^{6} - 182 T^{7} + 2 T^{8} + 284 T^{9} - 551 T^{10} + 568 T^{11} + 8 T^{12} - 1456 T^{13} + 3664 T^{14} - 6016 T^{15} + 7680 T^{16} - 7936 T^{17} + 6400 T^{18} - 3584 T^{19} + 1024 T^{20} \))(\( ( 1 - 2 T + 2 T^{2} + 7 T^{4} - 25 T^{5} + 36 T^{6} - 22 T^{7} + 16 T^{8} - 109 T^{9} + 219 T^{10} - 218 T^{11} + 64 T^{12} - 176 T^{13} + 576 T^{14} - 800 T^{15} + 448 T^{16} + 512 T^{18} - 1024 T^{19} + 1024 T^{20} )^{2} \))(\( 1 + T^{2} - 14 T^{4} - 29 T^{6} + 82 T^{8} + 297 T^{10} - 86 T^{12} - 1527 T^{14} - 1755 T^{16} + 2890 T^{18} + 11681 T^{20} + 11560 T^{22} - 28080 T^{24} - 97728 T^{26} - 22016 T^{28} + 304128 T^{30} + 335872 T^{32} - 475136 T^{34} - 917504 T^{36} + 262144 T^{38} + 1048576 T^{40} \))(\( 1 - T^{2} - 3 T^{4} + 18 T^{6} - 6 T^{8} - 22 T^{10} + 123 T^{12} - 112 T^{14} + 302 T^{16} + 828 T^{18} - 1871 T^{20} + 3312 T^{22} + 4832 T^{24} - 7168 T^{26} + 31488 T^{28} - 22528 T^{30} - 24576 T^{32} + 294912 T^{34} - 196608 T^{36} - 262144 T^{38} + 1048576 T^{40} \))
$3$ (\( 1 + 2 T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 + T^{2} + 9 T^{4} \))(\( ( 1 - T + 3 T^{2} )^{2} \))(\( ( 1 - T + 2 T^{2} - 3 T^{3} + 9 T^{4} )^{2} \))(\( 1 + 2 T + 6 T^{2} + 12 T^{3} + 23 T^{4} + 36 T^{5} + 54 T^{6} + 54 T^{7} + 81 T^{8} \))(\( 1 - 2 T + 6 T^{2} - 12 T^{3} + 23 T^{4} - 36 T^{5} + 54 T^{6} - 54 T^{7} + 81 T^{8} \))(\( 1 + 3 T^{2} + 4 T^{4} - 8 T^{5} + 25 T^{6} - 28 T^{7} + 75 T^{8} - 72 T^{9} + 108 T^{10} + 729 T^{12} + 2187 T^{14} \))(\( 1 + 3 T^{2} + 4 T^{4} + 8 T^{5} + 25 T^{6} + 28 T^{7} + 75 T^{8} + 72 T^{9} + 108 T^{10} + 729 T^{12} + 2187 T^{14} \))(\( ( 1 - 3 T^{2} )^{2} \))(\( ( 1 - 3 T^{2} )^{2} \))(\( ( 1 - 5 T^{2} + 9 T^{4} )^{2} \))(\( ( 1 - T^{2} + 9 T^{4} )^{2} \))(\( ( 1 - 3 T^{2} + 16 T^{4} - 27 T^{6} + 81 T^{8} )^{2} \))(\( 1 - 6 T^{2} + 17 T^{4} - 74 T^{6} + 316 T^{8} - 802 T^{10} + 2883 T^{12} - 11426 T^{14} + 25947 T^{16} - 64962 T^{18} + 230364 T^{20} - 485514 T^{22} + 1003833 T^{24} - 3188646 T^{26} + 4782969 T^{28} \))(\( ( 1 + 9 T^{4} )^{2} \))(\( ( 1 + 9 T^{4} )^{4} \))(\( 1 - 14 T^{12} + 531441 T^{24} \))(\( ( 1 - 4 T + 8 T^{2} - 14 T^{3} + 11 T^{4} + 8 T^{5} - 22 T^{6} + 38 T^{7} - 11 T^{8} - 82 T^{9} + 158 T^{10} - 246 T^{11} - 99 T^{12} + 1026 T^{13} - 1782 T^{14} + 1944 T^{15} + 8019 T^{16} - 30618 T^{17} + 52488 T^{18} - 78732 T^{19} + 59049 T^{20} )^{2} \))(\( 1 + 5 T + 12 T^{2} + 25 T^{3} + 49 T^{4} + 75 T^{5} + 108 T^{6} + 135 T^{7} + 81 T^{8} \))(\( ( 1 - 5 T + 14 T^{2} - 26 T^{3} + 42 T^{4} - 67 T^{5} + 126 T^{6} - 234 T^{7} + 378 T^{8} - 405 T^{9} + 243 T^{10} )( 1 + 6 T + 14 T^{2} + 7 T^{3} - 46 T^{4} - 133 T^{5} - 138 T^{6} + 63 T^{7} + 378 T^{8} + 486 T^{9} + 243 T^{10} ) \))(\( 1 - 7 T + 24 T^{2} - 59 T^{3} + 143 T^{4} - 362 T^{5} + 829 T^{6} - 1637 T^{7} + 3076 T^{8} - 5907 T^{9} + 10825 T^{10} - 17721 T^{11} + 27684 T^{12} - 44199 T^{13} + 67149 T^{14} - 87966 T^{15} + 104247 T^{16} - 129033 T^{17} + 157464 T^{18} - 137781 T^{19} + 59049 T^{20} \))(\( 1 + T + 6 T^{2} + 14 T^{3} + 27 T^{4} + 40 T^{5} + 108 T^{6} + 142 T^{7} + 185 T^{8} + 485 T^{9} + 1007 T^{10} + 1619 T^{11} + 3309 T^{12} + 9356 T^{13} + 14699 T^{14} + 23307 T^{15} + 48108 T^{16} + 86905 T^{17} + 82057 T^{18} + 156475 T^{19} + 360997 T^{20} + 469425 T^{21} + 738513 T^{22} + 2346435 T^{23} + 3896748 T^{24} + 5663601 T^{25} + 10715571 T^{26} + 20461572 T^{27} + 21710349 T^{28} + 31866777 T^{29} + 59462343 T^{30} + 85916295 T^{31} + 98316585 T^{32} + 226393866 T^{33} + 516560652 T^{34} + 573956280 T^{35} + 1162261467 T^{36} + 1807962282 T^{37} + 2324522934 T^{38} + 1162261467 T^{39} + 3486784401 T^{40} \))(\( ( 1 - 3 T^{2} + 20 T^{4} - 82 T^{6} + 224 T^{8} - 947 T^{10} + 2016 T^{12} - 6642 T^{14} + 14580 T^{16} - 19683 T^{18} + 59049 T^{20} )( 1 + 8 T^{2} + 20 T^{4} + 17 T^{6} + 114 T^{8} + 637 T^{10} + 1026 T^{12} + 1377 T^{14} + 14580 T^{16} + 52488 T^{18} + 59049 T^{20} ) \))(\( 1 + T^{2} + 36 T^{4} + 27 T^{6} + 759 T^{8} + 516 T^{10} + 11637 T^{12} + 7213 T^{14} + 142368 T^{16} + 78859 T^{18} + 1411015 T^{20} + 709731 T^{22} + 11531808 T^{24} + 5258277 T^{26} + 76350357 T^{28} + 30469284 T^{30} + 403363719 T^{32} + 129140163 T^{34} + 1549681956 T^{36} + 387420489 T^{38} + 3486784401 T^{40} \))
$5$ (\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( \))(\( 1 + 5 T + 15 T^{2} + 25 T^{3} + 25 T^{4} \))(\( \))(\( \))(\( \))(\( \))(\( \))
$7$ (\( 1 + T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 + 2 T + 10 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 - 2 T + 10 T^{2} - 14 T^{3} + 49 T^{4} \))(\( 1 - 3 T + 14 T^{2} - 11 T^{3} + 66 T^{4} - 77 T^{5} + 686 T^{6} - 1029 T^{7} + 2401 T^{8} \))(\( 1 + 6 T + 32 T^{2} + 114 T^{3} + 346 T^{4} + 798 T^{5} + 1568 T^{6} + 2058 T^{7} + 2401 T^{8} \))(\( 1 - 6 T + 32 T^{2} - 114 T^{3} + 346 T^{4} - 798 T^{5} + 1568 T^{6} - 2058 T^{7} + 2401 T^{8} \))(\( 1 - 3 T + 9 T^{2} - 14 T^{3} + 45 T^{4} + 35 T^{5} - 171 T^{6} + 1276 T^{7} - 1197 T^{8} + 1715 T^{9} + 15435 T^{10} - 33614 T^{11} + 151263 T^{12} - 352947 T^{13} + 823543 T^{14} \))(\( 1 + 3 T + 9 T^{2} + 14 T^{3} + 45 T^{4} - 35 T^{5} - 171 T^{6} - 1276 T^{7} - 1197 T^{8} - 1715 T^{9} + 15435 T^{10} + 33614 T^{11} + 151263 T^{12} + 352947 T^{13} + 823543 T^{14} \))(\( 1 - 13 T^{2} + 49 T^{4} \))(\( 1 - 13 T^{2} + 49 T^{4} \))(\( 1 - 16 T^{2} + 142 T^{4} - 784 T^{6} + 2401 T^{8} \))(\( 1 - 16 T^{2} + 142 T^{4} - 784 T^{6} + 2401 T^{8} \))(\( 1 - 19 T^{2} + 262 T^{4} - 2637 T^{6} + 20498 T^{8} - 129213 T^{10} + 629062 T^{12} - 2235331 T^{14} + 5764801 T^{16} \))(\( 1 - 9 T^{2} + 87 T^{4} - 482 T^{6} + 5189 T^{8} - 38727 T^{10} + 258883 T^{12} - 1361244 T^{14} + 12685267 T^{16} - 92983527 T^{18} + 610480661 T^{20} - 2778634082 T^{22} + 24575346663 T^{24} - 124571584809 T^{26} + 678223072849 T^{28} \))(\( 1 - 17 T^{4} + 2401 T^{8} \))(\( ( 1 - 89 T^{4} + 2401 T^{8} )^{2} \))(\( ( 1 + 49 T^{4} )^{6} \))(\( 1 - 237 T^{4} + 23161 T^{8} - 1134076 T^{12} + 24086022 T^{16} - 196683742 T^{20} + 57830538822 T^{24} - 6537722458876 T^{28} + 320578052862361 T^{32} - 7876204544995437 T^{36} + 79792266297612001 T^{40} \))(\( ( 1 - T + 7 T^{2} )^{4} \))(\( 1 + 5 T + 7 T^{2} + 22 T^{3} + 61 T^{4} + 63 T^{5} + 262 T^{6} - 704 T^{7} - 3165 T^{8} - 7828 T^{9} - 38149 T^{10} - 54796 T^{11} - 155085 T^{12} - 241472 T^{13} + 629062 T^{14} + 1058841 T^{15} + 7176589 T^{16} + 18117946 T^{17} + 40353607 T^{18} + 201768035 T^{19} + 282475249 T^{20} \))(\( 1 - 5 T + 18 T^{2} - 88 T^{3} + 347 T^{4} - 1075 T^{5} + 3628 T^{6} - 11550 T^{7} + 31166 T^{8} - 88994 T^{9} + 252361 T^{10} - 622958 T^{11} + 1527134 T^{12} - 3961650 T^{13} + 8710828 T^{14} - 18067525 T^{15} + 40824203 T^{16} - 72471784 T^{17} + 103766418 T^{18} - 201768035 T^{19} + 282475249 T^{20} \))(\( 1 - 4 T - T^{2} - 11 T^{3} + 245 T^{4} - 349 T^{5} - 1301 T^{6} - 1861 T^{7} + 18638 T^{8} + 28841 T^{9} - 155478 T^{10} - 268498 T^{11} + 305619 T^{12} + 4521142 T^{13} - 1974595 T^{14} - 24747851 T^{15} - 38560597 T^{16} + 137651474 T^{17} + 569072322 T^{18} - 697342953 T^{19} - 3108876707 T^{20} - 4881400671 T^{21} + 27884543778 T^{22} + 47214455582 T^{23} - 92583993397 T^{24} - 415937131757 T^{25} - 232309127155 T^{26} + 3723354846106 T^{27} + 1761832716819 T^{28} - 10834862772286 T^{29} - 43918686764022 T^{30} + 57028080594863 T^{31} + 257973910852238 T^{32} - 180310448367427 T^{33} - 882368217776549 T^{34} - 1656898966970107 T^{35} + 8142067989552245 T^{36} - 2558935653859277 T^{37} - 1628413597910449 T^{38} - 45595580741492572 T^{39} + 79792266297612001 T^{40} \))(\( 1 + 11 T^{2} - 49 T^{4} - 264 T^{6} + 5327 T^{8} - 16643 T^{10} - 180646 T^{12} + 1909248 T^{14} - 9814345 T^{16} - 82370310 T^{18} + 625944901 T^{20} - 4036145190 T^{22} - 23564242345 T^{24} + 224621117952 T^{26} - 1041388241446 T^{28} - 4701235569107 T^{30} + 73732536919727 T^{32} - 179050891232136 T^{34} - 1628413597910449 T^{36} + 17912549577014939 T^{38} + 79792266297612001 T^{40} \))(\( 1 - 11 T^{2} + 138 T^{4} - 1254 T^{6} + 8649 T^{8} - 66165 T^{10} + 205828 T^{12} + 319198 T^{14} - 15526568 T^{16} + 198842644 T^{18} - 1297359383 T^{20} + 9743289556 T^{22} - 37279289768 T^{24} + 37553325502 T^{26} + 1186557460228 T^{28} - 18689974850085 T^{30} + 119713293001449 T^{32} - 850491733352646 T^{34} + 4586144418604938 T^{36} - 17912549577014939 T^{38} + 79792266297612001 T^{40} \))
$11$ (\( 1 + 11 T^{2} \))(\( 1 - 2 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 6 T + 26 T^{2} + 66 T^{3} + 121 T^{4} \))(\( 1 + 2 T + 18 T^{2} + 22 T^{3} + 121 T^{4} \))(\( 1 - 4 T + 28 T^{2} - 92 T^{3} + 406 T^{4} - 1012 T^{5} + 3388 T^{6} - 5324 T^{7} + 14641 T^{8} \))(\( 1 - 2 T + 28 T^{2} - 22 T^{3} + 346 T^{4} - 242 T^{5} + 3388 T^{6} - 2662 T^{7} + 14641 T^{8} \))(\( 1 - 2 T + 28 T^{2} - 22 T^{3} + 346 T^{4} - 242 T^{5} + 3388 T^{6} - 2662 T^{7} + 14641 T^{8} \))(\( 1 + T + 19 T^{2} - 18 T^{3} + 247 T^{4} - 153 T^{5} + 3637 T^{6} - 1148 T^{7} + 40007 T^{8} - 18513 T^{9} + 328757 T^{10} - 263538 T^{11} + 3059969 T^{12} + 1771561 T^{13} + 19487171 T^{14} \))(\( 1 + T + 19 T^{2} - 18 T^{3} + 247 T^{4} - 153 T^{5} + 3637 T^{6} - 1148 T^{7} + 40007 T^{8} - 18513 T^{9} + 328757 T^{10} - 263538 T^{11} + 3059969 T^{12} + 1771561 T^{13} + 19487171 T^{14} \))(\( ( 1 - 2 T + 11 T^{2} )^{2} \))(\( ( 1 + T + 11 T^{2} )^{2} \))(\( ( 1 + 2 T + 18 T^{2} + 22 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 + 6 T + 26 T^{2} + 66 T^{3} + 121 T^{4} )^{2} \))(\( ( 1 - 4 T + 28 T^{2} - 92 T^{3} + 406 T^{4} - 1012 T^{5} + 3388 T^{6} - 5324 T^{7} + 14641 T^{8} )^{2} \))(\( ( 1 + T + 19 T^{2} - 18 T^{3} + 247 T^{4} - 153 T^{5} + 3637 T^{6} - 1148 T^{7} + 40007 T^{8} - 18513 T^{9} + 328757 T^{10} - 263538 T^{11} + 3059969 T^{12} + 1771561 T^{13} + 19487171 T^{14} )^{2} \))(\( ( 1 - 11 T^{2} )^{4} \))(\( ( 1 + 11 T^{2} + 121 T^{4} )^{4} \))(\( ( 1 - 11 T^{2} )^{12} \))(\( ( 1 - 42 T^{2} + 1081 T^{4} - 20956 T^{6} + 316762 T^{8} - 3842292 T^{10} + 38328202 T^{12} - 306816796 T^{14} + 1915057441 T^{16} - 9003073002 T^{18} + 25937424601 T^{20} )^{2} \))(\( 1 + 9 T + 25 T^{2} + 21 T^{3} + 4 T^{4} + 231 T^{5} + 3025 T^{6} + 11979 T^{7} + 14641 T^{8} \))(\( 1 - 8 T + 20 T^{2} - 116 T^{3} + 785 T^{4} - 1924 T^{5} + 7648 T^{6} - 42781 T^{7} + 84254 T^{8} - 306621 T^{9} + 1799073 T^{10} - 3372831 T^{11} + 10194734 T^{12} - 56941511 T^{13} + 111974368 T^{14} - 309862124 T^{15} + 1390675385 T^{16} - 2260511836 T^{17} + 4287177620 T^{18} - 18863581528 T^{19} + 25937424601 T^{20} \))(\( 1 - 7 T + 5 T^{2} + 64 T^{3} - 239 T^{4} + 243 T^{5} + 4448 T^{6} - 26384 T^{7} + 38597 T^{8} + 113996 T^{9} - 669129 T^{10} + 1253956 T^{11} + 4670237 T^{12} - 35117104 T^{13} + 65123168 T^{14} + 39135393 T^{15} - 423403079 T^{16} + 1247178944 T^{17} + 1071794405 T^{18} - 16505633837 T^{19} + 25937424601 T^{20} \))(\( 1 + 8 T + 8 T^{2} - 120 T^{3} - 561 T^{4} - 859 T^{5} + 2258 T^{6} + 21321 T^{7} + 77329 T^{8} + 120978 T^{9} - 353594 T^{10} - 3097611 T^{11} - 8842197 T^{12} - 10206633 T^{13} + 28541538 T^{14} + 311515082 T^{15} + 1139840185 T^{16} + 880981278 T^{17} - 5235886142 T^{18} - 18114167536 T^{19} - 48380815625 T^{20} - 199255842896 T^{21} - 633542223182 T^{22} + 1172586081018 T^{23} + 16688400148585 T^{24} + 50169815471182 T^{25} + 50563075600818 T^{26} - 198898402605243 T^{27} - 1895403454501557 T^{28} - 7304004705066201 T^{29} - 9171317714365994 T^{30} + 34516435287177558 T^{31} + 242691527943458209 T^{32} + 736058745620752851 T^{33} + 857475124230958178 T^{34} - 3588256177528044209 T^{35} - 25777798453463982321 T^{36} - 60653643419915252520 T^{37} + 44479338507937851848 T^{38} + \)\(48\!\cdots\!28\)\( T^{39} + \)\(67\!\cdots\!01\)\( T^{40} \))(\( ( 1 - 8 T + 20 T^{2} - 116 T^{3} + 785 T^{4} - 1924 T^{5} + 7648 T^{6} - 42781 T^{7} + 84254 T^{8} - 306621 T^{9} + 1799073 T^{10} - 3372831 T^{11} + 10194734 T^{12} - 56941511 T^{13} + 111974368 T^{14} - 309862124 T^{15} + 1390675385 T^{16} - 2260511836 T^{17} + 4287177620 T^{18} - 18863581528 T^{19} + 25937424601 T^{20} )^{2} \))(\( ( 1 - 7 T + 5 T^{2} + 64 T^{3} - 239 T^{4} + 243 T^{5} + 4448 T^{6} - 26384 T^{7} + 38597 T^{8} + 113996 T^{9} - 669129 T^{10} + 1253956 T^{11} + 4670237 T^{12} - 35117104 T^{13} + 65123168 T^{14} + 39135393 T^{15} - 423403079 T^{16} + 1247178944 T^{17} + 1071794405 T^{18} - 16505633837 T^{19} + 25937424601 T^{20} )^{2} \))
$13$ (\( 1 + 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))(\( 1 + T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( ( 1 + 3 T + 13 T^{2} )^{2} \))(\( 1 - 8 T + 37 T^{2} - 104 T^{3} + 169 T^{4} \))(\( 1 + 11 T^{2} + 160 T^{4} + 1859 T^{6} + 28561 T^{8} \))(\( 1 + 14 T + 118 T^{2} + 664 T^{3} + 2791 T^{4} + 8632 T^{5} + 19942 T^{6} + 30758 T^{7} + 28561 T^{8} \))(\( 1 - 14 T + 118 T^{2} - 664 T^{3} + 2791 T^{4} - 8632 T^{5} + 19942 T^{6} - 30758 T^{7} + 28561 T^{8} \))(\( 1 + 3 T + 45 T^{2} + 158 T^{3} + 1198 T^{4} + 4246 T^{5} + 21399 T^{6} + 68537 T^{7} + 278187 T^{8} + 717574 T^{9} + 2632006 T^{10} + 4512638 T^{11} + 16708185 T^{12} + 14480427 T^{13} + 62748517 T^{14} \))(\( 1 - 3 T + 45 T^{2} - 158 T^{3} + 1198 T^{4} - 4246 T^{5} + 21399 T^{6} - 68537 T^{7} + 278187 T^{8} - 717574 T^{9} + 2632006 T^{10} - 4512638 T^{11} + 16708185 T^{12} - 14480427 T^{13} + 62748517 T^{14} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - 25 T^{2} + 169 T^{4} \))(\( 1 - 10 T^{2} + 43 T^{4} - 1690 T^{6} + 28561 T^{8} \))(\( ( 1 - 17 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 11 T^{2} + 160 T^{4} - 1859 T^{6} + 28561 T^{8} )^{2} \))(\( 1 - 81 T^{2} + 3473 T^{4} - 100178 T^{6} + 2164530 T^{8} - 37581194 T^{10} + 558904747 T^{12} - 7537532339 T^{14} + 94454902243 T^{16} - 1073356481834 T^{18} + 10447772884770 T^{20} - 81718272168338 T^{22} + 478782542191577 T^{24} - 1887144894920961 T^{26} + 3937376385699289 T^{28} \))(\( ( 1 + 169 T^{4} )^{2} \))(\( ( 1 + 191 T^{4} + 28561 T^{8} )^{2} \))(\( 1 - 8482894 T^{12} + 23298085122481 T^{24} \))(\( ( 1 + 2 T + 2 T^{2} + 60 T^{3} + 339 T^{4} - 508 T^{5} + 106 T^{6} + 3702 T^{7} - 35227 T^{8} - 234016 T^{9} - 82360 T^{10} - 3042208 T^{11} - 5953363 T^{12} + 8133294 T^{13} + 3027466 T^{14} - 188616844 T^{15} + 1636288251 T^{16} + 3764911020 T^{17} + 1631461442 T^{18} + 21208998746 T^{19} + 137858491849 T^{20} )^{2} \))(\( 1 + 6 T + 3 T^{2} - 10 T^{3} + 81 T^{4} - 130 T^{5} + 507 T^{6} + 13182 T^{7} + 28561 T^{8} \))(\( 1 - 2 T^{2} - 11 T^{3} + 169 T^{4} - 407 T^{5} + 1785 T^{6} + 2068 T^{7} + 30475 T^{8} - 77154 T^{9} + 232145 T^{10} - 1003002 T^{11} + 5150275 T^{12} + 4543396 T^{13} + 50981385 T^{14} - 151116251 T^{15} + 815730721 T^{16} - 690233687 T^{17} - 1631461442 T^{18} + 137858491849 T^{20} \))(\( 1 - 3 T - 4 T^{2} + 150 T^{3} - 57 T^{4} - 1141 T^{5} + 7530 T^{6} + 26970 T^{7} - 69482 T^{8} + 33220 T^{9} + 2163305 T^{10} + 431860 T^{11} - 11742458 T^{12} + 59253090 T^{13} + 215064330 T^{14} - 423645313 T^{15} - 275128113 T^{16} + 9412277550 T^{17} - 3262922884 T^{18} - 31813498119 T^{19} + 137858491849 T^{20} \))(\( 1 + 10 T + 58 T^{2} + 323 T^{3} + 1705 T^{4} + 8003 T^{5} + 37572 T^{6} + 172909 T^{7} + 767395 T^{8} + 3344202 T^{9} + 13988859 T^{10} + 56848352 T^{11} + 227655708 T^{12} + 894452242 T^{13} + 3496893949 T^{14} + 13511663886 T^{15} + 51241017455 T^{16} + 193291836963 T^{17} + 714868254694 T^{18} + 2598123737952 T^{19} + 9385591752033 T^{20} + 33775608593376 T^{21} + 120812735043286 T^{22} + 424662165807711 T^{23} + 1463494699532255 T^{24} + 5016786219224598 T^{25} + 16878839185078741 T^{26} + 56125551712825114 T^{27} + 185705754826605468 T^{28} + 602848313140083296 T^{29} + 1928483004428310291 T^{30} + 5993346374059323474 T^{31} + 17878834032566306995 T^{32} + 52369831805759873977 T^{33} + \)\(14\!\cdots\!08\)\( T^{34} + \)\(40\!\cdots\!71\)\( T^{35} + \)\(11\!\cdots\!05\)\( T^{36} + \)\(27\!\cdots\!59\)\( T^{37} + \)\(65\!\cdots\!82\)\( T^{38} + \)\(14\!\cdots\!70\)\( T^{39} + \)\(19\!\cdots\!01\)\( T^{40} \))(\( 1 + 4 T^{2} + 342 T^{4} - 2773 T^{6} + 73417 T^{8} - 825567 T^{10} + 22844709 T^{12} - 179476406 T^{14} + 4528432155 T^{16} - 41811025240 T^{18} + 796007431989 T^{20} - 7066063265560 T^{22} + 129336550778955 T^{24} - 866298331768454 T^{26} + 18635130943605189 T^{28} - 113811421540303383 T^{30} + 1710475515437187577 T^{32} - 10918344717544128397 T^{34} + \)\(22\!\cdots\!22\)\( T^{36} + \)\(44\!\cdots\!16\)\( T^{38} + \)\(19\!\cdots\!01\)\( T^{40} \))(\( 1 + 17 T^{2} + 802 T^{4} + 13830 T^{6} + 308165 T^{8} + 5169515 T^{10} + 78001192 T^{12} + 1194559686 T^{14} + 15350809812 T^{16} + 211920374204 T^{18} + 2677593927009 T^{20} + 35814543240476 T^{22} + 438434479040532 T^{24} + 5765911443421974 T^{26} + 63627968589019432 T^{28} + 712661541490783235 T^{30} + 7179654401769357365 T^{32} + 54453915414221166870 T^{34} + \)\(53\!\cdots\!82\)\( T^{36} + \)\(19\!\cdots\!93\)\( T^{38} + \)\(19\!\cdots\!01\)\( T^{40} \))
$17$ (\( 1 - 5 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 5 T + 17 T^{2} \))(\( 1 + 6 T + 38 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 - 4 T + 18 T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 - T + 50 T^{2} - 27 T^{3} + 1154 T^{4} - 459 T^{5} + 14450 T^{6} - 4913 T^{7} + 83521 T^{8} \))(\( 1 + 14 T + 126 T^{2} + 778 T^{3} + 3726 T^{4} + 13226 T^{5} + 36414 T^{6} + 68782 T^{7} + 83521 T^{8} \))(\( 1 - 14 T + 126 T^{2} - 778 T^{3} + 3726 T^{4} - 13226 T^{5} + 36414 T^{6} - 68782 T^{7} + 83521 T^{8} \))(\( 1 - 10 T + 83 T^{2} - 508 T^{3} + 3281 T^{4} - 17046 T^{5} + 82619 T^{6} - 338120 T^{7} + 1404523 T^{8} - 4926294 T^{9} + 16119553 T^{10} - 42428668 T^{11} + 117848131 T^{12} - 241375690 T^{13} + 410338673 T^{14} \))(\( 1 + 10 T + 83 T^{2} + 508 T^{3} + 3281 T^{4} + 17046 T^{5} + 82619 T^{6} + 338120 T^{7} + 1404523 T^{8} + 4926294 T^{9} + 16119553 T^{10} + 42428668 T^{11} + 117848131 T^{12} + 241375690 T^{13} + 410338673 T^{14} \))(\( 1 - 25 T^{2} + 289 T^{4} \))(\( ( 1 - 17 T^{2} )^{2} \))(\( 1 - 20 T^{2} + 358 T^{4} - 5780 T^{6} + 83521 T^{8} \))(\( 1 - 40 T^{2} + 798 T^{4} - 11560 T^{6} + 83521 T^{8} \))(\( 1 - 99 T^{2} + 4754 T^{4} - 142653 T^{6} + 2909146 T^{8} - 41226717 T^{10} + 397058834 T^{12} - 2389619331 T^{14} + 6975757441 T^{16} \))(\( 1 - 66 T^{2} + 3291 T^{4} - 110900 T^{6} + 3207625 T^{8} - 74913886 T^{10} + 1573046043 T^{12} - 28033155416 T^{14} + 454610306427 T^{16} - 6256882672606 T^{18} + 77424269763625 T^{20} - 773611500206900 T^{22} + 6634635926377659 T^{24} - 38453067657164226 T^{26} + 168377826559400929 T^{28} \))(\( 1 - 457 T^{4} + 83521 T^{8} \))(\( ( 1 - 478 T^{4} + 83521 T^{8} )^{2} \))(\( ( 1 + 289 T^{4} )^{6} \))(\( 1 + 519 T^{4} + 89433 T^{8} - 14268808 T^{12} - 7240575434 T^{16} - 2204663931022 T^{20} - 604740100823114 T^{24} - 99535743580200328 T^{28} + 52105654542169215513 T^{32} + \)\(25\!\cdots\!39\)\( T^{36} + \)\(40\!\cdots\!01\)\( T^{40} \))(\( 1 - 17 T^{2} + 289 T^{4} - 4913 T^{6} + 83521 T^{8} \))(\( 1 - 23 T + 248 T^{2} - 1793 T^{3} + 10843 T^{4} - 61388 T^{5} + 327661 T^{6} - 1644533 T^{7} + 7815982 T^{8} - 35008785 T^{9} + 148068887 T^{10} - 595149345 T^{11} + 2258818798 T^{12} - 8079590629 T^{13} + 27366574381 T^{14} - 87162181516 T^{15} + 261723660667 T^{16} - 735737240689 T^{17} + 1729987845368 T^{18} - 2727521159431 T^{19} + 2015993900449 T^{20} \))(\( 1 - 10 T + 39 T^{2} - 99 T^{3} - 36 T^{4} + 2241 T^{5} - 11458 T^{6} + 44847 T^{7} - 59633 T^{8} - 522161 T^{9} + 3253139 T^{10} - 8876737 T^{11} - 17233937 T^{12} + 220333311 T^{13} - 956983618 T^{14} + 3181899537 T^{15} - 868952484 T^{16} - 40623528627 T^{17} + 272054540199 T^{18} - 1185878764970 T^{19} + 2015993900449 T^{20} \))(\( 1 - 9 T + 40 T^{2} - 100 T^{3} - 246 T^{4} + 2278 T^{5} - 8909 T^{6} + 24479 T^{7} + 1113 T^{8} + 224535 T^{9} - 2290561 T^{10} + 16349752 T^{11} - 91534141 T^{12} + 280206614 T^{13} - 628445950 T^{14} - 1744414036 T^{15} + 25418244278 T^{16} - 123431240367 T^{17} + 377484951692 T^{18} - 330981245066 T^{19} - 1445197923018 T^{20} - 5626681166122 T^{21} + 109093151038988 T^{22} - 606417683923071 T^{23} + 2122957180342838 T^{24} - 2476818479912852 T^{25} - 15169157480895550 T^{26} + 114979610154583222 T^{27} - 638519965186293181 T^{28} + 1938882370932578744 T^{29} - 4617757004606361889 T^{30} + 7695240237434375655 T^{31} + 648458550036723993 T^{32} + \)\(24\!\cdots\!23\)\( T^{33} - \)\(15\!\cdots\!61\)\( T^{34} + \)\(65\!\cdots\!54\)\( T^{35} - \)\(11\!\cdots\!26\)\( T^{36} - \)\(82\!\cdots\!00\)\( T^{37} + \)\(56\!\cdots\!60\)\( T^{38} - \)\(21\!\cdots\!77\)\( T^{39} + \)\(40\!\cdots\!01\)\( T^{40} \))(\( 1 + 33 T^{2} + 712 T^{4} + 5247 T^{6} - 63417 T^{8} - 2335300 T^{10} - 8634367 T^{12} + 479983097 T^{14} + 5253686816 T^{16} - 119789062789 T^{18} - 4528520895449 T^{20} - 34619039146021 T^{22} + 438793176559136 T^{24} + 11585625122671193 T^{26} - 60231249848574847 T^{28} - 4707950555718549700 T^{30} - 36948154418399753337 T^{32} + \)\(88\!\cdots\!63\)\( T^{34} + \)\(34\!\cdots\!72\)\( T^{36} + \)\(46\!\cdots\!97\)\( T^{38} + \)\(40\!\cdots\!01\)\( T^{40} \))(\( 1 + 22 T^{2} - 531 T^{4} - 9295 T^{6} + 328964 T^{8} + 3905715 T^{10} - 127070564 T^{12} - 852253985 T^{14} + 47749607943 T^{16} + 94272794099 T^{18} - 15171676237609 T^{20} + 27244837494611 T^{22} + 3988095005007303 T^{24} - 20571339368462465 T^{26} - 886413432355066724 T^{28} + 7873897616892166035 T^{30} + \)\(19\!\cdots\!04\)\( T^{32} - \)\(15\!\cdots\!55\)\( T^{34} - \)\(25\!\cdots\!11\)\( T^{36} + \)\(30\!\cdots\!98\)\( T^{38} + \)\(40\!\cdots\!01\)\( T^{40} \))
$19$ (\( 1 - 8 T + 19 T^{2} \))(\( 1 + 2 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( ( 1 + 2 T + 19 T^{2} )^{2} \))(\( 1 - 2 T - 6 T^{2} - 38 T^{3} + 361 T^{4} \))(\( 1 + 4 T + 60 T^{2} + 188 T^{3} + 1590 T^{4} + 3572 T^{5} + 21660 T^{6} + 27436 T^{7} + 130321 T^{8} \))(\( 1 + 4 T + 70 T^{2} + 200 T^{3} + 1918 T^{4} + 3800 T^{5} + 25270 T^{6} + 27436 T^{7} + 130321 T^{8} \))(\( 1 + 4 T + 70 T^{2} + 200 T^{3} + 1918 T^{4} + 3800 T^{5} + 25270 T^{6} + 27436 T^{7} + 130321 T^{8} \))(\( 1 - 15 T + 163 T^{2} - 1158 T^{3} + 6863 T^{4} - 31817 T^{5} + 140765 T^{6} - 580340 T^{7} + 2674535 T^{8} - 11485937 T^{9} + 47073317 T^{10} - 150911718 T^{11} + 403604137 T^{12} - 705688215 T^{13} + 893871739 T^{14} \))(\( 1 - 15 T + 163 T^{2} - 1158 T^{3} + 6863 T^{4} - 31817 T^{5} + 140765 T^{6} - 580340 T^{7} + 2674535 T^{8} - 11485937 T^{9} + 47073317 T^{10} - 150911718 T^{11} + 403604137 T^{12} - 705688215 T^{13} + 893871739 T^{14} \))(\( ( 1 - 2 T + 19 T^{2} )^{2} \))(\( ( 1 - 5 T + 19 T^{2} )^{2} \))(\( ( 1 + 2 T - 6 T^{2} + 38 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 - 2 T + 19 T^{2} )^{4} \))(\( ( 1 - 4 T + 60 T^{2} - 188 T^{3} + 1590 T^{4} - 3572 T^{5} + 21660 T^{6} - 27436 T^{7} + 130321 T^{8} )^{2} \))(\( ( 1 + 15 T + 163 T^{2} + 1158 T^{3} + 6863 T^{4} + 31817 T^{5} + 140765 T^{6} + 580340 T^{7} + 2674535 T^{8} + 11485937 T^{9} + 47073317 T^{10} + 150911718 T^{11} + 403604137 T^{12} + 705688215 T^{13} + 893871739 T^{14} )^{2} \))(\( ( 1 + 19 T^{2} )^{4} \))(\( ( 1 + 5 T^{2} + 361 T^{4} )^{4} \))(\( ( 1 + 19 T^{2} )^{12} \))(\( ( 1 + 72 T^{2} + 2599 T^{4} + 72796 T^{6} + 1835388 T^{8} + 39000088 T^{10} + 662575068 T^{12} + 9486847516 T^{14} + 122272244719 T^{16} + 1222816538952 T^{18} + 6131066257801 T^{20} )^{2} \))(\( 1 + 5 T + 21 T^{2} + 145 T^{3} + 956 T^{4} + 2755 T^{5} + 7581 T^{6} + 34295 T^{7} + 130321 T^{8} \))(\( 1 + 13 T + 29 T^{2} - 409 T^{3} - 2337 T^{4} + 5165 T^{5} + 66426 T^{6} + 2641 T^{7} - 1149892 T^{8} - 297132 T^{9} + 19829679 T^{10} - 5645508 T^{11} - 415111012 T^{12} + 18114619 T^{13} + 8656702746 T^{14} + 12789051335 T^{15} - 109946223897 T^{16} - 365593541251 T^{17} + 492523328189 T^{18} + 4194940071127 T^{19} + 6131066257801 T^{20} \))(\( 1 - 2 T - 59 T^{2} + 310 T^{3} + 1513 T^{4} - 14460 T^{5} + 481 T^{6} + 343914 T^{7} - 1093143 T^{8} - 3113594 T^{9} + 31471397 T^{10} - 59158286 T^{11} - 394624623 T^{12} + 2358906126 T^{13} + 62684401 T^{14} - 35804391540 T^{15} + 71180417953 T^{16} + 277100239090 T^{17} - 1002030219419 T^{18} - 645375395558 T^{19} + 6131066257801 T^{20} \))(\( 1 - 24 T + 252 T^{2} - 1489 T^{3} + 4733 T^{4} + 3733 T^{5} - 165357 T^{6} + 1237434 T^{7} - 5578089 T^{8} + 16320194 T^{9} - 18257942 T^{10} - 187138908 T^{11} + 1933541143 T^{12} - 11304701304 T^{13} + 48272065375 T^{14} - 142867417584 T^{15} + 120166092742 T^{16} + 1544637215496 T^{17} - 11207167930805 T^{18} + 52159457753326 T^{19} - 225110036080269 T^{20} + 991029697313194 T^{21} - 4045787623020605 T^{22} + 10594666661087064 T^{23} + 15660165372230182 T^{24} - 353753869812324816 T^{25} + 2271001843256470375 T^{26} - 10104953013482047656 T^{27} + 32838417894507695863 T^{28} - 60387423387396085332 T^{29} - \)\(11\!\cdots\!42\)\( T^{30} + \)\(19\!\cdots\!86\)\( T^{31} - \)\(12\!\cdots\!29\)\( T^{32} + \)\(52\!\cdots\!06\)\( T^{33} - \)\(13\!\cdots\!97\)\( T^{34} + \)\(56\!\cdots\!67\)\( T^{35} + \)\(13\!\cdots\!73\)\( T^{36} - \)\(81\!\cdots\!71\)\( T^{37} + \)\(26\!\cdots\!32\)\( T^{38} - \)\(47\!\cdots\!96\)\( T^{39} + \)\(37\!\cdots\!01\)\( T^{40} \))(\( ( 1 - 13 T + 29 T^{2} + 409 T^{3} - 2337 T^{4} - 5165 T^{5} + 66426 T^{6} - 2641 T^{7} - 1149892 T^{8} + 297132 T^{9} + 19829679 T^{10} + 5645508 T^{11} - 415111012 T^{12} - 18114619 T^{13} + 8656702746 T^{14} - 12789051335 T^{15} - 109946223897 T^{16} + 365593541251 T^{17} + 492523328189 T^{18} - 4194940071127 T^{19} + 6131066257801 T^{20} )^{2} \))(\( ( 1 + 2 T - 59 T^{2} - 310 T^{3} + 1513 T^{4} + 14460 T^{5} + 481 T^{6} - 343914 T^{7} - 1093143 T^{8} + 3113594 T^{9} + 31471397 T^{10} + 59158286 T^{11} - 394624623 T^{12} - 2358906126 T^{13} + 62684401 T^{14} + 35804391540 T^{15} + 71180417953 T^{16} - 277100239090 T^{17} - 1002030219419 T^{18} + 645375395558 T^{19} + 6131066257801 T^{20} )^{2} \))
$23$ (\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{4} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))(\( ( 1 + T )^{7} \))(\( ( 1 - T )^{7} \))(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{7} \))(\( 1 + 529 T^{4} \))(\( 1 - 1054 T^{4} + 279841 T^{8} \))(\( ( 1 + 529 T^{4} )^{3} \))(\( 1 - 112 T^{3} + 1429 T^{4} - 1424 T^{5} + 6272 T^{6} - 100048 T^{7} + 1214218 T^{8} - 2254896 T^{9} + 3256576 T^{10} - 51862608 T^{11} + 642321322 T^{12} - 1217284016 T^{13} + 1755162752 T^{14} - 9165352432 T^{15} + 211543285381 T^{16} - 381340450064 T^{17} + 41426511213649 T^{20} \))(\( 1 + T + T^{2} + T^{3} + T^{4} \))(\( 1 - 21 T + 243 T^{2} - 1913 T^{3} + 11771 T^{4} - 60543 T^{5} + 270733 T^{6} - 1011977 T^{7} + 2956581 T^{8} - 5876661 T^{9} + 6436343 T^{10} \))(\( 1 - 12 T - 10 T^{2} + 527 T^{3} - 32 T^{4} - 14103 T^{5} - 736 T^{6} + 278783 T^{7} - 121670 T^{8} - 3358092 T^{9} + 6436343 T^{10} \))(\( 1 + 11 T + 12 T^{2} - 429 T^{3} - 1627 T^{4} + 7370 T^{5} + 59423 T^{6} + 30723 T^{7} - 510938 T^{8} - 866525 T^{9} + 4291915 T^{10} - 19930075 T^{11} - 270286202 T^{12} + 373806741 T^{13} + 16628991743 T^{14} + 47435847910 T^{15} - 240854391403 T^{16} - 1460670116763 T^{17} + 939731823372 T^{18} + 19812679276093 T^{19} + 41426511213649 T^{20} \))(\( 1 - 45 T^{2} + 2245 T^{4} - 59797 T^{6} + 1905289 T^{8} - 39268725 T^{10} + 1007897881 T^{12} - 16733652277 T^{14} + 332340570805 T^{16} - 3523994337645 T^{18} + 41426511213649 T^{20} \))(\( 1 + 164 T^{2} + 12684 T^{4} + 617033 T^{6} + 21327758 T^{8} + 557972909 T^{10} + 11282383982 T^{12} + 172671131753 T^{14} + 1877687216076 T^{16} + 12843001586084 T^{18} + 41426511213649 T^{20} \))
$29$ (\( 1 + 5 T + 29 T^{2} \))(\( 1 - 7 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( 1 + 5 T + 29 T^{2} \))(\( ( 1 + 3 T + 29 T^{2} )^{2} \))(\( 1 + 10 T + 63 T^{2} + 290 T^{3} + 841 T^{4} \))(\( 1 - 19 T + 233 T^{2} - 1922 T^{3} + 12034 T^{4} - 55738 T^{5} + 195953 T^{6} - 463391 T^{7} + 707281 T^{8} \))(\( 1 - 4 T + 94 T^{2} - 344 T^{3} + 3775 T^{4} - 9976 T^{5} + 79054 T^{6} - 97556 T^{7} + 707281 T^{8} \))(\( 1 - 4 T + 94 T^{2} - 344 T^{3} + 3775 T^{4} - 9976 T^{5} + 79054 T^{6} - 97556 T^{7} + 707281 T^{8} \))(\( 1 - 3 T + 81 T^{2} - 226 T^{3} + 2202 T^{4} - 6878 T^{5} + 11647 T^{6} - 168501 T^{7} + 337763 T^{8} - 5784398 T^{9} + 53704578 T^{10} - 159845506 T^{11} + 1661403069 T^{12} - 1784469963 T^{13} + 17249876309 T^{14} \))(\( 1 - 3 T + 81 T^{2} - 226 T^{3} + 2202 T^{4} - 6878 T^{5} + 11647 T^{6} - 168501 T^{7} + 337763 T^{8} - 5784398 T^{9} + 53704578 T^{10} - 159845506 T^{11} + 1661403069 T^{12} - 1784469963 T^{13} + 17249876309 T^{14} \))(\( ( 1 + 7 T + 29 T^{2} )^{2} \))(\( ( 1 - 5 T + 29 T^{2} )^{2} \))(\( ( 1 - 10 T + 63 T^{2} - 290 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 - 3 T + 29 T^{2} )^{4} \))(\( ( 1 + 19 T + 233 T^{2} + 1922 T^{3} + 12034 T^{4} + 55738 T^{5} + 195953 T^{6} + 463391 T^{7} + 707281 T^{8} )^{2} \))(\( ( 1 + 3 T + 81 T^{2} + 226 T^{3} + 2202 T^{4} + 6878 T^{5} + 11647 T^{6} + 168501 T^{7} + 337763 T^{8} + 5784398 T^{9} + 53704578 T^{10} + 159845506 T^{11} + 1661403069 T^{12} + 1784469963 T^{13} + 17249876309 T^{14} )^{2} \))(\( ( 1 - 57 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 9 T^{2} + 841 T^{4} )^{4} \))(\( ( 1 + 30746 T^{6} + 594823321 T^{12} )^{2} \))(\( ( 1 - 193 T^{2} + 18883 T^{4} - 1197882 T^{6} + 54156853 T^{8} - 1813801707 T^{10} + 45545913373 T^{12} - 847239178842 T^{14} + 11232048770443 T^{16} - 96547557701473 T^{18} + 420707233300201 T^{20} )^{2} \))(\( 1 + 10 T + 31 T^{2} - 160 T^{3} - 2079 T^{4} - 4640 T^{5} + 26071 T^{6} + 243890 T^{7} + 707281 T^{8} \))(\( 1 - 2 T + 41 T^{2} - 222 T^{3} + 531 T^{4} - 9408 T^{5} + 47813 T^{6} - 301118 T^{7} + 2010297 T^{8} - 10226854 T^{9} + 44968155 T^{10} - 296578766 T^{11} + 1690659777 T^{12} - 7343966902 T^{13} + 33817226453 T^{14} - 192968889792 T^{15} + 315851183451 T^{16} - 3829472540598 T^{17} + 20510102931401 T^{18} - 29014291951738 T^{19} + 420707233300201 T^{20} \))(\( 1 - 14 T + 57 T^{2} - 458 T^{3} + 5001 T^{4} - 13986 T^{5} + 85645 T^{6} - 1071714 T^{7} + 1968673 T^{8} - 8608842 T^{9} + 157266187 T^{10} - 249656418 T^{11} + 1655653993 T^{12} - 26138032746 T^{13} + 60575081245 T^{14} - 286868929914 T^{15} + 2974711428321 T^{16} - 7900443349522 T^{17} + 28514045538777 T^{18} - 203100043662166 T^{19} + 420707233300201 T^{20} \))(\( 1 - 12 T - 67 T^{2} + 1195 T^{3} + 1042 T^{4} - 48597 T^{5} + 5197 T^{6} + 1150766 T^{7} + 1427500 T^{8} - 23690871 T^{9} - 186659295 T^{10} + 749599372 T^{11} + 10720023417 T^{12} - 31499319861 T^{13} - 376737927236 T^{14} + 1065343656837 T^{15} + 10045093559315 T^{16} - 25490540704614 T^{17} - 266261175986743 T^{18} + 297289837349525 T^{19} + 7599931488502746 T^{20} + 8621405283136225 T^{21} - 223925649004850863 T^{22} - 621688797244830846 T^{23} + 7104703817725872515 T^{24} + 21851422481588575713 T^{25} - \)\(22\!\cdots\!56\)\( T^{26} - \)\(54\!\cdots\!49\)\( T^{27} + \)\(53\!\cdots\!37\)\( T^{28} + \)\(10\!\cdots\!68\)\( T^{29} - \)\(78\!\cdots\!95\)\( T^{30} - \)\(28\!\cdots\!59\)\( T^{31} + \)\(50\!\cdots\!00\)\( T^{32} + \)\(11\!\cdots\!74\)\( T^{33} + \)\(15\!\cdots\!57\)\( T^{34} - \)\(41\!\cdots\!53\)\( T^{35} + \)\(26\!\cdots\!82\)\( T^{36} + \)\(86\!\cdots\!55\)\( T^{37} - \)\(14\!\cdots\!87\)\( T^{38} - \)\(73\!\cdots\!28\)\( T^{39} + \)\(17\!\cdots\!01\)\( T^{40} \))(\( ( 1 + 2 T + 41 T^{2} + 222 T^{3} + 531 T^{4} + 9408 T^{5} + 47813 T^{6} + 301118 T^{7} + 2010297 T^{8} + 10226854 T^{9} + 44968155 T^{10} + 296578766 T^{11} + 1690659777 T^{12} + 7343966902 T^{13} + 33817226453 T^{14} + 192968889792 T^{15} + 315851183451 T^{16} + 3829472540598 T^{17} + 20510102931401 T^{18} + 29014291951738 T^{19} + 420707233300201 T^{20} )^{2} \))(\( ( 1 + 14 T + 57 T^{2} + 458 T^{3} + 5001 T^{4} + 13986 T^{5} + 85645 T^{6} + 1071714 T^{7} + 1968673 T^{8} + 8608842 T^{9} + 157266187 T^{10} + 249656418 T^{11} + 1655653993 T^{12} + 26138032746 T^{13} + 60575081245 T^{14} + 286868929914 T^{15} + 2974711428321 T^{16} + 7900443349522 T^{17} + 28514045538777 T^{18} + 203100043662166 T^{19} + 420707233300201 T^{20} )^{2} \))
$31$ (\( 1 + 5 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 + 5 T + 31 T^{2} \))(\( 1 + 17 T^{2} + 961 T^{4} \))(\( 1 - 4 T + 61 T^{2} - 124 T^{3} + 961 T^{4} \))(\( 1 + T + 23 T^{2} + 104 T^{3} + 1648 T^{4} + 3224 T^{5} + 22103 T^{6} + 29791 T^{7} + 923521 T^{8} \))(\( 1 + 50 T^{2} - 256 T^{3} + 1011 T^{4} - 7936 T^{5} + 48050 T^{6} + 923521 T^{8} \))(\( 1 + 50 T^{2} - 256 T^{3} + 1011 T^{4} - 7936 T^{5} + 48050 T^{6} + 923521 T^{8} \))(\( 1 - 14 T + 231 T^{2} - 2080 T^{3} + 20508 T^{4} - 140424 T^{5} + 1028881 T^{6} - 5567026 T^{7} + 31895311 T^{8} - 134947464 T^{9} + 610953828 T^{10} - 1920923680 T^{11} + 6613333881 T^{12} - 12425051534 T^{13} + 27512614111 T^{14} \))(\( 1 - 14 T + 231 T^{2} - 2080 T^{3} + 20508 T^{4} - 140424 T^{5} + 1028881 T^{6} - 5567026 T^{7} + 31895311 T^{8} - 134947464 T^{9} + 610953828 T^{10} - 1920923680 T^{11} + 6613333881 T^{12} - 12425051534 T^{13} + 27512614111 T^{14} \))(\( ( 1 + 5 T + 31 T^{2} )^{2} \))(\( ( 1 + 2 T + 31 T^{2} )^{2} \))(\( ( 1 - 4 T + 61 T^{2} - 124 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 + 17 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 + T + 23 T^{2} + 104 T^{3} + 1648 T^{4} + 3224 T^{5} + 22103 T^{6} + 29791 T^{7} + 923521 T^{8} )^{2} \))(\( ( 1 - 14 T + 231 T^{2} - 2080 T^{3} + 20508 T^{4} - 140424 T^{5} + 1028881 T^{6} - 5567026 T^{7} + 31895311 T^{8} - 134947464 T^{9} + 610953828 T^{10} - 1920923680 T^{11} + 6613333881 T^{12} - 12425051534 T^{13} + 27512614111 T^{14} )^{2} \))(\( ( 1 + 3 T + 31 T^{2} )^{4} \))(\( ( 1 + 31 T^{2} )^{8} \))(\( ( 1 - 344 T^{3} + 29791 T^{6} )^{4} \))(\( ( 1 + T + 97 T^{2} + 62 T^{3} + 4277 T^{4} + 1947 T^{5} + 132587 T^{6} + 59582 T^{7} + 2889727 T^{8} + 923521 T^{9} + 28629151 T^{10} )^{4} \))(\( ( 1 - 11 T + 61 T^{2} - 341 T^{3} + 961 T^{4} )( 1 + 19 T + 151 T^{2} + 589 T^{3} + 961 T^{4} ) \))(\( 1 + 20 T + 127 T^{2} + 127 T^{3} - 1089 T^{4} - 3794 T^{5} - 73933 T^{6} - 716061 T^{7} - 2339386 T^{8} + 4043930 T^{9} + 65396035 T^{10} + 125361830 T^{11} - 2248149946 T^{12} - 21332173251 T^{13} - 68278678093 T^{14} - 108618998894 T^{15} - 966491508609 T^{16} + 3494101992097 T^{17} + 108317161755007 T^{18} + 528792443213420 T^{19} + 819628286980801 T^{20} \))(\( 1 - 10 T + 25 T^{2} - 226 T^{3} + 1925 T^{4} + 4982 T^{5} - 42879 T^{6} - 47226 T^{7} - 1407939 T^{8} + 6585942 T^{9} + 24254759 T^{10} + 204164202 T^{11} - 1353029379 T^{12} - 1406909766 T^{13} - 39599656959 T^{14} + 142630430282 T^{15} + 1708444585925 T^{16} - 6217850789086 T^{17} + 21322275936025 T^{18} - 264396221606710 T^{19} + 819628286980801 T^{20} \))(\( 1 - 10 T + 134 T^{2} - 758 T^{3} + 7675 T^{4} - 42437 T^{5} + 404282 T^{6} - 1932071 T^{7} + 15085785 T^{8} - 64870146 T^{9} + 524687482 T^{10} - 2365711093 T^{11} + 16855502897 T^{12} - 79312877915 T^{13} + 567068279230 T^{14} - 3353689420274 T^{15} + 21041878154409 T^{16} - 125443438747332 T^{17} + 716718317074566 T^{18} - 4602431108233134 T^{19} + 24926288490663857 T^{20} - 142675364355227154 T^{21} + 688766302708657926 T^{22} - 3737085483721767612 T^{23} + 19432616355037954089 T^{24} - 96013280820126807374 T^{25} + \)\(50\!\cdots\!30\)\( T^{26} - \)\(21\!\cdots\!65\)\( T^{27} + \)\(14\!\cdots\!77\)\( T^{28} - \)\(62\!\cdots\!03\)\( T^{29} + \)\(43\!\cdots\!82\)\( T^{30} - \)\(16\!\cdots\!26\)\( T^{31} + \)\(11\!\cdots\!85\)\( T^{32} - \)\(47\!\cdots\!61\)\( T^{33} + \)\(30\!\cdots\!22\)\( T^{34} - \)\(99\!\cdots\!87\)\( T^{35} + \)\(55\!\cdots\!75\)\( T^{36} - \)\(17\!\cdots\!38\)\( T^{37} + \)\(93\!\cdots\!94\)\( T^{38} - \)\(21\!\cdots\!10\)\( T^{39} + \)\(67\!\cdots\!01\)\( T^{40} \))(\( ( 1 + 20 T + 127 T^{2} + 127 T^{3} - 1089 T^{4} - 3794 T^{5} - 73933 T^{6} - 716061 T^{7} - 2339386 T^{8} + 4043930 T^{9} + 65396035 T^{10} + 125361830 T^{11} - 2248149946 T^{12} - 21332173251 T^{13} - 68278678093 T^{14} - 108618998894 T^{15} - 966491508609 T^{16} + 3494101992097 T^{17} + 108317161755007 T^{18} + 528792443213420 T^{19} + 819628286980801 T^{20} )^{2} \))(\( ( 1 - 10 T + 25 T^{2} - 226 T^{3} + 1925 T^{4} + 4982 T^{5} - 42879 T^{6} - 47226 T^{7} - 1407939 T^{8} + 6585942 T^{9} + 24254759 T^{10} + 204164202 T^{11} - 1353029379 T^{12} - 1406909766 T^{13} - 39599656959 T^{14} + 142630430282 T^{15} + 1708444585925 T^{16} - 6217850789086 T^{17} + 21322275936025 T^{18} - 264396221606710 T^{19} + 819628286980801 T^{20} )^{2} \))
$37$ (\( 1 + 7 T + 37 T^{2} \))(\( 1 + 11 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 - 4 T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 + 2 T + 70 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 - 6 T + 38 T^{2} - 222 T^{3} + 1369 T^{4} \))(\( 1 - 3 T + 32 T^{2} - 349 T^{3} + 1638 T^{4} - 12913 T^{5} + 43808 T^{6} - 151959 T^{7} + 1874161 T^{8} \))(\( 1 + 2 T + 76 T^{2} - 158 T^{3} + 2410 T^{4} - 5846 T^{5} + 104044 T^{6} + 101306 T^{7} + 1874161 T^{8} \))(\( 1 - 2 T + 76 T^{2} + 158 T^{3} + 2410 T^{4} + 5846 T^{5} + 104044 T^{6} - 101306 T^{7} + 1874161 T^{8} \))(\( 1 + 10 T + 143 T^{2} + 1100 T^{3} + 8905 T^{4} + 53670 T^{5} + 340191 T^{6} + 1982056 T^{7} + 12587067 T^{8} + 73474230 T^{9} + 451064965 T^{10} + 2061577100 T^{11} + 9916185851 T^{12} + 25657264090 T^{13} + 94931877133 T^{14} \))(\( 1 - 10 T + 143 T^{2} - 1100 T^{3} + 8905 T^{4} - 53670 T^{5} + 340191 T^{6} - 1982056 T^{7} + 12587067 T^{8} - 73474230 T^{9} + 451064965 T^{10} - 2061577100 T^{11} + 9916185851 T^{12} - 25657264090 T^{13} + 94931877133 T^{14} \))(\( 1 + 47 T^{2} + 1369 T^{4} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 - 40 T^{2} + 1518 T^{4} - 54760 T^{6} + 1874161 T^{8} \))(\( 1 - 136 T^{2} + 7342 T^{4} - 186184 T^{6} + 1874161 T^{8} \))(\( 1 - 55 T^{2} + 2206 T^{4} + 6831 T^{6} - 689950 T^{8} + 9351639 T^{10} + 4134399166 T^{12} - 141114952495 T^{14} + 3512479453921 T^{16} \))(\( 1 - 186 T^{2} + 16259 T^{4} - 943812 T^{6} + 44052665 T^{8} - 1850356102 T^{10} + 73113792403 T^{12} - 2759489016760 T^{14} + 100092781799707 T^{16} - 3467865242480422 T^{18} + 113027085977329985 T^{20} - 3315120258364086852 T^{22} + 78182773311141806891 T^{24} - \)\(12\!\cdots\!66\)\( T^{26} + \)\(90\!\cdots\!89\)\( T^{28} \))(\( 1 - 137 T^{4} + 1874161 T^{8} \))(\( ( 1 - 1838 T^{4} + 1874161 T^{8} )^{2} \))(\( ( 1 + 1369 T^{4} )^{6} \))(\( 1 - 9781 T^{4} + 44061273 T^{8} - 123293552508 T^{12} + 245670541820726 T^{16} - 377506395088955022 T^{20} + \)\(46\!\cdots\!86\)\( T^{24} - \)\(43\!\cdots\!68\)\( T^{28} + \)\(29\!\cdots\!13\)\( T^{32} - \)\(12\!\cdots\!21\)\( T^{36} + \)\(23\!\cdots\!01\)\( T^{40} \))(\( 1 - 14 T + 159 T^{2} - 1288 T^{3} + 9209 T^{4} - 47656 T^{5} + 217671 T^{6} - 709142 T^{7} + 1874161 T^{8} \))(\( 1 + 13 T + 132 T^{2} + 1235 T^{3} + 11171 T^{4} + 85668 T^{5} + 658381 T^{6} + 4704949 T^{7} + 33057222 T^{8} + 212975933 T^{9} + 1343462603 T^{10} + 7880109521 T^{11} + 45255336918 T^{12} + 238319781697 T^{13} + 1233911993341 T^{14} + 5940558108276 T^{15} + 28661729714939 T^{16} + 117240868259255 T^{17} + 463647287917572 T^{18} + 1689502617336001 T^{19} + 4808584372417849 T^{20} \))(\( 1 - 19 T + 137 T^{2} - 118 T^{3} - 6919 T^{4} + 76207 T^{5} - 426550 T^{6} + 880182 T^{7} + 7739069 T^{8} - 96108188 T^{9} + 657904633 T^{10} - 3556002956 T^{11} + 10594785461 T^{12} + 44583858846 T^{13} - 799423374550 T^{14} + 5284494931099 T^{15} - 17752261023871 T^{16} - 11201961501694 T^{17} + 481209685187177 T^{18} - 2469273056106463 T^{19} + 4808584372417849 T^{20} \))(\( 1 - 18 T + 85 T^{2} + 390 T^{3} - 6629 T^{4} + 30356 T^{5} + 95098 T^{6} - 1788792 T^{7} + 4202378 T^{8} + 48185338 T^{9} - 404071013 T^{10} + 1298535796 T^{11} + 380299965 T^{12} - 51711042538 T^{13} + 458631920536 T^{14} - 1459019174670 T^{15} - 10051521013052 T^{16} + 164054790080866 T^{17} - 618726163001666 T^{18} - 4578533633789962 T^{19} + 57065299869074243 T^{20} - 169405744450228594 T^{21} - 847036117149280754 T^{22} + 8309867281966105498 T^{23} - 18838168673342549372 T^{24} - \)\(10\!\cdots\!90\)\( T^{25} + \)\(11\!\cdots\!24\)\( T^{26} - \)\(49\!\cdots\!54\)\( T^{27} + \)\(13\!\cdots\!65\)\( T^{28} + \)\(16\!\cdots\!92\)\( T^{29} - \)\(19\!\cdots\!37\)\( T^{30} + \)\(85\!\cdots\!94\)\( T^{31} + \)\(27\!\cdots\!18\)\( T^{32} - \)\(43\!\cdots\!24\)\( T^{33} + \)\(85\!\cdots\!22\)\( T^{34} + \)\(10\!\cdots\!08\)\( T^{35} - \)\(81\!\cdots\!89\)\( T^{36} + \)\(17\!\cdots\!30\)\( T^{37} + \)\(14\!\cdots\!65\)\( T^{38} - \)\(11\!\cdots\!14\)\( T^{39} + \)\(23\!\cdots\!01\)\( T^{40} \))(\( 1 - 95 T^{2} + 7656 T^{4} - 513313 T^{6} + 30789635 T^{8} - 1625975604 T^{10} + 80154252193 T^{12} - 3672193774343 T^{14} + 158638771020972 T^{16} - 6410869881082021 T^{18} + 243616377651677183 T^{20} - 8776480867201286749 T^{22} + \)\(29\!\cdots\!92\)\( T^{24} - \)\(94\!\cdots\!87\)\( T^{26} + \)\(28\!\cdots\!53\)\( T^{28} - \)\(78\!\cdots\!96\)\( T^{30} + \)\(20\!\cdots\!35\)\( T^{32} - \)\(46\!\cdots\!57\)\( T^{34} + \)\(94\!\cdots\!96\)\( T^{36} - \)\(16\!\cdots\!55\)\( T^{38} + \)\(23\!\cdots\!01\)\( T^{40} \))(\( 1 + 87 T^{2} + 447 T^{4} - 133036 T^{6} - 2092233 T^{8} - 87018031 T^{10} - 15654598002 T^{12} - 326323343100 T^{14} + 19980205556335 T^{16} + 645214477995758 T^{18} + 2025678115514637 T^{20} + 883298620376192702 T^{22} + 37446122025666359935 T^{24} - \)\(83\!\cdots\!00\)\( T^{26} - \)\(54\!\cdots\!42\)\( T^{28} - \)\(41\!\cdots\!19\)\( T^{30} - \)\(13\!\cdots\!73\)\( T^{32} - \)\(11\!\cdots\!04\)\( T^{34} + \)\(55\!\cdots\!27\)\( T^{36} + \)\(14\!\cdots\!23\)\( T^{38} + \)\(23\!\cdots\!01\)\( T^{40} \))
$41$ (\( 1 + 7 T + 41 T^{2} \))(\( 1 - T + 41 T^{2} \))(\( 1 + 5 T + 41 T^{2} \))(\( 1 + 5 T + 41 T^{2} \))(\( 1 + 7 T + 41 T^{2} \))(\( 1 - 2 T + 63 T^{2} - 82 T^{3} + 1681 T^{4} \))(\( 1 + 6 T + 71 T^{2} + 246 T^{3} + 1681 T^{4} \))(\( 1 - 13 T + 209 T^{2} - 1602 T^{3} + 13682 T^{4} - 65682 T^{5} + 351329 T^{6} - 895973 T^{7} + 2825761 T^{8} \))(\( 1 + 8 T + 70 T^{2} + 616 T^{3} + 4863 T^{4} + 25256 T^{5} + 117670 T^{6} + 551368 T^{7} + 2825761 T^{8} \))(\( 1 + 8 T + 70 T^{2} + 616 T^{3} + 4863 T^{4} + 25256 T^{5} + 117670 T^{6} + 551368 T^{7} + 2825761 T^{8} \))(\( 1 - 19 T + 309 T^{2} - 3190 T^{3} + 30654 T^{4} - 228554 T^{5} + 1692151 T^{6} - 10621429 T^{7} + 69378191 T^{8} - 384199274 T^{9} + 2112704334 T^{10} - 9014177590 T^{11} + 35799566109 T^{12} - 90251980579 T^{13} + 194754273881 T^{14} \))(\( 1 - 19 T + 309 T^{2} - 3190 T^{3} + 30654 T^{4} - 228554 T^{5} + 1692151 T^{6} - 10621429 T^{7} + 69378191 T^{8} - 384199274 T^{9} + 2112704334 T^{10} - 9014177590 T^{11} + 35799566109 T^{12} - 90251980579 T^{13} + 194754273881 T^{14} \))(\( ( 1 - T + 41 T^{2} )^{2} \))(\( ( 1 + 5 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 71 T^{2} + 246 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 - 2 T + 63 T^{2} - 82 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 - 13 T + 209 T^{2} - 1602 T^{3} + 13682 T^{4} - 65682 T^{5} + 351329 T^{6} - 895973 T^{7} + 2825761 T^{8} )^{2} \))(\( ( 1 - 19 T + 309 T^{2} - 3190 T^{3} + 30654 T^{4} - 228554 T^{5} + 1692151 T^{6} - 10621429 T^{7} + 69378191 T^{8} - 384199274 T^{9} + 2112704334 T^{10} - 9014177590 T^{11} + 35799566109 T^{12} - 90251980579 T^{13} + 194754273881 T^{14} )^{2} \))(\( ( 1 - 7 T + 41 T^{2} )^{4} \))(\( ( 1 - 7 T + 41 T^{2} )^{8} \))(\( ( 1 + 426 T^{3} + 68921 T^{6} )^{4} \))(\( ( 1 + 9 T + 195 T^{2} + 1370 T^{3} + 15765 T^{4} + 82035 T^{5} + 646365 T^{6} + 2302970 T^{7} + 13439595 T^{8} + 25431849 T^{9} + 115856201 T^{10} )^{4} \))(\( 1 + 10 T - T^{2} - 410 T^{3} - 2839 T^{4} - 16810 T^{5} - 1681 T^{6} + 689210 T^{7} + 2825761 T^{8} \))(\( 1 + 5 T + 50 T^{2} - 681 T^{3} - 2573 T^{4} - 37436 T^{5} + 238919 T^{6} + 364515 T^{7} + 12937390 T^{8} - 71985111 T^{9} + 8447451 T^{10} - 2951389551 T^{11} + 21747752590 T^{12} + 25122738315 T^{13} + 675127992359 T^{14} - 4337192740636 T^{15} - 12222018212093 T^{16} - 132627660512961 T^{17} + 399246261456050 T^{18} + 1636909671969805 T^{19} + 13422659310152401 T^{20} \))(\( 1 - 7 T - 25 T^{2} + 583 T^{3} - 2660 T^{4} + 2131 T^{5} + 107915 T^{6} - 669350 T^{7} + 206320 T^{8} + 11256041 T^{9} + 10368863 T^{10} + 461497681 T^{11} + 346823920 T^{12} - 46132271350 T^{13} + 304941998315 T^{14} + 246889564331 T^{15} - 12635277281060 T^{16} + 113541741672623 T^{17} - 199623130728025 T^{18} - 2291673540757727 T^{19} + 13422659310152401 T^{20} \))(\( 1 - 10 T - 114 T^{2} + 1506 T^{3} + 2757 T^{4} - 92209 T^{5} + 243933 T^{6} + 2920729 T^{7} - 26804829 T^{8} - 21977155 T^{9} + 1492380725 T^{10} - 4237439576 T^{11} - 52174293824 T^{12} + 353017933581 T^{13} + 774069433040 T^{14} - 16950354155947 T^{15} + 38704074299184 T^{16} + 551121880563897 T^{17} - 4002933543559192 T^{18} - 8577951456589504 T^{19} + 203910150115021758 T^{20} - 351696009720169664 T^{21} - 6728931286723001752 T^{22} + 37983871130344345137 T^{23} + \)\(10\!\cdots\!24\)\( T^{24} - \)\(19\!\cdots\!47\)\( T^{25} + \)\(36\!\cdots\!40\)\( T^{26} + \)\(68\!\cdots\!61\)\( T^{27} - \)\(41\!\cdots\!04\)\( T^{28} - \)\(13\!\cdots\!36\)\( T^{29} + \)\(20\!\cdots\!25\)\( T^{30} - \)\(12\!\cdots\!55\)\( T^{31} - \)\(60\!\cdots\!49\)\( T^{32} + \)\(27\!\cdots\!09\)\( T^{33} + \)\(92\!\cdots\!13\)\( T^{34} - \)\(14\!\cdots\!09\)\( T^{35} + \)\(17\!\cdots\!37\)\( T^{36} + \)\(39\!\cdots\!86\)\( T^{37} - \)\(12\!\cdots\!94\)\( T^{38} - \)\(43\!\cdots\!10\)\( T^{39} + \)\(18\!\cdots\!01\)\( T^{40} \))(\( ( 1 + 5 T + 50 T^{2} - 681 T^{3} - 2573 T^{4} - 37436 T^{5} + 238919 T^{6} + 364515 T^{7} + 12937390 T^{8} - 71985111 T^{9} + 8447451 T^{10} - 2951389551 T^{11} + 21747752590 T^{12} + 25122738315 T^{13} + 675127992359 T^{14} - 4337192740636 T^{15} - 12222018212093 T^{16} - 132627660512961 T^{17} + 399246261456050 T^{18} + 1636909671969805 T^{19} + 13422659310152401 T^{20} )^{2} \))(\( ( 1 - 7 T - 25 T^{2} + 583 T^{3} - 2660 T^{4} + 2131 T^{5} + 107915 T^{6} - 669350 T^{7} + 206320 T^{8} + 11256041 T^{9} + 10368863 T^{10} + 461497681 T^{11} + 346823920 T^{12} - 46132271350 T^{13} + 304941998315 T^{14} + 246889564331 T^{15} - 12635277281060 T^{16} + 113541741672623 T^{17} - 199623130728025 T^{18} - 2291673540757727 T^{19} + 13422659310152401 T^{20} )^{2} \))
$43$ (\( 1 + 4 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 + 9 T + 43 T^{2} \))(\( 1 - 9 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( ( 1 + 43 T^{2} )^{2} \))(\( 1 - 6 T + 50 T^{2} - 258 T^{3} + 1849 T^{4} \))(\( 1 - 6 T + 136 T^{2} - 758 T^{3} + 8126 T^{4} - 32594 T^{5} + 251464 T^{6} - 477042 T^{7} + 3418801 T^{8} \))(\( 1 + 4 T + 54 T^{2} + 80 T^{3} + 2910 T^{4} + 3440 T^{5} + 99846 T^{6} + 318028 T^{7} + 3418801 T^{8} \))(\( 1 - 4 T + 54 T^{2} - 80 T^{3} + 2910 T^{4} - 3440 T^{5} + 99846 T^{6} - 318028 T^{7} + 3418801 T^{8} \))(\( 1 - 5 T + 157 T^{2} - 826 T^{3} + 13117 T^{4} - 70451 T^{5} + 759257 T^{6} - 3813708 T^{7} + 32648051 T^{8} - 130263899 T^{9} + 1042893319 T^{10} - 2823929626 T^{11} + 23080325551 T^{12} - 31606815245 T^{13} + 271818611107 T^{14} \))(\( 1 + 5 T + 157 T^{2} + 826 T^{3} + 13117 T^{4} + 70451 T^{5} + 759257 T^{6} + 3813708 T^{7} + 32648051 T^{8} + 130263899 T^{9} + 1042893319 T^{10} + 2823929626 T^{11} + 23080325551 T^{12} + 31606815245 T^{13} + 271818611107 T^{14} \))(\( ( 1 - 43 T^{2} )^{2} \))(\( 1 - 5 T^{2} + 1849 T^{4} \))(\( 1 - 64 T^{2} + 3102 T^{4} - 118336 T^{6} + 3418801 T^{8} \))(\( ( 1 - 43 T^{2} )^{4} \))(\( 1 - 236 T^{2} + 25652 T^{4} - 1747508 T^{6} + 86130678 T^{8} - 3231142292 T^{10} + 87699083252 T^{12} - 1491841679564 T^{14} + 11688200277601 T^{16} \))(\( 1 - 289 T^{2} + 42623 T^{4} - 4250466 T^{6} + 321236357 T^{8} - 19689394783 T^{10} + 1025794973227 T^{12} - 46846632791324 T^{14} + 1896694905496723 T^{16} - 67314122573515183 T^{18} + 2030651637135172493 T^{20} - 49680297881133612066 T^{22} + \)\(92\!\cdots\!27\)\( T^{24} - \)\(11\!\cdots\!89\)\( T^{26} + \)\(73\!\cdots\!49\)\( T^{28} \))(\( 1 - 3662 T^{4} + 3418801 T^{8} \))(\( ( 1 + 1927 T^{4} + 3418801 T^{8} )^{2} \))(\( ( 1 + 1849 T^{4} )^{6} \))(\( 1 - 2666 T^{4} - 1105447 T^{8} + 8937665552 T^{12} - 1848148296154 T^{16} - 20946707502982572 T^{20} - 6318451243039591354 T^{24} + \)\(10\!\cdots\!52\)\( T^{28} - \)\(44\!\cdots\!47\)\( T^{32} - \)\(36\!\cdots\!66\)\( T^{36} + \)\(46\!\cdots\!01\)\( T^{40} \))(\( ( 1 - 17 T + 147 T^{2} - 731 T^{3} + 1849 T^{4} )^{2} \))(\( 1 + 15 T + 204 T^{2} + 2129 T^{3} + 19643 T^{4} + 172738 T^{5} + 1385269 T^{6} + 10775981 T^{7} + 77916158 T^{8} + 539582197 T^{9} + 3599056165 T^{10} + 23202034471 T^{11} + 144066976142 T^{12} + 856765921367 T^{13} + 4735959042469 T^{14} + 25393944426934 T^{15} + 124170534371507 T^{16} + 578701823046803 T^{17} + 2384392856630604 T^{18} + 7538889179052645 T^{19} + 21611482313284249 T^{20} \))(\( 1 - 11 T + 23 T^{2} + 605 T^{3} - 5312 T^{4} + 29546 T^{5} - 40138 T^{6} - 747769 T^{7} + 9344490 T^{8} - 16662481 T^{9} - 37880567 T^{10} - 716486683 T^{11} + 17277962010 T^{12} - 59452869883 T^{13} - 137223834538 T^{14} + 4343511456878 T^{15} - 33579080516288 T^{16} + 164450259719735 T^{17} + 268828606384823 T^{18} - 5528518731305273 T^{19} + 21611482313284249 T^{20} \))(\( 1 + 35 T + 567 T^{2} + 6482 T^{3} + 66662 T^{4} + 645520 T^{5} + 5810987 T^{6} + 48597733 T^{7} + 371510041 T^{8} + 2643204420 T^{9} + 17674945398 T^{10} + 105727723373 T^{11} + 540972251826 T^{12} + 2059075592526 T^{13} + 649816071717 T^{14} - 88212600828558 T^{15} - 1205960437326518 T^{16} - 11953353936135423 T^{17} - 98903689285419458 T^{18} - 732724305899372468 T^{19} - 5012641069620623889 T^{20} - 31507145153673016124 T^{21} - \)\(18\!\cdots\!42\)\( T^{22} - \)\(95\!\cdots\!61\)\( T^{23} - \)\(41\!\cdots\!18\)\( T^{24} - \)\(12\!\cdots\!94\)\( T^{25} + \)\(41\!\cdots\!33\)\( T^{26} + \)\(55\!\cdots\!82\)\( T^{27} + \)\(63\!\cdots\!26\)\( T^{28} + \)\(53\!\cdots\!39\)\( T^{29} + \)\(38\!\cdots\!02\)\( T^{30} + \)\(24\!\cdots\!40\)\( T^{31} + \)\(14\!\cdots\!41\)\( T^{32} + \)\(83\!\cdots\!19\)\( T^{33} + \)\(42\!\cdots\!63\)\( T^{34} + \)\(20\!\cdots\!40\)\( T^{35} + \)\(91\!\cdots\!62\)\( T^{36} + \)\(38\!\cdots\!26\)\( T^{37} + \)\(14\!\cdots\!83\)\( T^{38} + \)\(38\!\cdots\!45\)\( T^{39} + \)\(46\!\cdots\!01\)\( T^{40} \))(\( 1 - 183 T^{2} + 17032 T^{4} - 1070101 T^{6} + 48071683 T^{8} - 1499573076 T^{10} + 20088412241 T^{12} + 1518264619593 T^{14} - 172051562979704 T^{16} + 11199305840697931 T^{18} - 548204245200745385 T^{20} + 20707516499450474419 T^{22} - \)\(58\!\cdots\!04\)\( T^{24} + \)\(95\!\cdots\!57\)\( T^{26} + \)\(23\!\cdots\!41\)\( T^{28} - \)\(32\!\cdots\!24\)\( T^{30} + \)\(19\!\cdots\!83\)\( T^{32} - \)\(79\!\cdots\!49\)\( T^{34} + \)\(23\!\cdots\!32\)\( T^{36} - \)\(46\!\cdots\!67\)\( T^{38} + \)\(46\!\cdots\!01\)\( T^{40} \))(\( 1 + 75 T^{2} + 3215 T^{4} + 40641 T^{6} - 7141602 T^{8} - 445771310 T^{10} - 16265324046 T^{12} - 157090046847 T^{14} + 18243350112832 T^{16} + 1117794806072099 T^{18} + 57621513305584613 T^{20} + 2066802596427311051 T^{22} + 62370383609100154432 T^{24} - \)\(99\!\cdots\!03\)\( T^{26} - \)\(19\!\cdots\!46\)\( T^{28} - \)\(96\!\cdots\!90\)\( T^{30} - \)\(28\!\cdots\!02\)\( T^{32} + \)\(30\!\cdots\!09\)\( T^{34} + \)\(43\!\cdots\!15\)\( T^{36} + \)\(18\!\cdots\!75\)\( T^{38} + \)\(46\!\cdots\!01\)\( T^{40} \))
$47$ (\( 1 - 2 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 89 T^{2} + 2209 T^{4} \))(\( 1 + 10 T + 99 T^{2} + 470 T^{3} + 2209 T^{4} \))(\( 1 + 6 T + 105 T^{2} + 298 T^{3} + 5324 T^{4} + 14006 T^{5} + 231945 T^{6} + 622938 T^{7} + 4879681 T^{8} \))(\( 1 + 2 T + 50 T^{2} + 116 T^{3} + 4795 T^{4} + 5452 T^{5} + 110450 T^{6} + 207646 T^{7} + 4879681 T^{8} \))(\( 1 - 2 T + 50 T^{2} - 116 T^{3} + 4795 T^{4} - 5452 T^{5} + 110450 T^{6} - 207646 T^{7} + 4879681 T^{8} \))(\( 1 + 14 T + 311 T^{2} + 2944 T^{3} + 38680 T^{4} + 282800 T^{5} + 2790681 T^{6} + 16514822 T^{7} + 131162007 T^{8} + 624705200 T^{9} + 4015873640 T^{10} + 14365780864 T^{11} + 71326297177 T^{12} + 150909014606 T^{13} + 506623120463 T^{14} \))(\( 1 - 14 T + 311 T^{2} - 2944 T^{3} + 38680 T^{4} - 282800 T^{5} + 2790681 T^{6} - 16514822 T^{7} + 131162007 T^{8} - 624705200 T^{9} + 4015873640 T^{10} - 14365780864 T^{11} + 71326297177 T^{12} - 150909014606 T^{13} + 506623120463 T^{14} \))(\( ( 1 - 47 T^{2} )^{2} \))(\( 1 - 58 T^{2} + 2209 T^{4} \))(\( 1 - 98 T^{2} + 4819 T^{4} - 216482 T^{6} + 4879681 T^{8} \))(\( ( 1 - 89 T^{2} + 2209 T^{4} )^{2} \))(\( 1 - 174 T^{2} + 18097 T^{4} - 1325054 T^{6} + 70989956 T^{8} - 2927044286 T^{10} + 88307587057 T^{12} - 1875583467246 T^{14} + 23811286661761 T^{16} \))(\( 1 - 426 T^{2} + 91649 T^{4} - 13054786 T^{6} + 1366728580 T^{8} - 110794740258 T^{10} + 7153829898723 T^{12} - 373225052641070 T^{14} + 15802810246279107 T^{16} - 540642988936897698 T^{18} + 14732261660118402820 T^{20} - \)\(31\!\cdots\!46\)\( T^{22} + \)\(48\!\cdots\!01\)\( T^{24} - \)\(49\!\cdots\!66\)\( T^{26} + \)\(25\!\cdots\!69\)\( T^{28} \))(\( ( 1 + 2209 T^{4} )^{2} \))(\( ( 1 - 4222 T^{4} + 4879681 T^{8} )^{2} \))(\( 1 + 20606906306 T^{12} + \)\(11\!\cdots\!41\)\( T^{24} \))(\( ( 1 - 4 T + 8 T^{2} + 330 T^{3} + 435 T^{4} - 17576 T^{5} + 121274 T^{6} + 601990 T^{7} - 5812707 T^{8} - 11707642 T^{9} + 393692622 T^{10} - 550259174 T^{11} - 12840269763 T^{12} + 62500407770 T^{13} + 591778433594 T^{14} - 4030967843032 T^{15} + 4688958668115 T^{16} + 167185629752790 T^{17} + 190490293294088 T^{18} - 4476521892411068 T^{19} + 52599132235830049 T^{20} )^{2} \))(\( 1 + 4 T - T^{2} - 242 T^{3} - 481 T^{4} - 11374 T^{5} - 2209 T^{6} + 415292 T^{7} + 4879681 T^{8} \))(\( ( 1 - 26 T + 424 T^{2} - 4806 T^{3} + 43985 T^{4} - 327085 T^{5} + 2067295 T^{6} - 10616454 T^{7} + 44020952 T^{8} - 126871706 T^{9} + 229345007 T^{10} )^{2} \))(\( ( 1 - 9 T + 230 T^{2} - 1595 T^{3} + 21279 T^{4} - 110169 T^{5} + 1000113 T^{6} - 3523355 T^{7} + 23879290 T^{8} - 43917129 T^{9} + 229345007 T^{10} )^{2} \))(\( ( 1 - T + 158 T^{2} - 376 T^{3} + 13303 T^{4} - 53535 T^{5} + 946350 T^{6} - 4112977 T^{7} + 59396726 T^{8} - 219980016 T^{9} + 3078120533 T^{10} - 10339060752 T^{11} + 131207367734 T^{12} - 427021611071 T^{13} + 4617886114350 T^{14} - 12277984949745 T^{15} + 143395901521687 T^{16} - 190490293294088 T^{17} + 3762183292558238 T^{18} - 1119130473102767 T^{19} + 52599132235830049 T^{20} )^{2} \))(\( ( 1 - 172 T^{2} + 17834 T^{4} - 1327814 T^{6} + 79791661 T^{8} - 4021116675 T^{10} + 176259779149 T^{12} - 6479308747334 T^{14} + 192236526177386 T^{16} - 4095541305822892 T^{18} + 52599132235830049 T^{20} )^{2} \))(\( ( 1 - 379 T^{2} + 66748 T^{4} - 7261499 T^{6} + 545746901 T^{8} - 29838753135 T^{10} + 1205554904309 T^{12} - 35433798701819 T^{14} + 719491064780092 T^{16} - 9024477644807419 T^{18} + 52599132235830049 T^{20} )^{2} \))
$53$ (\( 1 - T + 53 T^{2} \))(\( 1 + 11 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + T + 53 T^{2} \))(\( 1 - 8 T + 102 T^{2} - 424 T^{3} + 2809 T^{4} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( 1 + 19 T + 178 T^{2} + 929 T^{3} + 4474 T^{4} + 49237 T^{5} + 500002 T^{6} + 2828663 T^{7} + 7890481 T^{8} \))(\( 1 + 4 T + 108 T^{2} + 524 T^{3} + 8022 T^{4} + 27772 T^{5} + 303372 T^{6} + 595508 T^{7} + 7890481 T^{8} \))(\( 1 - 4 T + 108 T^{2} - 524 T^{3} + 8022 T^{4} - 27772 T^{5} + 303372 T^{6} - 595508 T^{7} + 7890481 T^{8} \))(\( 1 - 4 T + 247 T^{2} - 1232 T^{3} + 28177 T^{4} - 159580 T^{5} + 2044527 T^{6} - 11188576 T^{7} + 108359931 T^{8} - 448260220 T^{9} + 4194907229 T^{10} - 9721072592 T^{11} + 103294286771 T^{12} - 88657444516 T^{13} + 1174711139837 T^{14} \))(\( 1 + 4 T + 247 T^{2} + 1232 T^{3} + 28177 T^{4} + 159580 T^{5} + 2044527 T^{6} + 11188576 T^{7} + 108359931 T^{8} + 448260220 T^{9} + 4194907229 T^{10} + 9721072592 T^{11} + 103294286771 T^{12} + 88657444516 T^{13} + 1174711139837 T^{14} \))(\( 1 + 15 T^{2} + 2809 T^{4} \))(\( 1 - 102 T^{2} + 2809 T^{4} \))(\( ( 1 - 70 T^{2} + 2809 T^{4} )^{2} \))(\( 1 - 140 T^{2} + 9238 T^{4} - 393260 T^{6} + 7890481 T^{8} \))(\( 1 + 5 T^{2} + 5330 T^{4} + 141299 T^{6} + 14826810 T^{8} + 396908891 T^{10} + 42056263730 T^{12} + 110821805645 T^{14} + 62259690411361 T^{16} \))(\( 1 - 478 T^{2} + 107507 T^{4} - 15214028 T^{6} + 1537945801 T^{8} - 120516385506 T^{10} + 7812251270995 T^{12} - 439953264077096 T^{14} + 21944613820224955 T^{16} - 950932250023768386 T^{18} + 34087586130193169329 T^{20} - \)\(94\!\cdots\!08\)\( T^{22} + \)\(18\!\cdots\!43\)\( T^{24} - \)\(23\!\cdots\!98\)\( T^{26} + \)\(13\!\cdots\!69\)\( T^{28} \))(\( 1 + 4583 T^{4} + 7890481 T^{8} \))(\( ( 1 + 2809 T^{4} )^{4} \))(\( ( 1 + 2809 T^{4} )^{6} \))(\( 1 - 6865 T^{4} + 5634885 T^{8} + 55524537540 T^{12} - 66605380961110 T^{16} - 238481873986046502 T^{20} - \)\(52\!\cdots\!10\)\( T^{24} + \)\(34\!\cdots\!40\)\( T^{28} + \)\(27\!\cdots\!85\)\( T^{32} - \)\(26\!\cdots\!65\)\( T^{36} + \)\(30\!\cdots\!01\)\( T^{40} \))(\( 1 - 23 T + 196 T^{2} - 889 T^{3} + 4299 T^{4} - 47117 T^{5} + 550564 T^{6} - 3424171 T^{7} + 7890481 T^{8} \))(\( 1 + 6 T + 126 T^{2} + 1670 T^{3} + 18434 T^{4} + 163092 T^{5} + 1868723 T^{6} + 15540916 T^{7} + 130470814 T^{8} + 1013135108 T^{9} + 8246457637 T^{10} + 53696160724 T^{11} + 366492516526 T^{12} + 2313684951332 T^{13} + 14745123325763 T^{14} + 68204339344356 T^{15} + 408577833051986 T^{16} + 1961767603527790 T^{17} + 7844720991831486 T^{18} + 19798581550812798 T^{19} + 174887470365513049 T^{20} \))(\( 1 + 29 T + 425 T^{2} + 3671 T^{3} + 13160 T^{4} - 116600 T^{5} - 2282954 T^{6} - 17208509 T^{7} - 42065902 T^{8} + 503004225 T^{9} + 6387620997 T^{10} + 26659223925 T^{11} - 118163118718 T^{12} - 2561951194393 T^{13} - 18013605160874 T^{14} - 48761594483800 T^{15} + 291682992457640 T^{16} + 4312364594341627 T^{17} + 26460368424828425 T^{18} + 95693144162261857 T^{19} + 174887470365513049 T^{20} \))(\( 1 - 5 T + 51 T^{2} - 595 T^{3} + 2839 T^{4} - 26462 T^{5} + 145564 T^{6} - 743850 T^{7} + 5187559 T^{8} + 9941890 T^{9} - 35840051 T^{10} + 4581262764 T^{11} - 19433102310 T^{12} + 98940938897 T^{13} - 1096107884097 T^{14} - 4668708827649 T^{15} + 43678935628705 T^{16} - 633329500748410 T^{17} + 8062327369739114 T^{18} - 51635096968093848 T^{19} + 472566844582501503 T^{20} - 2736660139308973944 T^{21} + 22647077581597171226 T^{22} - 94288196082921035570 T^{23} + \)\(34\!\cdots\!05\)\( T^{24} - \)\(19\!\cdots\!57\)\( T^{25} - \)\(24\!\cdots\!13\)\( T^{26} + \)\(11\!\cdots\!89\)\( T^{27} - \)\(12\!\cdots\!10\)\( T^{28} + \)\(15\!\cdots\!12\)\( T^{29} - \)\(62\!\cdots\!99\)\( T^{30} + \)\(92\!\cdots\!30\)\( T^{31} + \)\(25\!\cdots\!19\)\( T^{32} - \)\(19\!\cdots\!50\)\( T^{33} + \)\(20\!\cdots\!16\)\( T^{34} - \)\(19\!\cdots\!34\)\( T^{35} + \)\(11\!\cdots\!19\)\( T^{36} - \)\(12\!\cdots\!35\)\( T^{37} + \)\(55\!\cdots\!39\)\( T^{38} - \)\(28\!\cdots\!85\)\( T^{39} + \)\(30\!\cdots\!01\)\( T^{40} \))(\( 1 - 216 T^{2} + 32704 T^{4} - 3636810 T^{6} + 340453908 T^{8} - 27604358766 T^{10} + 2015992644905 T^{12} - 134406454456966 T^{14} + 8337012739538290 T^{16} - 482415823090541720 T^{18} + 26382862698048183525 T^{20} - \)\(13\!\cdots\!80\)\( T^{22} + \)\(65\!\cdots\!90\)\( T^{24} - \)\(29\!\cdots\!14\)\( T^{26} + \)\(12\!\cdots\!05\)\( T^{28} - \)\(48\!\cdots\!34\)\( T^{30} + \)\(16\!\cdots\!28\)\( T^{32} - \)\(50\!\cdots\!90\)\( T^{34} + \)\(12\!\cdots\!84\)\( T^{36} - \)\(23\!\cdots\!24\)\( T^{38} + \)\(30\!\cdots\!01\)\( T^{40} \))(\( 1 - 9 T^{2} - 5973 T^{4} + 93349 T^{6} + 2713618 T^{8} - 506944042 T^{10} + 45539729090 T^{12} + 2245687637629 T^{14} - 67146752077196 T^{16} - 3814244938727185 T^{18} - 67285236704182443 T^{20} - 10714214032884662665 T^{22} - \)\(52\!\cdots\!76\)\( T^{24} + \)\(49\!\cdots\!41\)\( T^{26} + \)\(28\!\cdots\!90\)\( T^{28} - \)\(88\!\cdots\!58\)\( T^{30} + \)\(13\!\cdots\!38\)\( T^{32} + \)\(12\!\cdots\!81\)\( T^{34} - \)\(23\!\cdots\!33\)\( T^{36} - \)\(97\!\cdots\!01\)\( T^{38} + \)\(30\!\cdots\!01\)\( T^{40} \))
$59$ (\( 1 - 3 T + 59 T^{2} \))(\( 1 + 13 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 - 8 T + 59 T^{2} \))(\( 1 - 3 T + 59 T^{2} \))(\( 1 - 4 T + 102 T^{2} - 236 T^{3} + 3481 T^{4} \))(\( 1 + 38 T^{2} + 3481 T^{4} \))(\( 1 - 23 T + 336 T^{2} - 3511 T^{3} + 29550 T^{4} - 207149 T^{5} + 1169616 T^{6} - 4723717 T^{7} + 12117361 T^{8} \))(\( 1 + 216 T^{2} + 16 T^{3} + 18542 T^{4} + 944 T^{5} + 751896 T^{6} + 12117361 T^{8} \))(\( 1 + 216 T^{2} + 16 T^{3} + 18542 T^{4} + 944 T^{5} + 751896 T^{6} + 12117361 T^{8} \))(\( 1 + 16 T + 322 T^{2} + 2460 T^{3} + 24083 T^{4} + 27416 T^{5} + 111413 T^{6} - 7169964 T^{7} + 6573367 T^{8} + 95435096 T^{9} + 4946142457 T^{10} + 29808708060 T^{11} + 230205624278 T^{12} + 674888538256 T^{13} + 2488651484819 T^{14} \))(\( 1 + 16 T + 322 T^{2} + 2460 T^{3} + 24083 T^{4} + 27416 T^{5} + 111413 T^{6} - 7169964 T^{7} + 6573367 T^{8} + 95435096 T^{9} + 4946142457 T^{10} + 29808708060 T^{11} + 230205624278 T^{12} + 674888538256 T^{13} + 2488651484819 T^{14} \))(\( ( 1 - 13 T + 59 T^{2} )^{2} \))(\( ( 1 + 8 T + 59 T^{2} )^{2} \))(\( ( 1 + 38 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 + 4 T + 102 T^{2} + 236 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 + 23 T + 336 T^{2} + 3511 T^{3} + 29550 T^{4} + 207149 T^{5} + 1169616 T^{6} + 4723717 T^{7} + 12117361 T^{8} )^{2} \))(\( ( 1 - 16 T + 322 T^{2} - 2460 T^{3} + 24083 T^{4} - 27416 T^{5} + 111413 T^{6} + 7169964 T^{7} + 6573367 T^{8} - 95435096 T^{9} + 4946142457 T^{10} - 29808708060 T^{11} + 230205624278 T^{12} - 674888538256 T^{13} + 2488651484819 T^{14} )^{2} \))(\( ( 1 + 3 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 18 T^{2} + 3481 T^{4} )^{4} \))(\( ( 1 + 26 T^{2} + 3481 T^{4} )^{6} \))(\( ( 1 - 277 T^{2} + 38049 T^{4} - 3370504 T^{6} + 226355270 T^{8} - 13536944758 T^{10} + 787942694870 T^{12} - 40841613719944 T^{14} + 1604927124506409 T^{16} - 40672031216396917 T^{18} + 511116753300641401 T^{20} )^{2} \))(\( 1 + 23 T + 190 T^{2} + 853 T^{3} + 4569 T^{4} + 50327 T^{5} + 661390 T^{6} + 4723717 T^{7} + 12117361 T^{8} \))(\( 1 - 5 T + 142 T^{2} - 646 T^{3} + 8536 T^{4} - 26742 T^{5} + 287886 T^{6} + 702648 T^{7} + 10262887 T^{8} + 139977013 T^{9} + 674338952 T^{10} + 8258643767 T^{11} + 35725109647 T^{12} + 144309143592 T^{13} + 3488418588846 T^{14} - 19118505603858 T^{15} + 360053035159576 T^{16} - 1607668859193074 T^{17} + 20849922139813582 T^{18} - 43314979093274695 T^{19} + 511116753300641401 T^{20} \))(\( 1 + 21 T + 206 T^{2} + 2416 T^{3} + 25558 T^{4} + 134475 T^{5} + 585400 T^{6} + 1747337 T^{7} - 63466585 T^{8} - 768235069 T^{9} - 4979757289 T^{10} - 45325869071 T^{11} - 220927182385 T^{12} + 358866325723 T^{13} + 7093503129400 T^{14} + 96139445108025 T^{15} + 1078050078796678 T^{16} + 6012581987322704 T^{17} + 30247070146490126 T^{18} + 181922912191753719 T^{19} + 511116753300641401 T^{20} \))(\( 1 - 41 T + 913 T^{2} - 14997 T^{3} + 203431 T^{4} - 2350391 T^{5} + 23374344 T^{6} - 203007532 T^{7} + 1564347264 T^{8} - 10971437923 T^{9} + 75041826526 T^{10} - 567907579491 T^{11} + 5167877252932 T^{12} - 52599927939636 T^{13} + 526749214679551 T^{14} - 4821318377051737 T^{15} + 39545367549341390 T^{16} - 292455010641582662 T^{17} + 1999568112398060742 T^{18} - 13406494422249449930 T^{19} + 96691071763912858131 T^{20} - \)\(79\!\cdots\!70\)\( T^{21} + \)\(69\!\cdots\!02\)\( T^{22} - \)\(60\!\cdots\!98\)\( T^{23} + \)\(47\!\cdots\!90\)\( T^{24} - \)\(34\!\cdots\!63\)\( T^{25} + \)\(22\!\cdots\!91\)\( T^{26} - \)\(13\!\cdots\!84\)\( T^{27} + \)\(75\!\cdots\!72\)\( T^{28} - \)\(49\!\cdots\!49\)\( T^{29} + \)\(38\!\cdots\!26\)\( T^{30} - \)\(33\!\cdots\!57\)\( T^{31} + \)\(27\!\cdots\!84\)\( T^{32} - \)\(21\!\cdots\!28\)\( T^{33} + \)\(14\!\cdots\!84\)\( T^{34} - \)\(85\!\cdots\!09\)\( T^{35} + \)\(43\!\cdots\!71\)\( T^{36} - \)\(19\!\cdots\!43\)\( T^{37} + \)\(68\!\cdots\!73\)\( T^{38} - \)\(18\!\cdots\!99\)\( T^{39} + \)\(26\!\cdots\!01\)\( T^{40} \))(\( ( 1 + 5 T + 142 T^{2} + 646 T^{3} + 8536 T^{4} + 26742 T^{5} + 287886 T^{6} - 702648 T^{7} + 10262887 T^{8} - 139977013 T^{9} + 674338952 T^{10} - 8258643767 T^{11} + 35725109647 T^{12} - 144309143592 T^{13} + 3488418588846 T^{14} + 19118505603858 T^{15} + 360053035159576 T^{16} + 1607668859193074 T^{17} + 20849922139813582 T^{18} + 43314979093274695 T^{19} + 511116753300641401 T^{20} )^{2} \))(\( ( 1 - 21 T + 206 T^{2} - 2416 T^{3} + 25558 T^{4} - 134475 T^{5} + 585400 T^{6} - 1747337 T^{7} - 63466585 T^{8} + 768235069 T^{9} - 4979757289 T^{10} + 45325869071 T^{11} - 220927182385 T^{12} - 358866325723 T^{13} + 7093503129400 T^{14} - 96139445108025 T^{15} + 1078050078796678 T^{16} - 6012581987322704 T^{17} + 30247070146490126 T^{18} - 181922912191753719 T^{19} + 511116753300641401 T^{20} )^{2} \))
$61$ (\( 1 + 6 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 - 4 T + 46 T^{2} - 244 T^{3} + 3721 T^{4} \))(\( 1 - 2 T - 2 T^{2} - 122 T^{3} + 3721 T^{4} \))(\( 1 + 188 T^{2} + 136 T^{3} + 15462 T^{4} + 8296 T^{5} + 699548 T^{6} + 13845841 T^{8} \))(\( 1 + 8 T + 142 T^{2} + 316 T^{3} + 7126 T^{4} + 19276 T^{5} + 528382 T^{6} + 1815848 T^{7} + 13845841 T^{8} \))(\( 1 + 8 T + 142 T^{2} + 316 T^{3} + 7126 T^{4} + 19276 T^{5} + 528382 T^{6} + 1815848 T^{7} + 13845841 T^{8} \))(\( 1 - 40 T + 971 T^{2} - 17008 T^{3} + 237341 T^{4} - 2736312 T^{5} + 26811983 T^{6} - 225335392 T^{7} + 1635530963 T^{8} - 10181816952 T^{9} + 53871897521 T^{10} - 235490063728 T^{11} + 820103008271 T^{12} - 2060814974440 T^{13} + 3142742836021 T^{14} \))(\( 1 - 40 T + 971 T^{2} - 17008 T^{3} + 237341 T^{4} - 2736312 T^{5} + 26811983 T^{6} - 225335392 T^{7} + 1635530963 T^{8} - 10181816952 T^{9} + 53871897521 T^{10} - 235490063728 T^{11} + 820103008271 T^{12} - 2060814974440 T^{13} + 3142742836021 T^{14} \))(\( ( 1 + 8 T + 61 T^{2} )^{2} \))(\( ( 1 + 8 T + 61 T^{2} )^{2} \))(\( ( 1 - 2 T - 2 T^{2} - 122 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 - 4 T + 46 T^{2} - 244 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 + 188 T^{2} + 136 T^{3} + 15462 T^{4} + 8296 T^{5} + 699548 T^{6} + 13845841 T^{8} )^{2} \))(\( ( 1 - 40 T + 971 T^{2} - 17008 T^{3} + 237341 T^{4} - 2736312 T^{5} + 26811983 T^{6} - 225335392 T^{7} + 1635530963 T^{8} - 10181816952 T^{9} + 53871897521 T^{10} - 235490063728 T^{11} + 820103008271 T^{12} - 2060814974440 T^{13} + 3142742836021 T^{14} )^{2} \))(\( ( 1 - 61 T^{2} )^{4} \))(\( ( 1 + 10 T^{2} + 3721 T^{4} )^{4} \))(\( ( 1 - 61 T^{2} )^{12} \))(\( ( 1 - 288 T^{2} + 45599 T^{4} - 4912324 T^{6} + 406368068 T^{8} - 27198365512 T^{10} + 1512095581028 T^{12} - 68015257044484 T^{14} + 2349277550487239 T^{16} - 55211706143216928 T^{18} + 713342911662882601 T^{20} )^{2} \))(\( 1 + 27 T + 263 T^{2} + 909 T^{3} + 400 T^{4} + 55449 T^{5} + 978623 T^{6} + 6128487 T^{7} + 13845841 T^{8} \))(\( 1 + 3 T + 14 T^{2} - 174 T^{3} + 3200 T^{4} + 46207 T^{5} + 124734 T^{6} - 489978 T^{7} + 801426 T^{8} + 45141464 T^{9} + 1300242855 T^{10} + 2753629304 T^{11} + 2982106146 T^{12} - 111215696418 T^{13} + 1727047131294 T^{14} + 39026261280307 T^{15} + 164865197955200 T^{16} - 546837253467654 T^{17} + 2683902381961934 T^{18} + 35082438278502423 T^{19} + 713342911662882601 T^{20} \))(\( 1 - 3 T + 157 T^{2} - 695 T^{3} + 17192 T^{4} - 102450 T^{5} + 1128572 T^{6} - 10677101 T^{7} + 64622634 T^{8} - 839211059 T^{9} + 3256596793 T^{10} - 51191874599 T^{11} + 240460821114 T^{12} - 2423499062081 T^{13} + 15626028469052 T^{14} - 86528891037450 T^{15} + 885738276014312 T^{16} - 2184206271034595 T^{17} + 30098048140573117 T^{18} - 35082438278502423 T^{19} + 713342911662882601 T^{20} \))(\( 1 + 13 T - 60 T^{2} - 2612 T^{3} - 15003 T^{4} + 100279 T^{5} + 1903557 T^{6} + 10954221 T^{7} + 12672790 T^{8} - 800102006 T^{9} - 12112961179 T^{10} - 59157771400 T^{11} + 479177951078 T^{12} + 7550071333662 T^{13} + 31890998032060 T^{14} - 103532444522825 T^{15} - 2309029969616480 T^{16} - 22681070722503046 T^{17} - 90474577182005101 T^{18} + 916305827480323236 T^{19} + 15097916789735610599 T^{20} + 55894655476299717396 T^{21} - \)\(33\!\cdots\!21\)\( T^{22} - \)\(51\!\cdots\!26\)\( T^{23} - \)\(31\!\cdots\!80\)\( T^{24} - \)\(87\!\cdots\!25\)\( T^{25} + \)\(16\!\cdots\!60\)\( T^{26} + \)\(23\!\cdots\!02\)\( T^{27} + \)\(91\!\cdots\!18\)\( T^{28} - \)\(69\!\cdots\!00\)\( T^{29} - \)\(86\!\cdots\!79\)\( T^{30} - \)\(34\!\cdots\!66\)\( T^{31} + \)\(33\!\cdots\!90\)\( T^{32} + \)\(17\!\cdots\!01\)\( T^{33} + \)\(18\!\cdots\!37\)\( T^{34} + \)\(60\!\cdots\!79\)\( T^{35} - \)\(55\!\cdots\!83\)\( T^{36} - \)\(58\!\cdots\!52\)\( T^{37} - \)\(82\!\cdots\!60\)\( T^{38} + \)\(10\!\cdots\!33\)\( T^{39} + \)\(50\!\cdots\!01\)\( T^{40} \))(\( ( 1 + 3 T + 14 T^{2} - 174 T^{3} + 3200 T^{4} + 46207 T^{5} + 124734 T^{6} - 489978 T^{7} + 801426 T^{8} + 45141464 T^{9} + 1300242855 T^{10} + 2753629304 T^{11} + 2982106146 T^{12} - 111215696418 T^{13} + 1727047131294 T^{14} + 39026261280307 T^{15} + 164865197955200 T^{16} - 546837253467654 T^{17} + 2683902381961934 T^{18} + 35082438278502423 T^{19} + 713342911662882601 T^{20} )^{2} \))(\( ( 1 - 3 T + 157 T^{2} - 695 T^{3} + 17192 T^{4} - 102450 T^{5} + 1128572 T^{6} - 10677101 T^{7} + 64622634 T^{8} - 839211059 T^{9} + 3256596793 T^{10} - 51191874599 T^{11} + 240460821114 T^{12} - 2423499062081 T^{13} + 15626028469052 T^{14} - 86528891037450 T^{15} + 885738276014312 T^{16} - 2184206271034595 T^{17} + 30098048140573117 T^{18} - 35082438278502423 T^{19} + 713342911662882601 T^{20} )^{2} \))
$67$ (\( 1 + 13 T + 67 T^{2} \))(\( 1 + 5 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 - 13 T + 67 T^{2} \))(\( 1 - 10 T + 154 T^{2} - 670 T^{3} + 4489 T^{4} \))(\( 1 + 6 T + 98 T^{2} + 402 T^{3} + 4489 T^{4} \))(\( 1 - 3 T + 170 T^{2} - 391 T^{3} + 15834 T^{4} - 26197 T^{5} + 763130 T^{6} - 902289 T^{7} + 20151121 T^{8} \))(\( 1 - 2 T + 260 T^{2} - 390 T^{3} + 25866 T^{4} - 26130 T^{5} + 1167140 T^{6} - 601526 T^{7} + 20151121 T^{8} \))(\( 1 + 2 T + 260 T^{2} + 390 T^{3} + 25866 T^{4} + 26130 T^{5} + 1167140 T^{6} + 601526 T^{7} + 20151121 T^{8} \))(\( 1 + 4 T + 245 T^{2} + 680 T^{3} + 28669 T^{4} + 85884 T^{5} + 2488785 T^{6} + 7855600 T^{7} + 166748595 T^{8} + 385533276 T^{9} + 8622574447 T^{10} + 13702762280 T^{11} + 330780651215 T^{12} + 361833528676 T^{13} + 6060711605323 T^{14} \))(\( 1 - 4 T + 245 T^{2} - 680 T^{3} + 28669 T^{4} - 85884 T^{5} + 2488785 T^{6} - 7855600 T^{7} + 166748595 T^{8} - 385533276 T^{9} + 8622574447 T^{10} - 13702762280 T^{11} + 330780651215 T^{12} - 361833528676 T^{13} + 6060711605323 T^{14} \))(\( 1 - 109 T^{2} + 4489 T^{4} \))(\( 1 - 70 T^{2} + 4489 T^{4} \))(\( 1 - 160 T^{2} + 13758 T^{4} - 718240 T^{6} + 20151121 T^{8} \))(\( 1 - 208 T^{2} + 19294 T^{4} - 933712 T^{6} + 20151121 T^{8} \))(\( 1 - 331 T^{2} + 58222 T^{4} - 6599757 T^{6} + 524582210 T^{8} - 29626309173 T^{10} + 1173238566862 T^{12} - 29941724497939 T^{14} + 406067677556641 T^{16} \))(\( 1 - 474 T^{2} + 111923 T^{4} - 17875908 T^{6} + 2195266361 T^{8} - 220509971110 T^{10} + 18658416443395 T^{12} - 1349144763920056 T^{14} + 83757631414400155 T^{16} - 4443523109544114310 T^{18} + \)\(19\!\cdots\!09\)\( T^{20} - \)\(72\!\cdots\!28\)\( T^{22} + \)\(20\!\cdots\!27\)\( T^{24} - \)\(38\!\cdots\!14\)\( T^{26} + \)\(36\!\cdots\!29\)\( T^{28} \))(\( 1 + 3343 T^{4} + 20151121 T^{8} \))(\( ( 1 - 878 T^{4} + 20151121 T^{8} )^{2} \))(\( ( 1 + 4489 T^{4} )^{6} \))(\( 1 + 12179 T^{4} + 21394393 T^{8} - 187118931868 T^{12} + 373223367469206 T^{16} + 8514442786702047778 T^{20} + \)\(75\!\cdots\!26\)\( T^{24} - \)\(75\!\cdots\!88\)\( T^{28} + \)\(17\!\cdots\!73\)\( T^{32} + \)\(20\!\cdots\!99\)\( T^{36} + \)\(33\!\cdots\!01\)\( T^{40} \))(\( 1 - 7 T - 33 T^{2} - 155 T^{3} + 5816 T^{4} - 10385 T^{5} - 148137 T^{6} - 2105341 T^{7} + 20151121 T^{8} \))(\( 1 + 20 T + 223 T^{2} + 1822 T^{3} + 4262 T^{4} - 78106 T^{5} - 1241112 T^{6} - 7658230 T^{7} + 22056296 T^{8} + 902388884 T^{9} + 10137910717 T^{10} + 60460055228 T^{11} + 99010712744 T^{12} - 2303312229490 T^{13} - 25009798086552 T^{14} - 105452871607342 T^{15} + 385533624804278 T^{16} + 11042616544898506 T^{17} + 90553092095130943 T^{18} + 544130687925898940 T^{19} + 1822837804551761449 T^{20} \))(\( 1 + 45 T + 1023 T^{2} + 15905 T^{3} + 191575 T^{4} + 1861057 T^{5} + 14558842 T^{6} + 88766657 T^{7} + 371829810 T^{8} + 453912238 T^{9} - 4886911745 T^{10} + 30412119946 T^{11} + 1669144017090 T^{12} + 26697726059291 T^{13} + 293376986761882 T^{14} + 2512659781258099 T^{15} + 17329564564026175 T^{16} + 96395618082662315 T^{17} + 415407234140443743 T^{18} + 1224294047833272615 T^{19} + 1822837804551761449 T^{20} \))(\( 1 - 9 T - 337 T^{2} + 4839 T^{3} + 44298 T^{4} - 1132981 T^{5} - 440595 T^{6} + 154086318 T^{7} - 773767208 T^{8} - 12301905801 T^{9} + 141655410926 T^{10} + 326567723604 T^{11} - 13755036511502 T^{12} + 54542970952515 T^{13} + 727217719747252 T^{14} - 8656605590327801 T^{15} + 1622077958659168 T^{16} + 623781141371941467 T^{17} - 4122992200747057095 T^{18} - 18074669471187244023 T^{19} + \)\(39\!\cdots\!75\)\( T^{20} - \)\(12\!\cdots\!41\)\( T^{21} - \)\(18\!\cdots\!55\)\( T^{22} + \)\(18\!\cdots\!21\)\( T^{23} + \)\(32\!\cdots\!28\)\( T^{24} - \)\(11\!\cdots\!07\)\( T^{25} + \)\(65\!\cdots\!88\)\( T^{26} + \)\(33\!\cdots\!45\)\( T^{27} - \)\(55\!\cdots\!82\)\( T^{28} + \)\(88\!\cdots\!88\)\( T^{29} + \)\(25\!\cdots\!74\)\( T^{30} - \)\(15\!\cdots\!83\)\( T^{31} - \)\(63\!\cdots\!88\)\( T^{32} + \)\(84\!\cdots\!66\)\( T^{33} - \)\(16\!\cdots\!55\)\( T^{34} - \)\(27\!\cdots\!83\)\( T^{35} + \)\(73\!\cdots\!38\)\( T^{36} + \)\(53\!\cdots\!53\)\( T^{37} - \)\(24\!\cdots\!33\)\( T^{38} - \)\(44\!\cdots\!27\)\( T^{39} + \)\(33\!\cdots\!01\)\( T^{40} \))(\( 1 - 46 T^{2} - 14627 T^{4} + 776816 T^{6} + 99688748 T^{8} - 5244178286 T^{10} - 455118258258 T^{12} + 20062401076600 T^{14} + 1659953542143444 T^{16} - 35802325603195986 T^{18} - 6329662116487431139 T^{20} - \)\(16\!\cdots\!54\)\( T^{22} + \)\(33\!\cdots\!24\)\( T^{24} + \)\(18\!\cdots\!00\)\( T^{26} - \)\(18\!\cdots\!78\)\( T^{28} - \)\(95\!\cdots\!14\)\( T^{30} + \)\(81\!\cdots\!28\)\( T^{32} + \)\(28\!\cdots\!64\)\( T^{34} - \)\(24\!\cdots\!87\)\( T^{36} - \)\(34\!\cdots\!14\)\( T^{38} + \)\(33\!\cdots\!01\)\( T^{40} \))(\( 1 - 21 T^{2} - 1771 T^{4} - 615979 T^{6} + 42808677 T^{8} - 1157662231 T^{10} + 190482847556 T^{12} - 16987935147963 T^{14} + 1226862311475746 T^{16} - 81411190653864094 T^{18} + 4724969653276548983 T^{20} - \)\(36\!\cdots\!66\)\( T^{22} + \)\(24\!\cdots\!66\)\( T^{24} - \)\(15\!\cdots\!47\)\( T^{26} + \)\(77\!\cdots\!96\)\( T^{28} - \)\(21\!\cdots\!19\)\( T^{30} + \)\(35\!\cdots\!97\)\( T^{32} - \)\(22\!\cdots\!91\)\( T^{34} - \)\(29\!\cdots\!51\)\( T^{36} - \)\(15\!\cdots\!89\)\( T^{38} + \)\(33\!\cdots\!01\)\( T^{40} \))
$71$ (\( 1 - 13 T + 71 T^{2} \))(\( 1 - 5 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 - 13 T + 71 T^{2} \))(\( 1 - 20 T + 237 T^{2} - 1420 T^{3} + 5041 T^{4} \))(\( 1 + 8 T + 153 T^{2} + 568 T^{3} + 5041 T^{4} \))(\( 1 + 3 T + 135 T^{2} + 104 T^{3} + 9080 T^{4} + 7384 T^{5} + 680535 T^{6} + 1073733 T^{7} + 25411681 T^{8} \))(\( 1 + 24 T + 350 T^{2} + 3544 T^{3} + 32183 T^{4} + 251624 T^{5} + 1764350 T^{6} + 8589864 T^{7} + 25411681 T^{8} \))(\( 1 + 24 T + 350 T^{2} + 3544 T^{3} + 32183 T^{4} + 251624 T^{5} + 1764350 T^{6} + 8589864 T^{7} + 25411681 T^{8} \))(\( 1 + 14 T + 479 T^{2} + 4960 T^{3} + 95992 T^{4} + 781136 T^{5} + 10923513 T^{6} + 70967270 T^{7} + 775569423 T^{8} + 3937706576 T^{9} + 34356592712 T^{10} + 126041937760 T^{11} + 864225859129 T^{12} + 1793403974894 T^{13} + 9095120158391 T^{14} \))(\( 1 + 14 T + 479 T^{2} + 4960 T^{3} + 95992 T^{4} + 781136 T^{5} + 10923513 T^{6} + 70967270 T^{7} + 775569423 T^{8} + 3937706576 T^{9} + 34356592712 T^{10} + 126041937760 T^{11} + 864225859129 T^{12} + 1793403974894 T^{13} + 9095120158391 T^{14} \))(\( ( 1 - 5 T + 71 T^{2} )^{2} \))(\( ( 1 + 10 T + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 153 T^{2} + 568 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 20 T + 237 T^{2} - 1420 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 + 3 T + 135 T^{2} + 104 T^{3} + 9080 T^{4} + 7384 T^{5} + 680535 T^{6} + 1073733 T^{7} + 25411681 T^{8} )^{2} \))(\( ( 1 + 14 T + 479 T^{2} + 4960 T^{3} + 95992 T^{4} + 781136 T^{5} + 10923513 T^{6} + 70967270 T^{7} + 775569423 T^{8} + 3937706576 T^{9} + 34356592712 T^{10} + 126041937760 T^{11} + 864225859129 T^{12} + 1793403974894 T^{13} + 9095120158391 T^{14} )^{2} \))(\( ( 1 + 13 T + 71 T^{2} )^{4} \))(\( ( 1 - 2 T + 71 T^{2} )^{8} \))(\( ( 1 + 1176 T^{3} + 357911 T^{6} )^{4} \))(\( ( 1 - 11 T + 235 T^{2} - 1020 T^{3} + 15325 T^{4} - 20035 T^{5} + 1088075 T^{6} - 5141820 T^{7} + 84109085 T^{8} - 279528491 T^{9} + 1804229351 T^{10} )^{4} \))(\( 1 + 20 T + 169 T^{2} + 1600 T^{3} + 17121 T^{4} + 113600 T^{5} + 851929 T^{6} + 7158220 T^{7} + 25411681 T^{8} \))(\( 1 + 22 T + 204 T^{2} + 209 T^{3} - 1361 T^{4} + 99759 T^{5} + 1632143 T^{6} + 4544078 T^{7} - 8138253 T^{8} + 377062070 T^{9} + 8288280417 T^{10} + 26771406970 T^{11} - 41024933373 T^{12} + 1626375501058 T^{13} + 41475497262383 T^{14} + 179988115826409 T^{15} - 174344486416481 T^{16} + 1900880113103719 T^{17} + 131733720374135244 T^{18} + 1008667015805878682 T^{19} + 3255243551009881201 T^{20} \))(\( 1 + 14 T + 59 T^{2} + 140 T^{3} + 3909 T^{4} + 54686 T^{5} - 152597 T^{6} - 4301040 T^{7} - 22667179 T^{8} - 212067842 T^{9} - 1811694401 T^{10} - 15056816782 T^{11} - 114265249339 T^{12} - 1539389527440 T^{13} - 3877746285557 T^{14} + 98666086288786 T^{15} + 500744009847189 T^{16} + 1273316822174740 T^{17} + 38099458343499899 T^{18} + 641879010058286434 T^{19} + 3255243551009881201 T^{20} \))(\( 1 + 19 T + 83 T^{2} - 816 T^{3} - 6625 T^{4} + 14575 T^{5} + 69541 T^{6} - 1592636 T^{7} - 12108235 T^{8} - 196163533 T^{9} - 3746523573 T^{10} - 48113457043 T^{11} - 279634239359 T^{12} + 1030580907940 T^{13} + 17532711356992 T^{14} - 64779962713440 T^{15} - 898237358003269 T^{16} + 4646236140350778 T^{17} + 86466675434941796 T^{18} + 900300579683224304 T^{19} + 9271746160980739561 T^{20} + 63921341157508925584 T^{21} + \)\(43\!\cdots\!36\)\( T^{22} + \)\(16\!\cdots\!58\)\( T^{23} - \)\(22\!\cdots\!89\)\( T^{24} - \)\(11\!\cdots\!40\)\( T^{25} + \)\(22\!\cdots\!32\)\( T^{26} + \)\(93\!\cdots\!40\)\( T^{27} - \)\(18\!\cdots\!99\)\( T^{28} - \)\(22\!\cdots\!33\)\( T^{29} - \)\(12\!\cdots\!73\)\( T^{30} - \)\(45\!\cdots\!43\)\( T^{31} - \)\(19\!\cdots\!35\)\( T^{32} - \)\(18\!\cdots\!96\)\( T^{33} + \)\(57\!\cdots\!21\)\( T^{34} + \)\(85\!\cdots\!25\)\( T^{35} - \)\(27\!\cdots\!25\)\( T^{36} - \)\(24\!\cdots\!56\)\( T^{37} + \)\(17\!\cdots\!63\)\( T^{38} + \)\(28\!\cdots\!89\)\( T^{39} + \)\(10\!\cdots\!01\)\( T^{40} \))(\( ( 1 + 22 T + 204 T^{2} + 209 T^{3} - 1361 T^{4} + 99759 T^{5} + 1632143 T^{6} + 4544078 T^{7} - 8138253 T^{8} + 377062070 T^{9} + 8288280417 T^{10} + 26771406970 T^{11} - 41024933373 T^{12} + 1626375501058 T^{13} + 41475497262383 T^{14} + 179988115826409 T^{15} - 174344486416481 T^{16} + 1900880113103719 T^{17} + 131733720374135244 T^{18} + 1008667015805878682 T^{19} + 3255243551009881201 T^{20} )^{2} \))(\( ( 1 + 14 T + 59 T^{2} + 140 T^{3} + 3909 T^{4} + 54686 T^{5} - 152597 T^{6} - 4301040 T^{7} - 22667179 T^{8} - 212067842 T^{9} - 1811694401 T^{10} - 15056816782 T^{11} - 114265249339 T^{12} - 1539389527440 T^{13} - 3877746285557 T^{14} + 98666086288786 T^{15} + 500744009847189 T^{16} + 1273316822174740 T^{17} + 38099458343499899 T^{18} + 641879010058286434 T^{19} + 3255243551009881201 T^{20} )^{2} \))
$73$ (\( 1 + 8 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 3 T + 73 T^{2} \))(\( 1 - 3 T + 73 T^{2} \))(\( 1 - 8 T + 73 T^{2} \))(\( 1 + 22 T + 247 T^{2} + 1606 T^{3} + 5329 T^{4} \))(\( 1 + 101 T^{2} + 5329 T^{4} \))(\( 1 - 32 T + 635 T^{2} - 8400 T^{3} + 83736 T^{4} - 613200 T^{5} + 3383915 T^{6} - 12448544 T^{7} + 28398241 T^{8} \))(\( 1 + 18 T + 270 T^{2} + 2088 T^{3} + 20423 T^{4} + 152424 T^{5} + 1438830 T^{6} + 7002306 T^{7} + 28398241 T^{8} \))(\( 1 - 18 T + 270 T^{2} - 2088 T^{3} + 20423 T^{4} - 152424 T^{5} + 1438830 T^{6} - 7002306 T^{7} + 28398241 T^{8} \))(\( 1 + 3 T + 325 T^{2} + 658 T^{3} + 54034 T^{4} + 90182 T^{5} + 5763275 T^{6} + 7883729 T^{7} + 420719075 T^{8} + 480579878 T^{9} + 21020144578 T^{10} + 18686042578 T^{11} + 673748267725 T^{12} + 454002678867 T^{13} + 11047398519097 T^{14} \))(\( 1 - 3 T + 325 T^{2} - 658 T^{3} + 54034 T^{4} - 90182 T^{5} + 5763275 T^{6} - 7883729 T^{7} + 420719075 T^{8} - 480579878 T^{9} + 21020144578 T^{10} - 18686042578 T^{11} + 673748267725 T^{12} - 454002678867 T^{13} + 11047398519097 T^{14} \))(\( ( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} ) \))(\( 1 - 137 T^{2} + 5329 T^{4} \))(\( ( 1 - 101 T^{2} + 5329 T^{4} )^{2} \))(\( 1 - 10 T^{2} + 1003 T^{4} - 53290 T^{6} + 28398241 T^{8} \))(\( 1 - 246 T^{2} + 33097 T^{4} - 3307750 T^{6} + 267619412 T^{8} - 17626999750 T^{10} + 939896582377 T^{12} - 37228219667094 T^{14} + 806460091894081 T^{16} \))(\( 1 - 641 T^{2} + 209745 T^{4} - 45674594 T^{6} + 7341258170 T^{8} - 916942030850 T^{10} + 91525697961603 T^{12} - 7404928269089115 T^{14} + 487740444437382387 T^{16} - 26039540775107734850 T^{18} + \)\(11\!\cdots\!30\)\( T^{20} - \)\(36\!\cdots\!14\)\( T^{22} + \)\(90\!\cdots\!05\)\( T^{24} - \)\(14\!\cdots\!61\)\( T^{26} + \)\(12\!\cdots\!09\)\( T^{28} \))(\( ( 1 + 5329 T^{4} )^{2} \))(\( ( 1 + 9791 T^{4} + 28398241 T^{8} )^{2} \))(\( 1 + 223017449186 T^{12} + \)\(22\!\cdots\!21\)\( T^{24} \))(\( ( 1 - 28 T + 392 T^{2} - 4930 T^{3} + 65419 T^{4} - 742868 T^{5} + 7308506 T^{6} - 74556498 T^{7} + 765085933 T^{8} - 6852665726 T^{9} + 57335768430 T^{10} - 500244597998 T^{11} + 4077142936957 T^{12} - 29003745182466 T^{13} + 207548714737946 T^{14} - 1540018548148724 T^{15} + 9900133749600091 T^{16} - 54463674699148210 T^{17} + 316132356022479752 T^{18} - 1648404427831501564 T^{19} + 4297625829703557649 T^{20} )^{2} \))(\( 1 + 22 T + 111 T^{2} - 1564 T^{3} - 26011 T^{4} - 114172 T^{5} + 591519 T^{6} + 8558374 T^{7} + 28398241 T^{8} \))(\( 1 + 43 T + 797 T^{2} + 8021 T^{3} + 47021 T^{4} + 205129 T^{5} + 1802674 T^{6} + 24182707 T^{7} + 240208550 T^{8} + 1756457458 T^{9} + 12854913015 T^{10} + 128221394434 T^{11} + 1280071362950 T^{12} + 9407484129019 T^{13} + 51192770696434 T^{14} + 425247102800497 T^{15} + 7115886654335069 T^{16} + 88611183521677037 T^{17} + 642748693239582557 T^{18} + 2531478228455520259 T^{19} + 4297625829703557649 T^{20} \))(\( 1 + 19 T + 178 T^{2} + 444 T^{3} + 3164 T^{4} + 41113 T^{5} + 460294 T^{6} - 2252883 T^{7} - 34972209 T^{8} - 676028375 T^{9} - 5421480987 T^{10} - 49350071375 T^{11} - 186366901761 T^{12} - 876409786011 T^{13} + 13071539942854 T^{14} + 85230192403009 T^{15} + 478821491978396 T^{16} + 4905044942479068 T^{17} + 143549896357146418 T^{18} + 1118560147457090347 T^{19} + 4297625829703557649 T^{20} \))(\( 1 - 27 T - 49 T^{2} + 8346 T^{3} - 56095 T^{4} - 1063391 T^{5} + 14512055 T^{6} + 49029069 T^{7} - 1832046917 T^{8} + 4811768775 T^{9} + 142698735069 T^{10} - 1167290774645 T^{11} - 6314222788672 T^{12} + 130217378630554 T^{13} - 71752041870944 T^{14} - 10325321569056809 T^{15} + 48322092625455436 T^{16} + 592140752562355010 T^{17} - 6063599567403657515 T^{18} - 16569795153193735530 T^{19} + \)\(51\!\cdots\!14\)\( T^{20} - \)\(12\!\cdots\!90\)\( T^{21} - \)\(32\!\cdots\!35\)\( T^{22} + \)\(23\!\cdots\!70\)\( T^{23} + \)\(13\!\cdots\!76\)\( T^{24} - \)\(21\!\cdots\!37\)\( T^{25} - \)\(10\!\cdots\!16\)\( T^{26} + \)\(14\!\cdots\!38\)\( T^{27} - \)\(50\!\cdots\!32\)\( T^{28} - \)\(68\!\cdots\!85\)\( T^{29} + \)\(61\!\cdots\!81\)\( T^{30} + \)\(15\!\cdots\!75\)\( T^{31} - \)\(41\!\cdots\!57\)\( T^{32} + \)\(81\!\cdots\!77\)\( T^{33} + \)\(17\!\cdots\!95\)\( T^{34} - \)\(94\!\cdots\!87\)\( T^{35} - \)\(36\!\cdots\!95\)\( T^{36} + \)\(39\!\cdots\!38\)\( T^{37} - \)\(16\!\cdots\!81\)\( T^{38} - \)\(68\!\cdots\!99\)\( T^{39} + \)\(18\!\cdots\!01\)\( T^{40} \))(\( 1 + 255 T^{2} + 39445 T^{4} + 3420713 T^{6} + 194461677 T^{8} + 2942910685 T^{10} - 235079389780 T^{12} - 46381152759323 T^{14} - 4781652870590570 T^{16} - 644818957996522030 T^{18} - 51982877778765360153 T^{20} - \)\(34\!\cdots\!70\)\( T^{22} - \)\(13\!\cdots\!70\)\( T^{24} - \)\(70\!\cdots\!47\)\( T^{26} - \)\(18\!\cdots\!80\)\( T^{28} + \)\(12\!\cdots\!65\)\( T^{30} + \)\(44\!\cdots\!17\)\( T^{32} + \)\(41\!\cdots\!17\)\( T^{34} + \)\(25\!\cdots\!45\)\( T^{36} + \)\(88\!\cdots\!95\)\( T^{38} + \)\(18\!\cdots\!01\)\( T^{40} \))(\( 1 + 5 T^{2} + 21140 T^{4} - 287542 T^{6} + 153032352 T^{8} - 5619031639 T^{10} + 348646859798 T^{12} - 20932397834643 T^{14} - 784775606817541 T^{16} + 121474537515317943 T^{18} - 7351817297005411867 T^{20} + \)\(64\!\cdots\!47\)\( T^{22} - \)\(22\!\cdots\!81\)\( T^{24} - \)\(31\!\cdots\!27\)\( T^{26} + \)\(28\!\cdots\!38\)\( T^{28} - \)\(24\!\cdots\!11\)\( T^{30} + \)\(35\!\cdots\!92\)\( T^{32} - \)\(35\!\cdots\!78\)\( T^{34} + \)\(13\!\cdots\!40\)\( T^{36} + \)\(17\!\cdots\!45\)\( T^{38} + \)\(18\!\cdots\!01\)\( T^{40} \))
$79$ (\( 1 + 14 T + 79 T^{2} \))(\( 1 + 12 T + 79 T^{2} \))(\( 1 + 3 T + 79 T^{2} \))(\( 1 + 3 T + 79 T^{2} \))(\( 1 + 14 T + 79 T^{2} \))(\( 1 + 4 T + 82 T^{2} + 316 T^{3} + 6241 T^{4} \))(\( 1 - 22 T + 274 T^{2} - 1738 T^{3} + 6241 T^{4} \))(\( 1 - 2 T + 176 T^{2} - 826 T^{3} + 15838 T^{4} - 65254 T^{5} + 1098416 T^{6} - 986078 T^{7} + 38950081 T^{8} \))(\( 1 - 24 T + 494 T^{2} - 6100 T^{3} + 65598 T^{4} - 481900 T^{5} + 3083054 T^{6} - 11832936 T^{7} + 38950081 T^{8} \))(\( 1 - 24 T + 494 T^{2} - 6100 T^{3} + 65598 T^{4} - 481900 T^{5} + 3083054 T^{6} - 11832936 T^{7} + 38950081 T^{8} \))(\( 1 + T + 321 T^{2} + 1538 T^{3} + 46557 T^{4} + 374223 T^{5} + 4556893 T^{6} + 40938716 T^{7} + 359994547 T^{8} + 2335525743 T^{9} + 22954416723 T^{10} + 59905224578 T^{11} + 987735104079 T^{12} + 243087455521 T^{13} + 19203908986159 T^{14} \))(\( 1 + T + 321 T^{2} + 1538 T^{3} + 46557 T^{4} + 374223 T^{5} + 4556893 T^{6} + 40938716 T^{7} + 359994547 T^{8} + 2335525743 T^{9} + 22954416723 T^{10} + 59905224578 T^{11} + 987735104079 T^{12} + 243087455521 T^{13} + 19203908986159 T^{14} \))(\( ( 1 - 12 T + 79 T^{2} )^{2} \))(\( ( 1 - 3 T + 79 T^{2} )^{2} \))(\( ( 1 + 22 T + 274 T^{2} + 1738 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 - 4 T + 82 T^{2} - 316 T^{3} + 6241 T^{4} )^{2} \))(\( ( 1 + 2 T + 176 T^{2} + 826 T^{3} + 15838 T^{4} + 65254 T^{5} + 1098416 T^{6} + 986078 T^{7} + 38950081 T^{8} )^{2} \))(\( ( 1 - T + 321 T^{2} - 1538 T^{3} + 46557 T^{4} - 374223 T^{5} + 4556893 T^{6} - 40938716 T^{7} + 359994547 T^{8} - 2335525743 T^{9} + 22954416723 T^{10} - 59905224578 T^{11} + 987735104079 T^{12} - 243087455521 T^{13} + 19203908986159 T^{14} )^{2} \))(\( ( 1 + 79 T^{2} )^{4} \))(\( ( 1 + 125 T^{2} + 6241 T^{4} )^{4} \))(\( ( 1 + 79 T^{2} )^{12} \))(\( ( 1 + 332 T^{2} + 60799 T^{4} + 7894836 T^{6} + 804461788 T^{8} + 68672209888 T^{10} + 5020646018908 T^{12} + 307504501681716 T^{14} + 14779474208221279 T^{16} + 503680124888978252 T^{18} + 9468276082626847201 T^{20} )^{2} \))(\( 1 + 27 T + 470 T^{2} + 6117 T^{3} + 61789 T^{4} + 483243 T^{5} + 2933270 T^{6} + 13312053 T^{7} + 38950081 T^{8} \))(\( 1 - 51 T + 1114 T^{2} - 13295 T^{3} + 92135 T^{4} - 385584 T^{5} + 1188383 T^{6} - 2740799 T^{7} + 64216836 T^{8} - 2455180103 T^{9} + 33339862885 T^{10} - 193959228137 T^{11} + 400777273476 T^{12} - 1351320798161 T^{13} + 46287614109023 T^{14} - 1186463714552016 T^{15} + 22396862714427335 T^{16} - 255315969970983905 T^{17} + 1690059214235908954 T^{18} - 6112431395113534269 T^{19} + 9468276082626847201 T^{20} \))(\( 1 + 15 T + 36 T^{2} - 2262 T^{3} - 24256 T^{4} - 43814 T^{5} + 2049210 T^{6} + 18764080 T^{7} + 60623103 T^{8} - 1063681247 T^{9} - 12642166076 T^{10} - 84030818513 T^{11} + 378348785823 T^{12} + 9251423239120 T^{13} + 79816895486010 T^{14} - 134818149065786 T^{15} - 5896329321117376 T^{16} - 43439242126691658 T^{17} + 54615917156636196 T^{18} + 1797773939739274785 T^{19} + 9468276082626847201 T^{20} \))(\( 1 + 83 T + 3229 T^{2} + 78771 T^{3} + 1360907 T^{4} + 17747029 T^{5} + 178442571 T^{6} + 1318577173 T^{7} + 5245494785 T^{8} - 26916412207 T^{9} - 688944277333 T^{10} - 5280206060532 T^{11} + 11833858144127 T^{12} + 923189234494892 T^{13} + 15263056131282191 T^{14} + 169446648447312438 T^{15} + 1393749417833100974 T^{16} + 7898356705887080574 T^{17} + 15891588591444807484 T^{18} - \)\(26\!\cdots\!23\)\( T^{19} - \)\(36\!\cdots\!29\)\( T^{20} - \)\(20\!\cdots\!17\)\( T^{21} + \)\(99\!\cdots\!44\)\( T^{22} + \)\(38\!\cdots\!86\)\( T^{23} + \)\(54\!\cdots\!94\)\( T^{24} + \)\(52\!\cdots\!62\)\( T^{25} + \)\(37\!\cdots\!11\)\( T^{26} + \)\(17\!\cdots\!28\)\( T^{27} + \)\(17\!\cdots\!47\)\( T^{28} - \)\(63\!\cdots\!08\)\( T^{29} - \)\(65\!\cdots\!33\)\( T^{30} - \)\(20\!\cdots\!53\)\( T^{31} + \)\(30\!\cdots\!85\)\( T^{32} + \)\(61\!\cdots\!47\)\( T^{33} + \)\(65\!\cdots\!51\)\( T^{34} + \)\(51\!\cdots\!71\)\( T^{35} + \)\(31\!\cdots\!47\)\( T^{36} + \)\(14\!\cdots\!89\)\( T^{37} + \)\(46\!\cdots\!69\)\( T^{38} + \)\(94\!\cdots\!77\)\( T^{39} + \)\(89\!\cdots\!01\)\( T^{40} \))(\( ( 1 + 51 T + 1114 T^{2} + 13295 T^{3} + 92135 T^{4} + 385584 T^{5} + 1188383 T^{6} + 2740799 T^{7} + 64216836 T^{8} + 2455180103 T^{9} + 33339862885 T^{10} + 193959228137 T^{11} + 400777273476 T^{12} + 1351320798161 T^{13} + 46287614109023 T^{14} + 1186463714552016 T^{15} + 22396862714427335 T^{16} + 255315969970983905 T^{17} + 1690059214235908954 T^{18} + 6112431395113534269 T^{19} + 9468276082626847201 T^{20} )^{2} \))(\( ( 1 - 15 T + 36 T^{2} + 2262 T^{3} - 24256 T^{4} + 43814 T^{5} + 2049210 T^{6} - 18764080 T^{7} + 60623103 T^{8} + 1063681247 T^{9} - 12642166076 T^{10} + 84030818513 T^{11} + 378348785823 T^{12} - 9251423239120 T^{13} + 79816895486010 T^{14} + 134818149065786 T^{15} - 5896329321117376 T^{16} + 43439242126691658 T^{17} + 54615917156636196 T^{18} - 1797773939739274785 T^{19} + 9468276082626847201 T^{20} )^{2} \))
$83$ (\( 1 - 3 T + 83 T^{2} \))(\( 1 + 9 T + 83 T^{2} \))(\( 1 - 3 T + 83 T^{2} \))(\( 1 + 3 T + 83 T^{2} \))(\( 1 + 3 T + 83 T^{2} \))(\( 1 - 22 T + 282 T^{2} - 1826 T^{3} + 6889 T^{4} \))(\( 1 - 4 T + 150 T^{2} - 332 T^{3} + 6889 T^{4} \))(\( 1 - 21 T + 428 T^{2} - 5005 T^{3} + 56054 T^{4} - 415415 T^{5} + 2948492 T^{6} - 12007527 T^{7} + 47458321 T^{8} \))(\( 1 - 6 T + 62 T^{2} - 518 T^{3} + 11462 T^{4} - 42994 T^{5} + 427118 T^{6} - 3430722 T^{7} + 47458321 T^{8} \))(\( 1 + 6 T + 62 T^{2} + 518 T^{3} + 11462 T^{4} + 42994 T^{5} + 427118 T^{6} + 3430722 T^{7} + 47458321 T^{8} \))(\( 1 - 17 T + 541 T^{2} - 7850 T^{3} + 130949 T^{4} - 1547895 T^{5} + 17976145 T^{6} - 168233836 T^{7} + 1492020035 T^{8} - 10663448655 T^{9} + 74874935863 T^{10} - 372547819850 T^{11} + 2131020987863 T^{12} - 5557986347273 T^{13} + 27136050989627 T^{14} \))(\( 1 + 17 T + 541 T^{2} + 7850 T^{3} + 130949 T^{4} + 1547895 T^{5} + 17976145 T^{6} + 168233836 T^{7} + 1492020035 T^{8} + 10663448655 T^{9} + 74874935863 T^{10} + 372547819850 T^{11} + 2131020987863 T^{12} + 5557986347273 T^{13} + 27136050989627 T^{14} \))(\( 1 - 85 T^{2} + 6889 T^{4} \))(\( 1 - 157 T^{2} + 6889 T^{4} \))(\( 1 - 284 T^{2} + 33622 T^{4} - 1956476 T^{6} + 47458321 T^{8} \))(\( 1 - 80 T^{2} + 12958 T^{4} - 551120 T^{6} + 47458321 T^{8} \))(\( 1 - 415 T^{2} + 85082 T^{4} - 11381753 T^{6} + 1098256426 T^{8} - 78408896417 T^{10} + 4037848867322 T^{12} - 135680254948135 T^{14} + 2252292232139041 T^{16} \))(\( 1 - 793 T^{2} + 287679 T^{4} - 63388178 T^{6} + 9559967637 T^{8} - 1072224562311 T^{10} + 98276177858107 T^{12} - 8258776153235516 T^{14} + 677024589264499123 T^{16} - 50885977462239939831 T^{18} + \)\(31\!\cdots\!53\)\( T^{20} - \)\(14\!\cdots\!98\)\( T^{22} + \)\(44\!\cdots\!71\)\( T^{24} - \)\(84\!\cdots\!73\)\( T^{26} + \)\(73\!\cdots\!29\)\( T^{28} \))(\( 1 - 12097 T^{4} + 47458321 T^{8} \))(\( ( 1 - 9289 T^{4} + 47458321 T^{8} )^{2} \))(\( ( 1 + 6889 T^{4} )^{6} \))(\( 1 + 14383 T^{4} + 96015001 T^{8} + 196390156024 T^{12} - 4395513412321338 T^{16} - 50701641519546426142 T^{20} - \)\(20\!\cdots\!98\)\( T^{24} + \)\(44\!\cdots\!84\)\( T^{28} + \)\(10\!\cdots\!61\)\( T^{32} + \)\(72\!\cdots\!23\)\( T^{36} + \)\(24\!\cdots\!01\)\( T^{40} \))(\( 1 + 23 T + 166 T^{2} + 709 T^{3} + 6369 T^{4} + 58847 T^{5} + 1143574 T^{6} + 13151101 T^{7} + 47458321 T^{8} \))(\( 1 - 17 T - 47 T^{2} + 2793 T^{3} - 1329 T^{4} - 469277 T^{5} + 3476090 T^{6} + 30330137 T^{7} - 432941786 T^{8} - 1652517680 T^{9} + 51926903887 T^{10} - 137158967440 T^{11} - 2982535963754 T^{12} + 17342378044819 T^{13} + 164969395044890 T^{14} - 1848501175825111 T^{15} - 434503756207401 T^{16} + 75790990414028211 T^{17} - 105857734910534927 T^{18} - 3177984339548186851 T^{19} + 15516041187205853449 T^{20} \))(\( 1 + 18 T + 109 T^{2} + 72 T^{3} - 10248 T^{4} - 168066 T^{5} - 1355830 T^{6} - 6119988 T^{7} + 37604796 T^{8} + 775038374 T^{9} + 6144118025 T^{10} + 64328185042 T^{11} + 259059439644 T^{12} - 3499329578556 T^{13} - 64345415361430 T^{14} - 662018804706438 T^{15} - 3350484946285512 T^{16} + 1953795671253144 T^{17} + 245499853303155469 T^{18} + 3364924594815727254 T^{19} + 15516041187205853449 T^{20} \))(\( 1 + 67 T + 2213 T^{2} + 49993 T^{3} + 896668 T^{4} + 13779193 T^{5} + 188412483 T^{6} + 2340658030 T^{7} + 26777861702 T^{8} + 285062809625 T^{9} + 2847595768468 T^{10} + 26869752855934 T^{11} + 241233089991778 T^{12} + 2079971489872049 T^{13} + 17436911144135816 T^{14} + 144599134630260603 T^{15} + 1208646255676931134 T^{16} + 10315114326872771811 T^{17} + 90233346610071163341 T^{18} + \)\(80\!\cdots\!31\)\( T^{19} + \)\(72\!\cdots\!67\)\( T^{20} + \)\(66\!\cdots\!73\)\( T^{21} + \)\(62\!\cdots\!49\)\( T^{22} + \)\(58\!\cdots\!57\)\( T^{23} + \)\(57\!\cdots\!14\)\( T^{24} + \)\(56\!\cdots\!29\)\( T^{25} + \)\(57\!\cdots\!04\)\( T^{26} + \)\(56\!\cdots\!23\)\( T^{27} + \)\(54\!\cdots\!98\)\( T^{28} + \)\(50\!\cdots\!02\)\( T^{29} + \)\(44\!\cdots\!32\)\( T^{30} + \)\(36\!\cdots\!75\)\( T^{31} + \)\(28\!\cdots\!22\)\( T^{32} + \)\(20\!\cdots\!90\)\( T^{33} + \)\(13\!\cdots\!07\)\( T^{34} + \)\(84\!\cdots\!51\)\( T^{35} + \)\(45\!\cdots\!08\)\( T^{36} + \)\(21\!\cdots\!39\)\( T^{37} + \)\(77\!\cdots\!17\)\( T^{38} + \)\(19\!\cdots\!49\)\( T^{39} + \)\(24\!\cdots\!01\)\( T^{40} \))(\( 1 + 383 T^{2} + 94513 T^{4} + 16679161 T^{6} + 2461736189 T^{8} + 310519760693 T^{10} + 35421790331820 T^{12} + 3652697209072273 T^{14} + 351782736670566978 T^{16} + 31538475276366442758 T^{18} + \)\(26\!\cdots\!71\)\( T^{20} + \)\(21\!\cdots\!62\)\( T^{22} + \)\(16\!\cdots\!38\)\( T^{24} + \)\(11\!\cdots\!37\)\( T^{26} + \)\(79\!\cdots\!20\)\( T^{28} + \)\(48\!\cdots\!57\)\( T^{30} + \)\(26\!\cdots\!29\)\( T^{32} + \)\(12\!\cdots\!69\)\( T^{34} + \)\(47\!\cdots\!53\)\( T^{36} + \)\(13\!\cdots\!47\)\( T^{38} + \)\(24\!\cdots\!01\)\( T^{40} \))(\( 1 + 106 T^{2} - 11207 T^{4} - 1099468 T^{6} + 129181228 T^{8} + 6991110290 T^{10} - 1559480294962 T^{12} - 39656414748964 T^{14} + 14161201902344328 T^{16} + 125518515002511026 T^{18} - \)\(10\!\cdots\!03\)\( T^{20} + \)\(86\!\cdots\!14\)\( T^{22} + \)\(67\!\cdots\!88\)\( T^{24} - \)\(12\!\cdots\!16\)\( T^{26} - \)\(35\!\cdots\!42\)\( T^{28} + \)\(10\!\cdots\!10\)\( T^{30} + \)\(13\!\cdots\!08\)\( T^{32} - \)\(80\!\cdots\!72\)\( T^{34} - \)\(56\!\cdots\!67\)\( T^{36} + \)\(37\!\cdots\!54\)\( T^{38} + \)\(24\!\cdots\!01\)\( T^{40} \))
$89$ (\( 1 + 14 T + 89 T^{2} \))(\( 1 - 4 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 14 T + 89 T^{2} \))(\( 1 + 12 T + 194 T^{2} + 1068 T^{3} + 7921 T^{4} \))(\( 1 - 10 T + 198 T^{2} - 890 T^{3} + 7921 T^{4} \))(\( 1 + 140 T^{2} - 1496 T^{3} + 6326 T^{4} - 133144 T^{5} + 1108940 T^{6} + 62742241 T^{8} \))(\( 1 + 8 T + 270 T^{2} + 1764 T^{3} + 34598 T^{4} + 156996 T^{5} + 2138670 T^{6} + 5639752 T^{7} + 62742241 T^{8} \))(\( 1 + 8 T + 270 T^{2} + 1764 T^{3} + 34598 T^{4} + 156996 T^{5} + 2138670 T^{6} + 5639752 T^{7} + 62742241 T^{8} \))(\( 1 - 16 T + 379 T^{2} - 4856 T^{3} + 79377 T^{4} - 825904 T^{5} + 10350019 T^{6} - 90162448 T^{7} + 921151691 T^{8} - 6541985584 T^{9} + 55958324313 T^{10} - 304676322296 T^{11} + 2116358531171 T^{12} - 7951700655376 T^{13} + 44231334895529 T^{14} \))(\( 1 - 16 T + 379 T^{2} - 4856 T^{3} + 79377 T^{4} - 825904 T^{5} + 10350019 T^{6} - 90162448 T^{7} + 921151691 T^{8} - 6541985584 T^{9} + 55958324313 T^{10} - 304676322296 T^{11} + 2116358531171 T^{12} - 7951700655376 T^{13} + 44231334895529 T^{14} \))(\( ( 1 + 4 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 10 T + 198 T^{2} + 890 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 - 12 T + 194 T^{2} - 1068 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 140 T^{2} + 1496 T^{3} + 6326 T^{4} + 133144 T^{5} + 1108940 T^{6} + 62742241 T^{8} )^{2} \))(\( ( 1 + 16 T + 379 T^{2} + 4856 T^{3} + 79377 T^{4} + 825904 T^{5} + 10350019 T^{6} + 90162448 T^{7} + 921151691 T^{8} + 6541985584 T^{9} + 55958324313 T^{10} + 304676322296 T^{11} + 2116358531171 T^{12} + 7951700655376 T^{13} + 44231334895529 T^{14} )^{2} \))(\( ( 1 + 89 T^{2} )^{4} \))(\( ( 1 + 46 T^{2} + 7921 T^{4} )^{4} \))(\( ( 1 + 89 T^{2} )^{12} \))(\( ( 1 + 468 T^{2} + 124191 T^{4} + 22228084 T^{6} + 2951501052 T^{8} + 298597247008 T^{10} + 23378839832892 T^{12} + 1394639803296244 T^{14} + 61720603505737551 T^{16} + 1842323561068573908 T^{18} + 31181719929966183601 T^{20} )^{2} \))(\( 1 + T^{2} + 660 T^{3} + 5941 T^{4} + 58740 T^{5} + 7921 T^{6} + 62742241 T^{8} \))(\( 1 - 57 T + 1455 T^{2} - 22697 T^{3} + 269934 T^{4} - 3046104 T^{5} + 33584052 T^{6} - 328175911 T^{7} + 3078564586 T^{8} - 32141776413 T^{9} + 327813403533 T^{10} - 2860618100757 T^{11} + 24385310085706 T^{12} - 231353843801759 T^{13} + 2107138684340532 T^{14} - 17009625823836696 T^{15} + 134152147794266574 T^{16} - 1003918608123821713 T^{17} + 5727736712296527855 T^{18} - 19970315011326656913 T^{19} + 31181719929966183601 T^{20} \))(\( 1 - 25 T + 173 T^{2} + 1772 T^{3} - 48367 T^{4} + 349557 T^{5} + 2352100 T^{6} - 63458766 T^{7} + 346368857 T^{8} + 3220239858 T^{9} - 63184785399 T^{10} + 286601347362 T^{11} + 2743587716297 T^{12} - 44736462808254 T^{13} + 147576025056100 T^{14} + 1951947068814093 T^{15} - 24037494099910687 T^{16} + 78377925434877388 T^{17} + 681029863386460013 T^{18} - 8758910092687130225 T^{19} + 31181719929966183601 T^{20} \))(\( 1 + 5 T - 25 T^{2} - 1096 T^{3} - 8331 T^{4} - 8721 T^{5} + 899098 T^{6} + 2262003 T^{7} - 53415589 T^{8} - 1115445180 T^{9} + 273194454 T^{10} + 154552038615 T^{11} + 1491838219341 T^{12} - 1199327424269 T^{13} - 125456650170894 T^{14} - 1124099813937917 T^{15} + 622354984158761 T^{16} + 119069351123803568 T^{17} + 721825449679471296 T^{18} - 4533691496925569566 T^{19} - \)\(11\!\cdots\!23\)\( T^{20} - \)\(40\!\cdots\!74\)\( T^{21} + \)\(57\!\cdots\!16\)\( T^{22} + \)\(83\!\cdots\!92\)\( T^{23} + \)\(39\!\cdots\!01\)\( T^{24} - \)\(62\!\cdots\!33\)\( T^{25} - \)\(62\!\cdots\!34\)\( T^{26} - \)\(53\!\cdots\!01\)\( T^{27} + \)\(58\!\cdots\!21\)\( T^{28} + \)\(54\!\cdots\!35\)\( T^{29} + \)\(85\!\cdots\!54\)\( T^{30} - \)\(30\!\cdots\!20\)\( T^{31} - \)\(13\!\cdots\!69\)\( T^{32} + \)\(49\!\cdots\!07\)\( T^{33} + \)\(17\!\cdots\!18\)\( T^{34} - \)\(15\!\cdots\!29\)\( T^{35} - \)\(12\!\cdots\!91\)\( T^{36} - \)\(15\!\cdots\!84\)\( T^{37} - \)\(30\!\cdots\!25\)\( T^{38} + \)\(54\!\cdots\!45\)\( T^{39} + \)\(97\!\cdots\!01\)\( T^{40} \))(\( ( 1 + 57 T + 1455 T^{2} + 22697 T^{3} + 269934 T^{4} + 3046104 T^{5} + 33584052 T^{6} + 328175911 T^{7} + 3078564586 T^{8} + 32141776413 T^{9} + 327813403533 T^{10} + 2860618100757 T^{11} + 24385310085706 T^{12} + 231353843801759 T^{13} + 2107138684340532 T^{14} + 17009625823836696 T^{15} + 134152147794266574 T^{16} + 1003918608123821713 T^{17} + 5727736712296527855 T^{18} + 19970315011326656913 T^{19} + 31181719929966183601 T^{20} )^{2} \))(\( ( 1 + 25 T + 173 T^{2} - 1772 T^{3} - 48367 T^{4} - 349557 T^{5} + 2352100 T^{6} + 63458766 T^{7} + 346368857 T^{8} - 3220239858 T^{9} - 63184785399 T^{10} - 286601347362 T^{11} + 2743587716297 T^{12} + 44736462808254 T^{13} + 147576025056100 T^{14} - 1951947068814093 T^{15} - 24037494099910687 T^{16} - 78377925434877388 T^{17} + 681029863386460013 T^{18} + 8758910092687130225 T^{19} + 31181719929966183601 T^{20} )^{2} \))
$97$ (\( 1 + 14 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))(\( 1 + 22 T + 270 T^{2} + 2134 T^{3} + 9409 T^{4} \))(\( 1 + 10 T + 94 T^{2} + 970 T^{3} + 9409 T^{4} \))(\( 1 - 18 T + 460 T^{2} - 5038 T^{3} + 69350 T^{4} - 488686 T^{5} + 4328140 T^{6} - 16428114 T^{7} + 88529281 T^{8} \))(\( 1 + 34 T + 736 T^{2} + 10514 T^{3} + 119290 T^{4} + 1019858 T^{5} + 6925024 T^{6} + 31030882 T^{7} + 88529281 T^{8} \))(\( 1 - 34 T + 736 T^{2} - 10514 T^{3} + 119290 T^{4} - 1019858 T^{5} + 6925024 T^{6} - 31030882 T^{7} + 88529281 T^{8} \))(\( 1 + 24 T + 683 T^{2} + 11736 T^{3} + 196873 T^{4} + 2578984 T^{5} + 31528651 T^{6} + 323282256 T^{7} + 3058279147 T^{8} + 24265660456 T^{9} + 179680671529 T^{10} + 1038979641816 T^{11} + 5865153395531 T^{12} + 19991328118296 T^{13} + 80798284478113 T^{14} \))(\( 1 - 24 T + 683 T^{2} - 11736 T^{3} + 196873 T^{4} - 2578984 T^{5} + 31528651 T^{6} - 323282256 T^{7} + 3058279147 T^{8} - 24265660456 T^{9} + 179680671529 T^{10} - 1038979641816 T^{11} + 5865153395531 T^{12} - 19991328118296 T^{13} + 80798284478113 T^{14} \))(\( 1 + 2 T^{2} + 9409 T^{4} \))(\( 1 - 190 T^{2} + 9409 T^{4} \))(\( 1 - 88 T^{2} + 8254 T^{4} - 827992 T^{6} + 88529281 T^{8} \))(\( 1 - 56 T^{2} - 2178 T^{4} - 526904 T^{6} + 88529281 T^{8} \))(\( 1 - 596 T^{2} + 168932 T^{4} - 29484140 T^{6} + 3452957622 T^{8} - 277416273260 T^{10} + 14955428497892 T^{12} - 496451314937684 T^{14} + 7837433594376961 T^{16} \))(\( 1 - 790 T^{2} + 296907 T^{4} - 70460892 T^{6} + 11892212953 T^{8} - 1547259587530 T^{10} + 168500982547931 T^{12} - 16749342494044296 T^{14} + 1585425744793482779 T^{16} - \)\(13\!\cdots\!30\)\( T^{18} + \)\(99\!\cdots\!37\)\( T^{20} - \)\(55\!\cdots\!12\)\( T^{22} + \)\(21\!\cdots\!43\)\( T^{24} - \)\(54\!\cdots\!90\)\( T^{26} + \)\(65\!\cdots\!69\)\( T^{28} \))(\( 1 + 11458 T^{4} + 88529281 T^{8} \))(\( ( 1 + 3682 T^{4} + 88529281 T^{8} )^{2} \))(\( ( 1 + 9409 T^{4} )^{6} \))(\( 1 - 5386 T^{4} - 21562987 T^{8} - 1116224538328 T^{12} + 10456340019940986 T^{16} - 23761540774597810972 T^{20} + \)\(92\!\cdots\!66\)\( T^{24} - \)\(87\!\cdots\!08\)\( T^{28} - \)\(14\!\cdots\!67\)\( T^{32} - \)\(33\!\cdots\!06\)\( T^{36} + \)\(54\!\cdots\!01\)\( T^{40} \))(\( 1 - 2 T - 33 T^{2} + 830 T^{3} + 4361 T^{4} + 80510 T^{5} - 310497 T^{6} - 1825346 T^{7} + 88529281 T^{8} \))(\( 1 + 52 T + 1221 T^{2} + 17946 T^{3} + 192969 T^{4} + 1571526 T^{5} + 7814029 T^{6} - 34957602 T^{7} - 1703623889 T^{8} - 28959932998 T^{9} - 334806911165 T^{10} - 2809113500806 T^{11} - 16029397171601 T^{12} - 31904859490146 T^{13} + 691770369083149 T^{14} + 13495228484722182 T^{15} + 160737774819144201 T^{16} + 1450006013244215898 T^{17} + 9569506418734269381 T^{18} + 39532015050037391284 T^{19} + 73742412689492826049 T^{20} \))(\( 1 - 34 T + 333 T^{2} + 2173 T^{3} - 51172 T^{4} - 167353 T^{5} + 6267260 T^{6} + 25666611 T^{7} - 886006665 T^{8} - 2096067809 T^{9} + 115155056919 T^{10} - 203318577473 T^{11} - 8336436710985 T^{12} + 23425222861203 T^{13} + 554836021640060 T^{14} - 1437117154029721 T^{15} - 42624843436226788 T^{16} + 175574672170939549 T^{17} + 2609865386927528013 T^{18} - 25847855994255217378 T^{19} + 73742412689492826049 T^{20} \))(\( 1 + 18 T + 217 T^{2} + 459 T^{3} - 165 T^{4} + 58184 T^{5} + 2022945 T^{6} + 8627114 T^{7} - 72720422 T^{8} - 1290108908 T^{9} + 5885657778 T^{10} + 93480419036 T^{11} - 259130726070 T^{12} - 13697917648969 T^{13} - 218945380462 T^{14} + 1990820824616916 T^{15} + 15584041952796128 T^{16} + 15011258222155937 T^{17} - 70947882815197672 T^{18} + 20273662042860585271 T^{19} + \)\(30\!\cdots\!33\)\( T^{20} + \)\(19\!\cdots\!87\)\( T^{21} - \)\(66\!\cdots\!48\)\( T^{22} + \)\(13\!\cdots\!01\)\( T^{23} + \)\(13\!\cdots\!68\)\( T^{24} + \)\(17\!\cdots\!12\)\( T^{25} - \)\(18\!\cdots\!98\)\( T^{26} - \)\(11\!\cdots\!97\)\( T^{27} - \)\(20\!\cdots\!70\)\( T^{28} + \)\(71\!\cdots\!12\)\( T^{29} + \)\(43\!\cdots\!22\)\( T^{30} - \)\(92\!\cdots\!24\)\( T^{31} - \)\(50\!\cdots\!02\)\( T^{32} + \)\(58\!\cdots\!78\)\( T^{33} + \)\(13\!\cdots\!05\)\( T^{34} + \)\(36\!\cdots\!12\)\( T^{35} - \)\(10\!\cdots\!65\)\( T^{36} + \)\(27\!\cdots\!83\)\( T^{37} + \)\(12\!\cdots\!13\)\( T^{38} + \)\(10\!\cdots\!94\)\( T^{39} + \)\(54\!\cdots\!01\)\( T^{40} \))(\( 1 + 262 T^{2} + 10395 T^{4} - 1360736 T^{6} + 142025417 T^{8} + 17295320966 T^{10} - 4640138538829 T^{12} - 344058765984952 T^{14} + 40453471973019897 T^{16} + 1067309365275269694 T^{18} - \)\(43\!\cdots\!93\)\( T^{20} + \)\(10\!\cdots\!46\)\( T^{22} + \)\(35\!\cdots\!57\)\( T^{24} - \)\(28\!\cdots\!08\)\( T^{26} - \)\(36\!\cdots\!69\)\( T^{28} + \)\(12\!\cdots\!34\)\( T^{30} + \)\(98\!\cdots\!97\)\( T^{32} - \)\(88\!\cdots\!84\)\( T^{34} + \)\(63\!\cdots\!95\)\( T^{36} + \)\(15\!\cdots\!18\)\( T^{38} + \)\(54\!\cdots\!01\)\( T^{40} \))(\( 1 + 490 T^{2} + 156309 T^{4} + 37647965 T^{6} + 7493201100 T^{8} + 1283273511519 T^{10} + 193851024647560 T^{12} + 26217295914174839 T^{14} + 3205892538111604723 T^{16} + \)\(35\!\cdots\!51\)\( T^{18} + \)\(36\!\cdots\!75\)\( T^{20} + \)\(33\!\cdots\!59\)\( T^{22} + \)\(28\!\cdots\!63\)\( T^{24} + \)\(21\!\cdots\!31\)\( T^{26} + \)\(15\!\cdots\!60\)\( T^{28} + \)\(94\!\cdots\!31\)\( T^{30} + \)\(51\!\cdots\!00\)\( T^{32} + \)\(24\!\cdots\!85\)\( T^{34} + \)\(96\!\cdots\!89\)\( T^{36} + \)\(28\!\cdots\!10\)\( T^{38} + \)\(54\!\cdots\!01\)\( T^{40} \))
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