# Properties

 Label 675.2 Level 675 Weight 2 Dimension 11469 Nonzero newspaces 18 Newform subspaces 76 Sturm bound 64800 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$675 = 3^{3} \cdot 5^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$18$$ Newform subspaces: $$76$$ Sturm bound: $$64800$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(675))$$.

Total New Old
Modular forms 17040 12125 4915
Cusp forms 15361 11469 3892
Eisenstein series 1679 656 1023

## Trace form

 $$11469q - 54q^{2} - 78q^{3} - 92q^{4} - 64q^{5} - 120q^{6} - 91q^{7} - 26q^{8} - 72q^{9} + O(q^{10})$$ $$11469q - 54q^{2} - 78q^{3} - 92q^{4} - 64q^{5} - 120q^{6} - 91q^{7} - 26q^{8} - 72q^{9} - 104q^{10} - 61q^{11} - 60q^{12} - 69q^{13} + 7q^{14} - 96q^{15} - 104q^{16} - 15q^{17} - 63q^{18} - 78q^{19} - 32q^{20} - 132q^{21} - 33q^{22} - 20q^{23} - 90q^{24} - 96q^{25} - 126q^{26} - 81q^{27} - 170q^{28} + 2q^{29} - 96q^{30} - 109q^{31} - 112q^{32} - 96q^{33} - 75q^{34} - 100q^{35} - 246q^{36} - 92q^{37} - 174q^{38} - 159q^{39} - 192q^{40} - 209q^{41} - 246q^{42} - 201q^{43} - 421q^{44} - 156q^{45} - 223q^{46} - 231q^{47} - 327q^{48} - 158q^{49} - 184q^{50} - 354q^{51} - 197q^{52} - 186q^{53} - 270q^{54} - 248q^{55} - 241q^{56} - 147q^{57} - 63q^{58} - 8q^{59} - 168q^{60} - 73q^{61} + 4q^{62} - 63q^{63} - 144q^{64} - 96q^{65} - 129q^{66} - 78q^{67} - 223q^{68} - 63q^{69} - 240q^{70} + 11q^{71} - 246q^{72} - 149q^{73} - 371q^{74} - 168q^{75} - 506q^{76} - 393q^{77} - 366q^{78} - 333q^{79} - 552q^{80} - 276q^{81} - 684q^{82} - 493q^{83} - 522q^{84} - 256q^{85} - 757q^{86} - 303q^{87} - 546q^{88} - 579q^{89} - 324q^{90} - 371q^{91} - 847q^{92} - 399q^{93} - 387q^{94} - 212q^{95} - 552q^{96} - 212q^{97} - 725q^{98} - 339q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(675))$$

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
675.2.a $$\chi_{675}(1, \cdot)$$ 675.2.a.a 1 1
675.2.a.b 1
675.2.a.c 1
675.2.a.d 1
675.2.a.e 1
675.2.a.f 1
675.2.a.g 1
675.2.a.h 1
675.2.a.i 1
675.2.a.j 2
675.2.a.k 2
675.2.a.l 2
675.2.a.m 2
675.2.a.n 2
675.2.a.o 2
675.2.a.p 2
675.2.a.q 2
675.2.b $$\chi_{675}(649, \cdot)$$ 675.2.b.a 2 1
675.2.b.b 2
675.2.b.c 2
675.2.b.d 2
675.2.b.e 2
675.2.b.f 2
675.2.b.g 4
675.2.b.h 4
675.2.b.i 4
675.2.e $$\chi_{675}(226, \cdot)$$ 675.2.e.a 2 2
675.2.e.b 6
675.2.e.c 8
675.2.e.d 8
675.2.e.e 8
675.2.f $$\chi_{675}(107, \cdot)$$ 675.2.f.a 4 2
675.2.f.b 4
675.2.f.c 4
675.2.f.d 4
675.2.f.e 4
675.2.f.f 4
675.2.f.g 8
675.2.f.h 8
675.2.f.i 8
675.2.h $$\chi_{675}(136, \cdot)$$ 675.2.h.a 40 4
675.2.h.b 40
675.2.h.c 40
675.2.h.d 40
675.2.k $$\chi_{675}(199, \cdot)$$ 675.2.k.a 4 2
675.2.k.b 12
675.2.k.c 16
675.2.l $$\chi_{675}(76, \cdot)$$ 675.2.l.a 6 6
675.2.l.b 6
675.2.l.c 12
675.2.l.d 30
675.2.l.e 42
675.2.l.f 66
675.2.l.g 66
675.2.l.h 96
675.2.n $$\chi_{675}(109, \cdot)$$ 675.2.n.a 80 4
675.2.n.b 80
675.2.q $$\chi_{675}(143, \cdot)$$ 675.2.q.a 16 4
675.2.q.b 16
675.2.q.c 32
675.2.r $$\chi_{675}(46, \cdot)$$ 675.2.r.a 224 8
675.2.u $$\chi_{675}(49, \cdot)$$ 675.2.u.a 12 6
675.2.u.b 24
675.2.u.c 60
675.2.u.d 84
675.2.u.e 132
675.2.w $$\chi_{675}(53, \cdot)$$ 675.2.w.a 160 8
675.2.w.b 160
675.2.y $$\chi_{675}(19, \cdot)$$ 675.2.y.a 224 8
675.2.ba $$\chi_{675}(32, \cdot)$$ 675.2.ba.a 144 12
675.2.ba.b 192
675.2.ba.c 288
675.2.bc $$\chi_{675}(16, \cdot)$$ 675.2.bc.a 2112 24
675.2.bd $$\chi_{675}(8, \cdot)$$ 675.2.bd.a 448 16
675.2.bg $$\chi_{675}(4, \cdot)$$ 675.2.bg.a 2112 24
675.2.bi $$\chi_{675}(2, \cdot)$$ 675.2.bi.a 4224 48

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(675))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(675)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(135))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$1 + 2 T + 2 T^{2}$$)($$1 + T + 2 T^{2}$$)($$1 + T + 2 T^{2}$$)($$1 + 2 T^{2}$$)($$1 + 2 T^{2}$$)($$1 + 2 T^{2}$$)($$1 - T + 2 T^{2}$$)($$1 - T + 2 T^{2}$$)($$1 - 2 T + 2 T^{2}$$)($$1 + 3 T + 5 T^{2} + 6 T^{3} + 4 T^{4}$$)($$1 + T + T^{2} + 2 T^{3} + 4 T^{4}$$)($$1 + 2 T^{2} + 4 T^{4}$$)($$1 + 2 T^{2} + 4 T^{4}$$)($$1 - 3 T^{2} + 4 T^{4}$$)($$1 - 3 T^{2} + 4 T^{4}$$)($$1 - T + T^{2} - 2 T^{3} + 4 T^{4}$$)($$1 - 3 T + 5 T^{2} - 6 T^{3} + 4 T^{4}$$)($$( 1 - 2 T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$$)($$( 1 - 2 T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$$)($$1 - 3 T^{2} + 4 T^{4}$$)($$1 - 3 T^{2} + 4 T^{4}$$)($$( 1 - 2 T^{2} )^{2}$$)($$( 1 - 2 T^{2} )^{2}$$)($$( 1 - T + 2 T^{2} )^{2}( 1 + T + 2 T^{2} )^{2}$$)($$1 - T^{2} + 5 T^{4} - 4 T^{6} + 16 T^{8}$$)($$1 - T^{2} + 5 T^{4} - 4 T^{6} + 16 T^{8}$$)($$1 + T - T^{2} + 2 T^{3} + 4 T^{4}$$)($$1 + T - T^{3} - 2 T^{4} + T^{5} + 11 T^{6} + 2 T^{7} - 8 T^{8} - 8 T^{9} + 32 T^{11} + 64 T^{12}$$)($$1 + 2 T - 6 T^{3} - 9 T^{4} - 2 T^{5} + 9 T^{6} + 13 T^{7} + 7 T^{8} + 26 T^{9} + 36 T^{10} - 16 T^{11} - 144 T^{12} - 192 T^{13} + 256 T^{15} + 256 T^{16}$$)($$1 - 4 T^{2} + 7 T^{4} - 4 T^{6} + T^{8} - 16 T^{10} + 112 T^{12} - 256 T^{14} + 256 T^{16}$$)($$1 - 2 T + 6 T^{3} - 9 T^{4} + 2 T^{5} + 9 T^{6} - 13 T^{7} + 7 T^{8} - 26 T^{9} + 36 T^{10} + 16 T^{11} - 144 T^{12} + 192 T^{13} - 256 T^{15} + 256 T^{16}$$)($$1 - 7 T^{4} + 16 T^{8}$$)($$1 - 7 T^{4} + 16 T^{8}$$)($$( 1 - 2 T + 2 T^{2} )^{2}( 1 + 2 T + 2 T^{2} )^{2}$$)($$( 1 - 2 T + 2 T^{2} )^{2}( 1 + 2 T + 2 T^{2} )^{2}$$)($$1 - 7 T^{4} + 16 T^{8}$$)($$1 - 7 T^{4} + 16 T^{8}$$)($$( 1 - 2 T^{4} + 16 T^{8} )^{2}$$)($$1 + 7 T^{4} + 33 T^{8} + 112 T^{12} + 256 T^{16}$$)($$1 - T^{4} - 15 T^{8} - 16 T^{12} + 256 T^{16}$$)($$1 + 3 T^{2} + 5 T^{4} + 12 T^{6} + 16 T^{8}$$)($$1 + T^{2} - 2 T^{4} - 19 T^{6} - 14 T^{8} + 25 T^{10} + 197 T^{12} + 100 T^{14} - 224 T^{16} - 1216 T^{18} - 512 T^{20} + 1024 T^{22} + 4096 T^{24}$$)($$1 + 4 T^{2} + 6 T^{4} + 10 T^{6} + 19 T^{8} + 42 T^{10} + 95 T^{12} + 11 T^{14} - 267 T^{16} + 44 T^{18} + 1520 T^{20} + 2688 T^{22} + 4864 T^{24} + 10240 T^{26} + 24576 T^{28} + 65536 T^{30} + 65536 T^{32}$$)($$1 + 6 T + 18 T^{2} + 36 T^{3} + 54 T^{4} + 69 T^{5} + 91 T^{6} + 138 T^{7} + 216 T^{8} + 288 T^{9} + 288 T^{10} + 192 T^{11} + 64 T^{12}$$)($$1 - 6 T + 18 T^{2} - 36 T^{3} + 54 T^{4} - 69 T^{5} + 91 T^{6} - 138 T^{7} + 216 T^{8} - 288 T^{9} + 288 T^{10} - 192 T^{11} + 64 T^{12}$$)($$( 1 - 3 T + 3 T^{2} - 3 T^{4} + 6 T^{5} - 11 T^{6} + 12 T^{7} - 12 T^{8} + 48 T^{10} - 96 T^{11} + 64 T^{12} )( 1 - 3 T + 9 T^{2} - 18 T^{3} + 36 T^{4} - 57 T^{5} + 91 T^{6} - 114 T^{7} + 144 T^{8} - 144 T^{9} + 144 T^{10} - 96 T^{11} + 64 T^{12} )$$)($$1 + 6 T + 18 T^{2} + 36 T^{3} + 58 T^{4} + 78 T^{5} + 72 T^{6} - 149 T^{8} - 354 T^{9} - 576 T^{10} - 732 T^{11} - 530 T^{12} + 480 T^{13} + 2592 T^{14} + 5496 T^{15} + 8641 T^{16} + 10992 T^{17} + 10368 T^{18} + 3840 T^{19} - 8480 T^{20} - 23424 T^{21} - 36864 T^{22} - 45312 T^{23} - 38144 T^{24} + 73728 T^{26} + 159744 T^{27} + 237568 T^{28} + 294912 T^{29} + 294912 T^{30} + 196608 T^{31} + 65536 T^{32}$$)($$1 + 2 T^{4} - 5 T^{8} - 46 T^{12} - 239 T^{16} - 736 T^{20} - 1280 T^{24} + 8192 T^{28} + 65536 T^{32}$$)($$1 - 2 T^{6} - 27 T^{10} + 21 T^{12} - 108 T^{14} - 128 T^{18} + 4096 T^{24}$$)
$3$ ()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()($$1 + 9 T^{3} + 27 T^{6}$$)($$1 - 9 T^{3} + 27 T^{6}$$)($$1 - 6 T + 18 T^{2} - 39 T^{3} + 63 T^{4} - 81 T^{5} + 117 T^{6} - 243 T^{7} + 567 T^{8} - 1053 T^{9} + 1458 T^{10} - 1458 T^{11} + 729 T^{12}$$)()()($$1 + 27 T^{6} + 729 T^{12}$$)
$5$ ()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()
$7$ ($$1 - 3 T + 7 T^{2}$$)($$1 + 7 T^{2}$$)($$1 + 7 T^{2}$$)($$1 + 4 T + 7 T^{2}$$)($$1 - T + 7 T^{2}$$)($$1 - 4 T + 7 T^{2}$$)($$1 + 7 T^{2}$$)($$1 + 7 T^{2}$$)($$1 - 3 T + 7 T^{2}$$)($$( 1 + 7 T^{2} )^{2}$$)($$1 + 2 T + 2 T^{2} + 14 T^{3} + 49 T^{4}$$)($$( 1 + 3 T + 7 T^{2} )^{2}$$)($$( 1 - 3 T + 7 T^{2} )^{2}$$)($$( 1 + 3 T + 7 T^{2} )^{2}$$)($$( 1 - 3 T + 7 T^{2} )^{2}$$)($$1 + 2 T + 2 T^{2} + 14 T^{3} + 49 T^{4}$$)($$( 1 + 7 T^{2} )^{2}$$)($$1 - 5 T^{2} + 49 T^{4}$$)($$1 - 5 T^{2} + 49 T^{4}$$)($$( 1 - 7 T^{2} )^{2}$$)($$( 1 - 7 T^{2} )^{2}$$)($$1 + 2 T^{2} + 49 T^{4}$$)($$1 - 13 T^{2} + 49 T^{4}$$)($$( 1 - 5 T^{2} + 49 T^{4} )^{2}$$)($$( 1 - 2 T + 2 T^{2} - 14 T^{3} + 49 T^{4} )( 1 + 2 T + 2 T^{2} + 14 T^{3} + 49 T^{4} )$$)($$( 1 - 2 T + 2 T^{2} - 14 T^{3} + 49 T^{4} )( 1 + 2 T + 2 T^{2} + 14 T^{3} + 49 T^{4} )$$)($$1 + 3 T + 2 T^{2} + 21 T^{3} + 49 T^{4}$$)($$1 - 5 T + T^{2} + 14 T^{3} + 73 T^{4} - 173 T^{5} - 82 T^{6} - 1211 T^{7} + 3577 T^{8} + 4802 T^{9} + 2401 T^{10} - 84035 T^{11} + 117649 T^{12}$$)($$1 + T - 15 T^{2} + 22 T^{3} + 142 T^{4} - 303 T^{5} - 274 T^{6} + 1448 T^{7} - 633 T^{8} + 10136 T^{9} - 13426 T^{10} - 103929 T^{11} + 340942 T^{12} + 369754 T^{13} - 1764735 T^{14} + 823543 T^{15} + 5764801 T^{16}$$)($$1 - 16 T^{2} + 121 T^{4} - 592 T^{6} + 3280 T^{8} - 29008 T^{10} + 290521 T^{12} - 1882384 T^{14} + 5764801 T^{16}$$)($$1 - T - 15 T^{2} - 22 T^{3} + 142 T^{4} + 303 T^{5} - 274 T^{6} - 1448 T^{7} - 633 T^{8} - 10136 T^{9} - 13426 T^{10} + 103929 T^{11} + 340942 T^{12} - 369754 T^{13} - 1764735 T^{14} - 823543 T^{15} + 5764801 T^{16}$$)($$1 - 94 T^{4} + 2401 T^{8}$$)($$1 + 23 T^{4} + 2401 T^{8}$$)($$1 - 94 T^{4} + 2401 T^{8}$$)($$1 + 71 T^{4} + 2401 T^{8}$$)($$1 + 23 T^{4} + 2401 T^{8}$$)($$1 - 94 T^{4} + 2401 T^{8}$$)($$( 1 + 4 T + 8 T^{2} + 24 T^{3} + 71 T^{4} + 168 T^{5} + 392 T^{6} + 1372 T^{7} + 2401 T^{8} )^{2}$$)($$( 1 + 49 T^{4} )^{4}$$)($$( 1 - 2 T + 2 T^{2} + 6 T^{3} - 82 T^{4} + 42 T^{5} + 98 T^{6} - 686 T^{7} + 2401 T^{8} )^{2}$$)($$1 + 5 T^{2} - 24 T^{4} + 245 T^{6} + 2401 T^{8}$$)($$1 + 23 T^{2} + 287 T^{4} + 1944 T^{6} + 5053 T^{8} - 51983 T^{10} - 624746 T^{12} - 2547167 T^{14} + 12132253 T^{16} + 228709656 T^{18} + 1654497887 T^{20} + 6496930727 T^{22} + 13841287201 T^{24}$$)($$1 + 31 T^{2} + 465 T^{4} + 4686 T^{6} + 37554 T^{8} + 261471 T^{10} + 1619330 T^{12} + 9344750 T^{14} + 58806225 T^{16} + 457892750 T^{18} + 3888011330 T^{20} + 30761801679 T^{22} + 216491336754 T^{24} + 1323679016814 T^{26} + 6436198548465 T^{28} + 21024915258319 T^{30} + 33232930569601 T^{32}$$)($$1 + 6 T + 24 T^{2} + 64 T^{3} + 108 T^{4} + 108 T^{5} - 27 T^{6} + 756 T^{7} + 5292 T^{8} + 21952 T^{9} + 57624 T^{10} + 100842 T^{11} + 117649 T^{12}$$)($$1 - 6 T + 24 T^{2} - 64 T^{3} + 108 T^{4} - 108 T^{5} - 27 T^{6} - 756 T^{7} + 5292 T^{8} - 21952 T^{9} + 57624 T^{10} - 100842 T^{11} + 117649 T^{12}$$)($$1 - 6 T + 12 T^{2} + 11 T^{3} - 213 T^{4} + 678 T^{5} - 224 T^{6} - 3942 T^{7} + 15255 T^{8} - 25135 T^{9} - 22044 T^{10} + 210732 T^{11} - 647141 T^{12} + 1475124 T^{13} - 1080156 T^{14} - 8621305 T^{15} + 36627255 T^{16} - 66253194 T^{17} - 26353376 T^{18} + 558362154 T^{19} - 1227902613 T^{20} + 443889677 T^{21} + 3389702988 T^{22} - 11863960458 T^{23} + 13841287201 T^{24}$$)($$1 - 2 T + 2 T^{2} + 16 T^{3} - 66 T^{4} + 104 T^{5} + 52 T^{6} - 1072 T^{7} - 235 T^{8} - 2614 T^{9} - 2614 T^{10} - 626 T^{11} + 8430 T^{12} + 20146 T^{13} + 75264 T^{14} + 1168356 T^{15} + 4373152 T^{16} + 8178492 T^{17} + 3687936 T^{18} + 6910078 T^{19} + 20240430 T^{20} - 10521182 T^{21} - 307534486 T^{22} - 2152741402 T^{23} - 1354728235 T^{24} - 43259066704 T^{25} + 14688712948 T^{26} + 205641981272 T^{27} - 913524955266 T^{28} + 1550224166512 T^{29} + 1356446145698 T^{30} - 9495123019886 T^{31} + 33232930569601 T^{32}$$)($$1 + 38 T^{4} + 1681 T^{8} - 191482 T^{12} - 9175676 T^{16} - 459748282 T^{20} + 9690630481 T^{24} + 525968913638 T^{28} + 33232930569601 T^{32}$$)($$1 - 12 T^{2} + 24 T^{4} + 262 T^{6} - 1944 T^{8} + 8424 T^{10} - 38205 T^{12} + 412776 T^{14} - 4667544 T^{16} + 30824038 T^{18} + 138355224 T^{20} - 3389702988 T^{22} + 13841287201 T^{24}$$)
$11$ ($$1 - 2 T + 11 T^{2}$$)($$1 + 5 T + 11 T^{2}$$)($$1 - 5 T + 11 T^{2}$$)($$1 + 11 T^{2}$$)($$1 + 11 T^{2}$$)($$1 + 11 T^{2}$$)($$1 + 5 T + 11 T^{2}$$)($$1 - 5 T + 11 T^{2}$$)($$1 + 2 T + 11 T^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$1 + 2 T + 10 T^{2} + 22 T^{3} + 121 T^{4}$$)($$1 + 4 T^{2} + 121 T^{4}$$)($$1 + 4 T^{2} + 121 T^{4}$$)($$1 - 6 T^{2} + 121 T^{4}$$)($$1 - 6 T^{2} + 121 T^{4}$$)($$1 - 2 T + 10 T^{2} - 22 T^{3} + 121 T^{4}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 2 T + 11 T^{2} )^{2}$$)($$( 1 - 2 T + 11 T^{2} )^{2}$$)($$( 1 + 5 T + 11 T^{2} )^{2}$$)($$( 1 - 5 T + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 - 6 T^{2} + 121 T^{4} )^{2}$$)($$( 1 + 2 T + 10 T^{2} + 22 T^{3} + 121 T^{4} )^{2}$$)($$( 1 - 2 T + 10 T^{2} - 22 T^{3} + 121 T^{4} )^{2}$$)($$1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4}$$)($$1 + 2 T - 21 T^{2} - 14 T^{3} + 286 T^{4} - 58 T^{5} - 3673 T^{6} - 638 T^{7} + 34606 T^{8} - 18634 T^{9} - 307461 T^{10} + 322102 T^{11} + 1771561 T^{12}$$)($$1 + T - 18 T^{2} - 129 T^{3} + 120 T^{4} + 1886 T^{5} + 6087 T^{6} - 14944 T^{7} - 88007 T^{8} - 164384 T^{9} + 736527 T^{10} + 2510266 T^{11} + 1756920 T^{12} - 20775579 T^{13} - 31888098 T^{14} + 19487171 T^{15} + 214358881 T^{16}$$)($$( 1 - 6 T + 8 T^{2} - 36 T^{3} + 267 T^{4} - 396 T^{5} + 968 T^{6} - 7986 T^{7} + 14641 T^{8} )^{2}$$)($$1 + T - 18 T^{2} - 129 T^{3} + 120 T^{4} + 1886 T^{5} + 6087 T^{6} - 14944 T^{7} - 88007 T^{8} - 164384 T^{9} + 736527 T^{10} + 2510266 T^{11} + 1756920 T^{12} - 20775579 T^{13} - 31888098 T^{14} + 19487171 T^{15} + 214358881 T^{16}$$)($$( 1 - 13 T^{2} + 121 T^{4} )^{2}$$)($$( 1 + 14 T^{2} + 121 T^{4} )^{2}$$)($$( 1 - 11 T^{2} )^{4}$$)($$( 1 - 11 T^{2} )^{4}$$)($$( 1 + 14 T^{2} + 121 T^{4} )^{2}$$)($$( 1 - 13 T^{2} + 121 T^{4} )^{2}$$)($$( 1 - 28 T^{2} + 384 T^{4} - 3388 T^{6} + 14641 T^{8} )^{2}$$)($$( 1 - 11 T^{2} )^{8}$$)($$( 1 - 10 T^{2} + 78 T^{4} - 1210 T^{6} + 14641 T^{8} )^{2}$$)($$( 1 + 2 T - 7 T^{2} + 22 T^{3} + 121 T^{4} )^{2}$$)($$( 1 + 2 T - 21 T^{2} - 14 T^{3} + 286 T^{4} - 58 T^{5} - 3673 T^{6} - 638 T^{7} + 34606 T^{8} - 18634 T^{9} - 307461 T^{10} + 322102 T^{11} + 1771561 T^{12} )^{2}$$)($$( 1 + T - 18 T^{2} - 129 T^{3} + 120 T^{4} + 1886 T^{5} + 6087 T^{6} - 14944 T^{7} - 88007 T^{8} - 164384 T^{9} + 736527 T^{10} + 2510266 T^{11} + 1756920 T^{12} - 20775579 T^{13} - 31888098 T^{14} + 19487171 T^{15} + 214358881 T^{16} )^{2}$$)($$1 + 18 T + 135 T^{2} + 513 T^{3} + 675 T^{4} - 3033 T^{5} - 18422 T^{6} - 33363 T^{7} + 81675 T^{8} + 682803 T^{9} + 1976535 T^{10} + 2898918 T^{11} + 1771561 T^{12}$$)($$1 + 18 T + 135 T^{2} + 513 T^{3} + 675 T^{4} - 3033 T^{5} - 18422 T^{6} - 33363 T^{7} + 81675 T^{8} + 682803 T^{9} + 1976535 T^{10} + 2898918 T^{11} + 1771561 T^{12}$$)($$1 - 3 T - 15 T^{2} + 126 T^{3} - 201 T^{4} - 1488 T^{5} + 7145 T^{6} - 1530 T^{7} - 61974 T^{8} + 202716 T^{9} - 19692 T^{10} - 1304451 T^{11} + 4526883 T^{12} - 14348961 T^{13} - 2382732 T^{14} + 269814996 T^{15} - 907361334 T^{16} - 246408030 T^{17} + 12657803345 T^{18} - 28996910448 T^{19} - 43086135081 T^{20} + 297101409066 T^{21} - 389061369015 T^{22} - 855935011833 T^{23} + 3138428376721 T^{24}$$)($$( 1 + 34 T^{2} + 652 T^{4} + 414 T^{5} + 9016 T^{6} + 9072 T^{7} + 100687 T^{8} + 99792 T^{9} + 1090936 T^{10} + 551034 T^{11} + 9545932 T^{12} + 60233074 T^{14} + 214358881 T^{16} )^{2}$$)($$( 1 + 4 T^{2} - 105 T^{4} + 484 T^{6} + 14641 T^{8} )^{4}$$)($$( 1 + 18 T + 135 T^{2} + 513 T^{3} + 675 T^{4} - 3033 T^{5} - 18422 T^{6} - 33363 T^{7} + 81675 T^{8} + 682803 T^{9} + 1976535 T^{10} + 2898918 T^{11} + 1771561 T^{12} )^{2}$$)
$13$ ($$1 - 5 T + 13 T^{2}$$)($$1 - 5 T + 13 T^{2}$$)($$1 + 5 T + 13 T^{2}$$)($$1 - 5 T + 13 T^{2}$$)($$1 + 5 T + 13 T^{2}$$)($$1 + 5 T + 13 T^{2}$$)($$1 + 5 T + 13 T^{2}$$)($$1 - 5 T + 13 T^{2}$$)($$1 - 5 T + 13 T^{2}$$)($$( 1 + 13 T^{2} )^{2}$$)($$1 + 6 T + 22 T^{2} + 78 T^{3} + 169 T^{4}$$)($$( 1 + 3 T + 13 T^{2} )^{2}$$)($$( 1 - 3 T + 13 T^{2} )^{2}$$)($$( 1 - 2 T + 13 T^{2} )^{2}$$)($$( 1 + 2 T + 13 T^{2} )^{2}$$)($$1 + 6 T + 22 T^{2} + 78 T^{3} + 169 T^{4}$$)($$( 1 + 13 T^{2} )^{2}$$)($$1 - T^{2} + 169 T^{4}$$)($$1 - T^{2} + 169 T^{4}$$)($$1 - T^{2} + 169 T^{4}$$)($$1 - T^{2} + 169 T^{4}$$)($$1 - T^{2} + 169 T^{4}$$)($$1 - T^{2} + 169 T^{4}$$)($$( 1 - 22 T^{2} + 169 T^{4} )^{2}$$)($$1 - 8 T^{2} - 114 T^{4} - 1352 T^{6} + 28561 T^{8}$$)($$1 - 8 T^{2} - 114 T^{4} - 1352 T^{6} + 28561 T^{8}$$)($$( 1 - 5 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} )$$)($$1 - 4 T - 19 T^{2} + 60 T^{3} + 370 T^{4} - 536 T^{5} - 4235 T^{6} - 6968 T^{7} + 62530 T^{8} + 131820 T^{9} - 542659 T^{10} - 1485172 T^{11} + 4826809 T^{12}$$)($$1 - 2 T - 18 T^{2} + 102 T^{3} - 3 T^{4} - 1191 T^{5} + 3365 T^{6} + 5033 T^{7} - 45777 T^{8} + 65429 T^{9} + 568685 T^{10} - 2616627 T^{11} - 85683 T^{12} + 37871886 T^{13} - 86882562 T^{14} - 125497034 T^{15} + 815730721 T^{16}$$)($$( 1 - 20 T^{2} + 231 T^{4} - 3380 T^{6} + 28561 T^{8} )^{2}$$)($$1 + 2 T - 18 T^{2} - 102 T^{3} - 3 T^{4} + 1191 T^{5} + 3365 T^{6} - 5033 T^{7} - 45777 T^{8} - 65429 T^{9} + 568685 T^{10} + 2616627 T^{11} - 85683 T^{12} - 37871886 T^{13} - 86882562 T^{14} + 125497034 T^{15} + 815730721 T^{16}$$)($$1 - 337 T^{4} + 28561 T^{8}$$)($$( 1 + 169 T^{4} )^{2}$$)($$1 - 337 T^{4} + 28561 T^{8}$$)($$1 - 337 T^{4} + 28561 T^{8}$$)($$( 1 + 169 T^{4} )^{2}$$)($$1 - 337 T^{4} + 28561 T^{8}$$)($$( 1 - 8 T + 32 T^{2} - 144 T^{3} + 623 T^{4} - 1872 T^{5} + 5408 T^{6} - 17576 T^{7} + 28561 T^{8} )^{2}$$)($$( 1 + 169 T^{4} )^{4}$$)($$( 1 - 2 T + 2 T^{2} - 6 T^{3} - 82 T^{4} - 78 T^{5} + 338 T^{6} - 4394 T^{7} + 28561 T^{8} )^{2}$$)($$( 1 - T^{2} + 169 T^{4} )( 1 + 23 T^{2} + 169 T^{4} )$$)($$1 + 54 T^{2} + 1581 T^{4} + 30418 T^{6} + 431466 T^{8} + 4991934 T^{10} + 59312613 T^{12} + 843636846 T^{14} + 12323100426 T^{16} + 146821876162 T^{18} + 1289670269901 T^{20} + 7444358559846 T^{22} + 23298085122481 T^{24}$$)($$1 + 40 T^{2} + 726 T^{4} + 8330 T^{6} + 50411 T^{8} - 581655 T^{10} - 20871557 T^{12} - 333628385 T^{14} - 4436735157 T^{16} - 56383197065 T^{18} - 596112539477 T^{20} - 2807537588895 T^{22} + 41121801376331 T^{24} + 1148361237102170 T^{26} + 16914409798921206 T^{28} + 157495055427971560 T^{30} + 665416609183179841 T^{32}$$)($$1 - 9 T^{2} + 43 T^{3} - 171 T^{4} - 639 T^{5} + 3702 T^{6} - 8307 T^{7} - 28899 T^{8} + 94471 T^{9} - 257049 T^{10} + 4826809 T^{12}$$)($$1 - 9 T^{2} - 43 T^{3} - 171 T^{4} + 639 T^{5} + 3702 T^{6} + 8307 T^{7} - 28899 T^{8} - 94471 T^{9} - 257049 T^{10} + 4826809 T^{12}$$)($$1 - 6 T + 48 T^{2} - 214 T^{3} + 1488 T^{4} - 5928 T^{5} + 32329 T^{6} - 112023 T^{7} + 560277 T^{8} - 1799710 T^{9} + 8467593 T^{10} - 25055985 T^{11} + 112181629 T^{12} - 325727805 T^{13} + 1431023217 T^{14} - 3953962870 T^{15} + 16002071397 T^{16} - 41593355739 T^{17} + 156045908161 T^{18} - 371973208776 T^{19} + 1213807312848 T^{20} - 2269362865822 T^{21} + 6617207608752 T^{22} - 10752962364222 T^{23} + 23298085122481 T^{24}$$)($$1 - 2 T + 2 T^{2} - 56 T^{3} + 144 T^{4} - 658 T^{5} + 2596 T^{6} - 4150 T^{7} + 35702 T^{8} + 23108 T^{9} - 42562 T^{10} - 1025978 T^{11} - 7929096 T^{12} + 10433170 T^{13} - 40700658 T^{14} + 417980868 T^{15} - 885935405 T^{16} + 5433751284 T^{17} - 6878411202 T^{18} + 22921674490 T^{19} - 226462910856 T^{20} - 380938449554 T^{21} - 205438644658 T^{22} + 1449992730836 T^{23} + 29123218201142 T^{24} - 44008672397950 T^{25} + 357880644840004 T^{26} - 1179241539276346 T^{27} + 3354924257637264 T^{28} - 16961005969166168 T^{29} + 7874752771398578 T^{30} - 102371786028181514 T^{31} + 665416609183179841 T^{32}$$)($$1 + 116 T^{4} + 8266 T^{8} - 6024112 T^{12} - 1173111437 T^{16} - 172054662832 T^{20} + 6742830139786 T^{24} + 2702577874207796 T^{28} + 665416609183179841 T^{32}$$)($$1 + 18 T^{2} - 261 T^{4} - 8633 T^{6} - 40239 T^{8} + 953919 T^{10} + 19127910 T^{12} + 161212311 T^{14} - 1149266079 T^{16} - 41669842097 T^{18} - 212905718181 T^{20} + 2481452853282 T^{22} + 23298085122481 T^{24}$$)
$17$ ($$1 + 8 T + 17 T^{2}$$)($$1 + 4 T + 17 T^{2}$$)($$1 + 4 T + 17 T^{2}$$)($$1 + 17 T^{2}$$)($$1 + 17 T^{2}$$)($$1 + 17 T^{2}$$)($$1 - 4 T + 17 T^{2}$$)($$1 - 4 T + 17 T^{2}$$)($$1 - 8 T + 17 T^{2}$$)($$1 + 12 T + 65 T^{2} + 204 T^{3} + 289 T^{4}$$)($$1 + 4 T + 25 T^{2} + 68 T^{3} + 289 T^{4}$$)($$1 + 26 T^{2} + 289 T^{4}$$)($$1 + 26 T^{2} + 289 T^{4}$$)($$1 + 6 T^{2} + 289 T^{4}$$)($$1 + 6 T^{2} + 289 T^{4}$$)($$1 - 4 T + 25 T^{2} - 68 T^{3} + 289 T^{4}$$)($$1 - 12 T + 65 T^{2} - 204 T^{3} + 289 T^{4}$$)($$( 1 - 2 T + 17 T^{2} )( 1 + 2 T + 17 T^{2} )$$)($$( 1 - 2 T + 17 T^{2} )( 1 + 2 T + 17 T^{2} )$$)($$1 - 18 T^{2} + 289 T^{4}$$)($$1 - 18 T^{2} + 289 T^{4}$$)($$( 1 - 17 T^{2} )^{2}$$)($$( 1 - 17 T^{2} )^{2}$$)($$( 1 - 6 T^{2} + 289 T^{4} )^{2}$$)($$1 - 34 T^{2} + 659 T^{4} - 9826 T^{6} + 83521 T^{8}$$)($$1 - 34 T^{2} + 659 T^{4} - 9826 T^{6} + 83521 T^{8}$$)($$( 1 - 4 T + 17 T^{2} )^{2}$$)($$( 1 + 2 T + 43 T^{2} + 56 T^{3} + 731 T^{4} + 578 T^{5} + 4913 T^{6} )^{2}$$)($$( 1 - 11 T + 88 T^{2} - 451 T^{3} + 2111 T^{4} - 7667 T^{5} + 25432 T^{6} - 54043 T^{7} + 83521 T^{8} )^{2}$$)($$( 1 + 40 T^{2} + 786 T^{4} + 11560 T^{6} + 83521 T^{8} )^{2}$$)($$( 1 + 11 T + 88 T^{2} + 451 T^{3} + 2111 T^{4} + 7667 T^{5} + 25432 T^{6} + 54043 T^{7} + 83521 T^{8} )^{2}$$)($$1 - 94 T^{4} + 83521 T^{8}$$)($$1 - 94 T^{4} + 83521 T^{8}$$)($$( 1 + 289 T^{4} )^{2}$$)($$( 1 + 289 T^{4} )^{2}$$)($$1 - 94 T^{4} + 83521 T^{8}$$)($$1 - 94 T^{4} + 83521 T^{8}$$)($$1 - 76 T^{4} - 111450 T^{8} - 6347596 T^{12} + 6975757441 T^{16}$$)($$1 + 382 T^{4} + 62403 T^{8} + 31905022 T^{12} + 6975757441 T^{16}$$)($$( 1 + 151 T^{4} + 83521 T^{8} )^{2}$$)($$( 1 - 18 T^{2} + 289 T^{4} )^{2}$$)($$( 1 - 82 T^{2} + 3087 T^{4} - 67244 T^{6} + 892143 T^{8} - 6848722 T^{10} + 24137569 T^{12} )^{2}$$)($$( 1 - 55 T^{2} + 2044 T^{4} - 50325 T^{6} + 994815 T^{8} - 14543925 T^{10} + 170716924 T^{12} - 1327566295 T^{14} + 6975757441 T^{16} )^{2}$$)($$1 + 6 T - 24 T^{2} - 54 T^{3} + 1338 T^{4} + 1914 T^{5} - 18929 T^{6} + 32538 T^{7} + 386682 T^{8} - 265302 T^{9} - 2004504 T^{10} + 8519142 T^{11} + 24137569 T^{12}$$)($$1 - 6 T - 24 T^{2} + 54 T^{3} + 1338 T^{4} - 1914 T^{5} - 18929 T^{6} - 32538 T^{7} + 386682 T^{8} + 265302 T^{9} - 2004504 T^{10} - 8519142 T^{11} + 24137569 T^{12}$$)($$1 + 9 T - 30 T^{2} - 423 T^{3} + 1029 T^{4} + 14184 T^{5} - 23521 T^{6} - 296649 T^{7} + 637560 T^{8} + 4620213 T^{9} - 12537675 T^{10} - 28264410 T^{11} + 250681641 T^{12} - 480494970 T^{13} - 3623388075 T^{14} + 22699106469 T^{15} + 53249648760 T^{16} - 421199159193 T^{17} - 567739760449 T^{18} + 5820243737832 T^{19} + 7178054406789 T^{20} - 50162671758231 T^{21} - 60479817013470 T^{22} + 308447066768697 T^{23} + 582622237229761 T^{24}$$)($$1 + 964 T^{4} + 237772 T^{8} - 70157828 T^{12} - 47638889354 T^{16} - 5859651952388 T^{20} + 1658639798261452 T^{24} + 561647836689489604 T^{28} + 48661191875666868481 T^{32}$$)($$( 1 + 460 T^{4} + 144678 T^{8} + 38419660 T^{12} + 6975757441 T^{16} )^{2}$$)($$1 + 84 T^{2} + 3900 T^{4} + 127966 T^{6} + 3288456 T^{8} + 70189416 T^{10} + 1282121619 T^{12} + 20284741224 T^{14} + 274655133576 T^{16} + 3088788154654 T^{18} + 27205454019900 T^{20} + 169343487637716 T^{22} + 582622237229761 T^{24}$$)
$19$ ($$1 - T + 19 T^{2}$$)($$1 + 2 T + 19 T^{2}$$)($$1 + 2 T + 19 T^{2}$$)($$1 - 8 T + 19 T^{2}$$)($$1 + 7 T + 19 T^{2}$$)($$1 - 8 T + 19 T^{2}$$)($$1 + 2 T + 19 T^{2}$$)($$1 + 2 T + 19 T^{2}$$)($$1 - T + 19 T^{2}$$)($$1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4}$$)($$1 + 25 T^{2} + 361 T^{4}$$)($$( 1 - T + 19 T^{2} )^{2}$$)($$( 1 - T + 19 T^{2} )^{2}$$)($$( 1 - T + 19 T^{2} )^{2}$$)($$( 1 - T + 19 T^{2} )^{2}$$)($$1 + 25 T^{2} + 361 T^{4}$$)($$1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4}$$)($$( 1 + T + 19 T^{2} )^{2}$$)($$( 1 + T + 19 T^{2} )^{2}$$)($$( 1 - 2 T + 19 T^{2} )^{2}$$)($$( 1 - 2 T + 19 T^{2} )^{2}$$)($$( 1 + 8 T + 19 T^{2} )^{2}$$)($$( 1 - 7 T + 19 T^{2} )^{2}$$)($$( 1 + T + 19 T^{2} )^{4}$$)($$( 1 + 25 T^{2} + 361 T^{4} )^{2}$$)($$( 1 + 25 T^{2} + 361 T^{4} )^{2}$$)($$( 1 + 8 T + 19 T^{2} )^{2}$$)($$( 1 - 4 T + 53 T^{2} - 148 T^{3} + 1007 T^{4} - 1444 T^{5} + 6859 T^{6} )^{2}$$)($$( 1 - 2 T + 49 T^{2} - 34 T^{3} + 1115 T^{4} - 646 T^{5} + 17689 T^{6} - 13718 T^{7} + 130321 T^{8} )^{2}$$)($$( 1 - 2 T + 36 T^{2} - 38 T^{3} + 361 T^{4} )^{4}$$)($$( 1 - 2 T + 49 T^{2} - 34 T^{3} + 1115 T^{4} - 646 T^{5} + 17689 T^{6} - 13718 T^{7} + 130321 T^{8} )^{2}$$)($$( 1 - 34 T^{2} + 361 T^{4} )^{2}$$)($$( 1 + 11 T^{2} + 361 T^{4} )^{2}$$)($$( 1 + 26 T^{2} + 361 T^{4} )^{2}$$)($$( 1 + 11 T^{2} + 361 T^{4} )^{2}$$)($$( 1 + 11 T^{2} + 361 T^{4} )^{2}$$)($$( 1 - 34 T^{2} + 361 T^{4} )^{2}$$)($$( 1 - 29 T^{2} + 361 T^{4} )^{4}$$)($$( 1 + 22 T^{2} + 123 T^{4} + 7942 T^{6} + 130321 T^{8} )^{2}$$)($$( 1 - 29 T^{2} + 361 T^{4} )^{4}$$)($$( 1 - 8 T + 19 T^{2} )^{4}$$)($$( 1 + 4 T + 53 T^{2} + 148 T^{3} + 1007 T^{4} + 1444 T^{5} + 6859 T^{6} )^{4}$$)($$( 1 + 2 T + 49 T^{2} + 34 T^{3} + 1115 T^{4} + 646 T^{5} + 17689 T^{6} + 13718 T^{7} + 130321 T^{8} )^{4}$$)($$1 + 12 T + 51 T^{2} + 188 T^{3} + 1314 T^{4} + 5076 T^{5} + 12699 T^{6} + 96444 T^{7} + 474354 T^{8} + 1289492 T^{9} + 6646371 T^{10} + 29713188 T^{11} + 47045881 T^{12}$$)($$1 + 12 T + 51 T^{2} + 188 T^{3} + 1314 T^{4} + 5076 T^{5} + 12699 T^{6} + 96444 T^{7} + 474354 T^{8} + 1289492 T^{9} + 6646371 T^{10} + 29713188 T^{11} + 47045881 T^{12}$$)($$1 + 3 T - 75 T^{2} - 242 T^{3} + 3012 T^{4} + 9714 T^{5} - 85589 T^{6} - 257166 T^{7} + 1946502 T^{8} + 4391737 T^{9} - 39399504 T^{10} - 33490578 T^{11} + 763159453 T^{12} - 636320982 T^{13} - 14223220944 T^{14} + 30122924083 T^{15} + 253670087142 T^{16} - 636768475434 T^{17} - 4026609908909 T^{18} + 8683070072646 T^{19} + 51154491879492 T^{20} - 78090422862518 T^{21} - 459829969335075 T^{22} + 349470776694657 T^{23} + 2213314919066161 T^{24}$$)($$( 1 - 92 T^{2} + 4132 T^{4} - 123032 T^{6} + 2693650 T^{8} - 44414552 T^{10} + 538486372 T^{12} - 4328221052 T^{14} + 16983563041 T^{16} )^{2}$$)($$( 1 - 56 T^{2} + 1410 T^{4} - 20216 T^{6} + 130321 T^{8} )^{4}$$)($$( 1 - 12 T + 51 T^{2} - 188 T^{3} + 1314 T^{4} - 5076 T^{5} + 12699 T^{6} - 96444 T^{7} + 474354 T^{8} - 1289492 T^{9} + 6646371 T^{10} - 29713188 T^{11} + 47045881 T^{12} )^{2}$$)
$23$ ($$1 - 6 T + 23 T^{2}$$)($$1 - 3 T + 23 T^{2}$$)($$1 - 3 T + 23 T^{2}$$)($$1 + 23 T^{2}$$)($$1 + 23 T^{2}$$)($$1 + 23 T^{2}$$)($$1 + 3 T + 23 T^{2}$$)($$1 + 3 T + 23 T^{2}$$)($$1 + 6 T + 23 T^{2}$$)($$1 + 6 T + 35 T^{2} + 138 T^{3} + 529 T^{4}$$)($$( 1 + 3 T + 23 T^{2} )^{2}$$)($$1 - 4 T^{2} + 529 T^{4}$$)($$1 - 4 T^{2} + 529 T^{4}$$)($$( 1 + 23 T^{2} )^{2}$$)($$( 1 + 23 T^{2} )^{2}$$)($$( 1 - 3 T + 23 T^{2} )^{2}$$)($$1 - 6 T + 35 T^{2} - 138 T^{3} + 529 T^{4}$$)($$1 - 10 T^{2} + 529 T^{4}$$)($$1 - 10 T^{2} + 529 T^{4}$$)($$1 - 37 T^{2} + 529 T^{4}$$)($$1 - 37 T^{2} + 529 T^{4}$$)($$( 1 - 23 T^{2} )^{2}$$)($$( 1 - 23 T^{2} )^{2}$$)($$( 1 - 23 T^{2} )^{4}$$)($$( 1 - 37 T^{2} + 529 T^{4} )^{2}$$)($$( 1 - 37 T^{2} + 529 T^{4} )^{2}$$)($$1 + 3 T - 14 T^{2} + 69 T^{3} + 529 T^{4}$$)($$1 + 3 T - 27 T^{2} + 66 T^{3} + 405 T^{4} - 2625 T^{5} - 9794 T^{6} - 60375 T^{7} + 214245 T^{8} + 803022 T^{9} - 7555707 T^{10} + 19309029 T^{11} + 148035889 T^{12}$$)($$1 + 15 T + 76 T^{2} + 183 T^{3} + 1258 T^{4} + 9882 T^{5} + 28951 T^{6} + 29994 T^{7} + 75241 T^{8} + 689862 T^{9} + 15315079 T^{10} + 120234294 T^{11} + 352039978 T^{12} + 1177850769 T^{13} + 11250727564 T^{14} + 51072381705 T^{15} + 78310985281 T^{16}$$)($$1 - 88 T^{2} + 4753 T^{4} - 170104 T^{6} + 4569664 T^{8} - 89985016 T^{10} + 1330084273 T^{12} - 13027158232 T^{14} + 78310985281 T^{16}$$)($$1 - 15 T + 76 T^{2} - 183 T^{3} + 1258 T^{4} - 9882 T^{5} + 28951 T^{6} - 29994 T^{7} + 75241 T^{8} - 689862 T^{9} + 15315079 T^{10} - 120234294 T^{11} + 352039978 T^{12} - 1177850769 T^{13} + 11250727564 T^{14} - 51072381705 T^{15} + 78310985281 T^{16}$$)($$1 - 217 T^{4} + 279841 T^{8}$$)($$1 - 1054 T^{4} + 279841 T^{8}$$)($$( 1 + 529 T^{4} )^{2}$$)($$( 1 + 529 T^{4} )^{2}$$)($$1 - 1054 T^{4} + 279841 T^{8}$$)($$1 - 217 T^{4} + 279841 T^{8}$$)($$1 + 1424 T^{4} + 1024290 T^{8} + 398493584 T^{12} + 78310985281 T^{16}$$)($$1 - 98 T^{4} - 270237 T^{8} - 27424418 T^{12} + 78310985281 T^{16}$$)($$1 + 14 T^{4} - 420045 T^{8} + 3917774 T^{12} + 78310985281 T^{16}$$)($$1 + 37 T^{2} + 840 T^{4} + 19573 T^{6} + 279841 T^{8}$$)($$1 + 63 T^{2} + 1143 T^{4} + 30064 T^{6} + 1830141 T^{8} + 38353041 T^{10} + 434719014 T^{12} + 20288758689 T^{14} + 512148487581 T^{16} + 4450550966896 T^{18} + 89509456176183 T^{20} + 2609870206459887 T^{22} + 21914624432020321 T^{24}$$)($$1 + 73 T^{2} + 2802 T^{4} + 80831 T^{6} + 1616966 T^{8} + 14420082 T^{10} - 392881007 T^{12} - 25025527652 T^{14} - 736058803599 T^{16} - 13238504127908 T^{18} - 109944213879887 T^{20} + 2134689658322898 T^{22} + 126626200625877446 T^{24} + 3348546327910462319 T^{26} + 61404777658520939442 T^{28} +$$$$84\!\cdots\!57$$$$T^{30} +$$$$61\!\cdots\!61$$$$T^{32}$$)($$1 + 18 T + 198 T^{2} + 1656 T^{3} + 11520 T^{4} + 67716 T^{5} + 345961 T^{6} + 1557468 T^{7} + 6094080 T^{8} + 20148552 T^{9} + 55408518 T^{10} + 115854174 T^{11} + 148035889 T^{12}$$)($$1 - 18 T + 198 T^{2} - 1656 T^{3} + 11520 T^{4} - 67716 T^{5} + 345961 T^{6} - 1557468 T^{7} + 6094080 T^{8} - 20148552 T^{9} + 55408518 T^{10} - 115854174 T^{11} + 148035889 T^{12}$$)($$1 - 12 T + 48 T^{2} - 153 T^{3} - 336 T^{4} + 12228 T^{5} - 51922 T^{6} + 116820 T^{7} - 165330 T^{8} - 4324509 T^{9} + 14509764 T^{10} + 2453454 T^{11} + 107316369 T^{12} + 56429442 T^{13} + 7675665156 T^{14} - 52616301003 T^{15} - 46266112530 T^{16} + 751893589260 T^{17} - 7686319428658 T^{18} + 41634205565916 T^{19} - 26312491054416 T^{20} - 275576357203839 T^{21} + 1988472538255152 T^{22} - 11433717094967124 T^{23} + 21914624432020321 T^{24}$$)($$1 - 18 T + 162 T^{2} - 972 T^{3} + 4138 T^{4} - 11184 T^{5} + 3348 T^{6} + 119100 T^{7} - 338219 T^{8} - 2163498 T^{9} + 26656146 T^{10} - 182453766 T^{11} + 892508410 T^{12} - 1883089950 T^{13} - 11227491072 T^{14} + 141260851668 T^{15} - 837597200144 T^{16} + 3248999588364 T^{17} - 5939342777088 T^{18} - 22911555421650 T^{19} + 249760445962810 T^{20} - 1174335019617738 T^{21} + 3946066270423794 T^{22} - 7366333044933606 T^{23} - 26486263130754539 T^{24} + 214517281980243300 T^{25} + 138695959543296852 T^{26} - 10656224332509359568 T^{27} + 90682715899700088298 T^{28} -$$$$48\!\cdots\!76$$$$T^{29} +$$$$18\!\cdots\!58$$$$T^{30} -$$$$47\!\cdots\!26$$$$T^{31} +$$$$61\!\cdots\!61$$$$T^{32}$$)($$1 - 58 T^{4} + 491185 T^{8} + 60755174 T^{12} + 158716957636 T^{16} + 17001788647334 T^{20} + 38465181305247985 T^{24} - 1271048217057178618 T^{28} +$$$$61\!\cdots\!61$$$$T^{32}$$)($$1 - 72 T^{2} + 2628 T^{4} - 73730 T^{6} + 1554876 T^{8} - 25875612 T^{10} + 500700963 T^{12} - 13688198748 T^{14} + 435118054716 T^{16} - 10914686095970 T^{18} + 205801269318468 T^{20} - 2982708807382728 T^{22} + 21914624432020321 T^{24}$$)
$29$ ($$1 + 2 T + 29 T^{2}$$)($$1 + 10 T + 29 T^{2}$$)($$1 - 10 T + 29 T^{2}$$)($$1 + 29 T^{2}$$)($$1 + 29 T^{2}$$)($$1 + 29 T^{2}$$)($$1 + 10 T + 29 T^{2}$$)($$1 - 10 T + 29 T^{2}$$)($$1 - 2 T + 29 T^{2}$$)($$( 1 + 29 T^{2} )^{2}$$)($$1 + 10 T + 70 T^{2} + 290 T^{3} + 841 T^{4}$$)($$1 + 40 T^{2} + 841 T^{4}$$)($$1 + 40 T^{2} + 841 T^{4}$$)($$1 + 30 T^{2} + 841 T^{4}$$)($$1 + 30 T^{2} + 841 T^{4}$$)($$1 - 10 T + 70 T^{2} - 290 T^{3} + 841 T^{4}$$)($$( 1 + 29 T^{2} )^{2}$$)($$( 1 + 2 T + 29 T^{2} )^{2}$$)($$( 1 - 2 T + 29 T^{2} )^{2}$$)($$( 1 - 10 T + 29 T^{2} )^{2}$$)($$( 1 + 10 T + 29 T^{2} )^{2}$$)($$( 1 + 29 T^{2} )^{2}$$)($$( 1 + 29 T^{2} )^{2}$$)($$( 1 + 30 T^{2} + 841 T^{4} )^{2}$$)($$( 1 - 10 T + 70 T^{2} - 290 T^{3} + 841 T^{4} )^{2}$$)($$( 1 + 10 T + 70 T^{2} + 290 T^{3} + 841 T^{4} )^{2}$$)($$1 + T - 28 T^{2} + 29 T^{3} + 841 T^{4}$$)($$1 + 7 T - 9 T^{2} - 304 T^{3} - 803 T^{4} + 2929 T^{5} + 36038 T^{6} + 84941 T^{7} - 675323 T^{8} - 7414256 T^{9} - 6365529 T^{10} + 143578043 T^{11} + 594823321 T^{12}$$)($$1 - T - 75 T^{2} - 186 T^{3} + 3234 T^{4} + 10969 T^{5} - 64920 T^{6} - 187910 T^{7} + 1140565 T^{8} - 5449390 T^{9} - 54597720 T^{10} + 267522941 T^{11} + 2287346754 T^{12} - 3815073714 T^{13} - 44611749075 T^{14} - 17249876309 T^{15} + 500246412961 T^{16}$$)($$( 1 - 6 T - 19 T^{2} + 18 T^{3} + 1140 T^{4} + 522 T^{5} - 15979 T^{6} - 146334 T^{7} + 707281 T^{8} )^{2}$$)($$1 - T - 75 T^{2} - 186 T^{3} + 3234 T^{4} + 10969 T^{5} - 64920 T^{6} - 187910 T^{7} + 1140565 T^{8} - 5449390 T^{9} - 54597720 T^{10} + 267522941 T^{11} + 2287346754 T^{12} - 3815073714 T^{13} - 44611749075 T^{14} - 17249876309 T^{15} + 500246412961 T^{16}$$)($$( 1 + 6 T + 29 T^{2} )^{4}$$)($$( 1 - 6 T + 29 T^{2} )^{4}$$)($$( 1 + 29 T^{2} )^{4}$$)($$( 1 + 29 T^{2} )^{4}$$)($$( 1 + 6 T + 29 T^{2} )^{4}$$)($$( 1 - 6 T + 29 T^{2} )^{4}$$)($$( 1 + 20 T^{2} + 1728 T^{4} + 16820 T^{6} + 707281 T^{8} )^{2}$$)($$( 1 + 29 T^{2} )^{8}$$)($$( 1 + 50 T^{2} + 2118 T^{4} + 42050 T^{6} + 707281 T^{8} )^{2}$$)($$( 1 - T - 28 T^{2} - 29 T^{3} + 841 T^{4} )^{2}$$)($$( 1 - 7 T - 9 T^{2} + 304 T^{3} - 803 T^{4} - 2929 T^{5} + 36038 T^{6} - 84941 T^{7} - 675323 T^{8} + 7414256 T^{9} - 6365529 T^{10} - 143578043 T^{11} + 594823321 T^{12} )^{2}$$)($$( 1 + T - 75 T^{2} + 186 T^{3} + 3234 T^{4} - 10969 T^{5} - 64920 T^{6} + 187910 T^{7} + 1140565 T^{8} + 5449390 T^{9} - 54597720 T^{10} - 267522941 T^{11} + 2287346754 T^{12} + 3815073714 T^{13} - 44611749075 T^{14} + 17249876309 T^{15} + 500246412961 T^{16} )^{2}$$)($$1 + 21 T + 207 T^{2} + 1125 T^{3} + 1890 T^{4} - 22776 T^{5} - 210023 T^{6} - 660504 T^{7} + 1589490 T^{8} + 27437625 T^{9} + 146407167 T^{10} + 430734129 T^{11} + 594823321 T^{12}$$)($$1 + 21 T + 207 T^{2} + 1125 T^{3} + 1890 T^{4} - 22776 T^{5} - 210023 T^{6} - 660504 T^{7} + 1589490 T^{8} + 27437625 T^{9} + 146407167 T^{10} + 430734129 T^{11} + 594823321 T^{12}$$)($$1 + 6 T + 21 T^{2} + 252 T^{3} + 249 T^{4} - 984 T^{5} + 18431 T^{6} + 29592 T^{7} + 680634 T^{8} + 5882274 T^{9} + 10161684 T^{10} + 17557326 T^{11} + 254066229 T^{12} + 509162454 T^{13} + 8545976244 T^{14} + 143462780586 T^{15} + 481399496154 T^{16} + 606965921208 T^{17} + 10963188629351 T^{18} - 16973878288056 T^{19} + 124561356827289 T^{20} + 3655800785918988 T^{21} + 8834851899304221 T^{22} + 73203058594234974 T^{23} + 353814783205469041 T^{24}$$)($$1 - 148 T^{2} + 10806 T^{4} - 562376 T^{6} + 24743345 T^{8} - 973959144 T^{10} + 34914297094 T^{12} - 1155748123996 T^{14} + 35134519733316 T^{16} - 971984172280636 T^{18} + 24694218962941414 T^{20} - 579333612552397224 T^{22} + 12377769580906494545 T^{24} -$$$$23\!\cdots\!76$$$$T^{26} +$$$$38\!\cdots\!46$$$$T^{28} -$$$$44\!\cdots\!88$$$$T^{30} +$$$$25\!\cdots\!21$$$$T^{32}$$)($$( 1 - 31 T^{2} + 120 T^{4} - 26071 T^{6} + 707281 T^{8} )^{4}$$)($$( 1 - 21 T + 207 T^{2} - 1125 T^{3} + 1890 T^{4} + 22776 T^{5} - 210023 T^{6} + 660504 T^{7} + 1589490 T^{8} - 27437625 T^{9} + 146407167 T^{10} - 430734129 T^{11} + 594823321 T^{12} )^{2}$$)
$31$ ($$1 + 31 T^{2}$$)($$1 - 6 T + 31 T^{2}$$)($$1 - 6 T + 31 T^{2}$$)($$1 - 11 T + 31 T^{2}$$)($$1 + 4 T + 31 T^{2}$$)($$1 - 11 T + 31 T^{2}$$)($$1 - 6 T + 31 T^{2}$$)($$1 - 6 T + 31 T^{2}$$)($$1 + 31 T^{2}$$)($$1 + 8 T + 33 T^{2} + 248 T^{3} + 961 T^{4}$$)($$1 + 4 T + 53 T^{2} + 124 T^{3} + 961 T^{4}$$)($$( 1 - 2 T + 31 T^{2} )^{2}$$)($$( 1 - 2 T + 31 T^{2} )^{2}$$)($$( 1 + 3 T + 31 T^{2} )^{2}$$)($$( 1 + 3 T + 31 T^{2} )^{2}$$)($$1 + 4 T + 53 T^{2} + 124 T^{3} + 961 T^{4}$$)($$1 + 8 T + 33 T^{2} + 248 T^{3} + 961 T^{4}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 - 6 T + 31 T^{2} )^{2}$$)($$( 1 - 6 T + 31 T^{2} )^{2}$$)($$( 1 - 11 T + 31 T^{2} )^{2}$$)($$( 1 + 4 T + 31 T^{2} )^{2}$$)($$( 1 + 3 T + 31 T^{2} )^{4}$$)($$( 1 + 4 T + 53 T^{2} + 124 T^{3} + 961 T^{4} )^{2}$$)($$( 1 + 4 T + 53 T^{2} + 124 T^{3} + 961 T^{4} )^{2}$$)($$1 - 31 T^{2} + 961 T^{4}$$)($$1 + 8 T + 31 T^{2} + 208 T^{3} - 158 T^{4} - 7756 T^{5} - 34897 T^{6} - 240436 T^{7} - 151838 T^{8} + 6196528 T^{9} + 28629151 T^{10} + 229033208 T^{11} + 887503681 T^{12}$$)($$1 - 4 T - 66 T^{2} + 362 T^{3} + 1939 T^{4} - 11745 T^{5} - 45361 T^{6} + 144883 T^{7} + 1472277 T^{8} + 4491373 T^{9} - 43591921 T^{10} - 349895295 T^{11} + 1790707219 T^{12} + 10363752662 T^{13} - 58575242946 T^{14} - 110050456444 T^{15} + 852891037441 T^{16}$$)($$( 1 - 2 T - 56 T^{2} + 4 T^{3} + 2515 T^{4} + 124 T^{5} - 53816 T^{6} - 59582 T^{7} + 923521 T^{8} )^{2}$$)($$1 - 4 T - 66 T^{2} + 362 T^{3} + 1939 T^{4} - 11745 T^{5} - 45361 T^{6} + 144883 T^{7} + 1472277 T^{8} + 4491373 T^{9} - 43591921 T^{10} - 349895295 T^{11} + 1790707219 T^{12} + 10363752662 T^{13} - 58575242946 T^{14} - 110050456444 T^{15} + 852891037441 T^{16}$$)($$( 1 - 4 T + 31 T^{2} )^{4}$$)($$( 1 + 5 T + 31 T^{2} )^{4}$$)($$( 1 + 11 T + 31 T^{2} )^{4}$$)($$( 1 - 4 T + 31 T^{2} )^{4}$$)($$( 1 + 5 T + 31 T^{2} )^{4}$$)($$( 1 - 4 T + 31 T^{2} )^{4}$$)($$( 1 - 4 T + 12 T^{2} - 124 T^{3} + 961 T^{4} )^{4}$$)($$( 1 - 8 T + 33 T^{2} - 248 T^{3} + 961 T^{4} )^{4}$$)($$( 1 + T + 31 T^{2} )^{8}$$)($$( 1 - 31 T^{2} + 961 T^{4} )^{2}$$)($$( 1 + 8 T + 31 T^{2} + 208 T^{3} - 158 T^{4} - 7756 T^{5} - 34897 T^{6} - 240436 T^{7} - 151838 T^{8} + 6196528 T^{9} + 28629151 T^{10} + 229033208 T^{11} + 887503681 T^{12} )^{2}$$)($$( 1 - 4 T - 66 T^{2} + 362 T^{3} + 1939 T^{4} - 11745 T^{5} - 45361 T^{6} + 144883 T^{7} + 1472277 T^{8} + 4491373 T^{9} - 43591921 T^{10} - 349895295 T^{11} + 1790707219 T^{12} + 10363752662 T^{13} - 58575242946 T^{14} - 110050456444 T^{15} + 852891037441 T^{16} )^{2}$$)($$1 + 3 T + 24 T^{2} + 80 T^{3} + 423 T^{4} - 4653 T^{5} - 5787 T^{6} - 144243 T^{7} + 406503 T^{8} + 2383280 T^{9} + 22164504 T^{10} + 85887453 T^{11} + 887503681 T^{12}$$)($$1 + 3 T + 24 T^{2} + 80 T^{3} + 423 T^{4} - 4653 T^{5} - 5787 T^{6} - 144243 T^{7} + 406503 T^{8} + 2383280 T^{9} + 22164504 T^{10} + 85887453 T^{11} + 887503681 T^{12}$$)($$1 - 3 T + 84 T^{2} - 434 T^{3} + 5601 T^{4} - 30963 T^{5} + 266473 T^{6} - 1627992 T^{7} + 11453211 T^{8} - 69240287 T^{9} + 408317577 T^{10} - 2527882269 T^{11} + 13547586181 T^{12} - 78364350339 T^{13} + 392393191497 T^{14} - 2062737390017 T^{15} + 10577280875931 T^{16} - 46608028794792 T^{17} + 236495768387113 T^{18} - 851873070718893 T^{19} + 4777042700707041 T^{20} - 11474796017731214 T^{21} + 68848776106387284 T^{22} - 76225430689214493 T^{23} + 787662783788549761 T^{24}$$)($$( 1 + 2 T - 78 T^{2} + 76 T^{3} + 3500 T^{4} - 7572 T^{5} - 100340 T^{6} + 131474 T^{7} + 2627523 T^{8} + 4075694 T^{9} - 96426740 T^{10} - 225577452 T^{11} + 3232323500 T^{12} + 2175815476 T^{13} - 69225287118 T^{14} + 55025228222 T^{15} + 852891037441 T^{16} )^{2}$$)($$( 1 - 4 T - 44 T^{2} + 8 T^{3} + 2143 T^{4} + 248 T^{5} - 42284 T^{6} - 119164 T^{7} + 923521 T^{8} )^{4}$$)($$( 1 + 3 T + 24 T^{2} + 80 T^{3} + 423 T^{4} - 4653 T^{5} - 5787 T^{6} - 144243 T^{7} + 406503 T^{8} + 2383280 T^{9} + 22164504 T^{10} + 85887453 T^{11} + 887503681 T^{12} )^{2}$$)
$37$ ($$1 + 5 T + 37 T^{2}$$)($$1 + 5 T + 37 T^{2}$$)($$1 - 5 T + 37 T^{2}$$)($$1 + T + 37 T^{2}$$)($$1 + 11 T + 37 T^{2}$$)($$1 - T + 37 T^{2}$$)($$1 - 5 T + 37 T^{2}$$)($$1 + 5 T + 37 T^{2}$$)($$1 + 5 T + 37 T^{2}$$)($$( 1 + 37 T^{2} )^{2}$$)($$( 1 + 2 T + 37 T^{2} )^{2}$$)($$( 1 + 9 T + 37 T^{2} )^{2}$$)($$( 1 - 9 T + 37 T^{2} )^{2}$$)($$( 1 - T + 37 T^{2} )^{2}$$)($$( 1 + T + 37 T^{2} )^{2}$$)($$( 1 + 2 T + 37 T^{2} )^{2}$$)($$( 1 + 37 T^{2} )^{2}$$)($$1 - 49 T^{2} + 1369 T^{4}$$)($$1 - 49 T^{2} + 1369 T^{4}$$)($$1 - 49 T^{2} + 1369 T^{4}$$)($$1 - 49 T^{2} + 1369 T^{4}$$)($$1 - 73 T^{2} + 1369 T^{4}$$)($$1 + 47 T^{2} + 1369 T^{4}$$)($$( 1 - 73 T^{2} + 1369 T^{4} )^{2}$$)($$( 1 - 12 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2}$$)($$( 1 - 12 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2}$$)($$( 1 - 4 T + 37 T^{2} )^{2}$$)($$( 1 + 6 T + 99 T^{2} + 440 T^{3} + 3663 T^{4} + 8214 T^{5} + 50653 T^{6} )^{2}$$)($$( 1 - T + 49 T^{2} + 392 T^{3} + 241 T^{4} + 14504 T^{5} + 67081 T^{6} - 50653 T^{7} + 1874161 T^{8} )^{2}$$)($$( 1 + 56 T^{2} + 1369 T^{4} )^{4}$$)($$( 1 + T + 49 T^{2} - 392 T^{3} + 241 T^{4} - 14504 T^{5} + 67081 T^{6} + 50653 T^{7} + 1874161 T^{8} )^{2}$$)($$1 - 2737 T^{4} + 1874161 T^{8}$$)($$1 + 2303 T^{4} + 1874161 T^{8}$$)($$1 + 2591 T^{4} + 1874161 T^{8}$$)($$1 - 529 T^{4} + 1874161 T^{8}$$)($$1 + 2303 T^{4} + 1874161 T^{8}$$)($$1 - 2737 T^{4} + 1874161 T^{8}$$)($$( 1 - 8 T + 32 T^{2} - 144 T^{3} + 287 T^{4} - 5328 T^{5} + 43808 T^{6} - 405224 T^{7} + 1874161 T^{8} )^{2}$$)($$( 1 + 1369 T^{4} )^{4}$$)($$( 1 - 12 T + 37 T^{2} )^{4}( 1 + 2 T + 37 T^{2} )^{4}$$)($$( 1 - 58 T^{2} + 1369 T^{4} )^{2}$$)($$( 1 - 162 T^{2} + 11847 T^{4} - 534412 T^{6} + 16218543 T^{8} - 303614082 T^{10} + 2565726409 T^{12} )^{2}$$)($$( 1 - 97 T^{2} + 3667 T^{4} - 33124 T^{6} - 1092101 T^{8} - 45346756 T^{10} + 6872548387 T^{12} - 248875461673 T^{14} + 3512479453921 T^{16} )^{2}$$)($$1 + 6 T - 48 T^{2} - 206 T^{3} + 1818 T^{4} + 738 T^{5} - 83025 T^{6} + 27306 T^{7} + 2488842 T^{8} - 10434518 T^{9} - 89959728 T^{10} + 416063742 T^{11} + 2565726409 T^{12}$$)($$1 - 6 T - 48 T^{2} + 206 T^{3} + 1818 T^{4} - 738 T^{5} - 83025 T^{6} - 27306 T^{7} + 2488842 T^{8} + 10434518 T^{9} - 89959728 T^{10} - 416063742 T^{11} + 2565726409 T^{12}$$)($$1 - 3 T - 156 T^{2} + 107 T^{3} + 13731 T^{4} + 9132 T^{5} - 864755 T^{6} - 641043 T^{7} + 43249536 T^{8} + 18536771 T^{9} - 1953626739 T^{10} - 269355786 T^{11} + 78884071369 T^{12} - 9966164082 T^{13} - 2674515005691 T^{14} + 938943061463 T^{15} + 81056593639296 T^{16} - 44452458227151 T^{17} - 2218724740814795 T^{18} + 866917901978556 T^{19} + 48229855381789251 T^{20} + 13905906158073239 T^{21} - 750139162097184444 T^{22} - 533752865338381239 T^{23} + 6582952005840035281 T^{24}$$)($$( 1 + 2 T + 2 T^{2} - 50 T^{3} + 680 T^{4} + 6430 T^{5} + 12750 T^{6} + 67506 T^{7} - 1916078 T^{8} + 2497722 T^{9} + 17454750 T^{10} + 325698790 T^{11} + 1274429480 T^{12} - 3467197850 T^{13} + 5131452818 T^{14} + 189863754266 T^{15} + 3512479453921 T^{16} )^{2}$$)($$( 1 - 4244 T^{4} + 7905606 T^{8} - 7953939284 T^{12} + 3512479453921 T^{16} )^{2}$$)($$1 + 132 T^{2} + 8412 T^{4} + 391870 T^{6} + 16229592 T^{8} + 584807544 T^{10} + 20378076867 T^{12} + 800601527736 T^{14} + 30416868372312 T^{16} + 1005431207894830 T^{18} + 29546977166383452 T^{20} + 634733137159156068 T^{22} + 6582952005840035281 T^{24}$$)
$41$ ($$1 - 10 T + 41 T^{2}$$)($$1 + 10 T + 41 T^{2}$$)($$1 - 10 T + 41 T^{2}$$)($$1 + 41 T^{2}$$)($$1 + 41 T^{2}$$)($$1 + 41 T^{2}$$)($$1 + 10 T + 41 T^{2}$$)($$1 - 10 T + 41 T^{2}$$)($$1 + 10 T + 41 T^{2}$$)($$( 1 + 41 T^{2} )^{2}$$)($$1 - 2 T + 70 T^{2} - 82 T^{3} + 1681 T^{4}$$)($$1 + 64 T^{2} + 1681 T^{4}$$)($$1 + 64 T^{2} + 1681 T^{4}$$)($$1 + 54 T^{2} + 1681 T^{4}$$)($$1 + 54 T^{2} + 1681 T^{4}$$)($$1 + 2 T + 70 T^{2} + 82 T^{3} + 1681 T^{4}$$)($$( 1 + 41 T^{2} )^{2}$$)($$( 1 + 10 T + 41 T^{2} )^{2}$$)($$( 1 - 10 T + 41 T^{2} )^{2}$$)($$( 1 + 10 T + 41 T^{2} )^{2}$$)($$( 1 - 10 T + 41 T^{2} )^{2}$$)($$( 1 + 41 T^{2} )^{2}$$)($$( 1 + 41 T^{2} )^{2}$$)($$( 1 + 54 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 2 T + 70 T^{2} - 82 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 + 2 T + 70 T^{2} + 82 T^{3} + 1681 T^{4} )^{2}$$)($$1 - 5 T - 16 T^{2} - 205 T^{3} + 1681 T^{4}$$)($$1 + 13 T + 27 T^{2} - 292 T^{3} + 445 T^{4} + 22279 T^{5} + 169790 T^{6} + 913439 T^{7} + 748045 T^{8} - 20124932 T^{9} + 76295547 T^{10} + 1506130613 T^{11} + 4750104241 T^{12}$$)($$1 + 5 T - 114 T^{2} - 213 T^{3} + 9222 T^{4} + 3430 T^{5} - 507867 T^{6} - 107426 T^{7} + 20984173 T^{8} - 4404466 T^{9} - 853724427 T^{10} + 236399030 T^{11} + 26059167942 T^{12} - 24677370813 T^{13} - 541511883474 T^{14} + 973771369405 T^{15} + 7984925229121 T^{16}$$)($$( 1 - 12 T + 29 T^{2} - 396 T^{3} + 5640 T^{4} - 16236 T^{5} + 48749 T^{6} - 827052 T^{7} + 2825761 T^{8} )^{2}$$)($$1 + 5 T - 114 T^{2} - 213 T^{3} + 9222 T^{4} + 3430 T^{5} - 507867 T^{6} - 107426 T^{7} + 20984173 T^{8} - 4404466 T^{9} - 853724427 T^{10} + 236399030 T^{11} + 26059167942 T^{12} - 24677370813 T^{13} - 541511883474 T^{14} + 973771369405 T^{15} + 7984925229121 T^{16}$$)($$( 1 + 62 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 46 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 41 T^{2} )^{4}$$)($$( 1 - 41 T^{2} )^{4}$$)($$( 1 - 46 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 + 62 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 28 T^{2} - 816 T^{4} - 47068 T^{6} + 2825761 T^{8} )^{2}$$)($$( 1 - 41 T^{2} )^{8}$$)($$( 1 - 130 T^{2} + 7398 T^{4} - 218530 T^{6} + 2825761 T^{8} )^{2}$$)($$( 1 - 5 T - 16 T^{2} - 205 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 + 13 T + 27 T^{2} - 292 T^{3} + 445 T^{4} + 22279 T^{5} + 169790 T^{6} + 913439 T^{7} + 748045 T^{8} - 20124932 T^{9} + 76295547 T^{10} + 1506130613 T^{11} + 4750104241 T^{12} )^{2}$$)($$( 1 + 5 T - 114 T^{2} - 213 T^{3} + 9222 T^{4} + 3430 T^{5} - 507867 T^{6} - 107426 T^{7} + 20984173 T^{8} - 4404466 T^{9} - 853724427 T^{10} + 236399030 T^{11} + 26059167942 T^{12} - 24677370813 T^{13} - 541511883474 T^{14} + 973771369405 T^{15} + 7984925229121 T^{16} )^{2}$$)($$1 + 18 T + 171 T^{2} + 1143 T^{3} + 9009 T^{4} + 79119 T^{5} + 597574 T^{6} + 3243879 T^{7} + 15144129 T^{8} + 78776703 T^{9} + 483205131 T^{10} + 2085411618 T^{11} + 4750104241 T^{12}$$)($$1 + 18 T + 171 T^{2} + 1143 T^{3} + 9009 T^{4} + 79119 T^{5} + 597574 T^{6} + 3243879 T^{7} + 15144129 T^{8} + 78776703 T^{9} + 483205131 T^{10} + 2085411618 T^{11} + 4750104241 T^{12}$$)($$1 - 15 T + 93 T^{2} - 90 T^{3} - 2460 T^{4} + 12513 T^{5} + 27971 T^{6} - 441396 T^{7} + 3206862 T^{8} - 12736494 T^{9} - 41813613 T^{10} + 1731506832 T^{11} - 16389887967 T^{12} + 70991780112 T^{13} - 70288683453 T^{14} - 877811902974 T^{15} + 9061825571982 T^{16} - 51138463696596 T^{17} + 132865165725011 T^{18} + 2436960229072953 T^{19} - 19642916063637660 T^{20} - 29464374095456490 T^{21} + 1248307315844173293 T^{22} - 8254935475743726615 T^{23} + 22563490300366186081 T^{24}$$)($$( 1 - 12 T + 190 T^{2} - 1704 T^{3} + 16861 T^{4} - 130290 T^{5} + 1067482 T^{6} - 7225794 T^{7} + 51027208 T^{8} - 296257554 T^{9} + 1794437242 T^{10} - 8979717090 T^{11} + 47645156221 T^{12} - 197418966504 T^{13} + 902519805790 T^{14} - 2337051286572 T^{15} + 7984925229121 T^{16} )^{2}$$)($$( 1 - 18 T + 199 T^{2} - 1638 T^{3} + 11028 T^{4} - 67158 T^{5} + 334519 T^{6} - 1240578 T^{7} + 2825761 T^{8} )^{4}$$)($$( 1 + 18 T + 171 T^{2} + 1143 T^{3} + 9009 T^{4} + 79119 T^{5} + 597574 T^{6} + 3243879 T^{7} + 15144129 T^{8} + 78776703 T^{9} + 483205131 T^{10} + 2085411618 T^{11} + 4750104241 T^{12} )^{2}$$)
$43$ ($$1 + 4 T + 43 T^{2}$$)($$1 + 10 T + 43 T^{2}$$)($$1 - 10 T + 43 T^{2}$$)($$1 + 13 T + 43 T^{2}$$)($$1 + 8 T + 43 T^{2}$$)($$1 - 13 T + 43 T^{2}$$)($$1 - 10 T + 43 T^{2}$$)($$1 + 10 T + 43 T^{2}$$)($$1 + 4 T + 43 T^{2}$$)($$( 1 + 43 T^{2} )^{2}$$)($$1 - 6 T + 82 T^{2} - 258 T^{3} + 1849 T^{4}$$)($$( 1 + 6 T + 43 T^{2} )^{2}$$)($$( 1 - 6 T + 43 T^{2} )^{2}$$)($$( 1 + T + 43 T^{2} )^{2}$$)($$( 1 - T + 43 T^{2} )^{2}$$)($$1 - 6 T + 82 T^{2} - 258 T^{3} + 1849 T^{4}$$)($$( 1 + 43 T^{2} )^{2}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 + 14 T^{2} + 1849 T^{4}$$)($$1 + 14 T^{2} + 1849 T^{4}$$)($$1 + 83 T^{2} + 1849 T^{4}$$)($$1 - 22 T^{2} + 1849 T^{4}$$)($$( 1 - 85 T^{2} + 1849 T^{4} )^{2}$$)($$1 - 128 T^{2} + 7326 T^{4} - 236672 T^{6} + 3418801 T^{8}$$)($$1 - 128 T^{2} + 7326 T^{4} - 236672 T^{6} + 3418801 T^{8}$$)($$( 1 - 5 T + 43 T^{2} )( 1 + 13 T + 43 T^{2} )$$)($$1 - 10 T - 25 T^{2} + 462 T^{3} + 1690 T^{4} - 17990 T^{5} + 34975 T^{6} - 773570 T^{7} + 3124810 T^{8} + 36732234 T^{9} - 85470025 T^{10} - 1470084430 T^{11} + 6321363049 T^{12}$$)($$1 + 10 T - 24 T^{2} - 168 T^{3} + 2043 T^{4} - 8292 T^{5} - 128884 T^{6} + 10646 T^{7} + 2342736 T^{8} + 457778 T^{9} - 238306516 T^{10} - 659272044 T^{11} + 6984610443 T^{12} - 24697418424 T^{13} - 151712713176 T^{14} + 2718186111070 T^{15} + 11688200277601 T^{16}$$)($$1 - 88 T^{2} + 3838 T^{4} - 18304 T^{6} - 2480621 T^{8} - 33844096 T^{10} + 13121358238 T^{12} - 556279948312 T^{14} + 11688200277601 T^{16}$$)($$1 - 10 T - 24 T^{2} + 168 T^{3} + 2043 T^{4} + 8292 T^{5} - 128884 T^{6} - 10646 T^{7} + 2342736 T^{8} - 457778 T^{9} - 238306516 T^{10} + 659272044 T^{11} + 6984610443 T^{12} + 24697418424 T^{13} - 151712713176 T^{14} - 2718186111070 T^{15} + 11688200277601 T^{16}$$)($$1 + 1778 T^{4} + 3418801 T^{8}$$)($$1 - 3577 T^{4} + 3418801 T^{8}$$)($$1 + 3191 T^{4} + 3418801 T^{8}$$)($$1 - 3214 T^{4} + 3418801 T^{8}$$)($$1 - 3577 T^{4} + 3418801 T^{8}$$)($$1 + 1778 T^{4} + 3418801 T^{8}$$)($$( 1 + 4 T + 8 T^{2} + 132 T^{3} + 2078 T^{4} + 5676 T^{5} + 14792 T^{6} + 318028 T^{7} + 3418801 T^{8} )^{2}$$)($$( 1 + 1849 T^{4} )^{4}$$)($$( 1 + 22 T + 242 T^{2} + 2046 T^{3} + 14798 T^{4} + 87978 T^{5} + 447458 T^{6} + 1749154 T^{7} + 3418801 T^{8} )^{2}$$)($$( 1 - 61 T^{2} + 1849 T^{4} )( 1 + 83 T^{2} + 1849 T^{4} )$$)($$1 + 150 T^{2} + 13245 T^{4} + 587794 T^{6} + 8508330 T^{8} - 916818210 T^{10} - 62473985643 T^{12} - 1695196870290 T^{14} + 29088287112330 T^{16} + 3715659272023906 T^{18} + 154810212676825245 T^{20} + 3241722346992637350 T^{22} + 39959630797262576401 T^{24}$$)($$1 + 148 T^{2} + 8022 T^{4} + 218216 T^{6} + 12046721 T^{8} + 1190020152 T^{10} + 65107245958 T^{12} + 1936378110508 T^{14} + 52508765640996 T^{16} + 3580363126329292 T^{18} + 222588717588456358 T^{20} + 7522549416418163448 T^{22} +$$$$14\!\cdots\!21$$$$T^{24} +$$$$47\!\cdots\!84$$$$T^{26} +$$$$32\!\cdots\!22$$$$T^{28} +$$$$10\!\cdots\!52$$$$T^{30} +$$$$13\!\cdots\!01$$$$T^{32}$$)($$1 - 6 T + 156 T^{2} - 905 T^{3} + 13329 T^{4} - 66195 T^{5} + 704013 T^{6} - 2846385 T^{7} + 24645321 T^{8} - 71953835 T^{9} + 533332956 T^{10} - 882050658 T^{11} + 6321363049 T^{12}$$)($$1 + 6 T + 156 T^{2} + 905 T^{3} + 13329 T^{4} + 66195 T^{5} + 704013 T^{6} + 2846385 T^{7} + 24645321 T^{8} + 71953835 T^{9} + 533332956 T^{10} + 882050658 T^{11} + 6321363049 T^{12}$$)($$1 + 3 T - 60 T^{2} - 16 T^{3} + 606 T^{4} - 5874 T^{5} + 128269 T^{6} + 73818 T^{7} - 5307417 T^{8} + 22910987 T^{9} - 79924800 T^{10} - 580797228 T^{11} + 14492410483 T^{12} - 24974280804 T^{13} - 147780955200 T^{14} + 1821583843409 T^{15} - 18145002547017 T^{16} + 10851869245374 T^{17} + 810834916932181 T^{18} - 1596662521642518 T^{19} + 7083049368226206 T^{20} - 8041481790989488 T^{21} - 1296688938797054940 T^{22} + 2787881218413668121 T^{23} + 39959630797262576401 T^{24}$$)($$1 - 2 T + 2 T^{2} + 112 T^{3} - 3840 T^{4} + 7982 T^{5} - 2012 T^{6} - 464698 T^{7} + 6098798 T^{8} - 19506388 T^{9} - 1100914 T^{10} + 890327938 T^{11} - 7456003800 T^{12} + 38444523010 T^{13} - 1944910962 T^{14} - 1611174599916 T^{15} + 14665036034491 T^{16} - 69280507796388 T^{17} - 3596140368738 T^{18} + 3056608690956070 T^{19} - 25490593247443800 T^{20} + 130885723924780534 T^{21} - 6959277079726786 T^{22} - 5302199293874251516 T^{23} + 71283972476632423598 T^{24} -$$$$23\!\cdots\!14$$$$T^{25} - 43482302414327908988 T^{26} +$$$$74\!\cdots\!74$$$$T^{27} -$$$$15\!\cdots\!40$$$$T^{28} +$$$$19\!\cdots\!16$$$$T^{29} +$$$$14\!\cdots\!98$$$$T^{30} -$$$$63\!\cdots\!14$$$$T^{31} +$$$$13\!\cdots\!01$$$$T^{32}$$)($$1 - 2284 T^{4} + 1070026 T^{8} + 6146180048 T^{12} - 12328368670157 T^{16} + 21012566494282448 T^{20} + 12506678190240287626 T^{24} -$$$$91\!\cdots\!84$$$$T^{28} +$$$$13\!\cdots\!01$$$$T^{32}$$)($$1 - 276 T^{2} + 40134 T^{4} - 3953309 T^{6} + 292635369 T^{8} - 17126403723 T^{10} + 814017920361 T^{12} - 31666720483827 T^{14} + 1000462092172569 T^{16} - 24990301433879141 T^{18} + 469094229941238534 T^{20} - 5964769118466452724 T^{22} + 39959630797262576401 T^{24}$$)
$47$ ($$1 - 4 T + 47 T^{2}$$)($$1 - 5 T + 47 T^{2}$$)($$1 - 5 T + 47 T^{2}$$)($$1 + 47 T^{2}$$)($$1 + 47 T^{2}$$)($$1 + 47 T^{2}$$)($$1 + 5 T + 47 T^{2}$$)($$1 + 5 T + 47 T^{2}$$)($$1 + 4 T + 47 T^{2}$$)($$1 + 14 T^{2} + 2209 T^{4}$$)($$1 + 4 T + 46 T^{2} + 188 T^{3} + 2209 T^{4}$$)($$1 + 86 T^{2} + 2209 T^{4}$$)($$1 + 86 T^{2} + 2209 T^{4}$$)($$1 + 66 T^{2} + 2209 T^{4}$$)($$1 + 66 T^{2} + 2209 T^{4}$$)($$1 - 4 T + 46 T^{2} - 188 T^{3} + 2209 T^{4}$$)($$1 + 14 T^{2} + 2209 T^{4}$$)($$1 - 78 T^{2} + 2209 T^{4}$$)($$1 - 78 T^{2} + 2209 T^{4}$$)($$1 - 69 T^{2} + 2209 T^{4}$$)($$1 - 69 T^{2} + 2209 T^{4}$$)($$( 1 - 47 T^{2} )^{2}$$)($$( 1 - 47 T^{2} )^{2}$$)($$( 1 - 66 T^{2} + 2209 T^{4} )^{2}$$)($$1 - 76 T^{2} + 5030 T^{4} - 167884 T^{6} + 4879681 T^{8}$$)($$1 - 76 T^{2} + 5030 T^{4} - 167884 T^{6} + 4879681 T^{8}$$)($$1 + 7 T + 2 T^{2} + 329 T^{3} + 2209 T^{4}$$)($$1 + 13 T + 39 T^{2} - 16 T^{3} - 299 T^{4} - 19253 T^{5} - 232366 T^{6} - 904891 T^{7} - 660491 T^{8} - 1661168 T^{9} + 190307559 T^{10} + 2981485091 T^{11} + 10779215329 T^{12}$$)($$1 + 20 T + 105 T^{2} + 120 T^{3} + 6294 T^{4} + 71140 T^{5} + 174165 T^{6} + 1240450 T^{7} + 19222555 T^{8} + 58301150 T^{9} + 384730485 T^{10} + 7385968220 T^{11} + 30712712214 T^{12} + 27521400840 T^{13} + 1131817609545 T^{14} + 10132462409260 T^{15} + 23811286661761 T^{16}$$)($$1 - 160 T^{2} + 14809 T^{4} - 1019680 T^{6} + 55015600 T^{8} - 2252473120 T^{10} + 72263195929 T^{12} - 1724674452640 T^{14} + 23811286661761 T^{16}$$)($$1 - 20 T + 105 T^{2} - 120 T^{3} + 6294 T^{4} - 71140 T^{5} + 174165 T^{6} - 1240450 T^{7} + 19222555 T^{8} - 58301150 T^{9} + 384730485 T^{10} - 7385968220 T^{11} + 30712712214 T^{12} - 27521400840 T^{13} + 1131817609545 T^{14} - 10132462409260 T^{15} + 23811286661761 T^{16}$$)($$1 + 71 T^{4} + 4879681 T^{8}$$)($$1 - 4222 T^{4} + 4879681 T^{8}$$)($$( 1 + 2209 T^{4} )^{2}$$)($$( 1 + 2209 T^{4} )^{2}$$)($$1 - 4222 T^{4} + 4879681 T^{8}$$)($$1 + 71 T^{4} + 4879681 T^{8}$$)($$1 - 3964 T^{4} + 8158086 T^{8} - 19343055484 T^{12} + 23811286661761 T^{16}$$)($$( 1 - 4222 T^{4} + 4879681 T^{8} )^{2}$$)($$1 + 5444 T^{4} + 14797830 T^{8} + 26564983364 T^{12} + 23811286661761 T^{16}$$)($$1 + 45 T^{2} - 184 T^{4} + 99405 T^{6} + 4879681 T^{8}$$)($$1 + 91 T^{2} + 1339 T^{4} - 12268 T^{6} + 3554941 T^{8} - 111607535 T^{10} - 21624150754 T^{12} - 246541044815 T^{14} + 17346978053821 T^{16} - 132239413656172 T^{18} + 31883312840097979 T^{20} + 4786521033460534459 T^{22} +$$$$11\!\cdots\!41$$$$T^{24}$$)($$1 + 190 T^{2} + 18813 T^{4} + 1189930 T^{6} + 47942596 T^{8} + 692067060 T^{10} - 71396434957 T^{12} - 7544792481460 T^{14} - 431982830702721 T^{16} - 16666446591545140 T^{18} - 348391827127408717 T^{20} + 7459939861847962740 T^{22} +$$$$11\!\cdots\!56$$$$T^{24} +$$$$62\!\cdots\!70$$$$T^{26} +$$$$21\!\cdots\!33$$$$T^{28} +$$$$48\!\cdots\!10$$$$T^{30} +$$$$56\!\cdots\!21$$$$T^{32}$$)($$1 - 6 T + 621 T^{3} - 2439 T^{4} - 6873 T^{5} + 245629 T^{6} - 323031 T^{7} - 5387751 T^{8} + 64474083 T^{9} - 1376070042 T^{11} + 10779215329 T^{12}$$)($$1 + 6 T - 621 T^{3} - 2439 T^{4} + 6873 T^{5} + 245629 T^{6} + 323031 T^{7} - 5387751 T^{8} - 64474083 T^{9} + 1376070042 T^{11} + 10779215329 T^{12}$$)($$1 - 15 T + 111 T^{2} - 873 T^{3} + 6828 T^{4} - 69612 T^{5} + 654227 T^{6} - 4732173 T^{7} + 31522707 T^{8} - 170376048 T^{9} + 1258782219 T^{10} - 11485670769 T^{11} + 82734051465 T^{12} - 539826526143 T^{13} + 2780649921771 T^{14} - 17688952431504 T^{15} + 153820754416467 T^{16} - 1085300249810211 T^{17} + 7052053707045683 T^{18} - 35267048661670356 T^{19} + 162583465326504108 T^{20} - 977000903018715591 T^{21} + 5838503678177135439 T^{22} - 37082388226260184545 T^{23} +$$$$11\!\cdots\!41$$$$T^{24}$$)($$1 + 12 T + 72 T^{2} + 288 T^{3} - 134 T^{4} - 24762 T^{5} - 246024 T^{6} - 2286006 T^{7} - 18983651 T^{8} - 98916168 T^{9} - 204929766 T^{10} + 1977304884 T^{11} + 21327903874 T^{12} + 124668663210 T^{13} + 894258211950 T^{14} + 7685415723390 T^{15} + 46309407650224 T^{16} + 361214538999330 T^{17} + 1975416390197550 T^{18} + 12943474620451830 T^{19} + 104073367303784194 T^{20} + 453485002462114188 T^{21} - 2208982075035583014 T^{22} - 50113217696402345784 T^{23} -$$$$45\!\cdots\!11$$$$T^{24} -$$$$25\!\cdots\!02$$$$T^{25} -$$$$12\!\cdots\!76$$$$T^{26} -$$$$61\!\cdots\!86$$$$T^{27} -$$$$15\!\cdots\!94$$$$T^{28} +$$$$15\!\cdots\!76$$$$T^{29} +$$$$18\!\cdots\!68$$$$T^{30} +$$$$14\!\cdots\!16$$$$T^{31} +$$$$56\!\cdots\!21$$$$T^{32}$$)($$1 - 5722 T^{4} + 16357201 T^{8} - 37906653562 T^{12} + 84859867638724 T^{16} - 184972377160073722 T^{20} +$$$$38\!\cdots\!61$$$$T^{24} -$$$$66\!\cdots\!02$$$$T^{28} +$$$$56\!\cdots\!21$$$$T^{32}$$)($$1 + 36 T^{2} + 2574 T^{4} - 23141 T^{6} - 166887 T^{8} + 70522893 T^{10} + 7143449961 T^{12} + 155785070637 T^{14} - 814355323047 T^{16} - 249441821928389 T^{18} + 61290251867372814 T^{20} + 1893568760489881764 T^{22} +$$$$11\!\cdots\!41$$$$T^{24}$$)
$53$ ($$1 + 2 T + 53 T^{2}$$)($$1 - 2 T + 53 T^{2}$$)($$1 - 2 T + 53 T^{2}$$)($$1 + 53 T^{2}$$)($$1 + 53 T^{2}$$)($$1 + 53 T^{2}$$)($$1 + 2 T + 53 T^{2}$$)($$1 + 2 T + 53 T^{2}$$)($$1 - 2 T + 53 T^{2}$$)($$1 + 24 T + 245 T^{2} + 1272 T^{3} + 2809 T^{4}$$)($$1 + 4 T + 97 T^{2} + 212 T^{3} + 2809 T^{4}$$)($$1 + 8 T^{2} + 2809 T^{4}$$)($$1 + 8 T^{2} + 2809 T^{4}$$)($$1 + 78 T^{2} + 2809 T^{4}$$)($$1 + 78 T^{2} + 2809 T^{4}$$)($$1 - 4 T + 97 T^{2} - 212 T^{3} + 2809 T^{4}$$)($$1 - 24 T + 245 T^{2} - 1272 T^{3} + 2809 T^{4}$$)($$1 - 102 T^{2} + 2809 T^{4}$$)($$1 - 102 T^{2} + 2809 T^{4}$$)($$1 - 102 T^{2} + 2809 T^{4}$$)($$1 - 102 T^{2} + 2809 T^{4}$$)($$( 1 - 53 T^{2} )^{2}$$)($$( 1 - 53 T^{2} )^{2}$$)($$( 1 - 78 T^{2} + 2809 T^{4} )^{2}$$)($$1 - 178 T^{2} + 13331 T^{4} - 500002 T^{6} + 7890481 T^{8}$$)($$1 - 178 T^{2} + 13331 T^{4} - 500002 T^{6} + 7890481 T^{8}$$)($$( 1 + 2 T + 53 T^{2} )^{2}$$)($$( 1 + 2 T + 139 T^{2} + 188 T^{3} + 7367 T^{4} + 5618 T^{5} + 148877 T^{6} )^{2}$$)($$( 1 - 20 T + 298 T^{2} - 3001 T^{3} + 25499 T^{4} - 159053 T^{5} + 837082 T^{6} - 2977540 T^{7} + 7890481 T^{8} )^{2}$$)($$( 1 + 196 T^{2} + 15174 T^{4} + 550564 T^{6} + 7890481 T^{8} )^{2}$$)($$( 1 + 20 T + 298 T^{2} + 3001 T^{3} + 25499 T^{4} + 159053 T^{5} + 837082 T^{6} + 2977540 T^{7} + 7890481 T^{8} )^{2}$$)($$( 1 - 20 T + 200 T^{2} - 1060 T^{3} + 2809 T^{4} )( 1 + 20 T + 200 T^{2} + 1060 T^{3} + 2809 T^{4} )$$)($$( 1 - 20 T + 200 T^{2} - 1060 T^{3} + 2809 T^{4} )( 1 + 20 T + 200 T^{2} + 1060 T^{3} + 2809 T^{4} )$$)($$( 1 + 2809 T^{4} )^{2}$$)($$( 1 + 2809 T^{4} )^{2}$$)($$( 1 - 20 T + 200 T^{2} - 1060 T^{3} + 2809 T^{4} )( 1 + 20 T + 200 T^{2} + 1060 T^{3} + 2809 T^{4} )$$)($$( 1 - 20 T + 200 T^{2} - 1060 T^{3} + 2809 T^{4} )( 1 + 20 T + 200 T^{2} + 1060 T^{3} + 2809 T^{4} )$$)($$1 - 8464 T^{4} + 31941186 T^{8} - 66785031184 T^{12} + 62259690411361 T^{16}$$)($$1 - 1778 T^{4} - 4729197 T^{8} - 14029275218 T^{12} + 62259690411361 T^{16}$$)($$1 + 14 T^{4} - 15680685 T^{8} + 110466734 T^{12} + 62259690411361 T^{16}$$)($$( 1 - 102 T^{2} + 2809 T^{4} )^{2}$$)($$( 1 - 274 T^{2} + 33303 T^{4} - 2287964 T^{6} + 93548127 T^{8} - 2161991794 T^{10} + 22164361129 T^{12} )^{2}$$)($$( 1 - 196 T^{2} + 19762 T^{4} - 1503447 T^{6} + 91143129 T^{8} - 4223182623 T^{10} + 155931685522 T^{12} - 4344214781284 T^{14} + 62259690411361 T^{16} )^{2}$$)($$( 1 + 24 T + 330 T^{2} + 2871 T^{3} + 17490 T^{4} + 67416 T^{5} + 148877 T^{6} )^{2}$$)($$( 1 - 24 T + 330 T^{2} - 2871 T^{3} + 17490 T^{4} - 67416 T^{5} + 148877 T^{6} )^{2}$$)($$( 1 - 9 T + 210 T^{2} - 1872 T^{3} + 23856 T^{4} - 168327 T^{5} + 1634317 T^{6} - 8921331 T^{7} + 67011504 T^{8} - 278697744 T^{9} + 1657001010 T^{10} - 3763759437 T^{11} + 22164361129 T^{12} )^{2}$$)($$1 - 6680 T^{4} + 12266524 T^{8} + 25145244376 T^{12} - 161780081477882 T^{16} + 198408072989184856 T^{20} +$$$$76\!\cdots\!64$$$$T^{24} -$$$$32\!\cdots\!80$$$$T^{28} +$$$$38\!\cdots\!21$$$$T^{32}$$)($$( 1 - 1244 T^{4} + 14286246 T^{8} - 9815758364 T^{12} + 62259690411361 T^{16} )^{2}$$)($$( 1 - 84 T^{2} + 6072 T^{4} - 362545 T^{6} + 17056248 T^{8} - 662800404 T^{10} + 22164361129 T^{12} )^{2}$$)
$59$ ($$1 - 8 T + 59 T^{2}$$)($$1 + 5 T + 59 T^{2}$$)($$1 - 5 T + 59 T^{2}$$)($$1 + 59 T^{2}$$)($$1 + 59 T^{2}$$)($$1 + 59 T^{2}$$)($$1 + 5 T + 59 T^{2}$$)($$1 - 5 T + 59 T^{2}$$)($$1 + 8 T + 59 T^{2}$$)($$( 1 + 59 T^{2} )^{2}$$)($$1 - 10 T + 130 T^{2} - 590 T^{3} + 3481 T^{4}$$)($$1 + 46 T^{2} + 3481 T^{4}$$)($$1 + 46 T^{2} + 3481 T^{4}$$)($$1 + 6 T^{2} + 3481 T^{4}$$)($$1 + 6 T^{2} + 3481 T^{4}$$)($$1 + 10 T + 130 T^{2} + 590 T^{3} + 3481 T^{4}$$)($$( 1 + 59 T^{2} )^{2}$$)($$( 1 - 8 T + 59 T^{2} )^{2}$$)($$( 1 + 8 T + 59 T^{2} )^{2}$$)($$( 1 - 5 T + 59 T^{2} )^{2}$$)($$( 1 + 5 T + 59 T^{2} )^{2}$$)($$( 1 + 59 T^{2} )^{2}$$)($$( 1 + 59 T^{2} )^{2}$$)($$( 1 + 6 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 10 T + 130 T^{2} + 590 T^{3} + 3481 T^{4} )^{2}$$)($$( 1 - 10 T + 130 T^{2} - 590 T^{3} + 3481 T^{4} )^{2}$$)($$1 + 14 T + 137 T^{2} + 826 T^{3} + 3481 T^{4}$$)($$1 + 2 T - 153 T^{2} - 110 T^{3} + 14962 T^{4} + 3194 T^{5} - 1012513 T^{6} + 188446 T^{7} + 52082722 T^{8} - 22591690 T^{9} - 1853956233 T^{10} + 1429848598 T^{11} + 42180533641 T^{12}$$)($$1 - 17 T + 51 T^{2} + 144 T^{3} + 2220 T^{4} + 17291 T^{5} - 531846 T^{6} + 1855556 T^{7} + 4239943 T^{8} + 109477804 T^{9} - 1851355926 T^{10} + 3551208289 T^{11} + 26900541420 T^{12} + 102949099056 T^{13} + 2151207215691 T^{14} - 42307075241923 T^{15} + 146830437604321 T^{16}$$)($$( 1 - 12 T + 2 T^{2} - 288 T^{3} + 8187 T^{4} - 16992 T^{5} + 6962 T^{6} - 2464548 T^{7} + 12117361 T^{8} )^{2}$$)($$1 - 17 T + 51 T^{2} + 144 T^{3} + 2220 T^{4} + 17291 T^{5} - 531846 T^{6} + 1855556 T^{7} + 4239943 T^{8} + 109477804 T^{9} - 1851355926 T^{10} + 3551208289 T^{11} + 26900541420 T^{12} + 102949099056 T^{13} + 2151207215691 T^{14} - 42307075241923 T^{15} + 146830437604321 T^{16}$$)($$( 1 + 9 T + 59 T^{2} )^{4}$$)($$( 1 + 59 T^{2} )^{4}$$)($$( 1 + 59 T^{2} )^{4}$$)($$( 1 + 59 T^{2} )^{4}$$)($$( 1 + 59 T^{2} )^{4}$$)($$( 1 - 9 T + 59 T^{2} )^{4}$$)($$( 1 - 4 T^{2} + 1566 T^{4} - 13924 T^{6} + 12117361 T^{8} )^{2}$$)($$( 1 + 59 T^{2} )^{8}$$)($$( 1 + 170 T^{2} + 13998 T^{4} + 591770 T^{6} + 12117361 T^{8} )^{2}$$)($$( 1 - 14 T + 137 T^{2} - 826 T^{3} + 3481 T^{4} )^{2}$$)($$( 1 - 2 T - 153 T^{2} + 110 T^{3} + 14962 T^{4} - 3194 T^{5} - 1012513 T^{6} - 188446 T^{7} + 52082722 T^{8} + 22591690 T^{9} - 1853956233 T^{10} - 1429848598 T^{11} + 42180533641 T^{12} )^{2}$$)($$( 1 + 17 T + 51 T^{2} - 144 T^{3} + 2220 T^{4} - 17291 T^{5} - 531846 T^{6} - 1855556 T^{7} + 4239943 T^{8} - 109477804 T^{9} - 1851355926 T^{10} - 3551208289 T^{11} + 26900541420 T^{12} - 102949099056 T^{13} + 2151207215691 T^{14} + 42307075241923 T^{15} + 146830437604321 T^{16} )^{2}$$)($$1 + 144 T^{2} + 576 T^{3} + 8496 T^{4} + 97596 T^{5} + 406765 T^{6} + 5758164 T^{7} + 29574576 T^{8} + 118298304 T^{9} + 1744899984 T^{10} + 42180533641 T^{12}$$)($$1 + 144 T^{2} + 576 T^{3} + 8496 T^{4} + 97596 T^{5} + 406765 T^{6} + 5758164 T^{7} + 29574576 T^{8} + 118298304 T^{9} + 1744899984 T^{10} + 42180533641 T^{12}$$)($$1 + 12 T + 192 T^{2} + 2349 T^{3} + 25089 T^{4} + 223824 T^{5} + 1972808 T^{6} + 12709350 T^{7} + 71501877 T^{8} + 339681357 T^{9} - 107943444 T^{10} - 13247965206 T^{11} - 122980417173 T^{12} - 781629947154 T^{13} - 375751128564 T^{14} + 69763417419303 T^{15} + 866414055786597 T^{16} + 9086223139495650 T^{17} + 83214094211233928 T^{18} + 557019929938127856 T^{19} + 3683828849054809569 T^{20} + 20349377178020451711 T^{21} + 98134416633723148992 T^{22} +$$$$36\!\cdots\!08$$$$T^{23} +$$$$17\!\cdots\!81$$$$T^{24}$$)($$1 - 328 T^{2} + 54732 T^{4} - 6528848 T^{6} + 640897706 T^{8} - 55004293416 T^{10} + 4215408852016 T^{12} - 289798546717912 T^{14} + 17966936709291123 T^{16} - 1008788741125051672 T^{18} + 51079630822473449776 T^{20} -$$$$23\!\cdots\!56$$$$T^{22} +$$$$94\!\cdots\!26$$$$T^{24} -$$$$33\!\cdots\!48$$$$T^{26} +$$$$97\!\cdots\!92$$$$T^{28} -$$$$20\!\cdots\!08$$$$T^{30} +$$$$21\!\cdots\!41$$$$T^{32}$$)($$( 1 - 46 T^{2} - 1365 T^{4} - 160126 T^{6} + 12117361 T^{8} )^{4}$$)($$( 1 + 144 T^{2} - 576 T^{3} + 8496 T^{4} - 97596 T^{5} + 406765 T^{6} - 5758164 T^{7} + 29574576 T^{8} - 118298304 T^{9} + 1744899984 T^{10} + 42180533641 T^{12} )^{2}$$)
$61$ ($$1 - 7 T + 61 T^{2}$$)($$1 + 11 T + 61 T^{2}$$)($$1 + 11 T + 61 T^{2}$$)($$1 - 14 T + 61 T^{2}$$)($$1 + T + 61 T^{2}$$)($$1 - 14 T + 61 T^{2}$$)($$1 + 11 T + 61 T^{2}$$)($$1 + 11 T + 61 T^{2}$$)($$1 - 7 T + 61 T^{2}$$)($$1 + 2 T - 57 T^{2} + 122 T^{3} + 3721 T^{4}$$)($$1 - 6 T + 79 T^{2} - 366 T^{3} + 3721 T^{4}$$)($$( 1 + 13 T + 61 T^{2} )^{2}$$)($$( 1 + 13 T + 61 T^{2} )^{2}$$)($$( 1 - 7 T + 61 T^{2} )^{2}$$)($$( 1 - 7 T + 61 T^{2} )^{2}$$)($$1 - 6 T + 79 T^{2} - 366 T^{3} + 3721 T^{4}$$)($$1 + 2 T - 57 T^{2} + 122 T^{3} + 3721 T^{4}$$)($$( 1 - 7 T + 61 T^{2} )^{2}$$)($$( 1 - 7 T + 61 T^{2} )^{2}$$)($$( 1 + 11 T + 61 T^{2} )^{2}$$)($$( 1 + 11 T + 61 T^{2} )^{2}$$)($$( 1 - 14 T + 61 T^{2} )^{2}$$)($$( 1 + T + 61 T^{2} )^{2}$$)($$( 1 - 7 T + 61 T^{2} )^{4}$$)($$( 1 - 6 T + 79 T^{2} - 366 T^{3} + 3721 T^{4} )^{2}$$)($$( 1 - 6 T + 79 T^{2} - 366 T^{3} + 3721 T^{4} )^{2}$$)($$1 + 7 T - 12 T^{2} + 427 T^{3} + 3721 T^{4}$$)($$1 + T - 145 T^{2} - 240 T^{3} + 12217 T^{4} + 14087 T^{5} - 812786 T^{6} + 859307 T^{7} + 45459457 T^{8} - 54475440 T^{9} - 2007646945 T^{10} + 844596301 T^{11} + 51520374361 T^{12}$$)($$1 - 13 T - 72 T^{2} + 1443 T^{3} + 6378 T^{4} - 120042 T^{5} - 78037 T^{6} + 2420938 T^{7} + 9620433 T^{8} + 147677218 T^{9} - 290375677 T^{10} - 27247253202 T^{11} + 88308773898 T^{12} + 1218752462343 T^{13} - 3709466953992 T^{14} - 40855656868273 T^{15} + 191707312997281 T^{16}$$)($$( 1 + 4 T - 35 T^{2} - 284 T^{3} - 2096 T^{4} - 17324 T^{5} - 130235 T^{6} + 907924 T^{7} + 13845841 T^{8} )^{2}$$)($$1 - 13 T - 72 T^{2} + 1443 T^{3} + 6378 T^{4} - 120042 T^{5} - 78037 T^{6} + 2420938 T^{7} + 9620433 T^{8} + 147677218 T^{9} - 290375677 T^{10} - 27247253202 T^{11} + 88308773898 T^{12} + 1218752462343 T^{13} - 3709466953992 T^{14} - 40855656868273 T^{15} + 191707312997281 T^{16}$$)($$( 1 + T + 61 T^{2} )^{4}$$)($$( 1 + T + 61 T^{2} )^{4}$$)($$( 1 - 14 T + 61 T^{2} )^{4}$$)($$( 1 + T + 61 T^{2} )^{4}$$)($$( 1 + T + 61 T^{2} )^{4}$$)($$( 1 + T + 61 T^{2} )^{4}$$)($$( 1 + T + 61 T^{2} )^{8}$$)($$( 1 + 2 T - 57 T^{2} + 122 T^{3} + 3721 T^{4} )^{4}$$)($$( 1 + T + 61 T^{2} )^{8}$$)($$( 1 + 7 T - 12 T^{2} + 427 T^{3} + 3721 T^{4} )^{2}$$)($$( 1 + T - 145 T^{2} - 240 T^{3} + 12217 T^{4} + 14087 T^{5} - 812786 T^{6} + 859307 T^{7} + 45459457 T^{8} - 54475440 T^{9} - 2007646945 T^{10} + 844596301 T^{11} + 51520374361 T^{12} )^{2}$$)($$( 1 - 13 T - 72 T^{2} + 1443 T^{3} + 6378 T^{4} - 120042 T^{5} - 78037 T^{6} + 2420938 T^{7} + 9620433 T^{8} + 147677218 T^{9} - 290375677 T^{10} - 27247253202 T^{11} + 88308773898 T^{12} + 1218752462343 T^{13} - 3709466953992 T^{14} - 40855656868273 T^{15} + 191707312997281 T^{16} )^{2}$$)($$1 - 36 T + 756 T^{2} - 11590 T^{3} + 141336 T^{4} - 1424232 T^{5} + 12082719 T^{6} - 86878152 T^{7} + 525911256 T^{8} - 2630709790 T^{9} + 10467455796 T^{10} - 30405466836 T^{11} + 51520374361 T^{12}$$)($$1 - 36 T + 756 T^{2} - 11590 T^{3} + 141336 T^{4} - 1424232 T^{5} + 12082719 T^{6} - 86878152 T^{7} + 525911256 T^{8} - 2630709790 T^{9} + 10467455796 T^{10} - 30405466836 T^{11} + 51520374361 T^{12}$$)($$1 - 12 T - 51 T^{2} + 583 T^{3} + 2127 T^{4} + 45474 T^{5} - 455363 T^{6} - 2399139 T^{7} + 11507670 T^{8} + 53383966 T^{9} + 844033821 T^{10} - 2578276122 T^{11} - 56950876769 T^{12} - 157274843442 T^{13} + 3140649847941 T^{14} + 12117145986646 T^{15} + 159333369100470 T^{16} - 2026303924984839 T^{17} - 23460472230148043 T^{18} + 142913087725218954 T^{19} + 407761454745216687 T^{20} + 6817687172122304203 T^{21} - 36380488494807012651 T^{22} -$$$$52\!\cdots\!32$$$$T^{23} +$$$$26\!\cdots\!21$$$$T^{24}$$)($$( 1 - 4 T - 126 T^{2} + 1444 T^{3} + 6365 T^{4} - 126018 T^{5} + 435286 T^{6} + 4572842 T^{7} - 47796264 T^{8} + 278943362 T^{9} + 1619699206 T^{10} - 28603691658 T^{11} + 88128777965 T^{12} + 1219597058644 T^{13} - 6491567169486 T^{14} - 12570971344084 T^{15} + 191707312997281 T^{16} )^{2}$$)($$( 1 + 10 T - 41 T^{2} + 190 T^{3} + 10060 T^{4} + 11590 T^{5} - 152561 T^{6} + 2269810 T^{7} + 13845841 T^{8} )^{4}$$)($$( 1 - 36 T + 756 T^{2} - 11590 T^{3} + 141336 T^{4} - 1424232 T^{5} + 12082719 T^{6} - 86878152 T^{7} + 525911256 T^{8} - 2630709790 T^{9} + 10467455796 T^{10} - 30405466836 T^{11} + 51520374361 T^{12} )^{2}$$)
$67$ ($$1 - 9 T + 67 T^{2}$$)($$1 + 67 T^{2}$$)($$1 + 67 T^{2}$$)($$1 - 5 T + 67 T^{2}$$)($$1 + 5 T + 67 T^{2}$$)($$1 + 5 T + 67 T^{2}$$)($$1 + 67 T^{2}$$)($$1 + 67 T^{2}$$)($$1 - 9 T + 67 T^{2}$$)($$( 1 + 67 T^{2} )^{2}$$)($$1 - 16 T + 146 T^{2} - 1072 T^{3} + 4489 T^{4}$$)($$( 1 - 3 T + 67 T^{2} )^{2}$$)($$( 1 + 3 T + 67 T^{2} )^{2}$$)($$( 1 + 12 T + 67 T^{2} )^{2}$$)($$( 1 - 12 T + 67 T^{2} )^{2}$$)($$1 - 16 T + 146 T^{2} - 1072 T^{3} + 4489 T^{4}$$)($$( 1 + 67 T^{2} )^{2}$$)($$1 - 53 T^{2} + 4489 T^{4}$$)($$1 - 53 T^{2} + 4489 T^{4}$$)($$( 1 - 67 T^{2} )^{2}$$)($$( 1 - 67 T^{2} )^{2}$$)($$1 - 109 T^{2} + 4489 T^{4}$$)($$1 - 109 T^{2} + 4489 T^{4}$$)($$( 1 + 10 T^{2} + 4489 T^{4} )^{2}$$)($$1 - 36 T^{2} - 4010 T^{4} - 161604 T^{6} + 20151121 T^{8}$$)($$1 - 36 T^{2} - 4010 T^{4} - 161604 T^{6} + 20151121 T^{8}$$)($$1 + 3 T - 58 T^{2} + 201 T^{3} + 4489 T^{4}$$)($$1 - 11 T - 41 T^{2} + 152 T^{3} + 4753 T^{4} + 32755 T^{5} - 764902 T^{6} + 2194585 T^{7} + 21336217 T^{8} + 45715976 T^{9} - 826195961 T^{10} - 14851376177 T^{11} + 90458382169 T^{12}$$)($$1 - 17 T - 15 T^{2} + 1066 T^{3} + 7426 T^{4} - 68373 T^{5} - 833566 T^{6} - 1085128 T^{7} + 111947307 T^{8} - 72703576 T^{9} - 3741877774 T^{10} - 20564068599 T^{11} + 149642224546 T^{12} + 1439233364062 T^{13} - 1356875732535 T^{14} - 103032097290491 T^{15} + 406067677556641 T^{16}$$)($$1 - 184 T^{2} + 16657 T^{4} - 1512664 T^{6} + 123674896 T^{8} - 6790348696 T^{10} + 335657222497 T^{12} - 16644342319096 T^{14} + 406067677556641 T^{16}$$)($$1 + 17 T - 15 T^{2} - 1066 T^{3} + 7426 T^{4} + 68373 T^{5} - 833566 T^{6} + 1085128 T^{7} + 111947307 T^{8} + 72703576 T^{9} - 3741877774 T^{10} + 20564068599 T^{11} + 149642224546 T^{12} - 1439233364062 T^{13} - 1356875732535 T^{14} + 103032097290491 T^{15} + 406067677556641 T^{16}$$)($$1 - 8302 T^{4} + 20151121 T^{8}$$)($$1 - 8302 T^{4} + 20151121 T^{8}$$)($$1 + 2903 T^{4} + 20151121 T^{8}$$)($$1 + 2903 T^{4} + 20151121 T^{8}$$)($$1 - 8302 T^{4} + 20151121 T^{8}$$)($$1 - 8302 T^{4} + 20151121 T^{8}$$)($$( 1 - 20 T + 200 T^{2} - 2280 T^{3} + 23783 T^{4} - 152760 T^{5} + 897800 T^{6} - 6015260 T^{7} + 20151121 T^{8} )^{2}$$)($$( 1 + 4489 T^{4} )^{4}$$)($$( 1 + 16 T + 128 T^{2} + 912 T^{3} + 6398 T^{4} + 61104 T^{5} + 574592 T^{6} + 4812208 T^{7} + 20151121 T^{8} )^{2}$$)($$1 + 125 T^{2} + 11136 T^{4} + 561125 T^{6} + 20151121 T^{8}$$)($$1 + 203 T^{2} + 14531 T^{4} + 1222044 T^{6} + 166308757 T^{8} + 11407412521 T^{10} + 552166785598 T^{12} + 51207874806769 T^{14} + 3351307885666597 T^{16} + 110544123179333436 T^{18} + 5900569422575550371 T^{20} +$$$$37\!\cdots\!47$$$$T^{22} +$$$$81\!\cdots\!61$$$$T^{24}$$)($$1 + 319 T^{2} + 51321 T^{4} + 5350950 T^{6} + 412923954 T^{8} + 28055592807 T^{10} + 2076453240410 T^{12} + 167751222063326 T^{14} + 12304355330991753 T^{16} + 753035235842270414 T^{18} + 41842860498343999610 T^{20} +$$$$25\!\cdots\!83$$$$T^{22} +$$$$16\!\cdots\!14$$$$T^{24} +$$$$97\!\cdots\!50$$$$T^{26} +$$$$41\!\cdots\!81$$$$T^{28} +$$$$11\!\cdots\!51$$$$T^{30} +$$$$16\!\cdots\!81$$$$T^{32}$$)($$1 + 18 T + 234 T^{2} + 2860 T^{3} + 30024 T^{4} + 262980 T^{5} + 2254197 T^{6} + 17619660 T^{7} + 134777736 T^{8} + 860182180 T^{9} + 4715362314 T^{10} + 24302251926 T^{11} + 90458382169 T^{12}$$)($$1 - 18 T + 234 T^{2} - 2860 T^{3} + 30024 T^{4} - 262980 T^{5} + 2254197 T^{6} - 17619660 T^{7} + 134777736 T^{8} - 860182180 T^{9} + 4715362314 T^{10} - 24302251926 T^{11} + 90458382169 T^{12}$$)($$1 - 15 T + 255 T^{2} - 2968 T^{3} + 36174 T^{4} - 397221 T^{5} + 4107115 T^{6} - 41367024 T^{7} + 386429292 T^{8} - 3556146616 T^{9} + 31289775603 T^{10} - 264760435272 T^{11} + 2216964278029 T^{12} - 17738949163224 T^{13} + 140459802681867 T^{14} - 1069557324668008 T^{15} + 7786983421036332 T^{16} - 55850657704271568 T^{17} + 371522978282032435 T^{18} - 2407441924578007383 T^{19} + 14689092167933931534 T^{20} - 80748994088203402696 T^{21} +$$$$46\!\cdots\!95$$$$T^{22} -$$$$18\!\cdots\!45$$$$T^{23} +$$$$81\!\cdots\!61$$$$T^{24}$$)($$1 + 4 T + 8 T^{2} - 1436 T^{3} - 5070 T^{4} - 45274 T^{5} + 890512 T^{6} + 2479154 T^{7} + 72952373 T^{8} - 410747644 T^{9} - 246911326 T^{10} - 51154442144 T^{11} + 220045950810 T^{12} - 1378484916350 T^{13} + 21635958751422 T^{14} - 133914238479582 T^{15} + 1373516219103616 T^{16} - 8972253978131994 T^{17} + 97123818835133358 T^{18} - 414597258896175050 T^{19} + 4434172580332358010 T^{20} - 69064896673193309408 T^{21} - 22335199089162546094 T^{22} -$$$$24\!\cdots\!12$$$$T^{23} +$$$$29\!\cdots\!93$$$$T^{24} +$$$$67\!\cdots\!38$$$$T^{25} +$$$$16\!\cdots\!88$$$$T^{26} -$$$$55\!\cdots\!42$$$$T^{27} -$$$$41\!\cdots\!70$$$$T^{28} -$$$$78\!\cdots\!32$$$$T^{29} +$$$$29\!\cdots\!32$$$$T^{30} +$$$$98\!\cdots\!72$$$$T^{31} +$$$$16\!\cdots\!81$$$$T^{32}$$)($$1 - 5914 T^{4} + 8186161 T^{8} + 79915923398 T^{12} - 393198002490332 T^{16} + 1610395442219829158 T^{20} +$$$$33\!\cdots\!01$$$$T^{24} -$$$$48\!\cdots\!54$$$$T^{28} +$$$$16\!\cdots\!81$$$$T^{32}$$)($$1 - 144 T^{2} + 11844 T^{4} - 912746 T^{6} + 87406884 T^{8} - 6957232452 T^{10} + 499884420891 T^{12} - 31231016477028 T^{14} + 1761346695716964 T^{16} - 82565526491226074 T^{18} + 4809465572980856004 T^{20} -$$$$26\!\cdots\!56$$$$T^{22} +$$$$81\!\cdots\!61$$$$T^{24}$$)
$71$ ($$1 + 2 T + 71 T^{2}$$)($$1 - 5 T + 71 T^{2}$$)($$1 + 5 T + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$1 - 5 T + 71 T^{2}$$)($$1 + 5 T + 71 T^{2}$$)($$1 - 2 T + 71 T^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$1 + 22 T + 250 T^{2} + 1562 T^{3} + 5041 T^{4}$$)($$1 - 20 T^{2} + 5041 T^{4}$$)($$1 - 20 T^{2} + 5041 T^{4}$$)($$1 + 30 T^{2} + 5041 T^{4}$$)($$1 + 30 T^{2} + 5041 T^{4}$$)($$1 - 22 T + 250 T^{2} - 1562 T^{3} + 5041 T^{4}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 - 2 T + 71 T^{2} )^{2}$$)($$( 1 + 2 T + 71 T^{2} )^{2}$$)($$( 1 - 5 T + 71 T^{2} )^{2}$$)($$( 1 + 5 T + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 30 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 + 22 T + 250 T^{2} + 1562 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 - 22 T + 250 T^{2} - 1562 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 + 2 T + 71 T^{2} )^{2}$$)($$( 1 - 10 T + 121 T^{2} - 712 T^{3} + 8591 T^{4} - 50410 T^{5} + 357911 T^{6} )^{2}$$)($$( 1 - 8 T + 244 T^{2} - 1441 T^{3} + 24947 T^{4} - 102311 T^{5} + 1230004 T^{6} - 2863288 T^{7} + 25411681 T^{8} )^{2}$$)($$( 1 + 18 T + 196 T^{2} + 1278 T^{3} + 5041 T^{4} )^{4}$$)($$( 1 - 8 T + 244 T^{2} - 1441 T^{3} + 24947 T^{4} - 102311 T^{5} + 1230004 T^{6} - 2863288 T^{7} + 25411681 T^{8} )^{2}$$)($$( 1 - 133 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 + 2 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 - 71 T^{2} )^{4}$$)($$( 1 - 71 T^{2} )^{4}$$)($$( 1 + 2 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 - 133 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 - 100 T^{2} + 12528 T^{4} - 504100 T^{6} + 25411681 T^{8} )^{2}$$)($$( 1 - 71 T^{2} )^{8}$$)($$( 1 - 250 T^{2} + 25518 T^{4} - 1260250 T^{6} + 25411681 T^{8} )^{2}$$)($$( 1 + 2 T + 71 T^{2} )^{4}$$)($$( 1 - 10 T + 121 T^{2} - 712 T^{3} + 8591 T^{4} - 50410 T^{5} + 357911 T^{6} )^{4}$$)($$( 1 - 8 T + 244 T^{2} - 1441 T^{3} + 24947 T^{4} - 102311 T^{5} + 1230004 T^{6} - 2863288 T^{7} + 25411681 T^{8} )^{4}$$)($$1 - 3 T - 150 T^{2} - 63 T^{3} + 13371 T^{4} + 19698 T^{5} - 1081649 T^{6} + 1398558 T^{7} + 67403211 T^{8} - 22548393 T^{9} - 3811752150 T^{10} - 5412688053 T^{11} + 128100283921 T^{12}$$)($$1 - 3 T - 150 T^{2} - 63 T^{3} + 13371 T^{4} + 19698 T^{5} - 1081649 T^{6} + 1398558 T^{7} + 67403211 T^{8} - 22548393 T^{9} - 3811752150 T^{10} - 5412688053 T^{11} + 128100283921 T^{12}$$)($$1 - 27 T + 78 T^{2} + 2565 T^{3} + 13071 T^{4} - 524664 T^{5} - 751711 T^{6} + 30297321 T^{7} + 410765508 T^{8} - 3391054713 T^{9} - 30034133541 T^{10} + 13624108308 T^{11} + 3600759258249 T^{12} + 967311689868 T^{13} - 151402067180181 T^{14} - 1213695783384543 T^{15} + 10438242055098948 T^{16} + 54663315804868671 T^{17} - 96294392526538831 T^{18} - 4771882122782055624 T^{19} + 8440644406913342031 T^{20} +$$$$11\!\cdots\!15$$$$T^{21} +$$$$25\!\cdots\!78$$$$T^{22} -$$$$62\!\cdots\!17$$$$T^{23} +$$$$16\!\cdots\!41$$$$T^{24}$$)($$( 1 - 452 T^{2} + 95704 T^{4} - 12356144 T^{6} + 1062541066 T^{8} - 62287321904 T^{10} + 2431999518424 T^{12} - 57901328332292 T^{14} + 645753531245761 T^{16} )^{2}$$)($$( 1 - 32 T^{2} + 2562 T^{4} - 161312 T^{6} + 25411681 T^{8} )^{4}$$)($$( 1 - 3 T - 150 T^{2} - 63 T^{3} + 13371 T^{4} + 19698 T^{5} - 1081649 T^{6} + 1398558 T^{7} + 67403211 T^{8} - 22548393 T^{9} - 3811752150 T^{10} - 5412688053 T^{11} + 128100283921 T^{12} )^{2}$$)
$73$ ($$1 - 5 T + 73 T^{2}$$)($$1 + 10 T + 73 T^{2}$$)($$1 - 10 T + 73 T^{2}$$)($$1 - 17 T + 73 T^{2}$$)($$1 - 7 T + 73 T^{2}$$)($$1 + 17 T + 73 T^{2}$$)($$1 - 10 T + 73 T^{2}$$)($$1 + 10 T + 73 T^{2}$$)($$1 - 5 T + 73 T^{2}$$)($$( 1 + 73 T^{2} )^{2}$$)($$1 + 18 T + 214 T^{2} + 1314 T^{3} + 5329 T^{4}$$)($$( 1 + 9 T + 73 T^{2} )^{2}$$)($$( 1 - 9 T + 73 T^{2} )^{2}$$)($$( 1 - 11 T + 73 T^{2} )^{2}$$)($$( 1 + 11 T + 73 T^{2} )^{2}$$)($$1 + 18 T + 214 T^{2} + 1314 T^{3} + 5329 T^{4}$$)($$( 1 + 73 T^{2} )^{2}$$)($$1 - 121 T^{2} + 5329 T^{4}$$)($$1 - 121 T^{2} + 5329 T^{4}$$)($$1 - 46 T^{2} + 5329 T^{4}$$)($$1 - 46 T^{2} + 5329 T^{4}$$)($$1 + 143 T^{2} + 5329 T^{4}$$)($$1 - 97 T^{2} + 5329 T^{4}$$)($$( 1 - 25 T^{2} + 5329 T^{4} )^{2}$$)($$1 - 104 T^{2} + 9150 T^{4} - 554216 T^{6} + 28398241 T^{8}$$)($$1 - 104 T^{2} + 9150 T^{4} - 554216 T^{6} + 28398241 T^{8}$$)($$( 1 + 4 T + 73 T^{2} )^{2}$$)($$( 1 - 8 T + 155 T^{2} - 1040 T^{3} + 11315 T^{4} - 42632 T^{5} + 389017 T^{6} )^{2}$$)($$( 1 + 2 T + 196 T^{2} + 679 T^{3} + 18071 T^{4} + 49567 T^{5} + 1044484 T^{6} + 778034 T^{7} + 28398241 T^{8} )^{2}$$)($$( 1 + 74 T^{2} + 5329 T^{4} )^{4}$$)($$( 1 - 2 T + 196 T^{2} - 679 T^{3} + 18071 T^{4} - 49567 T^{5} + 1044484 T^{6} - 778034 T^{7} + 28398241 T^{8} )^{2}$$)($$1 - 1054 T^{4} + 28398241 T^{8}$$)($$1 - 5617 T^{4} + 28398241 T^{8}$$)($$1 + 9791 T^{4} + 28398241 T^{8}$$)($$1 - 1249 T^{4} + 28398241 T^{8}$$)($$1 - 5617 T^{4} + 28398241 T^{8}$$)($$1 - 1054 T^{4} + 28398241 T^{8}$$)($$( 1 + 4 T + 8 T^{2} + 192 T^{3} + 3983 T^{4} + 14016 T^{5} + 42632 T^{6} + 1556068 T^{7} + 28398241 T^{8} )^{2}$$)($$( 1 + 5329 T^{4} )^{4}$$)($$( 1 - 14 T + 98 T^{2} - 42 T^{3} - 4882 T^{4} - 3066 T^{5} + 522242 T^{6} - 5446238 T^{7} + 28398241 T^{8} )^{2}$$)($$( 1 - 130 T^{2} + 5329 T^{4} )^{2}$$)($$( 1 - 246 T^{2} + 30015 T^{4} - 2521972 T^{6} + 159949935 T^{8} - 6985967286 T^{10} + 151334226289 T^{12} )^{2}$$)($$( 1 - 388 T^{2} + 71842 T^{4} - 8513491 T^{6} + 722371129 T^{8} - 45368393539 T^{10} + 2040186429922 T^{12} - 58717679800132 T^{14} + 806460091894081 T^{16} )^{2}$$)($$1 - 6 T - 186 T^{2} + 418 T^{3} + 27828 T^{4} - 31752 T^{5} - 2245917 T^{6} - 2317896 T^{7} + 148295412 T^{8} + 162609106 T^{9} - 5282072826 T^{10} - 12438429558 T^{11} + 151334226289 T^{12}$$)($$1 + 6 T - 186 T^{2} - 418 T^{3} + 27828 T^{4} + 31752 T^{5} - 2245917 T^{6} + 2317896 T^{7} + 148295412 T^{8} - 162609106 T^{9} - 5282072826 T^{10} + 12438429558 T^{11} + 151334226289 T^{12}$$)($$1 + 6 T - 228 T^{2} - 2296 T^{3} + 24945 T^{4} + 381255 T^{5} - 980072 T^{6} - 40200363 T^{7} - 102286134 T^{8} + 2648934335 T^{9} + 21743689350 T^{10} - 78452536893 T^{11} - 2017821540323 T^{12} - 5727035193189 T^{13} + 115872120546150 T^{14} + 1030480488198695 T^{15} - 2904746284290294 T^{16} - 83338230563588259 T^{17} - 148318437827512808 T^{18} + 4211875922398326735 T^{19} + 20117146992297850545 T^{20} -$$$$13\!\cdots\!48$$$$T^{21} -$$$$97\!\cdots\!72$$$$T^{22} +$$$$18\!\cdots\!62$$$$T^{23} +$$$$22\!\cdots\!21$$$$T^{24}$$)($$( 1 - 4 T + 8 T^{2} + 292 T^{3} - 844 T^{4} - 28196 T^{5} + 162168 T^{6} + 417348 T^{7} - 41227034 T^{8} + 30466404 T^{9} + 864193272 T^{10} - 10968723332 T^{11} - 23968115404 T^{12} + 605336905156 T^{13} + 1210673810312 T^{14} - 44189594076388 T^{15} + 806460091894081 T^{16} )^{2}$$)($$( 1 + 5329 T^{4} )^{8}$$)($$1 + 408 T^{2} + 95268 T^{4} + 15399598 T^{6} + 1905199452 T^{8} + 187847914644 T^{10} + 15132874130115 T^{12} + 1001041537137876 T^{14} + 54104313190963932 T^{16} + 2330486248491631822 T^{18} + 76829840034565308708 T^{20} +$$$$17\!\cdots\!92$$$$T^{22} +$$$$22\!\cdots\!21$$$$T^{24}$$)
$79$ ($$1 + 3 T + 79 T^{2}$$)($$1 - 12 T + 79 T^{2}$$)($$1 - 12 T + 79 T^{2}$$)($$1 + 13 T + 79 T^{2}$$)($$1 - 17 T + 79 T^{2}$$)($$1 + 13 T + 79 T^{2}$$)($$1 - 12 T + 79 T^{2}$$)($$1 - 12 T + 79 T^{2}$$)($$1 + 3 T + 79 T^{2}$$)($$1 + 16 T + 177 T^{2} + 1264 T^{3} + 6241 T^{4}$$)($$1 + 16 T + 209 T^{2} + 1264 T^{3} + 6241 T^{4}$$)($$( 1 + 5 T + 79 T^{2} )^{2}$$)($$( 1 + 5 T + 79 T^{2} )^{2}$$)($$( 1 - 15 T + 79 T^{2} )^{2}$$)($$( 1 - 15 T + 79 T^{2} )^{2}$$)($$1 + 16 T + 209 T^{2} + 1264 T^{3} + 6241 T^{4}$$)($$1 + 16 T + 177 T^{2} + 1264 T^{3} + 6241 T^{4}$$)($$( 1 - 3 T + 79 T^{2} )^{2}$$)($$( 1 - 3 T + 79 T^{2} )^{2}$$)($$( 1 + 12 T + 79 T^{2} )^{2}$$)($$( 1 + 12 T + 79 T^{2} )^{2}$$)($$( 1 - 13 T + 79 T^{2} )^{2}$$)($$( 1 + 17 T + 79 T^{2} )^{2}$$)($$( 1 + 15 T + 79 T^{2} )^{4}$$)($$( 1 - 16 T + 209 T^{2} - 1264 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 - 16 T + 209 T^{2} - 1264 T^{3} + 6241 T^{4} )^{2}$$)($$1 - 6 T - 43 T^{2} - 474 T^{3} + 6241 T^{4}$$)($$1 + 2 T - 149 T^{2} - 374 T^{3} + 10642 T^{4} + 16154 T^{5} - 772597 T^{6} + 1276166 T^{7} + 66416722 T^{8} - 184396586 T^{9} - 5803562069 T^{10} + 6154112798 T^{11} + 243087455521 T^{12}$$)($$1 - 7 T - 234 T^{2} + 1199 T^{3} + 36520 T^{4} - 121434 T^{5} - 3999001 T^{6} + 3702556 T^{7} + 362101113 T^{8} + 292501924 T^{9} - 24957765241 T^{10} - 59871697926 T^{11} + 1422456958120 T^{12} + 3689390622401 T^{13} - 56882464591914 T^{14} - 134427362903113 T^{15} + 1517108809906561 T^{16}$$)($$( 1 + 8 T - 98 T^{2} + 32 T^{3} + 14947 T^{4} + 2528 T^{5} - 611618 T^{6} + 3944312 T^{7} + 38950081 T^{8} )^{2}$$)($$1 - 7 T - 234 T^{2} + 1199 T^{3} + 36520 T^{4} - 121434 T^{5} - 3999001 T^{6} + 3702556 T^{7} + 362101113 T^{8} + 292501924 T^{9} - 24957765241 T^{10} - 59871697926 T^{11} + 1422456958120 T^{12} + 3689390622401 T^{13} - 56882464591914 T^{14} - 134427362903113 T^{15} + 1517108809906561 T^{16}$$)($$( 1 - 58 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 - 157 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 + 11 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 + 131 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 - 157 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 - 58 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 - 286 T^{2} + 32715 T^{4} - 1784926 T^{6} + 38950081 T^{8} )^{2}$$)($$( 1 - 98 T^{2} + 3363 T^{4} - 611618 T^{6} + 38950081 T^{8} )^{2}$$)($$( 1 - 202 T^{2} + 19659 T^{4} - 1260682 T^{6} + 38950081 T^{8} )^{2}$$)($$( 1 + 6 T - 43 T^{2} + 474 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 - 2 T - 149 T^{2} + 374 T^{3} + 10642 T^{4} - 16154 T^{5} - 772597 T^{6} - 1276166 T^{7} + 66416722 T^{8} + 184396586 T^{9} - 5803562069 T^{10} - 6154112798 T^{11} + 243087455521 T^{12} )^{2}$$)($$( 1 + 7 T - 234 T^{2} - 1199 T^{3} + 36520 T^{4} + 121434 T^{5} - 3999001 T^{6} - 3702556 T^{7} + 362101113 T^{8} - 292501924 T^{9} - 24957765241 T^{10} + 59871697926 T^{11} + 1422456958120 T^{12} - 3689390622401 T^{13} - 56882464591914 T^{14} + 134427362903113 T^{15} + 1517108809906561 T^{16} )^{2}$$)($$1 + 12 T + 204 T^{2} + 2915 T^{3} + 31545 T^{4} + 326493 T^{5} + 3330513 T^{6} + 25792947 T^{7} + 196872345 T^{8} + 1437208685 T^{9} + 7945816524 T^{10} + 36924676788 T^{11} + 243087455521 T^{12}$$)($$1 + 12 T + 204 T^{2} + 2915 T^{3} + 31545 T^{4} + 326493 T^{5} + 3330513 T^{6} + 25792947 T^{7} + 196872345 T^{8} + 1437208685 T^{9} + 7945816524 T^{10} + 36924676788 T^{11} + 243087455521 T^{12}$$)($$1 + 42 T + 813 T^{2} + 9520 T^{3} + 72840 T^{4} + 356811 T^{5} + 973207 T^{6} - 893781 T^{7} - 62793603 T^{8} - 1355379536 T^{9} - 23955645108 T^{10} - 329298299862 T^{11} - 3388931313773 T^{12} - 26014565689098 T^{13} - 149507181119028 T^{14} - 668254971049904 T^{15} - 2445815923131843 T^{16} - 2750214545354619 T^{17} + 236574413325225847 T^{18} + 6852165969260378949 T^{19} +$$$$11\!\cdots\!40$$$$T^{20} +$$$$11\!\cdots\!80$$$$T^{21} +$$$$76\!\cdots\!13$$$$T^{22} +$$$$31\!\cdots\!18$$$$T^{23} +$$$$59\!\cdots\!41$$$$T^{24}$$)($$1 + 260 T^{2} + 23724 T^{4} + 1706392 T^{6} + 225017642 T^{8} + 14869625148 T^{10} - 181450880816 T^{12} - 19987311435172 T^{14} + 2160188956785123 T^{16} - 124740810666908452 T^{18} - 7067526505304546096 T^{20} +$$$$36\!\cdots\!08$$$$T^{22} +$$$$34\!\cdots\!62$$$$T^{24} +$$$$16\!\cdots\!92$$$$T^{26} +$$$$14\!\cdots\!84$$$$T^{28} +$$$$95\!\cdots\!60$$$$T^{30} +$$$$23\!\cdots\!21$$$$T^{32}$$)($$( 1 + 116 T^{2} - 854 T^{4} + 212048 T^{6} + 81847123 T^{8} + 1323391568 T^{10} - 33263369174 T^{12} + 28198144840436 T^{14} + 1517108809906561 T^{16} )^{2}$$)($$( 1 - 12 T + 204 T^{2} - 2915 T^{3} + 31545 T^{4} - 326493 T^{5} + 3330513 T^{6} - 25792947 T^{7} + 196872345 T^{8} - 1437208685 T^{9} + 7945816524 T^{10} - 36924676788 T^{11} + 243087455521 T^{12} )^{2}$$)
$83$ ($$1 - 6 T + 83 T^{2}$$)($$1 + 12 T + 83 T^{2}$$)($$1 + 12 T + 83 T^{2}$$)($$1 + 83 T^{2}$$)($$1 + 83 T^{2}$$)($$1 + 83 T^{2}$$)($$1 - 12 T + 83 T^{2}$$)($$1 - 12 T + 83 T^{2}$$)($$1 + 6 T + 83 T^{2}$$)($$1 + 6 T + 95 T^{2} + 498 T^{3} + 6889 T^{4}$$)($$( 1 - 3 T + 83 T^{2} )^{2}$$)($$1 + 164 T^{2} + 6889 T^{4}$$)($$1 + 164 T^{2} + 6889 T^{4}$$)($$1 - 86 T^{2} + 6889 T^{4}$$)($$1 - 86 T^{2} + 6889 T^{4}$$)($$( 1 + 3 T + 83 T^{2} )^{2}$$)($$1 - 6 T + 95 T^{2} - 498 T^{3} + 6889 T^{4}$$)($$1 - 130 T^{2} + 6889 T^{4}$$)($$1 - 130 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$( 1 - 83 T^{2} )^{2}$$)($$( 1 - 83 T^{2} )^{2}$$)($$( 1 + 86 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 157 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 157 T^{2} + 6889 T^{4} )^{2}$$)($$1 + 9 T - 2 T^{2} + 747 T^{3} + 6889 T^{4}$$)($$1 - 15 T - 51 T^{2} + 678 T^{3} + 17133 T^{4} - 80979 T^{5} - 925778 T^{6} - 6721257 T^{7} + 118029237 T^{8} + 387671586 T^{9} - 2420374371 T^{10} - 59085609645 T^{11} + 326940373369 T^{12}$$)($$1 + 30 T + 280 T^{2} + 1770 T^{3} + 42079 T^{4} + 523485 T^{5} + 2681215 T^{6} + 35481675 T^{7} + 533008645 T^{8} + 2944979025 T^{9} + 18470890135 T^{10} + 299321917695 T^{11} + 1996998689359 T^{12} + 6972101938110 T^{13} + 91543304543320 T^{14} + 814081529688810 T^{15} + 2252292232139041 T^{16}$$)($$1 - 160 T^{2} + 5929 T^{4} - 942880 T^{6} + 163131520 T^{8} - 6495500320 T^{10} + 281380385209 T^{12} - 52310459739040 T^{14} + 2252292232139041 T^{16}$$)($$1 - 30 T + 280 T^{2} - 1770 T^{3} + 42079 T^{4} - 523485 T^{5} + 2681215 T^{6} - 35481675 T^{7} + 533008645 T^{8} - 2944979025 T^{9} + 18470890135 T^{10} - 299321917695 T^{11} + 1996998689359 T^{12} - 6972101938110 T^{13} + 91543304543320 T^{14} - 814081529688810 T^{15} + 2252292232139041 T^{16}$$)($$1 + 9938 T^{4} + 47458321 T^{8}$$)($$1 + 9938 T^{4} + 47458321 T^{8}$$)($$( 1 + 6889 T^{4} )^{2}$$)($$( 1 + 6889 T^{4} )^{2}$$)($$1 + 9938 T^{4} + 47458321 T^{8}$$)($$1 + 9938 T^{4} + 47458321 T^{8}$$)($$1 + 17456 T^{4} + 170554626 T^{8} + 828432451376 T^{12} + 2252292232139041 T^{16}$$)($$1 - 9938 T^{4} + 51305523 T^{8} - 471640794098 T^{12} + 2252292232139041 T^{16}$$)($$1 - 19666 T^{4} + 177621555 T^{8} - 933315340786 T^{12} + 2252292232139041 T^{16}$$)($$1 + 85 T^{2} + 336 T^{4} + 585565 T^{6} + 47458321 T^{8}$$)($$1 + 327 T^{2} + 57207 T^{4} + 6488176 T^{6} + 532197333 T^{8} + 34415866233 T^{10} + 2415401371734 T^{12} + 237090902479137 T^{14} + 25257191864857893 T^{16} + 2121246683923784944 T^{18} +$$$$12\!\cdots\!87$$$$T^{20} +$$$$50\!\cdots\!23$$$$T^{22} +$$$$10\!\cdots\!61$$$$T^{24}$$)($$1 + 340 T^{2} + 56358 T^{4} + 5615330 T^{6} + 356102531 T^{8} + 15268102785 T^{10} + 850761191503 T^{12} + 106079060220415 T^{14} + 11086543633870179 T^{16} + 730778645858438935 T^{18} + 40375697720691846463 T^{20} +$$$$49\!\cdots\!65$$$$T^{22} +$$$$80\!\cdots\!71$$$$T^{24} +$$$$87\!\cdots\!70$$$$T^{26} +$$$$60\!\cdots\!38$$$$T^{28} +$$$$25\!\cdots\!60$$$$T^{30} +$$$$50\!\cdots\!81$$$$T^{32}$$)($$1 + 18 T - 72 T^{2} - 3609 T^{3} - 20907 T^{4} + 178965 T^{5} + 3381445 T^{6} + 14854095 T^{7} - 144028323 T^{8} - 2063579283 T^{9} - 3416999112 T^{10} + 70902731574 T^{11} + 326940373369 T^{12}$$)($$1 - 18 T - 72 T^{2} + 3609 T^{3} - 20907 T^{4} - 178965 T^{5} + 3381445 T^{6} - 14854095 T^{7} - 144028323 T^{8} + 2063579283 T^{9} - 3416999112 T^{10} - 70902731574 T^{11} + 326940373369 T^{12}$$)($$1 + 39 T + 912 T^{2} + 16200 T^{3} + 251079 T^{4} + 3515997 T^{5} + 45358019 T^{6} + 541131408 T^{7} + 6100532325 T^{8} + 65514800025 T^{9} + 671478204717 T^{10} + 6541571603403 T^{11} + 60933732837525 T^{12} + 542950443082449 T^{13} + 4625813352295413 T^{14} + 37460510961894675 T^{15} + 289521021350726325 T^{16} + 2131538609315815344 T^{17} + 14829367667138196011 T^{18} + 95410273871375563119 T^{19} +$$$$56\!\cdots\!39$$$$T^{20} +$$$$30\!\cdots\!00$$$$T^{21} +$$$$14\!\cdots\!88$$$$T^{22} +$$$$50\!\cdots\!13$$$$T^{23} +$$$$10\!\cdots\!61$$$$T^{24}$$)($$1 + 66 T + 2178 T^{2} + 47916 T^{3} + 791830 T^{4} + 10596156 T^{5} + 122712084 T^{6} + 1311937572 T^{7} + 13564902253 T^{8} + 136924099746 T^{9} + 1327585690602 T^{10} + 12258029803398 T^{11} + 109901521003222 T^{12} + 994600086849090 T^{13} + 9293464416138048 T^{14} + 88105947208965780 T^{15} + 817933709355268336 T^{16} + 7312793618344159740 T^{17} + 64022676362775012672 T^{18} +$$$$56\!\cdots\!30$$$$T^{19} +$$$$52\!\cdots\!62$$$$T^{20} +$$$$48\!\cdots\!14$$$$T^{21} +$$$$43\!\cdots\!38$$$$T^{22} +$$$$37\!\cdots\!42$$$$T^{23} +$$$$30\!\cdots\!73$$$$T^{24} +$$$$24\!\cdots\!16$$$$T^{25} +$$$$19\!\cdots\!16$$$$T^{26} +$$$$13\!\cdots\!52$$$$T^{27} +$$$$84\!\cdots\!30$$$$T^{28} +$$$$42\!\cdots\!08$$$$T^{29} +$$$$16\!\cdots\!62$$$$T^{30} +$$$$40\!\cdots\!62$$$$T^{31} +$$$$50\!\cdots\!81$$$$T^{32}$$)($$1 - 922 T^{4} - 40638479 T^{8} + 49260688838 T^{12} - 571334931683036 T^{16} + 2337829583554920998 T^{20} -$$$$91\!\cdots\!39$$$$T^{24} -$$$$98\!\cdots\!42$$$$T^{28} +$$$$50\!\cdots\!81$$$$T^{32}$$)($$1 + 468 T^{2} + 93294 T^{4} + 9694123 T^{6} + 419139873 T^{8} - 21991579731 T^{10} - 4161640619895 T^{12} - 151499992766859 T^{14} + 19891674636733233 T^{16} + 3169400193105010387 T^{18} +$$$$21\!\cdots\!54$$$$T^{20} +$$$$72\!\cdots\!32$$$$T^{22} +$$$$10\!\cdots\!61$$$$T^{24}$$)
$89$ ($$1 - 12 T + 89 T^{2}$$)($$1 + 89 T^{2}$$)($$1 + 89 T^{2}$$)($$1 + 89 T^{2}$$)($$1 + 89 T^{2}$$)($$1 + 89 T^{2}$$)($$1 + 89 T^{2}$$)($$1 + 89 T^{2}$$)($$1 + 12 T + 89 T^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$1 - 6 T + 70 T^{2} - 534 T^{3} + 7921 T^{4}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$1 + 6 T + 70 T^{2} + 534 T^{3} + 7921 T^{4}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 - 12 T + 89 T^{2} )^{2}$$)($$( 1 + 12 T + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{4}$$)($$( 1 + 6 T + 70 T^{2} + 534 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 - 6 T + 70 T^{2} - 534 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 - 15 T + 89 T^{2} )^{2}$$)($$( 1 - 3 T + 89 T^{2} )^{6}$$)($$( 1 - 9 T + 257 T^{2} - 1998 T^{3} + 31929 T^{4} - 177822 T^{5} + 2035697 T^{6} - 6344721 T^{7} + 62742241 T^{8} )^{2}$$)($$( 1 + 6 T + 79 T^{2} + 534 T^{3} + 7921 T^{4} )^{4}$$)($$( 1 - 9 T + 257 T^{2} - 1998 T^{3} + 31929 T^{4} - 177822 T^{5} + 2035697 T^{6} - 6344721 T^{7} + 62742241 T^{8} )^{2}$$)($$( 1 - 6 T + 89 T^{2} )^{4}$$)($$( 1 - 12 T + 89 T^{2} )^{4}$$)($$( 1 + 89 T^{2} )^{4}$$)($$( 1 + 89 T^{2} )^{4}$$)($$( 1 + 12 T + 89 T^{2} )^{4}$$)($$( 1 + 6 T + 89 T^{2} )^{4}$$)($$( 1 + 212 T^{2} + 25134 T^{4} + 1679252 T^{6} + 62742241 T^{8} )^{2}$$)($$( 1 + 89 T^{2} )^{8}$$)($$( 1 + 50 T^{2} + 1158 T^{4} + 396050 T^{6} + 62742241 T^{8} )^{2}$$)($$( 1 + 15 T + 89 T^{2} )^{4}$$)($$( 1 + 3 T + 89 T^{2} )^{12}$$)($$( 1 + 9 T + 257 T^{2} + 1998 T^{3} + 31929 T^{4} + 177822 T^{5} + 2035697 T^{6} + 6344721 T^{7} + 62742241 T^{8} )^{4}$$)($$1 - 3 T - 186 T^{2} + 585 T^{3} + 18915 T^{4} - 33708 T^{5} - 1703351 T^{6} - 3000012 T^{7} + 149825715 T^{8} + 412406865 T^{9} - 11670056826 T^{10} - 16752178347 T^{11} + 496981290961 T^{12}$$)($$1 - 3 T - 186 T^{2} + 585 T^{3} + 18915 T^{4} - 33708 T^{5} - 1703351 T^{6} - 3000012 T^{7} + 149825715 T^{8} + 412406865 T^{9} - 11670056826 T^{10} - 16752178347 T^{11} + 496981290961 T^{12}$$)($$1 - 9 T - 273 T^{2} + 2772 T^{3} + 38802 T^{4} - 449316 T^{5} - 3561871 T^{6} + 54551502 T^{7} + 157767516 T^{8} - 4371660207 T^{9} + 3816883044 T^{10} + 152630961444 T^{11} - 900621732009 T^{12} + 13584155568516 T^{13} + 30233530591524 T^{14} - 3081884924468583 T^{15} + 9898687510843356 T^{16} + 304618830200242398 T^{17} - 1770183247816548031 T^{18} - 19873846469919508164 T^{19} +$$$$15\!\cdots\!62$$$$T^{20} +$$$$97\!\cdots\!48$$$$T^{21} -$$$$85\!\cdots\!73$$$$T^{22} -$$$$24\!\cdots\!01$$$$T^{23} +$$$$24\!\cdots\!21$$$$T^{24}$$)($$( 1 + 412 T^{2} + 69850 T^{4} + 6725680 T^{6} + 546021283 T^{8} + 53274111280 T^{10} + 4382545533850 T^{12} + 204756291875932 T^{14} + 3936588805702081 T^{16} )^{2}$$)($$( 1 + 158 T^{2} + 14307 T^{4} + 1251518 T^{6} + 62742241 T^{8} )^{4}$$)($$( 1 + 3 T - 186 T^{2} - 585 T^{3} + 18915 T^{4} + 33708 T^{5} - 1703351 T^{6} + 3000012 T^{7} + 149825715 T^{8} - 412406865 T^{9} - 11670056826 T^{10} + 16752178347 T^{11} + 496981290961 T^{12} )^{2}$$)
$97$ ($$1 - 13 T + 97 T^{2}$$)($$1 + 5 T + 97 T^{2}$$)($$1 - 5 T + 97 T^{2}$$)($$1 - 14 T + 97 T^{2}$$)($$1 - 19 T + 97 T^{2}$$)($$1 + 14 T + 97 T^{2}$$)($$1 - 5 T + 97 T^{2}$$)($$1 + 5 T + 97 T^{2}$$)($$1 - 13 T + 97 T^{2}$$)($$( 1 + 97 T^{2} )^{2}$$)($$( 1 + 8 T + 97 T^{2} )^{2}$$)($$( 1 + 3 T + 97 T^{2} )^{2}$$)($$( 1 - 3 T + 97 T^{2} )^{2}$$)($$( 1 - 7 T + 97 T^{2} )^{2}$$)($$( 1 + 7 T + 97 T^{2} )^{2}$$)($$( 1 + 8 T + 97 T^{2} )^{2}$$)($$( 1 + 97 T^{2} )^{2}$$)($$1 - 25 T^{2} + 9409 T^{4}$$)($$1 - 25 T^{2} + 9409 T^{4}$$)($$1 - 169 T^{2} + 9409 T^{4}$$)($$1 - 169 T^{2} + 9409 T^{4}$$)($$1 + 2 T^{2} + 9409 T^{4}$$)($$1 + 167 T^{2} + 9409 T^{4}$$)($$( 1 - 145 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 - 18 T + 97 T^{2} )^{2}( 1 + 18 T + 97 T^{2} )^{2}$$)($$( 1 - 18 T + 97 T^{2} )^{2}( 1 + 18 T + 97 T^{2} )^{2}$$)($$1 - 2 T - 93 T^{2} - 194 T^{3} + 9409 T^{4}$$)($$1 + 18 T + 69 T^{2} + 214 T^{3} + 906 T^{4} - 163158 T^{5} - 2743251 T^{6} - 15826326 T^{7} + 8524554 T^{8} + 195312022 T^{9} + 6108520389 T^{10} + 154572124626 T^{11} + 832972004929 T^{12}$$)($$1 + 19 T - 108 T^{2} - 1825 T^{3} + 46754 T^{4} + 332118 T^{5} - 5651993 T^{6} - 4946342 T^{7} + 777287673 T^{8} - 479795174 T^{9} - 53179602137 T^{10} + 303115131414 T^{11} + 4139098003874 T^{12} - 15671895969025 T^{13} - 89960976532332 T^{14} + 1535167405084147 T^{15} + 7837433594376961 T^{16}$$)($$1 - 52 T^{2} - 12902 T^{4} + 167024 T^{6} + 129576019 T^{8} + 1571528816 T^{10} - 1142204783462 T^{12} - 43314544256308 T^{14} + 7837433594376961 T^{16}$$)($$1 - 19 T - 108 T^{2} + 1825 T^{3} + 46754 T^{4} - 332118 T^{5} - 5651993 T^{6} + 4946342 T^{7} + 777287673 T^{8} + 479795174 T^{9} - 53179602137 T^{10} - 303115131414 T^{11} + 4139098003874 T^{12} + 15671895969025 T^{13} - 89960976532332 T^{14} - 1535167405084147 T^{15} + 7837433594376961 T^{16}$$)($$1 + 17663 T^{4} + 88529281 T^{8}$$)($$1 - 16609 T^{4} + 88529281 T^{8}$$)($$1 - 18814 T^{4} + 88529281 T^{8}$$)($$1 + 9071 T^{4} + 88529281 T^{8}$$)($$1 - 16609 T^{4} + 88529281 T^{8}$$)($$1 + 17663 T^{4} + 88529281 T^{8}$$)($$( 1 + 16 T + 128 T^{2} + 864 T^{3} + 3983 T^{4} + 83808 T^{5} + 1204352 T^{6} + 14602768 T^{7} + 88529281 T^{8} )^{2}$$)($$( 1 + 9409 T^{4} )^{4}$$)($$( 1 + 4 T + 8 T^{2} + 228 T^{3} + 4898 T^{4} + 22116 T^{5} + 75272 T^{6} + 3650692 T^{7} + 88529281 T^{8} )^{2}$$)($$1 + 190 T^{2} + 26691 T^{4} + 1787710 T^{6} + 88529281 T^{8}$$)($$1 + 186 T^{2} - 1131 T^{4} - 466418 T^{6} + 278880666 T^{8} + 18455439810 T^{10} - 762781062579 T^{12} + 173647233172290 T^{14} + 24689104845781146 T^{16} - 388513136594974322 T^{18} - 8864137395240342891 T^{20} +$$$$13\!\cdots\!14$$$$T^{22} +$$$$69\!\cdots\!41$$$$T^{24}$$)($$1 + 577 T^{2} + 174522 T^{4} + 37353959 T^{6} + 6361534046 T^{8} + 912884200698 T^{10} + 114408541714153 T^{12} + 12837001127592472 T^{14} + 1305837592754805081 T^{16} +$$$$12\!\cdots\!48$$$$T^{18} +$$$$10\!\cdots\!93$$$$T^{20} +$$$$76\!\cdots\!42$$$$T^{22} +$$$$49\!\cdots\!06$$$$T^{24} +$$$$27\!\cdots\!91$$$$T^{26} +$$$$12\!\cdots\!02$$$$T^{28} +$$$$37\!\cdots\!13$$$$T^{30} +$$$$61\!\cdots\!21$$$$T^{32}$$)($$1 + 3 T - 42 T^{2} - 1904 T^{3} - 7479 T^{4} + 60777 T^{5} + 2561289 T^{6} + 5895369 T^{7} - 70369911 T^{8} - 1737729392 T^{9} - 3718229802 T^{10} + 25762020771 T^{11} + 832972004929 T^{12}$$)($$1 - 3 T - 42 T^{2} + 1904 T^{3} - 7479 T^{4} - 60777 T^{5} + 2561289 T^{6} - 5895369 T^{7} - 70369911 T^{8} + 1737729392 T^{9} - 3718229802 T^{10} - 25762020771 T^{11} + 832972004929 T^{12}$$)($$1 + 3 T + 102 T^{2} + 1010 T^{3} + 15132 T^{4} + 13512 T^{5} + 1127323 T^{6} + 7762230 T^{7} + 23311719 T^{8} - 575063737 T^{9} + 1596748254 T^{10} - 54554445012 T^{11} - 1453572795209 T^{12} - 5291781166164 T^{13} + 15023804321886 T^{14} - 524845146039001 T^{15} + 2063769721944039 T^{16} + 66656910163093110 T^{17} + 939028499512575067 T^{18} + 1091746419868262856 T^{19} +$$$$11\!\cdots\!52$$$$T^{20} +$$$$76\!\cdots\!70$$$$T^{21} +$$$$75\!\cdots\!98$$$$T^{22} +$$$$21\!\cdots\!59$$$$T^{23} +$$$$69\!\cdots\!41$$$$T^{24}$$)($$1 + 28 T + 392 T^{2} - 872 T^{3} - 117924 T^{4} - 2250436 T^{5} - 16405808 T^{6} + 121301108 T^{7} + 5089087514 T^{8} + 63345173552 T^{9} + 270560580248 T^{10} - 4797083097932 T^{11} - 105427115995440 T^{12} - 964302703147436 T^{13} - 1291090828127400 T^{14} + 85355358908186064 T^{15} + 1288991316725561923 T^{16} + 8279469814094048208 T^{17} - 12147873601850706600 T^{18} -$$$$88\!\cdots\!28$$$$T^{19} -$$$$93\!\cdots\!40$$$$T^{20} -$$$$41\!\cdots\!24$$$$T^{21} +$$$$22\!\cdots\!92$$$$T^{22} +$$$$51\!\cdots\!76$$$$T^{23} +$$$$39\!\cdots\!54$$$$T^{24} +$$$$92\!\cdots\!36$$$$T^{25} -$$$$12\!\cdots\!92$$$$T^{26} -$$$$16\!\cdots\!08$$$$T^{27} -$$$$81\!\cdots\!84$$$$T^{28} -$$$$58\!\cdots\!44$$$$T^{29} +$$$$25\!\cdots\!48$$$$T^{30} +$$$$17\!\cdots\!04$$$$T^{31} +$$$$61\!\cdots\!21$$$$T^{32}$$)($$1 + 21116 T^{4} + 182916106 T^{8} + 1814092199408 T^{12} + 21841526617008403 T^{16} +$$$$16\!\cdots\!48$$$$T^{20} +$$$$14\!\cdots\!66$$$$T^{24} +$$$$14\!\cdots\!56$$$$T^{28} +$$$$61\!\cdots\!21$$$$T^{32}$$)($$1 + 93 T^{2} - 1770 T^{4} - 1760936 T^{6} - 103886055 T^{8} + 10655050167 T^{10} + 2102618450697 T^{12} + 100253367021303 T^{14} - 9196957755076455 T^{16} - 1466810390471653544 T^{18} - 13872257462047220970 T^{20} +$$$$68\!\cdots\!57$$$$T^{22} +$$$$69\!\cdots\!41$$$$T^{24}$$)