# Properties

 Label 245.2 Level 245 Weight 2 Dimension 1925 Nonzero newspaces 12 Newform subspaces 46 Sturm bound 9408 Trace bound 2

## Defining parameters

 Level: $$N$$ = $$245 = 5 \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Newform subspaces: $$46$$ Sturm bound: $$9408$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(245))$$.

Total New Old
Modular forms 2592 2215 377
Cusp forms 2113 1925 188
Eisenstein series 479 290 189

## Trace form

 $$1925q - 27q^{2} - 30q^{3} - 39q^{4} - 50q^{5} - 114q^{6} - 44q^{7} - 75q^{8} - 57q^{9} + O(q^{10})$$ $$1925q - 27q^{2} - 30q^{3} - 39q^{4} - 50q^{5} - 114q^{6} - 44q^{7} - 75q^{8} - 57q^{9} - 72q^{10} - 114q^{11} - 102q^{12} - 60q^{13} - 72q^{14} - 113q^{15} - 171q^{16} - 72q^{17} - 135q^{18} - 78q^{19} - 116q^{20} - 158q^{21} - 138q^{22} - 90q^{23} - 102q^{24} - 66q^{25} - 156q^{26} - 66q^{27} - 80q^{28} - 72q^{29} - 27q^{30} - 126q^{31} - 63q^{32} - 42q^{33} - 60q^{34} - 57q^{35} - 111q^{36} - 4q^{37} - 18q^{38} + 32q^{39} + 66q^{40} - 72q^{41} + 42q^{42} - 30q^{43} + 78q^{44} - 5q^{45} + 6q^{46} - 54q^{47} + 104q^{48} + 40q^{49} - 201q^{50} - 126q^{51} + 92q^{52} - 96q^{53} + 18q^{54} - 18q^{55} - 12q^{56} - 90q^{57} + 72q^{58} - 18q^{59} + 19q^{60} - 22q^{61} - 6q^{62} - 60q^{63} + 21q^{64} - 49q^{65} - 222q^{66} - 30q^{67} - 84q^{68} - 90q^{69} + 3q^{70} - 258q^{71} - 195q^{72} - 48q^{73} - 96q^{74} - 51q^{75} - 210q^{76} - 126q^{77} - 30q^{78} - 66q^{79} - 5q^{80} - 129q^{81} + 54q^{82} - 6q^{83} + 208q^{84} - 87q^{85} - 36q^{86} + 78q^{87} + 240q^{88} + 267q^{90} - 82q^{91} + 48q^{92} + 270q^{93} + 120q^{94} + 101q^{95} + 300q^{96} + 42q^{97} + 408q^{98} - 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(245))$$

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
245.2.a $$\chi_{245}(1, \cdot)$$ 245.2.a.a 1 1
245.2.a.b 1
245.2.a.c 1
245.2.a.d 2
245.2.a.e 2
245.2.a.f 2
245.2.a.g 2
245.2.a.h 2
245.2.b $$\chi_{245}(99, \cdot)$$ 245.2.b.a 2 1
245.2.b.b 2
245.2.b.c 2
245.2.b.d 2
245.2.b.e 4
245.2.b.f 4
245.2.e $$\chi_{245}(116, \cdot)$$ 245.2.e.a 2 2
245.2.e.b 2
245.2.e.c 2
245.2.e.d 2
245.2.e.e 4
245.2.e.f 4
245.2.e.g 4
245.2.e.h 4
245.2.e.i 4
245.2.f $$\chi_{245}(48, \cdot)$$ 245.2.f.a 4 2
245.2.f.b 4
245.2.f.c 24
245.2.j $$\chi_{245}(79, \cdot)$$ 245.2.j.a 4 2
245.2.j.b 4
245.2.j.c 4
245.2.j.d 4
245.2.j.e 4
245.2.j.f 4
245.2.j.g 8
245.2.k $$\chi_{245}(36, \cdot)$$ 245.2.k.a 54 6
245.2.k.b 66
245.2.l $$\chi_{245}(68, \cdot)$$ 245.2.l.a 4 4
245.2.l.b 4
245.2.l.c 8
245.2.l.d 48
245.2.p $$\chi_{245}(29, \cdot)$$ 245.2.p.a 12 6
245.2.p.b 144
245.2.q $$\chi_{245}(11, \cdot)$$ 245.2.q.a 96 12
245.2.q.b 120
245.2.s $$\chi_{245}(13, \cdot)$$ 245.2.s.a 312 12
245.2.t $$\chi_{245}(4, \cdot)$$ 245.2.t.a 312 12
245.2.x $$\chi_{245}(3, \cdot)$$ 245.2.x.a 624 24

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(245))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(245)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 + 2 T + 2 T^{2}$$)($$1 + 2 T + 2 T^{2}$$)($$1 + 2 T^{2}$$)($$1 + T + 2 T^{3} + 4 T^{4}$$)($$1 + 2 T^{2} + 4 T^{4}$$)($$1 + 2 T^{2} + 4 T^{4}$$)($$1 - 2 T + 3 T^{2} - 4 T^{3} + 4 T^{4}$$)($$1 - 2 T + 3 T^{2} - 4 T^{3} + 4 T^{4}$$)($$( 1 - 2 T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$$)($$1 - 3 T^{2} + 4 T^{4}$$)($$1 - 3 T^{2} + 4 T^{4}$$)($$( 1 - 2 T^{2} )^{2}$$)($$( 1 + 2 T^{2} + 4 T^{4} )^{2}$$)($$( 1 - 3 T^{2} + 4 T^{4} )^{2}$$)($$1 - 2 T^{2} + 4 T^{4}$$)($$1 - 2 T^{2} + 4 T^{4}$$)($$1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4}$$)($$1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4}$$)($$1 + 2 T + T^{2} - 2 T^{3} - 3 T^{4} - 4 T^{5} + 4 T^{6} + 16 T^{7} + 16 T^{8}$$)($$( 1 - 2 T^{2} )^{2}( 1 + 2 T^{2} + 4 T^{4} )$$)($$( 1 - 2 T^{2} )^{2}( 1 + 2 T^{2} + 4 T^{4} )$$)($$1 - T + T^{2} + 4 T^{3} - 6 T^{4} + 8 T^{5} + 4 T^{6} - 8 T^{7} + 16 T^{8}$$)($$1 - T + T^{2} + 4 T^{3} - 6 T^{4} + 8 T^{5} + 4 T^{6} - 8 T^{7} + 16 T^{8}$$)($$1 - 2 T + 2 T^{2} - 2 T^{3} + T^{4} - 4 T^{5} + 8 T^{6} - 16 T^{7} + 16 T^{8}$$)($$1 - 2 T + 2 T^{2} - 2 T^{3} + T^{4} - 4 T^{5} + 8 T^{6} - 16 T^{7} + 16 T^{8}$$)($$( 1 - 2 T^{2} )^{2}( 1 + 2 T^{2} + 4 T^{4} )$$)($$( 1 + 2 T^{2} + 4 T^{4} )^{2}$$)($$1 + 3 T^{2} + 5 T^{4} + 12 T^{6} + 16 T^{8}$$)($$( 1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4} )( 1 + 2 T + 2 T^{2} + 4 T^{3} + 4 T^{4} )$$)($$( 1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4} )( 1 + 2 T + 2 T^{2} + 4 T^{3} + 4 T^{4} )$$)($$( 1 - 2 T^{2} )^{2}( 1 + 2 T^{2} + 4 T^{4} )$$)($$( 1 + 3 T^{2} + 5 T^{4} + 12 T^{6} + 16 T^{8} )^{2}$$)($$1 + 4 T + 5 T^{2} - 2 T^{3} - 11 T^{4} - 4 T^{5} + 20 T^{6} + 32 T^{7} + 16 T^{8}$$)($$1 - 2 T + 5 T^{2} - 8 T^{3} + 13 T^{4} - 16 T^{5} + 20 T^{6} - 16 T^{7} + 16 T^{8}$$)($$( 1 - 2 T + 2 T^{2} )^{4}( 1 + 2 T + 2 T^{2} + 4 T^{3} + 4 T^{4} )^{2}$$)($$( 1 - 2 T^{2} - 3 T^{4} + 13 T^{6} - 12 T^{8} - 32 T^{10} + 64 T^{12} )( 1 + 5 T^{2} + 18 T^{4} + 41 T^{6} + 72 T^{8} + 80 T^{10} + 64 T^{12} )$$)
$3$ ($$1 + 3 T + 3 T^{2}$$)($$1 - 3 T + 3 T^{2}$$)($$1 + T + 3 T^{2}$$)($$1 - T + 2 T^{2} - 3 T^{3} + 9 T^{4}$$)($$1 + 2 T + 5 T^{2} + 6 T^{3} + 9 T^{4}$$)($$1 - 2 T + 5 T^{2} - 6 T^{3} + 9 T^{4}$$)($$1 + 2 T + 5 T^{2} + 6 T^{3} + 9 T^{4}$$)($$1 - 2 T + 5 T^{2} - 6 T^{3} + 9 T^{4}$$)($$1 - 5 T^{2} + 9 T^{4}$$)($$1 - 5 T^{2} + 9 T^{4}$$)($$1 - 5 T^{2} + 9 T^{4}$$)($$1 - T^{2} + 9 T^{4}$$)($$( 1 - 3 T + 3 T^{2} )^{2}( 1 + 3 T + 3 T^{2} )^{2}$$)($$( 1 - 2 T + 3 T^{2} )^{2}( 1 + 2 T + 3 T^{2} )^{2}$$)($$1 + T - 2 T^{2} + 3 T^{3} + 9 T^{4}$$)($$1 - T - 2 T^{2} - 3 T^{3} + 9 T^{4}$$)($$( 1 + 3 T^{2} )( 1 + 3 T + 3 T^{2} )$$)($$( 1 - 3 T + 3 T^{2} )( 1 + 3 T^{2} )$$)($$1 - 2 T - T^{2} + 2 T^{3} + 4 T^{4} + 6 T^{5} - 9 T^{6} - 54 T^{7} + 81 T^{8}$$)($$1 + 2 T - T^{2} - 2 T^{3} + 4 T^{4} - 6 T^{5} - 9 T^{6} + 54 T^{7} + 81 T^{8}$$)($$1 - 2 T - T^{2} + 2 T^{3} + 4 T^{4} + 6 T^{5} - 9 T^{6} - 54 T^{7} + 81 T^{8}$$)($$1 + T - T^{2} - 4 T^{3} - 8 T^{4} - 12 T^{5} - 9 T^{6} + 27 T^{7} + 81 T^{8}$$)($$1 - T - T^{2} + 4 T^{3} - 8 T^{4} + 12 T^{5} - 9 T^{6} - 27 T^{7} + 81 T^{8}$$)($$1 + 2 T + 2 T^{2} + 4 T^{3} + 7 T^{4} + 12 T^{5} + 18 T^{6} + 54 T^{7} + 81 T^{8}$$)($$1 - 2 T + 2 T^{2} - 4 T^{3} + 7 T^{4} - 12 T^{5} + 18 T^{6} - 54 T^{7} + 81 T^{8}$$)($$( 1 + 3 T^{2} )^{2}( 1 + 3 T + 3 T^{2} )^{2}$$)($$1 + T^{2} - 8 T^{4} + 9 T^{6} + 81 T^{8}$$)($$1 + 5 T^{2} + 16 T^{4} + 45 T^{6} + 81 T^{8}$$)($$1 + 5 T^{2} + 16 T^{4} + 45 T^{6} + 81 T^{8}$$)($$1 + 5 T^{2} + 16 T^{4} + 45 T^{6} + 81 T^{8}$$)($$( 1 - 3 T + 3 T^{2} )^{2}( 1 + 3 T^{2} )^{2}$$)($$( 1 - 2 T + T^{2} - 6 T^{3} + 9 T^{4} )^{2}( 1 + 2 T + T^{2} + 6 T^{3} + 9 T^{4} )^{2}$$)($$1 - 2 T + 5 T^{2} - 10 T^{3} + 16 T^{4} - 30 T^{5} + 45 T^{6} - 54 T^{7} + 81 T^{8}$$)($$1 - 4 T + 5 T^{2} + 4 T^{3} - 20 T^{4} + 12 T^{5} + 45 T^{6} - 108 T^{7} + 81 T^{8}$$)($$1 + 17 T^{4} + 208 T^{8} + 1377 T^{12} + 6561 T^{16}$$)($$1 + 5 T^{2} + 2 T^{4} - 14 T^{6} + 45 T^{8} + 57 T^{10} - 512 T^{12} + 513 T^{14} + 3645 T^{16} - 10206 T^{18} + 13122 T^{20} + 295245 T^{22} + 531441 T^{24}$$)
$5$ ($$1 - T$$)($$1 + T$$)($$1 - T$$)($$( 1 + T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 + T )^{2}$$)($$( 1 - T )^{2}$$)($$1 - 4 T + 5 T^{2}$$)($$1 + 2 T + 5 T^{2}$$)($$1 - 2 T + 5 T^{2}$$)($$1 + 5 T^{2}$$)($$1 + 2 T^{2} + 25 T^{4}$$)($$1 - 8 T^{2} + 25 T^{4}$$)($$1 - T + T^{2}$$)($$1 + T + T^{2}$$)($$1 - T + T^{2}$$)($$1 + T + T^{2}$$)($$( 1 - T + T^{2} )^{2}$$)($$( 1 + T + T^{2} )^{2}$$)($$( 1 - T + T^{2} )^{2}$$)($$( 1 - T + T^{2} )^{2}$$)($$( 1 + T + T^{2} )^{2}$$)($$( 1 - 4 T + 5 T^{2} )^{2}$$)($$( 1 + 4 T + 5 T^{2} )^{2}$$)($$1 - 6 T + 17 T^{2} - 30 T^{3} + 25 T^{4}$$)($$1 - 5 T^{2} + 25 T^{4}$$)($$1 - 2 T - T^{2} - 10 T^{3} + 25 T^{4}$$)($$1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4}$$)($$1 - 4 T + 11 T^{2} - 20 T^{3} + 25 T^{4}$$)($$1 + 6 T + 17 T^{2} + 30 T^{3} + 25 T^{4}$$)($$1 + 8 T^{2} + 39 T^{4} + 200 T^{6} + 625 T^{8}$$)($$1 - 4 T + 11 T^{2} - 20 T^{3} + 25 T^{4}$$)($$1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4}$$)($$1 - 25 T^{4} + 625 T^{8}$$)($$1 + 2 T - T^{2} - 12 T^{3} - 19 T^{4} + 22 T^{5} + 139 T^{6} + 110 T^{7} - 475 T^{8} - 1500 T^{9} - 625 T^{10} + 6250 T^{11} + 15625 T^{12}$$)
$7$ ($$1 + 7 T^{2} + 49 T^{4} + 343 T^{6} + 2401 T^{8} + 16807 T^{10} + 117649 T^{12}$$)
$11$ ($$1 - T + 11 T^{2}$$)($$1 - T + 11 T^{2}$$)($$1 + 3 T + 11 T^{2}$$)($$1 - T + 18 T^{2} - 11 T^{3} + 121 T^{4}$$)($$1 + 6 T + 23 T^{2} + 66 T^{3} + 121 T^{4}$$)($$1 + 6 T + 23 T^{2} + 66 T^{3} + 121 T^{4}$$)($$1 - 4 T + 18 T^{2} - 44 T^{3} + 121 T^{4}$$)($$1 - 4 T + 18 T^{2} - 44 T^{3} + 121 T^{4}$$)($$( 1 + 3 T + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 3 T + 11 T^{2} )^{2}$$)($$( 1 - 5 T + 11 T^{2} )^{4}$$)($$( 1 + 11 T^{2} )^{4}$$)($$1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4}$$)($$1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4}$$)($$1 + T - 10 T^{2} + 11 T^{3} + 121 T^{4}$$)($$1 + T - 10 T^{2} + 11 T^{3} + 121 T^{4}$$)($$1 + 4 T - 2 T^{2} - 16 T^{3} + 27 T^{4} - 176 T^{5} - 242 T^{6} + 5324 T^{7} + 14641 T^{8}$$)($$( 1 - 6 T + 23 T^{2} - 66 T^{3} + 121 T^{4} )( 1 - 10 T^{2} + 121 T^{4} )$$)($$( 1 - 6 T + 23 T^{2} - 66 T^{3} + 121 T^{4} )( 1 - 10 T^{2} + 121 T^{4} )$$)($$1 + T - 17 T^{2} - 4 T^{3} + 192 T^{4} - 44 T^{5} - 2057 T^{6} + 1331 T^{7} + 14641 T^{8}$$)($$1 + T - 17 T^{2} - 4 T^{3} + 192 T^{4} - 44 T^{5} - 2057 T^{6} + 1331 T^{7} + 14641 T^{8}$$)($$( 1 + 2 T + 20 T^{2} + 22 T^{3} + 121 T^{4} )^{2}$$)($$( 1 + 2 T + 20 T^{2} + 22 T^{3} + 121 T^{4} )^{2}$$)($$( 1 + 5 T + 14 T^{2} + 55 T^{3} + 121 T^{4} )^{2}$$)($$( 1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4} )^{2}$$)($$( 1 - 11 T^{2} + 121 T^{4} )^{2}$$)($$( 1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4} )^{2}$$)($$( 1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4} )^{2}$$)($$( 1 + 5 T + 14 T^{2} + 55 T^{3} + 121 T^{4} )^{2}$$)($$( 1 - 11 T^{2} + 121 T^{4} )^{4}$$)($$1 - 2 T - 16 T^{2} + 4 T^{3} + 235 T^{4} + 44 T^{5} - 1936 T^{6} - 2662 T^{7} + 14641 T^{8}$$)($$1 - 2 T - 16 T^{2} + 4 T^{3} + 235 T^{4} + 44 T^{5} - 1936 T^{6} - 2662 T^{7} + 14641 T^{8}$$)($$( 1 - T - 10 T^{2} - 11 T^{3} + 121 T^{4} )^{4}$$)($$( 1 + 14 T + 73 T^{2} + 126 T^{3} - 327 T^{4} - 2128 T^{5} - 6819 T^{6} - 23408 T^{7} - 39567 T^{8} + 167706 T^{9} + 1068793 T^{10} + 2254714 T^{11} + 1771561 T^{12} )^{2}$$)
$13$ ($$1 + 3 T + 13 T^{2}$$)($$1 - 3 T + 13 T^{2}$$)($$1 + 5 T + 13 T^{2}$$)($$1 + 5 T + 28 T^{2} + 65 T^{3} + 169 T^{4}$$)($$1 + 6 T + 33 T^{2} + 78 T^{3} + 169 T^{4}$$)($$1 - 6 T + 33 T^{2} - 78 T^{3} + 169 T^{4}$$)($$1 - 4 T + 22 T^{2} - 52 T^{3} + 169 T^{4}$$)($$1 + 4 T + 22 T^{2} + 52 T^{3} + 169 T^{4}$$)($$1 - 25 T^{2} + 169 T^{4}$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$1 + 19 T^{2} + 169 T^{4}$$)($$( 1 - 7 T + 13 T^{2} )^{2}( 1 + 7 T + 13 T^{2} )^{2}$$)($$( 1 - 8 T^{2} + 169 T^{4} )^{2}$$)($$( 1 - 5 T + 13 T^{2} )^{2}$$)($$( 1 + 5 T + 13 T^{2} )^{2}$$)($$( 1 - 3 T + 13 T^{2} )^{2}$$)($$( 1 + 3 T + 13 T^{2} )^{2}$$)($$( 1 - 4 T + 22 T^{2} - 52 T^{3} + 169 T^{4} )^{2}$$)($$( 1 - 6 T + 33 T^{2} - 78 T^{3} + 169 T^{4} )^{2}$$)($$( 1 + 6 T + 33 T^{2} + 78 T^{3} + 169 T^{4} )^{2}$$)($$( 1 + 5 T + 28 T^{2} + 65 T^{3} + 169 T^{4} )^{2}$$)($$( 1 - 5 T + 28 T^{2} - 65 T^{3} + 169 T^{4} )^{2}$$)($$( 1 - 4 T + 8 T^{2} - 52 T^{3} + 169 T^{4} )^{2}$$)($$( 1 + 4 T + 8 T^{2} + 52 T^{3} + 169 T^{4} )^{2}$$)($$( 1 - 7 T + 13 T^{2} )^{2}( 1 + 7 T + 13 T^{2} )^{2}$$)($$( 1 + 19 T^{2} + 169 T^{4} )^{2}$$)($$( 1 - 22 T^{2} + 169 T^{4} )^{2}$$)($$( 1 - 25 T^{2} + 169 T^{4} )^{2}$$)($$( 1 - 25 T^{2} + 169 T^{4} )^{2}$$)($$( 1 - 7 T + 13 T^{2} )^{2}( 1 + 7 T + 13 T^{2} )^{2}$$)($$( 1 - 8 T^{2} + 169 T^{4} )^{4}$$)($$( 1 + 4 T + 8 T^{2} + 52 T^{3} + 169 T^{4} )^{2}$$)($$( 1 - 4 T + 8 T^{2} - 52 T^{3} + 169 T^{4} )^{2}$$)($$( 1 + 103 T^{4} + 28561 T^{8} )^{2}$$)($$1 - 6 T^{2} - 77 T^{4} + 1252 T^{6} + 23533 T^{8} + 175994 T^{10} - 4322513 T^{12} + 29742986 T^{14} + 672126013 T^{16} + 6043164868 T^{18} - 62811265517 T^{20} - 827150951094 T^{22} + 23298085122481 T^{24}$$)
$17$ ($$1 - 3 T + 17 T^{2}$$)($$1 + 3 T + 17 T^{2}$$)($$1 + 3 T + 17 T^{2}$$)($$1 - 5 T + 36 T^{2} - 85 T^{3} + 289 T^{4}$$)($$1 - 2 T + 17 T^{2} - 34 T^{3} + 289 T^{4}$$)($$1 + 2 T + 17 T^{2} + 34 T^{3} + 289 T^{4}$$)($$1 + 4 T + 30 T^{2} + 68 T^{3} + 289 T^{4}$$)($$1 - 4 T + 30 T^{2} - 68 T^{3} + 289 T^{4}$$)($$1 + 15 T^{2} + 289 T^{4}$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$1 - 29 T^{2} + 289 T^{4}$$)($$( 1 - 31 T^{2} + 289 T^{4} )^{2}$$)($$( 1 - 16 T^{2} + 289 T^{4} )^{2}$$)($$1 + 3 T - 8 T^{2} + 51 T^{3} + 289 T^{4}$$)($$1 - 3 T - 8 T^{2} - 51 T^{3} + 289 T^{4}$$)($$1 - 3 T - 8 T^{2} - 51 T^{3} + 289 T^{4}$$)($$1 + 3 T - 8 T^{2} + 51 T^{3} + 289 T^{4}$$)($$1 - 4 T - 14 T^{2} + 16 T^{3} + 339 T^{4} + 272 T^{5} - 4046 T^{6} - 19652 T^{7} + 83521 T^{8}$$)($$1 - 2 T - 13 T^{2} + 34 T^{3} - 68 T^{4} + 578 T^{5} - 3757 T^{6} - 9826 T^{7} + 83521 T^{8}$$)($$1 + 2 T - 13 T^{2} - 34 T^{3} - 68 T^{4} - 578 T^{5} - 3757 T^{6} + 9826 T^{7} + 83521 T^{8}$$)($$1 + 5 T - 11 T^{2} + 10 T^{3} + 582 T^{4} + 170 T^{5} - 3179 T^{6} + 24565 T^{7} + 83521 T^{8}$$)($$1 - 5 T - 11 T^{2} - 10 T^{3} + 582 T^{4} - 170 T^{5} - 3179 T^{6} - 24565 T^{7} + 83521 T^{8}$$)($$1 - 4 T + 8 T^{2} - 52 T^{3} + 322 T^{4} - 884 T^{5} + 2312 T^{6} - 19652 T^{7} + 83521 T^{8}$$)($$1 + 4 T + 8 T^{2} + 52 T^{3} + 322 T^{4} + 884 T^{5} + 2312 T^{6} + 19652 T^{7} + 83521 T^{8}$$)($$( 1 + 3 T + 20 T^{2} + 51 T^{3} + 289 T^{4} )^{2}$$)($$1 + 29 T^{2} + 552 T^{4} + 8381 T^{6} + 83521 T^{8}$$)($$( 1 - 8 T + 47 T^{2} - 136 T^{3} + 289 T^{4} )( 1 + 8 T + 47 T^{2} + 136 T^{3} + 289 T^{4} )$$)($$1 - 15 T^{2} - 64 T^{4} - 4335 T^{6} + 83521 T^{8}$$)($$1 - 15 T^{2} - 64 T^{4} - 4335 T^{6} + 83521 T^{8}$$)($$( 1 - 3 T + 20 T^{2} - 51 T^{3} + 289 T^{4} )^{2}$$)($$( 1 + 16 T^{2} - 33 T^{4} + 4624 T^{6} + 83521 T^{8} )^{2}$$)($$1 + 4 T + 20 T^{2} + 100 T^{3} + 271 T^{4} + 1700 T^{5} + 5780 T^{6} + 19652 T^{7} + 83521 T^{8}$$)($$1 + 8 T + 20 T^{2} - 52 T^{3} - 545 T^{4} - 884 T^{5} + 5780 T^{6} + 39304 T^{7} + 83521 T^{8}$$)($$1 - 263 T^{4} - 14352 T^{8} - 21966023 T^{12} + 6975757441 T^{16}$$)($$1 - 26 T^{2} + 891 T^{4} - 9884 T^{6} + 300429 T^{8} - 3560978 T^{10} + 113340359 T^{12} - 1029122642 T^{14} + 25092130509 T^{16} - 238575731996 T^{18} + 6215399879931 T^{20} - 52415841411674 T^{22} + 582622237229761 T^{24}$$)
$19$ ($$1 + 6 T + 19 T^{2}$$)($$1 - 6 T + 19 T^{2}$$)($$1 + 2 T + 19 T^{2}$$)($$1 - 6 T + 30 T^{2} - 114 T^{3} + 361 T^{4}$$)($$( 1 + 6 T + 19 T^{2} )^{2}$$)($$( 1 - 6 T + 19 T^{2} )^{2}$$)($$1 + 30 T^{2} + 361 T^{4}$$)($$1 + 30 T^{2} + 361 T^{4}$$)($$( 1 + 19 T^{2} )^{2}$$)($$( 1 - 6 T + 19 T^{2} )^{2}$$)($$( 1 + 6 T + 19 T^{2} )^{2}$$)($$( 1 + 19 T^{2} )^{2}$$)($$( 1 + 30 T^{2} + 361 T^{4} )^{2}$$)($$( 1 + 30 T^{2} + 361 T^{4} )^{2}$$)($$1 + 2 T - 15 T^{2} + 38 T^{3} + 361 T^{4}$$)($$1 - 2 T - 15 T^{2} - 38 T^{3} + 361 T^{4}$$)($$1 + 6 T + 17 T^{2} + 114 T^{3} + 361 T^{4}$$)($$1 - 6 T + 17 T^{2} - 114 T^{3} + 361 T^{4}$$)($$1 - 30 T^{2} + 539 T^{4} - 10830 T^{6} + 130321 T^{8}$$)($$( 1 + 6 T + 17 T^{2} + 114 T^{3} + 361 T^{4} )^{2}$$)($$( 1 - 6 T + 17 T^{2} - 114 T^{3} + 361 T^{4} )^{2}$$)($$1 + 6 T + 6 T^{2} - 48 T^{3} - 145 T^{4} - 912 T^{5} + 2166 T^{6} + 41154 T^{7} + 130321 T^{8}$$)($$1 - 6 T + 6 T^{2} + 48 T^{3} - 145 T^{4} + 912 T^{5} + 2166 T^{6} - 41154 T^{7} + 130321 T^{8}$$)($$( 1 + 2 T + 36 T^{2} + 38 T^{3} + 361 T^{4} )^{2}$$)($$( 1 - 2 T + 36 T^{2} - 38 T^{3} + 361 T^{4} )^{2}$$)($$1 - 30 T^{2} + 539 T^{4} - 10830 T^{6} + 130321 T^{8}$$)($$( 1 - 19 T^{2} + 361 T^{4} )^{2}$$)($$( 1 + 6 T + 17 T^{2} + 114 T^{3} + 361 T^{4} )^{2}$$)($$( 1 - 19 T^{2} + 361 T^{4} )^{2}$$)($$( 1 - 19 T^{2} + 361 T^{4} )^{2}$$)($$1 - 30 T^{2} + 539 T^{4} - 10830 T^{6} + 130321 T^{8}$$)($$( 1 - 30 T^{2} + 539 T^{4} - 10830 T^{6} + 130321 T^{8} )^{2}$$)($$1 + 2 T - 32 T^{2} - 4 T^{3} + 859 T^{4} - 76 T^{5} - 11552 T^{6} + 13718 T^{7} + 130321 T^{8}$$)($$1 - 2 T - 32 T^{2} + 4 T^{3} + 859 T^{4} + 76 T^{5} - 11552 T^{6} - 13718 T^{7} + 130321 T^{8}$$)($$( 1 - 28 T^{2} + 423 T^{4} - 10108 T^{6} + 130321 T^{8} )^{2}$$)($$( 1 + 4 T + 53 T^{2} + 144 T^{3} + 1007 T^{4} + 1444 T^{5} + 6859 T^{6} )^{4}$$)
$23$ ($$1 + 4 T + 23 T^{2}$$)($$1 + 4 T + 23 T^{2}$$)($$1 + 6 T + 23 T^{2}$$)($$1 + 2 T + 30 T^{2} + 46 T^{3} + 529 T^{4}$$)($$1 - 12 T + 80 T^{2} - 276 T^{3} + 529 T^{4}$$)($$1 - 12 T + 80 T^{2} - 276 T^{3} + 529 T^{4}$$)($$1 + 2 T + 45 T^{2} + 46 T^{3} + 529 T^{4}$$)($$1 + 2 T + 45 T^{2} + 46 T^{3} + 529 T^{4}$$)($$1 - 10 T^{2} + 529 T^{4}$$)($$1 - 37 T^{2} + 529 T^{4}$$)($$1 - 37 T^{2} + 529 T^{4}$$)($$( 1 - 23 T^{2} )^{2}$$)($$( 1 - 40 T^{2} + 529 T^{4} )^{2}$$)($$( 1 - 30 T^{2} + 529 T^{4} )^{2}$$)($$1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4}$$)($$1 - 6 T + 13 T^{2} - 138 T^{3} + 529 T^{4}$$)($$1 - 4 T - 7 T^{2} - 92 T^{3} + 529 T^{4}$$)($$1 - 4 T - 7 T^{2} - 92 T^{3} + 529 T^{4}$$)($$1 - 2 T - 41 T^{2} + 2 T^{3} + 1404 T^{4} + 46 T^{5} - 21689 T^{6} - 24334 T^{7} + 279841 T^{8}$$)($$1 + 12 T + 64 T^{2} + 408 T^{3} + 2559 T^{4} + 9384 T^{5} + 33856 T^{6} + 146004 T^{7} + 279841 T^{8}$$)($$1 + 12 T + 64 T^{2} + 408 T^{3} + 2559 T^{4} + 9384 T^{5} + 33856 T^{6} + 146004 T^{7} + 279841 T^{8}$$)($$1 - 2 T - 26 T^{2} + 32 T^{3} + 279 T^{4} + 736 T^{5} - 13754 T^{6} - 24334 T^{7} + 279841 T^{8}$$)($$1 - 2 T - 26 T^{2} + 32 T^{3} + 279 T^{4} + 736 T^{5} - 13754 T^{6} - 24334 T^{7} + 279841 T^{8}$$)($$1 + 10 T + 50 T^{2} + 220 T^{3} + 967 T^{4} + 5060 T^{5} + 26450 T^{6} + 121670 T^{7} + 279841 T^{8}$$)($$1 + 10 T + 50 T^{2} + 220 T^{3} + 967 T^{4} + 5060 T^{5} + 26450 T^{6} + 121670 T^{7} + 279841 T^{8}$$)($$1 + 40 T^{2} + 1071 T^{4} + 21160 T^{6} + 279841 T^{8}$$)($$( 1 + 23 T^{2} + 529 T^{4} )^{2}$$)($$1 + 37 T^{2} + 840 T^{4} + 19573 T^{6} + 279841 T^{8}$$)($$1 + 10 T^{2} - 429 T^{4} + 5290 T^{6} + 279841 T^{8}$$)($$1 + 10 T^{2} - 429 T^{4} + 5290 T^{6} + 279841 T^{8}$$)($$1 + 40 T^{2} + 1071 T^{4} + 21160 T^{6} + 279841 T^{8}$$)($$( 1 + 30 T^{2} + 371 T^{4} + 15870 T^{6} + 279841 T^{8} )^{2}$$)($$1 + 4 T + 53 T^{2} + 244 T^{3} + 1588 T^{4} + 5612 T^{5} + 28037 T^{6} + 48668 T^{7} + 279841 T^{8}$$)($$1 - 14 T + 53 T^{2} + 226 T^{3} - 2552 T^{4} + 5198 T^{5} + 28037 T^{6} - 170338 T^{7} + 279841 T^{8}$$)($$( 1 + 4 T + 8 T^{2} - 152 T^{3} - 833 T^{4} - 3496 T^{5} + 4232 T^{6} + 48668 T^{7} + 279841 T^{8} )^{2}$$)($$1 + 30 T^{2} + 539 T^{4} + 12228 T^{6} + 661141 T^{8} + 13159818 T^{10} + 257453015 T^{12} + 6961543722 T^{14} + 185014358581 T^{16} + 1810182850692 T^{18} + 42209621066459 T^{20} + 1242795336409470 T^{22} + 21914624432020321 T^{24}$$)
$29$ ($$1 + T + 29 T^{2}$$)($$1 + T + 29 T^{2}$$)($$1 - 3 T + 29 T^{2}$$)($$1 - T + 20 T^{2} - 29 T^{3} + 841 T^{4}$$)($$1 + 6 T + 35 T^{2} + 174 T^{3} + 841 T^{4}$$)($$1 + 6 T + 35 T^{2} + 174 T^{3} + 841 T^{4}$$)($$( 1 + T + 29 T^{2} )^{2}$$)($$( 1 + T + 29 T^{2} )^{2}$$)($$( 1 - 5 T + 29 T^{2} )^{2}$$)($$( 1 + 7 T + 29 T^{2} )^{2}$$)($$( 1 + 7 T + 29 T^{2} )^{2}$$)($$( 1 - 9 T + 29 T^{2} )^{2}$$)($$( 1 + 5 T + 29 T^{2} )^{4}$$)($$( 1 + 29 T^{2} )^{4}$$)($$( 1 - 3 T + 29 T^{2} )^{2}$$)($$( 1 - 3 T + 29 T^{2} )^{2}$$)($$( 1 + T + 29 T^{2} )^{2}$$)($$( 1 + T + 29 T^{2} )^{2}$$)($$( 1 + T + 29 T^{2} )^{4}$$)($$( 1 + 6 T + 35 T^{2} + 174 T^{3} + 841 T^{4} )^{2}$$)($$( 1 + 6 T + 35 T^{2} + 174 T^{3} + 841 T^{4} )^{2}$$)($$( 1 - T + 20 T^{2} - 29 T^{3} + 841 T^{4} )^{2}$$)($$( 1 - T + 20 T^{2} - 29 T^{3} + 841 T^{4} )^{2}$$)($$( 1 - 49 T^{2} + 841 T^{4} )^{2}$$)($$( 1 - 49 T^{2} + 841 T^{4} )^{2}$$)($$( 1 + 5 T + 29 T^{2} )^{4}$$)($$( 1 - 9 T + 29 T^{2} )^{4}$$)($$( 1 + 7 T + 29 T^{2} )^{4}$$)($$( 1 - 5 T + 29 T^{2} )^{4}$$)($$( 1 - 5 T + 29 T^{2} )^{4}$$)($$( 1 + 5 T + 29 T^{2} )^{4}$$)($$( 1 + 29 T^{2} )^{8}$$)($$( 1 - 49 T^{2} + 841 T^{4} )^{2}$$)($$( 1 - 49 T^{2} + 841 T^{4} )^{2}$$)($$( 1 - 49 T^{2} + 841 T^{4} )^{4}$$)($$( 1 - 7 T - 22 T^{2} + 574 T^{3} - 2183 T^{4} - 9863 T^{5} + 129240 T^{6} - 286027 T^{7} - 1835903 T^{8} + 13999286 T^{9} - 15560182 T^{10} - 143578043 T^{11} + 594823321 T^{12} )^{2}$$)
$31$ ($$1 + 6 T + 31 T^{2}$$)($$1 - 6 T + 31 T^{2}$$)($$1 - 4 T + 31 T^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$1 + 12 T + 80 T^{2} + 372 T^{3} + 961 T^{4}$$)($$1 - 12 T + 80 T^{2} - 372 T^{3} + 961 T^{4}$$)($$( 1 - 6 T + 31 T^{2} )^{2}$$)($$( 1 + 6 T + 31 T^{2} )^{2}$$)($$( 1 + 2 T + 31 T^{2} )^{2}$$)($$( 1 + 2 T + 31 T^{2} )^{2}$$)($$( 1 - 2 T + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 60 T^{2} + 961 T^{4} )^{2}$$)($$( 1 + 30 T^{2} + 961 T^{4} )^{2}$$)($$( 1 - 11 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} )$$)($$( 1 - 7 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} )$$)($$1 + 6 T + 5 T^{2} + 186 T^{3} + 961 T^{4}$$)($$1 - 6 T + 5 T^{2} - 186 T^{3} + 961 T^{4}$$)($$( 1 + 6 T + 5 T^{2} + 186 T^{3} + 961 T^{4} )^{2}$$)($$1 + 12 T + 64 T^{2} + 216 T^{3} + 975 T^{4} + 6696 T^{5} + 61504 T^{6} + 357492 T^{7} + 923521 T^{8}$$)($$1 - 12 T + 64 T^{2} - 216 T^{3} + 975 T^{4} - 6696 T^{5} + 61504 T^{6} - 357492 T^{7} + 923521 T^{8}$$)($$( 1 - 31 T^{2} + 961 T^{4} )^{2}$$)($$( 1 - 31 T^{2} + 961 T^{4} )^{2}$$)($$1 - 68 T^{2} + 2310 T^{4} - 65348 T^{6} + 923521 T^{8}$$)($$1 - 68 T^{2} + 2310 T^{4} - 65348 T^{6} + 923521 T^{8}$$)($$1 - 60 T^{2} + 2639 T^{4} - 57660 T^{6} + 923521 T^{8}$$)($$( 1 - 31 T^{2} + 961 T^{4} )^{2}$$)($$( 1 - 2 T - 27 T^{2} - 62 T^{3} + 961 T^{4} )^{2}$$)($$( 1 - 2 T - 27 T^{2} - 62 T^{3} + 961 T^{4} )^{2}$$)($$( 1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4} )^{2}$$)($$1 - 60 T^{2} + 2639 T^{4} - 57660 T^{6} + 923521 T^{8}$$)($$( 1 - 30 T^{2} - 61 T^{4} - 28830 T^{6} + 923521 T^{8} )^{2}$$)($$1 - 12 T + 106 T^{2} - 696 T^{3} + 3891 T^{4} - 21576 T^{5} + 101866 T^{6} - 357492 T^{7} + 923521 T^{8}$$)($$1 - 12 T + 106 T^{2} - 696 T^{3} + 3891 T^{4} - 21576 T^{5} + 101866 T^{6} - 357492 T^{7} + 923521 T^{8}$$)($$( 1 + 52 T^{2} + 1743 T^{4} + 49972 T^{6} + 923521 T^{8} )^{2}$$)($$( 1 - 6 T + 77 T^{2} - 268 T^{3} + 2387 T^{4} - 5766 T^{5} + 29791 T^{6} )^{4}$$)
$37$ ($$1 + 37 T^{2}$$)($$1 + 37 T^{2}$$)($$1 - 2 T + 37 T^{2}$$)($$( 1 - 6 T + 37 T^{2} )^{2}$$)($$1 + 4 T + 60 T^{2} + 148 T^{3} + 1369 T^{4}$$)($$1 + 4 T + 60 T^{2} + 148 T^{3} + 1369 T^{4}$$)($$( 1 + 37 T^{2} )^{2}$$)($$( 1 + 37 T^{2} )^{2}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 - 10 T^{2} + 1369 T^{4}$$)($$1 - 10 T^{2} + 1369 T^{4}$$)($$( 1 - 37 T^{2} )^{2}$$)($$( 1 - 68 T^{2} + 1369 T^{4} )^{2}$$)($$( 1 - 38 T^{2} + 1369 T^{4} )^{2}$$)($$1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4}$$)($$1 + 2 T - 33 T^{2} + 74 T^{3} + 1369 T^{4}$$)($$1 - 37 T^{2} + 1369 T^{4}$$)($$1 - 37 T^{2} + 1369 T^{4}$$)($$( 1 - 37 T^{2} + 1369 T^{4} )^{2}$$)($$1 - 4 T - 44 T^{2} + 56 T^{3} + 1639 T^{4} + 2072 T^{5} - 60236 T^{6} - 202612 T^{7} + 1874161 T^{8}$$)($$1 - 4 T - 44 T^{2} + 56 T^{3} + 1639 T^{4} + 2072 T^{5} - 60236 T^{6} - 202612 T^{7} + 1874161 T^{8}$$)($$( 1 + 6 T - T^{2} + 222 T^{3} + 1369 T^{4} )^{2}$$)($$( 1 + 6 T - T^{2} + 222 T^{3} + 1369 T^{4} )^{2}$$)($$1 - 238 T^{4} + 1874161 T^{8}$$)($$1 - 238 T^{4} + 1874161 T^{8}$$)($$1 + 68 T^{2} + 3255 T^{4} + 93092 T^{6} + 1874161 T^{8}$$)($$( 1 + 37 T^{2} + 1369 T^{4} )^{2}$$)($$1 + 10 T^{2} - 1269 T^{4} + 13690 T^{6} + 1874161 T^{8}$$)($$( 1 - 12 T + 107 T^{2} - 444 T^{3} + 1369 T^{4} )( 1 + 12 T + 107 T^{2} + 444 T^{3} + 1369 T^{4} )$$)($$( 1 - 12 T + 107 T^{2} - 444 T^{3} + 1369 T^{4} )( 1 + 12 T + 107 T^{2} + 444 T^{3} + 1369 T^{4} )$$)($$1 + 68 T^{2} + 3255 T^{4} + 93092 T^{6} + 1874161 T^{8}$$)($$( 1 + 38 T^{2} + 75 T^{4} + 52022 T^{6} + 1874161 T^{8} )^{2}$$)($$1 - 12 T + 72 T^{2} - 288 T^{3} + 983 T^{4} - 10656 T^{5} + 98568 T^{6} - 607836 T^{7} + 1874161 T^{8}$$)($$1 + 12 T + 72 T^{2} + 288 T^{3} + 983 T^{4} + 10656 T^{5} + 98568 T^{6} + 607836 T^{7} + 1874161 T^{8}$$)($$( 1 - 12 T + 72 T^{2} + 24 T^{3} - 1513 T^{4} + 888 T^{5} + 98568 T^{6} - 607836 T^{7} + 1874161 T^{8} )^{2}$$)($$1 - 46 T^{2} + 579 T^{4} + 1816 T^{6} - 1913083 T^{8} + 90111942 T^{10} - 1485070433 T^{12} + 123363248598 T^{14} - 3585425548363 T^{16} + 4659359158744 T^{18} + 2033725603820259 T^{20} - 221194881131221054 T^{22} + 6582952005840035281 T^{24}$$)
$41$ ($$1 + 6 T + 41 T^{2}$$)($$1 - 6 T + 41 T^{2}$$)($$1 - 12 T + 41 T^{2}$$)($$1 + 2 T + 66 T^{2} + 82 T^{3} + 1681 T^{4}$$)($$1 - 4 T + 68 T^{2} - 164 T^{3} + 1681 T^{4}$$)($$1 + 4 T + 68 T^{2} + 164 T^{3} + 1681 T^{4}$$)($$1 - 10 T + 99 T^{2} - 410 T^{3} + 1681 T^{4}$$)($$1 + 10 T + 99 T^{2} + 410 T^{3} + 1681 T^{4}$$)($$( 1 + 2 T + 41 T^{2} )^{2}$$)($$( 1 + 5 T + 41 T^{2} )^{2}$$)($$( 1 - 5 T + 41 T^{2} )^{2}$$)($$( 1 + 41 T^{2} )^{2}$$)($$( 1 - 16 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 + 64 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 + 12 T + 41 T^{2} )^{2}$$)($$( 1 - 12 T + 41 T^{2} )^{2}$$)($$( 1 - 6 T + 41 T^{2} )^{2}$$)($$( 1 + 6 T + 41 T^{2} )^{2}$$)($$( 1 - 10 T + 99 T^{2} - 410 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 + 4 T + 68 T^{2} + 164 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 - 4 T + 68 T^{2} - 164 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 + 2 T + 66 T^{2} + 82 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 - 2 T + 66 T^{2} - 82 T^{3} + 1681 T^{4} )^{2}$$)($$1 - 122 T^{2} + 6651 T^{4} - 205082 T^{6} + 2825761 T^{8}$$)($$1 - 122 T^{2} + 6651 T^{4} - 205082 T^{6} + 2825761 T^{8}$$)($$( 1 - 16 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 + 41 T^{2} )^{4}$$)($$( 1 + 5 T + 41 T^{2} )^{4}$$)($$( 1 + 2 T + 41 T^{2} )^{4}$$)($$( 1 - 2 T + 41 T^{2} )^{4}$$)($$( 1 - 16 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 + 64 T^{2} + 1681 T^{4} )^{4}$$)($$1 - 122 T^{2} + 6651 T^{4} - 205082 T^{6} + 2825761 T^{8}$$)($$1 - 122 T^{2} + 6651 T^{4} - 205082 T^{6} + 2825761 T^{8}$$)($$( 1 + 8 T^{2} + 1681 T^{4} )^{4}$$)($$( 1 - 2 T - 37 T^{2} + 156 T^{3} + 1485 T^{4} + 1554 T^{5} - 63713 T^{6} + 63714 T^{7} + 2496285 T^{8} + 10751676 T^{9} - 104553157 T^{10} - 231712402 T^{11} + 4750104241 T^{12} )^{2}$$)
$43$ ($$1 + 6 T + 43 T^{2}$$)($$1 + 6 T + 43 T^{2}$$)($$1 + 10 T + 43 T^{2}$$)($$1 - 10 T + 94 T^{2} - 430 T^{3} + 1849 T^{4}$$)($$( 1 - 2 T + 43 T^{2} )^{2}$$)($$( 1 - 2 T + 43 T^{2} )^{2}$$)($$1 - 10 T + 109 T^{2} - 430 T^{3} + 1849 T^{4}$$)($$1 - 10 T + 109 T^{2} - 430 T^{3} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 37 T^{2} + 1849 T^{4}$$)($$1 - 37 T^{2} + 1849 T^{4}$$)($$( 1 - 43 T^{2} )^{2}$$)($$( 1 - 43 T^{2} )^{4}$$)($$( 1 - 43 T^{2} )^{4}$$)($$( 1 + 10 T + 43 T^{2} )^{2}$$)($$( 1 + 10 T + 43 T^{2} )^{2}$$)($$( 1 + 6 T + 43 T^{2} )^{2}$$)($$( 1 + 6 T + 43 T^{2} )^{2}$$)($$( 1 - 10 T + 109 T^{2} - 430 T^{3} + 1849 T^{4} )^{2}$$)($$( 1 - 2 T + 43 T^{2} )^{4}$$)($$( 1 - 2 T + 43 T^{2} )^{4}$$)($$( 1 - 10 T + 94 T^{2} - 430 T^{3} + 1849 T^{4} )^{2}$$)($$( 1 - 10 T + 94 T^{2} - 430 T^{3} + 1849 T^{4} )^{2}$$)($$1 + 6 T + 18 T^{2} + 60 T^{3} - 889 T^{4} + 2580 T^{5} + 33282 T^{6} + 477042 T^{7} + 3418801 T^{8}$$)($$1 + 6 T + 18 T^{2} + 60 T^{3} - 889 T^{4} + 2580 T^{5} + 33282 T^{6} + 477042 T^{7} + 3418801 T^{8}$$)($$( 1 - 43 T^{2} )^{4}$$)($$( 1 - 43 T^{2} )^{4}$$)($$( 1 - 37 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 - 70 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 - 70 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 - 43 T^{2} )^{4}$$)($$( 1 - 43 T^{2} )^{8}$$)($$1 + 6 T + 18 T^{2} + 60 T^{3} - 889 T^{4} + 2580 T^{5} + 33282 T^{6} + 477042 T^{7} + 3418801 T^{8}$$)($$1 + 6 T + 18 T^{2} + 60 T^{3} - 889 T^{4} + 2580 T^{5} + 33282 T^{6} + 477042 T^{7} + 3418801 T^{8}$$)($$( 1 + 6 T + 18 T^{2} + 258 T^{3} + 1849 T^{4} )^{4}$$)($$1 + 86 T^{2} + 2019 T^{4} - 10076 T^{6} - 426043 T^{8} - 67792782 T^{10} - 6763193633 T^{12} - 125348853918 T^{14} - 1456556234443 T^{16} - 63694054081724 T^{18} + 23598476360476419 T^{20} + 1858587478942445414 T^{22} + 39959630797262576401 T^{24}$$)
$47$ ($$1 - 9 T + 47 T^{2}$$)($$1 + 9 T + 47 T^{2}$$)($$1 + 9 T + 47 T^{2}$$)($$1 - 5 T + 62 T^{2} - 235 T^{3} + 2209 T^{4}$$)($$1 - 6 T + 85 T^{2} - 282 T^{3} + 2209 T^{4}$$)($$1 + 6 T + 85 T^{2} + 282 T^{3} + 2209 T^{4}$$)($$( 1 + 2 T + 47 T^{2} )^{2}$$)($$( 1 - 2 T + 47 T^{2} )^{2}$$)($$1 - 85 T^{2} + 2209 T^{4}$$)($$( 1 - 47 T^{2} )^{2}$$)($$( 1 - 47 T^{2} )^{2}$$)($$1 + 31 T^{2} + 2209 T^{4}$$)($$( 1 - 19 T^{2} + 2209 T^{4} )^{2}$$)($$( 1 - 47 T^{2} )^{4}$$)($$1 + 9 T + 34 T^{2} + 423 T^{3} + 2209 T^{4}$$)($$1 - 9 T + 34 T^{2} - 423 T^{3} + 2209 T^{4}$$)($$1 - 9 T + 34 T^{2} - 423 T^{3} + 2209 T^{4}$$)($$1 + 9 T + 34 T^{2} + 423 T^{3} + 2209 T^{4}$$)($$( 1 - 2 T - 43 T^{2} - 94 T^{3} + 2209 T^{4} )^{2}$$)($$1 - 6 T - 49 T^{2} + 54 T^{3} + 3324 T^{4} + 2538 T^{5} - 108241 T^{6} - 622938 T^{7} + 4879681 T^{8}$$)($$1 + 6 T - 49 T^{2} - 54 T^{3} + 3324 T^{4} - 2538 T^{5} - 108241 T^{6} + 622938 T^{7} + 4879681 T^{8}$$)($$1 + 5 T - 37 T^{2} - 160 T^{3} + 460 T^{4} - 7520 T^{5} - 81733 T^{6} + 519115 T^{7} + 4879681 T^{8}$$)($$1 - 5 T - 37 T^{2} + 160 T^{3} + 460 T^{4} + 7520 T^{5} - 81733 T^{6} - 519115 T^{7} + 4879681 T^{8}$$)($$1 + 12 T + 72 T^{2} + 492 T^{3} + 3326 T^{4} + 23124 T^{5} + 159048 T^{6} + 1245876 T^{7} + 4879681 T^{8}$$)($$1 - 12 T + 72 T^{2} - 492 T^{3} + 3326 T^{4} - 23124 T^{5} + 159048 T^{6} - 1245876 T^{7} + 4879681 T^{8}$$)($$( 1 + 15 T + 122 T^{2} + 705 T^{3} + 2209 T^{4} )^{2}$$)($$1 - 31 T^{2} - 1248 T^{4} - 68479 T^{6} + 4879681 T^{8}$$)($$( 1 + 47 T^{2} + 2209 T^{4} )^{2}$$)($$1 + 85 T^{2} + 5016 T^{4} + 187765 T^{6} + 4879681 T^{8}$$)($$1 + 85 T^{2} + 5016 T^{4} + 187765 T^{6} + 4879681 T^{8}$$)($$( 1 - 15 T + 122 T^{2} - 705 T^{3} + 2209 T^{4} )^{2}$$)($$( 1 + 47 T^{2} + 2209 T^{4} )^{4}$$)($$1 + 18 T + 90 T^{2} - 528 T^{3} - 8377 T^{4} - 24816 T^{5} + 198810 T^{6} + 1868814 T^{7} + 4879681 T^{8}$$)($$1 + 6 T + 90 T^{2} + 672 T^{3} + 5159 T^{4} + 31584 T^{5} + 198810 T^{6} + 622938 T^{7} + 4879681 T^{8}$$)($$1 + 2017 T^{4} - 811392 T^{8} + 9842316577 T^{12} + 23811286661761 T^{16}$$)($$1 - 186 T^{2} + 18779 T^{4} - 1334988 T^{6} + 77995501 T^{8} - 4036709862 T^{10} + 195411750695 T^{12} - 8917092085158 T^{14} + 380593164315181 T^{16} - 14390123113631052 T^{18} + 447152152221209819 T^{20} - 9783438595864389114 T^{22} +$$$$11\!\cdots\!41$$$$T^{24}$$)
$53$ ($$1 + 10 T + 53 T^{2}$$)($$1 + 10 T + 53 T^{2}$$)($$1 - 12 T + 53 T^{2}$$)($$1 + 2 T + 90 T^{2} + 106 T^{3} + 2809 T^{4}$$)($$1 + 88 T^{2} + 2809 T^{4}$$)($$1 + 88 T^{2} + 2809 T^{4}$$)($$1 + 8 T + 114 T^{2} + 424 T^{3} + 2809 T^{4}$$)($$1 + 8 T + 114 T^{2} + 424 T^{3} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$( 1 - 53 T^{2} )^{2}$$)($$( 1 - 52 T^{2} + 2809 T^{4} )^{2}$$)($$( 1 - 42 T^{2} + 2809 T^{4} )^{2}$$)($$1 + 12 T + 91 T^{2} + 636 T^{3} + 2809 T^{4}$$)($$1 + 12 T + 91 T^{2} + 636 T^{3} + 2809 T^{4}$$)($$1 - 10 T + 47 T^{2} - 530 T^{3} + 2809 T^{4}$$)($$1 - 10 T + 47 T^{2} - 530 T^{3} + 2809 T^{4}$$)($$1 - 8 T - 50 T^{2} - 64 T^{3} + 6795 T^{4} - 3392 T^{5} - 140450 T^{6} - 1191016 T^{7} + 7890481 T^{8}$$)($$1 - 88 T^{2} + 4935 T^{4} - 247192 T^{6} + 7890481 T^{8}$$)($$1 - 88 T^{2} + 4935 T^{4} - 247192 T^{6} + 7890481 T^{8}$$)($$1 - 2 T - 86 T^{2} + 32 T^{3} + 5079 T^{4} + 1696 T^{5} - 241574 T^{6} - 297754 T^{7} + 7890481 T^{8}$$)($$1 - 2 T - 86 T^{2} + 32 T^{3} + 5079 T^{4} + 1696 T^{5} - 241574 T^{6} - 297754 T^{7} + 7890481 T^{8}$$)($$( 1 - 4 T + 53 T^{2} )^{2}( 1 + 14 T + 53 T^{2} )^{2}$$)($$( 1 - 4 T + 53 T^{2} )^{2}( 1 + 14 T + 53 T^{2} )^{2}$$)($$1 + 52 T^{2} - 105 T^{4} + 146068 T^{6} + 7890481 T^{8}$$)($$( 1 + 53 T^{2} + 2809 T^{4} )^{2}$$)($$1 + 70 T^{2} + 2091 T^{4} + 196630 T^{6} + 7890481 T^{8}$$)($$1 + 70 T^{2} + 2091 T^{4} + 196630 T^{6} + 7890481 T^{8}$$)($$1 + 70 T^{2} + 2091 T^{4} + 196630 T^{6} + 7890481 T^{8}$$)($$1 + 52 T^{2} - 105 T^{4} + 146068 T^{6} + 7890481 T^{8}$$)($$( 1 + 42 T^{2} - 1045 T^{4} + 117978 T^{6} + 7890481 T^{8} )^{2}$$)($$( 1 - 14 T + 143 T^{2} - 742 T^{3} + 2809 T^{4} )( 1 + 4 T - 37 T^{2} + 212 T^{3} + 2809 T^{4} )$$)($$( 1 - 14 T + 143 T^{2} - 742 T^{3} + 2809 T^{4} )( 1 + 4 T - 37 T^{2} + 212 T^{3} + 2809 T^{4} )$$)($$( 1 + 2 T + 2 T^{2} - 208 T^{3} - 3017 T^{4} - 11024 T^{5} + 5618 T^{6} + 297754 T^{7} + 7890481 T^{8} )^{2}$$)($$1 - 98 T^{2} + 11107 T^{4} - 632828 T^{6} + 47661821 T^{8} - 2416782074 T^{10} + 157695288575 T^{12} - 6788740845866 T^{14} + 376074693025901 T^{16} - 14026228324542812 T^{18} + 691518381398986627 T^{20} - 17138972095820278802 T^{22} +$$$$49\!\cdots\!41$$$$T^{24}$$)
$59$ ($$1 - 6 T + 59 T^{2}$$)($$1 + 6 T + 59 T^{2}$$)($$1 + 59 T^{2}$$)($$( 1 - 4 T + 59 T^{2} )^{2}$$)($$1 + 4 T + 104 T^{2} + 236 T^{3} + 3481 T^{4}$$)($$1 - 4 T + 104 T^{2} - 236 T^{3} + 3481 T^{4}$$)($$1 - 8 T + 62 T^{2} - 472 T^{3} + 3481 T^{4}$$)($$1 + 8 T + 62 T^{2} + 472 T^{3} + 3481 T^{4}$$)($$( 1 - 10 T + 59 T^{2} )^{2}$$)($$( 1 - 10 T + 59 T^{2} )^{2}$$)($$( 1 + 10 T + 59 T^{2} )^{2}$$)($$( 1 + 59 T^{2} )^{2}$$)($$( 1 + 116 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 46 T^{2} + 3481 T^{4} )^{2}$$)($$1 - 59 T^{2} + 3481 T^{4}$$)($$1 - 59 T^{2} + 3481 T^{4}$$)($$1 - 6 T - 23 T^{2} - 354 T^{3} + 3481 T^{4}$$)($$1 + 6 T - 23 T^{2} + 354 T^{3} + 3481 T^{4}$$)($$1 + 8 T + 2 T^{2} - 448 T^{3} - 3413 T^{4} - 26432 T^{5} + 6962 T^{6} + 1643032 T^{7} + 12117361 T^{8}$$)($$1 + 4 T - 88 T^{2} - 56 T^{3} + 6391 T^{4} - 3304 T^{5} - 306328 T^{6} + 821516 T^{7} + 12117361 T^{8}$$)($$1 - 4 T - 88 T^{2} + 56 T^{3} + 6391 T^{4} + 3304 T^{5} - 306328 T^{6} - 821516 T^{7} + 12117361 T^{8}$$)($$( 1 + 4 T - 43 T^{2} + 236 T^{3} + 3481 T^{4} )^{2}$$)($$( 1 - 4 T - 43 T^{2} - 236 T^{3} + 3481 T^{4} )^{2}$$)($$( 1 + 6 T + 100 T^{2} + 354 T^{3} + 3481 T^{4} )^{2}$$)($$( 1 - 6 T + 100 T^{2} - 354 T^{3} + 3481 T^{4} )^{2}$$)($$1 - 116 T^{2} + 9975 T^{4} - 403796 T^{6} + 12117361 T^{8}$$)($$( 1 - 59 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 10 T + 41 T^{2} + 590 T^{3} + 3481 T^{4} )^{2}$$)($$( 1 + 10 T + 41 T^{2} + 590 T^{3} + 3481 T^{4} )^{2}$$)($$( 1 - 10 T + 41 T^{2} - 590 T^{3} + 3481 T^{4} )^{2}$$)($$1 - 116 T^{2} + 9975 T^{4} - 403796 T^{6} + 12117361 T^{8}$$)($$( 1 - 46 T^{2} - 1365 T^{4} - 160126 T^{6} + 12117361 T^{8} )^{2}$$)($$1 + 6 T - 64 T^{2} - 108 T^{3} + 4395 T^{4} - 6372 T^{5} - 222784 T^{6} + 1232274 T^{7} + 12117361 T^{8}$$)($$1 - 6 T - 64 T^{2} + 108 T^{3} + 4395 T^{4} + 6372 T^{5} - 222784 T^{6} - 1232274 T^{7} + 12117361 T^{8}$$)($$( 1 - 28 T^{2} - 2697 T^{4} - 97468 T^{6} + 12117361 T^{8} )^{2}$$)($$( 1 + 18 T + 265 T^{2} + 3302 T^{3} + 32433 T^{4} + 294784 T^{5} + 2403549 T^{6} + 17392256 T^{7} + 112899273 T^{8} + 678161458 T^{9} + 3211100665 T^{10} + 12868637382 T^{11} + 42180533641 T^{12} )^{2}$$)
$61$ ($$1 + 61 T^{2}$$)($$1 + 61 T^{2}$$)($$1 + 8 T + 61 T^{2}$$)($$1 + 6 T - 22 T^{2} + 366 T^{3} + 3721 T^{4}$$)($$1 + 114 T^{2} + 3721 T^{4}$$)($$1 + 114 T^{2} + 3721 T^{4}$$)($$1 - 6 T + 59 T^{2} - 366 T^{3} + 3721 T^{4}$$)($$1 + 6 T + 59 T^{2} + 366 T^{3} + 3721 T^{4}$$)($$( 1 - 8 T + 61 T^{2} )^{2}$$)($$( 1 + 7 T + 61 T^{2} )^{2}$$)($$( 1 - 7 T + 61 T^{2} )^{2}$$)($$( 1 + 61 T^{2} )^{2}$$)($$( 1 + 114 T^{2} + 3721 T^{4} )^{2}$$)($$( 1 + 24 T^{2} + 3721 T^{4} )^{2}$$)($$1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4}$$)($$1 - 8 T + 3 T^{2} - 488 T^{3} + 3721 T^{4}$$)($$1 - 61 T^{2} + 3721 T^{4}$$)($$1 - 61 T^{2} + 3721 T^{4}$$)($$1 + 6 T - 23 T^{2} - 378 T^{3} - 2436 T^{4} - 23058 T^{5} - 85583 T^{6} + 1361886 T^{7} + 13845841 T^{8}$$)($$1 - 114 T^{2} + 9275 T^{4} - 424194 T^{6} + 13845841 T^{8}$$)($$1 - 114 T^{2} + 9275 T^{4} - 424194 T^{6} + 13845841 T^{8}$$)($$1 - 6 T + 58 T^{2} + 864 T^{3} - 5433 T^{4} + 52704 T^{5} + 215818 T^{6} - 1361886 T^{7} + 13845841 T^{8}$$)($$1 + 6 T + 58 T^{2} - 864 T^{3} - 5433 T^{4} - 52704 T^{5} + 215818 T^{6} + 1361886 T^{7} + 13845841 T^{8}$$)($$1 - 170 T^{2} + 13467 T^{4} - 632570 T^{6} + 13845841 T^{8}$$)($$1 - 170 T^{2} + 13467 T^{4} - 632570 T^{6} + 13845841 T^{8}$$)($$1 - 114 T^{2} + 9275 T^{4} - 424194 T^{6} + 13845841 T^{8}$$)($$( 1 - 61 T^{2} + 3721 T^{4} )^{2}$$)($$( 1 - 7 T - 12 T^{2} - 427 T^{3} + 3721 T^{4} )^{2}$$)($$( 1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4} )^{2}$$)($$( 1 - 8 T + 3 T^{2} - 488 T^{3} + 3721 T^{4} )^{2}$$)($$1 - 114 T^{2} + 9275 T^{4} - 424194 T^{6} + 13845841 T^{8}$$)($$( 1 - 24 T^{2} - 3145 T^{4} - 89304 T^{6} + 13845841 T^{8} )^{2}$$)($$1 - 12 T + 157 T^{2} - 1308 T^{3} + 11088 T^{4} - 79788 T^{5} + 584197 T^{6} - 2723772 T^{7} + 13845841 T^{8}$$)($$1 - 12 T + 157 T^{2} - 1308 T^{3} + 11088 T^{4} - 79788 T^{5} + 584197 T^{6} - 2723772 T^{7} + 13845841 T^{8}$$)($$( 1 + 82 T^{2} + 3003 T^{4} + 305122 T^{6} + 13845841 T^{8} )^{2}$$)($$( 1 + 14 T + 79 T^{2} + 868 T^{3} + 12653 T^{4} + 93898 T^{5} + 579363 T^{6} + 5727778 T^{7} + 47081813 T^{8} + 197019508 T^{9} + 1093821439 T^{10} + 11824348214 T^{11} + 51520374361 T^{12} )^{2}$$)
$67$ ($$1 + 14 T + 67 T^{2}$$)($$1 + 14 T + 67 T^{2}$$)($$1 + 4 T + 67 T^{2}$$)($$1 - 4 T + 70 T^{2} - 268 T^{3} + 4489 T^{4}$$)($$1 + 8 T + 132 T^{2} + 536 T^{3} + 4489 T^{4}$$)($$1 + 8 T + 132 T^{2} + 536 T^{3} + 4489 T^{4}$$)($$1 - 22 T + 253 T^{2} - 1474 T^{3} + 4489 T^{4}$$)($$1 - 22 T + 253 T^{2} - 1474 T^{3} + 4489 T^{4}$$)($$1 - 130 T^{2} + 4489 T^{4}$$)($$1 - 109 T^{2} + 4489 T^{4}$$)($$1 - 109 T^{2} + 4489 T^{4}$$)($$( 1 - 67 T^{2} )^{2}$$)($$( 1 - 80 T^{2} + 4489 T^{4} )^{2}$$)($$( 1 + 10 T^{2} + 4489 T^{4} )^{2}$$)($$1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4}$$)($$1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4}$$)($$1 - 14 T + 129 T^{2} - 938 T^{3} + 4489 T^{4}$$)($$1 - 14 T + 129 T^{2} - 938 T^{3} + 4489 T^{4}$$)($$1 + 22 T + 231 T^{2} + 2618 T^{3} + 27092 T^{4} + 175406 T^{5} + 1036959 T^{6} + 6616786 T^{7} + 20151121 T^{8}$$)($$1 - 8 T - 68 T^{2} + 16 T^{3} + 8647 T^{4} + 1072 T^{5} - 305252 T^{6} - 2406104 T^{7} + 20151121 T^{8}$$)($$1 - 8 T - 68 T^{2} + 16 T^{3} + 8647 T^{4} + 1072 T^{5} - 305252 T^{6} - 2406104 T^{7} + 20151121 T^{8}$$)($$1 + 4 T - 54 T^{2} - 256 T^{3} - 661 T^{4} - 17152 T^{5} - 242406 T^{6} + 1203052 T^{7} + 20151121 T^{8}$$)($$1 + 4 T - 54 T^{2} - 256 T^{3} - 661 T^{4} - 17152 T^{5} - 242406 T^{6} + 1203052 T^{7} + 20151121 T^{8}$$)($$1 - 14 T + 98 T^{2} - 756 T^{3} + 5663 T^{4} - 50652 T^{5} + 439922 T^{6} - 4210682 T^{7} + 20151121 T^{8}$$)($$1 - 14 T + 98 T^{2} - 756 T^{3} + 5663 T^{4} - 50652 T^{5} + 439922 T^{6} - 4210682 T^{7} + 20151121 T^{8}$$)($$1 + 80 T^{2} + 1911 T^{4} + 359120 T^{6} + 20151121 T^{8}$$)($$( 1 + 67 T^{2} + 4489 T^{4} )^{2}$$)($$( 1 - 13 T^{2} + 4489 T^{4} )( 1 + 122 T^{2} + 4489 T^{4} )$$)($$1 + 130 T^{2} + 12411 T^{4} + 583570 T^{6} + 20151121 T^{8}$$)($$1 + 130 T^{2} + 12411 T^{4} + 583570 T^{6} + 20151121 T^{8}$$)($$1 + 80 T^{2} + 1911 T^{4} + 359120 T^{6} + 20151121 T^{8}$$)($$( 1 - 10 T^{2} - 4389 T^{4} - 44890 T^{6} + 20151121 T^{8} )^{2}$$)($$1 + 22 T + 137 T^{2} - 834 T^{3} - 16648 T^{4} - 55878 T^{5} + 614993 T^{6} + 6616786 T^{7} + 20151121 T^{8}$$)($$1 - 8 T + 137 T^{2} - 1224 T^{3} + 11492 T^{4} - 82008 T^{5} + 614993 T^{6} - 2406104 T^{7} + 20151121 T^{8}$$)($$( 1 - 2 T + 2 T^{2} + 264 T^{3} - 4753 T^{4} + 17688 T^{5} + 8978 T^{6} - 601526 T^{7} + 20151121 T^{8} )^{2}$$)($$( 1 - 194 T^{2} + 18247 T^{4} - 1300796 T^{6} + 81910783 T^{8} - 3909317474 T^{10} + 90458382169 T^{12} )^{2}$$)
$71$ ($$1 + 8 T + 71 T^{2}$$)($$1 + 8 T + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$( 1 - 8 T + 71 T^{2} )^{2}$$)($$1 + 12 T + 170 T^{2} + 852 T^{3} + 5041 T^{4}$$)($$1 + 12 T + 170 T^{2} + 852 T^{3} + 5041 T^{4}$$)($$1 + 8 T + 86 T^{2} + 568 T^{3} + 5041 T^{4}$$)($$1 + 8 T + 86 T^{2} + 568 T^{3} + 5041 T^{4}$$)($$( 1 + 8 T + 71 T^{2} )^{2}$$)($$( 1 + 2 T + 71 T^{2} )^{2}$$)($$( 1 + 2 T + 71 T^{2} )^{2}$$)($$( 1 + 12 T + 71 T^{2} )^{2}$$)($$( 1 - 2 T + 71 T^{2} )^{4}$$)($$( 1 - 12 T + 71 T^{2} )^{4}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 8 T + 71 T^{2} )^{2}$$)($$( 1 + 8 T + 71 T^{2} )^{2}$$)($$( 1 + 8 T + 86 T^{2} + 568 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 + 12 T + 170 T^{2} + 852 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 + 12 T + 170 T^{2} + 852 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 - 8 T + 71 T^{2} )^{4}$$)($$( 1 - 8 T + 71 T^{2} )^{4}$$)($$( 1 - 6 T + 148 T^{2} - 426 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 - 6 T + 148 T^{2} - 426 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 - 2 T + 71 T^{2} )^{4}$$)($$( 1 + 12 T + 71 T^{2} )^{4}$$)($$( 1 + 2 T + 71 T^{2} )^{4}$$)($$( 1 + 8 T + 71 T^{2} )^{4}$$)($$( 1 + 8 T + 71 T^{2} )^{4}$$)($$( 1 - 2 T + 71 T^{2} )^{4}$$)($$( 1 - 12 T + 71 T^{2} )^{8}$$)($$( 1 - 6 T + 148 T^{2} - 426 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 - 6 T + 148 T^{2} - 426 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 + 6 T + 71 T^{2} )^{8}$$)($$( 1 + 12 T - 39 T^{2} - 1768 T^{3} - 8703 T^{4} + 56456 T^{5} + 1069593 T^{6} + 4008376 T^{7} - 43871823 T^{8} - 632786648 T^{9} - 991055559 T^{10} + 21650752212 T^{11} + 128100283921 T^{12} )^{2}$$)
$73$ ($$1 + 6 T + 73 T^{2}$$)($$1 - 6 T + 73 T^{2}$$)($$1 + 2 T + 73 T^{2}$$)($$1 - 8 T + 94 T^{2} - 584 T^{3} + 5329 T^{4}$$)($$1 + 74 T^{2} + 5329 T^{4}$$)($$1 + 74 T^{2} + 5329 T^{4}$$)($$1 + 4 T + 142 T^{2} + 292 T^{3} + 5329 T^{4}$$)($$1 - 4 T + 142 T^{2} - 292 T^{3} + 5329 T^{4}$$)($$( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} )$$)($$( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} )$$)($$( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} )$$)($$1 + 34 T^{2} + 5329 T^{4}$$)($$( 1 - 10 T + 73 T^{2} )^{2}( 1 + 10 T + 73 T^{2} )^{2}$$)($$( 1 + 16 T^{2} + 5329 T^{4} )^{2}$$)($$1 + 2 T - 69 T^{2} + 146 T^{3} + 5329 T^{4}$$)($$1 - 2 T - 69 T^{2} - 146 T^{3} + 5329 T^{4}$$)($$1 + 6 T - 37 T^{2} + 438 T^{3} + 5329 T^{4}$$)($$1 - 6 T - 37 T^{2} - 438 T^{3} + 5329 T^{4}$$)($$1 - 4 T - 126 T^{2} + 16 T^{3} + 13667 T^{4} + 1168 T^{5} - 671454 T^{6} - 1556068 T^{7} + 28398241 T^{8}$$)($$1 - 74 T^{2} + 147 T^{4} - 394346 T^{6} + 28398241 T^{8}$$)($$1 - 74 T^{2} + 147 T^{4} - 394346 T^{6} + 28398241 T^{8}$$)($$1 + 8 T - 30 T^{2} - 416 T^{3} - 1165 T^{4} - 30368 T^{5} - 159870 T^{6} + 3112136 T^{7} + 28398241 T^{8}$$)($$1 - 8 T - 30 T^{2} + 416 T^{3} - 1165 T^{4} + 30368 T^{5} - 159870 T^{6} - 3112136 T^{7} + 28398241 T^{8}$$)($$1 - 24 T + 288 T^{2} - 2904 T^{3} + 26978 T^{4} - 211992 T^{5} + 1534752 T^{6} - 9336408 T^{7} + 28398241 T^{8}$$)($$1 + 24 T + 288 T^{2} + 2904 T^{3} + 26978 T^{4} + 211992 T^{5} + 1534752 T^{6} + 9336408 T^{7} + 28398241 T^{8}$$)($$( 1 + 7 T + 73 T^{2} )^{2}( 1 + 17 T + 73 T^{2} )^{2}$$)($$1 - 34 T^{2} - 4173 T^{4} - 181186 T^{6} + 28398241 T^{8}$$)($$( 1 - 16 T + 183 T^{2} - 1168 T^{3} + 5329 T^{4} )( 1 + 16 T + 183 T^{2} + 1168 T^{3} + 5329 T^{4} )$$)($$( 1 - 16 T + 183 T^{2} - 1168 T^{3} + 5329 T^{4} )( 1 + 16 T + 183 T^{2} + 1168 T^{3} + 5329 T^{4} )$$)($$( 1 - 16 T + 183 T^{2} - 1168 T^{3} + 5329 T^{4} )( 1 + 16 T + 183 T^{2} + 1168 T^{3} + 5329 T^{4} )$$)($$( 1 - 17 T + 73 T^{2} )^{2}( 1 - 7 T + 73 T^{2} )^{2}$$)($$( 1 - 16 T^{2} - 5073 T^{4} - 85264 T^{6} + 28398241 T^{8} )^{2}$$)($$1 - 24 T + 144 T^{2} + 1752 T^{3} - 31057 T^{4} + 127896 T^{5} + 767376 T^{6} - 9336408 T^{7} + 28398241 T^{8}$$)($$1 + 144 T^{2} - 600 T^{3} + 10991 T^{4} - 43800 T^{5} + 767376 T^{6} + 28398241 T^{8}$$)($$( 1 - 5329 T^{4} + 28398241 T^{8} )^{2}$$)($$1 + 82 T^{2} - 9973 T^{4} - 748076 T^{6} + 51739229 T^{8} + 2152353442 T^{10} - 212272970505 T^{12} + 11469891492418 T^{14} + 1469303094296189 T^{16} - 113209502665369964 T^{18} - 8042826496459669813 T^{20} +$$$$35\!\cdots\!18$$$$T^{22} +$$$$22\!\cdots\!21$$$$T^{24}$$)
$79$ ($$1 + T + 79 T^{2}$$)($$1 + T + 79 T^{2}$$)($$1 + T + 79 T^{2}$$)($$1 + 9 T + 174 T^{2} + 711 T^{3} + 6241 T^{4}$$)($$1 + 14 T + 135 T^{2} + 1106 T^{3} + 6241 T^{4}$$)($$1 + 14 T + 135 T^{2} + 1106 T^{3} + 6241 T^{4}$$)($$1 - 24 T + 294 T^{2} - 1896 T^{3} + 6241 T^{4}$$)($$1 - 24 T + 294 T^{2} - 1896 T^{3} + 6241 T^{4}$$)($$( 1 - 5 T + 79 T^{2} )^{2}$$)($$( 1 - 2 T + 79 T^{2} )^{2}$$)($$( 1 - 2 T + 79 T^{2} )^{2}$$)($$( 1 - T + 79 T^{2} )^{2}$$)($$( 1 - 3 T + 79 T^{2} )^{4}$$)($$( 1 + 12 T + 79 T^{2} )^{4}$$)($$1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4}$$)($$1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4}$$)($$1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4}$$)($$1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4}$$)($$1 + 24 T + 282 T^{2} + 3264 T^{3} + 34691 T^{4} + 257856 T^{5} + 1759962 T^{6} + 11832936 T^{7} + 38950081 T^{8}$$)($$1 - 14 T + 61 T^{2} + 322 T^{3} - 3500 T^{4} + 25438 T^{5} + 380701 T^{6} - 6902546 T^{7} + 38950081 T^{8}$$)($$1 - 14 T + 61 T^{2} + 322 T^{3} - 3500 T^{4} + 25438 T^{5} + 380701 T^{6} - 6902546 T^{7} + 38950081 T^{8}$$)($$1 - 9 T - 93 T^{2} - 144 T^{3} + 17636 T^{4} - 11376 T^{5} - 580413 T^{6} - 4437351 T^{7} + 38950081 T^{8}$$)($$1 - 9 T - 93 T^{2} - 144 T^{3} + 17636 T^{4} - 11376 T^{5} - 580413 T^{6} - 4437351 T^{7} + 38950081 T^{8}$$)($$1 - 260 T^{2} + 29082 T^{4} - 1622660 T^{6} + 38950081 T^{8}$$)($$1 - 260 T^{2} + 29082 T^{4} - 1622660 T^{6} + 38950081 T^{8}$$)($$( 1 + 3 T - 70 T^{2} + 237 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 + T - 78 T^{2} + 79 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 + 2 T - 75 T^{2} + 158 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 + 5 T - 54 T^{2} + 395 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 + 5 T - 54 T^{2} + 395 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 + 3 T - 70 T^{2} + 237 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 - 12 T + 65 T^{2} - 948 T^{3} + 6241 T^{4} )^{4}$$)($$1 - 6 T + 148 T^{2} - 816 T^{3} + 13203 T^{4} - 64464 T^{5} + 923668 T^{6} - 2958234 T^{7} + 38950081 T^{8}$$)($$1 + 6 T + 148 T^{2} + 816 T^{3} + 13203 T^{4} + 64464 T^{5} + 923668 T^{6} + 2958234 T^{7} + 38950081 T^{8}$$)($$( 1 - 142 T^{2} + 6241 T^{4} )^{2}( 1 + 131 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 + 22 T + 361 T^{2} + 3580 T^{3} + 28519 T^{4} + 137302 T^{5} + 493039 T^{6} )^{4}$$)
$83$ ($$1 + 12 T + 83 T^{2}$$)($$1 - 12 T + 83 T^{2}$$)($$1 + 12 T + 83 T^{2}$$)($$( 1 + 4 T + 83 T^{2} )^{2}$$)($$( 1 + 83 T^{2} )^{2}$$)($$( 1 + 83 T^{2} )^{2}$$)($$1 + 2 T + 5 T^{2} + 166 T^{3} + 6889 T^{4}$$)($$1 - 2 T + 5 T^{2} - 166 T^{3} + 6889 T^{4}$$)($$1 - 150 T^{2} + 6889 T^{4}$$)($$1 - 45 T^{2} + 6889 T^{4}$$)($$1 - 45 T^{2} + 6889 T^{4}$$)($$1 - 86 T^{2} + 6889 T^{4}$$)($$( 1 + 26 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 94 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 12 T + 83 T^{2} )^{2}$$)($$( 1 + 12 T + 83 T^{2} )^{2}$$)($$( 1 - 12 T + 83 T^{2} )^{2}$$)($$( 1 + 12 T + 83 T^{2} )^{2}$$)($$( 1 + 2 T + 5 T^{2} + 166 T^{3} + 6889 T^{4} )^{2}$$)($$( 1 + 83 T^{2} )^{4}$$)($$( 1 + 83 T^{2} )^{4}$$)($$( 1 + 4 T + 83 T^{2} )^{4}$$)($$( 1 - 4 T + 83 T^{2} )^{4}$$)($$1 + 2 T + 2 T^{2} + 140 T^{3} + 9631 T^{4} + 11620 T^{5} + 13778 T^{6} + 1143574 T^{7} + 47458321 T^{8}$$)($$1 - 2 T + 2 T^{2} - 140 T^{3} + 9631 T^{4} - 11620 T^{5} + 13778 T^{6} - 1143574 T^{7} + 47458321 T^{8}$$)($$( 1 + 26 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 86 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 45 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 150 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 150 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 + 26 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 94 T^{2} + 6889 T^{4} )^{4}$$)($$1 - 2 T + 2 T^{2} - 140 T^{3} + 9631 T^{4} - 11620 T^{5} + 13778 T^{6} - 1143574 T^{7} + 47458321 T^{8}$$)($$1 + 2 T + 2 T^{2} + 140 T^{3} + 9631 T^{4} + 11620 T^{5} + 13778 T^{6} + 1143574 T^{7} + 47458321 T^{8}$$)($$( 1 + 7538 T^{4} + 47458321 T^{8} )^{2}$$)($$1 + 150 T^{2} + 16619 T^{4} + 805308 T^{6} - 30585899 T^{8} - 10519997022 T^{10} - 1242740775025 T^{12} - 72472259484558 T^{14} - 1451555412815579 T^{16} + 263287698197042652 T^{18} + 37430844605918722379 T^{20} +$$$$23\!\cdots\!50$$$$T^{22} +$$$$10\!\cdots\!61$$$$T^{24}$$)
$89$ ($$1 + 12 T + 89 T^{2}$$)($$1 - 12 T + 89 T^{2}$$)($$1 - 12 T + 89 T^{2}$$)($$1 + 6 T + 170 T^{2} + 534 T^{3} + 7921 T^{4}$$)($$( 1 - 8 T + 89 T^{2} )^{2}$$)($$( 1 + 8 T + 89 T^{2} )^{2}$$)($$1 - 6 T + 155 T^{2} - 534 T^{3} + 7921 T^{4}$$)($$1 + 6 T + 155 T^{2} + 534 T^{3} + 7921 T^{4}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 - 9 T + 89 T^{2} )^{2}$$)($$( 1 + 9 T + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 - 110 T^{2} + 7921 T^{4} )^{2}$$)($$( 1 + 160 T^{2} + 7921 T^{4} )^{2}$$)($$1 - 12 T + 55 T^{2} - 1068 T^{3} + 7921 T^{4}$$)($$1 + 12 T + 55 T^{2} + 1068 T^{3} + 7921 T^{4}$$)($$1 + 12 T + 55 T^{2} + 1068 T^{3} + 7921 T^{4}$$)($$1 - 12 T + 55 T^{2} - 1068 T^{3} + 7921 T^{4}$$)($$1 + 6 T - 119 T^{2} - 138 T^{3} + 12900 T^{4} - 12282 T^{5} - 942599 T^{6} + 4229814 T^{7} + 62742241 T^{8}$$)($$( 1 - 8 T - 25 T^{2} - 712 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 + 8 T - 25 T^{2} + 712 T^{3} + 7921 T^{4} )^{2}$$)($$1 - 6 T - 134 T^{2} + 48 T^{3} + 17775 T^{4} + 4272 T^{5} - 1061414 T^{6} - 4229814 T^{7} + 62742241 T^{8}$$)($$1 + 6 T - 134 T^{2} - 48 T^{3} + 17775 T^{4} - 4272 T^{5} - 1061414 T^{6} + 4229814 T^{7} + 62742241 T^{8}$$)($$( 1 - 16 T + 167 T^{2} - 1424 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 + 16 T + 167 T^{2} + 1424 T^{3} + 7921 T^{4} )^{2}$$)($$1 + 110 T^{2} + 4179 T^{4} + 871310 T^{6} + 62742241 T^{8}$$)($$( 1 - 89 T^{2} + 7921 T^{4} )^{2}$$)($$( 1 + 9 T - 8 T^{2} + 801 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 - 89 T^{2} + 7921 T^{4} )^{2}$$)($$( 1 - 89 T^{2} + 7921 T^{4} )^{2}$$)($$1 + 110 T^{2} + 4179 T^{4} + 871310 T^{6} + 62742241 T^{8}$$)($$( 1 - 160 T^{2} + 17679 T^{4} - 1267360 T^{6} + 62742241 T^{8} )^{2}$$)($$( 1 - 16 T + 89 T^{2} )^{2}( 1 + 16 T + 167 T^{2} + 1424 T^{3} + 7921 T^{4} )$$)($$( 1 + 16 T + 89 T^{2} )^{2}( 1 - 16 T + 167 T^{2} - 1424 T^{3} + 7921 T^{4} )$$)($$( 1 - 138 T^{2} + 11123 T^{4} - 1093098 T^{6} + 62742241 T^{8} )^{2}$$)($$( 1 + 26 T + 307 T^{2} + 2028 T^{3} + 485 T^{4} - 167042 T^{5} - 2169217 T^{6} - 14866738 T^{7} + 3841685 T^{8} + 1429677132 T^{9} + 19261867987 T^{10} + 145185545674 T^{11} + 496981290961 T^{12} )^{2}$$)
$97$ ($$1 - 15 T + 97 T^{2}$$)($$1 + 15 T + 97 T^{2}$$)($$1 - T + 97 T^{2}$$)($$1 - 9 T + 108 T^{2} - 873 T^{3} + 9409 T^{4}$$)($$1 + 18 T + 257 T^{2} + 1746 T^{3} + 9409 T^{4}$$)($$1 - 18 T + 257 T^{2} - 1746 T^{3} + 9409 T^{4}$$)($$1 + 12 T + 198 T^{2} + 1164 T^{3} + 9409 T^{4}$$)($$1 - 12 T + 198 T^{2} - 1164 T^{3} + 9409 T^{4}$$)($$1 - 145 T^{2} + 9409 T^{4}$$)($$1 + 62 T^{2} + 9409 T^{4}$$)($$1 + 62 T^{2} + 9409 T^{4}$$)($$1 - 149 T^{2} + 9409 T^{4}$$)($$( 1 - 191 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 - 176 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 + T + 97 T^{2} )^{2}$$)($$( 1 - T + 97 T^{2} )^{2}$$)($$( 1 + 15 T + 97 T^{2} )^{2}$$)($$( 1 - 15 T + 97 T^{2} )^{2}$$)($$( 1 + 12 T + 198 T^{2} + 1164 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 - 18 T + 257 T^{2} - 1746 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 + 18 T + 257 T^{2} + 1746 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 - 9 T + 108 T^{2} - 873 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 + 9 T + 108 T^{2} + 873 T^{3} + 9409 T^{4} )^{2}$$)($$1 + 4 T + 8 T^{2} + 12 T^{3} - 8818 T^{4} + 1164 T^{5} + 75272 T^{6} + 3650692 T^{7} + 88529281 T^{8}$$)($$1 - 4 T + 8 T^{2} - 12 T^{3} - 8818 T^{4} - 1164 T^{5} + 75272 T^{6} - 3650692 T^{7} + 88529281 T^{8}$$)($$( 1 - 191 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 - 149 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 + 62 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 - 145 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 - 145 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 - 191 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 - 176 T^{2} + 9409 T^{4} )^{4}$$)($$1 - 4 T + 8 T^{2} - 12 T^{3} - 8818 T^{4} - 1164 T^{5} + 75272 T^{6} - 3650692 T^{7} + 88529281 T^{8}$$)($$1 + 4 T + 8 T^{2} + 12 T^{3} - 8818 T^{4} + 1164 T^{5} + 75272 T^{6} + 3650692 T^{7} + 88529281 T^{8}$$)($$( 1 + 16903 T^{4} + 88529281 T^{8} )^{2}$$)($$( 1 - 318 T^{2} + 57791 T^{4} - 6730052 T^{6} + 543755519 T^{8} - 28152311358 T^{10} + 832972004929 T^{12} )^{2}$$)