# Properties

 Label 1200.2 Level 1200 Weight 2 Dimension 14747 Nonzero newspaces 28 Sturm bound 153600 Trace bound 25

## Defining parameters

 Level: $$N$$ = $$1200 = 2^{4} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$28$$ Sturm bound: $$153600$$ Trace bound: $$25$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1200))$$.

Total New Old
Modular forms 39968 15115 24853
Cusp forms 36833 14747 22086
Eisenstein series 3135 368 2767

## Trace form

 $$14747q - 19q^{3} - 56q^{4} - 48q^{6} - 44q^{7} - 12q^{8} - 15q^{9} + O(q^{10})$$ $$14747q - 19q^{3} - 56q^{4} - 48q^{6} - 44q^{7} - 12q^{8} - 15q^{9} - 64q^{10} - 12q^{11} - 24q^{12} - 86q^{13} + 12q^{14} - 36q^{15} - 64q^{16} - 30q^{17} - 16q^{18} - 92q^{19} - 78q^{21} - 32q^{22} - 40q^{23} + 4q^{24} - 32q^{25} + 20q^{26} - 31q^{27} + 80q^{28} + 6q^{29} - 12q^{31} + 160q^{32} - 10q^{33} + 200q^{34} + 24q^{35} + 8q^{36} + 66q^{37} + 216q^{38} + 52q^{39} + 96q^{40} + 122q^{41} + 92q^{42} + 28q^{43} + 184q^{44} - 14q^{45} + 128q^{46} + 48q^{47} + 40q^{48} - 13q^{49} + 80q^{50} + 38q^{51} + 48q^{52} + 46q^{53} - 72q^{54} - 28q^{55} + 38q^{57} - 32q^{58} + 28q^{59} - 64q^{60} - 46q^{61} - 12q^{62} + 202q^{63} - 80q^{64} + 8q^{65} - 116q^{66} + 220q^{67} - 192q^{68} + 90q^{69} - 208q^{70} + 312q^{71} - 228q^{72} + 2q^{73} - 300q^{74} + 128q^{75} - 352q^{76} + 112q^{77} - 312q^{78} + 324q^{79} - 160q^{80} - 51q^{81} - 280q^{82} + 436q^{83} - 336q^{84} + 128q^{85} - 272q^{86} + 268q^{87} - 432q^{88} + 74q^{89} - 152q^{90} + 244q^{91} - 304q^{92} + 110q^{93} - 312q^{94} + 312q^{95} - 224q^{96} + 66q^{97} - 136q^{98} + 56q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1200))$$

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
1200.2.a $$\chi_{1200}(1, \cdot)$$ 1200.2.a.a 1 1
1200.2.a.b 1
1200.2.a.c 1
1200.2.a.d 1
1200.2.a.e 1
1200.2.a.f 1
1200.2.a.g 1
1200.2.a.h 1
1200.2.a.i 1
1200.2.a.j 1
1200.2.a.k 1
1200.2.a.l 1
1200.2.a.m 1
1200.2.a.n 1
1200.2.a.o 1
1200.2.a.p 1
1200.2.a.q 1
1200.2.a.r 1
1200.2.a.s 1
1200.2.b $$\chi_{1200}(551, \cdot)$$ None 0 1
1200.2.d $$\chi_{1200}(649, \cdot)$$ None 0 1
1200.2.f $$\chi_{1200}(49, \cdot)$$ 1200.2.f.a 2 1
1200.2.f.b 2
1200.2.f.c 2
1200.2.f.d 2
1200.2.f.e 2
1200.2.f.f 2
1200.2.f.g 2
1200.2.f.h 2
1200.2.f.i 2
1200.2.h $$\chi_{1200}(1151, \cdot)$$ 1200.2.h.a 2 1
1200.2.h.b 2
1200.2.h.c 2
1200.2.h.d 2
1200.2.h.e 2
1200.2.h.f 2
1200.2.h.g 2
1200.2.h.h 2
1200.2.h.i 2
1200.2.h.j 4
1200.2.h.k 4
1200.2.h.l 4
1200.2.h.m 4
1200.2.h.n 4
1200.2.k $$\chi_{1200}(601, \cdot)$$ None 0 1
1200.2.m $$\chi_{1200}(599, \cdot)$$ None 0 1
1200.2.o $$\chi_{1200}(1199, \cdot)$$ 1200.2.o.a 4 1
1200.2.o.b 4
1200.2.o.c 4
1200.2.o.d 4
1200.2.o.e 4
1200.2.o.f 4
1200.2.o.g 4
1200.2.o.h 4
1200.2.o.i 4
1200.2.s $$\chi_{1200}(301, \cdot)$$ n/a 152 2
1200.2.t $$\chi_{1200}(299, \cdot)$$ n/a 280 2
1200.2.v $$\chi_{1200}(257, \cdot)$$ 1200.2.v.a 4 2
1200.2.v.b 4
1200.2.v.c 4
1200.2.v.d 4
1200.2.v.e 4
1200.2.v.f 4
1200.2.v.g 4
1200.2.v.h 4
1200.2.v.i 4
1200.2.v.j 4
1200.2.v.k 4
1200.2.v.l 8
1200.2.v.m 16
1200.2.w $$\chi_{1200}(607, \cdot)$$ 1200.2.w.a 4 2
1200.2.w.b 8
1200.2.w.c 8
1200.2.w.d 8
1200.2.w.e 8
1200.2.y $$\chi_{1200}(643, \cdot)$$ n/a 144 2
1200.2.bb $$\chi_{1200}(893, \cdot)$$ n/a 280 2
1200.2.bc $$\chi_{1200}(43, \cdot)$$ n/a 144 2
1200.2.bf $$\chi_{1200}(293, \cdot)$$ n/a 280 2
1200.2.bh $$\chi_{1200}(7, \cdot)$$ None 0 2
1200.2.bi $$\chi_{1200}(857, \cdot)$$ None 0 2
1200.2.bk $$\chi_{1200}(251, \cdot)$$ n/a 292 2
1200.2.bl $$\chi_{1200}(349, \cdot)$$ n/a 144 2
1200.2.bo $$\chi_{1200}(241, \cdot)$$ n/a 120 4
1200.2.bq $$\chi_{1200}(191, \cdot)$$ n/a 240 4
1200.2.bs $$\chi_{1200}(289, \cdot)$$ n/a 120 4
1200.2.bu $$\chi_{1200}(169, \cdot)$$ None 0 4
1200.2.bw $$\chi_{1200}(71, \cdot)$$ None 0 4
1200.2.by $$\chi_{1200}(239, \cdot)$$ n/a 240 4
1200.2.ca $$\chi_{1200}(119, \cdot)$$ None 0 4
1200.2.cc $$\chi_{1200}(121, \cdot)$$ None 0 4
1200.2.ce $$\chi_{1200}(59, \cdot)$$ n/a 1888 8
1200.2.cf $$\chi_{1200}(61, \cdot)$$ n/a 960 8
1200.2.cj $$\chi_{1200}(137, \cdot)$$ None 0 8
1200.2.ck $$\chi_{1200}(103, \cdot)$$ None 0 8
1200.2.cm $$\chi_{1200}(53, \cdot)$$ n/a 1888 8
1200.2.cp $$\chi_{1200}(67, \cdot)$$ n/a 960 8
1200.2.cq $$\chi_{1200}(173, \cdot)$$ n/a 1888 8
1200.2.ct $$\chi_{1200}(163, \cdot)$$ n/a 960 8
1200.2.cv $$\chi_{1200}(127, \cdot)$$ n/a 240 8
1200.2.cw $$\chi_{1200}(17, \cdot)$$ n/a 464 8
1200.2.da $$\chi_{1200}(109, \cdot)$$ n/a 960 8
1200.2.db $$\chi_{1200}(11, \cdot)$$ n/a 1888 8

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1200))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1200)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(150))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(200))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(240))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(300))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(400))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(600))$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ ($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 + T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 - T$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$1 + 3 T + 3 T^{2}$$)($$1 + 3 T + 3 T^{2}$$)($$1 + 3 T^{2}$$)($$1 + 3 T^{2}$$)($$1 + 3 T^{2}$$)($$1 + 3 T^{2}$$)($$1 + 3 T^{2}$$)($$1 - 3 T + 3 T^{2}$$)($$1 - 3 T + 3 T^{2}$$)($$( 1 + 2 T + 3 T^{2} )^{2}$$)($$1 + 9 T^{4}$$)($$1 - 4 T^{2} + 9 T^{4}$$)($$( 1 - 3 T^{2} )^{2}$$)($$( 1 - 2 T + 3 T^{2} )^{2}$$)($$( 1 + 3 T^{2} )^{2}$$)($$( 1 + 3 T^{2} )^{2}$$)($$1 + 3 T^{2} + 9 T^{4}$$)($$1 + 3 T^{2} + 9 T^{4}$$)($$1 + 9 T^{4}$$)($$1 + 9 T^{4}$$)($$( 1 - 3 T^{2} )^{2}$$)($$( 1 - 3 T^{2} )^{2}$$)($$( 1 - 3 T^{2} )^{2}$$)($$1 + 4 T + 8 T^{2} + 12 T^{3} + 9 T^{4}$$)($$1 + 4 T + 8 T^{2} + 12 T^{3} + 9 T^{4}$$)($$1 + 4 T + 8 T^{2} + 12 T^{3} + 9 T^{4}$$)($$1 - 2 T^{2} + 9 T^{4}$$)($$1 + 9 T^{4}$$)($$1 + 9 T^{4}$$)($$1 + 9 T^{4}$$)($$1 + 9 T^{4}$$)($$1 - 2 T + 2 T^{2} - 6 T^{3} + 9 T^{4}$$)($$( 1 - 2 T + 3 T^{2} )^{2}$$)($$1 - 4 T + 8 T^{2} - 12 T^{3} + 9 T^{4}$$)($$1 - 9 T^{4} + 81 T^{8}$$)($$1 - 7 T^{4} - 32 T^{8} - 567 T^{12} + 6561 T^{16}$$)($$1 + T^{4}$$)($$( 1 + T^{4} )^{2}$$)($$( 1 + T^{4} )^{2}$$)($$( 1 + T^{4} )^{2}$$)($$( 1 + T^{4} )^{2}$$)
$5$ 1
$7$ ($$1 + 4 T + 7 T^{2}$$)($$1 + 3 T + 7 T^{2}$$)($$1 + 3 T + 7 T^{2}$$)($$1 + 7 T^{2}$$)($$1 + 7 T^{2}$$)($$1 - T + 7 T^{2}$$)($$1 - 2 T + 7 T^{2}$$)($$1 - 2 T + 7 T^{2}$$)($$1 - 5 T + 7 T^{2}$$)($$1 + 5 T + 7 T^{2}$$)($$1 + 4 T + 7 T^{2}$$)($$1 + 2 T + 7 T^{2}$$)($$1 + 2 T + 7 T^{2}$$)($$1 + T + 7 T^{2}$$)($$1 + 7 T^{2}$$)($$1 - 3 T + 7 T^{2}$$)($$1 - 3 T + 7 T^{2}$$)($$1 - 4 T + 7 T^{2}$$)($$1 - 4 T + 7 T^{2}$$)($$1 - 13 T^{2} + 49 T^{4}$$)($$( 1 - 7 T^{2} )^{2}$$)($$1 - 5 T^{2} + 49 T^{4}$$)($$1 - 5 T^{2} + 49 T^{4}$$)($$1 + 2 T^{2} + 49 T^{4}$$)($$1 + 2 T^{2} + 49 T^{4}$$)($$( 1 - 7 T^{2} )^{2}$$)($$( 1 - 7 T^{2} )^{2}$$)($$1 + 11 T^{2} + 49 T^{4}$$)($$( 1 - 7 T^{2} )^{2}$$)($$( 1 - 7 T^{2} )^{2}$$)($$( 1 - T + 7 T^{2} )( 1 + T + 7 T^{2} )$$)($$( 1 - 5 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$$)($$( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$$)($$( 1 - 5 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$$)($$( 1 - T + 7 T^{2} )( 1 + T + 7 T^{2} )$$)($$( 1 - 7 T^{2} )^{2}$$)($$( 1 - 7 T^{2} )^{2}$$)($$( 1 - 7 T^{2} )^{4}$$)($$( 1 - 8 T^{2} + 49 T^{4} )^{2}$$)($$( 1 + 4 T^{2} + 49 T^{4} )^{2}$$)($$( 1 - 4 T + 7 T^{2} )^{2}( 1 + 4 T + 7 T^{2} )^{2}$$)($$( 1 - 7 T^{2} )^{4}$$)($$( 1 + 2 T^{2} + 49 T^{4} )^{2}$$)($$( 1 + 2 T^{2} + 49 T^{4} )^{2}$$)($$( 1 + 7 T^{2} )^{4}$$)($$( 1 + 7 T^{2} )^{4}$$)($$( 1 + 8 T^{2} + 49 T^{4} )^{2}$$)($$( 1 + 8 T^{2} + 49 T^{4} )^{2}$$)($$( 1 - 13 T^{2} + 49 T^{4} )^{2}$$)($$( 1 + 11 T^{2} + 49 T^{4} )^{2}$$)($$( 1 + 2 T^{2} + 49 T^{4} )^{2}$$)($$( 1 + 4 T + 8 T^{2} + 28 T^{3} + 49 T^{4} )^{2}$$)($$( 1 + 2 T + 2 T^{2} + 14 T^{3} + 49 T^{4} )^{2}$$)($$( 1 - 6 T + 18 T^{2} - 42 T^{3} + 49 T^{4} )^{2}$$)($$1 + 4 T + 8 T^{2} + 20 T^{3} + 46 T^{4} + 140 T^{5} + 392 T^{6} + 1372 T^{7} + 2401 T^{8}$$)($$1 - 94 T^{4} + 2401 T^{8}$$)($$1 + 23 T^{4} + 2401 T^{8}$$)($$( 1 + 49 T^{4} )^{2}$$)($$1 + 71 T^{4} + 2401 T^{8}$$)($$( 1 + 2 T + 2 T^{2} + 14 T^{3} + 49 T^{4} )^{2}$$)($$1 + 4 T + 8 T^{2} + 20 T^{3} + 46 T^{4} + 140 T^{5} + 392 T^{6} + 1372 T^{7} + 2401 T^{8}$$)($$( 1 - 4 T + 8 T^{2} - 28 T^{3} + 49 T^{4} )^{2}$$)($$( 1 - 94 T^{4} + 2401 T^{8} )^{2}$$)($$( 1 + 41 T^{4} + 1584 T^{8} + 98441 T^{12} + 5764801 T^{16} )^{2}$$)($$1 - 94 T^{4} + 2401 T^{8}$$)($$1 + 28 T^{4} - 1146 T^{8} + 67228 T^{12} + 5764801 T^{16}$$)($$( 1 + 2 T^{4} + 2401 T^{8} )^{2}$$)($$( 1 + 71 T^{4} + 2401 T^{8} )^{2}$$)($$( 1 + 71 T^{4} + 2401 T^{8} )^{2}$$)
$11$ ($$1 - 4 T + 11 T^{2}$$)($$1 + 2 T + 11 T^{2}$$)($$1 + 2 T + 11 T^{2}$$)($$1 + 4 T + 11 T^{2}$$)($$1 - 4 T + 11 T^{2}$$)($$1 + 6 T + 11 T^{2}$$)($$1 + 2 T + 11 T^{2}$$)($$1 + 2 T + 11 T^{2}$$)($$1 - 6 T + 11 T^{2}$$)($$1 - 6 T + 11 T^{2}$$)($$1 + 11 T^{2}$$)($$1 + 2 T + 11 T^{2}$$)($$1 + 2 T + 11 T^{2}$$)($$1 + 6 T + 11 T^{2}$$)($$1 - 4 T + 11 T^{2}$$)($$1 + 2 T + 11 T^{2}$$)($$1 + 2 T + 11 T^{2}$$)($$1 + 11 T^{2}$$)($$1 - 4 T + 11 T^{2}$$)($$( 1 + 6 T + 11 T^{2} )^{2}$$)($$( 1 + 4 T + 11 T^{2} )^{2}$$)($$( 1 + 2 T + 11 T^{2} )^{2}$$)($$( 1 + 2 T + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 - 4 T + 11 T^{2} )^{2}$$)($$( 1 - 4 T + 11 T^{2} )^{2}$$)($$( 1 - 6 T + 11 T^{2} )^{2}$$)($$( 1 + 3 T + 11 T^{2} )^{2}$$)($$( 1 - 3 T + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 11 T^{2} )^{2}$$)($$( 1 + 3 T + 11 T^{2} )^{2}$$)($$( 1 - 3 T + 11 T^{2} )^{2}$$)($$( 1 - 2 T^{2} + 121 T^{4} )^{2}$$)($$( 1 - 2 T^{2} + 121 T^{4} )^{2}$$)($$( 1 + 11 T^{2} )^{4}$$)($$( 1 + 10 T^{2} + 121 T^{4} )^{2}$$)($$( 1 - 2 T^{2} + 121 T^{4} )^{2}$$)($$( 1 + 10 T^{2} + 121 T^{4} )^{2}$$)($$( 1 + 10 T^{2} + 121 T^{4} )^{2}$$)($$( 1 + 3 T + 11 T^{2} )^{4}$$)($$( 1 - 3 T + 11 T^{2} )^{4}$$)($$( 1 - 2 T^{2} + 121 T^{4} )^{2}$$)($$( 1 - 2 T^{2} + 121 T^{4} )^{2}$$)($$( 1 + 11 T^{2} )^{4}$$)($$( 1 + 11 T^{2} )^{4}$$)($$( 1 + 11 T^{2} )^{4}$$)($$( 1 + 10 T^{2} + 121 T^{4} )^{2}$$)($$( 1 - 20 T^{2} + 121 T^{4} )^{2}$$)($$( 1 - 20 T^{2} + 121 T^{4} )^{2}$$)($$1 - 20 T^{2} + 214 T^{4} - 2420 T^{6} + 14641 T^{8}$$)($$( 1 - 11 T^{2} )^{4}$$)($$( 1 - 11 T^{2} )^{4}$$)($$( 1 - 11 T^{2} )^{4}$$)($$( 1 - 11 T^{2} )^{4}$$)($$( 1 - 2 T^{2} + 121 T^{4} )^{2}$$)($$1 - 20 T^{2} + 214 T^{4} - 2420 T^{6} + 14641 T^{8}$$)($$( 1 + 10 T^{2} + 121 T^{4} )^{2}$$)($$( 1 + 5 T^{2} + 121 T^{4} )^{4}$$)($$( 1 - 25 T^{2} + 324 T^{4} - 3025 T^{6} + 14641 T^{8} )^{4}$$)($$( 1 + 10 T^{2} + 121 T^{4} )^{2}$$)($$( 1 - 20 T^{2} + 121 T^{4} )^{4}$$)($$( 1 - 10 T^{2} + 121 T^{4} )^{4}$$)($$( 1 - 10 T^{2} + 121 T^{4} )^{4}$$)($$( 1 - 10 T^{2} + 121 T^{4} )^{4}$$)
$13$ ($$1 + 13 T^{2}$$)($$1 + 3 T + 13 T^{2}$$)($$1 + T + 13 T^{2}$$)($$1 - 2 T + 13 T^{2}$$)($$1 - 2 T + 13 T^{2}$$)($$1 - 5 T + 13 T^{2}$$)($$1 + 6 T + 13 T^{2}$$)($$1 - 2 T + 13 T^{2}$$)($$1 + 3 T + 13 T^{2}$$)($$1 - 3 T + 13 T^{2}$$)($$1 + 2 T + 13 T^{2}$$)($$1 + 2 T + 13 T^{2}$$)($$1 - 6 T + 13 T^{2}$$)($$1 + 5 T + 13 T^{2}$$)($$1 + 6 T + 13 T^{2}$$)($$1 - T + 13 T^{2}$$)($$1 - 3 T + 13 T^{2}$$)($$1 - 6 T + 13 T^{2}$$)($$1 + 13 T^{2}$$)($$1 - T^{2} + 169 T^{4}$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$1 - 17 T^{2} + 169 T^{4}$$)($$1 - 25 T^{2} + 169 T^{4}$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )$$)($$( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$1 - 17 T^{2} + 169 T^{4}$$)($$( 1 - 2 T + 13 T^{2} )^{2}$$)($$( 1 + 2 T + 13 T^{2} )^{2}$$)($$( 1 + 7 T + 13 T^{2} )^{2}$$)($$( 1 + 5 T + 13 T^{2} )^{2}$$)($$( 1 - 2 T + 13 T^{2} )^{2}$$)($$( 1 - 5 T + 13 T^{2} )^{2}$$)($$( 1 - 7 T + 13 T^{2} )^{2}$$)($$( 1 + 2 T + 13 T^{2} )^{2}$$)($$( 1 - 2 T + 13 T^{2} )^{2}$$)($$( 1 + 2 T^{2} + 169 T^{4} )^{2}$$)($$( 1 - 2 T + 13 T^{2} )^{4}$$)($$( 1 + 13 T^{2} )^{4}$$)($$( 1 + 4 T + 13 T^{2} )^{4}$$)($$( 1 + 2 T^{2} + 169 T^{4} )^{2}$$)($$( 1 - 6 T + 13 T^{2} )^{2}( 1 + 6 T + 13 T^{2} )^{2}$$)($$( 1 - 6 T + 13 T^{2} )^{2}( 1 + 6 T + 13 T^{2} )^{2}$$)($$( 1 - 22 T^{2} + 169 T^{4} )^{2}$$)($$( 1 - 22 T^{2} + 169 T^{4} )^{2}$$)($$( 1 - 22 T^{2} + 169 T^{4} )^{2}$$)($$( 1 - 22 T^{2} + 169 T^{4} )^{2}$$)($$( 1 + 23 T^{2} + 169 T^{4} )^{2}$$)($$( 1 - T^{2} + 169 T^{4} )^{2}$$)($$( 1 - 22 T^{2} + 169 T^{4} )^{2}$$)($$( 1 + 169 T^{4} )^{2}$$)($$( 1 + 169 T^{4} )^{2}$$)($$( 1 + 169 T^{4} )^{2}$$)($$1 + 4 T + 8 T^{2} - 4 T^{3} - 194 T^{4} - 52 T^{5} + 1352 T^{6} + 8788 T^{7} + 28561 T^{8}$$)($$1 + 146 T^{4} + 28561 T^{8}$$)($$1 - 337 T^{4} + 28561 T^{8}$$)($$( 1 + 169 T^{4} )^{2}$$)($$1 + 191 T^{4} + 28561 T^{8}$$)($$( 1 - 6 T + 18 T^{2} - 78 T^{3} + 169 T^{4} )^{2}$$)($$1 + 4 T + 8 T^{2} - 4 T^{3} - 194 T^{4} - 52 T^{5} + 1352 T^{6} + 8788 T^{7} + 28561 T^{8}$$)($$( 1 + 169 T^{4} )^{2}$$)($$( 1 + 169 T^{4} )^{4}$$)($$( 1 - 527 T^{4} + 126480 T^{8} - 15051647 T^{12} + 815730721 T^{16} )^{2}$$)($$( 1 + 6 T + 18 T^{2} + 78 T^{3} + 169 T^{4} )^{2}$$)($$( 1 - 142 T^{4} + 28561 T^{8} )^{2}$$)($$( 1 - 142 T^{4} + 28561 T^{8} )^{2}$$)($$( 1 + 191 T^{4} + 28561 T^{8} )^{2}$$)($$( 1 - 337 T^{4} + 28561 T^{8} )^{2}$$)
$17$ ($$1 - 4 T + 17 T^{2}$$)($$1 - 6 T + 17 T^{2}$$)($$1 + 2 T + 17 T^{2}$$)($$1 + 2 T + 17 T^{2}$$)($$1 + 2 T + 17 T^{2}$$)($$1 + 6 T + 17 T^{2}$$)($$1 + 2 T + 17 T^{2}$$)($$1 - 6 T + 17 T^{2}$$)($$1 + 2 T + 17 T^{2}$$)($$1 - 2 T + 17 T^{2}$$)($$1 + 6 T + 17 T^{2}$$)($$1 + 6 T + 17 T^{2}$$)($$1 - 2 T + 17 T^{2}$$)($$1 - 6 T + 17 T^{2}$$)($$1 - 6 T + 17 T^{2}$$)($$1 - 2 T + 17 T^{2}$$)($$1 + 6 T + 17 T^{2}$$)($$1 - 2 T + 17 T^{2}$$)($$1 + 4 T + 17 T^{2}$$)($$1 + 2 T^{2} + 289 T^{4}$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$1 + 2 T^{2} + 289 T^{4}$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$1 + 2 T^{2} + 289 T^{4}$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$1 + 2 T^{2} + 289 T^{4}$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$1 - 7 T^{2} + 289 T^{4}$$)($$1 - 7 T^{2} + 289 T^{4}$$)($$( 1 - 17 T^{2} )^{2}$$)($$( 1 - 17 T^{2} )^{2}$$)($$( 1 - 17 T^{2} )^{2}$$)($$( 1 - 17 T^{2} )^{2}$$)($$( 1 - 17 T^{2} )^{2}$$)($$1 - 7 T^{2} + 289 T^{4}$$)($$1 - 7 T^{2} + 289 T^{4}$$)($$( 1 - 22 T^{2} + 289 T^{4} )^{2}$$)($$( 1 + 2 T^{2} + 289 T^{4} )^{2}$$)($$( 1 - 17 T^{2} )^{4}$$)($$( 1 + 2 T^{2} + 289 T^{4} )^{2}$$)($$( 1 - 22 T^{2} + 289 T^{4} )^{2}$$)($$( 1 + 6 T + 17 T^{2} )^{4}$$)($$( 1 - 6 T + 17 T^{2} )^{4}$$)($$( 1 + 7 T^{2} + 289 T^{4} )^{2}$$)($$( 1 + 7 T^{2} + 289 T^{4} )^{2}$$)($$( 1 + 6 T + 17 T^{2} )^{4}$$)($$( 1 - 6 T + 17 T^{2} )^{4}$$)($$( 1 + 17 T^{2} )^{4}$$)($$( 1 + 17 T^{2} )^{4}$$)($$( 1 + 17 T^{2} )^{4}$$)($$1 - 254 T^{4} + 83521 T^{8}$$)($$( 1 - 16 T^{2} + 289 T^{4} )( 1 + 16 T^{2} + 289 T^{4} )$$)($$( 1 - 8 T + 32 T^{2} - 136 T^{3} + 289 T^{4} )( 1 + 8 T + 32 T^{2} + 136 T^{3} + 289 T^{4} )$$)($$1 + 4 T + 8 T^{2} + 12 T^{3} - 178 T^{4} + 204 T^{5} + 2312 T^{6} + 19652 T^{7} + 83521 T^{8}$$)($$( 1 + 289 T^{4} )^{2}$$)($$( 1 + 289 T^{4} )^{2}$$)($$1 - 382 T^{4} + 83521 T^{8}$$)($$( 1 + 289 T^{4} )^{2}$$)($$1 - 2 T^{4} + 83521 T^{8}$$)($$1 - 4 T + 8 T^{2} - 12 T^{3} - 178 T^{4} - 204 T^{5} + 2312 T^{6} - 19652 T^{7} + 83521 T^{8}$$)($$1 - 254 T^{4} + 83521 T^{8}$$)($$( 1 + 47 T^{4} + 83521 T^{8} )^{2}$$)($$( 1 + 17 T^{4} - 127584 T^{8} + 1419857 T^{12} + 6975757441 T^{16} )^{2}$$)($$( 1 - 2 T + 2 T^{2} - 34 T^{3} + 289 T^{4} )^{2}$$)($$( 1 + 8 T + 32 T^{2} + 104 T^{3} + 322 T^{4} + 1768 T^{5} + 9248 T^{6} + 39304 T^{7} + 83521 T^{8} )^{2}$$)($$( 1 - 382 T^{4} + 83521 T^{8} )^{2}$$)($$( 1 - 94 T^{4} + 83521 T^{8} )^{2}$$)($$( 1 - 94 T^{4} + 83521 T^{8} )^{2}$$)
$19$ ($$1 + 19 T^{2}$$)($$1 - 7 T + 19 T^{2}$$)($$1 - 5 T + 19 T^{2}$$)($$1 - 4 T + 19 T^{2}$$)($$1 + 4 T + 19 T^{2}$$)($$1 + 5 T + 19 T^{2}$$)($$1 + 19 T^{2}$$)($$1 + 8 T + 19 T^{2}$$)($$1 + T + 19 T^{2}$$)($$1 + T + 19 T^{2}$$)($$1 - 4 T + 19 T^{2}$$)($$1 + 8 T + 19 T^{2}$$)($$1 + 19 T^{2}$$)($$1 + 5 T + 19 T^{2}$$)($$1 - 4 T + 19 T^{2}$$)($$1 - 5 T + 19 T^{2}$$)($$1 - 7 T + 19 T^{2}$$)($$1 + 4 T + 19 T^{2}$$)($$1 + 19 T^{2}$$)($$( 1 - 5 T + 19 T^{2} )^{2}$$)($$( 1 + 4 T + 19 T^{2} )^{2}$$)($$( 1 + 7 T + 19 T^{2} )^{2}$$)($$( 1 + 5 T + 19 T^{2} )^{2}$$)($$( 1 + 4 T + 19 T^{2} )^{2}$$)($$( 1 - 4 T + 19 T^{2} )^{2}$$)($$( 1 + 4 T + 19 T^{2} )^{2}$$)($$( 1 - 4 T + 19 T^{2} )^{2}$$)($$( 1 - T + 19 T^{2} )^{2}$$)($$( 1 - 7 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} )$$)($$( 1 - 7 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} )$$)($$( 1 - 7 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} )$$)($$( 1 - T + 19 T^{2} )( 1 + T + 19 T^{2} )$$)($$( 1 - 8 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} )$$)($$( 1 - T + 19 T^{2} )( 1 + T + 19 T^{2} )$$)($$( 1 - 7 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} )$$)($$( 1 - 7 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} )$$)($$( 1 - 7 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} )$$)($$( 1 - 8 T + 19 T^{2} )^{2}( 1 + 8 T + 19 T^{2} )^{2}$$)($$( 1 - 14 T^{2} + 361 T^{4} )^{2}$$)($$( 1 - 19 T^{2} )^{4}$$)($$( 1 - 8 T + 19 T^{2} )^{2}( 1 + 8 T + 19 T^{2} )^{2}$$)($$( 1 - 8 T + 19 T^{2} )^{2}( 1 + 8 T + 19 T^{2} )^{2}$$)($$( 1 - 8 T + 19 T^{2} )^{2}( 1 + 8 T + 19 T^{2} )^{2}$$)($$( 1 - 8 T + 19 T^{2} )^{2}( 1 + 8 T + 19 T^{2} )^{2}$$)($$( 1 - 7 T + 19 T^{2} )^{2}( 1 + 7 T + 19 T^{2} )^{2}$$)($$( 1 - 7 T + 19 T^{2} )^{2}( 1 + 7 T + 19 T^{2} )^{2}$$)($$( 1 - 14 T^{2} + 361 T^{4} )^{2}$$)($$( 1 - 14 T^{2} + 361 T^{4} )^{2}$$)($$( 1 - 7 T + 19 T^{2} )^{2}( 1 + 7 T + 19 T^{2} )^{2}$$)($$( 1 - T + 19 T^{2} )^{2}( 1 + T + 19 T^{2} )^{2}$$)($$( 1 - 8 T + 19 T^{2} )^{2}( 1 + 8 T + 19 T^{2} )^{2}$$)($$( 1 - 22 T^{2} + 361 T^{4} )^{2}$$)($$( 1 - 22 T^{2} + 361 T^{4} )^{2}$$)($$( 1 - 22 T^{2} + 361 T^{4} )^{2}$$)($$1 - 52 T^{2} + 1270 T^{4} - 18772 T^{6} + 130321 T^{8}$$)($$( 1 + 26 T^{2} + 361 T^{4} )^{2}$$)($$( 1 - 37 T^{2} + 361 T^{4} )^{2}$$)($$( 1 - 22 T^{2} + 361 T^{4} )^{2}$$)($$( 1 + 11 T^{2} + 361 T^{4} )^{2}$$)($$( 1 - 34 T^{2} + 361 T^{4} )^{2}$$)($$1 - 52 T^{2} + 1270 T^{4} - 18772 T^{6} + 130321 T^{8}$$)($$( 1 - 22 T^{2} + 361 T^{4} )^{2}$$)($$( 1 - 37 T^{2} + 361 T^{4} )^{4}$$)($$( 1 - 2 T^{2} + 195 T^{4} - 722 T^{6} + 130321 T^{8} )^{4}$$)($$( 1 + 6 T^{2} + 361 T^{4} )^{2}$$)($$( 1 + 36 T^{2} + 662 T^{4} + 12996 T^{6} + 130321 T^{8} )^{2}$$)($$( 1 + 26 T^{2} + 361 T^{4} )^{4}$$)($$( 1 + 11 T^{2} + 361 T^{4} )^{4}$$)($$( 1 + 35 T^{2} + 361 T^{4} )^{4}$$)
$23$ ($$1 + 4 T + 23 T^{2}$$)($$1 + 6 T + 23 T^{2}$$)($$1 - 6 T + 23 T^{2}$$)($$1 + 8 T + 23 T^{2}$$)($$1 + 23 T^{2}$$)($$1 - 6 T + 23 T^{2}$$)($$1 + 4 T + 23 T^{2}$$)($$1 - 4 T + 23 T^{2}$$)($$1 - 2 T + 23 T^{2}$$)($$1 + 2 T + 23 T^{2}$$)($$1 + 23 T^{2}$$)($$1 + 4 T + 23 T^{2}$$)($$1 - 4 T + 23 T^{2}$$)($$1 + 6 T + 23 T^{2}$$)($$1 + 23 T^{2}$$)($$1 + 6 T + 23 T^{2}$$)($$1 - 6 T + 23 T^{2}$$)($$1 + 8 T + 23 T^{2}$$)($$1 - 4 T + 23 T^{2}$$)($$1 - 10 T^{2} + 529 T^{4}$$)($$1 + 18 T^{2} + 529 T^{4}$$)($$1 - 10 T^{2} + 529 T^{4}$$)($$1 - 10 T^{2} + 529 T^{4}$$)($$( 1 - 23 T^{2} )^{2}$$)($$1 + 18 T^{2} + 529 T^{4}$$)($$( 1 - 23 T^{2} )^{2}$$)($$( 1 - 23 T^{2} )^{2}$$)($$1 - 42 T^{2} + 529 T^{4}$$)($$( 1 + 6 T + 23 T^{2} )^{2}$$)($$( 1 + 6 T + 23 T^{2} )^{2}$$)($$( 1 + 23 T^{2} )^{2}$$)($$( 1 + 23 T^{2} )^{2}$$)($$( 1 + 23 T^{2} )^{2}$$)($$( 1 + 23 T^{2} )^{2}$$)($$( 1 + 23 T^{2} )^{2}$$)($$( 1 - 6 T + 23 T^{2} )^{2}$$)($$( 1 - 6 T + 23 T^{2} )^{2}$$)($$( 1 - 6 T + 23 T^{2} )^{4}$$)($$( 1 + 40 T^{2} + 529 T^{4} )^{2}$$)($$( 1 - 44 T^{2} + 529 T^{4} )^{2}$$)($$( 1 + 34 T^{2} + 529 T^{4} )^{2}$$)($$( 1 + 6 T + 23 T^{2} )^{4}$$)($$( 1 - 34 T^{2} + 529 T^{4} )^{2}$$)($$( 1 - 34 T^{2} + 529 T^{4} )^{2}$$)($$( 1 - 10 T^{2} + 529 T^{4} )^{2}$$)($$( 1 - 10 T^{2} + 529 T^{4} )^{2}$$)($$( 1 - 40 T^{2} + 529 T^{4} )^{2}$$)($$( 1 - 40 T^{2} + 529 T^{4} )^{2}$$)($$( 1 - 23 T^{2} )^{4}$$)($$( 1 - 23 T^{2} )^{4}$$)($$( 1 - 23 T^{2} )^{4}$$)($$1 - 958 T^{4} + 279841 T^{8}$$)($$1 - 158 T^{4} + 279841 T^{8}$$)($$1 - 158 T^{4} + 279841 T^{8}$$)($$1 - 12 T + 72 T^{2} - 444 T^{3} + 2542 T^{4} - 10212 T^{5} + 38088 T^{6} - 146004 T^{7} + 279841 T^{8}$$)($$( 1 + 529 T^{4} )^{2}$$)($$( 1 + 529 T^{4} )^{2}$$)($$1 + 98 T^{4} + 279841 T^{8}$$)($$( 1 + 529 T^{4} )^{2}$$)($$1 + 238 T^{4} + 279841 T^{8}$$)($$1 + 12 T + 72 T^{2} + 444 T^{3} + 2542 T^{4} + 10212 T^{5} + 38088 T^{6} + 146004 T^{7} + 279841 T^{8}$$)($$1 - 958 T^{4} + 279841 T^{8}$$)($$( 1 - 958 T^{4} + 279841 T^{8} )^{2}$$)($$( 1 + 292 T^{4} + 504966 T^{8} + 81713572 T^{12} + 78310985281 T^{16} )^{2}$$)($$1 - 158 T^{4} + 279841 T^{8}$$)($$1 - 700 T^{4} + 184518 T^{8} - 195888700 T^{12} + 78310985281 T^{16}$$)($$( 1 + 529 T^{4} )^{4}$$)($$( 1 - 958 T^{4} + 279841 T^{8} )^{2}$$)($$( 1 - 958 T^{4} + 279841 T^{8} )^{2}$$)
$29$ ($$1 + 6 T + 29 T^{2}$$)($$1 + 2 T + 29 T^{2}$$)($$1 - 10 T + 29 T^{2}$$)($$1 - 6 T + 29 T^{2}$$)($$1 + 2 T + 29 T^{2}$$)($$1 + 6 T + 29 T^{2}$$)($$1 + 29 T^{2}$$)($$1 - 8 T + 29 T^{2}$$)($$1 - 6 T + 29 T^{2}$$)($$1 - 6 T + 29 T^{2}$$)($$1 + 6 T + 29 T^{2}$$)($$1 - 8 T + 29 T^{2}$$)($$1 + 29 T^{2}$$)($$1 + 6 T + 29 T^{2}$$)($$1 + 2 T + 29 T^{2}$$)($$1 - 10 T + 29 T^{2}$$)($$1 + 2 T + 29 T^{2}$$)($$1 + 6 T + 29 T^{2}$$)($$1 + 6 T + 29 T^{2}$$)($$( 1 - 6 T + 29 T^{2} )^{2}$$)($$( 1 + 6 T + 29 T^{2} )^{2}$$)($$( 1 - 2 T + 29 T^{2} )^{2}$$)($$( 1 + 10 T + 29 T^{2} )^{2}$$)($$( 1 - 6 T + 29 T^{2} )^{2}$$)($$( 1 - 6 T + 29 T^{2} )^{2}$$)($$( 1 - 2 T + 29 T^{2} )^{2}$$)($$( 1 - 2 T + 29 T^{2} )^{2}$$)($$( 1 + 6 T + 29 T^{2} )^{2}$$)($$1 + 50 T^{2} + 841 T^{4}$$)($$1 + 50 T^{2} + 841 T^{4}$$)($$( 1 - 29 T^{2} )^{2}$$)($$( 1 - 29 T^{2} )^{2}$$)($$( 1 - 29 T^{2} )^{2}$$)($$( 1 - 29 T^{2} )^{2}$$)($$( 1 - 29 T^{2} )^{2}$$)($$1 + 50 T^{2} + 841 T^{4}$$)($$1 + 50 T^{2} + 841 T^{4}$$)($$( 1 - 50 T^{2} + 841 T^{4} )^{2}$$)($$( 1 - 29 T^{2} )^{4}$$)($$( 1 - 6 T + 29 T^{2} )^{2}( 1 + 6 T + 29 T^{2} )^{2}$$)($$( 1 - 22 T^{2} + 841 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 841 T^{4} )^{2}$$)($$( 1 - 22 T^{2} + 841 T^{4} )^{2}$$)($$( 1 - 22 T^{2} + 841 T^{4} )^{2}$$)($$( 1 + 50 T^{2} + 841 T^{4} )^{2}$$)($$( 1 + 50 T^{2} + 841 T^{4} )^{2}$$)($$( 1 - 29 T^{2} )^{4}$$)($$( 1 - 29 T^{2} )^{4}$$)($$( 1 - 29 T^{2} )^{4}$$)($$( 1 - 29 T^{2} )^{4}$$)($$( 1 - 29 T^{2} )^{4}$$)($$( 1 + 26 T^{2} + 841 T^{4} )^{2}$$)($$( 1 + 8 T^{2} + 841 T^{4} )^{2}$$)($$( 1 + 56 T^{2} + 841 T^{4} )^{2}$$)($$( 1 + 4 T + 30 T^{2} + 116 T^{3} + 841 T^{4} )^{2}$$)($$( 1 + 29 T^{2} )^{4}$$)($$( 1 + 29 T^{2} )^{4}$$)($$( 1 + 29 T^{2} )^{4}$$)($$( 1 + 29 T^{2} )^{4}$$)($$( 1 + 38 T^{2} + 841 T^{4} )^{2}$$)($$( 1 - 4 T + 30 T^{2} - 116 T^{3} + 841 T^{4} )^{2}$$)($$( 1 + 26 T^{2} + 841 T^{4} )^{2}$$)($$( 1 + 29 T^{2} )^{8}$$)($$( 1 + 4 T^{2} - 426 T^{4} + 3364 T^{6} + 707281 T^{8} )^{4}$$)($$( 1 - 10 T + 29 T^{2} )^{2}( 1 + 10 T + 29 T^{2} )^{2}$$)($$( 1 - 4 T + 8 T^{2} - 116 T^{3} + 841 T^{4} )^{2}( 1 + 4 T + 8 T^{2} + 116 T^{3} + 841 T^{4} )^{2}$$)($$( 1 - 29 T^{2} )^{8}$$)($$( 1 - 22 T^{2} + 841 T^{4} )^{4}$$)($$( 1 - 22 T^{2} + 841 T^{4} )^{4}$$)
$31$ ($$1 + 4 T + 31 T^{2}$$)($$1 - 5 T + 31 T^{2}$$)($$1 - 3 T + 31 T^{2}$$)($$1 + 8 T + 31 T^{2}$$)($$1 + 31 T^{2}$$)($$1 - T + 31 T^{2}$$)($$1 - 8 T + 31 T^{2}$$)($$1 + 31 T^{2}$$)($$1 + 3 T + 31 T^{2}$$)($$1 + 3 T + 31 T^{2}$$)($$1 + 8 T + 31 T^{2}$$)($$1 + 31 T^{2}$$)($$1 - 8 T + 31 T^{2}$$)($$1 - T + 31 T^{2}$$)($$1 - 8 T + 31 T^{2}$$)($$1 - 3 T + 31 T^{2}$$)($$1 - 5 T + 31 T^{2}$$)($$1 + 31 T^{2}$$)($$1 + 4 T + 31 T^{2}$$)($$( 1 - T + 31 T^{2} )^{2}$$)($$( 1 + 8 T + 31 T^{2} )^{2}$$)($$( 1 - 5 T + 31 T^{2} )^{2}$$)($$( 1 - 3 T + 31 T^{2} )^{2}$$)($$( 1 + 8 T + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 - 8 T + 31 T^{2} )^{2}$$)($$( 1 + 31 T^{2} )^{2}$$)($$( 1 + 3 T + 31 T^{2} )^{2}$$)($$1 - 50 T^{2} + 961 T^{4}$$)($$1 - 50 T^{2} + 961 T^{4}$$)($$( 1 - 11 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} )$$)($$( 1 - 7 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} )$$)($$( 1 - 4 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} )$$)($$( 1 - 7 T + 31 T^{2} )( 1 + 7 T + 31 T^{2} )$$)($$( 1 - 11 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} )$$)($$1 - 50 T^{2} + 961 T^{4}$$)($$1 - 50 T^{2} + 961 T^{4}$$)($$( 1 - 50 T^{2} + 961 T^{4} )^{2}$$)($$( 1 + 34 T^{2} + 961 T^{4} )^{2}$$)($$( 1 - 31 T^{2} )^{4}$$)($$( 1 - 50 T^{2} + 961 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 961 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 961 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 961 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 961 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 961 T^{4} )^{2}$$)($$( 1 + 34 T^{2} + 961 T^{4} )^{2}$$)($$( 1 + 34 T^{2} + 961 T^{4} )^{2}$$)($$( 1 - 11 T + 31 T^{2} )^{2}( 1 + 11 T + 31 T^{2} )^{2}$$)($$( 1 - 7 T + 31 T^{2} )^{2}( 1 + 7 T + 31 T^{2} )^{2}$$)($$( 1 - 4 T + 31 T^{2} )^{2}( 1 + 4 T + 31 T^{2} )^{2}$$)($$( 1 + 8 T + 31 T^{2} )^{4}$$)($$( 1 - 2 T + 31 T^{2} )^{4}$$)($$( 1 - 2 T + 31 T^{2} )^{4}$$)($$( 1 + 30 T^{2} + 961 T^{4} )^{2}$$)($$( 1 + 4 T + 31 T^{2} )^{4}$$)($$( 1 + 7 T + 31 T^{2} )^{4}$$)($$( 1 - 8 T + 31 T^{2} )^{4}$$)($$( 1 - 11 T + 31 T^{2} )^{4}$$)($$( 1 + 4 T + 31 T^{2} )^{4}$$)($$( 1 + 30 T^{2} + 961 T^{4} )^{2}$$)($$( 1 + 8 T + 31 T^{2} )^{4}$$)($$( 1 - 2 T + 31 T^{2} )^{8}$$)($$( 1 - 5 T + 60 T^{2} - 155 T^{3} + 961 T^{4} )^{8}$$)($$( 1 - 31 T^{2} )^{4}$$)($$( 1 + 10 T^{2} + 961 T^{4} )^{4}$$)($$( 1 - 50 T^{2} + 961 T^{4} )^{4}$$)($$( 1 - 7 T + 31 T^{2} )^{4}( 1 + 7 T + 31 T^{2} )^{4}$$)($$( 1 - 35 T^{2} + 961 T^{4} )^{4}$$)
$37$ ($$1 + 8 T + 37 T^{2}$$)($$1 - 10 T + 37 T^{2}$$)($$1 + 2 T + 37 T^{2}$$)($$1 + 6 T + 37 T^{2}$$)($$1 - 10 T + 37 T^{2}$$)($$1 - 2 T + 37 T^{2}$$)($$1 + 2 T + 37 T^{2}$$)($$1 + 10 T + 37 T^{2}$$)($$1 + 6 T + 37 T^{2}$$)($$1 - 6 T + 37 T^{2}$$)($$1 + 2 T + 37 T^{2}$$)($$1 - 10 T + 37 T^{2}$$)($$1 - 2 T + 37 T^{2}$$)($$1 + 2 T + 37 T^{2}$$)($$1 - 2 T + 37 T^{2}$$)($$1 - 2 T + 37 T^{2}$$)($$1 + 10 T + 37 T^{2}$$)($$1 - 6 T + 37 T^{2}$$)($$1 - 8 T + 37 T^{2}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} )$$)($$1 + 26 T^{2} + 1369 T^{4}$$)($$1 - 38 T^{2} + 1369 T^{4}$$)($$( 1 + 8 T + 37 T^{2} )^{2}$$)($$( 1 - 8 T + 37 T^{2} )^{2}$$)($$( 1 - 10 T + 37 T^{2} )^{2}$$)($$( 1 + 10 T + 37 T^{2} )^{2}$$)($$( 1 - 10 T + 37 T^{2} )^{2}$$)($$( 1 - 10 T + 37 T^{2} )^{2}$$)($$( 1 + 10 T + 37 T^{2} )^{2}$$)($$( 1 - 8 T + 37 T^{2} )^{2}$$)($$( 1 + 8 T + 37 T^{2} )^{2}$$)($$( 1 + 50 T^{2} + 1369 T^{4} )^{2}$$)($$( 1 + 2 T + 37 T^{2} )^{4}$$)($$( 1 + 37 T^{2} )^{4}$$)($$( 1 - 4 T + 37 T^{2} )^{4}$$)($$( 1 + 50 T^{2} + 1369 T^{4} )^{2}$$)($$( 1 - 58 T^{2} + 1369 T^{4} )^{2}$$)($$( 1 - 58 T^{2} + 1369 T^{4} )^{2}$$)($$( 1 - 10 T^{2} + 1369 T^{4} )^{2}$$)($$( 1 - 10 T^{2} + 1369 T^{4} )^{2}$$)($$( 1 - 12 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2}$$)($$( 1 - 12 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2}$$)($$( 1 + 26 T^{2} + 1369 T^{4} )^{2}$$)($$( 1 + 26 T^{2} + 1369 T^{4} )^{2}$$)($$( 1 + 26 T^{2} + 1369 T^{4} )^{2}$$)($$( 1 + 16 T + 128 T^{2} + 592 T^{3} + 1369 T^{4} )^{2}$$)($$( 1 + 12 T + 72 T^{2} + 444 T^{3} + 1369 T^{4} )^{2}$$)($$( 1 - 4 T + 8 T^{2} - 148 T^{3} + 1369 T^{4} )^{2}$$)($$1 - 12 T + 72 T^{2} - 468 T^{3} + 3038 T^{4} - 17316 T^{5} + 98568 T^{6} - 607836 T^{7} + 1874161 T^{8}$$)($$1 - 2062 T^{4} + 1874161 T^{8}$$)($$1 - 2062 T^{4} + 1874161 T^{8}$$)($$( 1 + 1369 T^{4} )^{2}$$)($$1 - 2062 T^{4} + 1874161 T^{8}$$)($$( 1 - 6 T + 18 T^{2} - 222 T^{3} + 1369 T^{4} )^{2}$$)($$1 - 12 T + 72 T^{2} - 468 T^{3} + 3038 T^{4} - 17316 T^{5} + 98568 T^{6} - 607836 T^{7} + 1874161 T^{8}$$)($$( 1 - 16 T + 128 T^{2} - 592 T^{3} + 1369 T^{4} )^{2}$$)($$( 1 + 1106 T^{4} + 1874161 T^{8} )^{2}$$)($$( 1 + 1988 T^{4} + 2835558 T^{8} + 3725832068 T^{12} + 3512479453921 T^{16} )^{2}$$)($$( 1 - 2 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2}$$)($$( 1 - 16 T + 128 T^{2} - 912 T^{3} + 6098 T^{4} - 33744 T^{5} + 175232 T^{6} - 810448 T^{7} + 1874161 T^{8} )^{2}$$)($$( 1 - 1582 T^{4} + 1874161 T^{8} )^{2}$$)($$( 1 + 1369 T^{4} )^{4}$$)($$( 1 + 1369 T^{4} )^{4}$$)
$41$ ($$1 + 10 T + 41 T^{2}$$)($$1 - 12 T + 41 T^{2}$$)($$1 + 8 T + 41 T^{2}$$)($$1 + 6 T + 41 T^{2}$$)($$1 - 10 T + 41 T^{2}$$)($$1 + 41 T^{2}$$)($$1 - 2 T + 41 T^{2}$$)($$1 - 2 T + 41 T^{2}$$)($$1 - 4 T + 41 T^{2}$$)($$1 - 4 T + 41 T^{2}$$)($$1 + 6 T + 41 T^{2}$$)($$1 - 2 T + 41 T^{2}$$)($$1 - 2 T + 41 T^{2}$$)($$1 + 41 T^{2}$$)($$1 + 6 T + 41 T^{2}$$)($$1 + 8 T + 41 T^{2}$$)($$1 - 12 T + 41 T^{2}$$)($$1 - 10 T + 41 T^{2}$$)($$1 + 10 T + 41 T^{2}$$)($$( 1 + 41 T^{2} )^{2}$$)($$( 1 + 6 T + 41 T^{2} )^{2}$$)($$( 1 - 12 T + 41 T^{2} )^{2}$$)($$( 1 + 8 T + 41 T^{2} )^{2}$$)($$( 1 + 6 T + 41 T^{2} )^{2}$$)($$( 1 - 10 T + 41 T^{2} )^{2}$$)($$( 1 + 6 T + 41 T^{2} )^{2}$$)($$( 1 - 10 T + 41 T^{2} )^{2}$$)($$( 1 - 4 T + 41 T^{2} )^{2}$$)($$1 - 55 T^{2} + 1681 T^{4}$$)($$1 - 55 T^{2} + 1681 T^{4}$$)($$( 1 - 41 T^{2} )^{2}$$)($$( 1 - 41 T^{2} )^{2}$$)($$( 1 - 41 T^{2} )^{2}$$)($$( 1 - 41 T^{2} )^{2}$$)($$( 1 - 41 T^{2} )^{2}$$)($$1 - 55 T^{2} + 1681 T^{4}$$)($$1 - 55 T^{2} + 1681 T^{4}$$)($$( 1 - 50 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 46 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 12 T + 41 T^{2} )^{2}( 1 + 12 T + 41 T^{2} )^{2}$$)($$( 1 + 62 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 + 62 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 + 62 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 55 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 55 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 46 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 46 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 41 T^{2} )^{4}$$)($$( 1 - 41 T^{2} )^{4}$$)($$( 1 - 41 T^{2} )^{4}$$)($$( 1 - 50 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 41 T^{2} )^{4}$$)($$( 1 - 41 T^{2} )^{4}$$)($$( 1 - 41 T^{2} )^{4}$$)($$( 1 - 41 T^{2} )^{4}$$)($$( 1 - 2 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 55 T^{2} + 1681 T^{4} )^{4}$$)($$( 1 - 25 T^{2} + 3312 T^{4} - 42025 T^{6} + 2825761 T^{8} )^{4}$$)($$( 1 + 41 T^{2} )^{4}$$)($$( 1 + 12 T + 94 T^{2} + 492 T^{3} + 1681 T^{4} )^{4}$$)($$( 1 - 6 T + 41 T^{2} )^{8}$$)($$( 1 + 41 T^{2} )^{8}$$)($$( 1 - 12 T + 41 T^{2} )^{8}$$)
$43$ ($$1 + 4 T + 43 T^{2}$$)($$1 + 3 T + 43 T^{2}$$)($$1 - T + 43 T^{2}$$)($$1 - 4 T + 43 T^{2}$$)($$1 - 4 T + 43 T^{2}$$)($$1 - T + 43 T^{2}$$)($$1 + 4 T + 43 T^{2}$$)($$1 - 12 T + 43 T^{2}$$)($$1 + 11 T + 43 T^{2}$$)($$1 - 11 T + 43 T^{2}$$)($$1 + 4 T + 43 T^{2}$$)($$1 + 12 T + 43 T^{2}$$)($$1 - 4 T + 43 T^{2}$$)($$1 + T + 43 T^{2}$$)($$1 - 12 T + 43 T^{2}$$)($$1 + T + 43 T^{2}$$)($$1 - 3 T + 43 T^{2}$$)($$1 + 4 T + 43 T^{2}$$)($$1 - 4 T + 43 T^{2}$$)($$1 - 85 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 77 T^{2} + 1849 T^{4}$$)($$1 - 85 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 + 58 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 + 35 T^{2} + 1849 T^{4}$$)($$1 - 74 T^{2} + 1849 T^{4}$$)($$1 - 74 T^{2} + 1849 T^{4}$$)($$( 1 - 13 T + 43 T^{2} )( 1 + 13 T + 43 T^{2} )$$)($$( 1 - 5 T + 43 T^{2} )( 1 + 5 T + 43 T^{2} )$$)($$( 1 - 8 T + 43 T^{2} )( 1 + 8 T + 43 T^{2} )$$)($$( 1 - 5 T + 43 T^{2} )( 1 + 5 T + 43 T^{2} )$$)($$( 1 - 13 T + 43 T^{2} )( 1 + 13 T + 43 T^{2} )$$)($$1 - 74 T^{2} + 1849 T^{4}$$)($$1 - 74 T^{2} + 1849 T^{4}$$)($$( 1 - 10 T + 43 T^{2} )^{2}( 1 + 10 T + 43 T^{2} )^{2}$$)($$( 1 - 80 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 + 76 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 - 38 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 - 10 T + 43 T^{2} )^{2}( 1 + 10 T + 43 T^{2} )^{2}$$)($$( 1 + 38 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 + 38 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 + 74 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 + 74 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 + 80 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 + 80 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 + 83 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 - 61 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 - 22 T^{2} + 1849 T^{4} )^{2}$$)($$( 1 + 4 T + 8 T^{2} + 172 T^{3} + 1849 T^{4} )^{2}$$)($$( 1 - 12 T + 72 T^{2} - 516 T^{3} + 1849 T^{4} )^{2}$$)($$( 1 + 4 T + 8 T^{2} + 172 T^{3} + 1849 T^{4} )^{2}$$)($$1 - 4 T + 8 T^{2} - 164 T^{3} + 3358 T^{4} - 7052 T^{5} + 14792 T^{6} - 318028 T^{7} + 3418801 T^{8}$$)($$1 - 3214 T^{4} + 3418801 T^{8}$$)($$1 + 23 T^{4} + 3418801 T^{8}$$)($$( 1 + 1849 T^{4} )^{2}$$)($$1 + 3191 T^{4} + 3418801 T^{8}$$)($$( 1 + 6 T + 18 T^{2} + 258 T^{3} + 1849 T^{4} )^{2}$$)($$1 - 4 T + 8 T^{2} - 164 T^{3} + 3358 T^{4} - 7052 T^{5} + 14792 T^{6} - 318028 T^{7} + 3418801 T^{8}$$)($$( 1 - 4 T + 8 T^{2} - 172 T^{3} + 1849 T^{4} )^{2}$$)($$( 1 + 1778 T^{4} + 3418801 T^{8} )^{2}$$)($$( 1 - 5047 T^{4} + 11852448 T^{8} - 17254688647 T^{12} + 11688200277601 T^{16} )^{2}$$)($$1 + 1202 T^{4} + 3418801 T^{8}$$)($$1 - 92 T^{4} - 6160986 T^{8} - 314529692 T^{12} + 11688200277601 T^{16}$$)($$( 1 - 3214 T^{4} + 3418801 T^{8} )^{2}$$)($$( 1 - 2473 T^{4} + 3418801 T^{8} )^{2}$$)($$( 1 + 3527 T^{4} + 3418801 T^{8} )^{2}$$)
$47$ ($$1 - 4 T + 47 T^{2}$$)($$1 - 10 T + 47 T^{2}$$)($$1 - 2 T + 47 T^{2}$$)($$1 + 47 T^{2}$$)($$1 - 8 T + 47 T^{2}$$)($$1 + 6 T + 47 T^{2}$$)($$1 + 8 T + 47 T^{2}$$)($$1 + 47 T^{2}$$)($$1 - 10 T + 47 T^{2}$$)($$1 + 10 T + 47 T^{2}$$)($$1 + 47 T^{2}$$)($$1 + 47 T^{2}$$)($$1 - 8 T + 47 T^{2}$$)($$1 - 6 T + 47 T^{2}$$)($$1 - 8 T + 47 T^{2}$$)($$1 + 2 T + 47 T^{2}$$)($$1 + 10 T + 47 T^{2}$$)($$1 - 8 T + 47 T^{2}$$)($$1 + 4 T + 47 T^{2}$$)($$1 - 58 T^{2} + 2209 T^{4}$$)($$( 1 - 47 T^{2} )^{2}$$)($$1 + 6 T^{2} + 2209 T^{4}$$)($$1 - 90 T^{2} + 2209 T^{4}$$)($$( 1 - 47 T^{2} )^{2}$$)($$1 - 30 T^{2} + 2209 T^{4}$$)($$1 - 30 T^{2} + 2209 T^{4}$$)($$1 - 30 T^{2} + 2209 T^{4}$$)($$1 + 6 T^{2} + 2209 T^{4}$$)($$( 1 - 6 T + 47 T^{2} )^{2}$$)($$( 1 - 6 T + 47 T^{2} )^{2}$$)($$( 1 + 47 T^{2} )^{2}$$)($$( 1 + 47 T^{2} )^{2}$$)($$( 1 + 47 T^{2} )^{2}$$)($$( 1 + 47 T^{2} )^{2}$$)($$( 1 + 47 T^{2} )^{2}$$)($$( 1 + 6 T + 47 T^{2} )^{2}$$)($$( 1 + 6 T + 47 T^{2} )^{2}$$)($$( 1 + 6 T + 47 T^{2} )^{4}$$)($$( 1 - 56 T^{2} + 2209 T^{4} )^{2}$$)($$( 1 + 4 T^{2} + 2209 T^{4} )^{2}$$)($$( 1 + 82 T^{2} + 2209 T^{4} )^{2}$$)($$( 1 - 6 T + 47 T^{2} )^{4}$$)($$( 1 - 82 T^{2} + 2209 T^{4} )^{2}$$)($$( 1 - 82 T^{2} + 2209 T^{4} )^{2}$$)($$( 1 - 58 T^{2} + 2209 T^{4} )^{2}$$)($$( 1 - 58 T^{2} + 2209 T^{4} )^{2}$$)($$( 1 + 56 T^{2} + 2209 T^{4} )^{2}$$)($$( 1 + 56 T^{2} + 2209 T^{4} )^{2}$$)($$( 1 - 47 T^{2} )^{4}$$)($$( 1 - 47 T^{2} )^{4}$$)($$( 1 - 47 T^{2} )^{4}$$)($$1 + 3682 T^{4} + 4879681 T^{8}$$)($$( 1 + 2209 T^{4} )^{2}$$)($$1 - 3518 T^{4} + 4879681 T^{8}$$)($$1 - 20 T + 200 T^{2} - 1860 T^{3} + 15182 T^{4} - 87420 T^{5} + 441800 T^{6} - 2076460 T^{7} + 4879681 T^{8}$$)($$( 1 + 2209 T^{4} )^{2}$$)($$( 1 + 2209 T^{4} )^{2}$$)($$1 - 4222 T^{4} + 4879681 T^{8}$$)($$( 1 + 2209 T^{4} )^{2}$$)($$( 1 - 14 T + 98 T^{2} - 658 T^{3} + 2209 T^{4} )( 1 + 14 T + 98 T^{2} + 658 T^{3} + 2209 T^{4} )$$)($$1 + 20 T + 200 T^{2} + 1860 T^{3} + 15182 T^{4} + 87420 T^{5} + 441800 T^{6} + 2076460 T^{7} + 4879681 T^{8}$$)($$1 + 3682 T^{4} + 4879681 T^{8}$$)($$( 1 + 2209 T^{4} )^{4}$$)($$( 1 - 3518 T^{4} + 4879681 T^{8} )^{4}$$)($$1 + 1666 T^{4} + 4879681 T^{8}$$)($$1 - 5692 T^{4} + 17637894 T^{8} - 27775144252 T^{12} + 23811286661761 T^{16}$$)($$( 1 - 1918 T^{4} + 4879681 T^{8} )^{2}$$)($$( 1 - 1054 T^{4} + 4879681 T^{8} )^{2}$$)($$( 1 - 1054 T^{4} + 4879681 T^{8} )^{2}$$)
$53$ ($$1 + 12 T + 53 T^{2}$$)($$1 + 53 T^{2}$$)($$1 - 4 T + 53 T^{2}$$)($$1 - 2 T + 53 T^{2}$$)($$1 - 10 T + 53 T^{2}$$)($$1 + 12 T + 53 T^{2}$$)($$1 + 6 T + 53 T^{2}$$)($$1 - 10 T + 53 T^{2}$$)($$1 + 8 T + 53 T^{2}$$)($$1 - 8 T + 53 T^{2}$$)($$1 - 6 T + 53 T^{2}$$)($$1 + 10 T + 53 T^{2}$$)($$1 - 6 T + 53 T^{2}$$)($$1 - 12 T + 53 T^{2}$$)($$1 + 6 T + 53 T^{2}$$)($$1 + 4 T + 53 T^{2}$$)($$1 + 53 T^{2}$$)($$1 + 10 T + 53 T^{2}$$)($$1 - 12 T + 53 T^{2}$$)($$1 + 38 T^{2} + 2809 T^{4}$$)($$1 - 102 T^{2} + 2809 T^{4}$$)($$( 1 - 53 T^{2} )^{2}$$)($$( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} )$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 6 T^{2} + 2809 T^{4}$$)($$1 - 42 T^{2} + 2809 T^{4}$$)($$1 + 2 T^{2} + 2809 T^{4}$$)($$1 + 2 T^{2} + 2809 T^{4}$$)($$( 1 - 53 T^{2} )^{2}$$)($$( 1 - 53 T^{2} )^{2}$$)($$( 1 - 53 T^{2} )^{2}$$)($$( 1 - 53 T^{2} )^{2}$$)($$( 1 - 53 T^{2} )^{2}$$)($$1 + 2 T^{2} + 2809 T^{4}$$)($$1 + 2 T^{2} + 2809 T^{4}$$)($$( 1 + 2 T^{2} + 2809 T^{4} )^{2}$$)($$( 1 - 70 T^{2} + 2809 T^{4} )^{2}$$)($$( 1 - 53 T^{2} )^{4}$$)($$( 1 - 70 T^{2} + 2809 T^{4} )^{2}$$)($$( 1 + 2 T^{2} + 2809 T^{4} )^{2}$$)($$( 1 - 6 T + 53 T^{2} )^{4}$$)($$( 1 + 6 T + 53 T^{2} )^{4}$$)($$( 1 - 2 T^{2} + 2809 T^{4} )^{2}$$)($$( 1 - 2 T^{2} + 2809 T^{4} )^{2}$$)($$( 1 - 6 T + 53 T^{2} )^{4}$$)($$( 1 + 6 T + 53 T^{2} )^{4}$$)($$( 1 + 53 T^{2} )^{4}$$)($$( 1 + 53 T^{2} )^{4}$$)($$( 1 + 53 T^{2} )^{4}$$)($$1 - 3854 T^{4} + 7890481 T^{8}$$)($$( 1 - 56 T^{2} + 2809 T^{4} )( 1 + 56 T^{2} + 2809 T^{4} )$$)($$1 - 4174 T^{4} + 7890481 T^{8}$$)($$( 1 - 6 T + 18 T^{2} - 318 T^{3} + 2809 T^{4} )^{2}$$)($$( 1 + 2809 T^{4} )^{2}$$)($$( 1 + 2809 T^{4} )^{2}$$)($$1 + 1778 T^{4} + 7890481 T^{8}$$)($$( 1 + 2809 T^{4} )^{2}$$)($$1 + 3598 T^{4} + 7890481 T^{8}$$)($$( 1 + 6 T + 18 T^{2} + 318 T^{3} + 2809 T^{4} )^{2}$$)($$1 - 3854 T^{4} + 7890481 T^{8}$$)($$( 1 - 718 T^{4} + 7890481 T^{8} )^{2}$$)($$( 1 - 28 T^{4} - 14631642 T^{8} - 220933468 T^{12} + 62259690411361 T^{16} )^{2}$$)($$( 1 + 2 T + 2 T^{2} + 106 T^{3} + 2809 T^{4} )^{2}$$)($$( 1 - 4 T + 8 T^{2} - 212 T^{3} + 2809 T^{4} )^{4}$$)($$( 1 - 2254 T^{4} + 7890481 T^{8} )^{2}$$)($$( 1 + 1778 T^{4} + 7890481 T^{8} )^{2}$$)($$( 1 - 2254 T^{4} + 7890481 T^{8} )^{2}$$)
$59$ ($$1 + 4 T + 59 T^{2}$$)($$1 - 6 T + 59 T^{2}$$)($$1 - 10 T + 59 T^{2}$$)($$1 + 4 T + 59 T^{2}$$)($$1 - 4 T + 59 T^{2}$$)($$1 - 6 T + 59 T^{2}$$)($$1 + 10 T + 59 T^{2}$$)($$1 - 6 T + 59 T^{2}$$)($$1 - 6 T + 59 T^{2}$$)($$1 - 6 T + 59 T^{2}$$)($$1 + 59 T^{2}$$)($$1 - 6 T + 59 T^{2}$$)($$1 + 10 T + 59 T^{2}$$)($$1 - 6 T + 59 T^{2}$$)($$1 + 12 T + 59 T^{2}$$)($$1 - 10 T + 59 T^{2}$$)($$1 - 6 T + 59 T^{2}$$)($$1 + 59 T^{2}$$)($$1 + 4 T + 59 T^{2}$$)($$( 1 + 6 T + 59 T^{2} )^{2}$$)($$( 1 - 4 T + 59 T^{2} )^{2}$$)($$( 1 + 6 T + 59 T^{2} )^{2}$$)($$( 1 + 10 T + 59 T^{2} )^{2}$$)($$( 1 + 59 T^{2} )^{2}$$)($$( 1 + 59 T^{2} )^{2}$$)($$( 1 - 12 T + 59 T^{2} )^{2}$$)($$( 1 + 4 T + 59 T^{2} )^{2}$$)($$( 1 + 6 T + 59 T^{2} )^{2}$$)($$( 1 + 12 T + 59 T^{2} )^{2}$$)($$( 1 - 12 T + 59 T^{2} )^{2}$$)($$( 1 + 59 T^{2} )^{2}$$)($$( 1 + 59 T^{2} )^{2}$$)($$( 1 + 59 T^{2} )^{2}$$)($$( 1 + 59 T^{2} )^{2}$$)($$( 1 + 59 T^{2} )^{2}$$)($$( 1 + 12 T + 59 T^{2} )^{2}$$)($$( 1 - 12 T + 59 T^{2} )^{2}$$)($$( 1 + 94 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 22 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 59 T^{2} )^{4}$$)($$( 1 + 106 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 94 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 106 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 106 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 - 12 T + 59 T^{2} )^{4}$$)($$( 1 + 12 T + 59 T^{2} )^{4}$$)($$( 1 + 22 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 22 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 59 T^{2} )^{4}$$)($$( 1 + 59 T^{2} )^{4}$$)($$( 1 + 59 T^{2} )^{4}$$)($$( 1 + 86 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 20 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 116 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 - 4 T + 59 T^{2} )^{4}$$)($$( 1 + 59 T^{2} )^{4}$$)($$( 1 + 59 T^{2} )^{4}$$)($$( 1 + 59 T^{2} )^{4}$$)($$( 1 + 59 T^{2} )^{4}$$)($$( 1 + 38 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 4 T + 59 T^{2} )^{4}$$)($$( 1 + 86 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 10 T^{2} + 3481 T^{4} )^{4}$$)($$( 1 + 64 T^{2} + 4686 T^{4} + 222784 T^{6} + 12117361 T^{8} )^{4}$$)($$( 1 - 10 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 20 T^{2} + 3481 T^{4} )^{4}$$)($$( 1 + 10 T^{2} + 3481 T^{4} )^{4}$$)($$( 1 + 10 T^{2} + 3481 T^{4} )^{4}$$)($$( 1 + 10 T^{2} + 3481 T^{4} )^{4}$$)
$61$ ($$1 - 2 T + 61 T^{2}$$)($$1 + 13 T + 61 T^{2}$$)($$1 - 7 T + 61 T^{2}$$)($$1 + 2 T + 61 T^{2}$$)($$1 + 2 T + 61 T^{2}$$)($$1 + 13 T + 61 T^{2}$$)($$1 - 2 T + 61 T^{2}$$)($$1 - 2 T + 61 T^{2}$$)($$1 - 3 T + 61 T^{2}$$)($$1 - 3 T + 61 T^{2}$$)($$1 + 10 T + 61 T^{2}$$)($$1 - 2 T + 61 T^{2}$$)($$1 - 2 T + 61 T^{2}$$)($$1 + 13 T + 61 T^{2}$$)($$1 - 14 T + 61 T^{2}$$)($$1 - 7 T + 61 T^{2}$$)($$1 + 13 T + 61 T^{2}$$)($$1 - 6 T + 61 T^{2}$$)($$1 - 2 T + 61 T^{2}$$)($$( 1 + 13 T + 61 T^{2} )^{2}$$)($$( 1 + 2 T + 61 T^{2} )^{2}$$)($$( 1 + 13 T + 61 T^{2} )^{2}$$)($$( 1 - 7 T + 61 T^{2} )^{2}$$)($$( 1 + 10 T + 61 T^{2} )^{2}$$)($$( 1 - 6 T + 61 T^{2} )^{2}$$)($$( 1 - 14 T + 61 T^{2} )^{2}$$)($$( 1 + 2 T + 61 T^{2} )^{2}$$)($$( 1 - 3 T + 61 T^{2} )^{2}$$)($$( 1 - 8 T + 61 T^{2} )^{2}$$)($$( 1 - 8 T + 61 T^{2} )^{2}$$)($$( 1 + T + 61 T^{2} )^{2}$$)($$( 1 + 13 T + 61 T^{2} )^{2}$$)($$( 1 - 14 T + 61 T^{2} )^{2}$$)($$( 1 + 13 T + 61 T^{2} )^{2}$$)($$( 1 + T + 61 T^{2} )^{2}$$)($$( 1 - 8 T + 61 T^{2} )^{2}$$)($$( 1 - 8 T + 61 T^{2} )^{2}$$)($$( 1 + 2 T + 61 T^{2} )^{4}$$)($$( 1 - 8 T + 61 T^{2} )^{4}$$)($$( 1 + 8 T + 61 T^{2} )^{4}$$)($$( 1 + 10 T + 61 T^{2} )^{4}$$)($$( 1 + 2 T + 61 T^{2} )^{4}$$)($$( 1 + 10 T + 61 T^{2} )^{4}$$)($$( 1 + 10 T + 61 T^{2} )^{4}$$)($$( 1 - 8 T + 61 T^{2} )^{4}$$)($$( 1 - 8 T + 61 T^{2} )^{4}$$)($$( 1 - 8 T + 61 T^{2} )^{4}$$)($$( 1 - 8 T + 61 T^{2} )^{4}$$)($$( 1 + T + 61 T^{2} )^{4}$$)($$( 1 + 13 T + 61 T^{2} )^{4}$$)($$( 1 - 14 T + 61 T^{2} )^{4}$$)($$( 1 + 6 T + 61 T^{2} )^{4}$$)($$( 1 + 6 T + 61 T^{2} )^{4}$$)($$( 1 + 6 T + 61 T^{2} )^{4}$$)($$( 1 - 12 T + 126 T^{2} - 732 T^{3} + 3721 T^{4} )^{2}$$)($$( 1 - 14 T + 61 T^{2} )^{4}$$)($$( 1 + 13 T + 61 T^{2} )^{4}$$)($$( 1 - 2 T + 61 T^{2} )^{4}$$)($$( 1 + T + 61 T^{2} )^{4}$$)($$( 1 + 6 T + 61 T^{2} )^{4}$$)($$( 1 - 12 T + 126 T^{2} - 732 T^{3} + 3721 T^{4} )^{2}$$)($$( 1 + 6 T + 61 T^{2} )^{4}$$)($$( 1 - 14 T + 61 T^{2} )^{8}$$)($$( 1 + 3 T + 116 T^{2} + 183 T^{3} + 3721 T^{4} )^{8}$$)($$( 1 - 4 T + 61 T^{2} )^{4}$$)($$( 1 + 4 T + 102 T^{2} + 244 T^{3} + 3721 T^{4} )^{4}$$)($$( 1 + 10 T + 61 T^{2} )^{8}$$)($$( 1 + T + 61 T^{2} )^{8}$$)($$( 1 - 11 T + 61 T^{2} )^{8}$$)
$67$ ($$1 - 4 T + 67 T^{2}$$)($$1 + 7 T + 67 T^{2}$$)($$1 + 3 T + 67 T^{2}$$)($$1 + 4 T + 67 T^{2}$$)($$1 - 12 T + 67 T^{2}$$)($$1 + 11 T + 67 T^{2}$$)($$1 + 8 T + 67 T^{2}$$)($$1 - 8 T + 67 T^{2}$$)($$1 - T + 67 T^{2}$$)($$1 + T + 67 T^{2}$$)($$1 + 4 T + 67 T^{2}$$)($$1 + 8 T + 67 T^{2}$$)($$1 - 8 T + 67 T^{2}$$)($$1 - 11 T + 67 T^{2}$$)($$1 - 4 T + 67 T^{2}$$)($$1 - 3 T + 67 T^{2}$$)($$1 - 7 T + 67 T^{2}$$)($$1 + 4 T + 67 T^{2}$$)($$1 + 4 T + 67 T^{2}$$)($$1 - 13 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 - 85 T^{2} + 4489 T^{4}$$)($$1 - 125 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 + 10 T^{2} + 4489 T^{4}$$)($$1 - 133 T^{2} + 4489 T^{4}$$)($$( 1 - 11 T + 67 T^{2} )( 1 + 11 T + 67 T^{2} )$$)($$( 1 - 11 T + 67 T^{2} )( 1 + 11 T + 67 T^{2} )$$)($$( 1 - 11 T + 67 T^{2} )( 1 + 11 T + 67 T^{2} )$$)($$( 1 - 5 T + 67 T^{2} )( 1 + 5 T + 67 T^{2} )$$)($$( 1 - 16 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} )$$)($$( 1 - 5 T + 67 T^{2} )( 1 + 5 T + 67 T^{2} )$$)($$( 1 - 11 T + 67 T^{2} )( 1 + 11 T + 67 T^{2} )$$)($$( 1 - 11 T + 67 T^{2} )( 1 + 11 T + 67 T^{2} )$$)($$( 1 - 11 T + 67 T^{2} )( 1 + 11 T + 67 T^{2} )$$)($$( 1 - 14 T + 67 T^{2} )^{2}( 1 + 14 T + 67 T^{2} )^{2}$$)($$( 1 - 80 T^{2} + 4489 T^{4} )^{2}$$)($$( 1 - 116 T^{2} + 4489 T^{4} )^{2}$$)($$( 1 - 86 T^{2} + 4489 T^{4} )^{2}$$)($$( 1 - 14 T + 67 T^{2} )^{2}( 1 + 14 T + 67 T^{2} )^{2}$$)($$( 1 + 86 T^{2} + 4489 T^{4} )^{2}$$)($$( 1 + 86 T^{2} + 4489 T^{4} )^{2}$$)($$( 1 - 13 T^{2} + 4489 T^{4} )^{2}$$)($$( 1 - 13 T^{2} + 4489 T^{4} )^{2}$$)($$( 1 + 80 T^{2} + 4489 T^{4} )^{2}$$)($$( 1 + 80 T^{2} + 4489 T^{4} )^{2}$$)($$( 1 - 13 T^{2} + 4489 T^{4} )^{2}$$)($$( 1 - 109 T^{2} + 4489 T^{4} )^{2}$$)($$( 1 + 122 T^{2} + 4489 T^{4} )^{2}$$)($$( 1 + 12 T + 72 T^{2} + 804 T^{3} + 4489 T^{4} )^{2}$$)($$( 1 + 8 T + 32 T^{2} + 536 T^{3} + 4489 T^{4} )^{2}$$)($$( 1 - 8 T + 32 T^{2} - 536 T^{3} + 4489 T^{4} )^{2}$$)($$1 - 12 T + 72 T^{2} + 180 T^{3} - 6274 T^{4} + 12060 T^{5} + 323208 T^{6} - 3609156 T^{7} + 20151121 T^{8}$$)($$1 + 5906 T^{4} + 20151121 T^{8}$$)($$1 + 2903 T^{4} + 20151121 T^{8}$$)($$( 1 + 4489 T^{4} )^{2}$$)($$1 - 8809 T^{4} + 20151121 T^{8}$$)($$( 1 + 2 T + 2 T^{2} + 134 T^{3} + 4489 T^{4} )^{2}$$)($$1 - 12 T + 72 T^{2} + 180 T^{3} - 6274 T^{4} + 12060 T^{5} + 323208 T^{6} - 3609156 T^{7} + 20151121 T^{8}$$)($$( 1 - 12 T + 72 T^{2} - 804 T^{3} + 4489 T^{4} )^{2}$$)($$( 1 + 2471 T^{4} + 20151121 T^{8} )^{2}$$)($$( 1 + 8183 T^{4} + 20151121 T^{8} )^{4}$$)($$1 + 4946 T^{4} + 20151121 T^{8}$$)($$1 + 2788 T^{4} - 12042906 T^{8} + 56181325348 T^{12} + 406067677556641 T^{16}$$)($$( 1 + 4946 T^{4} + 20151121 T^{8} )^{2}$$)($$( 1 + 8711 T^{4} + 20151121 T^{8} )^{2}$$)($$( 1 - 7753 T^{4} + 20151121 T^{8} )^{2}$$)
$71$ ($$1 + 71 T^{2}$$)($$1 - 4 T + 71 T^{2}$$)($$1 - 8 T + 71 T^{2}$$)($$1 + 8 T + 71 T^{2}$$)($$1 - 8 T + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$1 + 12 T + 71 T^{2}$$)($$1 - 4 T + 71 T^{2}$$)($$1 - 12 T + 71 T^{2}$$)($$1 - 12 T + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$1 - 4 T + 71 T^{2}$$)($$1 + 12 T + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$1 + 8 T + 71 T^{2}$$)($$1 - 8 T + 71 T^{2}$$)($$1 - 4 T + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 8 T + 71 T^{2} )^{2}$$)($$( 1 - 4 T + 71 T^{2} )^{2}$$)($$( 1 - 8 T + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 8 T + 71 T^{2} )^{2}$$)($$( 1 - 8 T + 71 T^{2} )^{2}$$)($$( 1 - 12 T + 71 T^{2} )^{2}$$)($$( 1 - 6 T + 71 T^{2} )^{2}$$)($$( 1 + 6 T + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 - 6 T + 71 T^{2} )^{2}$$)($$( 1 + 6 T + 71 T^{2} )^{2}$$)($$( 1 + 46 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 + 118 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 + 71 T^{2} )^{4}$$)($$( 1 - 50 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 + 46 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 - 6 T + 71 T^{2} )^{4}$$)($$( 1 + 6 T + 71 T^{2} )^{4}$$)($$( 1 + 118 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 + 118 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 + 71 T^{2} )^{4}$$)($$( 1 + 71 T^{2} )^{4}$$)($$( 1 + 71 T^{2} )^{4}$$)($$( 1 - 14 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 + 58 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 - 134 T^{2} + 5041 T^{4} )^{2}$$)($$1 - 132 T^{2} + 13286 T^{4} - 665412 T^{6} + 25411681 T^{8}$$)($$( 1 - 71 T^{2} )^{4}$$)($$( 1 - 71 T^{2} )^{4}$$)($$( 1 - 71 T^{2} )^{4}$$)($$( 1 - 71 T^{2} )^{4}$$)($$( 1 - 122 T^{2} + 5041 T^{4} )^{2}$$)($$1 - 132 T^{2} + 13286 T^{4} - 665412 T^{6} + 25411681 T^{8}$$)($$( 1 - 14 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 - 71 T^{2} )^{8}$$)($$( 1 - 172 T^{2} + 15366 T^{4} - 867052 T^{6} + 25411681 T^{8} )^{4}$$)($$( 1 - 110 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 - 124 T^{2} + 7782 T^{4} - 625084 T^{6} + 25411681 T^{8} )^{2}$$)($$( 1 + 50 T^{2} + 5041 T^{4} )^{4}$$)($$( 1 + 50 T^{2} + 5041 T^{4} )^{4}$$)($$( 1 - 94 T^{2} + 5041 T^{4} )^{4}$$)
$73$ ($$1 + 8 T + 73 T^{2}$$)($$1 + 6 T + 73 T^{2}$$)($$1 - 14 T + 73 T^{2}$$)($$1 + 10 T + 73 T^{2}$$)($$1 + 10 T + 73 T^{2}$$)($$1 - 2 T + 73 T^{2}$$)($$1 - 4 T + 73 T^{2}$$)($$1 - 4 T + 73 T^{2}$$)($$1 - 10 T + 73 T^{2}$$)($$1 + 10 T + 73 T^{2}$$)($$1 + 2 T + 73 T^{2}$$)($$1 + 4 T + 73 T^{2}$$)($$1 + 4 T + 73 T^{2}$$)($$1 + 2 T + 73 T^{2}$$)($$1 - 6 T + 73 T^{2}$$)($$1 + 14 T + 73 T^{2}$$)($$1 - 6 T + 73 T^{2}$$)($$1 - 14 T + 73 T^{2}$$)($$1 - 8 T + 73 T^{2}$$)($$1 - 142 T^{2} + 5329 T^{4}$$)($$1 - 46 T^{2} + 5329 T^{4}$$)($$( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} )$$)($$1 + 50 T^{2} + 5329 T^{4}$$)($$1 - 142 T^{2} + 5329 T^{4}$$)($$1 + 50 T^{2} + 5329 T^{4}$$)($$( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} )$$)($$1 - 46 T^{2} + 5329 T^{4}$$)($$1 - 46 T^{2} + 5329 T^{4}$$)($$( 1 + T + 73 T^{2} )^{2}$$)($$( 1 - T + 73 T^{2} )^{2}$$)($$( 1 + 10 T + 73 T^{2} )^{2}$$)($$( 1 - 10 T + 73 T^{2} )^{2}$$)($$( 1 + 10 T + 73 T^{2} )^{2}$$)($$( 1 + 10 T + 73 T^{2} )^{2}$$)($$( 1 - 10 T + 73 T^{2} )^{2}$$)($$( 1 - T + 73 T^{2} )^{2}$$)($$( 1 + T + 73 T^{2} )^{2}$$)($$( 1 + 50 T^{2} + 5329 T^{4} )^{2}$$)($$( 1 - 14 T + 73 T^{2} )^{4}$$)($$( 1 + 73 T^{2} )^{4}$$)($$( 1 - 2 T + 73 T^{2} )^{4}$$)($$( 1 + 50 T^{2} + 5329 T^{4} )^{2}$$)($$( 1 - 142 T^{2} + 5329 T^{4} )^{2}$$)($$( 1 - 142 T^{2} + 5329 T^{4} )^{2}$$)($$( 1 - 145 T^{2} + 5329 T^{4} )^{2}$$)($$( 1 - 145 T^{2} + 5329 T^{4} )^{2}$$)($$( 1 + 50 T^{2} + 5329 T^{4} )^{2}$$)($$( 1 + 50 T^{2} + 5329 T^{4} )^{2}$$)($$( 1 - 46 T^{2} + 5329 T^{4} )^{2}$$)($$( 1 - 46 T^{2} + 5329 T^{4} )^{2}$$)($$( 1 - 46 T^{2} + 5329 T^{4} )^{2}$$)($$( 1 + 16 T + 128 T^{2} + 1168 T^{3} + 5329 T^{4} )^{2}$$)($$( 1 - 16 T + 73 T^{2} )^{2}( 1 + 6 T + 73 T^{2} )^{2}$$)($$( 1 + 6 T + 18 T^{2} + 438 T^{3} + 5329 T^{4} )^{2}$$)($$1 + 4 T + 8 T^{2} + 44 T^{3} - 3602 T^{4} + 3212 T^{5} + 42632 T^{6} + 1556068 T^{7} + 28398241 T^{8}$$)($$1 - 8542 T^{4} + 28398241 T^{8}$$)($$1 - 8542 T^{4} + 28398241 T^{8}$$)($$( 1 + 5329 T^{4} )^{2}$$)($$1 - 8542 T^{4} + 28398241 T^{8}$$)($$( 1 + 2 T + 2 T^{2} + 146 T^{3} + 5329 T^{4} )^{2}$$)($$1 + 4 T + 8 T^{2} + 44 T^{3} - 3602 T^{4} + 3212 T^{5} + 42632 T^{6} + 1556068 T^{7} + 28398241 T^{8}$$)($$( 1 - 16 T + 128 T^{2} - 1168 T^{3} + 5329 T^{4} )^{2}$$)($$( 1 - 5617 T^{4} + 28398241 T^{8} )^{2}$$)($$( 1 - 13807 T^{4} + 93449088 T^{8} - 392094513487 T^{12} + 806460091894081 T^{16} )^{2}$$)($$( 1 - 6 T + 18 T^{2} - 438 T^{3} + 5329 T^{4} )^{2}$$)($$( 1 + 6 T + 18 T^{2} + 438 T^{3} + 5329 T^{4} )^{4}$$)($$( 1 - 1054 T^{4} + 28398241 T^{8} )^{2}$$)($$( 1 - 1054 T^{4} + 28398241 T^{8} )^{2}$$)($$( 1 - 1054 T^{4} + 28398241 T^{8} )^{2}$$)
$79$ ($$1 - 12 T + 79 T^{2}$$)($$1 - 8 T + 79 T^{2}$$)($$1 + 79 T^{2}$$)($$1 - 8 T + 79 T^{2}$$)($$1 + 79 T^{2}$$)($$1 + 8 T + 79 T^{2}$$)($$1 + 79 T^{2}$$)($$1 - 8 T + 79 T^{2}$$)($$1 - 8 T + 79 T^{2}$$)($$1 - 8 T + 79 T^{2}$$)($$1 + 8 T + 79 T^{2}$$)($$1 - 8 T + 79 T^{2}$$)($$1 + 79 T^{2}$$)($$1 + 8 T + 79 T^{2}$$)($$1 - 8 T + 79 T^{2}$$)($$1 + 79 T^{2}$$)($$1 - 8 T + 79 T^{2}$$)($$1 + 16 T + 79 T^{2}$$)($$1 - 12 T + 79 T^{2}$$)($$( 1 - 8 T + 79 T^{2} )^{2}$$)($$( 1 + 8 T + 79 T^{2} )^{2}$$)($$( 1 + 8 T + 79 T^{2} )^{2}$$)($$( 1 + 79 T^{2} )^{2}$$)($$( 1 - 8 T + 79 T^{2} )^{2}$$)($$( 1 - 16 T + 79 T^{2} )^{2}$$)($$( 1 + 8 T + 79 T^{2} )^{2}$$)($$( 1 + 79 T^{2} )^{2}$$)($$( 1 + 8 T + 79 T^{2} )^{2}$$)($$1 - 110 T^{2} + 6241 T^{4}$$)($$1 - 110 T^{2} + 6241 T^{4}$$)($$( 1 - 4 T + 79 T^{2} )( 1 + 4 T + 79 T^{2} )$$)($$( 1 - 4 T + 79 T^{2} )( 1 + 4 T + 79 T^{2} )$$)($$( 1 - 4 T + 79 T^{2} )( 1 + 4 T + 79 T^{2} )$$)($$( 1 - 4 T + 79 T^{2} )( 1 + 4 T + 79 T^{2} )$$)($$( 1 - 4 T + 79 T^{2} )( 1 + 4 T + 79 T^{2} )$$)($$1 - 110 T^{2} + 6241 T^{4}$$)($$1 - 110 T^{2} + 6241 T^{4}$$)($$( 1 - 50 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 - 134 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 - 79 T^{2} )^{4}$$)($$( 1 - 50 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 - 110 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 - 110 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 - 134 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 - 134 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 - 4 T + 79 T^{2} )^{2}( 1 + 4 T + 79 T^{2} )^{2}$$)($$( 1 - 4 T + 79 T^{2} )^{2}( 1 + 4 T + 79 T^{2} )^{2}$$)($$( 1 - 4 T + 79 T^{2} )^{2}( 1 + 4 T + 79 T^{2} )^{2}$$)($$( 1 - 79 T^{2} )^{4}$$)($$( 1 - 122 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 - 58 T^{2} + 6241 T^{4} )^{2}$$)($$1 - 292 T^{2} + 33670 T^{4} - 1822372 T^{6} + 38950081 T^{8}$$)($$( 1 - 142 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 - 142 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 + 98 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 - 142 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 - 122 T^{2} + 6241 T^{4} )^{2}$$)($$1 - 292 T^{2} + 33670 T^{4} - 1822372 T^{6} + 38950081 T^{8}$$)($$( 1 - 79 T^{2} )^{4}$$)($$( 1 + 38 T^{2} + 6241 T^{4} )^{4}$$)($$( 1 - 232 T^{2} + 24750 T^{4} - 1447912 T^{6} + 38950081 T^{8} )^{4}$$)($$( 1 + 126 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 + 204 T^{2} + 21350 T^{4} + 1273164 T^{6} + 38950081 T^{8} )^{2}$$)($$( 1 + 146 T^{2} + 6241 T^{4} )^{4}$$)($$( 1 + 146 T^{2} + 6241 T^{4} )^{4}$$)($$( 1 - 142 T^{2} + 6241 T^{4} )^{4}$$)
$83$ ($$1 + 4 T + 83 T^{2}$$)($$1 - 6 T + 83 T^{2}$$)($$1 - 6 T + 83 T^{2}$$)($$1 + 4 T + 83 T^{2}$$)($$1 - 12 T + 83 T^{2}$$)($$1 - 6 T + 83 T^{2}$$)($$1 + 4 T + 83 T^{2}$$)($$1 + 4 T + 83 T^{2}$$)($$1 - 6 T + 83 T^{2}$$)($$1 + 6 T + 83 T^{2}$$)($$1 - 12 T + 83 T^{2}$$)($$1 - 4 T + 83 T^{2}$$)($$1 - 4 T + 83 T^{2}$$)($$1 + 6 T + 83 T^{2}$$)($$1 + 12 T + 83 T^{2}$$)($$1 + 6 T + 83 T^{2}$$)($$1 + 6 T + 83 T^{2}$$)($$1 - 12 T + 83 T^{2}$$)($$1 - 4 T + 83 T^{2}$$)($$1 - 130 T^{2} + 6889 T^{4}$$)($$1 - 150 T^{2} + 6889 T^{4}$$)($$1 - 130 T^{2} + 6889 T^{4}$$)($$1 - 130 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 22 T^{2} + 6889 T^{4}$$)($$1 - 130 T^{2} + 6889 T^{4}$$)($$( 1 - 9 T + 83 T^{2} )^{2}$$)($$( 1 - 9 T + 83 T^{2} )^{2}$$)($$( 1 + 83 T^{2} )^{2}$$)($$( 1 + 83 T^{2} )^{2}$$)($$( 1 + 83 T^{2} )^{2}$$)($$( 1 + 83 T^{2} )^{2}$$)($$( 1 + 83 T^{2} )^{2}$$)($$( 1 + 9 T + 83 T^{2} )^{2}$$)($$( 1 + 9 T + 83 T^{2} )^{2}$$)($$( 1 - 6 T + 83 T^{2} )^{4}$$)($$( 1 + 112 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 + 76 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 + 58 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 + 6 T + 83 T^{2} )^{4}$$)($$( 1 - 58 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 58 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 85 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 85 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 112 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 112 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 - 83 T^{2} )^{4}$$)($$( 1 - 83 T^{2} )^{4}$$)($$( 1 - 83 T^{2} )^{4}$$)($$1 - 12878 T^{4} + 47458321 T^{8}$$)($$1 - 13294 T^{4} + 47458321 T^{8}$$)($$1 + 8722 T^{4} + 47458321 T^{8}$$)($$1 + 4 T + 8 T^{2} + 196 T^{3} + 3646 T^{4} + 16268 T^{5} + 55112 T^{6} + 2287148 T^{7} + 47458321 T^{8}$$)($$( 1 + 6889 T^{4} )^{2}$$)($$( 1 + 6889 T^{4} )^{2}$$)($$1 + 9938 T^{4} + 47458321 T^{8}$$)($$( 1 + 6889 T^{4} )^{2}$$)($$( 1 - 22 T + 242 T^{2} - 1826 T^{3} + 6889 T^{4} )( 1 + 22 T + 242 T^{2} + 1826 T^{3} + 6889 T^{4} )$$)($$1 - 4 T + 8 T^{2} - 196 T^{3} + 3646 T^{4} - 16268 T^{5} + 55112 T^{6} - 2287148 T^{7} + 47458321 T^{8}$$)($$1 - 12878 T^{4} + 47458321 T^{8}$$)($$( 1 + 10871 T^{4} + 47458321 T^{8} )^{2}$$)($$( 1 - 8167 T^{4} + 41873760 T^{8} - 387592107607 T^{12} + 2252292232139041 T^{16} )^{2}$$)($$1 + 8722 T^{4} + 47458321 T^{8}$$)($$( 1 + 12466 T^{4} + 47458321 T^{8} )^{2}$$)($$( 1 - 13294 T^{4} + 47458321 T^{8} )^{2}$$)($$( 1 + 3122 T^{4} + 47458321 T^{8} )^{2}$$)($$( 1 - 4 T + 8 T^{2} - 332 T^{3} + 6889 T^{4} )^{2}( 1 + 4 T + 8 T^{2} + 332 T^{3} + 6889 T^{4} )^{2}$$)
$89$ ($$1 + 10 T + 89 T^{2}$$)($$1 - 16 T + 89 T^{2}$$)($$1 + 89 T^{2}$$)($$1 + 6 T + 89 T^{2}$$)($$1 + 6 T + 89 T^{2}$$)($$1 + 89 T^{2}$$)($$1 + 10 T + 89 T^{2}$$)($$1 - 6 T + 89 T^{2}$$)($$1 + 16 T + 89 T^{2}$$)($$1 + 16 T + 89 T^{2}$$)($$1 - 18 T + 89 T^{2}$$)($$1 - 6 T + 89 T^{2}$$)($$1 + 10 T + 89 T^{2}$$)($$1 + 89 T^{2}$$)($$1 - 10 T + 89 T^{2}$$)($$1 + 89 T^{2}$$)($$1 - 16 T + 89 T^{2}$$)($$1 - 2 T + 89 T^{2}$$)($$1 + 10 T + 89 T^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 - 6 T + 89 T^{2} )^{2}$$)($$( 1 + 16 T + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 + 18 T + 89 T^{2} )^{2}$$)($$( 1 + 2 T + 89 T^{2} )^{2}$$)($$( 1 + 10 T + 89 T^{2} )^{2}$$)($$( 1 - 6 T + 89 T^{2} )^{2}$$)($$( 1 - 16 T + 89 T^{2} )^{2}$$)($$1 - 151 T^{2} + 7921 T^{4}$$)($$1 - 151 T^{2} + 7921 T^{4}$$)($$( 1 - 89 T^{2} )^{2}$$)($$( 1 - 89 T^{2} )^{2}$$)($$( 1 - 89 T^{2} )^{2}$$)($$( 1 - 89 T^{2} )^{2}$$)($$( 1 - 89 T^{2} )^{2}$$)($$1 - 151 T^{2} + 7921 T^{4}$$)($$1 - 151 T^{2} + 7921 T^{4}$$)($$( 1 - 18 T + 89 T^{2} )^{2}( 1 + 18 T + 89 T^{2} )^{2}$$)($$( 1 - 34 T^{2} + 7921 T^{4} )^{2}$$)($$( 1 - 6 T + 89 T^{2} )^{2}( 1 + 6 T + 89 T^{2} )^{2}$$)($$( 1 - 89 T^{2} )^{4}$$)($$( 1 - 18 T + 89 T^{2} )^{2}( 1 + 18 T + 89 T^{2} )^{2}$$)($$( 1 - 89 T^{2} )^{4}$$)($$( 1 - 89 T^{2} )^{4}$$)($$( 1 - 151 T^{2} + 7921 T^{4} )^{2}$$)($$( 1 - 151 T^{2} + 7921 T^{4} )^{2}$$)($$( 1 - 34 T^{2} + 7921 T^{4} )^{2}$$)($$( 1 - 34 T^{2} + 7921 T^{4} )^{2}$$)($$( 1 - 89 T^{2} )^{4}$$)($$( 1 - 89 T^{2} )^{4}$$)($$( 1 - 89 T^{2} )^{4}$$)($$( 1 + 50 T^{2} + 7921 T^{4} )^{2}$$)($$( 1 + 170 T^{2} + 7921 T^{4} )^{2}$$)($$( 1 + 170 T^{2} + 7921 T^{4} )^{2}$$)($$( 1 - 20 T + 246 T^{2} - 1780 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 + 89 T^{2} )^{4}$$)($$( 1 + 89 T^{2} )^{4}$$)($$( 1 + 89 T^{2} )^{4}$$)($$( 1 + 89 T^{2} )^{4}$$)($$( 1 + 158 T^{2} + 7921 T^{4} )^{2}$$)($$( 1 + 20 T + 246 T^{2} + 1780 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 + 50 T^{2} + 7921 T^{4} )^{2}$$)($$( 1 - 65 T^{2} + 7921 T^{4} )^{4}$$)($$( 1 + 97 T^{2} + 1488 T^{4} + 768337 T^{6} + 62742241 T^{8} )^{4}$$)($$( 1 - 114 T^{2} + 7921 T^{4} )^{2}$$)($$( 1 - 174 T^{2} + 7921 T^{4} )^{4}$$)($$( 1 + 146 T^{2} + 7921 T^{4} )^{4}$$)($$( 1 - 34 T^{2} + 7921 T^{4} )^{4}$$)($$( 1 - 34 T^{2} + 7921 T^{4} )^{4}$$)
$97$ ($$1 - 8 T + 97 T^{2}$$)($$1 + 7 T + 97 T^{2}$$)($$1 + 17 T + 97 T^{2}$$)($$1 + 2 T + 97 T^{2}$$)($$1 + 2 T + 97 T^{2}$$)($$1 + 7 T + 97 T^{2}$$)($$1 - 8 T + 97 T^{2}$$)($$1 - 8 T + 97 T^{2}$$)($$1 + 7 T + 97 T^{2}$$)($$1 - 7 T + 97 T^{2}$$)($$1 + 2 T + 97 T^{2}$$)($$1 + 8 T + 97 T^{2}$$)($$1 + 8 T + 97 T^{2}$$)($$1 - 7 T + 97 T^{2}$$)($$1 + 2 T + 97 T^{2}$$)($$1 - 17 T + 97 T^{2}$$)($$1 - 7 T + 97 T^{2}$$)($$1 + 2 T + 97 T^{2}$$)($$1 + 8 T + 97 T^{2}$$)($$1 - 145 T^{2} + 9409 T^{4}$$)($$1 - 190 T^{2} + 9409 T^{4}$$)($$1 - 145 T^{2} + 9409 T^{4}$$)($$1 + 95 T^{2} + 9409 T^{4}$$)($$1 - 190 T^{2} + 9409 T^{4}$$)($$1 - 190 T^{2} + 9409 T^{4}$$)($$1 - 190 T^{2} + 9409 T^{4}$$)($$1 - 190 T^{2} + 9409 T^{4}$$)($$1 - 145 T^{2} + 9409 T^{4}$$)($$( 1 + 10 T + 97 T^{2} )^{2}$$)($$( 1 - 10 T + 97 T^{2} )^{2}$$)($$( 1 + 19 T + 97 T^{2} )^{2}$$)($$( 1 + 5 T + 97 T^{2} )^{2}$$)($$( 1 - 14 T + 97 T^{2} )^{2}$$)($$( 1 - 5 T + 97 T^{2} )^{2}$$)($$( 1 - 19 T + 97 T^{2} )^{2}$$)($$( 1 - 10 T + 97 T^{2} )^{2}$$)($$( 1 + 10 T + 97 T^{2} )^{2}$$)($$( 1 + 97 T^{2} )^{4}$$)($$( 1 + 10 T + 97 T^{2} )^{4}$$)($$( 1 + 97 T^{2} )^{4}$$)($$( 1 + 10 T + 97 T^{2} )^{4}$$)($$( 1 + 97 T^{2} )^{4}$$)($$( 1 - 94 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 - 94 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 - 94 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 - 94 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 - 94 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 - 94 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 + 167 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 - 169 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 + 2 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 - 16 T + 128 T^{2} - 1552 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 + 6 T + 18 T^{2} + 582 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 - 18 T + 97 T^{2} )^{2}( 1 - 8 T + 97 T^{2} )^{2}$$)($$( 1 + 2 T + 2 T^{2} + 194 T^{3} + 9409 T^{4} )^{2}$$)($$1 - 18814 T^{4} + 88529281 T^{8}$$)($$1 + 9743 T^{4} + 88529281 T^{8}$$)($$( 1 + 9409 T^{4} )^{2}$$)($$1 + 9071 T^{4} + 88529281 T^{8}$$)($$( 1 + 18 T + 162 T^{2} + 1746 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 + 2 T + 2 T^{2} + 194 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 + 16 T + 128 T^{2} + 1552 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 + 2498 T^{4} + 88529281 T^{8} )^{2}$$)($$( 1 - 6223 T^{4} + 173952288 T^{8} - 550917715663 T^{12} + 7837433594376961 T^{16} )^{2}$$)($$( 1 - 6 T + 18 T^{2} - 582 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 + 6 T + 18 T^{2} + 582 T^{3} + 9409 T^{4} )^{4}$$)($$( 1 + 2498 T^{4} + 88529281 T^{8} )^{2}$$)($$( 1 - 16417 T^{4} + 88529281 T^{8} )^{2}$$)($$( 1 + 17663 T^{4} + 88529281 T^{8} )^{2}$$)