Properties

 Label 420.2 Level 420 Weight 2 Dimension 1708 Nonzero newspaces 24 Newform subspaces 57 Sturm bound 18432 Trace bound 9

Defining parameters

 Level: $$N$$ = $$420\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7$$ \) Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Newform subspaces: $$57$$ Sturm bound: $$18432$$ Trace bound: $$9$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(420))$$.

Total New Old
Modular forms 5088 1836 3252
Cusp forms 4129 1708 2421
Eisenstein series 959 128 831

Trace form

 $$1708q - 6q^{3} + 4q^{4} - 10q^{5} + 4q^{6} - 12q^{7} + 36q^{8} + 18q^{9} + O(q^{10})$$ $$1708q - 6q^{3} + 4q^{4} - 10q^{5} + 4q^{6} - 12q^{7} + 36q^{8} + 18q^{9} + 40q^{10} + 28q^{11} + 32q^{12} + 68q^{13} + 48q^{14} + 46q^{15} + 12q^{16} + 64q^{17} - 8q^{18} + 32q^{19} - 40q^{20} + 34q^{21} - 88q^{22} + 24q^{23} - 72q^{24} + 46q^{25} - 92q^{26} + 12q^{27} - 132q^{28} + 96q^{29} - 114q^{30} + 8q^{31} - 100q^{32} + 6q^{33} - 144q^{34} + 50q^{35} - 108q^{36} + 52q^{37} - 68q^{38} - 16q^{39} - 80q^{40} + 8q^{41} - 116q^{42} - 8q^{43} - 48q^{44} - 23q^{45} - 48q^{46} - 12q^{47} - 80q^{48} - 80q^{49} + 20q^{50} - 18q^{51} - 88q^{52} - 56q^{53} + 4q^{54} - 32q^{55} - 68q^{56} - 116q^{57} - 104q^{58} - 56q^{59} - 16q^{60} - 88q^{61} - 104q^{62} + 2q^{63} - 140q^{64} - 178q^{65} - 4q^{66} - 64q^{67} - 160q^{68} - 184q^{69} - 304q^{70} - 96q^{71} - 48q^{72} - 220q^{73} - 132q^{74} - 105q^{75} - 232q^{76} - 192q^{77} + 40q^{78} - 216q^{79} - 152q^{80} - 246q^{81} - 208q^{82} - 72q^{83} + 64q^{84} - 268q^{85} - 92q^{86} - 124q^{87} - 184q^{88} - 64q^{89} - 12q^{90} - 64q^{91} + 56q^{92} - 166q^{93} - 184q^{94} + 18q^{95} - 20q^{96} - 96q^{97} + 60q^{98} - 4q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(420))$$

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
420.2.a $$\chi_{420}(1, \cdot)$$ 420.2.a.a 1 1
420.2.a.b 1
420.2.a.c 1
420.2.a.d 1
420.2.c $$\chi_{420}(391, \cdot)$$ 420.2.c.a 16 1
420.2.c.b 16
420.2.d $$\chi_{420}(41, \cdot)$$ 420.2.d.a 2 1
420.2.d.b 2
420.2.d.c 4
420.2.d.d 4
420.2.f $$\chi_{420}(209, \cdot)$$ 420.2.f.a 8 1
420.2.f.b 8
420.2.i $$\chi_{420}(139, \cdot)$$ 420.2.i.a 48 1
420.2.k $$\chi_{420}(169, \cdot)$$ 420.2.k.a 2 1
420.2.k.b 2
420.2.l $$\chi_{420}(239, \cdot)$$ 420.2.l.a 4 1
420.2.l.b 4
420.2.l.c 8
420.2.l.d 8
420.2.l.e 8
420.2.l.f 8
420.2.l.g 16
420.2.l.h 16
420.2.n $$\chi_{420}(71, \cdot)$$ 420.2.n.a 24 1
420.2.n.b 24
420.2.q $$\chi_{420}(121, \cdot)$$ 420.2.q.a 2 2
420.2.q.b 2
420.2.q.c 4
420.2.q.d 4
420.2.s $$\chi_{420}(113, \cdot)$$ 420.2.s.a 24 2
420.2.t $$\chi_{420}(43, \cdot)$$ 420.2.t.a 4 2
420.2.t.b 4
420.2.t.c 32
420.2.t.d 32
420.2.w $$\chi_{420}(83, \cdot)$$ 420.2.w.a 8 2
420.2.w.b 8
420.2.w.c 160
420.2.x $$\chi_{420}(13, \cdot)$$ 420.2.x.a 16 2
420.2.ba $$\chi_{420}(179, \cdot)$$ 420.2.ba.a 8 2
420.2.ba.b 8
420.2.ba.c 160
420.2.bb $$\chi_{420}(109, \cdot)$$ 420.2.bb.a 16 2
420.2.bf $$\chi_{420}(11, \cdot)$$ 420.2.bf.a 128 2
420.2.bh $$\chi_{420}(101, \cdot)$$ 420.2.bh.a 10 2
420.2.bh.b 10
420.2.bi $$\chi_{420}(31, \cdot)$$ 420.2.bi.a 4 2
420.2.bi.b 4
420.2.bi.c 28
420.2.bi.d 28
420.2.bk $$\chi_{420}(19, \cdot)$$ 420.2.bk.a 96 2
420.2.bn $$\chi_{420}(89, \cdot)$$ 420.2.bn.a 32 2
420.2.bo $$\chi_{420}(73, \cdot)$$ 420.2.bo.a 32 4
420.2.br $$\chi_{420}(47, \cdot)$$ 420.2.br.a 352 4
420.2.bs $$\chi_{420}(67, \cdot)$$ 420.2.bs.a 192 4
420.2.bv $$\chi_{420}(53, \cdot)$$ 420.2.bv.a 8 4
420.2.bv.b 8
420.2.bv.c 48

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(420))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(420)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(140))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(210))$$$$^{\oplus 2}$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 - 2 T + 3 T^{2} - 4 T^{3} + 3 T^{4} + 2 T^{5} - 7 T^{6} + 12 T^{7} - 28 T^{8} + 24 T^{9} - 28 T^{10} + 16 T^{11} + 48 T^{12} - 128 T^{13} + 192 T^{14} - 256 T^{15} + 256 T^{16}$$)($$1 - 2 T + 3 T^{2} - 4 T^{3} + 3 T^{4} + 2 T^{5} - 7 T^{6} + 12 T^{7} - 28 T^{8} + 24 T^{9} - 28 T^{10} + 16 T^{11} + 48 T^{12} - 128 T^{13} + 192 T^{14} - 256 T^{15} + 256 T^{16}$$)($$( 1 + 2 T^{2} )^{2}$$)($$( 1 + 2 T^{2} )^{2}$$)($$1 - T^{2} - 2 T^{3} + 2 T^{4} - 4 T^{5} - 4 T^{6} + 16 T^{8}$$)($$1 - T^{2} + 2 T^{3} + 2 T^{4} + 4 T^{5} - 4 T^{6} + 16 T^{8}$$)($$1 - T^{2} - 2 T^{3} + 2 T^{4} - 4 T^{5} - 4 T^{6} + 16 T^{8}$$)($$1 - T^{2} + 2 T^{3} + 2 T^{4} + 4 T^{5} - 4 T^{6} + 16 T^{8}$$)($$1 - 3 T^{2} + 7 T^{4} - 13 T^{6} + 28 T^{8} - 52 T^{10} + 112 T^{12} - 192 T^{14} + 256 T^{16}$$)($$1 - 3 T^{2} + 7 T^{4} - 13 T^{6} + 28 T^{8} - 52 T^{10} + 112 T^{12} - 192 T^{14} + 256 T^{16}$$)($$( 1 - 2 T + 2 T^{2} )^{2}$$)($$( 1 - 2 T + 2 T^{2} )^{2}$$)($$( 1 + 2 T + 2 T^{2} )^{4}$$)($$( 1 - 2 T + 2 T^{2} )^{4}$$)($$( 1 - 2 T^{2} + 4 T^{4} )^{2}$$)($$( 1 - 2 T^{2} + 4 T^{4} )^{2}$$)($$( 1 + 2 T + 2 T^{2} )^{2}$$)($$1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4}$$)
$3$ ($$1 + T$$)($$1 + T$$)($$1 - T$$)($$1 - T$$)($$( 1 + T )^{16}$$)($$( 1 - T )^{16}$$)($$1 + 3 T + 3 T^{2}$$)($$1 - 3 T + 3 T^{2}$$)($$1 + 2 T + 2 T^{2} + 6 T^{3} + 9 T^{4}$$)($$1 - 2 T + 2 T^{2} - 6 T^{3} + 9 T^{4}$$)($$1 + T^{2} - 8 T^{4} + 9 T^{6} + 81 T^{8}$$)($$( 1 - 2 T^{2} + 9 T^{4} )^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$( 1 + 2 T + 3 T^{2} )^{2}$$)($$( 1 - 2 T + 3 T^{2} )^{2}$$)($$1 + 2 T + T^{2} + 2 T^{3} + 4 T^{4} + 6 T^{5} + 9 T^{6} + 54 T^{7} + 81 T^{8}$$)($$1 + 2 T + T^{2} + 2 T^{3} + 4 T^{4} + 6 T^{5} + 9 T^{6} + 54 T^{7} + 81 T^{8}$$)($$1 - 2 T + T^{2} - 2 T^{3} + 4 T^{4} - 6 T^{5} + 9 T^{6} - 54 T^{7} + 81 T^{8}$$)($$1 - 2 T + T^{2} - 2 T^{3} + 4 T^{4} - 6 T^{5} + 9 T^{6} - 54 T^{7} + 81 T^{8}$$)($$( 1 - 4 T^{3} - 2 T^{4} - 12 T^{5} + 81 T^{8} )^{2}$$)($$( 1 + 4 T^{3} - 2 T^{4} + 12 T^{5} + 81 T^{8} )^{2}$$)($$1 - T + T^{2}$$)($$1 - T + T^{2}$$)($$( 1 + T + T^{2} )^{2}$$)($$( 1 + T + T^{2} )^{2}$$)($$1 + T^{4}$$)($$1 + T^{4}$$)($$( 1 + 9 T^{4} )^{2}$$)($$( 1 + 9 T^{4} )^{2}$$)($$( 1 + T^{4} )^{4}$$)($$1 + 4 T^{2} + 7 T^{4} + 36 T^{6} + 81 T^{8}$$)($$( 1 - 4 T^{2} + 9 T^{4} )^{2}$$)($$( 1 - T^{2} + T^{4} )^{4}$$)($$1 + T + 2 T^{2} - T^{3} - 11 T^{4} - 12 T^{5} - 33 T^{6} - 9 T^{7} + 54 T^{8} + 81 T^{9} + 243 T^{10}$$)($$1 - T - T^{2} + 4 T^{3} + T^{4} - 21 T^{5} + 3 T^{6} + 36 T^{7} - 27 T^{8} - 81 T^{9} + 243 T^{10}$$)($$( 1 - T + T^{2} )^{2}$$)($$( 1 + T + T^{2} )^{2}$$)($$1 + 5 T^{2} + 16 T^{4} + 45 T^{6} + 81 T^{8}$$)($$( 1 - T - 2 T^{2} - 3 T^{3} + 9 T^{4} )^{2}$$)
$5$ ($$1 + T$$)($$1 - T$$)($$1 + T$$)($$1 - T$$)($$( 1 + T^{2} )^{8}$$)($$( 1 + T^{2} )^{8}$$)($$( 1 + T )^{2}$$)($$( 1 - T )^{2}$$)($$( 1 - T )^{4}$$)($$( 1 + T )^{4}$$)($$( 1 + 5 T^{2} )^{4}$$)($$( 1 - 5 T^{2} )^{4}$$)($$1 + 4 T + 5 T^{2}$$)($$1 - 4 T + 5 T^{2}$$)($$1 - 8 T^{2} + 25 T^{4}$$)($$1 - 8 T^{2} + 25 T^{4}$$)($$( 1 + 2 T + 5 T^{2} )^{4}$$)($$( 1 - 2 T + 5 T^{2} )^{4}$$)($$( 1 + 2 T + 5 T^{2} )^{4}$$)($$( 1 - 2 T + 5 T^{2} )^{4}$$)($$1 - 16 T^{2} + 156 T^{4} - 1152 T^{6} + 6534 T^{8} - 28800 T^{10} + 97500 T^{12} - 250000 T^{14} + 390625 T^{16}$$)($$1 - 16 T^{2} + 156 T^{4} - 1152 T^{6} + 6534 T^{8} - 28800 T^{10} + 97500 T^{12} - 250000 T^{14} + 390625 T^{16}$$)($$1 + T + T^{2}$$)($$1 - T + T^{2}$$)($$( 1 + T + T^{2} )^{2}$$)($$( 1 - T + T^{2} )^{2}$$)($$( 1 + 4 T + 5 T^{2} )^{2}$$)($$( 1 - 4 T + 5 T^{2} )^{2}$$)($$( 1 + 4 T^{2} + 25 T^{4} )^{2}$$)($$( 1 + 4 T^{2} + 25 T^{4} )^{2}$$)($$1 - 8 T^{2} - 4 T^{4} + 200 T^{6} - 986 T^{8} + 5000 T^{10} - 2500 T^{12} - 125000 T^{14} + 390625 T^{16}$$)($$( 1 - 5 T^{2} + 25 T^{4} )^{2}$$)($$( 1 - 5 T^{2} + 25 T^{4} )^{2}$$)($$1 - 2 T - 4 T^{2} + 28 T^{3} - 18 T^{4} - 134 T^{5} + 360 T^{6} + 274 T^{7} - 2201 T^{8} + 1370 T^{9} + 9000 T^{10} - 16750 T^{11} - 11250 T^{12} + 87500 T^{13} - 62500 T^{14} - 156250 T^{15} + 390625 T^{16}$$)($$( 1 + T + T^{2} )^{5}$$)($$( 1 - T + T^{2} )^{5}$$)($$1 - T^{2} + T^{4}$$)($$1 - T^{2} + T^{4}$$)($$( 1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4} )^{2}$$)($$( 1 - 4 T + 11 T^{2} - 20 T^{3} + 25 T^{4} )^{2}$$)
$7$ ($$1 + T$$)($$1 - T$$)($$1 - T$$)($$1 + T$$)($$1 + 4 T + 16 T^{2} + 68 T^{3} + 188 T^{4} + 468 T^{5} + 1328 T^{6} + 3284 T^{7} + 6854 T^{8} + 22988 T^{9} + 65072 T^{10} + 160524 T^{11} + 451388 T^{12} + 1142876 T^{13} + 1882384 T^{14} + 3294172 T^{15} + 5764801 T^{16}$$)($$1 - 4 T + 16 T^{2} - 68 T^{3} + 188 T^{4} - 468 T^{5} + 1328 T^{6} - 3284 T^{7} + 6854 T^{8} - 22988 T^{9} + 65072 T^{10} - 160524 T^{11} + 451388 T^{12} - 1142876 T^{13} + 1882384 T^{14} - 3294172 T^{15} + 5764801 T^{16}$$)($$1 - 4 T + 7 T^{2}$$)($$1 - 4 T + 7 T^{2}$$)($$1 + 6 T + 18 T^{2} + 42 T^{3} + 49 T^{4}$$)($$1 + 6 T + 18 T^{2} + 42 T^{3} + 49 T^{4}$$)($$( 1 - 7 T^{2} )^{4}$$)($$( 1 + 6 T^{2} + 49 T^{4} )^{2}$$)($$1 + T^{2}$$)($$1 + T^{2}$$)($$( 1 - T )^{4}$$)($$( 1 + T )^{4}$$)($$( 1 + T )^{8}$$)($$( 1 + T )^{8}$$)($$( 1 - T )^{8}$$)($$( 1 - T )^{8}$$)($$( 1 + T )^{16}$$)($$( 1 - T )^{16}$$)($$1 - 5 T + 7 T^{2}$$)($$1 + 5 T + 7 T^{2}$$)($$1 + 7 T^{2} + 49 T^{4}$$)($$1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4}$$)($$1 + T^{4}$$)($$1 + T^{4}$$)($$( 1 + 49 T^{4} )^{2}$$)($$( 1 + 49 T^{4} )^{2}$$)($$1 + 32 T^{3} + 36 T^{4} + 96 T^{5} + 512 T^{6} + 1216 T^{7} + 3334 T^{8} + 8512 T^{9} + 25088 T^{10} + 32928 T^{11} + 86436 T^{12} + 537824 T^{13} + 5764801 T^{16}$$)($$1 - 4 T^{2} - 33 T^{4} - 196 T^{6} + 2401 T^{8}$$)($$1 - 4 T^{2} - 33 T^{4} - 196 T^{6} + 2401 T^{8}$$)($$1 - 4 T^{2} - 62 T^{4} + 140 T^{6} + 3739 T^{8} + 6860 T^{10} - 148862 T^{12} - 470596 T^{14} + 5764801 T^{16}$$)($$1 + 5 T + 19 T^{2} + 6 T^{3} - 91 T^{4} - 533 T^{5} - 637 T^{6} + 294 T^{7} + 6517 T^{8} + 12005 T^{9} + 16807 T^{10}$$)($$1 + 5 T + 19 T^{2} + 6 T^{3} - 91 T^{4} - 533 T^{5} - 637 T^{6} + 294 T^{7} + 6517 T^{8} + 12005 T^{9} + 16807 T^{10}$$)($$( 1 + T + 7 T^{2} )^{2}$$)($$( 1 - T + 7 T^{2} )^{2}$$)($$1 - 6 T + 18 T^{2} - 36 T^{3} + 71 T^{4} - 252 T^{5} + 882 T^{6} - 2058 T^{7} + 2401 T^{8}$$)($$1 - 6 T + 18 T^{2} - 36 T^{3} + 71 T^{4} - 252 T^{5} + 882 T^{6} - 2058 T^{7} + 2401 T^{8}$$)
$11$ ($$1 - 2 T + 11 T^{2}$$)($$1 + 2 T + 11 T^{2}$$)($$1 - 6 T + 11 T^{2}$$)($$1 - 2 T + 11 T^{2}$$)($$1 - 68 T^{2} + 2180 T^{4} - 46812 T^{6} + 798068 T^{8} - 11533812 T^{10} + 145791676 T^{12} - 1699254444 T^{14} + 19011779286 T^{16} - 205609787724 T^{18} + 2134535928316 T^{20} - 20432851520532 T^{22} + 171072963441908 T^{24} - 1214182720422012 T^{26} + 6841773861251780 T^{28} - 25822988683660388 T^{30} + 45949729863572161 T^{32}$$)($$1 - 68 T^{2} + 2180 T^{4} - 46812 T^{6} + 798068 T^{8} - 11533812 T^{10} + 145791676 T^{12} - 1699254444 T^{14} + 19011779286 T^{16} - 205609787724 T^{18} + 2134535928316 T^{20} - 20432851520532 T^{22} + 171072963441908 T^{24} - 1214182720422012 T^{26} + 6841773861251780 T^{28} - 25822988683660388 T^{30} + 45949729863572161 T^{32}$$)($$1 + 5 T^{2} + 121 T^{4}$$)($$1 + 5 T^{2} + 121 T^{4}$$)($$1 - 16 T^{2} + 126 T^{4} - 1936 T^{6} + 14641 T^{8}$$)($$1 - 16 T^{2} + 126 T^{4} - 1936 T^{6} + 14641 T^{8}$$)($$( 1 - 3 T - 2 T^{2} - 33 T^{3} + 121 T^{4} )^{2}( 1 + 3 T - 2 T^{2} + 33 T^{3} + 121 T^{4} )^{2}$$)($$( 1 - 6 T + 11 T^{2} )^{4}( 1 + 6 T + 11 T^{2} )^{4}$$)($$( 1 + 4 T + 11 T^{2} )^{2}$$)($$( 1 - 4 T + 11 T^{2} )^{2}$$)($$( 1 + 4 T^{2} + 121 T^{4} )^{2}$$)($$( 1 + 4 T^{2} + 121 T^{4} )^{2}$$)($$( 1 - 2 T + 33 T^{2} - 50 T^{3} + 500 T^{4} - 550 T^{5} + 3993 T^{6} - 2662 T^{7} + 14641 T^{8} )^{2}$$)($$( 1 + 2 T + 33 T^{2} + 50 T^{3} + 500 T^{4} + 550 T^{5} + 3993 T^{6} + 2662 T^{7} + 14641 T^{8} )^{2}$$)($$( 1 + 2 T + 33 T^{2} + 50 T^{3} + 500 T^{4} + 550 T^{5} + 3993 T^{6} + 2662 T^{7} + 14641 T^{8} )^{2}$$)($$( 1 - 2 T + 33 T^{2} - 50 T^{3} + 500 T^{4} - 550 T^{5} + 3993 T^{6} - 2662 T^{7} + 14641 T^{8} )^{2}$$)($$( 1 + 22 T^{2} + 432 T^{4} + 4986 T^{6} + 65534 T^{8} + 603306 T^{10} + 6324912 T^{12} + 38974342 T^{14} + 214358881 T^{16} )^{2}$$)($$( 1 + 22 T^{2} + 432 T^{4} + 4986 T^{6} + 65534 T^{8} + 603306 T^{10} + 6324912 T^{12} + 38974342 T^{14} + 214358881 T^{16} )^{2}$$)($$1 - 2 T - 7 T^{2} - 22 T^{3} + 121 T^{4}$$)($$1 - 4 T + 5 T^{2} - 44 T^{3} + 121 T^{4}$$)($$1 + 2 T - 12 T^{2} - 12 T^{3} + 91 T^{4} - 132 T^{5} - 1452 T^{6} + 2662 T^{7} + 14641 T^{8}$$)($$1 - 4 T^{2} - 105 T^{4} - 484 T^{6} + 14641 T^{8}$$)($$( 1 - 6 T + 11 T^{2} )^{2}( 1 + 6 T + 11 T^{2} )^{2}$$)($$( 1 - 6 T + 11 T^{2} )^{2}( 1 + 6 T + 11 T^{2} )^{2}$$)($$( 1 - 2 T + 2 T^{2} - 22 T^{3} + 121 T^{4} )^{4}$$)($$( 1 + 2 T + 2 T^{2} + 22 T^{3} + 121 T^{4} )^{4}$$)($$( 1 - 4 T + 36 T^{2} - 116 T^{3} + 546 T^{4} - 1276 T^{5} + 4356 T^{6} - 5324 T^{7} + 14641 T^{8} )^{4}$$)($$( 1 - 11 T^{2} + 121 T^{4} )^{4}$$)($$( 1 - 11 T^{2} + 121 T^{4} )^{4}$$)($$( 1 + 4 T - 22 T^{2} - 68 T^{3} + 396 T^{4} + 526 T^{5} - 6648 T^{6} - 1364 T^{7} + 89791 T^{8} - 15004 T^{9} - 804408 T^{10} + 700106 T^{11} + 5797836 T^{12} - 10951468 T^{13} - 38974342 T^{14} + 77948684 T^{15} + 214358881 T^{16} )^{2}$$)($$1 + 6 T + 51 T^{2} + 234 T^{3} + 1195 T^{4} + 3666 T^{5} + 12622 T^{6} + 19434 T^{7} + 25645 T^{8} - 184704 T^{9} - 509783 T^{10} - 2031744 T^{11} + 3103045 T^{12} + 25866654 T^{13} + 184798702 T^{14} + 590412966 T^{15} + 2117015395 T^{16} + 4559998014 T^{17} + 10932302931 T^{18} + 14147686146 T^{19} + 25937424601 T^{20}$$)($$1 - 6 T + 51 T^{2} - 234 T^{3} + 1195 T^{4} - 3666 T^{5} + 12622 T^{6} - 19434 T^{7} + 25645 T^{8} + 184704 T^{9} - 509783 T^{10} + 2031744 T^{11} + 3103045 T^{12} - 25866654 T^{13} + 184798702 T^{14} - 590412966 T^{15} + 2117015395 T^{16} - 4559998014 T^{17} + 10932302931 T^{18} - 14147686146 T^{19} + 25937424601 T^{20}$$)($$1 + 18 T^{2} + 203 T^{4} + 2178 T^{6} + 14641 T^{8}$$)($$1 + 18 T^{2} + 203 T^{4} + 2178 T^{6} + 14641 T^{8}$$)($$1 + 20 T^{2} + 102 T^{4} + 1120 T^{6} + 25763 T^{8} + 135520 T^{10} + 1493382 T^{12} + 35431220 T^{14} + 214358881 T^{16}$$)($$1 + 20 T^{2} + 102 T^{4} + 1120 T^{6} + 25763 T^{8} + 135520 T^{10} + 1493382 T^{12} + 35431220 T^{14} + 214358881 T^{16}$$)
$13$ ($$1 - 4 T + 13 T^{2}$$)($$1 - 4 T + 13 T^{2}$$)($$1 + 4 T + 13 T^{2}$$)($$1 - 4 T + 13 T^{2}$$)($$1 - 100 T^{2} + 5348 T^{4} - 198140 T^{6} + 5637172 T^{8} - 129840148 T^{10} + 2495923420 T^{12} - 40770066124 T^{14} + 571339339990 T^{16} - 6890141174956 T^{18} + 71286068798620 T^{20} - 626713594927732 T^{22} + 4598414379961012 T^{24} - 27315281574960860 T^{26} + 124598159235028388 T^{28} - 393737638569928900 T^{30} + 665416609183179841 T^{32}$$)($$1 - 100 T^{2} + 5348 T^{4} - 198140 T^{6} + 5637172 T^{8} - 129840148 T^{10} + 2495923420 T^{12} - 40770066124 T^{14} + 571339339990 T^{16} - 6890141174956 T^{18} + 71286068798620 T^{20} - 626713594927732 T^{22} + 4598414379961012 T^{24} - 27315281574960860 T^{26} + 124598159235028388 T^{28} - 393737638569928900 T^{30} + 665416609183179841 T^{32}$$)($$( 1 - 7 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} )$$)($$( 1 - 7 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} )$$)($$1 - 40 T^{2} + 718 T^{4} - 6760 T^{6} + 28561 T^{8}$$)($$1 - 40 T^{2} + 718 T^{4} - 6760 T^{6} + 28561 T^{8}$$)($$( 1 - 19 T^{2} + 192 T^{4} - 3211 T^{6} + 28561 T^{8} )^{2}$$)($$( 1 + 18 T^{2} + 169 T^{4} )^{4}$$)($$( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )$$)($$1 - 22 T^{2} + 169 T^{4}$$)($$( 1 - 4 T + 13 T^{2} )^{2}( 1 + 4 T + 13 T^{2} )^{2}$$)($$( 1 - 4 T + 13 T^{2} )^{2}( 1 + 4 T + 13 T^{2} )^{2}$$)($$1 - 34 T^{2} + 593 T^{4} - 8610 T^{6} + 122100 T^{8} - 1455090 T^{10} + 16936673 T^{12} - 164111506 T^{14} + 815730721 T^{16}$$)($$1 - 34 T^{2} + 593 T^{4} - 8610 T^{6} + 122100 T^{8} - 1455090 T^{10} + 16936673 T^{12} - 164111506 T^{14} + 815730721 T^{16}$$)($$1 - 34 T^{2} + 593 T^{4} - 8610 T^{6} + 122100 T^{8} - 1455090 T^{10} + 16936673 T^{12} - 164111506 T^{14} + 815730721 T^{16}$$)($$1 - 34 T^{2} + 593 T^{4} - 8610 T^{6} + 122100 T^{8} - 1455090 T^{10} + 16936673 T^{12} - 164111506 T^{14} + 815730721 T^{16}$$)($$( 1 - 66 T^{2} + 2096 T^{4} - 42782 T^{6} + 637630 T^{8} - 7230158 T^{10} + 59863856 T^{12} - 318569394 T^{14} + 815730721 T^{16} )^{2}$$)($$( 1 - 66 T^{2} + 2096 T^{4} - 42782 T^{6} + 637630 T^{8} - 7230158 T^{10} + 59863856 T^{12} - 318569394 T^{14} + 815730721 T^{16} )^{2}$$)($$( 1 - T + 13 T^{2} )^{2}$$)($$( 1 - 7 T + 13 T^{2} )^{2}$$)($$( 1 + 19 T^{2} + 169 T^{4} )^{2}$$)($$( 1 + 2 T + 9 T^{2} + 26 T^{3} + 169 T^{4} )^{2}$$)($$( 1 + 6 T + 18 T^{2} + 78 T^{3} + 169 T^{4} )^{2}$$)($$( 1 - 6 T + 13 T^{2} )^{2}( 1 + 4 T + 13 T^{2} )^{2}$$)($$( 1 + 169 T^{4} )^{4}$$)($$( 1 + 169 T^{4} )^{4}$$)($$1 - 536 T^{4} + 97308 T^{8} - 1310248 T^{12} - 1567451002 T^{16} - 37421993128 T^{20} + 79377124999068 T^{24} - 12487773625649816 T^{28} + 665416609183179841 T^{32}$$)($$( 1 - 13 T^{2} )^{8}$$)($$( 1 - 13 T^{2} )^{8}$$)($$( 1 - 52 T^{2} + 1402 T^{4} - 25364 T^{6} + 362579 T^{8} - 4286516 T^{10} + 40042522 T^{12} - 250994068 T^{14} + 815730721 T^{16} )^{2}$$)($$1 - 49 T^{2} + 1364 T^{4} - 28371 T^{6} + 474775 T^{8} - 6687888 T^{10} + 80236975 T^{12} - 810304131 T^{14} + 6583767476 T^{16} - 39970805329 T^{18} + 137858491849 T^{20}$$)($$1 - 49 T^{2} + 1364 T^{4} - 28371 T^{6} + 474775 T^{8} - 6687888 T^{10} + 80236975 T^{12} - 810304131 T^{14} + 6583767476 T^{16} - 39970805329 T^{18} + 137858491849 T^{20}$$)($$1 - 38 T^{2} + 651 T^{4} - 6422 T^{6} + 28561 T^{8}$$)($$1 - 38 T^{2} + 651 T^{4} - 6422 T^{6} + 28561 T^{8}$$)($$( 1 + 4 T + 8 T^{2} + 52 T^{3} + 169 T^{4} )^{4}$$)($$( 1 + 4 T + 8 T^{2} + 52 T^{3} + 169 T^{4} )^{4}$$)
$17$ ($$1 - 6 T + 17 T^{2}$$)($$1 - 2 T + 17 T^{2}$$)($$1 - 6 T + 17 T^{2}$$)($$1 - 2 T + 17 T^{2}$$)($$1 - 168 T^{2} + 13880 T^{4} - 751096 T^{6} + 29923612 T^{8} - 935973160 T^{10} + 23941747080 T^{12} - 514532623928 T^{14} + 9440913455942 T^{16} - 148699928315192 T^{18} + 1999638657868680 T^{20} - 22592116731648040 T^{22} + 208739859070596892 T^{24} - 1514204954651642104 T^{26} + 8086796652749082680 T^{28} - 28287474861979356072 T^{30} + 48661191875666868481 T^{32}$$)($$1 - 168 T^{2} + 13880 T^{4} - 751096 T^{6} + 29923612 T^{8} - 935973160 T^{10} + 23941747080 T^{12} - 514532623928 T^{14} + 9440913455942 T^{16} - 148699928315192 T^{18} + 1999638657868680 T^{20} - 22592116731648040 T^{22} + 208739859070596892 T^{24} - 1514204954651642104 T^{26} + 8086796652749082680 T^{28} - 28287474861979356072 T^{30} + 48661191875666868481 T^{32}$$)($$( 1 - 3 T + 17 T^{2} )^{2}$$)($$( 1 + 3 T + 17 T^{2} )^{2}$$)($$( 1 + 14 T^{2} + 289 T^{4} )^{2}$$)($$( 1 + 14 T^{2} + 289 T^{4} )^{2}$$)($$( 1 + 29 T^{2} + 552 T^{4} + 8381 T^{6} + 83521 T^{8} )^{2}$$)($$( 1 - 18 T^{2} + 289 T^{4} )^{4}$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} )$$)($$( 1 + 16 T^{2} + 289 T^{4} )^{2}$$)($$( 1 + 16 T^{2} + 289 T^{4} )^{2}$$)($$( 1 - 2 T + 33 T^{2} - 50 T^{3} + 644 T^{4} - 850 T^{5} + 9537 T^{6} - 9826 T^{7} + 83521 T^{8} )^{2}$$)($$( 1 + 2 T + 33 T^{2} + 50 T^{3} + 644 T^{4} + 850 T^{5} + 9537 T^{6} + 9826 T^{7} + 83521 T^{8} )^{2}$$)($$( 1 - 2 T + 33 T^{2} - 50 T^{3} + 644 T^{4} - 850 T^{5} + 9537 T^{6} - 9826 T^{7} + 83521 T^{8} )^{2}$$)($$( 1 + 2 T + 33 T^{2} + 50 T^{3} + 644 T^{4} + 850 T^{5} + 9537 T^{6} + 9826 T^{7} + 83521 T^{8} )^{2}$$)($$( 1 + 60 T^{2} + 2308 T^{4} + 59972 T^{6} + 1182838 T^{8} + 17331908 T^{10} + 192766468 T^{12} + 1448254140 T^{14} + 6975757441 T^{16} )^{2}$$)($$( 1 + 60 T^{2} + 2308 T^{4} + 59972 T^{6} + 1182838 T^{8} + 17331908 T^{10} + 192766468 T^{12} + 1448254140 T^{14} + 6975757441 T^{16} )^{2}$$)($$1 - 4 T - T^{2} - 68 T^{3} + 289 T^{4}$$)($$1 - 6 T + 19 T^{2} - 102 T^{3} + 289 T^{4}$$)($$1 + 2 T - 24 T^{2} - 12 T^{3} + 427 T^{4} - 204 T^{5} - 6936 T^{6} + 9826 T^{7} + 83521 T^{8}$$)($$1 - 16 T^{2} - 33 T^{4} - 4624 T^{6} + 83521 T^{8}$$)($$( 1 - 8 T + 17 T^{2} )^{2}( 1 + 2 T + 17 T^{2} )^{2}$$)($$( 1 + 2 T + 2 T^{2} + 34 T^{3} + 289 T^{4} )^{2}$$)($$( 1 - 20 T^{2} + 289 T^{4} )^{2}( 1 + 20 T^{2} + 289 T^{4} )^{2}$$)($$( 1 - 20 T^{2} + 289 T^{4} )^{2}( 1 + 20 T^{2} + 289 T^{4} )^{2}$$)($$1 - 904 T^{4} + 210332 T^{8} + 67692360 T^{12} - 44568692154 T^{16} + 5653733599560 T^{20} + 1467225014080412 T^{24} - 526690502455703944 T^{28} + 48661191875666868481 T^{32}$$)($$( 1 - 17 T^{2} + 289 T^{4} )^{4}$$)($$( 1 - 17 T^{2} + 289 T^{4} )^{4}$$)($$1 + 84 T^{2} + 3752 T^{4} + 108144 T^{6} + 2173654 T^{8} + 30758664 T^{10} + 289342496 T^{12} + 1372999908 T^{14} + 141824131 T^{16} + 396796973412 T^{18} + 24166174608416 T^{20} + 742439374647816 T^{22} + 15162883064659414 T^{24} + 218017644370156656 T^{26} + 2185998634086063272 T^{28} + 14143737430989678036 T^{30} + 48661191875666868481 T^{32}$$)($$1 - 6 T - 15 T^{2} + 138 T^{3} + 193 T^{4} - 2754 T^{5} + 4928 T^{6} + 30306 T^{7} - 220151 T^{8} - 325680 T^{9} + 6075881 T^{10} - 5536560 T^{11} - 63623639 T^{12} + 148893378 T^{13} + 411591488 T^{14} - 3910286178 T^{15} + 4658550817 T^{16} + 56626736874 T^{17} - 104636361615 T^{18} - 711527258982 T^{19} + 2015993900449 T^{20}$$)($$1 + 6 T - 15 T^{2} - 138 T^{3} + 193 T^{4} + 2754 T^{5} + 4928 T^{6} - 30306 T^{7} - 220151 T^{8} + 325680 T^{9} + 6075881 T^{10} + 5536560 T^{11} - 63623639 T^{12} - 148893378 T^{13} + 411591488 T^{14} + 3910286178 T^{15} + 4658550817 T^{16} - 56626736874 T^{17} - 104636361615 T^{18} + 711527258982 T^{19} + 2015993900449 T^{20}$$)($$( 1 - 12 T + 65 T^{2} - 204 T^{3} + 289 T^{4} )^{2}$$)($$( 1 - 12 T + 65 T^{2} - 204 T^{3} + 289 T^{4} )^{2}$$)($$1 + 4 T + 8 T^{2} + 56 T^{3} + 494 T^{4} + 2756 T^{5} + 8640 T^{6} + 36748 T^{7} + 198675 T^{8} + 624716 T^{9} + 2496960 T^{10} + 13540228 T^{11} + 41259374 T^{12} + 79511992 T^{13} + 193100552 T^{14} + 1641354692 T^{15} + 6975757441 T^{16}$$)($$1 - 4 T + 8 T^{2} - 56 T^{3} + 494 T^{4} - 2756 T^{5} + 8640 T^{6} - 36748 T^{7} + 198675 T^{8} - 624716 T^{9} + 2496960 T^{10} - 13540228 T^{11} + 41259374 T^{12} - 79511992 T^{13} + 193100552 T^{14} - 1641354692 T^{15} + 6975757441 T^{16}$$)
$19$ ($$1 - 6 T + 19 T^{2}$$)($$1 - 2 T + 19 T^{2}$$)($$1 - 2 T + 19 T^{2}$$)($$1 + 2 T + 19 T^{2}$$)($$( 1 + 12 T + 158 T^{2} + 1308 T^{3} + 10440 T^{4} + 66012 T^{5} + 391538 T^{6} + 1971116 T^{7} + 9248974 T^{8} + 37451204 T^{9} + 141345218 T^{10} + 452776308 T^{11} + 1360551240 T^{12} + 3238737492 T^{13} + 7433249198 T^{14} + 10726460868 T^{15} + 16983563041 T^{16} )^{2}$$)($$( 1 - 12 T + 158 T^{2} - 1308 T^{3} + 10440 T^{4} - 66012 T^{5} + 391538 T^{6} - 1971116 T^{7} + 9248974 T^{8} - 37451204 T^{9} + 141345218 T^{10} - 452776308 T^{11} + 1360551240 T^{12} - 3238737492 T^{13} + 7433249198 T^{14} - 10726460868 T^{15} + 16983563041 T^{16} )^{2}$$)($$( 1 - 8 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} )$$)($$( 1 - 8 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} )$$)($$1 - 16 T^{2} + 286 T^{4} - 5776 T^{6} + 130321 T^{8}$$)($$1 - 16 T^{2} + 286 T^{4} - 5776 T^{6} + 130321 T^{8}$$)($$( 1 - 19 T^{2} )^{8}$$)($$( 1 - 6 T + 19 T^{2} )^{4}( 1 + 6 T + 19 T^{2} )^{4}$$)($$( 1 + 6 T + 19 T^{2} )^{2}$$)($$( 1 - 2 T + 19 T^{2} )^{2}$$)($$( 1 - 2 T^{2} + 361 T^{4} )^{2}$$)($$( 1 - 2 T^{2} + 361 T^{4} )^{2}$$)($$1 - 64 T^{2} + 1180 T^{4} + 10560 T^{6} - 634906 T^{8} + 3812160 T^{10} + 153778780 T^{12} - 3010936384 T^{14} + 16983563041 T^{16}$$)($$1 - 64 T^{2} + 1180 T^{4} + 10560 T^{6} - 634906 T^{8} + 3812160 T^{10} + 153778780 T^{12} - 3010936384 T^{14} + 16983563041 T^{16}$$)($$1 - 64 T^{2} + 1180 T^{4} + 10560 T^{6} - 634906 T^{8} + 3812160 T^{10} + 153778780 T^{12} - 3010936384 T^{14} + 16983563041 T^{16}$$)($$1 - 64 T^{2} + 1180 T^{4} + 10560 T^{6} - 634906 T^{8} + 3812160 T^{10} + 153778780 T^{12} - 3010936384 T^{14} + 16983563041 T^{16}$$)($$( 1 - 114 T^{2} + 6104 T^{4} - 202286 T^{6} + 4583854 T^{8} - 73025246 T^{10} + 795479384 T^{12} - 5363230434 T^{14} + 16983563041 T^{16} )^{2}$$)($$( 1 - 114 T^{2} + 6104 T^{4} - 202286 T^{6} + 4583854 T^{8} - 73025246 T^{10} + 795479384 T^{12} - 5363230434 T^{14} + 16983563041 T^{16} )^{2}$$)($$( 1 - 8 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} )$$)($$1 + 3 T - 10 T^{2} + 57 T^{3} + 361 T^{4}$$)($$1 + 6 T + 17 T^{2} - 114 T^{3} - 684 T^{4} - 2166 T^{5} + 6137 T^{6} + 41154 T^{7} + 130321 T^{8}$$)($$( 1 - 8 T + 19 T^{2} )^{2}( 1 + T + 19 T^{2} )^{2}$$)($$( 1 - 34 T^{2} + 361 T^{4} )^{2}$$)($$( 1 + 30 T^{2} + 361 T^{4} )^{2}$$)($$( 1 - 622 T^{4} + 130321 T^{8} )^{2}$$)($$( 1 - 622 T^{4} + 130321 T^{8} )^{2}$$)($$( 1 + 120 T^{2} + 6692 T^{4} + 228264 T^{6} + 5227942 T^{8} + 82403304 T^{10} + 872108132 T^{12} + 5645505720 T^{14} + 16983563041 T^{16} )^{2}$$)($$( 1 + 19 T^{2} + 361 T^{4} )^{4}$$)($$( 1 + 19 T^{2} + 361 T^{4} )^{4}$$)($$( 1 - 4 T - 18 T^{2} - 112 T^{3} + 697 T^{4} + 2652 T^{5} + 9806 T^{6} - 65960 T^{7} - 161964 T^{8} - 1253240 T^{9} + 3539966 T^{10} + 18190068 T^{11} + 90833737 T^{12} - 277323088 T^{13} - 846825858 T^{14} - 3575486956 T^{15} + 16983563041 T^{16} )^{2}$$)($$1 - 3 T + 83 T^{2} - 240 T^{3} + 3800 T^{4} - 10380 T^{5} + 124845 T^{6} - 315315 T^{7} + 3213415 T^{8} - 7312140 T^{9} + 67225536 T^{10} - 138930660 T^{11} + 1160042815 T^{12} - 2162745585 T^{13} + 16269925245 T^{14} - 25701907620 T^{15} + 178774347800 T^{16} - 214529217360 T^{17} + 1409635732403 T^{18} - 968063093337 T^{19} + 6131066257801 T^{20}$$)($$1 - 3 T + 83 T^{2} - 240 T^{3} + 3800 T^{4} - 10380 T^{5} + 124845 T^{6} - 315315 T^{7} + 3213415 T^{8} - 7312140 T^{9} + 67225536 T^{10} - 138930660 T^{11} + 1160042815 T^{12} - 2162745585 T^{13} + 16269925245 T^{14} - 25701907620 T^{15} + 178774347800 T^{16} - 214529217360 T^{17} + 1409635732403 T^{18} - 968063093337 T^{19} + 6131066257801 T^{20}$$)($$1 - 2 T - 23 T^{2} + 22 T^{3} + 292 T^{4} + 418 T^{5} - 8303 T^{6} - 13718 T^{7} + 130321 T^{8}$$)($$1 + 2 T - 23 T^{2} - 22 T^{3} + 292 T^{4} - 418 T^{5} - 8303 T^{6} + 13718 T^{7} + 130321 T^{8}$$)($$1 + 36 T^{2} + 646 T^{4} - 2592 T^{6} - 175677 T^{8} - 935712 T^{10} + 84187366 T^{12} + 1693651716 T^{14} + 16983563041 T^{16}$$)($$1 + 36 T^{2} + 646 T^{4} - 2592 T^{6} - 175677 T^{8} - 935712 T^{10} + 84187366 T^{12} + 1693651716 T^{14} + 16983563041 T^{16}$$)
$23$ ($$1 + 8 T + 23 T^{2}$$)($$1 - 4 T + 23 T^{2}$$)($$1 + 23 T^{2}$$)($$1 - 4 T + 23 T^{2}$$)($$1 - 176 T^{2} + 15448 T^{4} - 913680 T^{6} + 41467228 T^{8} - 1550033328 T^{10} + 49589827176 T^{12} - 1383348399760 T^{14} + 33907824809542 T^{16} - 731791303473040 T^{18} + 13877266826759016 T^{20} - 229460561690108592 T^{22} + 3247339481551871068 T^{24} - 37850574765686818320 T^{26} +$$$$33\!\cdots\!08$$$$T^{28} -$$$$20\!\cdots\!84$$$$T^{30} +$$$$61\!\cdots\!61$$$$T^{32}$$)($$1 - 176 T^{2} + 15448 T^{4} - 913680 T^{6} + 41467228 T^{8} - 1550033328 T^{10} + 49589827176 T^{12} - 1383348399760 T^{14} + 33907824809542 T^{16} - 731791303473040 T^{18} + 13877266826759016 T^{20} - 229460561690108592 T^{22} + 3247339481551871068 T^{24} - 37850574765686818320 T^{26} +$$$$33\!\cdots\!08$$$$T^{28} -$$$$20\!\cdots\!84$$$$T^{30} +$$$$61\!\cdots\!61$$$$T^{32}$$)($$( 1 - 23 T^{2} )^{2}$$)($$( 1 - 23 T^{2} )^{2}$$)($$( 1 - 2 T + 2 T^{2} - 46 T^{3} + 529 T^{4} )( 1 + 2 T + 2 T^{2} + 46 T^{3} + 529 T^{4} )$$)($$( 1 - 2 T + 2 T^{2} - 46 T^{3} + 529 T^{4} )( 1 + 2 T + 2 T^{2} + 46 T^{3} + 529 T^{4} )$$)($$( 1 + 23 T^{2} )^{8}$$)($$( 1 + 6 T^{2} + 529 T^{4} )^{4}$$)($$1 - 42 T^{2} + 529 T^{4}$$)($$1 - 10 T^{2} + 529 T^{4}$$)($$( 1 - 44 T^{2} + 529 T^{4} )^{2}$$)($$( 1 - 44 T^{2} + 529 T^{4} )^{2}$$)($$1 - 88 T^{2} + 4220 T^{4} - 145000 T^{6} + 3793350 T^{8} - 76705000 T^{10} + 1180929020 T^{12} - 13027158232 T^{14} + 78310985281 T^{16}$$)($$1 - 88 T^{2} + 4220 T^{4} - 145000 T^{6} + 3793350 T^{8} - 76705000 T^{10} + 1180929020 T^{12} - 13027158232 T^{14} + 78310985281 T^{16}$$)($$1 - 88 T^{2} + 4220 T^{4} - 145000 T^{6} + 3793350 T^{8} - 76705000 T^{10} + 1180929020 T^{12} - 13027158232 T^{14} + 78310985281 T^{16}$$)($$1 - 88 T^{2} + 4220 T^{4} - 145000 T^{6} + 3793350 T^{8} - 76705000 T^{10} + 1180929020 T^{12} - 13027158232 T^{14} + 78310985281 T^{16}$$)($$( 1 - 72 T^{2} + 3292 T^{4} - 107896 T^{6} + 2808070 T^{8} - 57076984 T^{10} + 921236572 T^{12} - 10658584008 T^{14} + 78310985281 T^{16} )^{2}$$)($$( 1 - 72 T^{2} + 3292 T^{4} - 107896 T^{6} + 2808070 T^{8} - 57076984 T^{10} + 921236572 T^{12} - 10658584008 T^{14} + 78310985281 T^{16} )^{2}$$)($$1 + 4 T - 7 T^{2} + 92 T^{3} + 529 T^{4}$$)($$1 - 2 T - 19 T^{2} - 46 T^{3} + 529 T^{4}$$)($$1 - 2 T - 36 T^{2} + 12 T^{3} + 979 T^{4} + 276 T^{5} - 19044 T^{6} - 24334 T^{7} + 279841 T^{8}$$)($$1 - 28 T^{2} + 255 T^{4} - 14812 T^{6} + 279841 T^{8}$$)($$1 - 158 T^{4} + 279841 T^{8}$$)($$1 - 158 T^{4} + 279841 T^{8}$$)($$( 1 - 10 T + 50 T^{2} - 230 T^{3} + 529 T^{4} )^{2}( 1 + 10 T + 50 T^{2} + 230 T^{3} + 529 T^{4} )^{2}$$)($$( 1 - 10 T + 50 T^{2} - 230 T^{3} + 529 T^{4} )^{2}( 1 + 10 T + 50 T^{2} + 230 T^{3} + 529 T^{4} )^{2}$$)($$( 1 - 4 T + 8 T^{2} + 4 T^{3} - 1548 T^{4} + 3956 T^{5} - 3432 T^{6} - 53556 T^{7} + 1130086 T^{8} - 1231788 T^{9} - 1815528 T^{10} + 48132652 T^{11} - 433193868 T^{12} + 25745372 T^{13} + 1184287112 T^{14} - 13619301788 T^{15} + 78310985281 T^{16} )^{2}$$)($$( 1 - 44 T^{2} + 529 T^{4} )^{2}( 1 + 44 T^{2} + 1407 T^{4} + 23276 T^{6} + 279841 T^{8} )$$)($$( 1 - 44 T^{2} + 529 T^{4} )^{2}( 1 + 44 T^{2} + 1407 T^{4} + 23276 T^{6} + 279841 T^{8} )$$)($$1 + 124 T^{2} + 8136 T^{4} + 362464 T^{6} + 12116710 T^{8} + 315447888 T^{10} + 6636136256 T^{12} + 123080808860 T^{14} + 2498537815875 T^{16} + 65109747886940 T^{18} + 1857063006015296 T^{20} + 46697608533252432 T^{22} + 948871498464145510 T^{24} + 15015618960544071136 T^{26} +$$$$17\!\cdots\!56$$$$T^{28} +$$$$14\!\cdots\!16$$$$T^{30} +$$$$61\!\cdots\!61$$$$T^{32}$$)($$1 - 24 T + 338 T^{2} - 3504 T^{3} + 29201 T^{4} - 203310 T^{5} + 1216412 T^{6} - 6430392 T^{7} + 31045441 T^{8} - 143820006 T^{9} + 675418266 T^{10} - 3307860138 T^{11} + 16423038289 T^{12} - 78238579464 T^{13} + 340401950492 T^{14} - 1308572895330 T^{15} + 4322795994689 T^{16} - 11930508366288 T^{17} + 26469113024978 T^{18} - 43227663875112 T^{19} + 41426511213649 T^{20}$$)($$1 + 24 T + 338 T^{2} + 3504 T^{3} + 29201 T^{4} + 203310 T^{5} + 1216412 T^{6} + 6430392 T^{7} + 31045441 T^{8} + 143820006 T^{9} + 675418266 T^{10} + 3307860138 T^{11} + 16423038289 T^{12} + 78238579464 T^{13} + 340401950492 T^{14} + 1308572895330 T^{15} + 4322795994689 T^{16} + 11930508366288 T^{17} + 26469113024978 T^{18} + 43227663875112 T^{19} + 41426511213649 T^{20}$$)($$1 - 18 T^{2} - 205 T^{4} - 9522 T^{6} + 279841 T^{8}$$)($$1 - 18 T^{2} - 205 T^{4} - 9522 T^{6} + 279841 T^{8}$$)($$1 - 2 T + 2 T^{2} + 68 T^{3} - 691 T^{4} + 1592 T^{5} + 510 T^{6} - 45566 T^{7} + 173700 T^{8} - 1048018 T^{9} + 269790 T^{10} + 19369864 T^{11} - 193370131 T^{12} + 437671324 T^{13} + 296071778 T^{14} - 6809650894 T^{15} + 78310985281 T^{16}$$)($$1 + 2 T + 2 T^{2} - 68 T^{3} - 691 T^{4} - 1592 T^{5} + 510 T^{6} + 45566 T^{7} + 173700 T^{8} + 1048018 T^{9} + 269790 T^{10} - 19369864 T^{11} - 193370131 T^{12} - 437671324 T^{13} + 296071778 T^{14} + 6809650894 T^{15} + 78310985281 T^{16}$$)
$29$ ($$1 + 2 T + 29 T^{2}$$)($$1 - 6 T + 29 T^{2}$$)($$1 - 6 T + 29 T^{2}$$)($$1 + 2 T + 29 T^{2}$$)($$( 1 - 8 T + 100 T^{2} - 360 T^{3} + 3380 T^{4} - 3064 T^{5} + 62140 T^{6} + 238824 T^{7} + 906806 T^{8} + 6925896 T^{9} + 52259740 T^{10} - 74727896 T^{11} + 2390609780 T^{12} - 7384013640 T^{13} + 59482332100 T^{14} - 137999010472 T^{15} + 500246412961 T^{16} )^{2}$$)($$( 1 - 8 T + 100 T^{2} - 360 T^{3} + 3380 T^{4} - 3064 T^{5} + 62140 T^{6} + 238824 T^{7} + 906806 T^{8} + 6925896 T^{9} + 52259740 T^{10} - 74727896 T^{11} + 2390609780 T^{12} - 7384013640 T^{13} + 59482332100 T^{14} - 137999010472 T^{15} + 500246412961 T^{16} )^{2}$$)($$1 - 31 T^{2} + 841 T^{4}$$)($$1 - 31 T^{2} + 841 T^{4}$$)($$( 1 - 10 T + 29 T^{2} )^{2}( 1 + 10 T + 29 T^{2} )^{2}$$)($$( 1 - 10 T + 29 T^{2} )^{2}( 1 + 10 T + 29 T^{2} )^{2}$$)($$( 1 - 9 T + 52 T^{2} - 261 T^{3} + 841 T^{4} )^{2}( 1 + 9 T + 52 T^{2} + 261 T^{3} + 841 T^{4} )^{2}$$)($$( 1 - 26 T^{2} + 841 T^{4} )^{4}$$)($$( 1 + 6 T + 29 T^{2} )^{2}$$)($$( 1 + 6 T + 29 T^{2} )^{2}$$)($$( 1 - 50 T^{2} + 841 T^{4} )^{2}$$)($$( 1 - 50 T^{2} + 841 T^{4} )^{2}$$)($$1 - 162 T^{2} + 12689 T^{4} - 630306 T^{6} + 21708724 T^{8} - 530087346 T^{10} + 8974688609 T^{12} - 96361378002 T^{14} + 500246412961 T^{16}$$)($$1 - 162 T^{2} + 12689 T^{4} - 630306 T^{6} + 21708724 T^{8} - 530087346 T^{10} + 8974688609 T^{12} - 96361378002 T^{14} + 500246412961 T^{16}$$)($$1 - 162 T^{2} + 12689 T^{4} - 630306 T^{6} + 21708724 T^{8} - 530087346 T^{10} + 8974688609 T^{12} - 96361378002 T^{14} + 500246412961 T^{16}$$)($$1 - 162 T^{2} + 12689 T^{4} - 630306 T^{6} + 21708724 T^{8} - 530087346 T^{10} + 8974688609 T^{12} - 96361378002 T^{14} + 500246412961 T^{16}$$)($$( 1 - 68 T^{2} + 3892 T^{4} - 150428 T^{6} + 5129398 T^{8} - 126509948 T^{10} + 2752737652 T^{12} - 40447985828 T^{14} + 500246412961 T^{16} )^{2}$$)($$( 1 - 68 T^{2} + 3892 T^{4} - 150428 T^{6} + 5129398 T^{8} - 126509948 T^{10} + 2752737652 T^{12} - 40447985828 T^{14} + 500246412961 T^{16} )^{2}$$)($$( 1 + 29 T^{2} )^{2}$$)($$( 1 + 2 T + 29 T^{2} )^{2}$$)($$( 1 - 10 T + 76 T^{2} - 290 T^{3} + 841 T^{4} )^{2}$$)($$( 1 + 12 T + 76 T^{2} + 348 T^{3} + 841 T^{4} )^{2}$$)($$( 1 - 29 T^{2} )^{4}$$)($$( 1 - 29 T^{2} )^{4}$$)($$( 1 + 29 T^{2} )^{8}$$)($$( 1 + 29 T^{2} )^{8}$$)($$( 1 - 136 T^{2} + 8924 T^{4} - 381688 T^{6} + 12377958 T^{8} - 320999608 T^{10} + 6311775644 T^{12} - 80895971656 T^{14} + 500246412961 T^{16} )^{2}$$)($$( 1 - 6 T + 7 T^{2} - 174 T^{3} + 841 T^{4} )^{2}( 1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4} )^{2}$$)($$( 1 - 6 T + 7 T^{2} - 174 T^{3} + 841 T^{4} )^{2}( 1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4} )^{2}$$)($$( 1 - 6 T + 50 T^{2} - 300 T^{3} + 2316 T^{4} - 8700 T^{5} + 42050 T^{6} - 146334 T^{7} + 707281 T^{8} )^{4}$$)($$1 - 148 T^{2} + 11438 T^{4} - 619594 T^{6} + 25499257 T^{8} - 826380936 T^{10} + 21444875137 T^{12} - 438227063914 T^{14} + 6803589145598 T^{16} - 74036469118228 T^{18} + 420707233300201 T^{20}$$)($$1 - 148 T^{2} + 11438 T^{4} - 619594 T^{6} + 25499257 T^{8} - 826380936 T^{10} + 21444875137 T^{12} - 438227063914 T^{14} + 6803589145598 T^{16} - 74036469118228 T^{18} + 420707233300201 T^{20}$$)($$( 1 - 12 T + 82 T^{2} - 348 T^{3} + 841 T^{4} )^{2}$$)($$( 1 - 12 T + 82 T^{2} - 348 T^{3} + 841 T^{4} )^{2}$$)($$( 1 + 8 T + 63 T^{2} + 232 T^{3} + 841 T^{4} )^{4}$$)($$( 1 - 8 T + 63 T^{2} - 232 T^{3} + 841 T^{4} )^{4}$$)
$31$ ($$1 - 10 T + 31 T^{2}$$)($$1 + 2 T + 31 T^{2}$$)($$1 + 10 T + 31 T^{2}$$)($$1 + 6 T + 31 T^{2}$$)($$( 1 - 4 T + 98 T^{2} - 516 T^{3} + 5624 T^{4} - 35252 T^{5} + 225022 T^{6} - 1588916 T^{7} + 7569102 T^{8} - 49256396 T^{9} + 216246142 T^{10} - 1050192332 T^{11} + 5193882104 T^{12} - 14772641916 T^{13} + 86975360738 T^{14} - 110050456444 T^{15} + 852891037441 T^{16} )^{2}$$)($$( 1 + 4 T + 98 T^{2} + 516 T^{3} + 5624 T^{4} + 35252 T^{5} + 225022 T^{6} + 1588916 T^{7} + 7569102 T^{8} + 49256396 T^{9} + 216246142 T^{10} + 1050192332 T^{11} + 5193882104 T^{12} + 14772641916 T^{13} + 86975360738 T^{14} + 110050456444 T^{15} + 852891037441 T^{16} )^{2}$$)($$( 1 - 4 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} )$$)($$( 1 - 4 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} )$$)($$1 - 112 T^{2} + 5038 T^{4} - 107632 T^{6} + 923521 T^{8}$$)($$1 - 112 T^{2} + 5038 T^{4} - 107632 T^{6} + 923521 T^{8}$$)($$( 1 - 31 T^{2} )^{8}$$)($$( 1 - 22 T^{2} + 961 T^{4} )^{4}$$)($$( 1 + 2 T + 31 T^{2} )^{2}$$)($$( 1 - 6 T + 31 T^{2} )^{2}$$)($$( 1 - 31 T^{2} )^{4}$$)($$( 1 - 31 T^{2} )^{4}$$)($$1 - 56 T^{2} + 2684 T^{4} - 115208 T^{6} + 3486342 T^{8} - 110714888 T^{10} + 2478730364 T^{12} - 49700206136 T^{14} + 852891037441 T^{16}$$)($$1 - 56 T^{2} + 2684 T^{4} - 115208 T^{6} + 3486342 T^{8} - 110714888 T^{10} + 2478730364 T^{12} - 49700206136 T^{14} + 852891037441 T^{16}$$)($$1 - 56 T^{2} + 2684 T^{4} - 115208 T^{6} + 3486342 T^{8} - 110714888 T^{10} + 2478730364 T^{12} - 49700206136 T^{14} + 852891037441 T^{16}$$)($$1 - 56 T^{2} + 2684 T^{4} - 115208 T^{6} + 3486342 T^{8} - 110714888 T^{10} + 2478730364 T^{12} - 49700206136 T^{14} + 852891037441 T^{16}$$)($$( 1 - 158 T^{2} + 12408 T^{4} - 637698 T^{6} + 23269838 T^{8} - 612827778 T^{10} + 11459048568 T^{12} - 140225581598 T^{14} + 852891037441 T^{16} )^{2}$$)($$( 1 - 158 T^{2} + 12408 T^{4} - 637698 T^{6} + 23269838 T^{8} - 612827778 T^{10} + 11459048568 T^{12} - 140225581598 T^{14} + 852891037441 T^{16} )^{2}$$)($$1 - 5 T - 6 T^{2} - 155 T^{3} + 961 T^{4}$$)($$( 1 - 4 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} )$$)($$1 + 2 T - 31 T^{2} - 54 T^{3} + 140 T^{4} - 1674 T^{5} - 29791 T^{6} + 59582 T^{7} + 923521 T^{8}$$)($$1 - 2 T + 13 T^{2} + 142 T^{3} - 1004 T^{4} + 4402 T^{5} + 12493 T^{6} - 59582 T^{7} + 923521 T^{8}$$)($$( 1 + 10 T^{2} + 961 T^{4} )^{2}$$)($$( 1 - 54 T^{2} + 961 T^{4} )^{2}$$)($$( 1 + 578 T^{4} + 923521 T^{8} )^{2}$$)($$( 1 + 578 T^{4} + 923521 T^{8} )^{2}$$)($$( 1 - 136 T^{2} + 8612 T^{4} - 354840 T^{6} + 11712390 T^{8} - 341001240 T^{10} + 7953362852 T^{12} - 120700500616 T^{14} + 852891037441 T^{16} )^{2}$$)($$( 1 + 31 T^{2} + 961 T^{4} )^{4}$$)($$( 1 + 31 T^{2} + 961 T^{4} )^{4}$$)($$( 1 - 22 T^{2} + 400 T^{3} - 59 T^{4} - 10600 T^{5} + 70338 T^{6} + 164200 T^{7} - 2333796 T^{8} + 5090200 T^{9} + 67594818 T^{10} - 315784600 T^{11} - 54487739 T^{12} + 11451660400 T^{13} - 19525080982 T^{14} + 852891037441 T^{16} )^{2}$$)($$1 - 15 T + 167 T^{2} - 1380 T^{3} + 9668 T^{4} - 61404 T^{5} + 363093 T^{6} - 2129475 T^{7} + 12161347 T^{8} - 68552376 T^{9} + 387742776 T^{10} - 2125123656 T^{11} + 11687054467 T^{12} - 63439189725 T^{13} + 335324010453 T^{14} - 1757944388004 T^{15} + 8580385587908 T^{16} - 37967407473180 T^{17} + 142432803252647 T^{18} - 396594332410065 T^{19} + 819628286980801 T^{20}$$)($$1 - 15 T + 167 T^{2} - 1380 T^{3} + 9668 T^{4} - 61404 T^{5} + 363093 T^{6} - 2129475 T^{7} + 12161347 T^{8} - 68552376 T^{9} + 387742776 T^{10} - 2125123656 T^{11} + 11687054467 T^{12} - 63439189725 T^{13} + 335324010453 T^{14} - 1757944388004 T^{15} + 8580385587908 T^{16} - 37967407473180 T^{17} + 142432803252647 T^{18} - 396594332410065 T^{19} + 819628286980801 T^{20}$$)($$1 - 6 T - 23 T^{2} + 18 T^{3} + 1404 T^{4} + 558 T^{5} - 22103 T^{6} - 178746 T^{7} + 923521 T^{8}$$)($$1 + 6 T - 23 T^{2} - 18 T^{3} + 1404 T^{4} - 558 T^{5} - 22103 T^{6} + 178746 T^{7} + 923521 T^{8}$$)($$( 1 - 6 T + 5 T^{2} - 186 T^{3} + 961 T^{4} )^{4}$$)($$( 1 - 6 T + 5 T^{2} - 186 T^{3} + 961 T^{4} )^{4}$$)
$37$ ($$1 - 2 T + 37 T^{2}$$)($$1 - 10 T + 37 T^{2}$$)($$1 - 2 T + 37 T^{2}$$)($$1 + 6 T + 37 T^{2}$$)($$( 1 - 12 T + 188 T^{2} - 1604 T^{3} + 16708 T^{4} - 119548 T^{5} + 988388 T^{6} - 6004372 T^{7} + 41848406 T^{8} - 222161764 T^{9} + 1353103172 T^{10} - 6055464844 T^{11} + 31313481988 T^{12} - 111227707028 T^{13} + 482356564892 T^{14} - 1139182525596 T^{15} + 3512479453921 T^{16} )^{2}$$)($$( 1 - 12 T + 188 T^{2} - 1604 T^{3} + 16708 T^{4} - 119548 T^{5} + 988388 T^{6} - 6004372 T^{7} + 41848406 T^{8} - 222161764 T^{9} + 1353103172 T^{10} - 6055464844 T^{11} + 31313481988 T^{12} - 111227707028 T^{13} + 482356564892 T^{14} - 1139182525596 T^{15} + 3512479453921 T^{16} )^{2}$$)($$( 1 + 8 T + 37 T^{2} )^{2}$$)($$( 1 + 8 T + 37 T^{2} )^{2}$$)($$( 1 + 54 T^{2} + 1369 T^{4} )^{2}$$)($$( 1 + 54 T^{2} + 1369 T^{4} )^{2}$$)($$( 1 - 37 T^{2} )^{8}$$)($$( 1 + 6 T^{2} + 1369 T^{4} )^{4}$$)($$1 - 58 T^{2} + 1369 T^{4}$$)($$1 - 58 T^{2} + 1369 T^{4}$$)($$( 1 - 38 T^{2} + 1369 T^{4} )^{2}$$)($$( 1 - 38 T^{2} + 1369 T^{4} )^{2}$$)($$1 - 160 T^{2} + 12124 T^{4} - 608352 T^{6} + 24287270 T^{8} - 832833888 T^{10} + 22722327964 T^{12} - 410516225440 T^{14} + 3512479453921 T^{16}$$)($$1 - 160 T^{2} + 12124 T^{4} - 608352 T^{6} + 24287270 T^{8} - 832833888 T^{10} + 22722327964 T^{12} - 410516225440 T^{14} + 3512479453921 T^{16}$$)($$1 - 160 T^{2} + 12124 T^{4} - 608352 T^{6} + 24287270 T^{8} - 832833888 T^{10} + 22722327964 T^{12} - 410516225440 T^{14} + 3512479453921 T^{16}$$)($$1 - 160 T^{2} + 12124 T^{4} - 608352 T^{6} + 24287270 T^{8} - 832833888 T^{10} + 22722327964 T^{12} - 410516225440 T^{14} + 3512479453921 T^{16}$$)($$( 1 - 148 T^{2} + 12948 T^{4} - 755340 T^{6} + 32573238 T^{8} - 1034060460 T^{10} + 24266636628 T^{12} - 379727508532 T^{14} + 3512479453921 T^{16} )^{2}$$)($$( 1 - 148 T^{2} + 12948 T^{4} - 755340 T^{6} + 32573238 T^{8} - 1034060460 T^{10} + 24266636628 T^{12} - 379727508532 T^{14} + 3512479453921 T^{16} )^{2}$$)($$1 - 5 T - 12 T^{2} - 185 T^{3} + 1369 T^{4}$$)($$1 - 7 T + 12 T^{2} - 259 T^{3} + 1369 T^{4}$$)($$1 - 4 T - 55 T^{2} + 12 T^{3} + 3080 T^{4} + 444 T^{5} - 75295 T^{6} - 202612 T^{7} + 1874161 T^{8}$$)($$1 - 2 T - 53 T^{2} + 34 T^{3} + 1732 T^{4} + 1258 T^{5} - 72557 T^{6} - 101306 T^{7} + 1874161 T^{8}$$)($$( 1 - 12 T + 37 T^{2} )^{2}( 1 + 2 T + 37 T^{2} )^{2}$$)($$( 1 + 6 T + 18 T^{2} + 222 T^{3} + 1369 T^{4} )^{2}$$)($$( 1 - 8 T + 37 T^{2} )^{4}( 1 - 10 T^{2} + 1369 T^{4} )^{2}$$)($$( 1 - 8 T + 37 T^{2} )^{4}( 1 - 10 T^{2} + 1369 T^{4} )^{2}$$)($$( 1 - 8 T + 32 T^{2} - 56 T^{3} - 2980 T^{4} + 15992 T^{5} - 31008 T^{6} - 263416 T^{7} + 5332518 T^{8} - 9746392 T^{9} - 42449952 T^{10} + 810042776 T^{11} - 5584999780 T^{12} - 3883261592 T^{13} + 82103245088 T^{14} - 759455017064 T^{15} + 3512479453921 T^{16} )^{2}$$)($$( 1 + 37 T^{2} + 1369 T^{4} )^{4}$$)($$( 1 + 37 T^{2} + 1369 T^{4} )^{4}$$)($$1 + 232 T^{2} + 28374 T^{4} + 2489048 T^{6} + 175050449 T^{8} + 10315517028 T^{10} + 522988033318 T^{12} + 23254660312732 T^{14} + 914412034849428 T^{16} + 31835629968130108 T^{18} + 980163775511296198 T^{20} + 26466794461228792452 T^{22} +$$$$61\!\cdots\!29$$$$T^{24} +$$$$11\!\cdots\!52$$$$T^{26} +$$$$18\!\cdots\!94$$$$T^{28} +$$$$20\!\cdots\!48$$$$T^{30} +$$$$12\!\cdots\!41$$$$T^{32}$$)($$1 + T - 117 T^{2} - 176 T^{3} + 6668 T^{4} + 11380 T^{5} - 299439 T^{6} - 438173 T^{7} + 12712375 T^{8} + 7307172 T^{9} - 492022188 T^{10} + 270365364 T^{11} + 17403241375 T^{12} - 22194776969 T^{13} - 561196895679 T^{14} + 789134230660 T^{15} + 17108263695212 T^{16} - 16708010375408 T^{17} - 410960096108757 T^{18} + 129961739795077 T^{19} + 4808584372417849 T^{20}$$)($$1 + T - 117 T^{2} - 176 T^{3} + 6668 T^{4} + 11380 T^{5} - 299439 T^{6} - 438173 T^{7} + 12712375 T^{8} + 7307172 T^{9} - 492022188 T^{10} + 270365364 T^{11} + 17403241375 T^{12} - 22194776969 T^{13} - 561196895679 T^{14} + 789134230660 T^{15} + 17108263695212 T^{16} - 16708010375408 T^{17} - 410960096108757 T^{18} + 129961739795077 T^{19} + 4808584372417849 T^{20}$$)($$1 - 2 T - 59 T^{2} + 22 T^{3} + 2452 T^{4} + 814 T^{5} - 80771 T^{6} - 101306 T^{7} + 1874161 T^{8}$$)($$1 - 2 T - 59 T^{2} + 22 T^{3} + 2452 T^{4} + 814 T^{5} - 80771 T^{6} - 101306 T^{7} + 1874161 T^{8}$$)($$( 1 - 8 T + 32 T^{2} + 336 T^{3} - 2713 T^{4} + 12432 T^{5} + 43808 T^{6} - 405224 T^{7} + 1874161 T^{8} )^{2}$$)($$( 1 - 8 T + 32 T^{2} + 336 T^{3} - 2713 T^{4} + 12432 T^{5} + 43808 T^{6} - 405224 T^{7} + 1874161 T^{8} )^{2}$$)
$41$ ($$1 - 10 T + 41 T^{2}$$)($$1 + 10 T + 41 T^{2}$$)($$1 + 6 T + 41 T^{2}$$)($$1 - 6 T + 41 T^{2}$$)($$1 - 184 T^{2} + 20472 T^{4} - 1751720 T^{6} + 121699868 T^{8} - 7243988536 T^{10} + 380165048008 T^{12} - 17911615742824 T^{14} + 768666981378246 T^{16} - 30109426063687144 T^{18} + 1074255566224134088 T^{20} - 34409700666608981176 T^{22} +$$$$97\!\cdots\!28$$$$T^{24} -$$$$23\!\cdots\!20$$$$T^{26} +$$$$46\!\cdots\!32$$$$T^{28} -$$$$69\!\cdots\!24$$$$T^{30} +$$$$63\!\cdots\!41$$$$T^{32}$$)($$1 - 184 T^{2} + 20472 T^{4} - 1751720 T^{6} + 121699868 T^{8} - 7243988536 T^{10} + 380165048008 T^{12} - 17911615742824 T^{14} + 768666981378246 T^{16} - 30109426063687144 T^{18} + 1074255566224134088 T^{20} - 34409700666608981176 T^{22} +$$$$97\!\cdots\!28$$$$T^{24} -$$$$23\!\cdots\!20$$$$T^{26} +$$$$46\!\cdots\!32$$$$T^{28} -$$$$69\!\cdots\!24$$$$T^{30} +$$$$63\!\cdots\!41$$$$T^{32}$$)($$( 1 - 6 T + 41 T^{2} )^{2}$$)($$( 1 + 6 T + 41 T^{2} )^{2}$$)($$( 1 - 16 T + 126 T^{2} - 656 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 + 16 T + 126 T^{2} + 656 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 + 41 T^{2} )^{8}$$)($$( 1 + 62 T^{2} + 1681 T^{4} )^{4}$$)($$( 1 - 8 T + 41 T^{2} )^{2}$$)($$( 1 + 41 T^{2} )^{2}$$)($$( 1 - 80 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 80 T^{2} + 1681 T^{4} )^{2}$$)($$1 - 224 T^{2} + 24956 T^{4} - 1767712 T^{6} + 86340934 T^{8} - 2971523872 T^{10} + 70519691516 T^{12} - 1064023349984 T^{14} + 7984925229121 T^{16}$$)($$1 - 224 T^{2} + 24956 T^{4} - 1767712 T^{6} + 86340934 T^{8} - 2971523872 T^{10} + 70519691516 T^{12} - 1064023349984 T^{14} + 7984925229121 T^{16}$$)($$1 - 224 T^{2} + 24956 T^{4} - 1767712 T^{6} + 86340934 T^{8} - 2971523872 T^{10} + 70519691516 T^{12} - 1064023349984 T^{14} + 7984925229121 T^{16}$$)($$1 - 224 T^{2} + 24956 T^{4} - 1767712 T^{6} + 86340934 T^{8} - 2971523872 T^{10} + 70519691516 T^{12} - 1064023349984 T^{14} + 7984925229121 T^{16}$$)($$( 1 - 84 T^{2} + 6292 T^{4} - 269932 T^{6} + 12822550 T^{8} - 453755692 T^{10} + 17779688212 T^{12} - 399008756244 T^{14} + 7984925229121 T^{16} )^{2}$$)($$( 1 - 84 T^{2} + 6292 T^{4} - 269932 T^{6} + 12822550 T^{8} - 453755692 T^{10} + 17779688212 T^{12} - 399008756244 T^{14} + 7984925229121 T^{16} )^{2}$$)($$( 1 - 2 T + 41 T^{2} )^{2}$$)($$( 1 + 8 T + 41 T^{2} )^{2}$$)($$( 1 + 6 T + 28 T^{2} + 246 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 + 64 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 8 T + 41 T^{2} )^{4}$$)($$( 1 + 41 T^{2} )^{4}$$)($$( 1 + 68 T^{2} + 1681 T^{4} )^{4}$$)($$( 1 + 68 T^{2} + 1681 T^{4} )^{4}$$)($$( 1 - 200 T^{2} + 20668 T^{4} - 1400376 T^{6} + 67532294 T^{8} - 2354032056 T^{10} + 58402828348 T^{12} - 950020848200 T^{14} + 7984925229121 T^{16} )^{2}$$)($$( 1 - 12 T + 103 T^{2} - 492 T^{3} + 1681 T^{4} )^{2}( 1 + 12 T + 103 T^{2} + 492 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 - 12 T + 103 T^{2} - 492 T^{3} + 1681 T^{4} )^{2}( 1 + 12 T + 103 T^{2} + 492 T^{3} + 1681 T^{4} )^{2}$$)($$( 1 - 12 T + 206 T^{2} - 1514 T^{3} + 13536 T^{4} - 62074 T^{5} + 346286 T^{6} - 827052 T^{7} + 2825761 T^{8} )^{4}$$)($$( 1 + 4 T + 90 T^{2} + 592 T^{3} + 3749 T^{4} + 36434 T^{5} + 153709 T^{6} + 995152 T^{7} + 6202890 T^{8} + 11303044 T^{9} + 115856201 T^{10} )^{2}$$)($$( 1 - 4 T + 90 T^{2} - 592 T^{3} + 3749 T^{4} - 36434 T^{5} + 153709 T^{6} - 995152 T^{7} + 6202890 T^{8} - 11303044 T^{9} + 115856201 T^{10} )^{2}$$)($$( 1 - 46 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 46 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 - 58 T^{2} + 2619 T^{4} - 97498 T^{6} + 2825761 T^{8} )^{2}$$)($$( 1 - 58 T^{2} + 2619 T^{4} - 97498 T^{6} + 2825761 T^{8} )^{2}$$)
$43$ ($$1 + 4 T + 43 T^{2}$$)($$1 - 12 T + 43 T^{2}$$)($$1 + 4 T + 43 T^{2}$$)($$1 + 4 T + 43 T^{2}$$)($$1 - 352 T^{2} + 65784 T^{4} - 8492960 T^{6} + 836964316 T^{8} - 66242040800 T^{10} + 4333734314568 T^{12} - 238312249642272 T^{14} + 11112687909569926 T^{16} - 440639349588560928 T^{18} + 14816175208379392968 T^{20} -$$$$41\!\cdots\!00$$$$T^{22} +$$$$97\!\cdots\!16$$$$T^{24} -$$$$18\!\cdots\!40$$$$T^{26} +$$$$26\!\cdots\!84$$$$T^{28} -$$$$26\!\cdots\!48$$$$T^{30} +$$$$13\!\cdots\!01$$$$T^{32}$$)($$1 - 352 T^{2} + 65784 T^{4} - 8492960 T^{6} + 836964316 T^{8} - 66242040800 T^{10} + 4333734314568 T^{12} - 238312249642272 T^{14} + 11112687909569926 T^{16} - 440639349588560928 T^{18} + 14816175208379392968 T^{20} -$$$$41\!\cdots\!00$$$$T^{22} +$$$$97\!\cdots\!16$$$$T^{24} -$$$$18\!\cdots\!40$$$$T^{26} +$$$$26\!\cdots\!84$$$$T^{28} -$$$$26\!\cdots\!48$$$$T^{30} +$$$$13\!\cdots\!01$$$$T^{32}$$)($$( 1 - 10 T + 43 T^{2} )^{2}$$)($$( 1 - 10 T + 43 T^{2} )^{2}$$)($$( 1 + 10 T + 106 T^{2} + 430 T^{3} + 1849 T^{4} )^{2}$$)($$( 1 + 10 T + 106 T^{2} + 430 T^{3} + 1849 T^{4} )^{2}$$)($$( 1 - 43 T^{2} )^{8}$$)($$( 1 - 66 T^{2} + 1849 T^{4} )^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$1 - 70 T^{2} + 1849 T^{4}$$)($$( 1 - 8 T + 43 T^{2} )^{4}$$)($$( 1 + 8 T + 43 T^{2} )^{4}$$)($$( 1 - 4 T + 116 T^{2} - 324 T^{3} + 6150 T^{4} - 13932 T^{5} + 214484 T^{6} - 318028 T^{7} + 3418801 T^{8} )^{2}$$)($$( 1 - 4 T + 116 T^{2} - 324 T^{3} + 6150 T^{4} - 13932 T^{5} + 214484 T^{6} - 318028 T^{7} + 3418801 T^{8} )^{2}$$)($$( 1 + 4 T + 116 T^{2} + 324 T^{3} + 6150 T^{4} + 13932 T^{5} + 214484 T^{6} + 318028 T^{7} + 3418801 T^{8} )^{2}$$)($$( 1 + 4 T + 116 T^{2} + 324 T^{3} + 6150 T^{4} + 13932 T^{5} + 214484 T^{6} + 318028 T^{7} + 3418801 T^{8} )^{2}$$)($$( 1 - 4 T + 76 T^{2} - 260 T^{3} + 4454 T^{4} - 11180 T^{5} + 140524 T^{6} - 318028 T^{7} + 3418801 T^{8} )^{4}$$)($$( 1 + 4 T + 76 T^{2} + 260 T^{3} + 4454 T^{4} + 11180 T^{5} + 140524 T^{6} + 318028 T^{7} + 3418801 T^{8} )^{4}$$)($$( 1 + 9 T + 43 T^{2} )^{2}$$)($$( 1 - 5 T + 43 T^{2} )^{2}$$)($$( 1 - 4 T + 27 T^{2} - 172 T^{3} + 1849 T^{4} )^{2}$$)($$( 1 + 2 T + 69 T^{2} + 86 T^{3} + 1849 T^{4} )^{2}$$)($$1 + 1202 T^{4} + 3418801 T^{8}$$)($$1 - 334 T^{4} + 3418801 T^{8}$$)($$( 1 + 1849 T^{4} )^{4}$$)($$( 1 + 1849 T^{4} )^{4}$$)($$( 1 - 24 T + 288 T^{2} - 2504 T^{3} + 19620 T^{4} - 145992 T^{5} + 988256 T^{6} - 5831128 T^{7} + 34926502 T^{8} - 250738504 T^{9} + 1827285344 T^{10} - 11607385944 T^{11} + 67076875620 T^{12} - 368109141272 T^{13} + 1820552558112 T^{14} - 6523646666568 T^{15} + 11688200277601 T^{16} )^{2}$$)($$( 1 - 76 T^{2} + 3927 T^{4} - 140524 T^{6} + 3418801 T^{8} )^{2}$$)($$( 1 - 76 T^{2} + 3927 T^{4} - 140524 T^{6} + 3418801 T^{8} )^{2}$$)($$( 1 - 64 T^{2} + 1858 T^{4} - 76444 T^{6} + 3291595 T^{8} - 141344956 T^{10} + 6352132258 T^{12} - 404567235136 T^{14} + 11688200277601 T^{16} )^{2}$$)($$( 1 + 13 T + 173 T^{2} + 1668 T^{3} + 14545 T^{4} + 96933 T^{5} + 625435 T^{6} + 3084132 T^{7} + 13754711 T^{8} + 44444413 T^{9} + 147008443 T^{10} )^{2}$$)($$( 1 + 13 T + 173 T^{2} + 1668 T^{3} + 14545 T^{4} + 96933 T^{5} + 625435 T^{6} + 3084132 T^{7} + 13754711 T^{8} + 44444413 T^{9} + 147008443 T^{10} )^{2}$$)($$1 - 86 T^{2} + 3819 T^{4} - 159014 T^{6} + 3418801 T^{8}$$)($$1 - 86 T^{2} + 3819 T^{4} - 159014 T^{6} + 3418801 T^{8}$$)($$( 1 - 14 T + 98 T^{2} - 868 T^{3} + 7327 T^{4} - 37324 T^{5} + 181202 T^{6} - 1113098 T^{7} + 3418801 T^{8} )^{2}$$)($$( 1 - 14 T + 98 T^{2} - 868 T^{3} + 7327 T^{4} - 37324 T^{5} + 181202 T^{6} - 1113098 T^{7} + 3418801 T^{8} )^{2}$$)
$47$ ($$1 + 8 T + 47 T^{2}$$)($$1 + 8 T + 47 T^{2}$$)($$1 + 47 T^{2}$$)($$1 + 47 T^{2}$$)($$( 1 - 8 T + 200 T^{2} - 1480 T^{3} + 21484 T^{4} - 142376 T^{5} + 1546616 T^{6} - 9131112 T^{7} + 83479334 T^{8} - 429162264 T^{9} + 3416474744 T^{10} - 14781903448 T^{11} + 104835066604 T^{12} - 339430610360 T^{13} + 2155843065800 T^{14} - 4052984963704 T^{15} + 23811286661761 T^{16} )^{2}$$)($$( 1 + 8 T + 200 T^{2} + 1480 T^{3} + 21484 T^{4} + 142376 T^{5} + 1546616 T^{6} + 9131112 T^{7} + 83479334 T^{8} + 429162264 T^{9} + 3416474744 T^{10} + 14781903448 T^{11} + 104835066604 T^{12} + 339430610360 T^{13} + 2155843065800 T^{14} + 4052984963704 T^{15} + 23811286661761 T^{16} )^{2}$$)($$( 1 - 3 T + 47 T^{2} )^{2}$$)($$( 1 + 3 T + 47 T^{2} )^{2}$$)($$( 1 - 2 T + 90 T^{2} - 94 T^{3} + 2209 T^{4} )^{2}$$)($$( 1 + 2 T + 90 T^{2} + 94 T^{3} + 2209 T^{4} )^{2}$$)($$( 1 - 31 T^{2} - 1248 T^{4} - 68479 T^{6} + 4879681 T^{8} )^{2}$$)($$( 1 - 58 T^{2} + 2209 T^{4} )^{4}$$)($$1 - 78 T^{2} + 2209 T^{4}$$)($$1 - 78 T^{2} + 2209 T^{4}$$)($$( 1 - 86 T^{2} + 2209 T^{4} )^{2}$$)($$( 1 - 86 T^{2} + 2209 T^{4} )^{2}$$)($$1 - 354 T^{2} + 55793 T^{4} - 5112098 T^{6} + 297791076 T^{8} - 11292624482 T^{10} + 272252042033 T^{12} - 3815842226466 T^{14} + 23811286661761 T^{16}$$)($$1 - 354 T^{2} + 55793 T^{4} - 5112098 T^{6} + 297791076 T^{8} - 11292624482 T^{10} + 272252042033 T^{12} - 3815842226466 T^{14} + 23811286661761 T^{16}$$)($$1 - 354 T^{2} + 55793 T^{4} - 5112098 T^{6} + 297791076 T^{8} - 11292624482 T^{10} + 272252042033 T^{12} - 3815842226466 T^{14} + 23811286661761 T^{16}$$)($$1 - 354 T^{2} + 55793 T^{4} - 5112098 T^{6} + 297791076 T^{8} - 11292624482 T^{10} + 272252042033 T^{12} - 3815842226466 T^{14} + 23811286661761 T^{16}$$)($$( 1 - 152 T^{2} + 16476 T^{4} - 1161512 T^{6} + 64108614 T^{8} - 2565780008 T^{10} + 80397624156 T^{12} - 1638440730008 T^{14} + 23811286661761 T^{16} )^{2}$$)($$( 1 - 152 T^{2} + 16476 T^{4} - 1161512 T^{6} + 64108614 T^{8} - 2565780008 T^{10} + 80397624156 T^{12} - 1638440730008 T^{14} + 23811286661761 T^{16} )^{2}$$)($$1 - 2 T - 43 T^{2} - 94 T^{3} + 2209 T^{4}$$)($$1 + 10 T + 53 T^{2} + 470 T^{3} + 2209 T^{4}$$)($$( 1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4} )^{2}$$)($$( 1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4} )^{2}$$)($$1 - 3518 T^{4} + 4879681 T^{8}$$)($$1 - 3518 T^{4} + 4879681 T^{8}$$)($$( 1 + 2209 T^{4} )^{4}$$)($$( 1 + 2209 T^{4} )^{4}$$)($$1 + 2312 T^{4} - 7152868 T^{8} - 8327985864 T^{12} + 35781048692550 T^{16} - 40637914388829384 T^{20} -$$$$17\!\cdots\!48$$$$T^{24} +$$$$26\!\cdots\!92$$$$T^{28} +$$$$56\!\cdots\!21$$$$T^{32}$$)($$( 1 - 4 T^{2} - 2193 T^{4} - 8836 T^{6} + 4879681 T^{8} )^{2}$$)($$( 1 - 4 T^{2} - 2193 T^{4} - 8836 T^{6} + 4879681 T^{8} )^{2}$$)($$1 + 132 T^{2} + 7724 T^{4} - 13800 T^{6} - 27329366 T^{8} - 1798257924 T^{10} - 24503383600 T^{12} + 3236589934428 T^{14} + 263856432834787 T^{16} + 7149627165151452 T^{18} - 119568695388631600 T^{20} - 19383809379876516996 T^{22} -$$$$65\!\cdots\!26$$$$T^{24} -$$$$72\!\cdots\!00$$$$T^{26} +$$$$89\!\cdots\!84$$$$T^{28} +$$$$33\!\cdots\!08$$$$T^{30} +$$$$56\!\cdots\!21$$$$T^{32}$$)($$1 - 14 T + 49 T^{2} + 70 T^{3} - 1449 T^{4} + 16780 T^{5} - 75362 T^{6} - 133028 T^{7} + 1885261 T^{8} - 57961722 T^{9} + 732803503 T^{10} - 2724200934 T^{11} + 4164541549 T^{12} - 13811366044 T^{13} - 367742519522 T^{14} + 3848409217460 T^{15} - 15619083011721 T^{16} + 35463618432410 T^{17} + 1166753046426289 T^{18} - 15667826623438738 T^{19} + 52599132235830049 T^{20}$$)($$1 + 14 T + 49 T^{2} - 70 T^{3} - 1449 T^{4} - 16780 T^{5} - 75362 T^{6} + 133028 T^{7} + 1885261 T^{8} + 57961722 T^{9} + 732803503 T^{10} + 2724200934 T^{11} + 4164541549 T^{12} + 13811366044 T^{13} - 367742519522 T^{14} - 3848409217460 T^{15} - 15619083011721 T^{16} - 35463618432410 T^{17} + 1166753046426289 T^{18} + 15667826623438738 T^{19} + 52599132235830049 T^{20}$$)($$1 + 8 T - 34 T^{2} + 32 T^{3} + 4387 T^{4} + 1504 T^{5} - 75106 T^{6} + 830584 T^{7} + 4879681 T^{8}$$)($$1 - 8 T - 34 T^{2} - 32 T^{3} + 4387 T^{4} - 1504 T^{5} - 75106 T^{6} - 830584 T^{7} + 4879681 T^{8}$$)($$( 1 - 10 T + 50 T^{2} + 440 T^{3} - 4409 T^{4} + 20680 T^{5} + 110450 T^{6} - 1038230 T^{7} + 4879681 T^{8} )^{2}$$)($$( 1 + 10 T + 50 T^{2} - 440 T^{3} - 4409 T^{4} - 20680 T^{5} + 110450 T^{6} + 1038230 T^{7} + 4879681 T^{8} )^{2}$$)
$53$ ($$1 - 4 T + 53 T^{2}$$)($$1 + 53 T^{2}$$)($$1 + 12 T + 53 T^{2}$$)($$1 - 8 T + 53 T^{2}$$)($$( 1 + 16 T + 318 T^{2} + 3232 T^{3} + 39656 T^{4} + 299616 T^{5} + 2879090 T^{6} + 18163120 T^{7} + 161612366 T^{8} + 962645360 T^{9} + 8087363810 T^{10} + 44605931232 T^{11} + 312904914536 T^{12} + 1351607833376 T^{13} + 7048266839022 T^{14} + 18795378237392 T^{15} + 62259690411361 T^{16} )^{2}$$)($$( 1 + 16 T + 318 T^{2} + 3232 T^{3} + 39656 T^{4} + 299616 T^{5} + 2879090 T^{6} + 18163120 T^{7} + 161612366 T^{8} + 962645360 T^{9} + 8087363810 T^{10} + 44605931232 T^{11} + 312904914536 T^{12} + 1351607833376 T^{13} + 7048266839022 T^{14} + 18795378237392 T^{15} + 62259690411361 T^{16} )^{2}$$)($$1 + 2 T^{2} + 2809 T^{4}$$)($$1 + 2 T^{2} + 2809 T^{4}$$)($$1 - 104 T^{2} + 7342 T^{4} - 292136 T^{6} + 7890481 T^{8}$$)($$1 - 104 T^{2} + 7342 T^{4} - 292136 T^{6} + 7890481 T^{8}$$)($$( 1 + 53 T^{2} )^{8}$$)($$( 1 + 66 T^{2} + 2809 T^{4} )^{4}$$)($$1 - 70 T^{2} + 2809 T^{4}$$)($$1 - 102 T^{2} + 2809 T^{4}$$)($$( 1 + 34 T^{2} + 2809 T^{4} )^{2}$$)($$( 1 + 34 T^{2} + 2809 T^{4} )^{2}$$)($$( 1 + 12 T^{2} + 256 T^{3} + 1046 T^{4} + 13568 T^{5} + 33708 T^{6} + 7890481 T^{8} )^{2}$$)($$( 1 + 12 T^{2} - 256 T^{3} + 1046 T^{4} - 13568 T^{5} + 33708 T^{6} + 7890481 T^{8} )^{2}$$)($$( 1 + 12 T^{2} + 256 T^{3} + 1046 T^{4} + 13568 T^{5} + 33708 T^{6} + 7890481 T^{8} )^{2}$$)($$( 1 + 12 T^{2} - 256 T^{3} + 1046 T^{4} - 13568 T^{5} + 33708 T^{6} + 7890481 T^{8} )^{2}$$)($$( 1 + 278 T^{2} + 37272 T^{4} + 3219258 T^{6} + 198845358 T^{8} + 9042895722 T^{10} + 294094007832 T^{12} + 6161692393862 T^{14} + 62259690411361 T^{16} )^{2}$$)($$( 1 + 278 T^{2} + 37272 T^{4} + 3219258 T^{6} + 198845358 T^{8} + 9042895722 T^{10} + 294094007832 T^{12} + 6161692393862 T^{14} + 62259690411361 T^{16} )^{2}$$)($$1 + 12 T + 91 T^{2} + 636 T^{3} + 2809 T^{4}$$)($$1 - 8 T + 11 T^{2} - 424 T^{3} + 2809 T^{4}$$)($$1 - 4 T - 66 T^{2} + 96 T^{3} + 3067 T^{4} + 5088 T^{5} - 185394 T^{6} - 595508 T^{7} + 7890481 T^{8}$$)($$1 - 34 T^{2} - 1653 T^{4} - 95506 T^{6} + 7890481 T^{8}$$)($$( 1 + 2 T + 2 T^{2} + 106 T^{3} + 2809 T^{4} )^{2}$$)($$( 1 - 14 T + 98 T^{2} - 742 T^{3} + 2809 T^{4} )^{2}$$)($$( 1 + 2809 T^{4} )^{4}$$)($$( 1 + 2809 T^{4} )^{4}$$)($$( 1 + 20 T + 200 T^{2} + 1284 T^{3} + 2996 T^{4} - 21028 T^{5} - 195432 T^{6} - 604308 T^{7} - 304634 T^{8} - 32028324 T^{9} - 548968488 T^{10} - 3130585556 T^{11} + 23639881076 T^{12} + 536963013012 T^{13} + 4432872225800 T^{14} + 23494222796740 T^{15} + 62259690411361 T^{16} )^{2}$$)($$( 1 - 53 T^{2} + 2809 T^{4} )^{4}$$)($$( 1 - 53 T^{2} + 2809 T^{4} )^{4}$$)($$1 + 264 T^{2} + 36932 T^{4} + 3411184 T^{6} + 225587818 T^{8} + 10591214456 T^{10} + 310610700432 T^{12} + 1653404256184 T^{14} - 250591876943757 T^{16} + 4644412555620856 T^{18} + 2450867830155387792 T^{20} +$$$$23\!\cdots\!24$$$$T^{22} +$$$$14\!\cdots\!98$$$$T^{24} +$$$$59\!\cdots\!16$$$$T^{26} +$$$$18\!\cdots\!12$$$$T^{28} +$$$$36\!\cdots\!16$$$$T^{30} +$$$$38\!\cdots\!21$$$$T^{32}$$)($$1 + 24 T + 337 T^{2} + 3480 T^{3} + 28655 T^{4} + 224976 T^{5} + 1724958 T^{6} + 14318448 T^{7} + 120990445 T^{8} + 964554888 T^{9} + 7393360287 T^{10} + 51121409064 T^{11} + 339862160005 T^{12} + 2131687582896 T^{13} + 13610748324798 T^{14} + 94083949233168 T^{15} + 635119768151495 T^{16} + 4087994766632760 T^{17} + 20981515668628657 T^{18} + 79194326203251192 T^{19} + 174887470365513049 T^{20}$$)($$1 - 24 T + 337 T^{2} - 3480 T^{3} + 28655 T^{4} - 224976 T^{5} + 1724958 T^{6} - 14318448 T^{7} + 120990445 T^{8} - 964554888 T^{9} + 7393360287 T^{10} - 51121409064 T^{11} + 339862160005 T^{12} - 2131687582896 T^{13} + 13610748324798 T^{14} - 94083949233168 T^{15} + 635119768151495 T^{16} - 4087994766632760 T^{17} + 20981515668628657 T^{18} - 79194326203251192 T^{19} + 174887470365513049 T^{20}$$)($$1 + 12 T + 14 T^{2} + 288 T^{3} + 6459 T^{4} + 15264 T^{5} + 39326 T^{6} + 1786524 T^{7} + 7890481 T^{8}$$)($$1 + 12 T + 14 T^{2} + 288 T^{3} + 6459 T^{4} + 15264 T^{5} + 39326 T^{6} + 1786524 T^{7} + 7890481 T^{8}$$)($$1 + 16 T + 128 T^{2} + 32 T^{3} - 7582 T^{4} - 68368 T^{5} - 122880 T^{6} + 2359024 T^{7} + 29894739 T^{8} + 125028272 T^{9} - 345169920 T^{10} - 10178422736 T^{11} - 59825626942 T^{12} + 13382255776 T^{13} + 2837038224512 T^{14} + 18795378237392 T^{15} + 62259690411361 T^{16}$$)($$1 - 16 T + 128 T^{2} - 32 T^{3} - 7582 T^{4} + 68368 T^{5} - 122880 T^{6} - 2359024 T^{7} + 29894739 T^{8} - 125028272 T^{9} - 345169920 T^{10} + 10178422736 T^{11} - 59825626942 T^{12} - 13382255776 T^{13} + 2837038224512 T^{14} - 18795378237392 T^{15} + 62259690411361 T^{16}$$)
$59$ ($$1 + 8 T + 59 T^{2}$$)($$1 + 8 T + 59 T^{2}$$)($$1 + 59 T^{2}$$)($$1 + 59 T^{2}$$)($$( 1 - 4 T + 216 T^{2} - 212 T^{3} + 21484 T^{4} + 35116 T^{5} + 1537192 T^{6} + 4969884 T^{7} + 95982982 T^{8} + 293223156 T^{9} + 5350965352 T^{10} + 7212088964 T^{11} + 260329383724 T^{12} - 151563951388 T^{13} + 9110995266456 T^{14} - 9954605939276 T^{15} + 146830437604321 T^{16} )^{2}$$)($$( 1 + 4 T + 216 T^{2} + 212 T^{3} + 21484 T^{4} - 35116 T^{5} + 1537192 T^{6} - 4969884 T^{7} + 95982982 T^{8} - 293223156 T^{9} + 5350965352 T^{10} - 7212088964 T^{11} + 260329383724 T^{12} + 151563951388 T^{13} + 9110995266456 T^{14} + 9954605939276 T^{15} + 146830437604321 T^{16} )^{2}$$)($$( 1 - 6 T + 59 T^{2} )^{2}$$)($$( 1 + 6 T + 59 T^{2} )^{2}$$)($$( 1 + 38 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 38 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 59 T^{2} )^{8}$$)($$( 1 + 38 T^{2} + 3481 T^{4} )^{4}$$)($$( 1 + 4 T + 59 T^{2} )^{2}$$)($$( 1 + 4 T + 59 T^{2} )^{2}$$)($$( 1 + 59 T^{2} )^{4}$$)($$( 1 + 59 T^{2} )^{4}$$)($$( 1 - 4 T + 96 T^{2} + 444 T^{3} + 2126 T^{4} + 26196 T^{5} + 334176 T^{6} - 821516 T^{7} + 12117361 T^{8} )^{2}$$)($$( 1 + 4 T + 96 T^{2} - 444 T^{3} + 2126 T^{4} - 26196 T^{5} + 334176 T^{6} + 821516 T^{7} + 12117361 T^{8} )^{2}$$)($$( 1 + 4 T + 96 T^{2} - 444 T^{3} + 2126 T^{4} - 26196 T^{5} + 334176 T^{6} + 821516 T^{7} + 12117361 T^{8} )^{2}$$)($$( 1 - 4 T + 96 T^{2} + 444 T^{3} + 2126 T^{4} + 26196 T^{5} + 334176 T^{6} - 821516 T^{7} + 12117361 T^{8} )^{2}$$)($$( 1 + 304 T^{2} + 44556 T^{4} + 4247040 T^{6} + 291601382 T^{8} + 14783946240 T^{10} + 539901136716 T^{12} + 12822882226864 T^{14} + 146830437604321 T^{16} )^{2}$$)($$( 1 + 304 T^{2} + 44556 T^{4} + 4247040 T^{6} + 291601382 T^{8} + 14783946240 T^{10} + 539901136716 T^{12} + 12822882226864 T^{14} + 146830437604321 T^{16} )^{2}$$)($$1 - 8 T + 5 T^{2} - 472 T^{3} + 3481 T^{4}$$)($$1 + 10 T + 41 T^{2} + 590 T^{3} + 3481 T^{4}$$)($$1 + 6 T - 28 T^{2} - 324 T^{3} - 1509 T^{4} - 19116 T^{5} - 97468 T^{6} + 1232274 T^{7} + 12117361 T^{8}$$)($$1 - 12 T + 8 T^{2} - 216 T^{3} + 6519 T^{4} - 12744 T^{5} + 27848 T^{6} - 2464548 T^{7} + 12117361 T^{8}$$)($$( 1 - 10 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 - 10 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 59 T^{2} )^{8}$$)($$( 1 + 59 T^{2} )^{8}$$)($$( 1 + 280 T^{2} + 33212 T^{4} + 2343784 T^{6} + 136126182 T^{8} + 8158712104 T^{10} + 402441793532 T^{12} + 11810549419480 T^{14} + 146830437604321 T^{16} )^{2}$$)($$( 1 - 59 T^{2} + 3481 T^{4} )^{4}$$)($$( 1 - 59 T^{2} + 3481 T^{4} )^{4}$$)($$( 1 + 14 T + 98 T^{2} + 2364 T^{3} + 23888 T^{4} + 127648 T^{5} + 2057308 T^{6} + 17027622 T^{7} + 74320339 T^{8} + 1004629698 T^{9} + 7161489148 T^{10} + 26216218592 T^{11} + 289459519568 T^{12} + 1690081042836 T^{13} + 4133692296818 T^{14} + 34841120787466 T^{15} + 146830437604321 T^{16} )^{2}$$)($$1 - 135 T^{2} - 756 T^{3} + 7351 T^{4} + 84450 T^{5} - 41974 T^{6} - 3597210 T^{7} - 8726459 T^{8} + 56020614 T^{9} + 414268763 T^{10} + 3305216226 T^{11} - 30376803779 T^{12} - 738791392590 T^{13} - 508614110614 T^{14} + 60375357050550 T^{15} + 310069102794991 T^{16} - 1881420522523164 T^{17} - 19822109076583335 T^{18} + 511116753300641401 T^{20}$$)($$1 - 135 T^{2} + 756 T^{3} + 7351 T^{4} - 84450 T^{5} - 41974 T^{6} + 3597210 T^{7} - 8726459 T^{8} - 56020614 T^{9} + 414268763 T^{10} - 3305216226 T^{11} - 30376803779 T^{12} + 738791392590 T^{13} - 508614110614 T^{14} - 60375357050550 T^{15} + 310069102794991 T^{16} + 1881420522523164 T^{17} - 19822109076583335 T^{18} + 511116753300641401 T^{20}$$)($$1 - 8 T - 22 T^{2} + 256 T^{3} + 139 T^{4} + 15104 T^{5} - 76582 T^{6} - 1643032 T^{7} + 12117361 T^{8}$$)($$1 + 8 T - 22 T^{2} - 256 T^{3} + 139 T^{4} - 15104 T^{5} - 76582 T^{6} + 1643032 T^{7} + 12117361 T^{8}$$)($$( 1 - 18 T + 136 T^{2} - 1260 T^{3} + 12747 T^{4} - 74340 T^{5} + 473416 T^{6} - 3696822 T^{7} + 12117361 T^{8} )^{2}$$)($$( 1 + 18 T + 136 T^{2} + 1260 T^{3} + 12747 T^{4} + 74340 T^{5} + 473416 T^{6} + 3696822 T^{7} + 12117361 T^{8} )^{2}$$)
$61$ ($$1 - 6 T + 61 T^{2}$$)($$1 + 2 T + 61 T^{2}$$)($$1 - 14 T + 61 T^{2}$$)($$1 + 10 T + 61 T^{2}$$)($$1 - 424 T^{2} + 85912 T^{4} - 11360056 T^{6} + 1147532060 T^{8} - 97928338472 T^{10} + 7427530642088 T^{12} - 510650158156408 T^{14} + 32321138943506822 T^{16} - 1900129238499994168 T^{18} +$$$$10\!\cdots\!08$$$$T^{20} -$$$$50\!\cdots\!92$$$$T^{22} +$$$$21\!\cdots\!60$$$$T^{24} -$$$$81\!\cdots\!56$$$$T^{26} +$$$$22\!\cdots\!52$$$$T^{28} -$$$$41\!\cdots\!84$$$$T^{30} +$$$$36\!\cdots\!61$$$$T^{32}$$)($$1 - 424 T^{2} + 85912 T^{4} - 11360056 T^{6} + 1147532060 T^{8} - 97928338472 T^{10} + 7427530642088 T^{12} - 510650158156408 T^{14} + 32321138943506822 T^{16} - 1900129238499994168 T^{18} +$$$$10\!\cdots\!08$$$$T^{20} -$$$$50\!\cdots\!92$$$$T^{22} +$$$$21\!\cdots\!60$$$$T^{24} -$$$$81\!\cdots\!56$$$$T^{26} +$$$$22\!\cdots\!52$$$$T^{28} -$$$$41\!\cdots\!84$$$$T^{30} +$$$$36\!\cdots\!61$$$$T^{32}$$)($$( 1 - 14 T + 61 T^{2} )( 1 + 14 T + 61 T^{2} )$$)($$( 1 - 14 T + 61 T^{2} )( 1 + 14 T + 61 T^{2} )$$)($$1 - 52 T^{2} + 2998 T^{4} - 193492 T^{6} + 13845841 T^{8}$$)($$1 - 52 T^{2} + 2998 T^{4} - 193492 T^{6} + 13845841 T^{8}$$)($$( 1 - 61 T^{2} )^{8}$$)($$( 1 - 61 T^{2} )^{8}$$)($$( 1 - 14 T + 61 T^{2} )^{2}$$)($$( 1 + 2 T + 61 T^{2} )^{2}$$)($$( 1 + 10 T + 61 T^{2} )^{4}$$)($$( 1 + 10 T + 61 T^{2} )^{4}$$)($$( 1 + 8 T + 96 T^{2} + 232 T^{3} + 2958 T^{4} + 14152 T^{5} + 357216 T^{6} + 1815848 T^{7} + 13845841 T^{8} )^{2}$$)($$( 1 + 8 T + 96 T^{2} + 232 T^{3} + 2958 T^{4} + 14152 T^{5} + 357216 T^{6} + 1815848 T^{7} + 13845841 T^{8} )^{2}$$)($$( 1 + 8 T + 96 T^{2} + 232 T^{3} + 2958 T^{4} + 14152 T^{5} + 357216 T^{6} + 1815848 T^{7} + 13845841 T^{8} )^{2}$$)($$( 1 + 8 T + 96 T^{2} + 232 T^{3} + 2958 T^{4} + 14152 T^{5} + 357216 T^{6} + 1815848 T^{7} + 13845841 T^{8} )^{2}$$)($$( 1 - 10 T + 236 T^{2} - 1522 T^{3} + 20638 T^{4} - 92842 T^{5} + 878156 T^{6} - 2269810 T^{7} + 13845841 T^{8} )^{4}$$)($$( 1 - 10 T + 236 T^{2} - 1522 T^{3} + 20638 T^{4} - 92842 T^{5} + 878156 T^{6} - 2269810 T^{7} + 13845841 T^{8} )^{4}$$)($$( 1 - 13 T + 61 T^{2} )( 1 - T + 61 T^{2} )$$)($$1 - 6 T - 25 T^{2} - 366 T^{3} + 3721 T^{4}$$)($$( 1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4} )^{2}$$)($$1 - 8 T - 2 T^{2} + 448 T^{3} - 3269 T^{4} + 27328 T^{5} - 7442 T^{6} - 1815848 T^{7} + 13845841 T^{8}$$)($$( 1 - 8 T + 61 T^{2} )^{4}$$)($$( 1 + 61 T^{2} )^{4}$$)($$( 1 - 61 T^{2} )^{8}$$)($$( 1 - 61 T^{2} )^{8}$$)($$( 1 - 312 T^{2} + 47324 T^{4} - 4644168 T^{6} + 328520806 T^{8} - 17280949128 T^{10} + 655240579484 T^{12} - 16074356800632 T^{14} + 191707312997281 T^{16} )^{2}$$)($$( 1 - 8 T + 61 T^{2} )^{4}( 1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4} )^{2}$$)($$( 1 - 8 T + 61 T^{2} )^{4}( 1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4} )^{2}$$)($$( 1 + 16 T + 48 T^{2} - 408 T^{3} - 2562 T^{4} - 7524 T^{5} - 100912 T^{6} - 1615000 T^{7} - 17451933 T^{8} - 98515000 T^{9} - 375493552 T^{10} - 1707805044 T^{11} - 35473044642 T^{12} - 344595290808 T^{13} + 2472977969328 T^{14} + 50283885376336 T^{15} + 191707312997281 T^{16} )^{2}$$)($$1 - 42 T + 1112 T^{2} - 22008 T^{3} + 361073 T^{4} - 5062200 T^{5} + 62481246 T^{6} - 687242394 T^{7} + 6821292673 T^{8} - 61325603712 T^{9} + 502052393310 T^{10} - 3740861826432 T^{11} + 25382030036233 T^{12} - 155990965832514 T^{13} + 865105397597886 T^{14} - 4275515394922200 T^{15} + 18602616131649353 T^{16} - 69165484335150168 T^{17} + 213178532052976472 T^{18} - 491154135899033922 T^{19} + 713342911662882601 T^{20}$$)($$1 - 42 T + 1112 T^{2} - 22008 T^{3} + 361073 T^{4} - 5062200 T^{5} + 62481246 T^{6} - 687242394 T^{7} + 6821292673 T^{8} - 61325603712 T^{9} + 502052393310 T^{10} - 3740861826432 T^{11} + 25382030036233 T^{12} - 155990965832514 T^{13} + 865105397597886 T^{14} - 4275515394922200 T^{15} + 18602616131649353 T^{16} - 69165484335150168 T^{17} + 213178532052976472 T^{18} - 491154135899033922 T^{19} + 713342911662882601 T^{20}$$)($$1 + 24 T + 346 T^{2} + 3696 T^{3} + 31707 T^{4} + 225456 T^{5} + 1287466 T^{6} + 5447544 T^{7} + 13845841 T^{8}$$)($$1 + 24 T + 346 T^{2} + 3696 T^{3} + 31707 T^{4} + 225456 T^{5} + 1287466 T^{6} + 5447544 T^{7} + 13845841 T^{8}$$)($$( 1 + 12 T - 3 T^{2} + 300 T^{3} + 9104 T^{4} + 18300 T^{5} - 11163 T^{6} + 2723772 T^{7} + 13845841 T^{8} )^{2}$$)($$( 1 + 12 T - 3 T^{2} + 300 T^{3} + 9104 T^{4} + 18300 T^{5} - 11163 T^{6} + 2723772 T^{7} + 13845841 T^{8} )^{2}$$)
$67$ ($$1 - 12 T + 67 T^{2}$$)($$1 + 12 T + 67 T^{2}$$)($$1 + 4 T + 67 T^{2}$$)($$1 + 12 T + 67 T^{2}$$)($$1 - 568 T^{2} + 166008 T^{4} - 32876264 T^{6} + 4920317404 T^{8} - 589683946296 T^{10} + 58602724633032 T^{12} - 4934611468716584 T^{14} + 356328084895246342 T^{16} - 22151470883068745576 T^{18} +$$$$11\!\cdots\!72$$$$T^{20} -$$$$53\!\cdots\!24$$$$T^{22} +$$$$19\!\cdots\!64$$$$T^{24} -$$$$59\!\cdots\!36$$$$T^{26} +$$$$13\!\cdots\!88$$$$T^{28} -$$$$20\!\cdots\!72$$$$T^{30} +$$$$16\!\cdots\!81$$$$T^{32}$$)($$1 - 568 T^{2} + 166008 T^{4} - 32876264 T^{6} + 4920317404 T^{8} - 589683946296 T^{10} + 58602724633032 T^{12} - 4934611468716584 T^{14} + 356328084895246342 T^{16} - 22151470883068745576 T^{18} +$$$$11\!\cdots\!72$$$$T^{20} -$$$$53\!\cdots\!24$$$$T^{22} +$$$$19\!\cdots\!64$$$$T^{24} -$$$$59\!\cdots\!36$$$$T^{26} +$$$$13\!\cdots\!88$$$$T^{28} -$$$$20\!\cdots\!72$$$$T^{30} +$$$$16\!\cdots\!81$$$$T^{32}$$)($$( 1 - 2 T + 67 T^{2} )^{2}$$)($$( 1 - 2 T + 67 T^{2} )^{2}$$)($$( 1 - 6 T + 98 T^{2} - 402 T^{3} + 4489 T^{4} )^{2}$$)($$( 1 - 6 T + 98 T^{2} - 402 T^{3} + 4489 T^{4} )^{2}$$)($$( 1 - 67 T^{2} )^{8}$$)($$( 1 - 114 T^{2} + 4489 T^{4} )^{4}$$)($$1 - 118 T^{2} + 4489 T^{4}$$)($$1 + 10 T^{2} + 4489 T^{4}$$)($$( 1 + 4 T + 67 T^{2} )^{4}$$)($$( 1 - 4 T + 67 T^{2} )^{4}$$)($$( 1 - 12 T + 144 T^{2} - 300 T^{3} + 3470 T^{4} - 20100 T^{5} + 646416 T^{6} - 3609156 T^{7} + 20151121 T^{8} )^{2}$$)($$( 1 - 12 T + 144 T^{2} - 300 T^{3} + 3470 T^{4} - 20100 T^{5} + 646416 T^{6} - 3609156 T^{7} + 20151121 T^{8} )^{2}$$)($$( 1 + 12 T + 144 T^{2} + 300 T^{3} + 3470 T^{4} + 20100 T^{5} + 646416 T^{6} + 3609156 T^{7} + 20151121 T^{8} )^{2}$$)($$( 1 + 12 T + 144 T^{2} + 300 T^{3} + 3470 T^{4} + 20100 T^{5} + 646416 T^{6} + 3609156 T^{7} + 20151121 T^{8} )^{2}$$)($$( 1 + 14 T + 232 T^{2} + 2310 T^{3} + 21246 T^{4} + 154770 T^{5} + 1041448 T^{6} + 4210682 T^{7} + 20151121 T^{8} )^{4}$$)($$( 1 - 14 T + 232 T^{2} - 2310 T^{3} + 21246 T^{4} - 154770 T^{5} + 1041448 T^{6} - 4210682 T^{7} + 20151121 T^{8} )^{4}$$)($$1 + 9 T + 14 T^{2} + 603 T^{3} + 4489 T^{4}$$)($$1 + 3 T - 58 T^{2} + 201 T^{3} + 4489 T^{4}$$)($$1 - 4 T - 115 T^{2} + 12 T^{3} + 11600 T^{4} + 804 T^{5} - 516235 T^{6} - 1203052 T^{7} + 20151121 T^{8}$$)($$1 - 2 T - 113 T^{2} + 34 T^{3} + 8932 T^{4} + 2278 T^{5} - 507257 T^{6} - 601526 T^{7} + 20151121 T^{8}$$)($$1 - 4078 T^{4} + 20151121 T^{8}$$)($$1 - 4078 T^{4} + 20151121 T^{8}$$)($$( 1 + 4489 T^{4} )^{4}$$)($$( 1 + 4489 T^{4} )^{4}$$)($$( 1 + 24 T + 288 T^{2} + 2984 T^{3} + 22788 T^{4} + 56616 T^{5} - 752032 T^{6} - 14609960 T^{7} - 156156506 T^{8} - 978867320 T^{9} - 3375871648 T^{10} + 17027998008 T^{11} + 459203745348 T^{12} + 4028773319288 T^{13} + 26052014064672 T^{14} + 145457078527752 T^{15} + 406067677556641 T^{16} )^{2}$$)($$( 1 - 116 T^{2} + 4489 T^{4} )^{2}( 1 + 116 T^{2} + 8967 T^{4} + 520724 T^{6} + 20151121 T^{8} )$$)($$( 1 - 116 T^{2} + 4489 T^{4} )^{2}( 1 + 116 T^{2} + 8967 T^{4} + 520724 T^{6} + 20151121 T^{8} )$$)($$1 + 284 T^{2} + 48342 T^{4} + 5247504 T^{6} + 382477089 T^{8} + 13407940164 T^{10} - 693108843514 T^{12} - 155646496729232 T^{14} - 13431345849238284 T^{16} - 698697123817522448 T^{18} - 13966920171820679194 T^{20} +$$$$12\!\cdots\!16$$$$T^{22} +$$$$15\!\cdots\!49$$$$T^{24} +$$$$95\!\cdots\!96$$$$T^{26} +$$$$39\!\cdots\!62$$$$T^{28} +$$$$10\!\cdots\!36$$$$T^{30} +$$$$16\!\cdots\!81$$$$T^{32}$$)($$1 - 7 T - 94 T^{2} + 1731 T^{3} + 26 T^{4} - 170241 T^{5} + 879508 T^{6} + 10247793 T^{7} - 116682655 T^{8} - 286659444 T^{9} + 9801469996 T^{10} - 19206182748 T^{11} - 523788438295 T^{12} + 3082156966059 T^{13} + 17723072128468 T^{14} - 229846648340787 T^{15} + 2351917936394 T^{16} + 10491091788814113 T^{17} - 38170361690324254 T^{18} - 190445740774064629 T^{19} + 1822837804551761449 T^{20}$$)($$1 - 7 T - 94 T^{2} + 1731 T^{3} + 26 T^{4} - 170241 T^{5} + 879508 T^{6} + 10247793 T^{7} - 116682655 T^{8} - 286659444 T^{9} + 9801469996 T^{10} - 19206182748 T^{11} - 523788438295 T^{12} + 3082156966059 T^{13} + 17723072128468 T^{14} - 229846648340787 T^{15} + 2351917936394 T^{16} + 10491091788814113 T^{17} - 38170361690324254 T^{18} - 190445740774064629 T^{19} + 1822837804551761449 T^{20}$$)($$1 - 18 T + 253 T^{2} - 2610 T^{3} + 23772 T^{4} - 174870 T^{5} + 1135717 T^{6} - 5413734 T^{7} + 20151121 T^{8}$$)($$1 + 18 T + 253 T^{2} + 2610 T^{3} + 23772 T^{4} + 174870 T^{5} + 1135717 T^{6} + 5413734 T^{7} + 20151121 T^{8}$$)($$1 + 22 T + 242 T^{2} - 44 T^{3} - 27227 T^{4} - 347336 T^{5} - 1051490 T^{6} + 15257682 T^{7} + 240623364 T^{8} + 1022264694 T^{9} - 4720138610 T^{10} - 104465817368 T^{11} - 548654571467 T^{12} - 59405504708 T^{13} + 21890928484898 T^{14} + 133335655317106 T^{15} + 406067677556641 T^{16}$$)($$1 + 22 T + 242 T^{2} - 44 T^{3} - 27227 T^{4} - 347336 T^{5} - 1051490 T^{6} + 15257682 T^{7} + 240623364 T^{8} + 1022264694 T^{9} - 4720138610 T^{10} - 104465817368 T^{11} - 548654571467 T^{12} - 59405504708 T^{13} + 21890928484898 T^{14} + 133335655317106 T^{15} + 406067677556641 T^{16}$$)
$71$ ($$1 + 6 T + 71 T^{2}$$)($$1 + 10 T + 71 T^{2}$$)($$1 - 6 T + 71 T^{2}$$)($$1 + 14 T + 71 T^{2}$$)($$1 - 444 T^{2} + 111268 T^{4} - 19597764 T^{6} + 2684602292 T^{8} - 301990393612 T^{10} + 28967151924188 T^{12} - 2434802829480948 T^{14} + 182479018420426774 T^{16} - 12273841063413458868 T^{18} +$$$$73\!\cdots\!28$$$$T^{20} -$$$$38\!\cdots\!52$$$$T^{22} +$$$$17\!\cdots\!12$$$$T^{24} -$$$$63\!\cdots\!64$$$$T^{26} +$$$$18\!\cdots\!88$$$$T^{28} -$$$$36\!\cdots\!64$$$$T^{30} +$$$$41\!\cdots\!21$$$$T^{32}$$)($$1 - 444 T^{2} + 111268 T^{4} - 19597764 T^{6} + 2684602292 T^{8} - 301990393612 T^{10} + 28967151924188 T^{12} - 2434802829480948 T^{14} + 182479018420426774 T^{16} - 12273841063413458868 T^{18} +$$$$73\!\cdots\!28$$$$T^{20} -$$$$38\!\cdots\!52$$$$T^{22} +$$$$17\!\cdots\!12$$$$T^{24} -$$$$63\!\cdots\!64$$$$T^{26} +$$$$18\!\cdots\!88$$$$T^{28} -$$$$36\!\cdots\!64$$$$T^{30} +$$$$41\!\cdots\!21$$$$T^{32}$$)($$1 - 34 T^{2} + 5041 T^{4}$$)($$1 - 34 T^{2} + 5041 T^{4}$$)($$1 - 32 T^{2} + 9838 T^{4} - 161312 T^{6} + 25411681 T^{8}$$)($$1 - 32 T^{2} + 9838 T^{4} - 161312 T^{6} + 25411681 T^{8}$$)($$( 1 - 12 T + 71 T^{2} )^{4}( 1 + 12 T + 71 T^{2} )^{4}$$)($$( 1 + 58 T^{2} + 5041 T^{4} )^{4}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 + 8 T + 71 T^{2} )^{2}$$)($$( 1 - 20 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 - 20 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 + 8 T + 71 T^{2} )^{8}$$)($$( 1 - 8 T + 71 T^{2} )^{8}$$)($$( 1 - 8 T + 71 T^{2} )^{8}$$)($$( 1 + 8 T + 71 T^{2} )^{8}$$)($$( 1 + 226 T^{2} + 18304 T^{4} + 119582 T^{6} - 52128898 T^{8} + 602812862 T^{10} + 465135409024 T^{12} + 28950664166146 T^{14} + 645753531245761 T^{16} )^{2}$$)($$( 1 + 226 T^{2} + 18304 T^{4} + 119582 T^{6} - 52128898 T^{8} + 602812862 T^{10} + 465135409024 T^{12} + 28950664166146 T^{14} + 645753531245761 T^{16} )^{2}$$)($$( 1 - 2 T + 71 T^{2} )^{2}$$)($$( 1 + 71 T^{2} )^{2}$$)($$( 1 - 22 T + 256 T^{2} - 1562 T^{3} + 5041 T^{4} )^{2}$$)($$( 1 - 20 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 - 70 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 + 58 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 - 22 T + 242 T^{2} - 1562 T^{3} + 5041 T^{4} )^{4}$$)($$( 1 + 22 T + 242 T^{2} + 1562 T^{3} + 5041 T^{4} )^{4}$$)($$( 1 + 8 T + 140 T^{2} + 1024 T^{3} + 14962 T^{4} + 72704 T^{5} + 705740 T^{6} + 2863288 T^{7} + 25411681 T^{8} )^{4}$$)($$( 1 + 71 T^{2} )^{8}$$)($$( 1 + 71 T^{2} )^{8}$$)($$( 1 + 14 T + 158 T^{2} + 444 T^{3} + 3552 T^{4} + 31524 T^{5} + 796478 T^{6} + 5010754 T^{7} + 25411681 T^{8} )^{4}$$)($$1 - 422 T^{2} + 92093 T^{4} - 13410012 T^{6} + 1429352290 T^{8} - 115763220252 T^{10} + 7205364893890 T^{12} - 340770947150172 T^{14} + 11797139447136653 T^{16} - 272507990185711142 T^{18} + 3255243551009881201 T^{20}$$)($$1 - 422 T^{2} + 92093 T^{4} - 13410012 T^{6} + 1429352290 T^{8} - 115763220252 T^{10} + 7205364893890 T^{12} - 340770947150172 T^{14} + 11797139447136653 T^{16} - 272507990185711142 T^{18} + 3255243551009881201 T^{20}$$)($$1 + 28 T^{2} + 3366 T^{4} + 141148 T^{6} + 25411681 T^{8}$$)($$1 + 28 T^{2} + 3366 T^{4} + 141148 T^{6} + 25411681 T^{8}$$)($$( 1 - 260 T^{2} + 26938 T^{4} - 1310660 T^{6} + 25411681 T^{8} )^{2}$$)($$( 1 - 260 T^{2} + 26938 T^{4} - 1310660 T^{6} + 25411681 T^{8} )^{2}$$)
$73$ ($$1 + 12 T + 73 T^{2}$$)($$1 - 4 T + 73 T^{2}$$)($$1 + 4 T + 73 T^{2}$$)($$1 - 4 T + 73 T^{2}$$)($$1 - 708 T^{2} + 243620 T^{4} - 54480956 T^{6} + 8938972724 T^{8} - 1152660018548 T^{10} + 122264196408284 T^{12} - 11016340703744524 T^{14} + 860580405090458646 T^{16} - 58706079610254568396 T^{18} +$$$$34\!\cdots\!44$$$$T^{20} -$$$$17\!\cdots\!72$$$$T^{22} +$$$$72\!\cdots\!44$$$$T^{24} -$$$$23\!\cdots\!44$$$$T^{26} +$$$$55\!\cdots\!20$$$$T^{28} -$$$$86\!\cdots\!72$$$$T^{30} +$$$$65\!\cdots\!61$$$$T^{32}$$)($$1 - 708 T^{2} + 243620 T^{4} - 54480956 T^{6} + 8938972724 T^{8} - 1152660018548 T^{10} + 122264196408284 T^{12} - 11016340703744524 T^{14} + 860580405090458646 T^{16} - 58706079610254568396 T^{18} +$$$$34\!\cdots\!44$$$$T^{20} -$$$$17\!\cdots\!72$$$$T^{22} +$$$$72\!\cdots\!44$$$$T^{24} -$$$$23\!\cdots\!44$$$$T^{26} +$$$$55\!\cdots\!20$$$$T^{28} -$$$$86\!\cdots\!72$$$$T^{30} +$$$$65\!\cdots\!61$$$$T^{32}$$)($$1 - 98 T^{2} + 5329 T^{4}$$)($$1 - 98 T^{2} + 5329 T^{4}$$)($$1 - 120 T^{2} + 12638 T^{4} - 639480 T^{6} + 28398241 T^{8}$$)($$1 - 120 T^{2} + 12638 T^{4} - 639480 T^{6} + 28398241 T^{8}$$)($$( 1 + 34 T^{2} + 5329 T^{4} )^{4}$$)($$( 1 + 74 T^{2} + 5329 T^{4} )^{4}$$)($$1 - 46 T^{2} + 5329 T^{4}$$)($$1 + 50 T^{2} + 5329 T^{4}$$)($$( 1 - 16 T + 73 T^{2} )^{2}( 1 + 16 T + 73 T^{2} )^{2}$$)($$( 1 - 16 T + 73 T^{2} )^{2}( 1 + 16 T + 73 T^{2} )^{2}$$)($$( 1 - 82 T^{2} + 5329 T^{4} )^{4}$$)($$( 1 - 82 T^{2} + 5329 T^{4} )^{4}$$)($$( 1 - 82 T^{2} + 5329 T^{4} )^{4}$$)($$( 1 - 82 T^{2} + 5329 T^{4} )^{4}$$)($$( 1 - 234 T^{2} + 39488 T^{4} - 4281494 T^{6} + 369066238 T^{8} - 22816081526 T^{10} + 1121389740608 T^{12} - 35412208951626 T^{14} + 806460091894081 T^{16} )^{2}$$)($$( 1 - 234 T^{2} + 39488 T^{4} - 4281494 T^{6} + 369066238 T^{8} - 22816081526 T^{10} + 1121389740608 T^{12} - 35412208951626 T^{14} + 806460091894081 T^{16} )^{2}$$)($$1 + T - 72 T^{2} + 73 T^{3} + 5329 T^{4}$$)($$1 + 15 T + 152 T^{2} + 1095 T^{3} + 5329 T^{4}$$)($$1 + 29 T^{2} - 4488 T^{4} + 154541 T^{6} + 28398241 T^{8}$$)($$1 + 10 T - 53 T^{2} + 70 T^{3} + 10780 T^{4} + 5110 T^{5} - 282437 T^{6} + 3890170 T^{7} + 28398241 T^{8}$$)($$( 1 + 2 T + 2 T^{2} + 146 T^{3} + 5329 T^{4} )^{2}$$)($$( 1 - 16 T + 73 T^{2} )^{2}( 1 - 6 T + 73 T^{2} )^{2}$$)($$( 1 + 5329 T^{4} )^{4}$$)($$( 1 + 5329 T^{4} )^{4}$$)($$1 - 9816 T^{4} + 48230108 T^{8} - 385344995944 T^{12} + 2907384584774982 T^{16} - 10943120062961734504 T^{20} +$$$$38\!\cdots\!48$$$$T^{24} -$$$$22\!\cdots\!36$$$$T^{28} +$$$$65\!\cdots\!61$$$$T^{32}$$)($$( 1 + 73 T^{2} + 5329 T^{4} )^{4}$$)($$( 1 + 73 T^{2} + 5329 T^{4} )^{4}$$)($$1 + 352 T^{2} + 59958 T^{4} + 7351304 T^{6} + 775760945 T^{8} + 70538292468 T^{10} + 5572268648038 T^{12} + 419953342117060 T^{14} + 31250122207352820 T^{16} + 2237931360141812740 T^{18} +$$$$15\!\cdots\!58$$$$T^{20} +$$$$10\!\cdots\!52$$$$T^{22} +$$$$62\!\cdots\!45$$$$T^{24} +$$$$31\!\cdots\!96$$$$T^{26} +$$$$13\!\cdots\!18$$$$T^{28} +$$$$42\!\cdots\!68$$$$T^{30} +$$$$65\!\cdots\!61$$$$T^{32}$$)($$1 + 3 T + 115 T^{2} + 336 T^{3} + 8912 T^{4} + 58260 T^{5} + 290497 T^{6} + 1508853 T^{7} - 7279937 T^{8} - 55999116 T^{9} - 744209196 T^{10} - 4087935468 T^{11} - 38794784273 T^{12} + 586969467501 T^{13} + 8249603815777 T^{14} + 120777151008180 T^{15} + 1348690624687568 T^{16} + 3711925902416592 T^{17} + 92742910567819315 T^{18} + 176614760124803739 T^{19} + 4297625829703557649 T^{20}$$)($$1 + 3 T + 115 T^{2} + 336 T^{3} + 8912 T^{4} + 58260 T^{5} + 290497 T^{6} + 1508853 T^{7} - 7279937 T^{8} - 55999116 T^{9} - 744209196 T^{10} - 4087935468 T^{11} - 38794784273 T^{12} + 586969467501 T^{13} + 8249603815777 T^{14} + 120777151008180 T^{15} + 1348690624687568 T^{16} + 3711925902416592 T^{17} + 92742910567819315 T^{18} + 176614760124803739 T^{19} + 4297625829703557649 T^{20}$$)($$1 - 18 T + 277 T^{2} - 3042 T^{3} + 31116 T^{4} - 222066 T^{5} + 1476133 T^{6} - 7002306 T^{7} + 28398241 T^{8}$$)($$1 - 18 T + 277 T^{2} - 3042 T^{3} + 31116 T^{4} - 222066 T^{5} + 1476133 T^{6} - 7002306 T^{7} + 28398241 T^{8}$$)($$1 + 7294 T^{4} + 24804195 T^{8} + 207136769854 T^{12} + 806460091894081 T^{16}$$)($$1 + 7294 T^{4} + 24804195 T^{8} + 207136769854 T^{12} + 806460091894081 T^{16}$$)
$79$ ($$1 + 8 T + 79 T^{2}$$)($$1 + 79 T^{2}$$)($$1 + 16 T + 79 T^{2}$$)($$1 + 8 T + 79 T^{2}$$)($$1 - 776 T^{2} + 298264 T^{4} - 75873816 T^{6} + 14350843100 T^{8} - 2143612302472 T^{10} + 261769978394792 T^{12} - 26666593413127256 T^{14} + 2290442673574914502 T^{16} -$$$$16\!\cdots\!96$$$$T^{18} +$$$$10\!\cdots\!52$$$$T^{20} -$$$$52\!\cdots\!12$$$$T^{22} +$$$$21\!\cdots\!00$$$$T^{24} -$$$$71\!\cdots\!16$$$$T^{26} +$$$$17\!\cdots\!24$$$$T^{28} -$$$$28\!\cdots\!56$$$$T^{30} +$$$$23\!\cdots\!21$$$$T^{32}$$)($$1 - 776 T^{2} + 298264 T^{4} - 75873816 T^{6} + 14350843100 T^{8} - 2143612302472 T^{10} + 261769978394792 T^{12} - 26666593413127256 T^{14} + 2290442673574914502 T^{16} -$$$$16\!\cdots\!96$$$$T^{18} +$$$$10\!\cdots\!52$$$$T^{20} -$$$$52\!\cdots\!12$$$$T^{22} +$$$$21\!\cdots\!00$$$$T^{24} -$$$$71\!\cdots\!16$$$$T^{26} +$$$$17\!\cdots\!24$$$$T^{28} -$$$$28\!\cdots\!56$$$$T^{30} +$$$$23\!\cdots\!21$$$$T^{32}$$)($$( 1 + 13 T + 79 T^{2} )^{2}$$)($$( 1 + 13 T + 79 T^{2} )^{2}$$)($$( 1 - 12 T + 174 T^{2} - 948 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 - 12 T + 174 T^{2} - 948 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} )^{4}$$)($$( 1 + 12 T + 79 T^{2} )^{8}$$)($$( 1 + 79 T^{2} )^{2}$$)($$( 1 + 16 T + 79 T^{2} )^{2}$$)($$( 1 - 79 T^{2} )^{4}$$)($$( 1 - 79 T^{2} )^{4}$$)($$1 - 130 T^{2} + 3089 T^{4} - 667586 T^{6} + 117965092 T^{8} - 4166404226 T^{10} + 120316800209 T^{12} - 31601369217730 T^{14} + 1517108809906561 T^{16}$$)($$1 - 130 T^{2} + 3089 T^{4} - 667586 T^{6} + 117965092 T^{8} - 4166404226 T^{10} + 120316800209 T^{12} - 31601369217730 T^{14} + 1517108809906561 T^{16}$$)($$1 - 130 T^{2} + 3089 T^{4} - 667586 T^{6} + 117965092 T^{8} - 4166404226 T^{10} + 120316800209 T^{12} - 31601369217730 T^{14} + 1517108809906561 T^{16}$$)($$1 - 130 T^{2} + 3089 T^{4} - 667586 T^{6} + 117965092 T^{8} - 4166404226 T^{10} + 120316800209 T^{12} - 31601369217730 T^{14} + 1517108809906561 T^{16}$$)($$( 1 - 300 T^{2} + 46388 T^{4} - 4850900 T^{6} + 410340886 T^{8} - 30274466900 T^{10} + 1806816357428 T^{12} - 72926236656300 T^{14} + 1517108809906561 T^{16} )^{2}$$)($$( 1 - 300 T^{2} + 46388 T^{4} - 4850900 T^{6} + 410340886 T^{8} - 30274466900 T^{10} + 1806816357428 T^{12} - 72926236656300 T^{14} + 1517108809906561 T^{16} )^{2}$$)($$1 - 3 T - 70 T^{2} - 237 T^{3} + 6241 T^{4}$$)($$1 + T - 78 T^{2} + 79 T^{3} + 6241 T^{4}$$)($$1 - 6 T - 103 T^{2} + 114 T^{3} + 10236 T^{4} + 9006 T^{5} - 642823 T^{6} - 2958234 T^{7} + 38950081 T^{8}$$)($$( 1 + 11 T + 42 T^{2} + 869 T^{3} + 6241 T^{4} )^{2}$$)($$( 1 + 30 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 + 30 T^{2} + 6241 T^{4} )^{2}$$)($$( 1 + 79 T^{2} )^{8}$$)($$( 1 + 79 T^{2} )^{8}$$)($$( 1 - 248 T^{2} + 39836 T^{4} - 4744648 T^{6} + 419330758 T^{8} - 29611348168 T^{10} + 1551615426716 T^{12} - 60285688969208 T^{14} + 1517108809906561 T^{16} )^{2}$$)($$( 1 + 79 T^{2} + 6241 T^{4} )^{4}$$)($$( 1 + 79 T^{2} + 6241 T^{4} )^{4}$$)($$( 1 + 8 T - 18 T^{2} + 632 T^{3} + 6121 T^{4} - 6180 T^{5} + 974510 T^{6} + 7889020 T^{7} - 17559900 T^{8} + 623232580 T^{9} + 6081916910 T^{10} - 3046981020 T^{11} + 238413445801 T^{12} + 1944699644168 T^{13} - 4375574199378 T^{14} + 153631271889272 T^{15} + 1517108809906561 T^{16} )^{2}$$)($$1 - T - 201 T^{2} + 740 T^{3} + 18128 T^{4} - 100900 T^{5} - 805347 T^{6} + 5115611 T^{7} + 21370651 T^{8} - 77003688 T^{9} - 699661200 T^{10} - 6083291352 T^{11} + 133374232891 T^{12} + 2522195731829 T^{13} - 31368330883107 T^{14} - 310474990659100 T^{15} + 4406689393684688 T^{16} + 14210892649757660 T^{17} - 304938870791218761 T^{18} - 119851595982618319 T^{19} + 9468276082626847201 T^{20}$$)($$1 - T - 201 T^{2} + 740 T^{3} + 18128 T^{4} - 100900 T^{5} - 805347 T^{6} + 5115611 T^{7} + 21370651 T^{8} - 77003688 T^{9} - 699661200 T^{10} - 6083291352 T^{11} + 133374232891 T^{12} + 2522195731829 T^{13} - 31368330883107 T^{14} - 310474990659100 T^{15} + 4406689393684688 T^{16} + 14210892649757660 T^{17} - 304938870791218761 T^{18} - 119851595982618319 T^{19} + 9468276082626847201 T^{20}$$)($$1 + 6 T + 137 T^{2} + 750 T^{3} + 10332 T^{4} + 59250 T^{5} + 855017 T^{6} + 2958234 T^{7} + 38950081 T^{8}$$)($$1 - 6 T + 137 T^{2} - 750 T^{3} + 10332 T^{4} - 59250 T^{5} + 855017 T^{6} - 2958234 T^{7} + 38950081 T^{8}$$)($$1 + 132 T^{2} + 4150 T^{4} + 104544 T^{6} + 28505811 T^{8} + 652459104 T^{10} + 161642836150 T^{12} + 32087544128772 T^{14} + 1517108809906561 T^{16}$$)($$1 + 132 T^{2} + 4150 T^{4} + 104544 T^{6} + 28505811 T^{8} + 652459104 T^{10} + 161642836150 T^{12} + 32087544128772 T^{14} + 1517108809906561 T^{16}$$)
$83$ ($$1 + 4 T + 83 T^{2}$$)($$1 + 12 T + 83 T^{2}$$)($$1 + 12 T + 83 T^{2}$$)($$1 - 12 T + 83 T^{2}$$)($$( 1 - 4 T + 196 T^{2} + 268 T^{3} + 25748 T^{4} + 39276 T^{5} + 3021596 T^{6} + 7672636 T^{7} + 246037366 T^{8} + 636828788 T^{9} + 20815774844 T^{10} + 22457506212 T^{11} + 1221956849108 T^{12} + 1055662892324 T^{13} + 64080313180324 T^{14} - 108544203958508 T^{15} + 2252292232139041 T^{16} )^{2}$$)($$( 1 + 4 T + 196 T^{2} - 268 T^{3} + 25748 T^{4} - 39276 T^{5} + 3021596 T^{6} - 7672636 T^{7} + 246037366 T^{8} - 636828788 T^{9} + 20815774844 T^{10} - 22457506212 T^{11} + 1221956849108 T^{12} - 1055662892324 T^{13} + 64080313180324 T^{14} + 108544203958508 T^{15} + 2252292232139041 T^{16} )^{2}$$)($$( 1 + 12 T + 83 T^{2} )^{2}$$)($$( 1 - 12 T + 83 T^{2} )^{2}$$)($$( 1 - 10 T + 186 T^{2} - 830 T^{3} + 6889 T^{4} )^{2}$$)($$( 1 + 10 T + 186 T^{2} + 830 T^{3} + 6889 T^{4} )^{2}$$)($$( 1 - 86 T^{2} + 6889 T^{4} )^{4}$$)($$( 1 - 66 T^{2} + 6889 T^{4} )^{4}$$)($$1 + 90 T^{2} + 6889 T^{4}$$)($$1 + 90 T^{2} + 6889 T^{4}$$)($$( 1 - 18 T + 83 T^{2} )^{2}( 1 + 18 T + 83 T^{2} )^{2}$$)($$( 1 - 18 T + 83 T^{2} )^{2}( 1 + 18 T + 83 T^{2} )^{2}$$)($$1 - 232 T^{2} + 25980 T^{4} - 1355288 T^{6} + 66491558 T^{8} - 9336579032 T^{10} + 1232967179580 T^{12} - 75850166621608 T^{14} + 2252292232139041 T^{16}$$)($$1 - 232 T^{2} + 25980 T^{4} - 1355288 T^{6} + 66491558 T^{8} - 9336579032 T^{10} + 1232967179580 T^{12} - 75850166621608 T^{14} + 2252292232139041 T^{16}$$)($$1 - 232 T^{2} + 25980 T^{4} - 1355288 T^{6} + 66491558 T^{8} - 9336579032 T^{10} + 1232967179580 T^{12} - 75850166621608 T^{14} + 2252292232139041 T^{16}$$)($$1 - 232 T^{2} + 25980 T^{4} - 1355288 T^{6} + 66491558 T^{8} - 9336579032 T^{10} + 1232967179580 T^{12} - 75850166621608 T^{14} + 2252292232139041 T^{16}$$)($$( 1 - 284 T^{2} + 25348 T^{4} + 201580 T^{6} - 152756234 T^{8} + 1388684620 T^{10} + 1202973520708 T^{12} - 92851066036796 T^{14} + 2252292232139041 T^{16} )^{2}$$)($$( 1 - 284 T^{2} + 25348 T^{4} + 201580 T^{6} - 152756234 T^{8} + 1388684620 T^{10} + 1202973520708 T^{12} - 92851066036796 T^{14} + 2252292232139041 T^{16} )^{2}$$)($$( 1 + 18 T + 83 T^{2} )^{2}$$)($$( 1 - 8 T + 83 T^{2} )^{2}$$)($$( 1 + 6 T + 112 T^{2} + 498 T^{3} + 6889 T^{4} )^{2}$$)($$( 1 + 12 T + 184 T^{2} + 996 T^{3} + 6889 T^{4} )^{2}$$)($$( 1 + 6889 T^{4} )^{2}$$)($$1 - 5678 T^{4} + 47458321 T^{8}$$)($$( 1 + 6889 T^{4} )^{4}$$)($$( 1 + 6889 T^{4} )^{4}$$)($$1 + 11592 T^{4} + 91463132 T^{8} + 885997919352 T^{12} + 6666213559678726 T^{16} + 42047973661939327992 T^{20} +$$$$20\!\cdots\!12$$$$T^{24} +$$$$12\!\cdots\!12$$$$T^{28} +$$$$50\!\cdots\!81$$$$T^{32}$$)($$( 1 - 76 T^{2} - 1113 T^{4} - 523564 T^{6} + 47458321 T^{8} )^{2}$$)($$( 1 - 76 T^{2} - 1113 T^{4} - 523564 T^{6} + 47458321 T^{8} )^{2}$$)($$( 1 - 300 T^{2} + 53248 T^{4} - 6367056 T^{6} + 599335434 T^{8} - 43862648784 T^{10} + 2527060676608 T^{12} - 98082112010700 T^{14} + 2252292232139041 T^{16} )^{2}$$)($$( 1 + 4 T + 36 T^{2} + 304 T^{3} + 3029 T^{4} - 33442 T^{5} + 251407 T^{6} + 2094256 T^{7} + 20584332 T^{8} + 189833284 T^{9} + 3939040643 T^{10} )^{2}$$)($$( 1 - 4 T + 36 T^{2} - 304 T^{3} + 3029 T^{4} + 33442 T^{5} + 251407 T^{6} - 2094256 T^{7} + 20584332 T^{8} - 189833284 T^{9} + 3939040643 T^{10} )^{2}$$)($$( 1 + 2 T + 83 T^{2} )^{4}$$)($$( 1 - 2 T + 83 T^{2} )^{4}$$)($$( 1 - 22 T + 242 T^{2} - 3036 T^{3} + 35063 T^{4} - 251988 T^{5} + 1667138 T^{6} - 12579314 T^{7} + 47458321 T^{8} )^{2}$$)($$( 1 + 22 T + 242 T^{2} + 3036 T^{3} + 35063 T^{4} + 251988 T^{5} + 1667138 T^{6} + 12579314 T^{7} + 47458321 T^{8} )^{2}$$)
$89$ ($$1 + 10 T + 89 T^{2}$$)($$1 - 2 T + 89 T^{2}$$)($$1 - 6 T + 89 T^{2}$$)($$1 + 14 T + 89 T^{2}$$)($$1 - 864 T^{2} + 376504 T^{4} - 109545120 T^{6} + 23755420700 T^{8} - 4063039933920 T^{10} + 566169346665480 T^{12} - 65504477701979168 T^{14} + 6355980862575907782 T^{16} -$$$$51\!\cdots\!28$$$$T^{18} +$$$$35\!\cdots\!80$$$$T^{20} -$$$$20\!\cdots\!20$$$$T^{22} +$$$$93\!\cdots\!00$$$$T^{24} -$$$$34\!\cdots\!20$$$$T^{26} +$$$$92\!\cdots\!84$$$$T^{28} -$$$$16\!\cdots\!24$$$$T^{30} +$$$$15\!\cdots\!61$$$$T^{32}$$)($$1 - 864 T^{2} + 376504 T^{4} - 109545120 T^{6} + 23755420700 T^{8} - 4063039933920 T^{10} + 566169346665480 T^{12} - 65504477701979168 T^{14} + 6355980862575907782 T^{16} -$$$$51\!\cdots\!28$$$$T^{18} +$$$$35\!\cdots\!80$$$$T^{20} -$$$$20\!\cdots\!20$$$$T^{22} +$$$$93\!\cdots\!00$$$$T^{24} -$$$$34\!\cdots\!20$$$$T^{26} +$$$$92\!\cdots\!84$$$$T^{28} -$$$$16\!\cdots\!24$$$$T^{30} +$$$$15\!\cdots\!61$$$$T^{32}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 + 89 T^{2} )^{2}$$)($$( 1 - 16 T + 222 T^{2} - 1424 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 + 16 T + 222 T^{2} + 1424 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 + 89 T^{2} )^{8}$$)($$( 1 + 158 T^{2} + 7921 T^{4} )^{4}$$)($$( 1 + 8 T + 89 T^{2} )^{2}$$)($$( 1 + 16 T + 89 T^{2} )^{2}$$)($$( 1 - 128 T^{2} + 7921 T^{4} )^{2}$$)($$( 1 - 128 T^{2} + 7921 T^{4} )^{2}$$)($$1 - 360 T^{2} + 59996 T^{4} - 6261336 T^{6} + 552707974 T^{8} - 49596042456 T^{10} + 3764283491036 T^{12} - 178913264745960 T^{14} + 3936588805702081 T^{16}$$)($$1 - 360 T^{2} + 59996 T^{4} - 6261336 T^{6} + 552707974 T^{8} - 49596042456 T^{10} + 3764283491036 T^{12} - 178913264745960 T^{14} + 3936588805702081 T^{16}$$)($$1 - 360 T^{2} + 59996 T^{4} - 6261336 T^{6} + 552707974 T^{8} - 49596042456 T^{10} + 3764283491036 T^{12} - 178913264745960 T^{14} + 3936588805702081 T^{16}$$)($$1 - 360 T^{2} + 59996 T^{4} - 6261336 T^{6} + 552707974 T^{8} - 49596042456 T^{10} + 3764283491036 T^{12} - 178913264745960 T^{14} + 3936588805702081 T^{16}$$)($$( 1 - 184 T^{2} + 18396 T^{4} - 1862280 T^{6} + 181662342 T^{8} - 14751119880 T^{10} + 1154206265436 T^{12} - 91444557536824 T^{14} + 3936588805702081 T^{16} )^{2}$$)($$( 1 - 184 T^{2} + 18396 T^{4} - 1862280 T^{6} + 181662342 T^{8} - 14751119880 T^{10} + 1154206265436 T^{12} - 91444557536824 T^{14} + 3936588805702081 T^{16} )^{2}$$)($$1 - 4 T - 73 T^{2} - 356 T^{3} + 7921 T^{4}$$)($$1 + 2 T - 85 T^{2} + 178 T^{3} + 7921 T^{4}$$)($$1 - 2 T + 348 T^{3} - 8261 T^{4} + 30972 T^{5} - 1409938 T^{7} + 62742241 T^{8}$$)($$1 - 12 T - 52 T^{2} - 216 T^{3} + 17679 T^{4} - 19224 T^{5} - 411892 T^{6} - 8459628 T^{7} + 62742241 T^{8}$$)($$( 1 - 114 T^{2} + 7921 T^{4} )^{2}$$)($$( 1 - 89 T^{2} )^{4}$$)($$( 1 - 172 T^{2} + 7921 T^{4} )^{4}$$)($$( 1 - 172 T^{2} + 7921 T^{4} )^{4}$$)($$( 1 + 328 T^{2} + 42716 T^{4} + 2964280 T^{6} + 188103750 T^{8} + 23480061880 T^{10} + 2680097566556 T^{12} + 163009863435208 T^{14} + 3936588805702081 T^{16} )^{2}$$)($$( 1 + 6 T + 89 T^{2} )^{4}( 1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 - 6 T + 89 T^{2} )^{4}( 1 - 6 T - 53 T^{2} - 534 T^{3} + 7921 T^{4} )^{2}$$)($$( 1 + 8 T + 2 T^{2} + 1724 T^{3} + 19584 T^{4} + 80534 T^{5} + 2467704 T^{6} + 22993064 T^{7} + 80738407 T^{8} + 2046382696 T^{9} + 19546683384 T^{10} + 56773973446 T^{11} + 1228744047744 T^{12} + 9626918490076 T^{13} + 993962581922 T^{14} + 353850679164232 T^{15} + 3936588805702081 T^{16} )^{2}$$)($$1 - 28 T + 118 T^{2} + 2240 T^{3} + 12999 T^{4} - 635638 T^{5} + 2053984 T^{6} + 15180164 T^{7} + 276922069 T^{8} - 3387791550 T^{9} + 10662822610 T^{10} - 301513447950 T^{11} + 2193499708549 T^{12} + 10701545034916 T^{13} + 128871559138144 T^{14} - 3549440380043462 T^{15} + 6460259801202039 T^{16} + 99078190165984960 T^{17} + 464517479072845558 T^{18} - 9809979303809585852 T^{19} + 31181719929966183601 T^{20}$$)($$1 + 28 T + 118 T^{2} - 2240 T^{3} + 12999 T^{4} + 635638 T^{5} + 2053984 T^{6} - 15180164 T^{7} + 276922069 T^{8} + 3387791550 T^{9} + 10662822610 T^{10} + 301513447950 T^{11} + 2193499708549 T^{12} - 10701545034916 T^{13} + 128871559138144 T^{14} + 3549440380043462 T^{15} + 6460259801202039 T^{16} - 99078190165984960 T^{17} + 464517479072845558 T^{18} + 9809979303809585852 T^{19} + 31181719929966183601 T^{20}$$)($$1 + 36 T + 682 T^{2} + 9000 T^{3} + 93027 T^{4} + 801000 T^{5} + 5402122 T^{6} + 25378884 T^{7} + 62742241 T^{8}$$)($$1 + 36 T + 682 T^{2} + 9000 T^{3} + 93027 T^{4} + 801000 T^{5} + 5402122 T^{6} + 25378884 T^{7} + 62742241 T^{8}$$)($$( 1 + 97 T^{2} + 1488 T^{4} + 768337 T^{6} + 62742241 T^{8} )^{2}$$)($$( 1 + 97 T^{2} + 1488 T^{4} + 768337 T^{6} + 62742241 T^{8} )^{2}$$)
$97$ ($$1 - 8 T + 97 T^{2}$$)($$1 + 8 T + 97 T^{2}$$)($$1 + 16 T + 97 T^{2}$$)($$1 - 8 T + 97 T^{2}$$)($$1 - 708 T^{2} + 266468 T^{4} - 70482684 T^{6} + 14473556148 T^{8} - 2426815167348 T^{10} + 342304459764508 T^{12} - 41313766425365708 T^{14} + 4305828967872497814 T^{16} -$$$$38\!\cdots\!72$$$$T^{18} +$$$$30\!\cdots\!48$$$$T^{20} -$$$$20\!\cdots\!92$$$$T^{22} +$$$$11\!\cdots\!28$$$$T^{24} -$$$$51\!\cdots\!16$$$$T^{26} +$$$$18\!\cdots\!88$$$$T^{28} -$$$$46\!\cdots\!52$$$$T^{30} +$$$$61\!\cdots\!21$$$$T^{32}$$)($$1 - 708 T^{2} + 266468 T^{4} - 70482684 T^{6} + 14473556148 T^{8} - 2426815167348 T^{10} + 342304459764508 T^{12} - 41313766425365708 T^{14} + 4305828967872497814 T^{16} -$$$$38\!\cdots\!72$$$$T^{18} +$$$$30\!\cdots\!48$$$$T^{20} -$$$$20\!\cdots\!92$$$$T^{22} +$$$$11\!\cdots\!28$$$$T^{24} -$$$$51\!\cdots\!16$$$$T^{26} +$$$$18\!\cdots\!88$$$$T^{28} -$$$$46\!\cdots\!52$$$$T^{30} +$$$$61\!\cdots\!21$$$$T^{32}$$)($$1 - 191 T^{2} + 9409 T^{4}$$)($$1 - 191 T^{2} + 9409 T^{4}$$)($$1 - 120 T^{2} + 17918 T^{4} - 1129080 T^{6} + 88529281 T^{8}$$)($$1 - 120 T^{2} + 17918 T^{4} - 1129080 T^{6} + 88529281 T^{8}$$)($$( 1 + 149 T^{2} + 12792 T^{4} + 1401941 T^{6} + 88529281 T^{8} )^{2}$$)($$( 1 + 122 T^{2} + 9409 T^{4} )^{4}$$)($$1 - 94 T^{2} + 9409 T^{4}$$)($$1 + 2 T^{2} + 9409 T^{4}$$)($$( 1 - 158 T^{2} + 9409 T^{4} )^{2}$$)($$( 1 - 158 T^{2} + 9409 T^{4} )^{2}$$)($$1 - 82 T^{2} - 11855 T^{4} - 200178 T^{6} + 251318948 T^{8} - 1883474802 T^{10} - 1049514626255 T^{12} - 68303704404178 T^{14} + 7837433594376961 T^{16}$$)($$1 - 82 T^{2} - 11855 T^{4} - 200178 T^{6} + 251318948 T^{8} - 1883474802 T^{10} - 1049514626255 T^{12} - 68303704404178 T^{14} + 7837433594376961 T^{16}$$)($$1 - 82 T^{2} - 11855 T^{4} - 200178 T^{6} + 251318948 T^{8} - 1883474802 T^{10} - 1049514626255 T^{12} - 68303704404178 T^{14} + 7837433594376961 T^{16}$$)($$1 - 82 T^{2} - 11855 T^{4} - 200178 T^{6} + 251318948 T^{8} - 1883474802 T^{10} - 1049514626255 T^{12} - 68303704404178 T^{14} + 7837433594376961 T^{16}$$)($$( 1 - 266 T^{2} + 44320 T^{4} - 5389846 T^{6} + 579408254 T^{8} - 50713061014 T^{10} + 3923617733920 T^{12} - 221570553311114 T^{14} + 7837433594376961 T^{16} )^{2}$$)($$( 1 - 266 T^{2} + 44320 T^{4} - 5389846 T^{6} + 579408254 T^{8} - 50713061014 T^{10} + 3923617733920 T^{12} - 221570553311114 T^{14} + 7837433594376961 T^{16} )^{2}$$)($$( 1 - 10 T + 97 T^{2} )^{2}$$)($$( 1 + 10 T + 97 T^{2} )^{2}$$)($$( 1 - 8 T + 97 T^{2} )^{4}$$)($$( 1 - 16 T + 186 T^{2} - 1552 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 - 6 T + 18 T^{2} - 582 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 + 18 T + 162 T^{2} + 1746 T^{3} + 9409 T^{4} )^{2}$$)($$( 1 + 9409 T^{4} )^{4}$$)($$( 1 + 9409 T^{4} )^{4}$$)($$1 - 1624 T^{4} + 150045276 T^{8} - 609733450088 T^{12} + 17981575892543942 T^{16} - 53979263937940026728 T^{20} +$$$$11\!\cdots\!36$$$$T^{24} -$$$$11\!\cdots\!84$$$$T^{28} +$$$$61\!\cdots\!21$$$$T^{32}$$)($$( 1 - 97 T^{2} )^{8}$$)($$( 1 - 97 T^{2} )^{8}$$)($$( 1 - 580 T^{2} + 159772 T^{4} - 27295900 T^{6} + 3171169558 T^{8} - 256827123100 T^{10} + 14144500283932 T^{12} - 483123762858820 T^{14} + 7837433594376961 T^{16} )^{2}$$)($$1 - 758 T^{2} + 269933 T^{4} - 59888792 T^{6} + 9235543570 T^{8} - 1040392525668 T^{10} + 86897229450130 T^{12} - 5301911695718552 T^{14} + 224846632206499757 T^{16} - 5940774664537736438 T^{18} + 73742412689492826049 T^{20}$$)($$1 - 758 T^{2} + 269933 T^{4} - 59888792 T^{6} + 9235543570 T^{8} - 1040392525668 T^{10} + 86897229450130 T^{12} - 5301911695718552 T^{14} + 224846632206499757 T^{16} - 5940774664537736438 T^{18} + 73742412689492826049 T^{20}$$)($$1 - 164 T^{2} + 13254 T^{4} - 1543076 T^{6} + 88529281 T^{8}$$)($$1 - 164 T^{2} + 13254 T^{4} - 1543076 T^{6} + 88529281 T^{8}$$)($$( 1 + 24 T + 288 T^{2} + 3528 T^{3} + 40718 T^{4} + 342216 T^{5} + 2709792 T^{6} + 21904152 T^{7} + 88529281 T^{8} )^{2}$$)($$( 1 + 24 T + 288 T^{2} + 3528 T^{3} + 40718 T^{4} + 342216 T^{5} + 2709792 T^{6} + 21904152 T^{7} + 88529281 T^{8} )^{2}$$)