Properties

 Label 324.3 Level 324 Weight 3 Dimension 2632 Nonzero newspaces 8 Newform subspaces 38 Sturm bound 17496 Trace bound 1

Defining parameters

 Level: $$N$$ = $$324 = 2^{2} \cdot 3^{4}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$8$$ Newform subspaces: $$38$$ Sturm bound: $$17496$$ Trace bound: $$1$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(324))$$.

Total New Old
Modular forms 6102 2744 3358
Cusp forms 5562 2632 2930
Eisenstein series 540 112 428

Trace form

 $$2632q - 12q^{2} - 20q^{4} - 15q^{5} - 18q^{6} + 3q^{7} - 15q^{8} - 36q^{9} + O(q^{10})$$ $$2632q - 12q^{2} - 20q^{4} - 15q^{5} - 18q^{6} + 3q^{7} - 15q^{8} - 36q^{9} - 37q^{10} - 36q^{11} - 18q^{12} - 79q^{13} - 57q^{14} - 32q^{16} - 30q^{17} - 18q^{18} - 72q^{19} + 51q^{20} - 171q^{21} + 48q^{22} - 63q^{23} - 18q^{24} - 63q^{25} + 165q^{26} + 27q^{27} + 87q^{28} + 3q^{29} - 18q^{30} + 81q^{31} + 78q^{32} + 153q^{33} + 26q^{34} + 486q^{35} - 18q^{36} + 152q^{37} - 90q^{38} + 65q^{40} + 570q^{41} + 477q^{42} + 270q^{43} + 849q^{44} + 396q^{45} + 351q^{46} + 567q^{47} + 477q^{48} + 205q^{49} + 498q^{50} + 126q^{51} + 11q^{52} + 6q^{53} - 144q^{54} - 126q^{55} - 495q^{56} - 252q^{57} - 187q^{58} - 630q^{59} - 837q^{60} - 307q^{61} - 1203q^{62} - 540q^{63} - 695q^{64} - 735q^{65} - 954q^{66} - 612q^{67} - 1068q^{68} + 468q^{69} - 405q^{70} + 324q^{71} - 18q^{72} - 277q^{73} - 465q^{74} + 450q^{75} - 546q^{76} - 231q^{77} - 99q^{78} - 273q^{79} - 834q^{80} - 108q^{81} - 514q^{82} - 189q^{83} - 99q^{84} + 520q^{85} - 624q^{86} - 1008q^{87} - 708q^{88} + 321q^{89} - 1089q^{90} + 483q^{91} - 2091q^{92} + 792q^{93} - 651q^{94} + 612q^{95} - 1305q^{96} + 1160q^{97} - 2067q^{98} - 252q^{99} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(324))$$

We only show spaces with odd 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
324.3.c $$\chi_{324}(161, \cdot)$$ 324.3.c.a 4 1
324.3.c.b 4
324.3.d $$\chi_{324}(163, \cdot)$$ 324.3.d.a 2 1
324.3.d.b 2
324.3.d.c 2
324.3.d.d 2
324.3.d.e 6
324.3.d.f 6
324.3.d.g 8
324.3.d.h 8
324.3.d.i 8
324.3.f $$\chi_{324}(55, \cdot)$$ 324.3.f.a 2 2
324.3.f.b 2
324.3.f.c 2
324.3.f.d 2
324.3.f.e 2
324.3.f.f 2
324.3.f.g 2
324.3.f.h 2
324.3.f.i 2
324.3.f.j 2
324.3.f.k 4
324.3.f.l 4
324.3.f.m 4
324.3.f.n 4
324.3.f.o 8
324.3.f.p 8
324.3.f.q 12
324.3.f.r 12
324.3.f.s 16
324.3.g $$\chi_{324}(53, \cdot)$$ 324.3.g.a 2 2
324.3.g.b 2
324.3.g.c 4
324.3.g.d 8
324.3.j $$\chi_{324}(19, \cdot)$$ 324.3.j.a 204 6
324.3.k $$\chi_{324}(17, \cdot)$$ 324.3.k.a 36 6
324.3.n $$\chi_{324}(7, \cdot)$$ 324.3.n.a 1908 18
324.3.o $$\chi_{324}(5, \cdot)$$ 324.3.o.a 324 18

Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(324))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(324)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 9}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(162))$$$$^{\oplus 2}$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$( 1 + 2 T )^{2}$$)($$1 + 2 T + 4 T^{2}$$)($$1 - 2 T + 4 T^{2}$$)($$( 1 - 2 T )^{2}$$)($$1 + T + 2 T^{2} + 4 T^{3} + 8 T^{4} + 16 T^{5} + 64 T^{6}$$)($$1 - T + 2 T^{2} - 4 T^{3} + 8 T^{4} - 16 T^{5} + 64 T^{6}$$)($$1 + 3 T + 2 T^{2} - 12 T^{3} - 36 T^{4} - 48 T^{5} + 32 T^{6} + 192 T^{7} + 256 T^{8}$$)($$1 + 5 T^{2} + 24 T^{4} + 80 T^{6} + 256 T^{8}$$)($$1 - 3 T + 2 T^{2} + 12 T^{3} - 36 T^{4} + 48 T^{5} + 32 T^{6} - 192 T^{7} + 256 T^{8}$$)($$( 1 + 2 T )^{2}$$)($$( 1 + 2 T )^{2}$$)($$1 + 2 T + 4 T^{2}$$)($$1 + 2 T + 4 T^{2}$$)($$1 + 2 T + 4 T^{2}$$)($$1 - 2 T + 4 T^{2}$$)($$1 - 2 T + 4 T^{2}$$)($$1 - 2 T + 4 T^{2}$$)($$( 1 - 2 T )^{2}$$)($$( 1 - 2 T )^{2}$$)($$( 1 + 2 T + 4 T^{2} )^{2}$$)($$1 + 3 T + 7 T^{2} + 12 T^{3} + 16 T^{4}$$)($$1 - 3 T + 7 T^{2} - 12 T^{3} + 16 T^{4}$$)($$( 1 - 2 T + 4 T^{2} )^{2}$$)($$1 + 2 T^{2} - 12 T^{4} + 32 T^{6} + 256 T^{8}$$)($$( 1 - 2 T^{2} + 16 T^{4} )^{2}$$)($$1 + T - T^{2} - 6 T^{3} - 8 T^{4} + 8 T^{5} + 112 T^{6} + 32 T^{7} - 128 T^{8} - 384 T^{9} - 256 T^{10} + 1024 T^{11} + 4096 T^{12}$$)($$1 - T - T^{2} + 6 T^{3} - 8 T^{4} - 8 T^{5} + 112 T^{6} - 32 T^{7} - 128 T^{8} + 384 T^{9} - 256 T^{10} - 1024 T^{11} + 4096 T^{12}$$)($$1 - 5 T^{2} + T^{4} + 40 T^{6} - 80 T^{8} + 640 T^{10} + 256 T^{12} - 20480 T^{14} + 65536 T^{16}$$)
$3$ 1
$5$ ($$1 - 64 T^{2} + 2031 T^{4} - 40000 T^{6} + 390625 T^{8}$$)($$1 - 37 T^{2} + 924 T^{4} - 23125 T^{6} + 390625 T^{8}$$)($$1 + 8 T + 39 T^{2} + 200 T^{3} + 625 T^{4}$$)($$( 1 - 4 T + 25 T^{2} )^{2}$$)($$( 1 + 4 T + 25 T^{2} )^{2}$$)($$1 - 8 T + 39 T^{2} - 200 T^{3} + 625 T^{4}$$)($$( 1 + T + 38 T^{2} + 109 T^{3} + 950 T^{4} + 625 T^{5} + 15625 T^{6} )^{2}$$)($$( 1 - T + 38 T^{2} - 109 T^{3} + 950 T^{4} - 625 T^{5} + 15625 T^{6} )^{2}$$)($$( 1 - 3 T + 47 T^{2} + 30 T^{3} + 804 T^{4} + 750 T^{5} + 29375 T^{6} - 46875 T^{7} + 390625 T^{8} )^{2}$$)($$( 1 + 38 T^{2} + 699 T^{4} + 23750 T^{6} + 390625 T^{8} )^{2}$$)($$( 1 + 3 T + 47 T^{2} - 30 T^{3} + 804 T^{4} - 750 T^{5} + 29375 T^{6} + 46875 T^{7} + 390625 T^{8} )^{2}$$)($$1 + 2 T - 21 T^{2} + 50 T^{3} + 625 T^{4}$$)($$1 - 7 T + 24 T^{2} - 175 T^{3} + 625 T^{4}$$)($$1 + 7 T + 24 T^{2} + 175 T^{3} + 625 T^{4}$$)($$1 - 2 T - 21 T^{2} - 50 T^{3} + 625 T^{4}$$)($$1 - 8 T + 39 T^{2} - 200 T^{3} + 625 T^{4}$$)($$1 + 8 T + 39 T^{2} + 200 T^{3} + 625 T^{4}$$)($$1 + 2 T - 21 T^{2} + 50 T^{3} + 625 T^{4}$$)($$1 - 7 T + 24 T^{2} - 175 T^{3} + 625 T^{4}$$)($$1 + 7 T + 24 T^{2} + 175 T^{3} + 625 T^{4}$$)($$1 - 2 T - 21 T^{2} - 50 T^{3} + 625 T^{4}$$)($$( 1 + 8 T + 25 T^{2} )^{2}( 1 - 8 T + 39 T^{2} - 200 T^{3} + 625 T^{4} )$$)($$1 - 37 T^{2} + 744 T^{4} - 23125 T^{6} + 390625 T^{8}$$)($$1 - 37 T^{2} + 744 T^{4} - 23125 T^{6} + 390625 T^{8}$$)($$( 1 - 8 T + 25 T^{2} )^{2}( 1 + 8 T + 39 T^{2} + 200 T^{3} + 625 T^{4} )$$)($$1 - 44 T^{2} + 922 T^{4} + 10384 T^{6} - 572429 T^{8} + 6490000 T^{10} + 360156250 T^{12} - 10742187500 T^{14} + 152587890625 T^{16}$$)($$1 - 44 T^{2} + 922 T^{4} + 10384 T^{6} - 572429 T^{8} + 6490000 T^{10} + 360156250 T^{12} - 10742187500 T^{14} + 152587890625 T^{16}$$)($$( 1 + T - 37 T^{2} - 180 T^{3} + 385 T^{4} + 2867 T^{5} + 6406 T^{6} + 71675 T^{7} + 240625 T^{8} - 2812500 T^{9} - 14453125 T^{10} + 9765625 T^{11} + 244140625 T^{12} )^{2}$$)($$( 1 - T - 37 T^{2} + 180 T^{3} + 385 T^{4} - 2867 T^{5} + 6406 T^{6} - 71675 T^{7} + 240625 T^{8} + 2812500 T^{9} - 14453125 T^{10} - 9765625 T^{11} + 244140625 T^{12} )^{2}$$)($$( 1 - 38 T^{2} + 745 T^{4} + 20938 T^{6} - 804524 T^{8} + 13086250 T^{10} + 291015625 T^{12} - 9277343750 T^{14} + 152587890625 T^{16} )^{2}$$)($$( 1 - 5 T + 25 T^{2} )( 1 + 5 T + 25 T^{2} )$$)($$( 1 - 5 T + 25 T^{2} )( 1 + 5 T + 25 T^{2} )$$)($$1 - 31 T^{2} + 336 T^{4} - 19375 T^{6} + 390625 T^{8}$$)($$1 + 64 T^{2} + 2065 T^{4} + 49984 T^{6} + 1174336 T^{8} + 31240000 T^{10} + 806640625 T^{12} + 15625000000 T^{14} + 152587890625 T^{16}$$)
$7$ ($$( 1 + 2 T + 72 T^{2} + 98 T^{3} + 2401 T^{4} )^{2}$$)($$( 1 - T + 24 T^{2} - 49 T^{3} + 2401 T^{4} )^{2}$$)($$( 1 - 7 T )^{2}( 1 + 7 T )^{2}$$)($$1 - 86 T^{2} + 2401 T^{4}$$)($$1 - 86 T^{2} + 2401 T^{4}$$)($$( 1 - 7 T )^{2}( 1 + 7 T )^{2}$$)($$1 - 114 T^{2} + 7599 T^{4} - 404924 T^{6} + 18245199 T^{8} - 657187314 T^{10} + 13841287201 T^{12}$$)($$1 - 114 T^{2} + 7599 T^{4} - 404924 T^{6} + 18245199 T^{8} - 657187314 T^{10} + 13841287201 T^{12}$$)($$1 - 167 T^{2} + 14701 T^{4} - 959570 T^{6} + 51275386 T^{8} - 2303927570 T^{10} + 84748339501 T^{12} - 2311494962567 T^{14} + 33232930569601 T^{16}$$)($$( 1 - 40 T^{2} - 498 T^{4} - 96040 T^{6} + 5764801 T^{8} )^{2}$$)($$1 - 167 T^{2} + 14701 T^{4} - 959570 T^{6} + 51275386 T^{8} - 2303927570 T^{10} + 84748339501 T^{12} - 2311494962567 T^{14} + 33232930569601 T^{16}$$)($$1 - 12 T + 97 T^{2} - 588 T^{3} + 2401 T^{4}$$)($$( 1 + 2 T + 49 T^{2} )( 1 + 13 T + 49 T^{2} )$$)($$( 1 - 13 T + 49 T^{2} )( 1 - 2 T + 49 T^{2} )$$)($$1 + 12 T + 97 T^{2} + 588 T^{3} + 2401 T^{4}$$)($$( 1 - 7 T + 49 T^{2} )( 1 + 7 T + 49 T^{2} )$$)($$( 1 - 7 T + 49 T^{2} )( 1 + 7 T + 49 T^{2} )$$)($$1 + 12 T + 97 T^{2} + 588 T^{3} + 2401 T^{4}$$)($$( 1 - 13 T + 49 T^{2} )( 1 - 2 T + 49 T^{2} )$$)($$( 1 + 2 T + 49 T^{2} )( 1 + 13 T + 49 T^{2} )$$)($$1 - 12 T + 97 T^{2} - 588 T^{3} + 2401 T^{4}$$)($$( 1 - 7 T + 49 T^{2} )^{2}( 1 + 7 T + 49 T^{2} )^{2}$$)($$1 + 59 T^{2} + 1080 T^{4} + 141659 T^{6} + 5764801 T^{8}$$)($$1 + 59 T^{2} + 1080 T^{4} + 141659 T^{6} + 5764801 T^{8}$$)($$( 1 - 7 T + 49 T^{2} )^{2}( 1 + 7 T + 49 T^{2} )^{2}$$)($$( 1 + 6 T + 53 T^{2} + 246 T^{3} - 132 T^{4} + 12054 T^{5} + 127253 T^{6} + 705894 T^{7} + 5764801 T^{8} )^{2}$$)($$( 1 - 6 T + 53 T^{2} - 246 T^{3} - 132 T^{4} - 12054 T^{5} + 127253 T^{6} - 705894 T^{7} + 5764801 T^{8} )^{2}$$)($$1 + 114 T^{2} + 5397 T^{4} + 56438 T^{6} - 6661734 T^{8} - 425700582 T^{10} - 21918600819 T^{12} - 1022107097382 T^{14} - 38403570824934 T^{16} + 781174567050038 T^{18} + 179358126284136597 T^{20} + 9096318357927768114 T^{22} +$$$$19\!\cdots\!01$$$$T^{24}$$)($$1 + 114 T^{2} + 5397 T^{4} + 56438 T^{6} - 6661734 T^{8} - 425700582 T^{10} - 21918600819 T^{12} - 1022107097382 T^{14} - 38403570824934 T^{16} + 781174567050038 T^{18} + 179358126284136597 T^{20} + 9096318357927768114 T^{22} +$$$$19\!\cdots\!01$$$$T^{24}$$)($$( 1 + 40 T^{2} + 2098 T^{4} - 212000 T^{6} - 9358397 T^{8} - 509012000 T^{10} + 12094552498 T^{12} + 553651488040 T^{14} + 33232930569601 T^{16} )^{2}$$)($$( 1 - 2 T + 49 T^{2} )( 1 + 13 T + 49 T^{2} )$$)($$( 1 - 11 T + 49 T^{2} )( 1 + 13 T + 49 T^{2} )$$)($$( 1 - 7 T )^{4}( 1 + 7 T + 49 T^{2} )^{2}$$)($$( 1 - 2 T - 68 T^{2} + 52 T^{3} + 2587 T^{4} + 2548 T^{5} - 163268 T^{6} - 235298 T^{7} + 5764801 T^{8} )^{2}$$)
$11$ ($$1 - 232 T^{2} + 27186 T^{4} - 3396712 T^{6} + 214358881 T^{8}$$)($$1 - 70 T^{2} - 12261 T^{4} - 1024870 T^{6} + 214358881 T^{8}$$)($$( 1 - 11 T )^{2}( 1 + 11 T )^{2}$$)($$1 - 95 T^{2} + 14641 T^{4}$$)($$1 - 95 T^{2} + 14641 T^{4}$$)($$( 1 - 11 T )^{2}( 1 + 11 T )^{2}$$)($$1 - 210 T^{2} + 37791 T^{4} - 4769852 T^{6} + 553298031 T^{8} - 45015365010 T^{10} + 3138428376721 T^{12}$$)($$1 - 210 T^{2} + 37791 T^{4} - 4769852 T^{6} + 553298031 T^{8} - 45015365010 T^{10} + 3138428376721 T^{12}$$)($$1 - 524 T^{2} + 134482 T^{4} - 22990832 T^{6} + 3065351611 T^{8} - 336608771312 T^{10} + 28827411034642 T^{12} - 1644536469401804 T^{14} + 45949729863572161 T^{16}$$)($$( 1 - 208 T^{2} + 39870 T^{4} - 3045328 T^{6} + 214358881 T^{8} )^{2}$$)($$1 - 524 T^{2} + 134482 T^{4} - 22990832 T^{6} + 3065351611 T^{8} - 336608771312 T^{10} + 28827411034642 T^{12} - 1644536469401804 T^{14} + 45949729863572161 T^{16}$$)($$1 - 12 T + 169 T^{2} - 1452 T^{3} + 14641 T^{4}$$)($$1 + 15 T + 196 T^{2} + 1815 T^{3} + 14641 T^{4}$$)($$1 + 15 T + 196 T^{2} + 1815 T^{3} + 14641 T^{4}$$)($$1 - 12 T + 169 T^{2} - 1452 T^{3} + 14641 T^{4}$$)($$( 1 - 11 T + 121 T^{2} )( 1 + 11 T + 121 T^{2} )$$)($$( 1 - 11 T + 121 T^{2} )( 1 + 11 T + 121 T^{2} )$$)($$1 + 12 T + 169 T^{2} + 1452 T^{3} + 14641 T^{4}$$)($$1 - 15 T + 196 T^{2} - 1815 T^{3} + 14641 T^{4}$$)($$1 - 15 T + 196 T^{2} - 1815 T^{3} + 14641 T^{4}$$)($$1 + 12 T + 169 T^{2} + 1452 T^{3} + 14641 T^{4}$$)($$( 1 - 11 T + 121 T^{2} )^{2}( 1 + 11 T + 121 T^{2} )^{2}$$)($$( 1 + 21 T + 268 T^{2} + 2541 T^{3} + 14641 T^{4} )^{2}$$)($$( 1 - 21 T + 268 T^{2} - 2541 T^{3} + 14641 T^{4} )^{2}$$)($$( 1 - 11 T + 121 T^{2} )^{2}( 1 + 11 T + 121 T^{2} )^{2}$$)($$1 + 124 T^{2} + 250 T^{4} - 1755344 T^{6} - 210683021 T^{8} - 25699991504 T^{10} + 53589720250 T^{12} + 389165118713404 T^{14} + 45949729863572161 T^{16}$$)($$1 + 124 T^{2} + 250 T^{4} - 1755344 T^{6} - 210683021 T^{8} - 25699991504 T^{10} + 53589720250 T^{12} + 389165118713404 T^{14} + 45949729863572161 T^{16}$$)($$1 + 210 T^{2} + 6309 T^{4} - 1603594 T^{6} - 126807270 T^{8} - 7112331078 T^{10} - 1334567686275 T^{12} - 104131639312998 T^{14} - 27182264499864870 T^{16} - 5032764914339535274 T^{18} +$$$$28\!\cdots\!49$$$$T^{20} +$$$$14\!\cdots\!10$$$$T^{22} +$$$$98\!\cdots\!41$$$$T^{24}$$)($$1 + 210 T^{2} + 6309 T^{4} - 1603594 T^{6} - 126807270 T^{8} - 7112331078 T^{10} - 1334567686275 T^{12} - 104131639312998 T^{14} - 27182264499864870 T^{16} - 5032764914339535274 T^{18} +$$$$28\!\cdots\!49$$$$T^{20} +$$$$14\!\cdots\!10$$$$T^{22} +$$$$98\!\cdots\!41$$$$T^{24}$$)($$( 1 + 208 T^{2} + 3394 T^{4} + 2202304 T^{6} + 741829795 T^{8} + 32243932864 T^{10} + 727534042114 T^{12} + 652793102357968 T^{14} + 45949729863572161 T^{16} )^{2}$$)($$( 1 - 11 T + 121 T^{2} )( 1 + 11 T + 121 T^{2} )$$)($$( 1 - 11 T + 121 T^{2} )( 1 + 11 T + 121 T^{2} )$$)($$1 + 161 T^{2} + 11280 T^{4} + 2357201 T^{6} + 214358881 T^{8}$$)($$1 + 232 T^{2} + 26638 T^{4} - 486272 T^{6} - 263317469 T^{8} - 7119508352 T^{10} + 5710091872078 T^{12} + 728115383399272 T^{14} + 45949729863572161 T^{16}$$)
$13$ ($$( 1 + 2 T + 231 T^{2} + 338 T^{3} + 28561 T^{4} )^{2}$$)($$( 1 + 5 T + 270 T^{2} + 845 T^{3} + 28561 T^{4} )^{2}$$)($$1 - 10 T - 69 T^{2} - 1690 T^{3} + 28561 T^{4}$$)($$( 1 + 22 T + 169 T^{2} )^{2}$$)($$( 1 + 22 T + 169 T^{2} )^{2}$$)($$1 - 10 T - 69 T^{2} - 1690 T^{3} + 28561 T^{4}$$)($$( 1 - 3 T + 342 T^{2} - 23 T^{3} + 57798 T^{4} - 85683 T^{5} + 4826809 T^{6} )^{2}$$)($$( 1 - 3 T + 342 T^{2} - 23 T^{3} + 57798 T^{4} - 85683 T^{5} + 4826809 T^{6} )^{2}$$)($$( 1 - 23 T + 805 T^{2} - 11762 T^{3} + 214858 T^{4} - 1987778 T^{5} + 22991605 T^{6} - 111016607 T^{7} + 815730721 T^{8} )^{2}$$)($$( 1 + 8 T + 297 T^{2} + 1352 T^{3} + 28561 T^{4} )^{4}$$)($$( 1 - 23 T + 805 T^{2} - 11762 T^{3} + 214858 T^{4} - 1987778 T^{5} + 22991605 T^{6} - 111016607 T^{7} + 815730721 T^{8} )^{2}$$)($$1 + 2 T - 165 T^{2} + 338 T^{3} + 28561 T^{4}$$)($$1 + 20 T + 231 T^{2} + 3380 T^{3} + 28561 T^{4}$$)($$1 + 20 T + 231 T^{2} + 3380 T^{3} + 28561 T^{4}$$)($$1 + 2 T - 165 T^{2} + 338 T^{3} + 28561 T^{4}$$)($$1 - 10 T - 69 T^{2} - 1690 T^{3} + 28561 T^{4}$$)($$1 - 10 T - 69 T^{2} - 1690 T^{3} + 28561 T^{4}$$)($$1 + 2 T - 165 T^{2} + 338 T^{3} + 28561 T^{4}$$)($$1 + 20 T + 231 T^{2} + 3380 T^{3} + 28561 T^{4}$$)($$1 + 20 T + 231 T^{2} + 3380 T^{3} + 28561 T^{4}$$)($$1 + 2 T - 165 T^{2} + 338 T^{3} + 28561 T^{4}$$)($$( 1 + 10 T + 169 T^{2} )^{2}( 1 - 10 T - 69 T^{2} - 1690 T^{3} + 28561 T^{4} )$$)($$( 1 - 16 T + 87 T^{2} - 2704 T^{3} + 28561 T^{4} )^{2}$$)($$( 1 - 16 T + 87 T^{2} - 2704 T^{3} + 28561 T^{4} )^{2}$$)($$( 1 + 10 T + 169 T^{2} )^{2}( 1 - 10 T - 69 T^{2} - 1690 T^{3} + 28561 T^{4} )$$)($$( 1 - 2 T - 155 T^{2} + 358 T^{3} - 3956 T^{4} + 60502 T^{5} - 4426955 T^{6} - 9653618 T^{7} + 815730721 T^{8} )^{2}$$)($$( 1 - 2 T - 155 T^{2} + 358 T^{3} - 3956 T^{4} + 60502 T^{5} - 4426955 T^{6} - 9653618 T^{7} + 815730721 T^{8} )^{2}$$)($$( 1 + 3 T - 333 T^{2} + 980 T^{3} + 59097 T^{4} - 253239 T^{5} - 10369818 T^{6} - 42797391 T^{7} + 1687869417 T^{8} + 4730272820 T^{9} - 271638330093 T^{10} + 413575475547 T^{11} + 23298085122481 T^{12} )^{2}$$)($$( 1 + 3 T - 333 T^{2} + 980 T^{3} + 59097 T^{4} - 253239 T^{5} - 10369818 T^{6} - 42797391 T^{7} + 1687869417 T^{8} + 4730272820 T^{9} - 271638330093 T^{10} + 413575475547 T^{11} + 23298085122481 T^{12} )^{2}$$)($$( 1 - 8 T - 233 T^{2} + 328 T^{3} + 48832 T^{4} + 55432 T^{5} - 6654713 T^{6} - 38614472 T^{7} + 815730721 T^{8} )^{4}$$)($$( 1 + T + 169 T^{2} )( 1 + 22 T + 169 T^{2} )$$)($$( 1 - 23 T + 169 T^{2} )( 1 + T + 169 T^{2} )$$)($$( 1 + 14 T + 27 T^{2} + 2366 T^{3} + 28561 T^{4} )^{2}$$)($$( 1 - 2 T - 227 T^{2} + 214 T^{3} + 24124 T^{4} + 36166 T^{5} - 6483347 T^{6} - 9653618 T^{7} + 815730721 T^{8} )^{2}$$)
$17$ ($$1 + 392 T^{2} + 164391 T^{4} + 32740232 T^{6} + 6975757441 T^{8}$$)($$1 - 769 T^{2} + 298176 T^{4} - 64227649 T^{6} + 6975757441 T^{8}$$)($$1 - 16 T - 33 T^{2} - 4624 T^{3} + 83521 T^{4}$$)($$( 1 + 11 T + 289 T^{2} )^{2}$$)($$( 1 - 11 T + 289 T^{2} )^{2}$$)($$1 + 16 T - 33 T^{2} + 4624 T^{3} + 83521 T^{4}$$)($$( 1 - 5 T + 710 T^{2} - 2657 T^{3} + 205190 T^{4} - 417605 T^{5} + 24137569 T^{6} )^{2}$$)($$( 1 + 5 T + 710 T^{2} + 2657 T^{3} + 205190 T^{4} + 417605 T^{5} + 24137569 T^{6} )^{2}$$)($$( 1 + 3 T + 578 T^{2} + 6549 T^{3} + 169242 T^{4} + 1892661 T^{5} + 48275138 T^{6} + 72412707 T^{7} + 6975757441 T^{8} )^{2}$$)($$( 1 + 398 T^{2} + 115443 T^{4} + 33241358 T^{6} + 6975757441 T^{8} )^{2}$$)($$( 1 - 3 T + 578 T^{2} - 6549 T^{3} + 169242 T^{4} - 1892661 T^{5} + 48275138 T^{6} - 72412707 T^{7} + 6975757441 T^{8} )^{2}$$)($$( 1 + 10 T + 289 T^{2} )^{2}$$)($$( 1 - 8 T + 289 T^{2} )^{2}$$)($$( 1 + 8 T + 289 T^{2} )^{2}$$)($$( 1 - 10 T + 289 T^{2} )^{2}$$)($$( 1 - 16 T + 289 T^{2} )^{2}$$)($$( 1 + 16 T + 289 T^{2} )^{2}$$)($$( 1 + 10 T + 289 T^{2} )^{2}$$)($$( 1 - 8 T + 289 T^{2} )^{2}$$)($$( 1 + 8 T + 289 T^{2} )^{2}$$)($$( 1 - 10 T + 289 T^{2} )^{2}$$)($$( 1 + 16 T - 33 T^{2} + 4624 T^{3} + 83521 T^{4} )^{2}$$)($$( 1 + 370 T^{2} + 83521 T^{4} )^{2}$$)($$( 1 + 370 T^{2} + 83521 T^{4} )^{2}$$)($$( 1 - 16 T - 33 T^{2} - 4624 T^{3} + 83521 T^{4} )^{2}$$)($$( 1 + 140 T^{2} + 136662 T^{4} + 11692940 T^{6} + 6975757441 T^{8} )^{2}$$)($$( 1 + 140 T^{2} + 136662 T^{4} + 11692940 T^{6} + 6975757441 T^{8} )^{2}$$)($$( 1 + 5 T + 710 T^{2} + 2657 T^{3} + 205190 T^{4} + 417605 T^{5} + 24137569 T^{6} )^{4}$$)($$( 1 - 5 T + 710 T^{2} - 2657 T^{3} + 205190 T^{4} - 417605 T^{5} + 24137569 T^{6} )^{4}$$)($$( 1 + 398 T^{2} + 115443 T^{4} + 33241358 T^{6} + 6975757441 T^{8} )^{4}$$)($$( 1 - 17 T )^{2}( 1 + 17 T )^{2}$$)($$( 1 - 17 T )^{2}( 1 + 17 T )^{2}$$)($$( 1 - 254 T^{2} + 83521 T^{4} )^{2}$$)($$( 1 + 392 T^{2} + 164391 T^{4} + 32740232 T^{6} + 6975757441 T^{8} )^{2}$$)
$19$ ($$( 1 + 14 T + 96 T^{2} + 5054 T^{3} + 130321 T^{4} )^{2}$$)($$( 1 - T + 648 T^{2} - 361 T^{3} + 130321 T^{4} )^{2}$$)($$( 1 - 19 T )^{2}( 1 + 19 T )^{2}$$)($$1 - 479 T^{2} + 130321 T^{4}$$)($$1 - 479 T^{2} + 130321 T^{4}$$)($$( 1 - 19 T )^{2}( 1 + 19 T )^{2}$$)($$1 - 690 T^{2} + 175551 T^{4} - 20841212 T^{6} + 22877981871 T^{8} - 11718658498290 T^{10} + 2213314919066161 T^{12}$$)($$1 - 690 T^{2} + 175551 T^{4} - 20841212 T^{6} + 22877981871 T^{8} - 11718658498290 T^{10} + 2213314919066161 T^{12}$$)($$1 - 1673 T^{2} + 1559890 T^{4} - 937716023 T^{6} + 401371470970 T^{8} - 122204089833383 T^{10} + 26492490152025490 T^{12} - 3702875859597687353 T^{14} +$$$$28\!\cdots\!81$$$$T^{16}$$)($$( 1 - 616 T^{2} + 353454 T^{4} - 80277736 T^{6} + 16983563041 T^{8} )^{2}$$)($$1 - 1673 T^{2} + 1559890 T^{4} - 937716023 T^{6} + 401371470970 T^{8} - 122204089833383 T^{10} + 26492490152025490 T^{12} - 3702875859597687353 T^{14} +$$$$28\!\cdots\!81$$$$T^{16}$$)($$1 - 290 T^{2} + 130321 T^{4}$$)($$1 - 614 T^{2} + 130321 T^{4}$$)($$1 - 614 T^{2} + 130321 T^{4}$$)($$1 - 290 T^{2} + 130321 T^{4}$$)($$( 1 - 19 T )^{2}( 1 + 19 T )^{2}$$)($$( 1 - 19 T )^{2}( 1 + 19 T )^{2}$$)($$1 - 290 T^{2} + 130321 T^{4}$$)($$1 - 614 T^{2} + 130321 T^{4}$$)($$1 - 614 T^{2} + 130321 T^{4}$$)($$1 - 290 T^{2} + 130321 T^{4}$$)($$( 1 - 19 T )^{4}( 1 + 19 T )^{4}$$)($$( 1 + 682 T^{2} + 130321 T^{4} )^{2}$$)($$( 1 + 682 T^{2} + 130321 T^{4} )^{2}$$)($$( 1 - 19 T )^{4}( 1 + 19 T )^{4}$$)($$( 1 - 695 T^{2} + 130321 T^{4} )^{4}$$)($$( 1 - 695 T^{2} + 130321 T^{4} )^{4}$$)($$( 1 - 690 T^{2} + 175551 T^{4} - 20841212 T^{6} + 22877981871 T^{8} - 11718658498290 T^{10} + 2213314919066161 T^{12} )^{2}$$)($$( 1 - 690 T^{2} + 175551 T^{4} - 20841212 T^{6} + 22877981871 T^{8} - 11718658498290 T^{10} + 2213314919066161 T^{12} )^{2}$$)($$( 1 - 616 T^{2} + 353454 T^{4} - 80277736 T^{6} + 16983563041 T^{8} )^{4}$$)($$( 1 + 37 T + 361 T^{2} )^{2}$$)($$( 1 - 26 T + 361 T^{2} )^{2}$$)($$( 1 - 8 T + 361 T^{2} )^{4}$$)($$( 1 + 14 T + 96 T^{2} + 5054 T^{3} + 130321 T^{4} )^{4}$$)
$23$ ($$1 - 352 T^{2} + 528450 T^{4} - 98504032 T^{6} + 78310985281 T^{8}$$)($$1 - 433 T^{2} + 525696 T^{4} - 121171153 T^{6} + 78310985281 T^{8}$$)($$( 1 - 23 T )^{2}( 1 + 23 T )^{2}$$)($$1 - 470 T^{2} + 279841 T^{4}$$)($$1 - 470 T^{2} + 279841 T^{4}$$)($$( 1 - 23 T )^{2}( 1 + 23 T )^{2}$$)($$1 - 306 T^{2} + 387951 T^{4} - 110145596 T^{6} + 108564595791 T^{8} - 23963161495986 T^{10} + 21914624432020321 T^{12}$$)($$1 - 306 T^{2} + 387951 T^{4} - 110145596 T^{6} + 108564595791 T^{8} - 23963161495986 T^{10} + 21914624432020321 T^{12}$$)($$1 - 2687 T^{2} + 3500317 T^{4} - 2971858562 T^{6} + 1824468134410 T^{8} - 831647871848642 T^{10} + 274113273065834077 T^{12} - 58884595848838602527 T^{14} +$$$$61\!\cdots\!61$$$$T^{16}$$)($$( 1 - 1360 T^{2} + 879582 T^{4} - 380583760 T^{6} + 78310985281 T^{8} )^{2}$$)($$1 - 2687 T^{2} + 3500317 T^{4} - 2971858562 T^{6} + 1824468134410 T^{8} - 831647871848642 T^{10} + 274113273065834077 T^{12} - 58884595848838602527 T^{14} +$$$$61\!\cdots\!61$$$$T^{16}$$)($$1 - 48 T + 1297 T^{2} - 25392 T^{3} + 279841 T^{4}$$)($$1 + 6 T + 541 T^{2} + 3174 T^{3} + 279841 T^{4}$$)($$1 + 6 T + 541 T^{2} + 3174 T^{3} + 279841 T^{4}$$)($$1 - 48 T + 1297 T^{2} - 25392 T^{3} + 279841 T^{4}$$)($$( 1 - 23 T + 529 T^{2} )( 1 + 23 T + 529 T^{2} )$$)($$( 1 - 23 T + 529 T^{2} )( 1 + 23 T + 529 T^{2} )$$)($$1 + 48 T + 1297 T^{2} + 25392 T^{3} + 279841 T^{4}$$)($$1 - 6 T + 541 T^{2} - 3174 T^{3} + 279841 T^{4}$$)($$1 - 6 T + 541 T^{2} - 3174 T^{3} + 279841 T^{4}$$)($$1 + 48 T + 1297 T^{2} + 25392 T^{3} + 279841 T^{4}$$)($$( 1 - 23 T + 529 T^{2} )^{2}( 1 + 23 T + 529 T^{2} )^{2}$$)($$( 1 + 30 T + 829 T^{2} + 15870 T^{3} + 279841 T^{4} )^{2}$$)($$( 1 - 30 T + 829 T^{2} - 15870 T^{3} + 279841 T^{4} )^{2}$$)($$( 1 - 23 T + 529 T^{2} )^{2}( 1 + 23 T + 529 T^{2} )^{2}$$)($$1 + 604 T^{2} - 268070 T^{4} + 44215216 T^{6} + 220143229459 T^{8} + 12373230260656 T^{10} - 20992825824277670 T^{12} + 13236433156940273884 T^{14} +$$$$61\!\cdots\!61$$$$T^{16}$$)($$1 + 604 T^{2} - 268070 T^{4} + 44215216 T^{6} + 220143229459 T^{8} + 12373230260656 T^{10} - 20992825824277670 T^{12} + 13236433156940273884 T^{14} +$$$$61\!\cdots\!61$$$$T^{16}$$)($$1 + 306 T^{2} - 294315 T^{4} - 101578186 T^{6} + 8236830234 T^{8} + 252722985690 T^{10} + 6510830262749901 T^{12} + 70722253038475290 T^{14} +$$$$64\!\cdots\!54$$$$T^{16} -$$$$22\!\cdots\!06$$$$T^{18} -$$$$18\!\cdots\!15$$$$T^{20} +$$$$52\!\cdots\!06$$$$T^{22} +$$$$48\!\cdots\!41$$$$T^{24}$$)($$1 + 306 T^{2} - 294315 T^{4} - 101578186 T^{6} + 8236830234 T^{8} + 252722985690 T^{10} + 6510830262749901 T^{12} + 70722253038475290 T^{14} +$$$$64\!\cdots\!54$$$$T^{16} -$$$$22\!\cdots\!06$$$$T^{18} -$$$$18\!\cdots\!15$$$$T^{20} +$$$$52\!\cdots\!06$$$$T^{22} +$$$$48\!\cdots\!41$$$$T^{24}$$)($$( 1 + 1360 T^{2} + 970018 T^{4} + 435064000 T^{6} + 177759595843 T^{8} + 121748744824000 T^{10} + 75963065320305058 T^{12} + 29803889227547636560 T^{14} +$$$$61\!\cdots\!61$$$$T^{16} )^{2}$$)($$( 1 - 23 T + 529 T^{2} )( 1 + 23 T + 529 T^{2} )$$)($$( 1 - 23 T + 529 T^{2} )( 1 + 23 T + 529 T^{2} )$$)($$1 - 238 T^{2} - 223197 T^{4} - 66602158 T^{6} + 78310985281 T^{8}$$)($$1 + 352 T^{2} - 404546 T^{4} - 10993664 T^{6} + 166274997955 T^{8} - 3076477927424 T^{10} - 31680395851487426 T^{12} + 7713947800071152992 T^{14} +$$$$61\!\cdots\!61$$$$T^{16}$$)
$29$ ($$1 + 344 T^{2} + 3399 T^{4} + 243304664 T^{6} + 500246412961 T^{8}$$)($$1 - 277 T^{2} - 170724 T^{4} - 195916837 T^{6} + 500246412961 T^{8}$$)($$1 - 40 T + 759 T^{2} - 33640 T^{3} + 707281 T^{4}$$)($$( 1 - 34 T + 841 T^{2} )^{2}$$)($$( 1 + 34 T + 841 T^{2} )^{2}$$)($$1 + 40 T + 759 T^{2} + 33640 T^{3} + 707281 T^{4}$$)($$( 1 - 11 T + 662 T^{2} + 14017 T^{3} + 556742 T^{4} - 7780091 T^{5} + 594823321 T^{6} )^{2}$$)($$( 1 + 11 T + 662 T^{2} - 14017 T^{3} + 556742 T^{4} + 7780091 T^{5} + 594823321 T^{6} )^{2}$$)($$( 1 - 21 T + 2873 T^{2} - 39750 T^{3} + 3357342 T^{4} - 33429750 T^{5} + 2032018313 T^{6} - 12491289741 T^{7} + 500246412961 T^{8} )^{2}$$)($$( 1 + 2942 T^{2} + 3563811 T^{4} + 2080820702 T^{6} + 500246412961 T^{8} )^{2}$$)($$( 1 + 21 T + 2873 T^{2} + 39750 T^{3} + 3357342 T^{4} + 33429750 T^{5} + 2032018313 T^{6} + 12491289741 T^{7} + 500246412961 T^{8} )^{2}$$)($$1 + 26 T - 165 T^{2} + 21866 T^{3} + 707281 T^{4}$$)($$1 - 10 T - 741 T^{2} - 8410 T^{3} + 707281 T^{4}$$)($$1 + 10 T - 741 T^{2} + 8410 T^{3} + 707281 T^{4}$$)($$1 - 26 T - 165 T^{2} - 21866 T^{3} + 707281 T^{4}$$)($$1 + 40 T + 759 T^{2} + 33640 T^{3} + 707281 T^{4}$$)($$1 - 40 T + 759 T^{2} - 33640 T^{3} + 707281 T^{4}$$)($$1 + 26 T - 165 T^{2} + 21866 T^{3} + 707281 T^{4}$$)($$1 - 10 T - 741 T^{2} - 8410 T^{3} + 707281 T^{4}$$)($$1 + 10 T - 741 T^{2} + 8410 T^{3} + 707281 T^{4}$$)($$1 - 26 T - 165 T^{2} - 21866 T^{3} + 707281 T^{4}$$)($$( 1 - 40 T + 841 T^{2} )^{2}( 1 + 40 T + 759 T^{2} + 33640 T^{3} + 707281 T^{4} )$$)($$1 + 866 T^{2} + 42675 T^{4} + 612505346 T^{6} + 500246412961 T^{8}$$)($$1 + 866 T^{2} + 42675 T^{4} + 612505346 T^{6} + 500246412961 T^{8}$$)($$( 1 + 40 T + 841 T^{2} )^{2}( 1 - 40 T + 759 T^{2} - 33640 T^{3} + 707281 T^{4} )$$)($$1 - 2468 T^{2} + 3338026 T^{4} - 3303260048 T^{6} + 2770686029299 T^{8} - 2336333070009488 T^{10} + 1669835532870554986 T^{12} -$$$$87\!\cdots\!88$$$$T^{14} +$$$$25\!\cdots\!21$$$$T^{16}$$)($$1 - 2468 T^{2} + 3338026 T^{4} - 3303260048 T^{6} + 2770686029299 T^{8} - 2336333070009488 T^{10} + 1669835532870554986 T^{12} -$$$$87\!\cdots\!88$$$$T^{14} +$$$$25\!\cdots\!21$$$$T^{16}$$)($$( 1 - 11 T - 541 T^{2} - 35316 T^{3} + 35689 T^{4} + 13747487 T^{5} + 931978726 T^{6} + 11561636567 T^{7} + 25242151609 T^{8} - 21006780404436 T^{9} - 270633309411901 T^{10} - 4627779566302211 T^{11} + 353814783205469041 T^{12} )^{2}$$)($$( 1 + 11 T - 541 T^{2} + 35316 T^{3} + 35689 T^{4} - 13747487 T^{5} + 931978726 T^{6} - 11561636567 T^{7} + 25242151609 T^{8} + 21006780404436 T^{9} - 270633309411901 T^{10} + 4627779566302211 T^{11} + 353814783205469041 T^{12} )^{2}$$)($$( 1 - 2942 T^{2} + 5091553 T^{4} - 6323090558 T^{6} + 6078727925476 T^{8} - 4472201812952798 T^{10} + 2547031124650818433 T^{12} -$$$$10\!\cdots\!22$$$$T^{14} +$$$$25\!\cdots\!21$$$$T^{16} )^{2}$$)($$( 1 - 29 T + 841 T^{2} )( 1 + 29 T + 841 T^{2} )$$)($$( 1 - 29 T + 841 T^{2} )( 1 + 29 T + 841 T^{2} )$$)($$1 + 1358 T^{2} + 1136883 T^{4} + 960487598 T^{6} + 500246412961 T^{8}$$)($$1 - 344 T^{2} + 114937 T^{4} + 485440072 T^{6} - 583931664176 T^{8} + 343342539564232 T^{10} + 57496821966498457 T^{12} -$$$$12\!\cdots\!04$$$$T^{14} +$$$$25\!\cdots\!21$$$$T^{16}$$)
$31$ ($$( 1 - 16 T + 1014 T^{2} - 15376 T^{3} + 923521 T^{4} )^{2}$$)($$( 1 - 7 T + 1266 T^{2} - 6727 T^{3} + 923521 T^{4} )^{2}$$)($$( 1 - 31 T )^{2}( 1 + 31 T )^{2}$$)($$1 - 1874 T^{2} + 923521 T^{4}$$)($$1 - 1874 T^{2} + 923521 T^{4}$$)($$( 1 - 31 T )^{2}( 1 + 31 T )^{2}$$)($$1 - 390 T^{2} + 363663 T^{4} - 1746543380 T^{6} + 335850417423 T^{8} - 332627504601990 T^{10} + 787662783788549761 T^{12}$$)($$1 - 390 T^{2} + 363663 T^{4} - 1746543380 T^{6} + 335850417423 T^{8} - 332627504601990 T^{10} + 787662783788549761 T^{12}$$)($$1 - 4715 T^{2} + 11501641 T^{4} - 18322192394 T^{6} + 20727776670694 T^{8} - 16920929441899274 T^{10} + 9809646524763940681 T^{12} -$$$$37\!\cdots\!15$$$$T^{14} +$$$$72\!\cdots\!81$$$$T^{16}$$)($$( 1 - 1300 T^{2} + 952614 T^{4} - 1200577300 T^{6} + 852891037441 T^{8} )^{2}$$)($$1 - 4715 T^{2} + 11501641 T^{4} - 18322192394 T^{6} + 20727776670694 T^{8} - 16920929441899274 T^{10} + 9809646524763940681 T^{12} -$$$$37\!\cdots\!15$$$$T^{14} +$$$$72\!\cdots\!81$$$$T^{16}$$)($$1 - 12 T + 1009 T^{2} - 11532 T^{3} + 923521 T^{4}$$)($$( 1 - 31 T )^{2}( 1 - 31 T + 961 T^{2} )$$)($$( 1 + 31 T )^{2}( 1 + 31 T + 961 T^{2} )$$)($$1 + 12 T + 1009 T^{2} + 11532 T^{3} + 923521 T^{4}$$)($$( 1 - 31 T + 961 T^{2} )( 1 + 31 T + 961 T^{2} )$$)($$( 1 - 31 T + 961 T^{2} )( 1 + 31 T + 961 T^{2} )$$)($$1 + 12 T + 1009 T^{2} + 11532 T^{3} + 923521 T^{4}$$)($$( 1 + 31 T )^{2}( 1 + 31 T + 961 T^{2} )$$)($$( 1 - 31 T )^{2}( 1 - 31 T + 961 T^{2} )$$)($$1 - 12 T + 1009 T^{2} - 11532 T^{3} + 923521 T^{4}$$)($$( 1 - 31 T + 961 T^{2} )^{2}( 1 + 31 T + 961 T^{2} )^{2}$$)($$1 + 1883 T^{2} + 2622168 T^{4} + 1738990043 T^{6} + 852891037441 T^{8}$$)($$1 + 1883 T^{2} + 2622168 T^{4} + 1738990043 T^{6} + 852891037441 T^{8}$$)($$( 1 - 31 T + 961 T^{2} )^{2}( 1 + 31 T + 961 T^{2} )^{2}$$)($$( 1 - 48 T + 1922 T^{2} - 55392 T^{3} + 1146243 T^{4} - 53231712 T^{5} + 1775007362 T^{6} - 42600176688 T^{7} + 852891037441 T^{8} )^{2}$$)($$( 1 + 48 T + 1922 T^{2} + 55392 T^{3} + 1146243 T^{4} + 53231712 T^{5} + 1775007362 T^{6} + 42600176688 T^{7} + 852891037441 T^{8} )^{2}$$)($$1 + 390 T^{2} - 211563 T^{4} - 3351258190 T^{6} - 884751558054 T^{8} + 705817384212990 T^{10} + 4373878248652847373 T^{12} +$$$$65\!\cdots\!90$$$$T^{14} -$$$$75\!\cdots\!14$$$$T^{16} -$$$$26\!\cdots\!90$$$$T^{18} -$$$$15\!\cdots\!03$$$$T^{20} +$$$$26\!\cdots\!90$$$$T^{22} +$$$$62\!\cdots\!21$$$$T^{24}$$)($$1 + 390 T^{2} - 211563 T^{4} - 3351258190 T^{6} - 884751558054 T^{8} + 705817384212990 T^{10} + 4373878248652847373 T^{12} +$$$$65\!\cdots\!90$$$$T^{14} -$$$$75\!\cdots\!14$$$$T^{16} -$$$$26\!\cdots\!90$$$$T^{18} -$$$$15\!\cdots\!03$$$$T^{20} +$$$$26\!\cdots\!90$$$$T^{22} +$$$$62\!\cdots\!21$$$$T^{24}$$)($$( 1 + 1300 T^{2} + 737386 T^{4} - 1162756400 T^{6} - 1506168094445 T^{8} - 1073829953284400 T^{10} + 628909910534469226 T^{12} +$$$$10\!\cdots\!00$$$$T^{14} +$$$$72\!\cdots\!81$$$$T^{16} )^{2}$$)($$( 1 - 59 T + 961 T^{2} )( 1 + 13 T + 961 T^{2} )$$)($$( 1 - 59 T + 961 T^{2} )( 1 + 13 T + 961 T^{2} )$$)($$( 1 + 35 T + 264 T^{2} + 33635 T^{3} + 923521 T^{4} )^{2}$$)($$( 1 + 16 T - 758 T^{2} - 14528 T^{3} - 141341 T^{4} - 13961408 T^{5} - 700028918 T^{6} + 14200058896 T^{7} + 852891037441 T^{8} )^{2}$$)
$37$ ($$( 1 - 28 T + 2907 T^{2} - 38332 T^{3} + 1874161 T^{4} )^{2}$$)($$( 1 + 32 T + 1806 T^{2} + 43808 T^{3} + 1874161 T^{4} )^{2}$$)($$1 - 70 T + 3531 T^{2} - 95830 T^{3} + 1874161 T^{4}$$)($$( 1 + 16 T + 1369 T^{2} )^{2}$$)($$( 1 + 16 T + 1369 T^{2} )^{2}$$)($$1 - 70 T + 3531 T^{2} - 95830 T^{3} + 1874161 T^{4}$$)($$( 1 - 27 T + 78 T^{2} + 70681 T^{3} + 106782 T^{4} - 50602347 T^{5} + 2565726409 T^{6} )^{2}$$)($$( 1 - 27 T + 78 T^{2} + 70681 T^{3} + 106782 T^{4} - 50602347 T^{5} + 2565726409 T^{6} )^{2}$$)($$( 1 - 14 T + 3040 T^{2} - 66050 T^{3} + 4581118 T^{4} - 90422450 T^{5} + 5697449440 T^{6} - 35920169726 T^{7} + 3512479453921 T^{8} )^{2}$$)($$( 1 + 56 T + 3465 T^{2} + 76664 T^{3} + 1874161 T^{4} )^{4}$$)($$( 1 - 14 T + 3040 T^{2} - 66050 T^{3} + 4581118 T^{4} - 90422450 T^{5} + 5697449440 T^{6} - 35920169726 T^{7} + 3512479453921 T^{8} )^{2}$$)($$( 1 - 26 T + 1369 T^{2} )^{2}$$)($$( 1 + 10 T + 1369 T^{2} )^{2}$$)($$( 1 + 10 T + 1369 T^{2} )^{2}$$)($$( 1 - 26 T + 1369 T^{2} )^{2}$$)($$( 1 + 70 T + 1369 T^{2} )^{2}$$)($$( 1 + 70 T + 1369 T^{2} )^{2}$$)($$( 1 - 26 T + 1369 T^{2} )^{2}$$)($$( 1 + 10 T + 1369 T^{2} )^{2}$$)($$( 1 + 10 T + 1369 T^{2} )^{2}$$)($$( 1 - 26 T + 1369 T^{2} )^{2}$$)($$( 1 - 70 T + 3531 T^{2} - 95830 T^{3} + 1874161 T^{4} )^{2}$$)($$( 1 - 26 T + 1369 T^{2} )^{4}$$)($$( 1 - 26 T + 1369 T^{2} )^{4}$$)($$( 1 - 70 T + 3531 T^{2} - 95830 T^{3} + 1874161 T^{4} )^{2}$$)($$( 1 + 14 T + 2607 T^{2} + 19166 T^{3} + 1874161 T^{4} )^{4}$$)($$( 1 + 14 T + 2607 T^{2} + 19166 T^{3} + 1874161 T^{4} )^{4}$$)($$( 1 - 27 T + 78 T^{2} + 70681 T^{3} + 106782 T^{4} - 50602347 T^{5} + 2565726409 T^{6} )^{4}$$)($$( 1 - 27 T + 78 T^{2} + 70681 T^{3} + 106782 T^{4} - 50602347 T^{5} + 2565726409 T^{6} )^{4}$$)($$( 1 + 56 T + 3465 T^{2} + 76664 T^{3} + 1874161 T^{4} )^{8}$$)($$( 1 + 73 T + 1369 T^{2} )^{2}$$)($$( 1 - 26 T + 1369 T^{2} )^{2}$$)($$( 1 - 44 T + 1369 T^{2} )^{4}$$)($$( 1 - 28 T + 2907 T^{2} - 38332 T^{3} + 1874161 T^{4} )^{4}$$)
$41$ ($$1 - 1720 T^{2} + 170322 T^{4} - 4860308920 T^{6} + 7984925229121 T^{8}$$)($$1 - 3502 T^{2} + 8546451 T^{4} - 9895815022 T^{6} + 7984925229121 T^{8}$$)($$( 1 - 80 T + 1681 T^{2} )^{2}$$)($$( 1 - 13 T + 1681 T^{2} )^{2}$$)($$( 1 + 13 T + 1681 T^{2} )^{2}$$)($$( 1 + 80 T + 1681 T^{2} )^{2}$$)($$( 1 + 46 T + 4031 T^{2} + 132676 T^{3} + 6776111 T^{4} + 129985006 T^{5} + 4750104241 T^{6} )^{2}$$)($$( 1 - 46 T + 4031 T^{2} - 132676 T^{3} + 6776111 T^{4} - 129985006 T^{5} + 4750104241 T^{6} )^{2}$$)($$( 1 - 42 T + 6188 T^{2} - 192468 T^{3} + 15263853 T^{4} - 323538708 T^{5} + 17485809068 T^{6} - 199504378122 T^{7} + 7984925229121 T^{8} )^{2}$$)($$( 1 + 6548 T^{2} + 16366950 T^{4} + 18503083028 T^{6} + 7984925229121 T^{8} )^{2}$$)($$( 1 + 42 T + 6188 T^{2} + 192468 T^{3} + 15263853 T^{4} + 323538708 T^{5} + 17485809068 T^{6} + 199504378122 T^{7} + 7984925229121 T^{8} )^{2}$$)($$1 - 58 T + 1683 T^{2} - 97498 T^{3} + 2825761 T^{4}$$)($$1 + 50 T + 819 T^{2} + 84050 T^{3} + 2825761 T^{4}$$)($$1 - 50 T + 819 T^{2} - 84050 T^{3} + 2825761 T^{4}$$)($$1 + 58 T + 1683 T^{2} + 97498 T^{3} + 2825761 T^{4}$$)($$1 - 80 T + 4719 T^{2} - 134480 T^{3} + 2825761 T^{4}$$)($$1 + 80 T + 4719 T^{2} + 134480 T^{3} + 2825761 T^{4}$$)($$1 - 58 T + 1683 T^{2} - 97498 T^{3} + 2825761 T^{4}$$)($$1 + 50 T + 819 T^{2} + 84050 T^{3} + 2825761 T^{4}$$)($$1 - 50 T + 819 T^{2} - 84050 T^{3} + 2825761 T^{4}$$)($$1 + 58 T + 1683 T^{2} + 97498 T^{3} + 2825761 T^{4}$$)($$( 1 - 80 T + 4719 T^{2} - 134480 T^{3} + 2825761 T^{4} )^{2}$$)($$1 - 3310 T^{2} + 8130339 T^{4} - 9353268910 T^{6} + 7984925229121 T^{8}$$)($$1 - 3310 T^{2} + 8130339 T^{4} - 9353268910 T^{6} + 7984925229121 T^{8}$$)($$( 1 + 80 T + 4719 T^{2} + 134480 T^{3} + 2825761 T^{4} )^{2}$$)($$1 - 3140 T^{2} + 4692298 T^{4} + 1520450800 T^{6} - 9144788425517 T^{8} + 4296430573058800 T^{10} + 37467648682754010058 T^{12} -$$$$70\!\cdots\!40$$$$T^{14} +$$$$63\!\cdots\!41$$$$T^{16}$$)($$1 - 3140 T^{2} + 4692298 T^{4} + 1520450800 T^{6} - 9144788425517 T^{8} + 4296430573058800 T^{10} + 37467648682754010058 T^{12} -$$$$70\!\cdots\!40$$$$T^{14} +$$$$63\!\cdots\!41$$$$T^{16}$$)($$( 1 + 46 T - 1915 T^{2} - 79926 T^{3} + 3369754 T^{4} + 41399750 T^{5} - 6190684259 T^{6} + 69592979750 T^{7} + 9522119432794 T^{8} - 379656831566166 T^{9} - 15291131813766715 T^{10} + 617442328267010446 T^{11} + 22563490300366186081 T^{12} )^{2}$$)($$( 1 - 46 T - 1915 T^{2} + 79926 T^{3} + 3369754 T^{4} - 41399750 T^{5} - 6190684259 T^{6} - 69592979750 T^{7} + 9522119432794 T^{8} + 379656831566166 T^{9} - 15291131813766715 T^{10} - 617442328267010446 T^{11} + 22563490300366186081 T^{12} )^{2}$$)($$( 1 - 6548 T^{2} + 26509354 T^{4} - 70164622544 T^{6} + 138733939406035 T^{8} - 198268453964555984 T^{10} +$$$$21\!\cdots\!34$$$$T^{12} -$$$$14\!\cdots\!88$$$$T^{14} +$$$$63\!\cdots\!41$$$$T^{16} )^{2}$$)($$( 1 - 41 T + 1681 T^{2} )( 1 + 41 T + 1681 T^{2} )$$)($$( 1 - 41 T + 1681 T^{2} )( 1 + 41 T + 1681 T^{2} )$$)($$1 + 2066 T^{2} + 1442595 T^{4} + 5838022226 T^{6} + 7984925229121 T^{8}$$)($$1 + 1720 T^{2} + 2788078 T^{4} - 9427664000 T^{6} - 16315646987837 T^{8} - 26640325252304000 T^{10} + 22262594362957219438 T^{12} +$$$$38\!\cdots\!20$$$$T^{14} +$$$$63\!\cdots\!41$$$$T^{16}$$)
$43$ ($$( 1 + 26 T + 1680 T^{2} + 48074 T^{3} + 3418801 T^{4} )^{2}$$)($$( 1 - 23 T + 1849 T^{2} )^{4}$$)($$( 1 - 43 T )^{2}( 1 + 43 T )^{2}$$)($$1 - 1175 T^{2} + 3418801 T^{4}$$)($$1 - 1175 T^{2} + 3418801 T^{4}$$)($$( 1 - 43 T )^{2}( 1 + 43 T )^{2}$$)($$1 - 4722 T^{2} + 12428319 T^{4} - 26111008508 T^{6} + 42489949425519 T^{8} - 55191681710831922 T^{10} + 39959630797262576401 T^{12}$$)($$1 - 4722 T^{2} + 12428319 T^{4} - 26111008508 T^{6} + 42489949425519 T^{8} - 55191681710831922 T^{10} + 39959630797262576401 T^{12}$$)($$1 - 10292 T^{2} + 53105962 T^{4} - 172233596384 T^{6} + 381742267864051 T^{8} - 588832391551215584 T^{10} +$$$$62\!\cdots\!62$$$$T^{12} -$$$$41\!\cdots\!92$$$$T^{14} +$$$$13\!\cdots\!01$$$$T^{16}$$)($$( 1 + 3416 T^{2} + 8731374 T^{4} + 11678624216 T^{6} + 11688200277601 T^{8} )^{2}$$)($$1 - 10292 T^{2} + 53105962 T^{4} - 172233596384 T^{6} + 381742267864051 T^{8} - 588832391551215584 T^{10} +$$$$62\!\cdots\!62$$$$T^{12} -$$$$41\!\cdots\!92$$$$T^{14} +$$$$13\!\cdots\!01$$$$T^{16}$$)($$1 - 84 T + 4201 T^{2} - 155316 T^{3} + 3418801 T^{4}$$)($$1 - 30 T + 2149 T^{2} - 55470 T^{3} + 3418801 T^{4}$$)($$1 + 30 T + 2149 T^{2} + 55470 T^{3} + 3418801 T^{4}$$)($$1 + 84 T + 4201 T^{2} + 155316 T^{3} + 3418801 T^{4}$$)($$( 1 - 43 T + 1849 T^{2} )( 1 + 43 T + 1849 T^{2} )$$)($$( 1 - 43 T + 1849 T^{2} )( 1 + 43 T + 1849 T^{2} )$$)($$1 + 84 T + 4201 T^{2} + 155316 T^{3} + 3418801 T^{4}$$)($$1 + 30 T + 2149 T^{2} + 55470 T^{3} + 3418801 T^{4}$$)($$1 - 30 T + 2149 T^{2} - 55470 T^{3} + 3418801 T^{4}$$)($$1 - 84 T + 4201 T^{2} - 155316 T^{3} + 3418801 T^{4}$$)($$( 1 - 43 T + 1849 T^{2} )^{2}( 1 + 43 T + 1849 T^{2} )^{2}$$)($$1 + 3542 T^{2} + 9126963 T^{4} + 12109393142 T^{6} + 11688200277601 T^{8}$$)($$1 + 3542 T^{2} + 9126963 T^{4} + 12109393142 T^{6} + 11688200277601 T^{8}$$)($$( 1 - 43 T + 1849 T^{2} )^{2}( 1 + 43 T + 1849 T^{2} )^{2}$$)($$( 1 - 120 T + 9458 T^{2} - 558960 T^{3} + 27153363 T^{4} - 1033517040 T^{5} + 32335019858 T^{6} - 758563565880 T^{7} + 11688200277601 T^{8} )^{2}$$)($$( 1 + 120 T + 9458 T^{2} + 558960 T^{3} + 27153363 T^{4} + 1033517040 T^{5} + 32335019858 T^{6} + 758563565880 T^{7} + 11688200277601 T^{8} )^{2}$$)($$1 + 4722 T^{2} + 9868965 T^{4} + 6464505302 T^{6} - 11323018434534 T^{8} - 21567457514631462 T^{10} - 26989739893391669379 T^{12} -$$$$73\!\cdots\!62$$$$T^{14} -$$$$13\!\cdots\!34$$$$T^{16} +$$$$25\!\cdots\!02$$$$T^{18} +$$$$13\!\cdots\!65$$$$T^{20} +$$$$22\!\cdots\!22$$$$T^{22} +$$$$15\!\cdots\!01$$$$T^{24}$$)($$1 + 4722 T^{2} + 9868965 T^{4} + 6464505302 T^{6} - 11323018434534 T^{8} - 21567457514631462 T^{10} - 26989739893391669379 T^{12} -$$$$73\!\cdots\!62$$$$T^{14} -$$$$13\!\cdots\!34$$$$T^{16} +$$$$25\!\cdots\!02$$$$T^{18} +$$$$13\!\cdots\!65$$$$T^{20} +$$$$22\!\cdots\!22$$$$T^{22} +$$$$15\!\cdots\!01$$$$T^{24}$$)($$( 1 - 3416 T^{2} + 2937682 T^{4} - 6469125152 T^{6} + 24654511328419 T^{8} - 22116651538782752 T^{10} + 34336215567903460882 T^{12} -$$$$13\!\cdots\!16$$$$T^{14} +$$$$13\!\cdots\!01$$$$T^{16} )^{2}$$)($$( 1 - 83 T + 1849 T^{2} )( 1 + 61 T + 1849 T^{2} )$$)($$( 1 - 83 T + 1849 T^{2} )( 1 + 61 T + 1849 T^{2} )$$)($$( 1 - 83 T + 1849 T^{2} )^{2}( 1 + 61 T + 1849 T^{2} )^{2}$$)($$( 1 - 26 T - 1004 T^{2} + 52468 T^{3} - 1846325 T^{4} + 97013332 T^{5} - 3432476204 T^{6} - 164355439274 T^{7} + 11688200277601 T^{8} )^{2}$$)
$47$ ($$1 - 4948 T^{2} + 13045686 T^{4} - 24144661588 T^{6} + 23811286661761 T^{8}$$)($$1 - 7297 T^{2} + 22583760 T^{4} - 35607032257 T^{6} + 23811286661761 T^{8}$$)($$( 1 - 47 T )^{2}( 1 + 47 T )^{2}$$)($$1 - 4406 T^{2} + 4879681 T^{4}$$)($$1 - 4406 T^{2} + 4879681 T^{4}$$)($$( 1 - 47 T )^{2}( 1 + 47 T )^{2}$$)($$1 - 5046 T^{2} + 9746319 T^{4} - 14628306740 T^{6} + 47558927644239 T^{8} - 120151752495246006 T^{10} +$$$$11\!\cdots\!41$$$$T^{12}$$)($$1 - 5046 T^{2} + 9746319 T^{4} - 14628306740 T^{6} + 47558927644239 T^{8} - 120151752495246006 T^{10} +$$$$11\!\cdots\!41$$$$T^{12}$$)($$1 - 12983 T^{2} + 78335149 T^{4} - 294042673394 T^{6} + 766851321282202 T^{8} - 1434834446549907314 T^{10} +$$$$18\!\cdots\!89$$$$T^{12} -$$$$15\!\cdots\!03$$$$T^{14} +$$$$56\!\cdots\!21$$$$T^{16}$$)($$( 1 - 3460 T^{2} + 11818374 T^{4} - 16883696260 T^{6} + 23811286661761 T^{8} )^{2}$$)($$1 - 12983 T^{2} + 78335149 T^{4} - 294042673394 T^{6} + 766851321282202 T^{8} - 1434834446549907314 T^{10} +$$$$18\!\cdots\!89$$$$T^{12} -$$$$15\!\cdots\!03$$$$T^{14} +$$$$56\!\cdots\!21$$$$T^{16}$$)($$1 - 120 T + 7009 T^{2} - 265080 T^{3} + 4879681 T^{4}$$)($$1 + 150 T + 9709 T^{2} + 331350 T^{3} + 4879681 T^{4}$$)($$1 + 150 T + 9709 T^{2} + 331350 T^{3} + 4879681 T^{4}$$)($$1 - 120 T + 7009 T^{2} - 265080 T^{3} + 4879681 T^{4}$$)($$( 1 - 47 T + 2209 T^{2} )( 1 + 47 T + 2209 T^{2} )$$)($$( 1 - 47 T + 2209 T^{2} )( 1 + 47 T + 2209 T^{2} )$$)($$1 + 120 T + 7009 T^{2} + 265080 T^{3} + 4879681 T^{4}$$)($$1 - 150 T + 9709 T^{2} - 331350 T^{3} + 4879681 T^{4}$$)($$1 - 150 T + 9709 T^{2} - 331350 T^{3} + 4879681 T^{4}$$)($$1 + 120 T + 7009 T^{2} + 265080 T^{3} + 4879681 T^{4}$$)($$( 1 - 47 T + 2209 T^{2} )^{2}( 1 + 47 T + 2209 T^{2} )^{2}$$)($$( 1 - 6 T + 2221 T^{2} - 13254 T^{3} + 4879681 T^{4} )^{2}$$)($$( 1 + 6 T + 2221 T^{2} + 13254 T^{3} + 4879681 T^{4} )^{2}$$)($$( 1 - 47 T + 2209 T^{2} )^{2}( 1 + 47 T + 2209 T^{2} )^{2}$$)($$1 + 4444 T^{2} + 5312410 T^{4} + 20786205616 T^{6} + 88238287231699 T^{8} + 101430052606488496 T^{10} +$$$$12\!\cdots\!10$$$$T^{12} +$$$$51\!\cdots\!04$$$$T^{14} +$$$$56\!\cdots\!21$$$$T^{16}$$)($$1 + 4444 T^{2} + 5312410 T^{4} + 20786205616 T^{6} + 88238287231699 T^{8} + 101430052606488496 T^{10} +$$$$12\!\cdots\!10$$$$T^{12} +$$$$51\!\cdots\!04$$$$T^{14} +$$$$56\!\cdots\!21$$$$T^{16}$$)($$1 + 5046 T^{2} + 15715797 T^{4} + 19923312194 T^{6} - 26382629404518 T^{8} - 217240801372523922 T^{10} -$$$$62\!\cdots\!35$$$$T^{12} -$$$$10\!\cdots\!82$$$$T^{14} -$$$$62\!\cdots\!98$$$$T^{16} +$$$$23\!\cdots\!54$$$$T^{18} +$$$$89\!\cdots\!37$$$$T^{20} +$$$$13\!\cdots\!46$$$$T^{22} +$$$$13\!\cdots\!81$$$$T^{24}$$)($$1 + 5046 T^{2} + 15715797 T^{4} + 19923312194 T^{6} - 26382629404518 T^{8} - 217240801372523922 T^{10} -$$$$62\!\cdots\!35$$$$T^{12} -$$$$10\!\cdots\!82$$$$T^{14} -$$$$62\!\cdots\!98$$$$T^{16} +$$$$23\!\cdots\!54$$$$T^{18} +$$$$89\!\cdots\!37$$$$T^{20} +$$$$13\!\cdots\!46$$$$T^{22} +$$$$13\!\cdots\!81$$$$T^{24}$$)($$( 1 + 3460 T^{2} + 153226 T^{4} + 7124181520 T^{6} + 57445088282515 T^{8} + 34763733203695120 T^{10} + 3648508210034990986 T^{12} +$$$$40\!\cdots\!60$$$$T^{14} +$$$$56\!\cdots\!21$$$$T^{16} )^{2}$$)($$( 1 - 47 T + 2209 T^{2} )( 1 + 47 T + 2209 T^{2} )$$)($$( 1 - 47 T + 2209 T^{2} )( 1 + 47 T + 2209 T^{2} )$$)($$1 + 1502 T^{2} - 2623677 T^{4} + 7329280862 T^{6} + 23811286661761 T^{8}$$)($$1 + 4948 T^{2} + 11437018 T^{4} + 16260731152 T^{6} + 26910851011411 T^{8} + 79347180848522512 T^{10} +$$$$27\!\cdots\!98$$$$T^{12} +$$$$57\!\cdots\!68$$$$T^{14} +$$$$56\!\cdots\!21$$$$T^{16}$$)
$53$ ($$1 - 7960 T^{2} + 30066162 T^{4} - 62808228760 T^{6} + 62259690411361 T^{8}$$)($$1 - 7204 T^{2} + 26018214 T^{4} - 56843025124 T^{6} + 62259690411361 T^{8}$$)($$( 1 - 56 T + 2809 T^{2} )^{2}$$)($$( 1 - 52 T + 2809 T^{2} )^{2}$$)($$( 1 + 52 T + 2809 T^{2} )^{2}$$)($$( 1 + 56 T + 2809 T^{2} )^{2}$$)($$( 1 + 58 T + 8567 T^{2} + 320716 T^{3} + 24064703 T^{4} + 457647898 T^{5} + 22164361129 T^{6} )^{2}$$)($$( 1 - 58 T + 8567 T^{2} - 320716 T^{3} + 24064703 T^{4} - 457647898 T^{5} + 22164361129 T^{6} )^{2}$$)($$( 1 - 18 T + 10016 T^{2} - 126558 T^{3} + 40472766 T^{4} - 355501422 T^{5} + 79031057696 T^{6} - 398958500322 T^{7} + 62259690411361 T^{8} )^{2}$$)($$( 1 + 5492 T^{2} + 15934278 T^{4} + 43334521652 T^{6} + 62259690411361 T^{8} )^{2}$$)($$( 1 + 18 T + 10016 T^{2} + 126558 T^{3} + 40472766 T^{4} + 355501422 T^{5} + 79031057696 T^{6} + 398958500322 T^{7} + 62259690411361 T^{8} )^{2}$$)($$( 1 - 74 T + 2809 T^{2} )^{2}$$)($$( 1 - 47 T + 2809 T^{2} )^{2}$$)($$( 1 + 47 T + 2809 T^{2} )^{2}$$)($$( 1 + 74 T + 2809 T^{2} )^{2}$$)($$( 1 + 56 T + 2809 T^{2} )^{2}$$)($$( 1 - 56 T + 2809 T^{2} )^{2}$$)($$( 1 - 74 T + 2809 T^{2} )^{2}$$)($$( 1 - 47 T + 2809 T^{2} )^{2}$$)($$( 1 + 47 T + 2809 T^{2} )^{2}$$)($$( 1 + 74 T + 2809 T^{2} )^{2}$$)($$( 1 + 56 T + 2809 T^{2} )^{4}$$)($$( 1 + 925 T^{2} + 7890481 T^{4} )^{2}$$)($$( 1 + 925 T^{2} + 7890481 T^{4} )^{2}$$)($$( 1 - 56 T + 2809 T^{2} )^{4}$$)($$( 1 - 508 T^{2} + 14912358 T^{4} - 4008364348 T^{6} + 62259690411361 T^{8} )^{2}$$)($$( 1 - 508 T^{2} + 14912358 T^{4} - 4008364348 T^{6} + 62259690411361 T^{8} )^{2}$$)($$( 1 - 58 T + 8567 T^{2} - 320716 T^{3} + 24064703 T^{4} - 457647898 T^{5} + 22164361129 T^{6} )^{4}$$)($$( 1 + 58 T + 8567 T^{2} + 320716 T^{3} + 24064703 T^{4} + 457647898 T^{5} + 22164361129 T^{6} )^{4}$$)($$( 1 + 5492 T^{2} + 15934278 T^{4} + 43334521652 T^{6} + 62259690411361 T^{8} )^{4}$$)($$( 1 - 53 T )^{2}( 1 + 53 T )^{2}$$)($$( 1 - 53 T )^{2}( 1 + 53 T )^{2}$$)($$( 1 - 5537 T^{2} + 7890481 T^{4} )^{2}$$)($$( 1 - 7960 T^{2} + 30066162 T^{4} - 62808228760 T^{6} + 62259690411361 T^{8} )^{2}$$)
$59$ ($$1 - 6868 T^{2} + 24265878 T^{4} - 83222035348 T^{6} + 146830437604321 T^{8}$$)($$1 - 8110 T^{2} + 32295219 T^{4} - 98271797710 T^{6} + 146830437604321 T^{8}$$)($$( 1 - 59 T )^{2}( 1 + 59 T )^{2}$$)($$1 - 4079 T^{2} + 12117361 T^{4}$$)($$1 - 4079 T^{2} + 12117361 T^{4}$$)($$( 1 - 59 T )^{2}( 1 + 59 T )^{2}$$)($$1 - 7494 T^{2} + 32890719 T^{4} - 116096191700 T^{6} + 398548715672559 T^{8} - 1100347299406781574 T^{10} +$$$$17\!\cdots\!81$$$$T^{12}$$)($$1 - 7494 T^{2} + 32890719 T^{4} - 116096191700 T^{6} + 398548715672559 T^{8} - 1100347299406781574 T^{10} +$$$$17\!\cdots\!81$$$$T^{12}$$)($$1 - 18092 T^{2} + 151416802 T^{4} - 803198812400 T^{6} + 3155407101414283 T^{8} - 9732649964622076400 T^{10} +$$$$22\!\cdots\!42$$$$T^{12} -$$$$32\!\cdots\!52$$$$T^{14} +$$$$21\!\cdots\!41$$$$T^{16}$$)($$( 1 - 12580 T^{2} + 63740454 T^{4} - 152436401380 T^{6} + 146830437604321 T^{8} )^{2}$$)($$1 - 18092 T^{2} + 151416802 T^{4} - 803198812400 T^{6} + 3155407101414283 T^{8} - 9732649964622076400 T^{10} +$$$$22\!\cdots\!42$$$$T^{12} -$$$$32\!\cdots\!52$$$$T^{14} +$$$$21\!\cdots\!41$$$$T^{16}$$)($$1 - 156 T + 11593 T^{2} - 543036 T^{3} + 12117361 T^{4}$$)($$1 + 60 T + 4681 T^{2} + 208860 T^{3} + 12117361 T^{4}$$)($$1 + 60 T + 4681 T^{2} + 208860 T^{3} + 12117361 T^{4}$$)($$1 - 156 T + 11593 T^{2} - 543036 T^{3} + 12117361 T^{4}$$)($$( 1 - 59 T + 3481 T^{2} )( 1 + 59 T + 3481 T^{2} )$$)($$( 1 - 59 T + 3481 T^{2} )( 1 + 59 T + 3481 T^{2} )$$)($$1 + 156 T + 11593 T^{2} + 543036 T^{3} + 12117361 T^{4}$$)($$1 - 60 T + 4681 T^{2} - 208860 T^{3} + 12117361 T^{4}$$)($$1 - 60 T + 4681 T^{2} - 208860 T^{3} + 12117361 T^{4}$$)($$1 + 156 T + 11593 T^{2} + 543036 T^{3} + 12117361 T^{4}$$)($$( 1 - 59 T + 3481 T^{2} )^{2}( 1 + 59 T + 3481 T^{2} )^{2}$$)($$( 1 - 132 T + 9289 T^{2} - 459492 T^{3} + 12117361 T^{4} )^{2}$$)($$( 1 + 132 T + 9289 T^{2} + 459492 T^{3} + 12117361 T^{4} )^{2}$$)($$( 1 - 59 T + 3481 T^{2} )^{2}( 1 + 59 T + 3481 T^{2} )^{2}$$)($$1 + 6076 T^{2} + 12975610 T^{4} - 1777570256 T^{6} - 20949143941901 T^{8} - 21539460494814416 T^{10} +$$$$19\!\cdots\!10$$$$T^{12} +$$$$10\!\cdots\!56$$$$T^{14} +$$$$21\!\cdots\!41$$$$T^{16}$$)($$1 + 6076 T^{2} + 12975610 T^{4} - 1777570256 T^{6} - 20949143941901 T^{8} - 21539460494814416 T^{10} +$$$$19\!\cdots\!10$$$$T^{12} +$$$$10\!\cdots\!56$$$$T^{14} +$$$$21\!\cdots\!41$$$$T^{16}$$)($$1 + 7494 T^{2} + 23269317 T^{4} + 14290664786 T^{6} - 186774179935398 T^{8} - 1054613632918700418 T^{10} -$$$$43\!\cdots\!15$$$$T^{12} -$$$$12\!\cdots\!98$$$$T^{14} -$$$$27\!\cdots\!58$$$$T^{16} +$$$$25\!\cdots\!66$$$$T^{18} +$$$$50\!\cdots\!97$$$$T^{20} +$$$$19\!\cdots\!94$$$$T^{22} +$$$$31\!\cdots\!61$$$$T^{24}$$)($$1 + 7494 T^{2} + 23269317 T^{4} + 14290664786 T^{6} - 186774179935398 T^{8} - 1054613632918700418 T^{10} -$$$$43\!\cdots\!15$$$$T^{12} -$$$$12\!\cdots\!98$$$$T^{14} -$$$$27\!\cdots\!58$$$$T^{16} +$$$$25\!\cdots\!66$$$$T^{18} +$$$$50\!\cdots\!97$$$$T^{20} +$$$$19\!\cdots\!94$$$$T^{22} +$$$$31\!\cdots\!61$$$$T^{24}$$)($$( 1 + 12580 T^{2} + 94515946 T^{4} + 496982108560 T^{6} + 1998365109161395 T^{8} + 6022111619962710160 T^{10} +$$$$13\!\cdots\!66$$$$T^{12} +$$$$22\!\cdots\!80$$$$T^{14} +$$$$21\!\cdots\!41$$$$T^{16} )^{2}$$)($$( 1 - 59 T + 3481 T^{2} )( 1 + 59 T + 3481 T^{2} )$$)($$( 1 - 59 T + 3481 T^{2} )( 1 + 59 T + 3481 T^{2} )$$)($$1 + 6638 T^{2} + 31945683 T^{4} + 80435042318 T^{6} + 146830437604321 T^{8}$$)($$1 + 6868 T^{2} + 22903546 T^{4} + 213979408 T^{6} - 129566541263501 T^{8} + 2592865733302288 T^{10} +$$$$33\!\cdots\!66$$$$T^{12} +$$$$12\!\cdots\!08$$$$T^{14} +$$$$21\!\cdots\!41$$$$T^{16}$$)
$61$ ($$( 1 + 32 T + 5511 T^{2} + 119072 T^{3} + 13845841 T^{4} )^{2}$$)($$( 1 + 41 T + 7194 T^{2} + 152561 T^{3} + 13845841 T^{4} )^{2}$$)($$1 - 22 T - 3237 T^{2} - 81862 T^{3} + 13845841 T^{4}$$)($$( 1 + 16 T + 3721 T^{2} )^{2}$$)($$( 1 + 16 T + 3721 T^{2} )^{2}$$)($$1 - 22 T - 3237 T^{2} - 81862 T^{3} + 13845841 T^{4}$$)($$( 1 - 27 T + 6342 T^{2} - 99743 T^{3} + 23598582 T^{4} - 373837707 T^{5} + 51520374361 T^{6} )^{2}$$)($$( 1 - 27 T + 6342 T^{2} - 99743 T^{3} + 23598582 T^{4} - 373837707 T^{5} + 51520374361 T^{6} )^{2}$$)($$( 1 - 17 T + 3871 T^{2} - 95678 T^{3} + 31663708 T^{4} - 356017838 T^{5} + 53597250511 T^{6} - 875846364137 T^{7} + 191707312997281 T^{8} )^{2}$$)($$( 1 + 8 T + 4665 T^{2} + 29768 T^{3} + 13845841 T^{4} )^{4}$$)($$( 1 - 17 T + 3871 T^{2} - 95678 T^{3} + 31663708 T^{4} - 356017838 T^{5} + 53597250511 T^{6} - 875846364137 T^{7} + 191707312997281 T^{8} )^{2}$$)($$1 + 26 T - 3045 T^{2} + 96746 T^{3} + 13845841 T^{4}$$)($$1 - 64 T + 375 T^{2} - 238144 T^{3} + 13845841 T^{4}$$)($$1 - 64 T + 375 T^{2} - 238144 T^{3} + 13845841 T^{4}$$)($$1 + 26 T - 3045 T^{2} + 96746 T^{3} + 13845841 T^{4}$$)($$1 - 22 T - 3237 T^{2} - 81862 T^{3} + 13845841 T^{4}$$)($$1 - 22 T - 3237 T^{2} - 81862 T^{3} + 13845841 T^{4}$$)($$1 + 26 T - 3045 T^{2} + 96746 T^{3} + 13845841 T^{4}$$)($$1 - 64 T + 375 T^{2} - 238144 T^{3} + 13845841 T^{4}$$)($$1 - 64 T + 375 T^{2} - 238144 T^{3} + 13845841 T^{4}$$)($$1 + 26 T - 3045 T^{2} + 96746 T^{3} + 13845841 T^{4}$$)($$( 1 + 22 T + 3721 T^{2} )^{2}( 1 - 22 T - 3237 T^{2} - 81862 T^{3} + 13845841 T^{4} )$$)($$( 1 + 8 T - 3657 T^{2} + 29768 T^{3} + 13845841 T^{4} )^{2}$$)($$( 1 + 8 T - 3657 T^{2} + 29768 T^{3} + 13845841 T^{4} )^{2}$$)($$( 1 + 22 T + 3721 T^{2} )^{2}( 1 - 22 T - 3237 T^{2} - 81862 T^{3} + 13845841 T^{4} )$$)($$( 1 + 10 T - 7187 T^{2} - 1550 T^{3} + 38882428 T^{4} - 5767550 T^{5} - 99510059267 T^{6} + 515203743610 T^{7} + 191707312997281 T^{8} )^{2}$$)($$( 1 + 10 T - 7187 T^{2} - 1550 T^{3} + 38882428 T^{4} - 5767550 T^{5} - 99510059267 T^{6} + 515203743610 T^{7} + 191707312997281 T^{8} )^{2}$$)($$( 1 + 27 T - 5613 T^{2} - 28252 T^{3} + 13929321 T^{4} - 267915615 T^{5} - 46766410362 T^{6} - 996914003415 T^{7} + 192863163803961 T^{8} - 1455553616446972 T^{9} - 1076053147853738253 T^{10} + 19260258614897830227 T^{11} +$$$$26\!\cdots\!21$$$$T^{12} )^{2}$$)($$( 1 + 27 T - 5613 T^{2} - 28252 T^{3} + 13929321 T^{4} - 267915615 T^{5} - 46766410362 T^{6} - 996914003415 T^{7} + 192863163803961 T^{8} - 1455553616446972 T^{9} - 1076053147853738253 T^{10} + 19260258614897830227 T^{11} +$$$$26\!\cdots\!21$$$$T^{12} )^{2}$$)($$( 1 - 8 T - 4601 T^{2} + 22216 T^{3} + 7678240 T^{4} + 82665736 T^{5} - 63704714441 T^{6} - 412162994888 T^{7} + 191707312997281 T^{8} )^{4}$$)($$( 1 - 74 T + 3721 T^{2} )( 1 + 121 T + 3721 T^{2} )$$)($$( 1 - 47 T + 3721 T^{2} )( 1 + 121 T + 3721 T^{2} )$$)($$( 1 + 20 T - 3321 T^{2} + 74420 T^{3} + 13845841 T^{4} )^{2}$$)($$( 1 - 32 T - 4487 T^{2} + 61792 T^{3} + 12714976 T^{4} + 229928032 T^{5} - 62126288567 T^{6} - 1648651979552 T^{7} + 191707312997281 T^{8} )^{2}$$)
$67$ ($$( 1 - 10 T + 8760 T^{2} - 44890 T^{3} + 20151121 T^{4} )^{2}$$)($$( 1 + 116 T + 9669 T^{2} + 520724 T^{3} + 20151121 T^{4} )^{2}$$)($$( 1 - 67 T )^{2}( 1 + 67 T )^{2}$$)($$( 1 - 67 T + 4489 T^{2} )( 1 + 67 T + 4489 T^{2} )$$)($$( 1 - 67 T + 4489 T^{2} )( 1 + 67 T + 4489 T^{2} )$$)($$( 1 - 67 T )^{2}( 1 + 67 T )^{2}$$)($$1 - 12786 T^{2} + 95739519 T^{4} - 512264211836 T^{6} + 1929258631850799 T^{8} - 5191981325239211826 T^{10} +$$$$81\!\cdots\!61$$$$T^{12}$$)($$1 - 12786 T^{2} + 95739519 T^{4} - 512264211836 T^{6} + 1929258631850799 T^{8} - 5191981325239211826 T^{10} +$$$$81\!\cdots\!61$$$$T^{12}$$)($$1 - 25148 T^{2} + 302080258 T^{4} - 2289407522192 T^{6} + 12118574906350123 T^{8} - 46134127998001177232 T^{10} +$$$$12\!\cdots\!78$$$$T^{12} -$$$$20\!\cdots\!28$$$$T^{14} +$$$$16\!\cdots\!81$$$$T^{16}$$)($$( 1 - 12904 T^{2} + 75872814 T^{4} - 260030065384 T^{6} + 406067677556641 T^{8} )^{2}$$)($$1 - 25148 T^{2} + 302080258 T^{4} - 2289407522192 T^{6} + 12118574906350123 T^{8} - 46134127998001177232 T^{10} +$$$$12\!\cdots\!78$$$$T^{12} -$$$$20\!\cdots\!28$$$$T^{14} +$$$$16\!\cdots\!81$$$$T^{16}$$)($$1 - 12 T + 4537 T^{2} - 53868 T^{3} + 20151121 T^{4}$$)($$1 + 150 T + 11989 T^{2} + 673350 T^{3} + 20151121 T^{4}$$)($$1 - 150 T + 11989 T^{2} - 673350 T^{3} + 20151121 T^{4}$$)($$1 + 12 T + 4537 T^{2} + 53868 T^{3} + 20151121 T^{4}$$)($$( 1 - 67 T + 4489 T^{2} )( 1 + 67 T + 4489 T^{2} )$$)($$( 1 - 67 T + 4489 T^{2} )( 1 + 67 T + 4489 T^{2} )$$)($$1 + 12 T + 4537 T^{2} + 53868 T^{3} + 20151121 T^{4}$$)($$1 - 150 T + 11989 T^{2} - 673350 T^{3} + 20151121 T^{4}$$)($$1 + 150 T + 11989 T^{2} + 673350 T^{3} + 20151121 T^{4}$$)($$1 - 12 T + 4537 T^{2} - 53868 T^{3} + 20151121 T^{4}$$)($$( 1 - 67 T + 4489 T^{2} )^{2}( 1 + 67 T + 4489 T^{2} )^{2}$$)($$1 + 5078 T^{2} + 5634963 T^{4} + 102327392438 T^{6} + 406067677556641 T^{8}$$)($$1 + 5078 T^{2} + 5634963 T^{4} + 102327392438 T^{6} + 406067677556641 T^{8}$$)($$( 1 - 67 T + 4489 T^{2} )^{2}( 1 + 67 T + 4489 T^{2} )^{2}$$)($$( 1 + 114 T + 10553 T^{2} + 709194 T^{3} + 37996068 T^{4} + 3183571866 T^{5} + 212654779913 T^{6} + 10312255567266 T^{7} + 406067677556641 T^{8} )^{2}$$)($$( 1 - 114 T + 10553 T^{2} - 709194 T^{3} + 37996068 T^{4} - 3183571866 T^{5} + 212654779913 T^{6} - 10312255567266 T^{7} + 406067677556641 T^{8} )^{2}$$)($$1 + 12786 T^{2} + 67742277 T^{4} + 199597066262 T^{6} + 686986653965466 T^{8} + 4900908833643326682 T^{10} +$$$$27\!\cdots\!01$$$$T^{12} +$$$$98\!\cdots\!22$$$$T^{14} +$$$$27\!\cdots\!06$$$$T^{16} +$$$$16\!\cdots\!82$$$$T^{18} +$$$$11\!\cdots\!37$$$$T^{20} +$$$$42\!\cdots\!86$$$$T^{22} +$$$$66\!\cdots\!21$$$$T^{24}$$)($$1 + 12786 T^{2} + 67742277 T^{4} + 199597066262 T^{6} + 686986653965466 T^{8} + 4900908833643326682 T^{10} +$$$$27\!\cdots\!01$$$$T^{12} +$$$$98\!\cdots\!22$$$$T^{14} +$$$$27\!\cdots\!06$$$$T^{16} +$$$$16\!\cdots\!82$$$$T^{18} +$$$$11\!\cdots\!37$$$$T^{20} +$$$$42\!\cdots\!86$$$$T^{22} +$$$$66\!\cdots\!21$$$$T^{24}$$)($$( 1 + 12904 T^{2} + 90640402 T^{4} + 459002661088 T^{6} + 1995188263006819 T^{8} + 9249418162906279648 T^{10} +$$$$36\!\cdots\!82$$$$T^{12} +$$$$10\!\cdots\!44$$$$T^{14} +$$$$16\!\cdots\!81$$$$T^{16} )^{2}$$)($$( 1 - 122 T + 4489 T^{2} )( 1 + 109 T + 4489 T^{2} )$$)($$( 1 + 13 T + 4489 T^{2} )( 1 + 109 T + 4489 T^{2} )$$)($$( 1 + 14 T - 4293 T^{2} + 62846 T^{3} + 20151121 T^{4} )^{2}$$)($$( 1 + 10 T - 8660 T^{2} - 2180 T^{3} + 56137579 T^{4} - 9786020 T^{5} - 174508707860 T^{6} + 904583821690 T^{7} + 406067677556641 T^{8} )^{2}$$)
$71$ ($$1 - 7168 T^{2} + 21615810 T^{4} - 182150929408 T^{6} + 645753531245761 T^{8}$$)($$1 - 18616 T^{2} + 137194926 T^{4} - 473063853496 T^{6} + 645753531245761 T^{8}$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$1 - 21714 T^{2} + 225392559 T^{4} - 1424221410044 T^{6} + 5727603809081679 T^{8} - 14021892177470454354 T^{10} +$$$$16\!\cdots\!41$$$$T^{12}$$)($$1 - 21714 T^{2} + 225392559 T^{4} - 1424221410044 T^{6} + 5727603809081679 T^{8} - 14021892177470454354 T^{10} +$$$$16\!\cdots\!41$$$$T^{12}$$)($$1 - 12968 T^{2} + 137492380 T^{4} - 912038324888 T^{6} + 5454839368725190 T^{8} - 23176426971828216728 T^{10} +$$$$88\!\cdots\!80$$$$T^{12} -$$$$21\!\cdots\!88$$$$T^{14} +$$$$41\!\cdots\!21$$$$T^{16}$$)($$( 1 - 7312 T^{2} + 62463966 T^{4} - 185810211472 T^{6} + 645753531245761 T^{8} )^{2}$$)($$1 - 12968 T^{2} + 137492380 T^{4} - 912038324888 T^{6} + 5454839368725190 T^{8} - 23176426971828216728 T^{10} +$$$$88\!\cdots\!80$$$$T^{12} -$$$$21\!\cdots\!88$$$$T^{14} +$$$$41\!\cdots\!21$$$$T^{16}$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$( 1 - 71 T )^{4}( 1 + 71 T )^{4}$$)($$( 1 - 6194 T^{2} + 25411681 T^{4} )^{2}$$)($$( 1 - 6194 T^{2} + 25411681 T^{4} )^{2}$$)($$( 1 - 71 T )^{4}( 1 + 71 T )^{4}$$)($$( 1 - 292 T^{2} + 42446598 T^{4} - 7420210852 T^{6} + 645753531245761 T^{8} )^{2}$$)($$( 1 - 292 T^{2} + 42446598 T^{4} - 7420210852 T^{6} + 645753531245761 T^{8} )^{2}$$)($$( 1 - 21714 T^{2} + 225392559 T^{4} - 1424221410044 T^{6} + 5727603809081679 T^{8} - 14021892177470454354 T^{10} +$$$$16\!\cdots\!41$$$$T^{12} )^{2}$$)($$( 1 - 21714 T^{2} + 225392559 T^{4} - 1424221410044 T^{6} + 5727603809081679 T^{8} - 14021892177470454354 T^{10} +$$$$16\!\cdots\!41$$$$T^{12} )^{2}$$)($$( 1 - 7312 T^{2} + 62463966 T^{4} - 185810211472 T^{6} + 645753531245761 T^{8} )^{4}$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$( 1 - 71 T )^{2}( 1 + 71 T )^{2}$$)($$( 1 + 5794 T^{2} + 25411681 T^{4} )^{2}$$)($$( 1 - 7168 T^{2} + 21615810 T^{4} - 182150929408 T^{6} + 645753531245761 T^{8} )^{2}$$)
$73$ ($$( 1 + 128 T + 12567 T^{2} + 682112 T^{3} + 28398241 T^{4} )^{2}$$)($$( 1 - 43 T + 10452 T^{2} - 229147 T^{3} + 28398241 T^{4} )^{2}$$)($$1 + 110 T + 6771 T^{2} + 586190 T^{3} + 28398241 T^{4}$$)($$( 1 + 25 T + 5329 T^{2} )^{2}$$)($$( 1 + 25 T + 5329 T^{2} )^{2}$$)($$1 + 110 T + 6771 T^{2} + 586190 T^{3} + 28398241 T^{4}$$)($$( 1 + 39 T + 7086 T^{2} - 32189 T^{3} + 37761294 T^{4} + 1107531399 T^{5} + 151334226289 T^{6} )^{2}$$)($$( 1 + 39 T + 7086 T^{2} - 32189 T^{3} + 37761294 T^{4} + 1107531399 T^{5} + 151334226289 T^{6} )^{2}$$)($$( 1 - 29 T + 7774 T^{2} - 620747 T^{3} + 46170850 T^{4} - 3307960763 T^{5} + 220767925534 T^{6} - 4388692562381 T^{7} + 806460091894081 T^{8} )^{2}$$)($$( 1 - 94 T + 12639 T^{2} - 500926 T^{3} + 28398241 T^{4} )^{4}$$)($$( 1 - 29 T + 7774 T^{2} - 620747 T^{3} + 46170850 T^{4} - 3307960763 T^{5} + 220767925534 T^{6} - 4388692562381 T^{7} + 806460091894081 T^{8} )^{2}$$)($$( 1 + 46 T + 5329 T^{2} )^{2}$$)($$( 1 + 55 T + 5329 T^{2} )^{2}$$)($$( 1 + 55 T + 5329 T^{2} )^{2}$$)($$( 1 + 46 T + 5329 T^{2} )^{2}$$)($$( 1 - 110 T + 5329 T^{2} )^{2}$$)($$( 1 - 110 T + 5329 T^{2} )^{2}$$)($$( 1 + 46 T + 5329 T^{2} )^{2}$$)($$( 1 + 55 T + 5329 T^{2} )^{2}$$)($$( 1 + 55 T + 5329 T^{2} )^{2}$$)($$( 1 + 46 T + 5329 T^{2} )^{2}$$)($$( 1 + 110 T + 6771 T^{2} + 586190 T^{3} + 28398241 T^{4} )^{2}$$)($$( 1 + 19 T + 5329 T^{2} )^{4}$$)($$( 1 + 19 T + 5329 T^{2} )^{4}$$)($$( 1 + 110 T + 6771 T^{2} + 586190 T^{3} + 28398241 T^{4} )^{2}$$)($$( 1 - 58 T + 10779 T^{2} - 309082 T^{3} + 28398241 T^{4} )^{4}$$)($$( 1 - 58 T + 10779 T^{2} - 309082 T^{3} + 28398241 T^{4} )^{4}$$)($$( 1 + 39 T + 7086 T^{2} - 32189 T^{3} + 37761294 T^{4} + 1107531399 T^{5} + 151334226289 T^{6} )^{4}$$)($$( 1 + 39 T + 7086 T^{2} - 32189 T^{3} + 37761294 T^{4} + 1107531399 T^{5} + 151334226289 T^{6} )^{4}$$)($$( 1 - 94 T + 12639 T^{2} - 500926 T^{3} + 28398241 T^{4} )^{8}$$)($$( 1 - 143 T + 5329 T^{2} )^{2}$$)($$( 1 + 46 T + 5329 T^{2} )^{2}$$)($$( 1 - 89 T + 5329 T^{2} )^{4}$$)($$( 1 + 128 T + 12567 T^{2} + 682112 T^{3} + 28398241 T^{4} )^{4}$$)
$79$ ($$( 1 - 154 T + 17088 T^{2} - 961114 T^{3} + 38950081 T^{4} )^{2}$$)($$( 1 + 83 T + 12348 T^{2} + 518003 T^{3} + 38950081 T^{4} )^{2}$$)($$( 1 - 79 T )^{2}( 1 + 79 T )^{2}$$)($$1 - 11714 T^{2} + 38950081 T^{4}$$)($$1 - 11714 T^{2} + 38950081 T^{4}$$)($$( 1 - 79 T )^{2}( 1 + 79 T )^{2}$$)($$1 - 29682 T^{2} + 402704079 T^{4} - 3200381370428 T^{6} + 15685356496080399 T^{8} - 45030823695646543602 T^{10} +$$$$59\!\cdots\!41$$$$T^{12}$$)($$1 - 29682 T^{2} + 402704079 T^{4} - 3200381370428 T^{6} + 15685356496080399 T^{8} - 45030823695646543602 T^{10} +$$$$59\!\cdots\!41$$$$T^{12}$$)($$1 - 23147 T^{2} + 207724873 T^{4} - 836021205386 T^{6} + 2483172469984678 T^{8} - 32563093667502336266 T^{10} +$$$$31\!\cdots\!53$$$$T^{12} -$$$$13\!\cdots\!27$$$$T^{14} +$$$$23\!\cdots\!21$$$$T^{16}$$)($$( 1 - 15496 T^{2} + 116442894 T^{4} - 603570455176 T^{6} + 1517108809906561 T^{8} )^{2}$$)($$1 - 23147 T^{2} + 207724873 T^{4} - 836021205386 T^{6} + 2483172469984678 T^{8} - 32563093667502336266 T^{10} +$$$$31\!\cdots\!53$$$$T^{12} -$$$$13\!\cdots\!27$$$$T^{14} +$$$$23\!\cdots\!21$$$$T^{16}$$)($$1 + 204 T + 20113 T^{2} + 1273164 T^{3} + 38950081 T^{4}$$)($$1 - 12 T + 6289 T^{2} - 74892 T^{3} + 38950081 T^{4}$$)($$1 + 12 T + 6289 T^{2} + 74892 T^{3} + 38950081 T^{4}$$)($$1 - 204 T + 20113 T^{2} - 1273164 T^{3} + 38950081 T^{4}$$)($$( 1 - 79 T + 6241 T^{2} )( 1 + 79 T + 6241 T^{2} )$$)($$( 1 - 79 T + 6241 T^{2} )( 1 + 79 T + 6241 T^{2} )$$)($$1 - 204 T + 20113 T^{2} - 1273164 T^{3} + 38950081 T^{4}$$)($$1 + 12 T + 6289 T^{2} + 74892 T^{3} + 38950081 T^{4}$$)($$1 - 12 T + 6289 T^{2} - 74892 T^{3} + 38950081 T^{4}$$)($$1 + 204 T + 20113 T^{2} + 1273164 T^{3} + 38950081 T^{4}$$)($$( 1 - 79 T + 6241 T^{2} )^{2}( 1 + 79 T + 6241 T^{2} )^{2}$$)($$1 + 9986 T^{2} + 60770115 T^{4} + 388955508866 T^{6} + 1517108809906561 T^{8}$$)($$1 + 9986 T^{2} + 60770115 T^{4} + 388955508866 T^{6} + 1517108809906561 T^{8}$$)($$( 1 - 79 T + 6241 T^{2} )^{2}( 1 + 79 T + 6241 T^{2} )^{2}$$)($$( 1 + 330 T + 54917 T^{2} + 6143610 T^{3} + 534190908 T^{4} + 38342270010 T^{5} + 2139021598277 T^{6} + 80218860321930 T^{7} + 1517108809906561 T^{8} )^{2}$$)($$( 1 - 330 T + 54917 T^{2} - 6143610 T^{3} + 534190908 T^{4} - 38342270010 T^{5} + 2139021598277 T^{6} - 80218860321930 T^{7} + 1517108809906561 T^{8} )^{2}$$)($$1 + 29682 T^{2} + 478317045 T^{4} + 5552299732022 T^{6} + 51491498910113946 T^{8} +$$$$40\!\cdots\!78$$$$T^{10} +$$$$27\!\cdots\!81$$$$T^{12} +$$$$15\!\cdots\!18$$$$T^{14} +$$$$78\!\cdots\!06$$$$T^{16} +$$$$32\!\cdots\!02$$$$T^{18} +$$$$11\!\cdots\!45$$$$T^{20} +$$$$26\!\cdots\!82$$$$T^{22} +$$$$34\!\cdots\!81$$$$T^{24}$$)($$1 + 29682 T^{2} + 478317045 T^{4} + 5552299732022 T^{6} + 51491498910113946 T^{8} +$$$$40\!\cdots\!78$$$$T^{10} +$$$$27\!\cdots\!81$$$$T^{12} +$$$$15\!\cdots\!18$$$$T^{14} +$$$$78\!\cdots\!06$$$$T^{16} +$$$$32\!\cdots\!02$$$$T^{18} +$$$$11\!\cdots\!45$$$$T^{20} +$$$$26\!\cdots\!82$$$$T^{22} +$$$$34\!\cdots\!81$$$$T^{24}$$)($$( 1 + 15496 T^{2} + 123683122 T^{4} + 597258175072 T^{6} + 2688910979781379 T^{8} + 23263254296966580832 T^{10} +$$$$18\!\cdots\!42$$$$T^{12} +$$$$91\!\cdots\!36$$$$T^{14} +$$$$23\!\cdots\!21$$$$T^{16} )^{2}$$)($$( 1 - 131 T + 6241 T^{2} )( 1 + 142 T + 6241 T^{2} )$$)($$( 1 - 131 T + 6241 T^{2} )( 1 - 11 T + 6241 T^{2} )$$)($$( 1 + 110 T + 5859 T^{2} + 686510 T^{3} + 38950081 T^{4} )^{2}$$)($$( 1 + 154 T + 6628 T^{2} + 709324 T^{3} + 105038107 T^{4} + 4426891084 T^{5} + 258161136868 T^{6} + 37435468150234 T^{7} + 1517108809906561 T^{8} )^{2}$$)
$83$ ($$1 - 340 T^{2} - 86452986 T^{4} - 16135829140 T^{6} + 2252292232139041 T^{8}$$)($$1 - 26017 T^{2} + 263650560 T^{4} - 1234723137457 T^{6} + 2252292232139041 T^{8}$$)($$( 1 - 83 T )^{2}( 1 + 83 T )^{2}$$)($$1 - 12578 T^{2} + 47458321 T^{4}$$)($$1 - 12578 T^{2} + 47458321 T^{4}$$)($$( 1 - 83 T )^{2}( 1 + 83 T )^{2}$$)($$1 - 6438 T^{2} + 91575999 T^{4} - 403734732692 T^{6} + 4346043156437679 T^{8} - 14500257390511145958 T^{10} +$$$$10\!\cdots\!61$$$$T^{12}$$)($$1 - 6438 T^{2} + 91575999 T^{4} - 403734732692 T^{6} + 4346043156437679 T^{8} - 14500257390511145958 T^{10} +$$$$10\!\cdots\!61$$$$T^{12}$$)($$1 - 17795 T^{2} + 288209353 T^{4} - 2684318937722 T^{6} + 22778145105251062 T^{8} -$$$$12\!\cdots\!62$$$$T^{10} +$$$$64\!\cdots\!73$$$$T^{12} -$$$$19\!\cdots\!95$$$$T^{14} +$$$$50\!\cdots\!81$$$$T^{16}$$)($$( 1 - 26452 T^{2} + 269840070 T^{4} - 1255367507092 T^{6} + 2252292232139041 T^{8} )^{2}$$)($$1 - 17795 T^{2} + 288209353 T^{4} - 2684318937722 T^{6} + 22778145105251062 T^{8} -$$$$12\!\cdots\!62$$$$T^{10} +$$$$64\!\cdots\!73$$$$T^{12} -$$$$19\!\cdots\!95$$$$T^{14} +$$$$50\!\cdots\!81$$$$T^{16}$$)($$1 - 84 T + 9241 T^{2} - 578676 T^{3} + 47458321 T^{4}$$)($$1 + 51 T + 7756 T^{2} + 351339 T^{3} + 47458321 T^{4}$$)($$1 + 51 T + 7756 T^{2} + 351339 T^{3} + 47458321 T^{4}$$)($$1 - 84 T + 9241 T^{2} - 578676 T^{3} + 47458321 T^{4}$$)($$( 1 - 83 T + 6889 T^{2} )( 1 + 83 T + 6889 T^{2} )$$)($$( 1 - 83 T + 6889 T^{2} )( 1 + 83 T + 6889 T^{2} )$$)($$1 + 84 T + 9241 T^{2} + 578676 T^{3} + 47458321 T^{4}$$)($$1 - 51 T + 7756 T^{2} - 351339 T^{3} + 47458321 T^{4}$$)($$1 - 51 T + 7756 T^{2} - 351339 T^{3} + 47458321 T^{4}$$)($$1 + 84 T + 9241 T^{2} + 578676 T^{3} + 47458321 T^{4}$$)($$( 1 - 83 T + 6889 T^{2} )^{2}( 1 + 83 T + 6889 T^{2} )^{2}$$)($$( 1 + 201 T + 20356 T^{2} + 1384689 T^{3} + 47458321 T^{4} )^{2}$$)($$( 1 - 201 T + 20356 T^{2} - 1384689 T^{3} + 47458321 T^{4} )^{2}$$)($$( 1 - 83 T + 6889 T^{2} )^{2}( 1 + 83 T + 6889 T^{2} )^{2}$$)($$1 + 26116 T^{2} + 416905450 T^{4} + 4445553374224 T^{6} + 35678198362101619 T^{8} +$$$$21\!\cdots\!04$$$$T^{10} +$$$$93\!\cdots\!50$$$$T^{12} +$$$$27\!\cdots\!76$$$$T^{14} +$$$$50\!\cdots\!81$$$$T^{16}$$)($$1 + 26116 T^{2} + 416905450 T^{4} + 4445553374224 T^{6} + 35678198362101619 T^{8} +$$$$21\!\cdots\!04$$$$T^{10} +$$$$93\!\cdots\!50$$$$T^{12} +$$$$27\!\cdots\!76$$$$T^{14} +$$$$50\!\cdots\!81$$$$T^{16}$$)($$1 + 6438 T^{2} - 50128155 T^{4} - 217903183822 T^{6} + 1440876227339226 T^{8} - 4486982814512549538 T^{10} -$$$$11\!\cdots\!39$$$$T^{12} -$$$$21\!\cdots\!98$$$$T^{14} +$$$$32\!\cdots\!66$$$$T^{16} -$$$$23\!\cdots\!42$$$$T^{18} -$$$$25\!\cdots\!55$$$$T^{20} +$$$$15\!\cdots\!38$$$$T^{22} +$$$$11\!\cdots\!21$$$$T^{24}$$)($$1 + 6438 T^{2} - 50128155 T^{4} - 217903183822 T^{6} + 1440876227339226 T^{8} - 4486982814512549538 T^{10} -$$$$11\!\cdots\!39$$$$T^{12} -$$$$21\!\cdots\!98$$$$T^{14} +$$$$32\!\cdots\!66$$$$T^{16} -$$$$23\!\cdots\!42$$$$T^{18} -$$$$25\!\cdots\!55$$$$T^{20} +$$$$15\!\cdots\!38$$$$T^{22} +$$$$11\!\cdots\!21$$$$T^{24}$$)($$( 1 + 26452 T^{2} + 429868234 T^{4} + 4627074517456 T^{6} + 37354389847868275 T^{8} +$$$$21\!\cdots\!76$$$$T^{10} +$$$$96\!\cdots\!94$$$$T^{12} +$$$$28\!\cdots\!72$$$$T^{14} +$$$$50\!\cdots\!81$$$$T^{16} )^{2}$$)($$( 1 - 83 T + 6889 T^{2} )( 1 + 83 T + 6889 T^{2} )$$)($$( 1 - 83 T + 6889 T^{2} )( 1 + 83 T + 6889 T^{2} )$$)($$1 + 13049 T^{2} + 122818080 T^{4} + 619283630729 T^{6} + 2252292232139041 T^{8}$$)($$1 + 340 T^{2} + 86568586 T^{4} - 61665673520 T^{6} + 5216340374269555 T^{8} - 2926549328593359920 T^{10} +$$$$19\!\cdots\!26$$$$T^{12} +$$$$36\!\cdots\!40$$$$T^{14} +$$$$50\!\cdots\!81$$$$T^{16}$$)
$89$ ($$1 - 19120 T^{2} + 179727999 T^{4} - 1199631647920 T^{6} + 3936588805702081 T^{8}$$)($$1 - 6916 T^{2} + 69013446 T^{4} - 433925338756 T^{6} + 3936588805702081 T^{8}$$)($$1 - 160 T + 17679 T^{2} - 1267360 T^{3} + 62742241 T^{4}$$)($$( 1 + 2 T + 7921 T^{2} )^{2}$$)($$( 1 - 2 T + 7921 T^{2} )^{2}$$)($$1 + 160 T + 17679 T^{2} + 1267360 T^{3} + 62742241 T^{4}$$)($$( 1 - 125 T + 19286 T^{2} - 1872473 T^{3} + 152764406 T^{4} - 7842780125 T^{5} + 496981290961 T^{6} )^{2}$$)($$( 1 + 125 T + 19286 T^{2} + 1872473 T^{3} + 152764406 T^{4} + 7842780125 T^{5} + 496981290961 T^{6} )^{2}$$)($$( 1 - 96 T + 27716 T^{2} - 1940016 T^{3} + 308634966 T^{4} - 15366866736 T^{5} + 1738963951556 T^{6} - 47710203932256 T^{7} + 3936588805702081 T^{8} )^{2}$$)($$( 1 + 15758 T^{2} + 176527923 T^{4} + 988692233678 T^{6} + 3936588805702081 T^{8} )^{2}$$)($$( 1 + 96 T + 27716 T^{2} + 1940016 T^{3} + 308634966 T^{4} + 15366866736 T^{5} + 1738963951556 T^{6} + 47710203932256 T^{7} + 3936588805702081 T^{8} )^{2}$$)($$( 1 + 82 T + 7921 T^{2} )^{2}$$)($$( 1 + 10 T + 7921 T^{2} )^{2}$$)($$( 1 - 10 T + 7921 T^{2} )^{2}$$)($$( 1 - 82 T + 7921 T^{2} )^{2}$$)($$( 1 - 160 T + 7921 T^{2} )^{2}$$)($$( 1 + 160 T + 7921 T^{2} )^{2}$$)($$( 1 + 82 T + 7921 T^{2} )^{2}$$)($$( 1 + 10 T + 7921 T^{2} )^{2}$$)($$( 1 - 10 T + 7921 T^{2} )^{2}$$)($$( 1 - 82 T + 7921 T^{2} )^{2}$$)($$( 1 + 160 T + 17679 T^{2} + 1267360 T^{3} + 62742241 T^{4} )^{2}$$)($$( 1 + 9550 T^{2} + 62742241 T^{4} )^{2}$$)($$( 1 + 9550 T^{2} + 62742241 T^{4} )^{2}$$)($$( 1 - 160 T + 17679 T^{2} - 1267360 T^{3} + 62742241 T^{4} )^{2}$$)($$( 1 + 30668 T^{2} + 360580758 T^{4} + 1924179046988 T^{6} + 3936588805702081 T^{8} )^{2}$$)($$( 1 + 30668 T^{2} + 360580758 T^{4} + 1924179046988 T^{6} + 3936588805702081 T^{8} )^{2}$$)($$( 1 + 125 T + 19286 T^{2} + 1872473 T^{3} + 152764406 T^{4} + 7842780125 T^{5} + 496981290961 T^{6} )^{4}$$)($$( 1 - 125 T + 19286 T^{2} - 1872473 T^{3} + 152764406 T^{4} - 7842780125 T^{5} + 496981290961 T^{6} )^{4}$$)($$( 1 + 15758 T^{2} + 176527923 T^{4} + 988692233678 T^{6} + 3936588805702081 T^{8} )^{4}$$)($$( 1 - 89 T )^{2}( 1 + 89 T )^{2}$$)($$( 1 - 89 T )^{2}( 1 + 89 T )^{2}$$)($$( 1 - 15518 T^{2} + 62742241 T^{4} )^{2}$$)($$( 1 - 19120 T^{2} + 179727999 T^{4} - 1199631647920 T^{6} + 3936588805702081 T^{8} )^{2}$$)
$97$ ($$( 1 + 80 T + 7350 T^{2} + 752720 T^{3} + 88529281 T^{4} )^{2}$$)($$( 1 - 196 T + 28125 T^{2} - 1844164 T^{3} + 88529281 T^{4} )^{2}$$)($$( 1 + 130 T + 9409 T^{2} )^{2}$$)($$( 1 + 43 T + 9409 T^{2} )^{2}$$)($$( 1 + 43 T + 9409 T^{2} )^{2}$$)($$( 1 + 130 T + 9409 T^{2} )^{2}$$)($$( 1 + 102 T + 23727 T^{2} + 1550164 T^{3} + 223247343 T^{4} + 9029986662 T^{5} + 832972004929 T^{6} )^{2}$$)($$( 1 + 102 T + 23727 T^{2} + 1550164 T^{3} + 223247343 T^{4} + 9029986662 T^{5} + 832972004929 T^{6} )^{2}$$)($$( 1 - 74 T + 35344 T^{2} - 2077892 T^{3} + 488109505 T^{4} - 19550885828 T^{5} + 3128978907664 T^{6} - 61639928364746 T^{7} + 7837433594376961 T^{8} )^{2}$$)($$( 1 - 232 T + 32046 T^{2} - 2182888 T^{3} + 88529281 T^{4} )^{4}$$)($$( 1 - 74 T + 35344 T^{2} - 2077892 T^{3} + 488109505 T^{4} - 19550885828 T^{5} + 3128978907664 T^{6} - 61639928364746 T^{7} + 7837433594376961 T^{8} )^{2}$$)($$( 1 - 167 T + 9409 T^{2} )( 1 + 169 T + 9409 T^{2} )$$)($$1 - 25 T - 8784 T^{2} - 235225 T^{3} + 88529281 T^{4}$$)($$1 - 25 T - 8784 T^{2} - 235225 T^{3} + 88529281 T^{4}$$)($$( 1 - 167 T + 9409 T^{2} )( 1 + 169 T + 9409 T^{2} )$$)($$1 - 130 T + 7491 T^{2} - 1223170 T^{3} + 88529281 T^{4}$$)($$1 - 130 T + 7491 T^{2} - 1223170 T^{3} + 88529281 T^{4}$$)($$( 1 - 167 T + 9409 T^{2} )( 1 + 169 T + 9409 T^{2} )$$)($$1 - 25 T - 8784 T^{2} - 235225 T^{3} + 88529281 T^{4}$$)($$1 - 25 T - 8784 T^{2} - 235225 T^{3} + 88529281 T^{4}$$)($$( 1 - 167 T + 9409 T^{2} )( 1 + 169 T + 9409 T^{2} )$$)($$( 1 - 130 T + 7491 T^{2} - 1223170 T^{3} + 88529281 T^{4} )^{2}$$)($$( 1 + 119 T + 4752 T^{2} + 1119671 T^{3} + 88529281 T^{4} )^{2}$$)($$( 1 + 119 T + 4752 T^{2} + 1119671 T^{3} + 88529281 T^{4} )^{2}$$)($$( 1 - 130 T + 7491 T^{2} - 1223170 T^{3} + 88529281 T^{4} )^{2}$$)($$( 1 - 62 T - 4415 T^{2} + 654658 T^{3} - 56486396 T^{4} + 6159677122 T^{5} - 390856775615 T^{6} - 51644264305598 T^{7} + 7837433594376961 T^{8} )^{2}$$)($$( 1 - 62 T - 4415 T^{2} + 654658 T^{3} - 56486396 T^{4} + 6159677122 T^{5} - 390856775615 T^{6} - 51644264305598 T^{7} + 7837433594376961 T^{8} )^{2}$$)($$( 1 - 102 T - 13323 T^{2} + 680174 T^{3} + 181606458 T^{4} - 268269918 T^{5} - 2149095910131 T^{6} - 2524151658462 T^{7} + 16077489151696698 T^{8} + 566565900480577646 T^{9} -$$$$10\!\cdots\!03$$$$T^{10} -$$$$75\!\cdots\!98$$$$T^{11} +$$$$69\!\cdots\!41$$$$T^{12} )^{2}$$)($$( 1 - 102 T - 13323 T^{2} + 680174 T^{3} + 181606458 T^{4} - 268269918 T^{5} - 2149095910131 T^{6} - 2524151658462 T^{7} + 16077489151696698 T^{8} + 566565900480577646 T^{9} -$$$$10\!\cdots\!03$$$$T^{10} -$$$$75\!\cdots\!98$$$$T^{11} +$$$$69\!\cdots\!41$$$$T^{12} )^{2}$$)($$( 1 + 232 T + 21778 T^{2} + 3068896 T^{3} + 431986819 T^{4} + 28875242464 T^{5} + 1927990681618 T^{6} + 193249505143528 T^{7} + 7837433594376961 T^{8} )^{4}$$)($$( 1 - 167 T + 9409 T^{2} )( 1 - 2 T + 9409 T^{2} )$$)($$( 1 - 167 T + 9409 T^{2} )( 1 + 169 T + 9409 T^{2} )$$)($$( 1 + 11 T - 9288 T^{2} + 103499 T^{3} + 88529281 T^{4} )^{2}$$)($$( 1 - 80 T - 950 T^{2} + 917440 T^{3} - 94724381 T^{4} + 8632192960 T^{5} - 84102816950 T^{6} - 66637760394320 T^{7} + 7837433594376961 T^{8} )^{2}$$)