Properties

Label 320.2
Level 320
Weight 2
Dimension 1518
Nonzero newspaces 14
Newform subspaces 42
Sturm bound 12288
Trace bound 12

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Defining parameters

Level: \( N \) = \( 320\( 320 = 2^{6} \cdot 5 \) \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 14 \)
Newform subspaces: \( 42 \)
Sturm bound: \(12288\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(320))\).

Total New Old
Modular forms 3360 1650 1710
Cusp forms 2785 1518 1267
Eisenstein series 575 132 443

Trace form

\( 1518q - 16q^{2} - 12q^{3} - 16q^{4} - 24q^{5} - 48q^{6} - 8q^{7} - 16q^{8} - 14q^{9} + O(q^{10}) \) \( 1518q - 16q^{2} - 12q^{3} - 16q^{4} - 24q^{5} - 48q^{6} - 8q^{7} - 16q^{8} - 14q^{9} - 24q^{10} - 28q^{11} - 16q^{12} - 16q^{14} - 12q^{15} - 48q^{16} - 12q^{17} - 16q^{18} + 4q^{19} - 24q^{20} - 56q^{21} - 32q^{22} - 8q^{23} - 96q^{24} - 46q^{25} - 128q^{26} - 24q^{27} - 96q^{28} - 48q^{29} - 104q^{30} - 80q^{31} - 96q^{32} - 64q^{33} - 96q^{34} - 20q^{35} - 208q^{36} - 32q^{37} - 96q^{38} - 16q^{39} - 64q^{40} - 60q^{41} - 96q^{42} + 12q^{43} - 32q^{44} - 20q^{45} - 48q^{46} + 24q^{47} - 16q^{48} - 10q^{49} - 88q^{51} + 80q^{52} + 32q^{53} + 112q^{54} - 80q^{55} + 64q^{56} - 32q^{57} + 128q^{58} - 148q^{59} + 72q^{60} - 32q^{61} + 48q^{62} - 200q^{63} + 176q^{64} - 96q^{65} + 112q^{66} - 236q^{67} + 80q^{68} - 88q^{69} + 72q^{70} - 224q^{71} + 128q^{72} - 84q^{73} + 96q^{74} - 176q^{75} + 80q^{76} - 120q^{77} + 32q^{78} - 144q^{79} - 64q^{80} - 218q^{81} - 176q^{82} - 92q^{83} - 240q^{84} - 128q^{85} - 256q^{86} - 120q^{87} - 176q^{88} - 180q^{89} - 168q^{90} - 88q^{91} - 320q^{92} - 192q^{93} - 208q^{94} - 84q^{95} - 320q^{96} - 124q^{97} - 288q^{98} - 132q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)

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
320.2.a \(\chi_{320}(1, \cdot)\) 320.2.a.a 1 1
320.2.a.b 1
320.2.a.c 1
320.2.a.d 1
320.2.a.e 1
320.2.a.f 1
320.2.a.g 2
320.2.c \(\chi_{320}(129, \cdot)\) 320.2.c.a 2 1
320.2.c.b 2
320.2.c.c 2
320.2.c.d 4
320.2.d \(\chi_{320}(161, \cdot)\) 320.2.d.a 4 1
320.2.d.b 4
320.2.f \(\chi_{320}(289, \cdot)\) 320.2.f.a 4 1
320.2.f.b 8
320.2.j \(\chi_{320}(47, \cdot)\) 320.2.j.a 2 2
320.2.j.b 18
320.2.l \(\chi_{320}(81, \cdot)\) 320.2.l.a 16 2
320.2.n \(\chi_{320}(63, \cdot)\) 320.2.n.a 2 2
320.2.n.b 2
320.2.n.c 2
320.2.n.d 2
320.2.n.e 2
320.2.n.f 2
320.2.n.g 2
320.2.n.h 2
320.2.n.i 4
320.2.o \(\chi_{320}(223, \cdot)\) 320.2.o.a 2 2
320.2.o.b 2
320.2.o.c 2
320.2.o.d 2
320.2.o.e 8
320.2.o.f 8
320.2.q \(\chi_{320}(49, \cdot)\) 320.2.q.a 2 2
320.2.q.b 2
320.2.q.c 16
320.2.s \(\chi_{320}(207, \cdot)\) 320.2.s.a 2 2
320.2.s.b 18
320.2.u \(\chi_{320}(87, \cdot)\) None 0 4
320.2.x \(\chi_{320}(41, \cdot)\) None 0 4
320.2.z \(\chi_{320}(9, \cdot)\) None 0 4
320.2.ba \(\chi_{320}(7, \cdot)\) None 0 4
320.2.bd \(\chi_{320}(43, \cdot)\) 320.2.bd.a 368 8
320.2.be \(\chi_{320}(21, \cdot)\) 320.2.be.a 256 8
320.2.bf \(\chi_{320}(29, \cdot)\) 320.2.bf.a 368 8
320.2.bj \(\chi_{320}(3, \cdot)\) 320.2.bj.a 368 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(320))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(320)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + 2 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( ( 1 - 3 T^{2} )^{2} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( ( 1 - 2 T + 2 T^{2} - 6 T^{3} + 9 T^{4} )( 1 + 2 T + 2 T^{2} + 6 T^{3} + 9 T^{4} ) \))(\( 1 - 4 T^{2} + 10 T^{4} - 36 T^{6} + 81 T^{8} \))(\( 1 - 4 T^{2} + 10 T^{4} - 36 T^{6} + 81 T^{8} \))(\( ( 1 + 3 T^{2} )^{4} \))(\( ( 1 + 9 T^{4} )^{4} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 - 22 T^{2} + 249 T^{4} - 1952 T^{6} + 12020 T^{8} - 62040 T^{10} + 277684 T^{12} - 1097312 T^{14} + 3868246 T^{16} - 12237572 T^{18} + 34814214 T^{20} - 88882272 T^{22} + 202431636 T^{24} - 407044440 T^{26} + 709768980 T^{28} - 1037372832 T^{30} + 1190959281 T^{32} - 947027862 T^{34} + 387420489 T^{36} \))(\( 1 + 8 T^{3} - 8 T^{4} + 8 T^{5} + 32 T^{6} - 16 T^{7} + 4 T^{8} + 16 T^{9} + 160 T^{10} - 664 T^{11} + 424 T^{12} - 88 T^{13} - 3904 T^{14} + 32 T^{15} - 7802 T^{16} + 96 T^{17} - 35136 T^{18} - 2376 T^{19} + 34344 T^{20} - 161352 T^{21} + 116640 T^{22} + 34992 T^{23} + 26244 T^{24} - 314928 T^{25} + 1889568 T^{26} + 1417176 T^{27} - 4251528 T^{28} + 12754584 T^{29} + 43046721 T^{32} \))(\( 1 + 4 T + 8 T^{2} + 12 T^{3} + 9 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 6 T^{3} + 9 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 6 T^{3} + 9 T^{4} \))(\( 1 + 9 T^{4} \))(\( 1 + 9 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 6 T^{3} + 9 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 6 T^{3} + 9 T^{4} \))(\( 1 - 4 T + 8 T^{2} - 12 T^{3} + 9 T^{4} \))(\( ( 1 - 3 T^{2} )^{2}( 1 + 3 T^{2} )^{2} \))(\( 1 + 2 T + 2 T^{2} + 6 T^{3} + 9 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 6 T^{3} + 9 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 6 T^{3} + 9 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 6 T^{3} + 9 T^{4} \))(\( 1 + 8 T^{4} + 94 T^{8} + 648 T^{12} + 6561 T^{16} \))(\( 1 + 8 T^{4} + 94 T^{8} + 648 T^{12} + 6561 T^{16} \))(\( 1 + 2 T + 2 T^{2} + 6 T^{3} + 9 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 6 T^{3} + 9 T^{4} \))(\( 1 - 8 T^{4} - 60 T^{8} + 424 T^{12} + 3334 T^{16} + 34344 T^{20} - 393660 T^{24} - 4251528 T^{28} + 43046721 T^{32} \))(\( ( 1 - 2 T + 3 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} - 4 T^{3} + 64 T^{4} - 32 T^{5} + 280 T^{6} - 132 T^{7} + 1010 T^{8} - 416 T^{9} + 3030 T^{10} - 1188 T^{11} + 7560 T^{12} - 2592 T^{13} + 15552 T^{14} - 2916 T^{15} + 24057 T^{16} + 19683 T^{18} )^{2} \))
$5$ (\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( ( 1 - 5 T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 - 5 T^{2} )^{2} \))(\( ( 1 + 2 T^{2} + 25 T^{4} )^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 + 4 T + 5 T^{2} + 4 T^{4} + 48 T^{5} + 20 T^{6} - 384 T^{7} - 986 T^{8} - 1576 T^{9} - 4930 T^{10} - 9600 T^{11} + 2500 T^{12} + 30000 T^{13} + 12500 T^{14} + 390625 T^{16} + 1562500 T^{17} + 1953125 T^{18} \))(\( ( 1 + T^{4} )^{4} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 4 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( ( 1 - 2 T + 5 T^{2} )^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 34 T^{4} + 625 T^{8} \))(\( 1 - 34 T^{4} + 625 T^{8} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( ( 1 + 4 T + 8 T^{2} + 4 T^{3} - 14 T^{4} + 20 T^{5} + 200 T^{6} + 500 T^{7} + 625 T^{8} )^{2} \))(\( 1 + 4 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} - 16 T^{3} + 36 T^{4} - 104 T^{5} + 308 T^{6} - 688 T^{7} + 1510 T^{8} - 2572 T^{9} + 7550 T^{10} - 17200 T^{11} + 38500 T^{12} - 65000 T^{13} + 112500 T^{14} - 250000 T^{15} + 390625 T^{16} - 781250 T^{17} + 1953125 T^{18} \))
$7$ (\( 1 + 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 6 T^{2} + 49 T^{4} \))(\( ( 1 - 7 T^{2} )^{2} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( ( 1 - 6 T + 18 T^{2} - 42 T^{3} + 49 T^{4} )( 1 + 6 T + 18 T^{2} + 42 T^{3} + 49 T^{4} ) \))(\( ( 1 + 6 T + 20 T^{2} + 42 T^{3} + 49 T^{4} )^{2} \))(\( ( 1 - 6 T + 20 T^{2} - 42 T^{3} + 49 T^{4} )^{2} \))(\( ( 1 + 6 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 - 12 T^{2} + 49 T^{4} )^{4} \))(\( 1 - 6 T + 18 T^{2} - 42 T^{3} + 49 T^{4} \))(\( 1 + 2 T + 2 T^{2} - 18 T^{3} - 31 T^{4} + 232 T^{5} + 688 T^{6} + 1720 T^{7} - 4140 T^{8} - 11256 T^{9} + 3048 T^{10} + 91832 T^{11} + 432692 T^{12} + 46104 T^{13} - 615536 T^{14} - 3870968 T^{15} - 2489450 T^{16} + 35542124 T^{17} + 73581516 T^{18} + 248794868 T^{19} - 121983050 T^{20} - 1327742024 T^{21} - 1477901936 T^{22} + 774869928 T^{23} + 50905781108 T^{24} + 75627600776 T^{25} + 17571113448 T^{26} - 454220200392 T^{27} - 1169447530860 T^{28} + 3401001997960 T^{29} + 9522805594288 T^{30} + 22478250414424 T^{31} - 21024915258319 T^{32} - 85456107178974 T^{33} + 66465861139202 T^{34} + 465261027974414 T^{35} + 1628413597910449 T^{36} \))(\( 1 - 48 T^{2} + 1224 T^{4} - 21712 T^{6} + 299140 T^{8} - 3398704 T^{10} + 32996376 T^{12} - 279256528 T^{14} + 2080544454 T^{16} - 13683569872 T^{18} + 79224298776 T^{20} - 399854126896 T^{22} + 1724482571140 T^{24} - 6133102606288 T^{26} + 16941735534024 T^{28} - 32554707496752 T^{30} + 33232930569601 T^{32} \))(\( 1 - 4 T + 8 T^{2} - 28 T^{3} + 49 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 42 T^{3} + 49 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 14 T^{3} + 49 T^{4} \))(\( 1 + 49 T^{4} \))(\( 1 + 49 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 - 6 T + 18 T^{2} - 42 T^{3} + 49 T^{4} \))(\( 1 + 4 T + 8 T^{2} + 28 T^{3} + 49 T^{4} \))(\( 1 - 34 T^{4} + 2401 T^{8} \))(\( 1 + 2 T + 2 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 14 T^{3} + 49 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 14 T^{3} + 49 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 14 T^{3} + 49 T^{4} \))(\( ( 1 + 2 T + 2 T^{2} - 6 T^{3} - 82 T^{4} - 42 T^{5} + 98 T^{6} + 686 T^{7} + 2401 T^{8} )^{2} \))(\( ( 1 - 2 T + 2 T^{2} + 6 T^{3} - 82 T^{4} + 42 T^{5} + 98 T^{6} - 686 T^{7} + 2401 T^{8} )^{2} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 + 24 T^{2} + 340 T^{4} + 3528 T^{6} + 28410 T^{8} + 172872 T^{10} + 816340 T^{12} + 2823576 T^{14} + 5764801 T^{16} )^{2} \))(\( 1 - 6 T + 18 T^{2} - 42 T^{3} + 49 T^{4} \))(\( 1 + 2 T + 2 T^{2} - 18 T^{3} - 31 T^{4} + 232 T^{5} + 688 T^{6} + 1720 T^{7} - 4140 T^{8} - 11256 T^{9} + 3048 T^{10} + 91832 T^{11} + 432692 T^{12} + 46104 T^{13} - 615536 T^{14} - 3870968 T^{15} - 2489450 T^{16} + 35542124 T^{17} + 73581516 T^{18} + 248794868 T^{19} - 121983050 T^{20} - 1327742024 T^{21} - 1477901936 T^{22} + 774869928 T^{23} + 50905781108 T^{24} + 75627600776 T^{25} + 17571113448 T^{26} - 454220200392 T^{27} - 1169447530860 T^{28} + 3401001997960 T^{29} + 9522805594288 T^{30} + 22478250414424 T^{31} - 21024915258319 T^{32} - 85456107178974 T^{33} + 66465861139202 T^{34} + 465261027974414 T^{35} + 1628413597910449 T^{36} \))
$11$ (\( 1 + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 - 4 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 - 10 T^{2} + 121 T^{4} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( ( 1 - 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{4} \))(\( ( 1 - 10 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 - 10 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 - 18 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 - 18 T^{2} + 121 T^{4} )^{4} \))(\( 1 - 2 T + 2 T^{2} - 22 T^{3} + 121 T^{4} \))(\( 1 - 2 T + 2 T^{2} + 58 T^{3} - 175 T^{4} - 288 T^{5} + 2608 T^{6} - 8640 T^{7} - 7884 T^{8} + 120024 T^{9} - 227528 T^{10} + 65960 T^{11} + 5424292 T^{12} - 10553216 T^{13} - 2414512 T^{14} + 173878688 T^{15} - 432854994 T^{16} - 815210044 T^{17} + 5890482188 T^{18} - 8967310484 T^{19} - 52375454274 T^{20} + 231432533728 T^{21} - 35350870192 T^{22} - 1699605990016 T^{23} + 9609464159812 T^{24} + 1285373799160 T^{25} - 48772647476168 T^{26} + 283010313664584 T^{27} - 204490655554284 T^{28} - 2465092834079040 T^{29} + 8185021206488368 T^{30} - 9942541097452128 T^{31} - 66456220877067175 T^{32} + 242280393826107758 T^{33} + 91899459727144322 T^{34} - 1010894056998587542 T^{35} + 5559917313492231481 T^{36} \))(\( 1 - 8 T + 32 T^{2} - 168 T^{3} + 792 T^{4} - 2440 T^{5} + 8288 T^{6} - 32296 T^{7} + 96540 T^{8} - 322856 T^{9} + 1332000 T^{10} - 4791368 T^{11} + 16873512 T^{12} - 64066088 T^{13} + 231743072 T^{14} - 781448008 T^{15} + 2600362246 T^{16} - 8595928088 T^{17} + 28040911712 T^{18} - 85271963128 T^{19} + 247045089192 T^{20} - 771654607768 T^{21} + 2359719252000 T^{22} - 6291550080376 T^{23} + 20694206371740 T^{24} - 76152278628536 T^{25} + 214969375093088 T^{26} - 696160476290840 T^{27} + 2485635274363032 T^{28} - 5799815640180408 T^{29} + 12151994674663712 T^{30} - 33417985355325208 T^{31} + 45949729863572161 T^{32} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( 1 + 14 T^{2} + 121 T^{4} \))(\( 1 - 18 T^{2} + 121 T^{4} \))(\( ( 1 - 11 T^{2} )^{2} \))(\( ( 1 - 10 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 4 T + 11 T^{2} )^{2} \))(\( ( 1 - 4 T + 11 T^{2} )^{2} \))(\( ( 1 - 4 T + 11 T^{2} )^{2} \))(\( ( 1 + 24 T^{2} + 302 T^{4} + 2904 T^{6} + 14641 T^{8} )^{2} \))(\( ( 1 + 24 T^{2} + 302 T^{4} + 2904 T^{6} + 14641 T^{8} )^{2} \))(\( 1 - 6 T + 18 T^{2} - 66 T^{3} + 121 T^{4} \))(\( 1 - 6 T + 18 T^{2} - 66 T^{3} + 121 T^{4} \))(\( ( 1 + 4 T + 8 T^{2} + 36 T^{3} + 92 T^{4} + 68 T^{5} + 184 T^{6} + 324 T^{7} - 1370 T^{8} + 3564 T^{9} + 22264 T^{10} + 90508 T^{11} + 1346972 T^{12} + 5797836 T^{13} + 14172488 T^{14} + 77948684 T^{15} + 214358881 T^{16} )^{2} \))(\( 1 - 2 T + 2 T^{2} - 22 T^{3} + 121 T^{4} \))(\( 1 - 2 T + 2 T^{2} + 58 T^{3} - 175 T^{4} - 288 T^{5} + 2608 T^{6} - 8640 T^{7} - 7884 T^{8} + 120024 T^{9} - 227528 T^{10} + 65960 T^{11} + 5424292 T^{12} - 10553216 T^{13} - 2414512 T^{14} + 173878688 T^{15} - 432854994 T^{16} - 815210044 T^{17} + 5890482188 T^{18} - 8967310484 T^{19} - 52375454274 T^{20} + 231432533728 T^{21} - 35350870192 T^{22} - 1699605990016 T^{23} + 9609464159812 T^{24} + 1285373799160 T^{25} - 48772647476168 T^{26} + 283010313664584 T^{27} - 204490655554284 T^{28} - 2465092834079040 T^{29} + 8185021206488368 T^{30} - 9942541097452128 T^{31} - 66456220877067175 T^{32} + 242280393826107758 T^{33} + 91899459727144322 T^{34} - 1010894056998587542 T^{35} + 5559917313492231481 T^{36} \))
$13$ (\( 1 + 2 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( ( 1 - 2 T + 13 T^{2} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} ) \))(\( ( 1 - 13 T^{2} )^{4} \))(\( ( 1 - 14 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 14 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 + 6 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 6 T^{2} + 169 T^{4} )^{4} \))(\( ( 1 + 2 T + 13 T^{2} )^{2} \))(\( ( 1 + 61 T^{2} + 16 T^{3} + 1908 T^{4} + 928 T^{5} + 40580 T^{6} + 27056 T^{7} + 660406 T^{8} + 451904 T^{9} + 8585278 T^{10} + 4572464 T^{11} + 89154260 T^{12} + 26504608 T^{13} + 708427044 T^{14} + 77228944 T^{15} + 3827659537 T^{16} + 10604499373 T^{18} )^{2} \))(\( 1 + 128 T^{3} + 40 T^{4} - 640 T^{5} + 8192 T^{6} + 2560 T^{7} - 44900 T^{8} + 355840 T^{9} + 204800 T^{10} - 987520 T^{11} + 12327832 T^{12} - 6963328 T^{13} + 8765440 T^{14} + 221769728 T^{15} - 1025974394 T^{16} + 2883006464 T^{17} + 1481359360 T^{18} - 15298431616 T^{19} + 352095209752 T^{20} - 366659263360 T^{21} + 988530483200 T^{22} + 22328432289280 T^{23} - 36626309372900 T^{24} + 27147518394880 T^{25} + 1129336765227008 T^{26} - 1146982652183680 T^{27} + 931923404899240 T^{28} + 38768013643808384 T^{29} + 665416609183179841 T^{32} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( 1 + 6 T + 18 T^{2} + 78 T^{3} + 169 T^{4} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( ( 1 - 6 T + 13 T^{2} )( 1 - 4 T + 13 T^{2} ) \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( 1 + 6 T + 18 T^{2} + 78 T^{3} + 169 T^{4} \))(\( ( 1 - 6 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \))(\( ( 1 - 4 T + 13 T^{2} )^{2}( 1 + 6 T + 13 T^{2} )^{2} \))(\( 1 + 6 T + 18 T^{2} + 78 T^{3} + 169 T^{4} \))(\( 1 - 6 T + 18 T^{2} - 78 T^{3} + 169 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 78 T^{3} + 169 T^{4} \))(\( 1 - 6 T + 18 T^{2} - 78 T^{3} + 169 T^{4} \))(\( ( 1 + 62 T^{4} + 28561 T^{8} )^{2} \))(\( ( 1 + 62 T^{4} + 28561 T^{8} )^{2} \))(\( 1 - 6 T + 18 T^{2} - 78 T^{3} + 169 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 78 T^{3} + 169 T^{4} \))(\( ( 1 - 140 T^{4} + 49734 T^{8} - 3998540 T^{12} + 815730721 T^{16} )^{2} \))(\( 1 - 22 T^{2} + 169 T^{4} \))(\( 1 - 122 T^{2} + 7537 T^{4} - 313680 T^{6} + 9882340 T^{8} - 250866392 T^{10} + 5327881268 T^{12} - 96936565808 T^{14} + 1533425252030 T^{16} - 21263532733660 T^{18} + 259148867593070 T^{20} - 2768605256042288 T^{22} + 25716665255313812 T^{24} - 204639422820828632 T^{26} + 1362364488339046660 T^{28} - 7308143341219840080 T^{30} + 29676005819015541193 T^{32} - 81180826320347940602 T^{34} + \)\(11\!\cdots\!29\)\( T^{36} \))
$17$ (\( 1 + 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( ( 1 - 2 T + 17 T^{2} )^{2} \))(\( ( 1 - 2 T + 17 T^{2} )( 1 + 2 T + 17 T^{2} ) \))(\( ( 1 - 17 T^{2} )^{2} \))(\( ( 1 - 17 T^{2} )^{2} \))(\( ( 1 - 17 T^{2} )^{4} \))(\( ( 1 + 22 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 + 22 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 17 T^{2} )^{4} \))(\( ( 1 - 10 T^{2} + 289 T^{4} )^{4} \))(\( 1 - 2 T + 2 T^{2} - 34 T^{3} + 289 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 134 T^{3} + 1017 T^{4} + 5360 T^{5} + 22832 T^{6} + 149296 T^{7} + 676660 T^{8} + 2517768 T^{9} + 14077048 T^{10} + 72254792 T^{11} + 312308676 T^{12} + 1215242960 T^{13} + 6226069072 T^{14} + 26188169744 T^{15} + 97051677358 T^{16} + 475514965764 T^{17} + 2098086654444 T^{18} + 8083754417988 T^{19} + 28047934756462 T^{20} + 128662477952272 T^{21} + 520007514962512 T^{22} + 1725471223456720 T^{23} + 7538372216248644 T^{24} + 29648935467171016 T^{25} + 98198072333314168 T^{26} + 298576760632098696 T^{27} + 1364142432677820340 T^{28} + 5116657031144376368 T^{29} + 13302430920429903152 T^{30} + 53088538256375822320 T^{31} + \)\(17\!\cdots\!93\)\( T^{32} + \)\(38\!\cdots\!62\)\( T^{33} + \)\(87\!\cdots\!58\)\( T^{34} + \)\(49\!\cdots\!62\)\( T^{35} + \)\(14\!\cdots\!09\)\( T^{36} \))(\( ( 1 + 64 T^{2} - 64 T^{3} + 2156 T^{4} - 3904 T^{5} + 51008 T^{6} - 111744 T^{7} + 963814 T^{8} - 1899648 T^{9} + 14741312 T^{10} - 19180352 T^{11} + 180071276 T^{12} - 90870848 T^{13} + 1544804416 T^{14} + 6975757441 T^{16} )^{2} \))(\( ( 1 + 2 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( 1 - 2 T + 2 T^{2} - 34 T^{3} + 289 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 34 T^{3} + 289 T^{4} \))(\( ( 1 + 2 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 8 T + 17 T^{2} )( 1 + 2 T + 17 T^{2} ) \))(\( 1 - 2 T + 2 T^{2} - 34 T^{3} + 289 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 34 T^{3} + 289 T^{4} \))(\( ( 1 + 2 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 2 T + 2 T^{2} - 34 T^{3} + 289 T^{4} )^{2} \))(\( ( 1 - 2 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 2 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 2 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 2 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))(\( ( 1 - 8 T + 17 T^{2} )^{4}( 1 + 2 T + 17 T^{2} )^{4} \))(\( ( 1 - 8 T + 17 T^{2} )^{4}( 1 + 2 T + 17 T^{2} )^{4} \))(\( 1 - 18 T^{2} + 289 T^{4} \))(\( 1 - 18 T^{2} + 289 T^{4} \))(\( ( 1 - 40 T^{2} + 870 T^{4} - 11560 T^{6} + 83521 T^{8} )^{4} \))(\( 1 - 2 T + 2 T^{2} - 34 T^{3} + 289 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 134 T^{3} + 1017 T^{4} + 5360 T^{5} + 22832 T^{6} + 149296 T^{7} + 676660 T^{8} + 2517768 T^{9} + 14077048 T^{10} + 72254792 T^{11} + 312308676 T^{12} + 1215242960 T^{13} + 6226069072 T^{14} + 26188169744 T^{15} + 97051677358 T^{16} + 475514965764 T^{17} + 2098086654444 T^{18} + 8083754417988 T^{19} + 28047934756462 T^{20} + 128662477952272 T^{21} + 520007514962512 T^{22} + 1725471223456720 T^{23} + 7538372216248644 T^{24} + 29648935467171016 T^{25} + 98198072333314168 T^{26} + 298576760632098696 T^{27} + 1364142432677820340 T^{28} + 5116657031144376368 T^{29} + 13302430920429903152 T^{30} + 53088538256375822320 T^{31} + \)\(17\!\cdots\!93\)\( T^{32} + \)\(38\!\cdots\!62\)\( T^{33} + \)\(87\!\cdots\!58\)\( T^{34} + \)\(49\!\cdots\!62\)\( T^{35} + \)\(14\!\cdots\!09\)\( T^{36} \))
$19$ (\( 1 + 4 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 - 4 T + 19 T^{2} )^{2} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{4} \))(\( ( 1 - 34 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 - 34 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 - 2 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 - 2 T^{2} + 361 T^{4} )^{4} \))(\( 1 + 6 T + 18 T^{2} + 114 T^{3} + 361 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 102 T^{3} + 641 T^{4} + 1264 T^{5} + 6448 T^{6} + 94800 T^{7} + 201588 T^{8} + 348536 T^{9} + 6629176 T^{10} + 35889000 T^{11} + 72631588 T^{12} + 371841296 T^{13} + 3644025680 T^{14} + 12117184176 T^{15} + 34196073198 T^{16} + 241157330252 T^{17} + 1442387298060 T^{18} + 4581989274788 T^{19} + 12344782424478 T^{20} + 83111766263184 T^{21} + 474893070643280 T^{22} + 920715861184304 T^{23} + 3417017045889028 T^{24} + 32080162840971000 T^{25} + 112587028505884216 T^{26} + 112468279433101544 T^{27} + 1235949384777587988 T^{28} + 11043276543551161200 T^{29} + 14271454598138606128 T^{30} + 53154971096292922576 T^{31} + \)\(51\!\cdots\!61\)\( T^{32} + \)\(15\!\cdots\!98\)\( T^{33} + \)\(57\!\cdots\!62\)\( T^{34} + \)\(10\!\cdots\!78\)\( T^{35} + \)\(10\!\cdots\!41\)\( T^{36} \))(\( 1 - 8 T + 32 T^{2} - 328 T^{3} + 2456 T^{4} - 8488 T^{5} + 43104 T^{6} - 333736 T^{7} + 1234332 T^{8} - 3448552 T^{9} + 27714848 T^{10} - 141668776 T^{11} + 366540968 T^{12} - 1925486856 T^{13} + 13830797408 T^{14} - 50280116744 T^{15} + 147942268806 T^{16} - 955322218136 T^{17} + 4992917864288 T^{18} - 13206914345304 T^{19} + 47767985490728 T^{20} - 350785914584824 T^{21} + 1303869440941088 T^{22} - 3082563173271928 T^{23} + 20963355335523612 T^{24} - 107692501505972344 T^{25} + 264273479976254304 T^{26} - 988769317528082872 T^{27} + 5435901441226491416 T^{28} - 13793378575620315352 T^{29} + 25568213945052291872 T^{30} - \)\(12\!\cdots\!92\)\( T^{31} + \)\(28\!\cdots\!81\)\( T^{32} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( ( 1 - 4 T + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( ( 1 - 4 T + 19 T^{2} )^{2} \))(\( ( 1 - 4 T + 19 T^{2} )^{2} \))(\( ( 1 - 10 T^{2} + 361 T^{4} )^{2} \))(\( 1 - 2 T^{2} + 361 T^{4} \))(\( 1 - 2 T^{2} + 361 T^{4} \))(\( 1 - 2 T^{2} + 361 T^{4} \))(\( 1 - 2 T^{2} + 361 T^{4} \))(\( ( 1 - 8 T + 19 T^{2} )^{4}( 1 + 8 T + 19 T^{2} )^{4} \))(\( ( 1 - 8 T + 19 T^{2} )^{4}( 1 + 8 T + 19 T^{2} )^{4} \))(\( 1 - 2 T + 2 T^{2} - 38 T^{3} + 361 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 38 T^{3} + 361 T^{4} \))(\( ( 1 - 4 T + 8 T^{2} + 28 T^{3} - 484 T^{4} + 220 T^{5} + 3384 T^{6} - 22692 T^{7} + 191206 T^{8} - 431148 T^{9} + 1221624 T^{10} + 1508980 T^{11} - 63075364 T^{12} + 69330772 T^{13} + 376367048 T^{14} - 3575486956 T^{15} + 16983563041 T^{16} )^{2} \))(\( 1 - 6 T + 18 T^{2} - 114 T^{3} + 361 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 102 T^{3} + 641 T^{4} - 1264 T^{5} + 6448 T^{6} - 94800 T^{7} + 201588 T^{8} - 348536 T^{9} + 6629176 T^{10} - 35889000 T^{11} + 72631588 T^{12} - 371841296 T^{13} + 3644025680 T^{14} - 12117184176 T^{15} + 34196073198 T^{16} - 241157330252 T^{17} + 1442387298060 T^{18} - 4581989274788 T^{19} + 12344782424478 T^{20} - 83111766263184 T^{21} + 474893070643280 T^{22} - 920715861184304 T^{23} + 3417017045889028 T^{24} - 32080162840971000 T^{25} + 112587028505884216 T^{26} - 112468279433101544 T^{27} + 1235949384777587988 T^{28} - 11043276543551161200 T^{29} + 14271454598138606128 T^{30} - 53154971096292922576 T^{31} + \)\(51\!\cdots\!61\)\( T^{32} - \)\(15\!\cdots\!98\)\( T^{33} + \)\(57\!\cdots\!62\)\( T^{34} - \)\(10\!\cdots\!78\)\( T^{35} + \)\(10\!\cdots\!41\)\( T^{36} \))
$23$ (\( 1 + 6 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 38 T^{2} + 529 T^{4} \))(\( ( 1 - 23 T^{2} )^{2} \))(\( 1 - 42 T^{2} + 529 T^{4} \))(\( 1 - 42 T^{2} + 529 T^{4} \))(\( ( 1 - 2 T + 2 T^{2} - 46 T^{3} + 529 T^{4} )( 1 + 2 T + 2 T^{2} + 46 T^{3} + 529 T^{4} ) \))(\( ( 1 + 6 T + 28 T^{2} + 138 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 - 6 T + 28 T^{2} - 138 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 - 26 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 + 4 T^{2} + 529 T^{4} )^{4} \))(\( 1 - 2 T + 2 T^{2} - 46 T^{3} + 529 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 70 T^{3} - 591 T^{4} + 2960 T^{5} - 2288 T^{6} + 63760 T^{7} + 89092 T^{8} - 1178512 T^{9} + 744232 T^{10} - 17437280 T^{11} - 143361852 T^{12} + 676178128 T^{13} - 657066064 T^{14} + 23455281104 T^{15} + 63771483110 T^{16} - 805933417604 T^{17} + 643942666316 T^{18} - 18536468604892 T^{19} + 33735114565190 T^{20} + 285380405192368 T^{21} - 183874024415824 T^{22} + 4352114360905904 T^{23} - 21222699209506428 T^{24} - 59370894670464160 T^{25} + 58281541197649192 T^{26} - 2122680025366083056 T^{27} + 3690770737046416708 T^{28} + 60751150164591985520 T^{29} - 50140660700462494448 T^{30} + \)\(14\!\cdots\!80\)\( T^{31} - \)\(68\!\cdots\!19\)\( T^{32} - \)\(18\!\cdots\!90\)\( T^{33} + \)\(12\!\cdots\!22\)\( T^{34} - \)\(28\!\cdots\!06\)\( T^{35} + \)\(32\!\cdots\!69\)\( T^{36} \))(\( 1 - 240 T^{2} + 27048 T^{4} - 1894608 T^{6} + 92250500 T^{8} - 3330863280 T^{10} + 94505221048 T^{12} - 2284353093520 T^{14} + 52374241549254 T^{16} - 1208422786472080 T^{18} + 26446435563293368 T^{20} - 493087306792255920 T^{22} + 7224227547664890500 T^{24} - 78486999557469104592 T^{26} + \)\(59\!\cdots\!08\)\( T^{28} - \)\(27\!\cdots\!60\)\( T^{30} + \)\(61\!\cdots\!61\)\( T^{32} \))(\( 1 - 4 T + 8 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 46 T^{3} + 529 T^{4} \))(\( 1 + 10 T + 50 T^{2} + 230 T^{3} + 529 T^{4} \))(\( 1 + 529 T^{4} \))(\( 1 + 529 T^{4} \))(\( 1 - 10 T + 50 T^{2} - 230 T^{3} + 529 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 46 T^{3} + 529 T^{4} \))(\( 1 + 4 T + 8 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 + 542 T^{4} + 279841 T^{8} \))(\( 1 + 6 T + 18 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 18 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 - 6 T + 18 T^{2} - 138 T^{3} + 529 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 138 T^{3} + 529 T^{4} \))(\( ( 1 - 6 T + 18 T^{2} - 102 T^{3} + 542 T^{4} - 2346 T^{5} + 9522 T^{6} - 73002 T^{7} + 279841 T^{8} )^{2} \))(\( ( 1 + 6 T + 18 T^{2} + 102 T^{3} + 542 T^{4} + 2346 T^{5} + 9522 T^{6} + 73002 T^{7} + 279841 T^{8} )^{2} \))(\( ( 1 - 8 T + 23 T^{2} )^{2} \))(\( ( 1 + 8 T + 23 T^{2} )^{2} \))(\( ( 1 + 152 T^{2} + 10564 T^{4} + 442664 T^{6} + 12324922 T^{8} + 234169256 T^{10} + 2956240324 T^{12} + 22501455128 T^{14} + 78310985281 T^{16} )^{2} \))(\( 1 - 2 T + 2 T^{2} - 46 T^{3} + 529 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 70 T^{3} - 591 T^{4} + 2960 T^{5} - 2288 T^{6} + 63760 T^{7} + 89092 T^{8} - 1178512 T^{9} + 744232 T^{10} - 17437280 T^{11} - 143361852 T^{12} + 676178128 T^{13} - 657066064 T^{14} + 23455281104 T^{15} + 63771483110 T^{16} - 805933417604 T^{17} + 643942666316 T^{18} - 18536468604892 T^{19} + 33735114565190 T^{20} + 285380405192368 T^{21} - 183874024415824 T^{22} + 4352114360905904 T^{23} - 21222699209506428 T^{24} - 59370894670464160 T^{25} + 58281541197649192 T^{26} - 2122680025366083056 T^{27} + 3690770737046416708 T^{28} + 60751150164591985520 T^{29} - 50140660700462494448 T^{30} + \)\(14\!\cdots\!80\)\( T^{31} - \)\(68\!\cdots\!19\)\( T^{32} - \)\(18\!\cdots\!90\)\( T^{33} + \)\(12\!\cdots\!22\)\( T^{34} - \)\(28\!\cdots\!06\)\( T^{35} + \)\(32\!\cdots\!69\)\( T^{36} \))
$29$ (\( 1 + 6 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 10 T + 29 T^{2} )^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{4} \))(\( ( 1 - 29 T^{2} )^{4} \))(\( ( 1 - 29 T^{2} )^{4} \))(\( ( 1 - 29 T^{2} )^{4} \))(\( ( 1 - 10 T^{2} + 841 T^{4} )^{4} \))(\( ( 1 - 10 T + 29 T^{2} )( 1 - 4 T + 29 T^{2} ) \))(\( 1 + 14 T + 98 T^{2} + 726 T^{3} + 6401 T^{4} + 42960 T^{5} + 237680 T^{6} + 1513232 T^{7} + 10244180 T^{8} + 56892360 T^{9} + 292560952 T^{10} + 1753452328 T^{11} + 10724984644 T^{12} + 55021906480 T^{13} + 273776558096 T^{14} + 1576335370736 T^{15} + 8981682474190 T^{16} + 44280736253716 T^{17} + 221031341187660 T^{18} + 1284141351357764 T^{19} + 7553594960793790 T^{20} + 38445243356880304 T^{21} + 193636957786696976 T^{22} + 1128562522075345520 T^{23} + 6379470983618082724 T^{24} + 30246835771728097352 T^{25} + \)\(14\!\cdots\!72\)\( T^{26} + \)\(82\!\cdots\!40\)\( T^{27} + \)\(43\!\cdots\!80\)\( T^{28} + \)\(18\!\cdots\!28\)\( T^{29} + \)\(84\!\cdots\!80\)\( T^{30} + \)\(44\!\cdots\!40\)\( T^{31} + \)\(19\!\cdots\!81\)\( T^{32} + \)\(62\!\cdots\!74\)\( T^{33} + \)\(24\!\cdots\!58\)\( T^{34} + \)\(10\!\cdots\!26\)\( T^{35} + \)\(21\!\cdots\!61\)\( T^{36} \))(\( 1 + 16 T + 128 T^{2} + 752 T^{3} + 3192 T^{4} + 13520 T^{5} + 90496 T^{6} + 729776 T^{7} + 5562460 T^{8} + 31115472 T^{9} + 137176192 T^{10} + 479468336 T^{11} + 834351048 T^{12} + 2544133520 T^{13} + 40190292352 T^{14} + 425020413168 T^{15} + 3004549440774 T^{16} + 12325591981872 T^{17} + 33800035868032 T^{18} + 62048872419280 T^{19} + 590120643580488 T^{20} + 9834446480478064 T^{21} + 81595598087573632 T^{22} + 536738043296152848 T^{23} + 2782600662239044060 T^{24} + 10586966961685775344 T^{25} + 38072321784734989696 T^{26} + \)\(16\!\cdots\!80\)\( T^{27} + \)\(11\!\cdots\!72\)\( T^{28} + \)\(77\!\cdots\!28\)\( T^{29} + \)\(38\!\cdots\!68\)\( T^{30} + \)\(13\!\cdots\!84\)\( T^{31} + \)\(25\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 10 T + 29 T^{2} )( 1 + 10 T + 29 T^{2} ) \))(\( ( 1 - 29 T^{2} )^{2} \))(\( 1 + 6 T^{2} + 841 T^{4} \))(\( ( 1 - 10 T + 29 T^{2} )( 1 + 10 T + 29 T^{2} ) \))(\( ( 1 - 10 T + 29 T^{2} )( 1 + 10 T + 29 T^{2} ) \))(\( 1 + 6 T^{2} + 841 T^{4} \))(\( ( 1 - 29 T^{2} )^{2} \))(\( ( 1 - 10 T + 29 T^{2} )( 1 + 10 T + 29 T^{2} ) \))(\( ( 1 - 10 T + 29 T^{2} )^{2}( 1 + 10 T + 29 T^{2} )^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 - 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 2 T + 29 T^{2} )^{2} \))(\( ( 1 + 30 T^{2} + 841 T^{4} )^{4} \))(\( ( 1 + 30 T^{2} + 841 T^{4} )^{4} \))(\( ( 1 - 10 T + 29 T^{2} )( 1 + 4 T + 29 T^{2} ) \))(\( ( 1 - 10 T + 29 T^{2} )( 1 + 4 T + 29 T^{2} ) \))(\( ( 1 + 8 T + 32 T^{2} - 72 T^{3} + 380 T^{4} + 12232 T^{5} + 88288 T^{6} + 148152 T^{7} - 290138 T^{8} + 4296408 T^{9} + 74250208 T^{10} + 298326248 T^{11} + 268766780 T^{12} - 1476802728 T^{13} + 19034346272 T^{14} + 137999010472 T^{15} + 500246412961 T^{16} )^{2} \))(\( ( 1 + 4 T + 29 T^{2} )( 1 + 10 T + 29 T^{2} ) \))(\( 1 - 14 T + 98 T^{2} - 726 T^{3} + 6401 T^{4} - 42960 T^{5} + 237680 T^{6} - 1513232 T^{7} + 10244180 T^{8} - 56892360 T^{9} + 292560952 T^{10} - 1753452328 T^{11} + 10724984644 T^{12} - 55021906480 T^{13} + 273776558096 T^{14} - 1576335370736 T^{15} + 8981682474190 T^{16} - 44280736253716 T^{17} + 221031341187660 T^{18} - 1284141351357764 T^{19} + 7553594960793790 T^{20} - 38445243356880304 T^{21} + 193636957786696976 T^{22} - 1128562522075345520 T^{23} + 6379470983618082724 T^{24} - 30246835771728097352 T^{25} + \)\(14\!\cdots\!72\)\( T^{26} - \)\(82\!\cdots\!40\)\( T^{27} + \)\(43\!\cdots\!80\)\( T^{28} - \)\(18\!\cdots\!28\)\( T^{29} + \)\(84\!\cdots\!80\)\( T^{30} - \)\(44\!\cdots\!40\)\( T^{31} + \)\(19\!\cdots\!81\)\( T^{32} - \)\(62\!\cdots\!74\)\( T^{33} + \)\(24\!\cdots\!58\)\( T^{34} - \)\(10\!\cdots\!26\)\( T^{35} + \)\(21\!\cdots\!61\)\( T^{36} \))
$31$ (\( 1 - 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 + 30 T^{2} + 961 T^{4} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{4} \))(\( ( 1 - 12 T + 86 T^{2} - 372 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 + 12 T + 86 T^{2} + 372 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 + 31 T^{2} )^{4} \))(\( ( 1 + 14 T^{2} + 961 T^{4} )^{4} \))(\( 1 - 58 T^{2} + 961 T^{4} \))(\( 1 - 362 T^{2} + 62649 T^{4} - 6948784 T^{6} + 560274836 T^{8} - 35376015000 T^{10} + 1837904876644 T^{12} - 81110278812112 T^{14} + 3093814373899278 T^{16} - 102716502829267196 T^{18} + 2973155613317206158 T^{20} - 74907045798840486352 T^{22} + \)\(16\!\cdots\!64\)\( T^{24} - \)\(30\!\cdots\!00\)\( T^{26} + \)\(45\!\cdots\!36\)\( T^{28} - \)\(54\!\cdots\!24\)\( T^{30} + \)\(47\!\cdots\!29\)\( T^{32} - \)\(26\!\cdots\!22\)\( T^{34} + \)\(69\!\cdots\!41\)\( T^{36} \))(\( ( 1 + 152 T^{2} - 64 T^{3} + 11900 T^{4} - 5824 T^{5} + 611496 T^{6} - 292480 T^{7} + 22230150 T^{8} - 9066880 T^{9} + 587647656 T^{10} - 173502784 T^{11} + 10989899900 T^{12} - 1832265664 T^{13} + 134900559512 T^{14} + 852891037441 T^{16} )^{2} \))(\( 1 - 46 T^{2} + 961 T^{4} \))(\( 1 + 38 T^{2} + 961 T^{4} \))(\( 1 - 58 T^{2} + 961 T^{4} \))(\( ( 1 - 31 T^{2} )^{2} \))(\( ( 1 - 31 T^{2} )^{2} \))(\( 1 - 58 T^{2} + 961 T^{4} \))(\( 1 + 38 T^{2} + 961 T^{4} \))(\( 1 - 46 T^{2} + 961 T^{4} \))(\( ( 1 - 50 T^{2} + 961 T^{4} )^{2} \))(\( 1 - 26 T^{2} + 961 T^{4} \))(\( 1 - 26 T^{2} + 961 T^{4} \))(\( 1 - 26 T^{2} + 961 T^{4} \))(\( 1 - 26 T^{2} + 961 T^{4} \))(\( ( 1 - 64 T^{2} + 2190 T^{4} - 61504 T^{6} + 923521 T^{8} )^{2} \))(\( ( 1 - 64 T^{2} + 2190 T^{4} - 61504 T^{6} + 923521 T^{8} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 31 T^{2} )^{2} \))(\( ( 1 + 4 T + 52 T^{2} + 292 T^{3} + 1510 T^{4} + 9052 T^{5} + 49972 T^{6} + 119164 T^{7} + 923521 T^{8} )^{4} \))(\( 1 - 58 T^{2} + 961 T^{4} \))(\( 1 - 362 T^{2} + 62649 T^{4} - 6948784 T^{6} + 560274836 T^{8} - 35376015000 T^{10} + 1837904876644 T^{12} - 81110278812112 T^{14} + 3093814373899278 T^{16} - 102716502829267196 T^{18} + 2973155613317206158 T^{20} - 74907045798840486352 T^{22} + \)\(16\!\cdots\!64\)\( T^{24} - \)\(30\!\cdots\!00\)\( T^{26} + \)\(45\!\cdots\!36\)\( T^{28} - \)\(54\!\cdots\!24\)\( T^{30} + \)\(47\!\cdots\!29\)\( T^{32} - \)\(26\!\cdots\!22\)\( T^{34} + \)\(69\!\cdots\!41\)\( T^{36} \))
$37$ (\( 1 + 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( ( 1 - 10 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )( 1 + 2 T + 37 T^{2} ) \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( 1 - 58 T^{2} + 1369 T^{4} \))(\( ( 1 - 37 T^{2} )^{4} \))(\( ( 1 - 38 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 - 38 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 + 54 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 + 66 T^{2} + 1369 T^{4} )^{4} \))(\( ( 1 + 6 T + 37 T^{2} )^{2} \))(\( ( 1 - 4 T + 197 T^{2} - 1024 T^{3} + 20644 T^{4} - 111280 T^{5} + 1450996 T^{6} - 7367808 T^{7} + 72944518 T^{8} - 328519384 T^{9} + 2698947166 T^{10} - 10086529152 T^{11} + 73497300388 T^{12} - 208556636080 T^{13} + 1431536648308 T^{14} - 2627303842816 T^{15} + 18701579795201 T^{16} - 14049917815684 T^{17} + 129961739795077 T^{18} )^{2} \))(\( 1 + 16 T + 128 T^{2} + 1296 T^{3} + 13064 T^{4} + 96944 T^{5} + 718720 T^{6} + 5993264 T^{7} + 42082268 T^{8} + 267178192 T^{9} + 1965302400 T^{10} + 13774031568 T^{11} + 85362600888 T^{12} + 558679840240 T^{13} + 3804460563840 T^{14} + 23317949683568 T^{15} + 136425609221766 T^{16} + 862764138292016 T^{17} + 5208306511896960 T^{18} + 28298809947676720 T^{19} + 159983257442854968 T^{20} + 955145852768034576 T^{21} + 5042428269351081600 T^{22} + 25363727295561083536 T^{23} + \)\(14\!\cdots\!28\)\( T^{24} + \)\(77\!\cdots\!28\)\( T^{25} + \)\(34\!\cdots\!80\)\( T^{26} + \)\(17\!\cdots\!72\)\( T^{27} + \)\(85\!\cdots\!84\)\( T^{28} + \)\(31\!\cdots\!12\)\( T^{29} + \)\(11\!\cdots\!92\)\( T^{30} + \)\(53\!\cdots\!88\)\( T^{31} + \)\(12\!\cdots\!41\)\( T^{32} \))(\( 1 + 2 T + 2 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 74 T^{3} + 1369 T^{4} \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 2 T + 37 T^{2} ) \))(\( ( 1 - 2 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 - 2 T + 37 T^{2} ) \))(\( ( 1 - 12 T + 37 T^{2} )( 1 + 2 T + 37 T^{2} ) \))(\( 1 - 2 T + 2 T^{2} - 74 T^{3} + 1369 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 74 T^{3} + 1369 T^{4} \))(\( ( 1 - 2 T + 37 T^{2} )^{2}( 1 + 12 T + 37 T^{2} )^{2} \))(\( 1 + 6 T + 18 T^{2} + 222 T^{3} + 1369 T^{4} \))(\( 1 - 6 T + 18 T^{2} - 222 T^{3} + 1369 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 222 T^{3} + 1369 T^{4} \))(\( 1 - 6 T + 18 T^{2} - 222 T^{3} + 1369 T^{4} \))(\( ( 1 - 2338 T^{4} + 1874161 T^{8} )^{2} \))(\( ( 1 - 2338 T^{4} + 1874161 T^{8} )^{2} \))(\( 1 - 6 T + 18 T^{2} - 222 T^{3} + 1369 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 222 T^{3} + 1369 T^{4} \))(\( ( 1 - 92 T^{4} + 1830438 T^{8} - 172422812 T^{12} + 3512479453921 T^{16} )^{2} \))(\( 1 - 38 T^{2} + 1369 T^{4} \))(\( 1 - 378 T^{2} + 71905 T^{4} - 9096912 T^{6} + 856912292 T^{8} - 63946093016 T^{10} + 3934223155252 T^{12} - 205214014299312 T^{14} + 9255275087166462 T^{16} - 365303320505490396 T^{18} + 12670471594330886478 T^{20} - \)\(38\!\cdots\!32\)\( T^{22} + \)\(10\!\cdots\!68\)\( T^{24} - \)\(22\!\cdots\!36\)\( T^{26} + \)\(41\!\cdots\!08\)\( T^{28} - \)\(59\!\cdots\!72\)\( T^{30} + \)\(64\!\cdots\!45\)\( T^{32} - \)\(46\!\cdots\!98\)\( T^{34} + \)\(16\!\cdots\!29\)\( T^{36} \))
$41$ (\( 1 - 6 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 10 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{2} \))(\( ( 1 + 62 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 12 T + 106 T^{2} - 492 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 - 12 T + 106 T^{2} - 492 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{4} \))(\( ( 1 + 4 T + 41 T^{2} )^{8} \))(\( 1 - 66 T^{2} + 1681 T^{4} \))(\( 1 - 450 T^{2} + 100441 T^{4} - 14781456 T^{6} + 1610393956 T^{8} - 138340541496 T^{10} + 9747518002260 T^{12} - 578326413361776 T^{14} + 29398753828363198 T^{16} - 1293459229377566220 T^{18} + 49419305185478535838 T^{20} - \)\(16\!\cdots\!36\)\( T^{22} + \)\(46\!\cdots\!60\)\( T^{24} - \)\(11\!\cdots\!16\)\( T^{26} + \)\(21\!\cdots\!56\)\( T^{28} - \)\(33\!\cdots\!36\)\( T^{30} + \)\(38\!\cdots\!01\)\( T^{32} - \)\(28\!\cdots\!50\)\( T^{34} + \)\(10\!\cdots\!21\)\( T^{36} \))(\( 1 - 272 T^{2} + 40392 T^{4} - 4239344 T^{6} + 349394844 T^{8} - 23832542160 T^{10} + 1384432491384 T^{12} - 69587337339184 T^{14} + 3050875549332934 T^{16} - 116976314067168304 T^{18} + 3912075341285743224 T^{20} - \)\(11\!\cdots\!60\)\( T^{22} + \)\(27\!\cdots\!24\)\( T^{24} - \)\(56\!\cdots\!44\)\( T^{26} + \)\(91\!\cdots\!52\)\( T^{28} - \)\(10\!\cdots\!92\)\( T^{30} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 10 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 8 T + 41 T^{2} )^{2} \))(\( ( 1 + 8 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 10 T + 41 T^{2} )^{2} \))(\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 - 2 T + 41 T^{2} )^{4} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 70 T^{2} + 246 T^{3} + 1681 T^{4} )^{4} \))(\( ( 1 + 6 T + 70 T^{2} + 246 T^{3} + 1681 T^{4} )^{4} \))(\( ( 1 - 41 T^{2} )^{2} \))(\( ( 1 - 41 T^{2} )^{2} \))(\( ( 1 - 136 T^{2} + 9988 T^{4} - 572632 T^{6} + 26690182 T^{8} - 962594392 T^{10} + 28223700868 T^{12} - 646014176776 T^{14} + 7984925229121 T^{16} )^{2} \))(\( 1 - 66 T^{2} + 1681 T^{4} \))(\( 1 - 450 T^{2} + 100441 T^{4} - 14781456 T^{6} + 1610393956 T^{8} - 138340541496 T^{10} + 9747518002260 T^{12} - 578326413361776 T^{14} + 29398753828363198 T^{16} - 1293459229377566220 T^{18} + 49419305185478535838 T^{20} - \)\(16\!\cdots\!36\)\( T^{22} + \)\(46\!\cdots\!60\)\( T^{24} - \)\(11\!\cdots\!16\)\( T^{26} + \)\(21\!\cdots\!56\)\( T^{28} - \)\(33\!\cdots\!36\)\( T^{30} + \)\(38\!\cdots\!01\)\( T^{32} - \)\(28\!\cdots\!50\)\( T^{34} + \)\(10\!\cdots\!21\)\( T^{36} \))
$43$ (\( 1 + 10 T + 43 T^{2} \))(\( 1 + 2 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 2 T + 43 T^{2} \))(\( 1 - 10 T + 43 T^{2} \))(\( 1 + 14 T^{2} + 1849 T^{4} \))(\( ( 1 - 43 T^{2} )^{2} \))(\( 1 - 50 T^{2} + 1849 T^{4} \))(\( 1 - 50 T^{2} + 1849 T^{4} \))(\( ( 1 - 18 T + 162 T^{2} - 774 T^{3} + 1849 T^{4} )( 1 + 18 T + 162 T^{2} + 774 T^{3} + 1849 T^{4} ) \))(\( 1 - 68 T^{2} + 2154 T^{4} - 125732 T^{6} + 3418801 T^{8} \))(\( 1 - 68 T^{2} + 2154 T^{4} - 125732 T^{6} + 3418801 T^{8} \))(\( ( 1 + 43 T^{2} )^{4} \))(\( ( 1 + 80 T^{2} + 1849 T^{4} )^{4} \))(\( ( 1 + 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 22 T + 459 T^{2} - 5948 T^{3} + 73264 T^{4} - 695720 T^{5} + 6433304 T^{6} - 49524844 T^{7} + 378530410 T^{8} - 2482332748 T^{9} + 16276807630 T^{10} - 91571436556 T^{11} + 511492701128 T^{12} - 2378528231720 T^{13} + 10770426567952 T^{14} - 37599467415452 T^{15} + 124764742498113 T^{16} - 257140406107222 T^{17} + 502592611936843 T^{18} )^{2} \))(\( 1 + 8 T + 32 T^{2} - 96 T^{3} + 856 T^{4} + 25008 T^{5} + 177280 T^{6} + 438536 T^{7} + 1211268 T^{8} + 28586088 T^{9} + 308777024 T^{10} + 655622544 T^{11} + 4559169480 T^{12} + 75563226240 T^{13} + 727663699104 T^{14} + 1380447398312 T^{15} - 6951849427450 T^{16} + 59359238127416 T^{17} + 1345450179643296 T^{18} + 6007805428663680 T^{19} + 15586893177393480 T^{20} + 96382049389138992 T^{21} + 1951891669893786176 T^{22} + 7770230737142479416 T^{23} + 14157542973849208068 T^{24} + \)\(22\!\cdots\!48\)\( T^{25} + \)\(38\!\cdots\!20\)\( T^{26} + \)\(23\!\cdots\!56\)\( T^{27} + \)\(34\!\cdots\!56\)\( T^{28} - \)\(16\!\cdots\!28\)\( T^{29} + \)\(23\!\cdots\!68\)\( T^{30} + \)\(25\!\cdots\!56\)\( T^{31} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( 1 - 12 T + 72 T^{2} - 516 T^{3} + 1849 T^{4} \))(\( 1 + 10 T + 50 T^{2} + 430 T^{3} + 1849 T^{4} \))(\( 1 - 6 T + 18 T^{2} - 258 T^{3} + 1849 T^{4} \))(\( 1 + 1849 T^{4} \))(\( 1 + 1849 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 - 10 T + 50 T^{2} - 430 T^{3} + 1849 T^{4} \))(\( 1 + 12 T + 72 T^{2} + 516 T^{3} + 1849 T^{4} \))(\( 1 + 2702 T^{4} + 3418801 T^{8} \))(\( 1 - 6 T + 18 T^{2} - 258 T^{3} + 1849 T^{4} \))(\( 1 - 6 T + 18 T^{2} - 258 T^{3} + 1849 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 + 2632 T^{4} + 3107358 T^{8} + 8998284232 T^{12} + 11688200277601 T^{16} \))(\( 1 + 2632 T^{4} + 3107358 T^{8} + 8998284232 T^{12} + 11688200277601 T^{16} \))(\( 1 + 6 T + 18 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 - 6 T + 18 T^{2} - 258 T^{3} + 1849 T^{4} \))(\( 1 + 4568 T^{4} + 15432388 T^{8} + 32835546440 T^{12} + 67805368306822 T^{16} + 112258199004618440 T^{20} + \)\(18\!\cdots\!88\)\( T^{24} + \)\(18\!\cdots\!68\)\( T^{28} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( 1 - 70 T^{2} + 1849 T^{4} \))(\( 1 - 434 T^{2} + 95497 T^{4} - 14132576 T^{6} + 1575069332 T^{8} - 140307196616 T^{10} + 10347976565460 T^{12} - 645785319162016 T^{14} + 34557565852762614 T^{16} - 1597142837246964908 T^{18} + 63896939261758073286 T^{20} - \)\(22\!\cdots\!16\)\( T^{22} + \)\(65\!\cdots\!40\)\( T^{24} - \)\(16\!\cdots\!16\)\( T^{26} + \)\(34\!\cdots\!68\)\( T^{28} - \)\(56\!\cdots\!76\)\( T^{30} + \)\(70\!\cdots\!53\)\( T^{32} - \)\(59\!\cdots\!34\)\( T^{34} + \)\(25\!\cdots\!49\)\( T^{36} \))
$47$ (\( 1 - 6 T + 47 T^{2} \))(\( 1 - 2 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 4 T + 47 T^{2} \))(\( 1 + 2 T + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 + 86 T^{2} + 2209 T^{4} \))(\( ( 1 - 47 T^{2} )^{2} \))(\( 1 - 58 T^{2} + 2209 T^{4} \))(\( 1 - 58 T^{2} + 2209 T^{4} \))(\( ( 1 - 14 T + 98 T^{2} - 658 T^{3} + 2209 T^{4} )( 1 + 14 T + 98 T^{2} + 658 T^{3} + 2209 T^{4} ) \))(\( ( 1 - 6 T + 76 T^{2} - 282 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 + 6 T + 76 T^{2} + 282 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 + 86 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 - 76 T^{2} + 2209 T^{4} )^{4} \))(\( 1 + 14 T + 98 T^{2} + 658 T^{3} + 2209 T^{4} \))(\( 1 - 38 T + 722 T^{2} - 10058 T^{3} + 122161 T^{4} - 1328456 T^{5} + 12862768 T^{6} - 113701112 T^{7} + 943490484 T^{8} - 7442197960 T^{9} + 56278247848 T^{10} - 412597571480 T^{11} + 2981952610452 T^{12} - 21538353011032 T^{13} + 155091730527504 T^{14} - 1106483733730792 T^{15} + 7843790068463798 T^{16} - 55222405019152308 T^{17} + 382643757483978924 T^{18} - 2595453035900158476 T^{19} + 17326932261236529782 T^{20} - \)\(11\!\cdots\!16\)\( T^{21} + \)\(75\!\cdots\!24\)\( T^{22} - \)\(49\!\cdots\!24\)\( T^{23} + \)\(32\!\cdots\!08\)\( T^{24} - \)\(20\!\cdots\!40\)\( T^{25} + \)\(13\!\cdots\!28\)\( T^{26} - \)\(83\!\cdots\!20\)\( T^{27} + \)\(49\!\cdots\!16\)\( T^{28} - \)\(28\!\cdots\!36\)\( T^{29} + \)\(14\!\cdots\!88\)\( T^{30} - \)\(72\!\cdots\!12\)\( T^{31} + \)\(31\!\cdots\!09\)\( T^{32} - \)\(12\!\cdots\!94\)\( T^{33} + \)\(40\!\cdots\!62\)\( T^{34} - \)\(10\!\cdots\!06\)\( T^{35} + \)\(12\!\cdots\!89\)\( T^{36} \))(\( ( 1 - 20 T + 368 T^{2} - 4188 T^{3} + 44660 T^{4} - 366244 T^{5} + 2985808 T^{6} - 20612540 T^{7} + 150587482 T^{8} - 968789380 T^{9} + 6595649872 T^{10} - 38024550812 T^{11} + 217926553460 T^{12} - 960496889316 T^{13} + 3966751241072 T^{14} - 10132462409260 T^{15} + 23811286661761 T^{16} )^{2} \))(\( 1 + 4 T + 8 T^{2} + 188 T^{3} + 2209 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 + 14 T + 98 T^{2} + 658 T^{3} + 2209 T^{4} \))(\( 1 + 2209 T^{4} \))(\( 1 + 2209 T^{4} \))(\( 1 - 14 T + 98 T^{2} - 658 T^{3} + 2209 T^{4} \))(\( 1 - 6 T + 18 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 - 4 T + 8 T^{2} - 188 T^{3} + 2209 T^{4} \))(\( 1 + 3326 T^{4} + 4879681 T^{8} \))(\( 1 + 18 T + 162 T^{2} + 846 T^{3} + 2209 T^{4} \))(\( 1 - 18 T + 162 T^{2} - 846 T^{3} + 2209 T^{4} \))(\( 1 - 18 T + 162 T^{2} - 846 T^{3} + 2209 T^{4} \))(\( 1 + 18 T + 162 T^{2} + 846 T^{3} + 2209 T^{4} \))(\( ( 1 + 6 T + 18 T^{2} + 246 T^{3} + 3326 T^{4} + 11562 T^{5} + 39762 T^{6} + 622938 T^{7} + 4879681 T^{8} )^{2} \))(\( ( 1 - 6 T + 18 T^{2} - 246 T^{3} + 3326 T^{4} - 11562 T^{5} + 39762 T^{6} - 622938 T^{7} + 4879681 T^{8} )^{2} \))(\( 1 - 90 T^{2} + 2209 T^{4} \))(\( 1 - 90 T^{2} + 2209 T^{4} \))(\( ( 1 - 296 T^{2} + 41044 T^{4} - 3480152 T^{6} + 197533306 T^{8} - 7687655768 T^{10} + 200281626964 T^{12} - 3190647737384 T^{14} + 23811286661761 T^{16} )^{2} \))(\( 1 - 14 T + 98 T^{2} - 658 T^{3} + 2209 T^{4} \))(\( 1 + 38 T + 722 T^{2} + 10058 T^{3} + 122161 T^{4} + 1328456 T^{5} + 12862768 T^{6} + 113701112 T^{7} + 943490484 T^{8} + 7442197960 T^{9} + 56278247848 T^{10} + 412597571480 T^{11} + 2981952610452 T^{12} + 21538353011032 T^{13} + 155091730527504 T^{14} + 1106483733730792 T^{15} + 7843790068463798 T^{16} + 55222405019152308 T^{17} + 382643757483978924 T^{18} + 2595453035900158476 T^{19} + 17326932261236529782 T^{20} + \)\(11\!\cdots\!16\)\( T^{21} + \)\(75\!\cdots\!24\)\( T^{22} + \)\(49\!\cdots\!24\)\( T^{23} + \)\(32\!\cdots\!08\)\( T^{24} + \)\(20\!\cdots\!40\)\( T^{25} + \)\(13\!\cdots\!28\)\( T^{26} + \)\(83\!\cdots\!20\)\( T^{27} + \)\(49\!\cdots\!16\)\( T^{28} + \)\(28\!\cdots\!36\)\( T^{29} + \)\(14\!\cdots\!88\)\( T^{30} + \)\(72\!\cdots\!12\)\( T^{31} + \)\(31\!\cdots\!09\)\( T^{32} + \)\(12\!\cdots\!94\)\( T^{33} + \)\(40\!\cdots\!62\)\( T^{34} + \)\(10\!\cdots\!06\)\( T^{35} + \)\(12\!\cdots\!89\)\( T^{36} \))
$53$ (\( 1 - 6 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))(\( ( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))(\( ( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))(\( ( 1 - 53 T^{2} )^{4} \))(\( ( 1 + 2 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 + 2 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 - 74 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 + 53 T^{2} )^{8} \))(\( 1 - 42 T^{2} + 2809 T^{4} \))(\( 1 - 646 T^{2} + 204289 T^{4} - 42062000 T^{6} + 6331181988 T^{8} - 742044595240 T^{10} + 70453884825524 T^{12} - 5564449393062864 T^{14} + 372091290097786238 T^{16} - 21285258439059863076 T^{18} + \)\(10\!\cdots\!42\)\( T^{20} - \)\(43\!\cdots\!84\)\( T^{22} + \)\(15\!\cdots\!96\)\( T^{24} - \)\(46\!\cdots\!40\)\( T^{26} + \)\(11\!\cdots\!12\)\( T^{28} - \)\(20\!\cdots\!00\)\( T^{30} + \)\(28\!\cdots\!41\)\( T^{32} - \)\(25\!\cdots\!66\)\( T^{34} + \)\(10\!\cdots\!89\)\( T^{36} \))(\( 1 - 16 T + 128 T^{2} - 1296 T^{3} + 9192 T^{4} - 18480 T^{5} - 41088 T^{6} + 1772880 T^{7} - 34968676 T^{8} + 254931120 T^{9} - 1352123776 T^{10} + 9282442928 T^{11} - 26207739176 T^{12} - 138779462128 T^{13} + 1397369412992 T^{14} - 16971119010160 T^{15} + 177919428600838 T^{16} - 899469307538480 T^{17} + 3925210681094528 T^{18} - 20661069983230256 T^{19} - 206791668021183656 T^{20} + 3881875796519323504 T^{21} - 29968959662371103104 T^{22} + \)\(29\!\cdots\!40\)\( T^{23} - \)\(21\!\cdots\!36\)\( T^{24} + \)\(58\!\cdots\!40\)\( T^{25} - \)\(71\!\cdots\!12\)\( T^{26} - \)\(17\!\cdots\!60\)\( T^{27} + \)\(45\!\cdots\!72\)\( T^{28} - \)\(33\!\cdots\!08\)\( T^{29} + \)\(17\!\cdots\!32\)\( T^{30} - \)\(11\!\cdots\!12\)\( T^{31} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( 1 - 14 T + 98 T^{2} - 742 T^{3} + 2809 T^{4} \))(\( ( 1 - 14 T + 53 T^{2} )( 1 + 4 T + 53 T^{2} ) \))(\( 1 - 2 T + 2 T^{2} - 106 T^{3} + 2809 T^{4} \))(\( ( 1 - 4 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))(\( ( 1 + 4 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))(\( 1 - 2 T + 2 T^{2} - 106 T^{3} + 2809 T^{4} \))(\( ( 1 - 14 T + 53 T^{2} )( 1 + 4 T + 53 T^{2} ) \))(\( 1 - 14 T + 98 T^{2} - 742 T^{3} + 2809 T^{4} \))(\( ( 1 - 14 T + 98 T^{2} - 742 T^{3} + 2809 T^{4} )^{2} \))(\( ( 1 - 14 T + 53 T^{2} )( 1 + 4 T + 53 T^{2} ) \))(\( ( 1 - 4 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))(\( ( 1 - 14 T + 53 T^{2} )( 1 + 4 T + 53 T^{2} ) \))(\( ( 1 - 4 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))(\( ( 1 + 2846 T^{4} + 7890481 T^{8} )^{2} \))(\( ( 1 + 2846 T^{4} + 7890481 T^{8} )^{2} \))(\( ( 1 + 4 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))(\( ( 1 - 14 T + 53 T^{2} )( 1 - 4 T + 53 T^{2} ) \))(\( 1 + 8488 T^{4} + 28367644 T^{8} + 65683864984 T^{12} + 173166077304070 T^{16} + 518277288662817304 T^{20} + \)\(17\!\cdots\!84\)\( T^{24} + \)\(41\!\cdots\!08\)\( T^{28} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( ( 1 + 8 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 341 T^{2} - 2064 T^{3} + 56388 T^{4} - 330040 T^{5} + 5912980 T^{6} - 32036656 T^{7} + 432884038 T^{8} - 2061378468 T^{9} + 22942854014 T^{10} - 89990966704 T^{11} + 880306723460 T^{12} - 2604174349240 T^{13} + 23581207459284 T^{14} - 45747241370256 T^{15} + 400576498684417 T^{16} - 373558142468166 T^{17} + 3299763591802133 T^{18} )^{2} \))
$59$ (\( 1 - 12 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 10 T^{2} + 3481 T^{4} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 - 12 T + 59 T^{2} )^{2} \))(\( ( 1 + 12 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{4} \))(\( ( 1 - 82 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 82 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 + 78 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 114 T^{2} + 3481 T^{4} )^{4} \))(\( 1 - 6 T + 18 T^{2} - 354 T^{3} + 3481 T^{4} \))(\( 1 - 10 T + 50 T^{2} - 494 T^{3} - 1743 T^{4} + 33136 T^{5} - 122192 T^{6} + 748688 T^{7} + 22720756 T^{8} - 207434808 T^{9} + 904475000 T^{10} - 8738584488 T^{11} - 73057283740 T^{12} + 1079521529168 T^{13} - 5065988762672 T^{14} + 53579997360688 T^{15} - 92361378765970 T^{16} - 1839910849923292 T^{17} + 8984420762513708 T^{18} - 108554740145474228 T^{19} - 321509959484341570 T^{20} + 11004206277940740752 T^{21} - 61386414659239948592 T^{22} + \)\(77\!\cdots\!32\)\( T^{23} - \)\(30\!\cdots\!40\)\( T^{24} - \)\(21\!\cdots\!72\)\( T^{25} + \)\(13\!\cdots\!00\)\( T^{26} - \)\(17\!\cdots\!12\)\( T^{27} + \)\(11\!\cdots\!56\)\( T^{28} + \)\(22\!\cdots\!92\)\( T^{29} - \)\(21\!\cdots\!52\)\( T^{30} + \)\(34\!\cdots\!44\)\( T^{31} - \)\(10\!\cdots\!23\)\( T^{32} - \)\(18\!\cdots\!06\)\( T^{33} + \)\(10\!\cdots\!50\)\( T^{34} - \)\(12\!\cdots\!90\)\( T^{35} + \)\(75\!\cdots\!21\)\( T^{36} \))(\( 1 - 8 T + 32 T^{2} - 200 T^{3} + 2328 T^{4} - 36840 T^{5} + 240224 T^{6} - 3629928 T^{7} + 20717084 T^{8} + 58513304 T^{9} - 285716192 T^{10} + 1869112408 T^{11} + 49873912872 T^{12} - 239683519560 T^{13} + 68645494368 T^{14} + 16019603732152 T^{15} - 420891847268346 T^{16} + 945156620196968 T^{17} + 238954965895008 T^{18} - 49225961563713240 T^{19} + 604340206752570792 T^{20} + 1336273878041601992 T^{21} - 12051661448434415072 T^{22} + \)\(14\!\cdots\!76\)\( T^{23} + \)\(30\!\cdots\!64\)\( T^{24} - \)\(31\!\cdots\!92\)\( T^{25} + \)\(12\!\cdots\!24\)\( T^{26} - \)\(11\!\cdots\!60\)\( T^{27} + \)\(41\!\cdots\!68\)\( T^{28} - \)\(20\!\cdots\!00\)\( T^{29} + \)\(19\!\cdots\!52\)\( T^{30} - \)\(29\!\cdots\!92\)\( T^{31} + \)\(21\!\cdots\!41\)\( T^{32} \))(\( ( 1 + 4 T + 59 T^{2} )^{2} \))(\( ( 1 - 12 T + 59 T^{2} )^{2} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 + 4 T + 59 T^{2} )^{2} \))(\( ( 1 + 12 T + 59 T^{2} )^{2} \))(\( ( 1 - 4 T + 59 T^{2} )^{2} \))(\( ( 1 + 70 T^{2} + 3481 T^{4} )^{2} \))(\( 1 - 18 T^{2} + 3481 T^{4} \))(\( 1 - 18 T^{2} + 3481 T^{4} \))(\( 1 - 18 T^{2} + 3481 T^{4} \))(\( 1 - 18 T^{2} + 3481 T^{4} \))(\( ( 1 - 90 T^{2} + 3481 T^{4} )^{4} \))(\( ( 1 - 90 T^{2} + 3481 T^{4} )^{4} \))(\( 1 + 18 T + 162 T^{2} + 1062 T^{3} + 3481 T^{4} \))(\( 1 + 18 T + 162 T^{2} + 1062 T^{3} + 3481 T^{4} \))(\( ( 1 - 12 T + 72 T^{2} - 396 T^{3} + 6748 T^{4} - 83052 T^{5} + 589176 T^{6} - 3781452 T^{7} + 22178598 T^{8} - 223105668 T^{9} + 2050921656 T^{10} - 17057136708 T^{11} + 81767952028 T^{12} - 283110022404 T^{13} + 3036998422152 T^{14} - 29863817817828 T^{15} + 146830437604321 T^{16} )^{2} \))(\( 1 + 6 T + 18 T^{2} + 354 T^{3} + 3481 T^{4} \))(\( 1 + 10 T + 50 T^{2} + 494 T^{3} - 1743 T^{4} - 33136 T^{5} - 122192 T^{6} - 748688 T^{7} + 22720756 T^{8} + 207434808 T^{9} + 904475000 T^{10} + 8738584488 T^{11} - 73057283740 T^{12} - 1079521529168 T^{13} - 5065988762672 T^{14} - 53579997360688 T^{15} - 92361378765970 T^{16} + 1839910849923292 T^{17} + 8984420762513708 T^{18} + 108554740145474228 T^{19} - 321509959484341570 T^{20} - 11004206277940740752 T^{21} - 61386414659239948592 T^{22} - \)\(77\!\cdots\!32\)\( T^{23} - \)\(30\!\cdots\!40\)\( T^{24} + \)\(21\!\cdots\!72\)\( T^{25} + \)\(13\!\cdots\!00\)\( T^{26} + \)\(17\!\cdots\!12\)\( T^{27} + \)\(11\!\cdots\!56\)\( T^{28} - \)\(22\!\cdots\!92\)\( T^{29} - \)\(21\!\cdots\!52\)\( T^{30} - \)\(34\!\cdots\!44\)\( T^{31} - \)\(10\!\cdots\!23\)\( T^{32} + \)\(18\!\cdots\!06\)\( T^{33} + \)\(10\!\cdots\!50\)\( T^{34} + \)\(12\!\cdots\!90\)\( T^{35} + \)\(75\!\cdots\!21\)\( T^{36} \))
$61$ (\( 1 + 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( ( 1 - 2 T + 61 T^{2} )^{2} \))(\( ( 1 + 10 T + 61 T^{2} )^{2} \))(\( ( 1 - 10 T + 61 T^{2} )^{2} \))(\( ( 1 - 10 T + 61 T^{2} )^{2} \))(\( ( 1 - 58 T^{2} + 3721 T^{4} )^{2} \))(\( 1 - 76 T^{2} + 1974 T^{4} - 282796 T^{6} + 13845841 T^{8} \))(\( 1 - 76 T^{2} + 1974 T^{4} - 282796 T^{6} + 13845841 T^{8} \))(\( ( 1 - 61 T^{2} )^{4} \))(\( ( 1 - 110 T^{2} + 3721 T^{4} )^{4} \))(\( ( 1 - 10 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( 1 - 14 T + 98 T^{2} - 134 T^{3} + 5041 T^{4} - 83168 T^{5} + 679312 T^{6} - 36608 T^{7} + 160260 T^{8} - 147217176 T^{9} + 2084286776 T^{10} + 4953407144 T^{11} - 49660935404 T^{12} - 134974970304 T^{13} + 7721336684016 T^{14} + 9084322150944 T^{15} - 105587914401314 T^{16} - 961048211302948 T^{17} + 38943687185882188 T^{18} - 58623940889479828 T^{19} - 392892629487289394 T^{20} + 2061968526143420064 T^{21} + \)\(10\!\cdots\!56\)\( T^{22} - \)\(11\!\cdots\!04\)\( T^{23} - \)\(25\!\cdots\!44\)\( T^{24} + \)\(15\!\cdots\!24\)\( T^{25} + \)\(39\!\cdots\!56\)\( T^{26} - \)\(17\!\cdots\!16\)\( T^{27} + \)\(11\!\cdots\!60\)\( T^{28} - \)\(15\!\cdots\!88\)\( T^{29} + \)\(18\!\cdots\!52\)\( T^{30} - \)\(13\!\cdots\!08\)\( T^{31} + \)\(49\!\cdots\!81\)\( T^{32} - \)\(80\!\cdots\!34\)\( T^{33} + \)\(36\!\cdots\!78\)\( T^{34} - \)\(31\!\cdots\!94\)\( T^{35} + \)\(13\!\cdots\!81\)\( T^{36} \))(\( 1 - 16 T + 128 T^{2} - 592 T^{3} - 1656 T^{4} + 23440 T^{5} + 12160 T^{6} - 1905456 T^{7} + 29925468 T^{8} - 173074768 T^{9} + 361620096 T^{10} + 4542346608 T^{11} - 68895125960 T^{12} + 357047597520 T^{13} - 1589796719232 T^{14} + 13970550247952 T^{15} - 108713958564090 T^{16} + 852203565125072 T^{17} - 5915633592262272 T^{18} + 81043020732687120 T^{19} - 953910959717132360 T^{20} + 3836449142976697008 T^{21} + 18630802722380758656 T^{22} - \)\(54\!\cdots\!28\)\( T^{23} + \)\(57\!\cdots\!08\)\( T^{24} - \)\(22\!\cdots\!96\)\( T^{25} + \)\(86\!\cdots\!60\)\( T^{26} + \)\(10\!\cdots\!40\)\( T^{27} - \)\(43\!\cdots\!76\)\( T^{28} - \)\(95\!\cdots\!52\)\( T^{29} + \)\(12\!\cdots\!48\)\( T^{30} - \)\(96\!\cdots\!16\)\( T^{31} + \)\(36\!\cdots\!61\)\( T^{32} \))(\( ( 1 - 4 T + 61 T^{2} )^{2} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( ( 1 - 12 T + 61 T^{2} )^{2} \))(\( ( 1 + 12 T + 61 T^{2} )^{2} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( ( 1 + 2 T + 61 T^{2} )^{2} \))(\( ( 1 - 4 T + 61 T^{2} )^{2} \))(\( ( 1 + 6 T + 61 T^{2} )^{4} \))(\( ( 1 - 10 T + 61 T^{2} )( 1 + 10 T + 61 T^{2} ) \))(\( ( 1 - 10 T + 61 T^{2} )( 1 + 10 T + 61 T^{2} ) \))(\( ( 1 - 10 T + 61 T^{2} )( 1 + 10 T + 61 T^{2} ) \))(\( ( 1 - 10 T + 61 T^{2} )( 1 + 10 T + 61 T^{2} ) \))(\( ( 1 - 112 T^{2} + 9822 T^{4} - 416752 T^{6} + 13845841 T^{8} )^{2} \))(\( ( 1 - 112 T^{2} + 9822 T^{4} - 416752 T^{6} + 13845841 T^{8} )^{2} \))(\( 1 + 10 T + 50 T^{2} + 610 T^{3} + 3721 T^{4} \))(\( 1 + 10 T + 50 T^{2} + 610 T^{3} + 3721 T^{4} \))(\( ( 1 + 2162 T^{4} + 13845841 T^{8} )^{4} \))(\( ( 1 - 10 T + 61 T^{2} )( 1 + 12 T + 61 T^{2} ) \))(\( 1 - 14 T + 98 T^{2} - 134 T^{3} + 5041 T^{4} - 83168 T^{5} + 679312 T^{6} - 36608 T^{7} + 160260 T^{8} - 147217176 T^{9} + 2084286776 T^{10} + 4953407144 T^{11} - 49660935404 T^{12} - 134974970304 T^{13} + 7721336684016 T^{14} + 9084322150944 T^{15} - 105587914401314 T^{16} - 961048211302948 T^{17} + 38943687185882188 T^{18} - 58623940889479828 T^{19} - 392892629487289394 T^{20} + 2061968526143420064 T^{21} + \)\(10\!\cdots\!56\)\( T^{22} - \)\(11\!\cdots\!04\)\( T^{23} - \)\(25\!\cdots\!44\)\( T^{24} + \)\(15\!\cdots\!24\)\( T^{25} + \)\(39\!\cdots\!56\)\( T^{26} - \)\(17\!\cdots\!16\)\( T^{27} + \)\(11\!\cdots\!60\)\( T^{28} - \)\(15\!\cdots\!88\)\( T^{29} + \)\(18\!\cdots\!52\)\( T^{30} - \)\(13\!\cdots\!08\)\( T^{31} + \)\(49\!\cdots\!81\)\( T^{32} - \)\(80\!\cdots\!34\)\( T^{33} + \)\(36\!\cdots\!78\)\( T^{34} - \)\(31\!\cdots\!94\)\( T^{35} + \)\(13\!\cdots\!81\)\( T^{36} \))
$67$ (\( 1 - 2 T + 67 T^{2} \))(\( 1 + 6 T + 67 T^{2} \))(\( 1 + 8 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 - 6 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))(\( 1 + 126 T^{2} + 4489 T^{4} \))(\( ( 1 - 67 T^{2} )^{2} \))(\( 1 + 62 T^{2} + 4489 T^{4} \))(\( 1 + 62 T^{2} + 4489 T^{4} \))(\( ( 1 - 6 T + 18 T^{2} - 402 T^{3} + 4489 T^{4} )( 1 + 6 T + 18 T^{2} + 402 T^{3} + 4489 T^{4} ) \))(\( 1 - 164 T^{2} + 13002 T^{4} - 736196 T^{6} + 20151121 T^{8} \))(\( 1 - 164 T^{2} + 13002 T^{4} - 736196 T^{6} + 20151121 T^{8} \))(\( ( 1 + 67 T^{2} )^{4} \))(\( ( 1 + 128 T^{2} + 4489 T^{4} )^{4} \))(\( ( 1 + 4 T + 67 T^{2} )^{2} \))(\( ( 1 + 6 T + 339 T^{2} + 2332 T^{3} + 57824 T^{4} + 422744 T^{5} + 6773640 T^{6} + 47574572 T^{7} + 596885338 T^{8} + 3741287532 T^{9} + 39991317646 T^{10} + 213562253708 T^{11} + 2037260287320 T^{12} + 8518765496024 T^{13} + 78069634187168 T^{14} + 210948947218108 T^{15} + 2054581234204497 T^{16} + 2436406065339846 T^{17} + 27206534396294947 T^{18} )^{2} \))(\( 1 + 40 T + 800 T^{2} + 13360 T^{3} + 209304 T^{4} + 2744320 T^{5} + 31574400 T^{6} + 351104968 T^{7} + 3607784068 T^{8} + 33764313640 T^{9} + 312105577280 T^{10} + 2836999004832 T^{11} + 24392707271560 T^{12} + 209387952429520 T^{13} + 1822526446481312 T^{14} + 15227799511864392 T^{15} + 123927887608689286 T^{16} + 1020262567294914264 T^{17} + 8181321218254609568 T^{18} + 62976148736559723760 T^{19} + \)\(49\!\cdots\!60\)\( T^{20} + \)\(38\!\cdots\!24\)\( T^{21} + \)\(28\!\cdots\!20\)\( T^{22} + \)\(20\!\cdots\!20\)\( T^{23} + \)\(14\!\cdots\!88\)\( T^{24} + \)\(95\!\cdots\!96\)\( T^{25} + \)\(57\!\cdots\!00\)\( T^{26} + \)\(33\!\cdots\!60\)\( T^{27} + \)\(17\!\cdots\!44\)\( T^{28} + \)\(73\!\cdots\!20\)\( T^{29} + \)\(29\!\cdots\!00\)\( T^{30} + \)\(98\!\cdots\!20\)\( T^{31} + \)\(16\!\cdots\!81\)\( T^{32} \))(\( 1 - 20 T + 200 T^{2} - 1340 T^{3} + 4489 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 134 T^{3} + 4489 T^{4} \))(\( 1 + 14 T + 98 T^{2} + 938 T^{3} + 4489 T^{4} \))(\( 1 + 4489 T^{4} \))(\( 1 + 4489 T^{4} \))(\( 1 - 14 T + 98 T^{2} - 938 T^{3} + 4489 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 134 T^{3} + 4489 T^{4} \))(\( 1 + 20 T + 200 T^{2} + 1340 T^{3} + 4489 T^{4} \))(\( 1 - 2578 T^{4} + 20151121 T^{8} \))(\( 1 - 18 T + 162 T^{2} - 1206 T^{3} + 4489 T^{4} \))(\( 1 - 18 T + 162 T^{2} - 1206 T^{3} + 4489 T^{4} \))(\( 1 + 18 T + 162 T^{2} + 1206 T^{3} + 4489 T^{4} \))(\( 1 + 18 T + 162 T^{2} + 1206 T^{3} + 4489 T^{4} \))(\( 1 - 56 T^{4} - 39549474 T^{8} - 1128462776 T^{12} + 406067677556641 T^{16} \))(\( 1 - 56 T^{4} - 39549474 T^{8} - 1128462776 T^{12} + 406067677556641 T^{16} \))(\( 1 - 6 T + 18 T^{2} - 402 T^{3} + 4489 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 402 T^{3} + 4489 T^{4} \))(\( 1 + 6296 T^{4} + 28867012 T^{8} + 143453549192 T^{12} + 987214874886406 T^{16} + 2890749827647444232 T^{20} + \)\(11\!\cdots\!92\)\( T^{24} + \)\(51\!\cdots\!56\)\( T^{28} + \)\(16\!\cdots\!81\)\( T^{32} \))(\( 1 - 118 T^{2} + 4489 T^{4} \))(\( 1 - 642 T^{2} + 202585 T^{4} - 42240800 T^{6} + 6587340692 T^{8} - 822533069448 T^{10} + 85863586532372 T^{12} - 7723657296997344 T^{14} + 611883598063154038 T^{16} - 43282699253224131468 T^{18} + \)\(27\!\cdots\!82\)\( T^{20} - \)\(15\!\cdots\!24\)\( T^{22} + \)\(77\!\cdots\!68\)\( T^{24} - \)\(33\!\cdots\!68\)\( T^{26} + \)\(12\!\cdots\!08\)\( T^{28} - \)\(34\!\cdots\!00\)\( T^{30} + \)\(74\!\cdots\!65\)\( T^{32} - \)\(10\!\cdots\!02\)\( T^{34} + \)\(74\!\cdots\!09\)\( T^{36} \))
$71$ (\( 1 - 12 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 + 110 T^{2} + 5041 T^{4} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 8 T + 71 T^{2} )^{2} \))(\( ( 1 - 8 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{4} \))(\( ( 1 + 12 T + 70 T^{2} + 852 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 12 T + 70 T^{2} - 852 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 + 71 T^{2} )^{4} \))(\( ( 1 + 94 T^{2} + 5041 T^{4} )^{4} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 487 T^{2} + 5408 T^{3} + 109276 T^{4} + 1117104 T^{5} + 15152068 T^{6} + 140510560 T^{7} + 1464429734 T^{8} + 11951169672 T^{9} + 103974511114 T^{10} + 708313732960 T^{11} + 5423091809948 T^{12} + 28387490491824 T^{13} + 197158966559876 T^{14} + 692766335444768 T^{15} + 4429323517136417 T^{16} + 7749042374949132 T^{17} + 45848500718449031 T^{18} )^{2} \))(\( 1 - 496 T^{2} + 126200 T^{4} - 22164176 T^{6} + 3035981212 T^{8} - 345871731440 T^{10} + 33930788172232 T^{12} - 2913247940484688 T^{14} + 220255011325810374 T^{16} - 14685682867983312208 T^{18} + \)\(86\!\cdots\!92\)\( T^{20} - \)\(44\!\cdots\!40\)\( T^{22} + \)\(19\!\cdots\!32\)\( T^{24} - \)\(72\!\cdots\!76\)\( T^{26} + \)\(20\!\cdots\!00\)\( T^{28} - \)\(41\!\cdots\!76\)\( T^{30} + \)\(41\!\cdots\!21\)\( T^{32} \))(\( 1 + 2 T^{2} + 5041 T^{4} \))(\( 1 - 138 T^{2} + 5041 T^{4} \))(\( 1 - 106 T^{2} + 5041 T^{4} \))(\( ( 1 - 71 T^{2} )^{2} \))(\( ( 1 - 71 T^{2} )^{2} \))(\( 1 - 106 T^{2} + 5041 T^{4} \))(\( 1 - 138 T^{2} + 5041 T^{4} \))(\( 1 + 2 T^{2} + 5041 T^{4} \))(\( ( 1 - 34 T^{2} + 5041 T^{4} )^{2} \))(\( 1 - 106 T^{2} + 5041 T^{4} \))(\( 1 - 106 T^{2} + 5041 T^{4} \))(\( 1 - 106 T^{2} + 5041 T^{4} \))(\( 1 - 106 T^{2} + 5041 T^{4} \))(\( ( 1 - 80 T^{2} + 4878 T^{4} - 403280 T^{6} + 25411681 T^{8} )^{2} \))(\( ( 1 - 80 T^{2} + 4878 T^{4} - 403280 T^{6} + 25411681 T^{8} )^{2} \))(\( 1 - 106 T^{2} + 5041 T^{4} \))(\( 1 - 106 T^{2} + 5041 T^{4} \))(\( ( 1 - 312 T^{2} + 52060 T^{4} - 5897736 T^{6} + 485188230 T^{8} - 29730487176 T^{10} + 1322932112860 T^{12} - 39967288583352 T^{14} + 645753531245761 T^{16} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 12 T + 487 T^{2} + 5408 T^{3} + 109276 T^{4} + 1117104 T^{5} + 15152068 T^{6} + 140510560 T^{7} + 1464429734 T^{8} + 11951169672 T^{9} + 103974511114 T^{10} + 708313732960 T^{11} + 5423091809948 T^{12} + 28387490491824 T^{13} + 197158966559876 T^{14} + 692766335444768 T^{15} + 4429323517136417 T^{16} + 7749042374949132 T^{17} + 45848500718449031 T^{18} )^{2} \))
$73$ (\( 1 - 2 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( ( 1 + 6 T + 73 T^{2} )^{2} \))(\( ( 1 - 6 T + 73 T^{2} )( 1 + 6 T + 73 T^{2} ) \))(\( 1 - 82 T^{2} + 5329 T^{4} \))(\( 1 - 82 T^{2} + 5329 T^{4} \))(\( ( 1 - 73 T^{2} )^{4} \))(\( ( 1 + 8 T + 54 T^{2} + 584 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 + 8 T + 54 T^{2} + 584 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 73 T^{2} )^{4} \))(\( ( 1 - 122 T^{2} + 5329 T^{4} )^{4} \))(\( 1 + 6 T + 18 T^{2} + 438 T^{3} + 5329 T^{4} \))(\( 1 - 14 T + 98 T^{2} - 478 T^{3} + 18985 T^{4} - 253168 T^{5} + 1798064 T^{6} - 6514992 T^{7} + 139557044 T^{8} - 2029936680 T^{9} + 15767462456 T^{10} - 33693552040 T^{11} + 292899083780 T^{12} - 8285915235920 T^{13} + 88264019259856 T^{14} - 73937299816080 T^{15} - 2231393636040914 T^{16} - 15114080754166388 T^{17} + 440374853480206540 T^{18} - 1103327895054146324 T^{19} - 11891096686462030706 T^{20} - 28762866562551993360 T^{21} + \)\(25\!\cdots\!96\)\( T^{22} - \)\(17\!\cdots\!60\)\( T^{23} + \)\(44\!\cdots\!20\)\( T^{24} - \)\(37\!\cdots\!80\)\( T^{25} + \)\(12\!\cdots\!36\)\( T^{26} - \)\(11\!\cdots\!40\)\( T^{27} + \)\(59\!\cdots\!56\)\( T^{28} - \)\(20\!\cdots\!84\)\( T^{29} + \)\(41\!\cdots\!44\)\( T^{30} - \)\(42\!\cdots\!44\)\( T^{31} + \)\(23\!\cdots\!65\)\( T^{32} - \)\(42\!\cdots\!46\)\( T^{33} + \)\(63\!\cdots\!78\)\( T^{34} - \)\(66\!\cdots\!42\)\( T^{35} + \)\(34\!\cdots\!69\)\( T^{36} \))(\( 1 - 608 T^{2} + 176152 T^{4} - 32725024 T^{6} + 4446757724 T^{8} - 480608521056 T^{10} + 44061150589096 T^{12} - 3604673662492192 T^{14} + 272235901061020742 T^{16} - 19209305947420891168 T^{18} + \)\(12\!\cdots\!36\)\( T^{20} - \)\(72\!\cdots\!84\)\( T^{22} + \)\(35\!\cdots\!44\)\( T^{24} - \)\(14\!\cdots\!76\)\( T^{26} + \)\(40\!\cdots\!92\)\( T^{28} - \)\(74\!\cdots\!72\)\( T^{30} + \)\(65\!\cdots\!61\)\( T^{32} \))(\( 1 + 6 T + 18 T^{2} + 438 T^{3} + 5329 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( 1 - 18 T + 162 T^{2} - 1314 T^{3} + 5329 T^{4} \))(\( ( 1 - 16 T + 73 T^{2} )( 1 + 6 T + 73 T^{2} ) \))(\( ( 1 + 6 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} ) \))(\( 1 - 18 T + 162 T^{2} - 1314 T^{3} + 5329 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 146 T^{3} + 5329 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 438 T^{3} + 5329 T^{4} \))(\( ( 1 + 14 T + 98 T^{2} + 1022 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 16 T + 73 T^{2} )( 1 + 6 T + 73 T^{2} ) \))(\( ( 1 - 16 T + 73 T^{2} )( 1 + 6 T + 73 T^{2} ) \))(\( ( 1 - 16 T + 73 T^{2} )( 1 + 6 T + 73 T^{2} ) \))(\( ( 1 - 16 T + 73 T^{2} )( 1 + 6 T + 73 T^{2} ) \))(\( ( 1 + 16 T + 128 T^{2} + 1008 T^{3} + 7838 T^{4} + 73584 T^{5} + 682112 T^{6} + 6224272 T^{7} + 28398241 T^{8} )^{2} \))(\( ( 1 + 16 T + 128 T^{2} + 1008 T^{3} + 7838 T^{4} + 73584 T^{5} + 682112 T^{6} + 6224272 T^{7} + 28398241 T^{8} )^{2} \))(\( ( 1 - 6 T + 73 T^{2} )^{2} \))(\( ( 1 + 6 T + 73 T^{2} )^{2} \))(\( ( 1 + 128 T^{2} + 11692 T^{4} + 338816 T^{6} + 16421926 T^{8} + 1805550464 T^{10} + 332032233772 T^{12} + 19370780964992 T^{14} + 806460091894081 T^{16} )^{2} \))(\( 1 - 6 T + 18 T^{2} - 438 T^{3} + 5329 T^{4} \))(\( 1 + 14 T + 98 T^{2} + 478 T^{3} + 18985 T^{4} + 253168 T^{5} + 1798064 T^{6} + 6514992 T^{7} + 139557044 T^{8} + 2029936680 T^{9} + 15767462456 T^{10} + 33693552040 T^{11} + 292899083780 T^{12} + 8285915235920 T^{13} + 88264019259856 T^{14} + 73937299816080 T^{15} - 2231393636040914 T^{16} + 15114080754166388 T^{17} + 440374853480206540 T^{18} + 1103327895054146324 T^{19} - 11891096686462030706 T^{20} + 28762866562551993360 T^{21} + \)\(25\!\cdots\!96\)\( T^{22} + \)\(17\!\cdots\!60\)\( T^{23} + \)\(44\!\cdots\!20\)\( T^{24} + \)\(37\!\cdots\!80\)\( T^{25} + \)\(12\!\cdots\!36\)\( T^{26} + \)\(11\!\cdots\!40\)\( T^{27} + \)\(59\!\cdots\!56\)\( T^{28} + \)\(20\!\cdots\!84\)\( T^{29} + \)\(41\!\cdots\!44\)\( T^{30} + \)\(42\!\cdots\!44\)\( T^{31} + \)\(23\!\cdots\!65\)\( T^{32} + \)\(42\!\cdots\!46\)\( T^{33} + \)\(63\!\cdots\!78\)\( T^{34} + \)\(66\!\cdots\!42\)\( T^{35} + \)\(34\!\cdots\!69\)\( T^{36} \))
$79$ (\( 1 + 8 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 8 T + 79 T^{2} \))(\( 1 + 30 T^{2} + 6241 T^{4} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 - 16 T + 79 T^{2} )^{2} \))(\( ( 1 + 16 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{4} \))(\( ( 1 - 12 T + 79 T^{2} )^{4} \))(\( ( 1 + 12 T + 79 T^{2} )^{4} \))(\( ( 1 + 79 T^{2} )^{4} \))(\( ( 1 + 110 T^{2} + 6241 T^{4} )^{4} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 391 T^{2} + 2080 T^{3} + 75204 T^{4} + 283424 T^{5} + 9848140 T^{6} + 28571616 T^{7} + 990116222 T^{8} + 2449460656 T^{9} + 78219181538 T^{10} + 178315455456 T^{11} + 4855517097460 T^{12} + 11039387757344 T^{13} + 231406949430396 T^{14} + 505621907483680 T^{15} + 7508728413588169 T^{16} + 12136870479252488 T^{17} + 119851595982618319 T^{18} )^{2} \))(\( ( 1 + 8 T + 472 T^{2} + 4072 T^{3} + 104764 T^{4} + 914440 T^{5} + 14420328 T^{6} + 117234472 T^{7} + 1358280582 T^{8} + 9261523288 T^{9} + 89997267048 T^{10} + 450854583160 T^{11} + 4080566285884 T^{12} + 12529773656728 T^{13} + 114737279005912 T^{14} + 153631271889272 T^{15} + 1517108809906561 T^{16} )^{2} \))(\( ( 1 - 16 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 16 T + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{4} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 + 79 T^{2} )^{2} \))(\( ( 1 - 12 T + 79 T^{2} )^{8} \))(\( ( 1 + 12 T + 79 T^{2} )^{8} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 + 4 T + 196 T^{2} + 484 T^{3} + 18118 T^{4} + 38236 T^{5} + 1223236 T^{6} + 1972156 T^{7} + 38950081 T^{8} )^{4} \))(\( ( 1 + 8 T + 79 T^{2} )^{2} \))(\( ( 1 - 8 T + 391 T^{2} - 2080 T^{3} + 75204 T^{4} - 283424 T^{5} + 9848140 T^{6} - 28571616 T^{7} + 990116222 T^{8} - 2449460656 T^{9} + 78219181538 T^{10} - 178315455456 T^{11} + 4855517097460 T^{12} - 11039387757344 T^{13} + 231406949430396 T^{14} - 505621907483680 T^{15} + 7508728413588169 T^{16} - 12136870479252488 T^{17} + 119851595982618319 T^{18} )^{2} \))
$83$ (\( 1 - 6 T + 83 T^{2} \))(\( 1 + 10 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 + 16 T + 83 T^{2} \))(\( 1 - 10 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 + 158 T^{2} + 6889 T^{4} \))(\( ( 1 - 83 T^{2} )^{2} \))(\( 1 - 162 T^{2} + 6889 T^{4} \))(\( 1 - 162 T^{2} + 6889 T^{4} \))(\( ( 1 - 22 T + 242 T^{2} - 1826 T^{3} + 6889 T^{4} )( 1 + 22 T + 242 T^{2} + 1826 T^{3} + 6889 T^{4} ) \))(\( 1 - 308 T^{2} + 37386 T^{4} - 2121812 T^{6} + 47458321 T^{8} \))(\( 1 - 308 T^{2} + 37386 T^{4} - 2121812 T^{6} + 47458321 T^{8} \))(\( ( 1 + 83 T^{2} )^{4} \))(\( ( 1 + 16 T^{2} + 6889 T^{4} )^{4} \))(\( 1 - 162 T^{2} + 6889 T^{4} \))(\( 1 - 822 T^{2} + 339161 T^{4} - 93784032 T^{6} + 19542251380 T^{8} - 3265482130776 T^{10} + 454015681415604 T^{12} - 53737884583975712 T^{14} + 5490944378360489558 T^{16} - \)\(48\!\cdots\!20\)\( T^{18} + \)\(37\!\cdots\!62\)\( T^{20} - \)\(25\!\cdots\!52\)\( T^{22} + \)\(14\!\cdots\!76\)\( T^{24} - \)\(73\!\cdots\!16\)\( T^{26} + \)\(30\!\cdots\!20\)\( T^{28} - \)\(10\!\cdots\!52\)\( T^{30} + \)\(24\!\cdots\!69\)\( T^{32} - \)\(41\!\cdots\!82\)\( T^{34} + \)\(34\!\cdots\!09\)\( T^{36} \))(\( 1 + 40 T + 800 T^{2} + 11296 T^{3} + 140440 T^{4} + 1818288 T^{5} + 24179328 T^{6} + 306333608 T^{7} + 3572255108 T^{8} + 38587570376 T^{9} + 403383965760 T^{10} + 4243238443024 T^{11} + 44734530847368 T^{12} + 453650945068800 T^{13} + 4347518328900000 T^{14} + 40108758042139144 T^{15} + 365359573042238342 T^{16} + 3329026917497548952 T^{17} + 29950053767792100000 T^{18} + \)\(25\!\cdots\!00\)\( T^{19} + \)\(21\!\cdots\!28\)\( T^{20} + \)\(16\!\cdots\!32\)\( T^{21} + \)\(13\!\cdots\!40\)\( T^{22} + \)\(10\!\cdots\!52\)\( T^{23} + \)\(80\!\cdots\!28\)\( T^{24} + \)\(57\!\cdots\!24\)\( T^{25} + \)\(37\!\cdots\!72\)\( T^{26} + \)\(23\!\cdots\!96\)\( T^{27} + \)\(15\!\cdots\!40\)\( T^{28} + \)\(10\!\cdots\!48\)\( T^{29} + \)\(58\!\cdots\!00\)\( T^{30} + \)\(24\!\cdots\!80\)\( T^{31} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 - 4 T + 8 T^{2} - 332 T^{3} + 6889 T^{4} \))(\( 1 + 10 T + 50 T^{2} + 830 T^{3} + 6889 T^{4} \))(\( 1 + 10 T + 50 T^{2} + 830 T^{3} + 6889 T^{4} \))(\( 1 + 6889 T^{4} \))(\( 1 + 6889 T^{4} \))(\( 1 - 10 T + 50 T^{2} - 830 T^{3} + 6889 T^{4} \))(\( 1 - 10 T + 50 T^{2} - 830 T^{3} + 6889 T^{4} \))(\( 1 + 4 T + 8 T^{2} + 332 T^{3} + 6889 T^{4} \))(\( 1 + 2606 T^{4} + 47458321 T^{8} \))(\( 1 - 6 T + 18 T^{2} - 498 T^{3} + 6889 T^{4} \))(\( 1 - 6 T + 18 T^{2} - 498 T^{3} + 6889 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 498 T^{3} + 6889 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 498 T^{3} + 6889 T^{4} \))(\( 1 + 8200 T^{4} + 98353758 T^{8} + 389158232200 T^{12} + 2252292232139041 T^{16} \))(\( 1 + 8200 T^{4} + 98353758 T^{8} + 389158232200 T^{12} + 2252292232139041 T^{16} \))(\( 1 + 18 T + 162 T^{2} + 1494 T^{3} + 6889 T^{4} \))(\( 1 - 18 T + 162 T^{2} - 1494 T^{3} + 6889 T^{4} \))(\( 1 - 24808 T^{4} + 301625668 T^{8} - 2745693101560 T^{12} + 20938093531246342 T^{16} - \)\(13\!\cdots\!60\)\( T^{20} + \)\(67\!\cdots\!88\)\( T^{24} - \)\(26\!\cdots\!88\)\( T^{28} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( ( 1 - 2 T + 83 T^{2} )^{2} \))(\( ( 1 + 20 T + 611 T^{2} + 9668 T^{3} + 176280 T^{4} + 2256568 T^{5} + 31051408 T^{6} + 330148068 T^{7} + 3680856986 T^{8} + 32879739720 T^{9} + 305511129838 T^{10} + 2274390040452 T^{11} + 17754791426096 T^{12} + 107092928502328 T^{13} + 694374084548040 T^{14} + 3160859529731492 T^{15} + 16580127154662097 T^{16} + 45045844642780820 T^{17} + 186940255267540403 T^{18} )^{2} \))
$89$ (\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{4} \))(\( ( 1 + 12 T + 166 T^{2} + 1068 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 12 T + 166 T^{2} + 1068 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 14 T + 89 T^{2} )^{4} \))(\( ( 1 + 2 T + 89 T^{2} )^{8} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 + 6 T + 353 T^{2} + 1520 T^{3} + 61156 T^{4} + 191528 T^{5} + 7861620 T^{6} + 23163024 T^{7} + 859994622 T^{8} + 2479282468 T^{9} + 76539521358 T^{10} + 183474313104 T^{11} + 5542198389780 T^{12} + 12016895934248 T^{13} + 341498739663044 T^{14} + 755411562260720 T^{15} + 15613661218121737 T^{16} + 23619532834212486 T^{17} + 350356403707485209 T^{18} )^{2} \))(\( 1 - 1008 T^{2} + 500216 T^{4} - 162007248 T^{6} + 38289207708 T^{8} - 6996120084720 T^{10} + 1021580363534536 T^{12} - 121542047545014352 T^{14} + 11903420607294617798 T^{16} - \)\(96\!\cdots\!92\)\( T^{18} + \)\(64\!\cdots\!76\)\( T^{20} - \)\(34\!\cdots\!20\)\( T^{22} + \)\(15\!\cdots\!48\)\( T^{24} - \)\(50\!\cdots\!48\)\( T^{26} + \)\(12\!\cdots\!36\)\( T^{28} - \)\(19\!\cdots\!28\)\( T^{30} + \)\(15\!\cdots\!61\)\( T^{32} \))(\( ( 1 - 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )( 1 + 10 T + 89 T^{2} ) \))(\( ( 1 - 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )( 1 + 10 T + 89 T^{2} ) \))(\( ( 1 - 10 T + 89 T^{2} )( 1 + 10 T + 89 T^{2} ) \))(\( ( 1 - 89 T^{2} )^{2} \))(\( ( 1 - 10 T + 89 T^{2} )( 1 + 10 T + 89 T^{2} ) \))(\( ( 1 - 89 T^{2} )^{2} \))(\( ( 1 - 114 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 - 89 T^{2} )^{2} \))(\( ( 1 - 89 T^{2} )^{2} \))(\( ( 1 - 89 T^{2} )^{2} \))(\( ( 1 - 89 T^{2} )^{2} \))(\( ( 1 - 116 T^{2} + 7110 T^{4} - 918836 T^{6} + 62742241 T^{8} )^{2} \))(\( ( 1 - 116 T^{2} + 7110 T^{4} - 918836 T^{6} + 62742241 T^{8} )^{2} \))(\( 1 - 34 T^{2} + 7921 T^{4} \))(\( 1 - 34 T^{2} + 7921 T^{4} \))(\( ( 1 - 504 T^{2} + 120796 T^{4} - 18233160 T^{6} + 1917111942 T^{8} - 144424860360 T^{10} + 7579011743836 T^{12} - 250478570644344 T^{14} + 3936588805702081 T^{16} )^{2} \))(\( ( 1 + 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 6 T + 353 T^{2} - 1520 T^{3} + 61156 T^{4} - 191528 T^{5} + 7861620 T^{6} - 23163024 T^{7} + 859994622 T^{8} - 2479282468 T^{9} + 76539521358 T^{10} - 183474313104 T^{11} + 5542198389780 T^{12} - 12016895934248 T^{13} + 341498739663044 T^{14} - 755411562260720 T^{15} + 15613661218121737 T^{16} - 23619532834212486 T^{17} + 350356403707485209 T^{18} )^{2} \))
$97$ (\( 1 - 2 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 + 14 T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( ( 1 - 2 T + 97 T^{2} )^{2} \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \))(\( 1 + 62 T^{2} + 9409 T^{4} \))(\( 1 + 62 T^{2} + 9409 T^{4} \))(\( ( 1 - 97 T^{2} )^{4} \))(\( ( 1 - 8 T + 102 T^{2} - 776 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 - 8 T + 102 T^{2} - 776 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 - 97 T^{2} )^{4} \))(\( ( 1 + 22 T^{2} + 9409 T^{4} )^{4} \))(\( 1 + 22 T + 242 T^{2} + 2134 T^{3} + 9409 T^{4} \))(\( 1 - 18 T + 162 T^{2} - 1234 T^{3} + 9625 T^{4} - 177840 T^{5} + 2403248 T^{6} - 33068464 T^{7} + 465762612 T^{8} - 3963438712 T^{9} + 29377109048 T^{10} - 206755021688 T^{11} + 2522153752132 T^{12} - 44692244379088 T^{13} + 500529043592144 T^{14} - 5501619757610192 T^{15} + 44798006883295918 T^{16} - 270735800376809964 T^{17} + 2482816968072160076 T^{18} - 26261372636550566508 T^{19} + \)\(42\!\cdots\!62\)\( T^{20} - \)\(50\!\cdots\!16\)\( T^{21} + \)\(44\!\cdots\!64\)\( T^{22} - \)\(38\!\cdots\!16\)\( T^{23} + \)\(21\!\cdots\!28\)\( T^{24} - \)\(16\!\cdots\!44\)\( T^{25} + \)\(23\!\cdots\!28\)\( T^{26} - \)\(30\!\cdots\!04\)\( T^{27} + \)\(34\!\cdots\!88\)\( T^{28} - \)\(23\!\cdots\!92\)\( T^{29} + \)\(16\!\cdots\!68\)\( T^{30} - \)\(11\!\cdots\!80\)\( T^{31} + \)\(62\!\cdots\!25\)\( T^{32} - \)\(78\!\cdots\!62\)\( T^{33} + \)\(99\!\cdots\!02\)\( T^{34} - \)\(10\!\cdots\!66\)\( T^{35} + \)\(57\!\cdots\!89\)\( T^{36} \))(\( ( 1 + 336 T^{2} - 416 T^{3} + 55308 T^{4} - 280480 T^{5} + 5933488 T^{6} - 54427584 T^{7} + 538019110 T^{8} - 5279475648 T^{9} + 55828188592 T^{10} - 255986523040 T^{11} + 4896377473548 T^{12} - 3572333546912 T^{13} + 279878593656144 T^{14} + 7837433594376961 T^{16} )^{2} \))(\( 1 + 6 T + 18 T^{2} + 582 T^{3} + 9409 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 582 T^{3} + 9409 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 582 T^{3} + 9409 T^{4} \))(\( ( 1 - 18 T + 97 T^{2} )( 1 + 8 T + 97 T^{2} ) \))(\( ( 1 - 18 T + 97 T^{2} )( 1 - 8 T + 97 T^{2} ) \))(\( 1 + 6 T + 18 T^{2} + 582 T^{3} + 9409 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 582 T^{3} + 9409 T^{4} \))(\( 1 + 6 T + 18 T^{2} + 582 T^{3} + 9409 T^{4} \))(\( ( 1 + 14 T + 98 T^{2} + 1358 T^{3} + 9409 T^{4} )^{2} \))(\( 1 + 14 T + 98 T^{2} + 1358 T^{3} + 9409 T^{4} \))(\( 1 + 14 T + 98 T^{2} + 1358 T^{3} + 9409 T^{4} \))(\( 1 + 14 T + 98 T^{2} + 1358 T^{3} + 9409 T^{4} \))(\( 1 + 14 T + 98 T^{2} + 1358 T^{3} + 9409 T^{4} \))(\( ( 1 + 16 T + 128 T^{2} + 1392 T^{3} + 15038 T^{4} + 135024 T^{5} + 1204352 T^{6} + 14602768 T^{7} + 88529281 T^{8} )^{2} \))(\( ( 1 + 16 T + 128 T^{2} + 1392 T^{3} + 15038 T^{4} + 135024 T^{5} + 1204352 T^{6} + 14602768 T^{7} + 88529281 T^{8} )^{2} \))(\( 1 - 50 T^{2} + 9409 T^{4} \))(\( 1 - 50 T^{2} + 9409 T^{4} \))(\( ( 1 - 576 T^{2} + 159724 T^{4} - 27489216 T^{6} + 3203946342 T^{8} - 258646033344 T^{10} + 14140250878444 T^{12} - 479791874839104 T^{14} + 7837433594376961 T^{16} )^{2} \))(\( 1 + 22 T + 242 T^{2} + 2134 T^{3} + 9409 T^{4} \))(\( 1 - 18 T + 162 T^{2} - 1234 T^{3} + 9625 T^{4} - 177840 T^{5} + 2403248 T^{6} - 33068464 T^{7} + 465762612 T^{8} - 3963438712 T^{9} + 29377109048 T^{10} - 206755021688 T^{11} + 2522153752132 T^{12} - 44692244379088 T^{13} + 500529043592144 T^{14} - 5501619757610192 T^{15} + 44798006883295918 T^{16} - 270735800376809964 T^{17} + 2482816968072160076 T^{18} - 26261372636550566508 T^{19} + \)\(42\!\cdots\!62\)\( T^{20} - \)\(50\!\cdots\!16\)\( T^{21} + \)\(44\!\cdots\!64\)\( T^{22} - \)\(38\!\cdots\!16\)\( T^{23} + \)\(21\!\cdots\!28\)\( T^{24} - \)\(16\!\cdots\!44\)\( T^{25} + \)\(23\!\cdots\!28\)\( T^{26} - \)\(30\!\cdots\!04\)\( T^{27} + \)\(34\!\cdots\!88\)\( T^{28} - \)\(23\!\cdots\!92\)\( T^{29} + \)\(16\!\cdots\!68\)\( T^{30} - \)\(11\!\cdots\!80\)\( T^{31} + \)\(62\!\cdots\!25\)\( T^{32} - \)\(78\!\cdots\!62\)\( T^{33} + \)\(99\!\cdots\!02\)\( T^{34} - \)\(10\!\cdots\!66\)\( T^{35} + \)\(57\!\cdots\!89\)\( T^{36} \))
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