Properties

Label 99.2
Level 99
Weight 2
Dimension 240
Nonzero newspaces 8
Newform subspaces 19
Sturm bound 1440
Trace bound 3

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Defining parameters

Level: \( N \) = \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 19 \)
Sturm bound: \(1440\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(99))\).

Total New Old
Modular forms 440 320 120
Cusp forms 281 240 41
Eisenstein series 159 80 79

Trace form

\( 240q - 15q^{2} - 20q^{3} - 15q^{4} - 15q^{5} - 20q^{6} - 20q^{7} - 25q^{8} - 20q^{9} + O(q^{10}) \) \( 240q - 15q^{2} - 20q^{3} - 15q^{4} - 15q^{5} - 20q^{6} - 20q^{7} - 25q^{8} - 20q^{9} - 60q^{10} - 20q^{11} - 40q^{12} - 20q^{13} - 30q^{14} - 20q^{15} - 45q^{16} - 30q^{17} - 20q^{18} - 60q^{19} - 10q^{20} - 20q^{21} - 45q^{22} - 25q^{23} + 10q^{24} - 5q^{25} + 20q^{26} + 10q^{27} + 20q^{28} + 20q^{29} + 40q^{30} + 5q^{31} + 95q^{32} + 30q^{33} + 10q^{34} + 40q^{35} + 50q^{36} - 35q^{37} + 50q^{38} + 10q^{39} + 20q^{40} + 40q^{42} - 20q^{43} - 25q^{44} - 30q^{45} - 110q^{46} - 50q^{47} + 20q^{48} - 70q^{49} + 5q^{50} - 10q^{51} - 20q^{52} + 10q^{53} + 60q^{54} - 25q^{55} + 60q^{56} + 60q^{57} + 60q^{58} + 75q^{59} + 120q^{60} + 20q^{61} + 180q^{62} + 60q^{63} + 105q^{64} + 90q^{65} + 110q^{66} + 65q^{67} + 160q^{68} + 60q^{69} + 90q^{70} + 75q^{71} + 130q^{72} - 30q^{73} + 150q^{74} + 50q^{75} + 10q^{76} + 60q^{77} + 60q^{78} - 20q^{79} - 120q^{80} - 20q^{81} - 10q^{82} - 110q^{83} - 110q^{84} - 80q^{85} - 160q^{86} - 120q^{87} - 95q^{88} - 145q^{89} - 220q^{90} - 40q^{91} - 220q^{92} - 120q^{93} - 90q^{94} - 210q^{95} - 310q^{96} - 75q^{97} - 275q^{98} - 180q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)

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
99.2.a \(\chi_{99}(1, \cdot)\) 99.2.a.a 1 1
99.2.a.b 1
99.2.a.c 1
99.2.a.d 1
99.2.d \(\chi_{99}(98, \cdot)\) 99.2.d.a 4 1
99.2.e \(\chi_{99}(34, \cdot)\) 99.2.e.a 2 2
99.2.e.b 2
99.2.e.c 2
99.2.e.d 6
99.2.e.e 8
99.2.f \(\chi_{99}(37, \cdot)\) 99.2.f.a 4 4
99.2.f.b 4
99.2.f.c 8
99.2.g \(\chi_{99}(32, \cdot)\) 99.2.g.a 4 2
99.2.g.b 16
99.2.j \(\chi_{99}(8, \cdot)\) 99.2.j.a 16 4
99.2.m \(\chi_{99}(4, \cdot)\) 99.2.m.a 8 8
99.2.m.b 72
99.2.p \(\chi_{99}(2, \cdot)\) 99.2.p.a 80 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(99))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(99)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))(\( 1 - T + 2 T^{2} \))(\( 1 - 2 T + 2 T^{2} \))(\( ( 1 + T^{2} + 4 T^{4} )^{2} \))(\( 1 + T - T^{2} + 2 T^{3} + 4 T^{4} \))(\( 1 - 2 T^{2} + 4 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4} \))(\( 1 - 3 T^{2} + 2 T^{3} + 3 T^{4} - 3 T^{5} - T^{6} - 6 T^{7} + 12 T^{8} + 16 T^{9} - 48 T^{10} + 64 T^{12} \))(\( 1 + T + 2 T^{2} + 3 T^{3} + 2 T^{4} - 4 T^{5} + T^{6} - 6 T^{7} - 11 T^{8} - 12 T^{9} + 4 T^{10} - 32 T^{11} + 32 T^{12} + 96 T^{13} + 128 T^{14} + 128 T^{15} + 256 T^{16} \))(\( 1 - T + 4 T^{2} - 2 T^{3} + 9 T^{4} - 4 T^{5} + 16 T^{6} - 8 T^{7} + 16 T^{8} \))(\( 1 - 3 T + 2 T^{2} + T^{4} + 8 T^{6} - 24 T^{7} + 16 T^{8} \))(\( 1 - 3 T^{2} + 2 T^{6} + 9 T^{8} + 8 T^{10} - 192 T^{14} + 256 T^{16} \))(\( ( 1 - 2 T^{2} + 4 T^{4} )^{2} \))(\( 1 - T^{2} - 6 T^{4} + T^{6} + 8 T^{8} + 30 T^{10} - 35 T^{12} - 100 T^{14} + 393 T^{16} - 400 T^{18} - 560 T^{20} + 1920 T^{22} + 2048 T^{24} + 1024 T^{26} - 24576 T^{28} - 16384 T^{30} + 65536 T^{32} \))(\( 1 - 2 T^{2} + 5 T^{4} - 20 T^{6} + 30 T^{8} - 106 T^{10} + 212 T^{12} - 350 T^{14} + 1105 T^{16} - 1400 T^{18} + 3392 T^{20} - 6784 T^{22} + 7680 T^{24} - 20480 T^{26} + 20480 T^{28} - 32768 T^{30} + 65536 T^{32} \))(\( ( 1 - T + 4 T^{2} - 2 T^{3} + 9 T^{4} - 4 T^{5} + 16 T^{6} - 8 T^{7} + 16 T^{8} )( 1 + 5 T + 13 T^{2} + 25 T^{3} + 39 T^{4} + 50 T^{5} + 52 T^{6} + 40 T^{7} + 16 T^{8} ) \))
$3$ (\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 + 9 T^{3} + 27 T^{6} \))(\( 1 - 5 T + 15 T^{2} - 35 T^{3} + 67 T^{4} - 105 T^{5} + 135 T^{6} - 135 T^{7} + 81 T^{8} \))(\( 1 + T - 2 T^{2} + 3 T^{3} + 9 T^{4} \))(\( ( 1 + 3 T + 3 T^{2} - 3 T^{3} - 15 T^{4} - 9 T^{5} + 27 T^{6} + 81 T^{7} + 81 T^{8} )^{2} \))(\( 1 - 3 T + 6 T^{2} - 9 T^{3} + 9 T^{4} - 27 T^{5} + 54 T^{6} - 81 T^{7} + 81 T^{8} \))
$5$ (\( 1 + 4 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))(\( ( 1 - 8 T^{2} + 25 T^{4} )^{2} \))(\( 1 + T - 4 T^{2} + 5 T^{3} + 25 T^{4} \))(\( 1 - 3 T + 4 T^{2} - 15 T^{3} + 25 T^{4} \))(\( 1 - 2 T - T^{2} - 10 T^{3} + 25 T^{4} \))(\( 1 + 3 T - 6 T^{2} - 13 T^{3} + 63 T^{4} + 60 T^{5} - 259 T^{6} + 300 T^{7} + 1575 T^{8} - 1625 T^{9} - 3750 T^{10} + 9375 T^{11} + 15625 T^{12} \))(\( 1 + 4 T + 5 T^{2} - 18 T^{3} - 94 T^{4} - 232 T^{5} - 110 T^{6} + 1011 T^{7} + 3826 T^{8} + 5055 T^{9} - 2750 T^{10} - 29000 T^{11} - 58750 T^{12} - 56250 T^{13} + 78125 T^{14} + 312500 T^{15} + 390625 T^{16} \))(\( 1 - 3 T - T^{2} + 3 T^{3} + 16 T^{4} + 15 T^{5} - 25 T^{6} - 375 T^{7} + 625 T^{8} \))(\( 1 - T + T^{2} - 11 T^{3} + 36 T^{4} - 55 T^{5} + 25 T^{6} - 125 T^{7} + 625 T^{8} \))(\( 1 - 9 T^{2} + 21 T^{4} + 161 T^{6} - 1644 T^{8} + 4025 T^{10} + 13125 T^{12} - 140625 T^{14} + 390625 T^{16} \))(\( ( 1 + 3 T + 5 T^{2} )^{2}( 1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4} ) \))(\( ( 1 + 13 T^{2} + 88 T^{4} + 72 T^{5} + 430 T^{6} + 729 T^{7} + 1846 T^{8} + 3645 T^{9} + 10750 T^{10} + 9000 T^{11} + 55000 T^{12} + 203125 T^{14} + 390625 T^{16} )^{2} \))(\( 1 + 26 T^{2} + 267 T^{4} + 1158 T^{6} - 345 T^{8} - 23178 T^{10} - 84123 T^{12} - 137046 T^{14} - 351264 T^{16} - 3426150 T^{18} - 52576875 T^{20} - 362156250 T^{22} - 134765625 T^{24} + 11308593750 T^{26} + 65185546875 T^{28} + 158691406250 T^{30} + 152587890625 T^{32} \))(\( 1 - 6 T + 25 T^{2} - 54 T^{3} + 84 T^{4} - 84 T^{5} + 395 T^{6} - 1746 T^{7} + 5171 T^{8} - 8730 T^{9} + 9875 T^{10} - 10500 T^{11} + 52500 T^{12} - 168750 T^{13} + 390625 T^{14} - 468750 T^{15} + 390625 T^{16} \))
$7$ (\( 1 + 2 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))(\( ( 1 - 8 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 - T + 7 T^{2} )( 1 + 5 T + 7 T^{2} ) \))(\( ( 1 - 5 T + 7 T^{2} )( 1 + T + 7 T^{2} ) \))(\( ( 1 - T + 7 T^{2} )( 1 + 5 T + 7 T^{2} ) \))(\( 1 - 3 T - 12 T^{2} + 19 T^{3} + 171 T^{4} - 126 T^{5} - 1161 T^{6} - 882 T^{7} + 8379 T^{8} + 6517 T^{9} - 28812 T^{10} - 50421 T^{11} + 117649 T^{12} \))(\( 1 + T - 21 T^{2} - 10 T^{3} + 254 T^{4} + 36 T^{5} - 2408 T^{6} - 83 T^{7} + 18573 T^{8} - 581 T^{9} - 117992 T^{10} + 12348 T^{11} + 609854 T^{12} - 168070 T^{13} - 2470629 T^{14} + 823543 T^{15} + 5764801 T^{16} \))(\( 1 - T - 6 T^{2} + 13 T^{3} + 29 T^{4} + 91 T^{5} - 294 T^{6} - 343 T^{7} + 2401 T^{8} \))(\( 1 + 3 T + 2 T^{2} - 15 T^{3} - 59 T^{4} - 105 T^{5} + 98 T^{6} + 1029 T^{7} + 2401 T^{8} \))(\( ( 1 + 3 T + 12 T^{2} + 35 T^{3} + 141 T^{4} + 245 T^{5} + 588 T^{6} + 1029 T^{7} + 2401 T^{8} )^{2} \))(\( ( 1 + 7 T^{2} + 49 T^{4} )^{2} \))(\( 1 + 23 T^{2} + 219 T^{4} + 922 T^{6} + 284 T^{8} - 9168 T^{10} + 53788 T^{12} + 1337633 T^{14} + 12397533 T^{16} + 65544017 T^{18} + 129144988 T^{20} - 1078606032 T^{22} + 1637203484 T^{24} + 260442179578 T^{26} + 3031241897019 T^{28} + 15599130675527 T^{30} + 33232930569601 T^{32} \))(\( ( 1 + 13 T^{2} + 20 T^{3} + 80 T^{4} + 260 T^{5} + 783 T^{6} + 2170 T^{7} + 6819 T^{8} + 15190 T^{9} + 38367 T^{10} + 89180 T^{11} + 192080 T^{12} + 336140 T^{13} + 1529437 T^{14} + 5764801 T^{16} )^{2} \))(\( ( 1 - 4 T + 9 T^{2} - 8 T^{3} - 31 T^{4} - 56 T^{5} + 441 T^{6} - 1372 T^{7} + 2401 T^{8} )( 1 + 5 T + 18 T^{2} + 55 T^{3} + 149 T^{4} + 385 T^{5} + 882 T^{6} + 1715 T^{7} + 2401 T^{8} ) \))
$11$ (\( 1 + T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))(\( 1 + 10 T^{2} + 121 T^{4} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( ( 1 - T + T^{2} )^{3} \))(\( ( 1 + T + T^{2} )^{4} \))(\( 1 - 11 T + 51 T^{2} - 121 T^{3} + 121 T^{4} \))(\( 1 + 9 T + 41 T^{2} + 99 T^{3} + 121 T^{4} \))(\( 1 - 19 T^{2} + 231 T^{4} - 2299 T^{6} + 14641 T^{8} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 + 12 T + 88 T^{2} + 480 T^{3} + 2146 T^{4} + 8004 T^{5} + 25888 T^{6} + 79956 T^{7} + 254659 T^{8} + 879516 T^{9} + 3132448 T^{10} + 10653324 T^{11} + 31419586 T^{12} + 77304480 T^{13} + 155897368 T^{14} + 233846052 T^{15} + 214358881 T^{16} \))(\( 1 - 60 T^{2} + 1779 T^{4} - 33610 T^{6} + 439341 T^{8} - 4066810 T^{10} + 26046339 T^{12} - 106293660 T^{14} + 214358881 T^{16} \))(\( 1 - T - 20 T^{2} + T^{3} + 309 T^{4} + 11 T^{5} - 2420 T^{6} - 1331 T^{7} + 14641 T^{8} \))
$13$ (\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( ( 1 - 2 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 7 T + 13 T^{2} )( 1 + 5 T + 13 T^{2} ) \))(\( ( 1 - 5 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))(\( 1 + 4 T + 3 T^{2} + 52 T^{3} + 169 T^{4} \))(\( 1 - 9 T + 27 T^{2} - 20 T^{3} + 117 T^{4} - 1467 T^{5} + 7086 T^{6} - 19071 T^{7} + 19773 T^{8} - 43940 T^{9} + 771147 T^{10} - 3341637 T^{11} + 4826809 T^{12} \))(\( 1 + 7 T + 12 T^{2} + 23 T^{3} + 77 T^{4} - 624 T^{5} - 1550 T^{6} + 622 T^{7} - 8472 T^{8} + 8086 T^{9} - 261950 T^{10} - 1370928 T^{11} + 2199197 T^{12} + 8539739 T^{13} + 57921708 T^{14} + 439239619 T^{15} + 815730721 T^{16} \))(\( 1 - 7 T + 6 T^{2} + 49 T^{3} - 181 T^{4} + 637 T^{5} + 1014 T^{6} - 15379 T^{7} + 28561 T^{8} \))(\( 1 + 9 T + 18 T^{2} - 115 T^{3} - 789 T^{4} - 1495 T^{5} + 3042 T^{6} + 19773 T^{7} + 28561 T^{8} \))(\( ( 1 + 3 T + 6 T^{2} + 59 T^{3} + 339 T^{4} + 767 T^{5} + 1014 T^{6} + 6591 T^{7} + 28561 T^{8} )^{2} \))(\( ( 1 + 13 T^{2} + 169 T^{4} )^{2} \))(\( 1 + 53 T^{2} + 1500 T^{4} + 25933 T^{6} + 263753 T^{8} + 468144 T^{10} - 38632730 T^{12} - 890236186 T^{14} - 13299736152 T^{16} - 150449915434 T^{18} - 1103389401530 T^{20} + 2259641672496 T^{22} + 215151424855913 T^{24} + 3575084269120117 T^{26} + 34947127683721500 T^{28} + 208680948442062317 T^{30} + 665416609183179841 T^{32} \))(\( ( 1 + 7 T^{2} + 80 T^{3} + 170 T^{4} + 560 T^{5} + 4587 T^{6} + 13570 T^{7} + 40179 T^{8} + 176410 T^{9} + 775203 T^{10} + 1230320 T^{11} + 4855370 T^{12} + 29703440 T^{13} + 33787663 T^{14} + 815730721 T^{16} )^{2} \))(\( 1 - 8 T + 13 T^{2} + 80 T^{3} - 400 T^{4} + 1168 T^{5} - 2101 T^{6} - 18940 T^{7} + 139519 T^{8} - 246220 T^{9} - 355069 T^{10} + 2566096 T^{11} - 11424400 T^{12} + 29703440 T^{13} + 62748517 T^{14} - 501988136 T^{15} + 815730721 T^{16} \))
$17$ (\( 1 - 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( ( 1 + 17 T^{2} )^{4} \))(\( ( 1 - 4 T + 17 T^{2} )^{2} \))(\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( ( 1 - 4 T + 17 T^{2} )^{2} \))(\( ( 1 + 3 T + 45 T^{2} + 103 T^{3} + 765 T^{4} + 867 T^{5} + 4913 T^{6} )^{2} \))(\( ( 1 + 5 T + 44 T^{2} + 86 T^{3} + 682 T^{4} + 1462 T^{5} + 12716 T^{6} + 24565 T^{7} + 83521 T^{8} )^{2} \))(\( 1 + 12 T + 37 T^{2} - 180 T^{3} - 1619 T^{4} - 3060 T^{5} + 10693 T^{6} + 58956 T^{7} + 83521 T^{8} \))(\( 1 + 2 T - 13 T^{2} + 20 T^{3} + 341 T^{4} + 340 T^{5} - 3757 T^{6} + 9826 T^{7} + 83521 T^{8} \))(\( 1 - 279 T^{4} - 1420 T^{6} + 82101 T^{8} - 410380 T^{10} - 23302359 T^{12} + 6975757441 T^{16} \))(\( ( 1 + 17 T^{2} )^{4} \))(\( ( 1 + 43 T^{2} + 1684 T^{4} + 38266 T^{6} + 797440 T^{8} + 11058874 T^{10} + 140649364 T^{12} + 1037915467 T^{14} + 6975757441 T^{16} )^{2} \))(\( 1 - 58 T^{2} + 1230 T^{4} + 3270 T^{6} - 669405 T^{8} + 13275246 T^{10} - 49036968 T^{12} - 2836388280 T^{14} + 74928517905 T^{16} - 819716212920 T^{18} - 4095616604328 T^{20} + 320432166316974 T^{22} - 4669606909792605 T^{24} + 6592300054468230 T^{26} + 716625351792606030 T^{28} - 9765913940445253882 T^{30} + 48661191875666868481 T^{32} \))(\( ( 1 - 6 T + 19 T^{2} - 132 T^{3} + 829 T^{4} - 2244 T^{5} + 5491 T^{6} - 29478 T^{7} + 83521 T^{8} )^{2} \))
$19$ (\( 1 + 6 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( 1 + 19 T^{2} \))(\( ( 1 + 16 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 - 6 T + 19 T^{2} )^{2} \))(\( ( 1 - 2 T + 19 T^{2} )^{2} \))(\( ( 1 + 6 T + 19 T^{2} )^{2} \))(\( ( 1 + 9 T + 75 T^{2} + 333 T^{3} + 1425 T^{4} + 3249 T^{5} + 6859 T^{6} )^{2} \))(\( ( 1 - 9 T + 76 T^{2} - 432 T^{3} + 2112 T^{4} - 8208 T^{5} + 27436 T^{6} - 61731 T^{7} + 130321 T^{8} )^{2} \))(\( 1 + 10 T + 21 T^{2} - 70 T^{3} - 469 T^{4} - 1330 T^{5} + 7581 T^{6} + 68590 T^{7} + 130321 T^{8} \))(\( 1 + 10 T + 21 T^{2} - 70 T^{3} - 469 T^{4} - 1330 T^{5} + 7581 T^{6} + 68590 T^{7} + 130321 T^{8} \))(\( ( 1 - 6 T - 3 T^{2} + 122 T^{3} - 525 T^{4} + 2318 T^{5} - 1083 T^{6} - 41154 T^{7} + 130321 T^{8} )^{2} \))(\( ( 1 - 19 T^{2} )^{4} \))(\( ( 1 - 89 T^{2} + 4078 T^{4} - 125462 T^{6} + 2786848 T^{8} - 45291782 T^{10} + 531449038 T^{12} - 4187083409 T^{14} + 16983563041 T^{16} )^{2} \))(\( ( 1 + 34 T^{2} + 20 T^{3} + 395 T^{4} + 680 T^{5} + 1356 T^{6} + 48280 T^{7} - 47451 T^{8} + 917320 T^{9} + 489516 T^{10} + 4664120 T^{11} + 51476795 T^{12} + 49521980 T^{13} + 1599559954 T^{14} + 16983563041 T^{16} )^{2} \))(\( ( 1 + T - 18 T^{2} - 37 T^{3} + 305 T^{4} - 703 T^{5} - 6498 T^{6} + 6859 T^{7} + 130321 T^{8} )^{2} \))
$23$ (\( 1 - 4 T + 23 T^{2} \))(\( 1 + 8 T + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 - T + 23 T^{2} \))(\( ( 1 - 38 T^{2} + 529 T^{4} )^{2} \))(\( 1 - 4 T - 7 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 + 3 T - 14 T^{2} + 69 T^{3} + 529 T^{4} \))(\( 1 - T - 22 T^{2} - 23 T^{3} + 529 T^{4} \))(\( 1 - 6 T - 36 T^{2} + 82 T^{3} + 1986 T^{4} - 1806 T^{5} - 47893 T^{6} - 41538 T^{7} + 1050594 T^{8} + 997694 T^{9} - 10074276 T^{10} - 38618058 T^{11} + 148035889 T^{12} \))(\( 1 + 14 T + 53 T^{2} + 96 T^{3} + 1775 T^{4} + 8902 T^{5} - 9839 T^{6} + 41958 T^{7} + 1213519 T^{8} + 965034 T^{9} - 5204831 T^{10} + 108310634 T^{11} + 496717775 T^{12} + 617888928 T^{13} + 7845902117 T^{14} + 47667556258 T^{15} + 78310985281 T^{16} \))(\( ( 1 - 4 T + 45 T^{2} - 92 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 - 2 T + 27 T^{2} - 46 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 + 20 T^{2} + 753 T^{4} + 10580 T^{6} + 279841 T^{8} )^{2} \))(\( ( 1 - 9 T + 58 T^{2} - 207 T^{3} + 529 T^{4} )( 1 + 9 T + 58 T^{2} + 207 T^{3} + 529 T^{4} ) \))(\( ( 1 - 6 T + 67 T^{2} - 330 T^{3} + 1765 T^{4} - 8928 T^{5} + 54913 T^{6} - 259650 T^{7} + 1729831 T^{8} - 5971950 T^{9} + 29048977 T^{10} - 108626976 T^{11} + 493919365 T^{12} - 2123993190 T^{13} + 9918404563 T^{14} - 20428952682 T^{15} + 78310985281 T^{16} )^{2} \))(\( ( 1 - 102 T^{2} + 5430 T^{4} - 195472 T^{6} + 5177079 T^{8} - 103404688 T^{10} + 1519536630 T^{12} - 15099660678 T^{14} + 78310985281 T^{16} )^{2} \))(\( ( 1 + 7 T - 8 T^{2} + 77 T^{3} + 1593 T^{4} + 1771 T^{5} - 4232 T^{6} + 85169 T^{7} + 279841 T^{8} )^{2} \))
$29$ (\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( ( 1 + 10 T^{2} + 841 T^{4} )^{2} \))(\( 1 + 6 T + 7 T^{2} + 174 T^{3} + 841 T^{4} \))(\( 1 - 6 T + 7 T^{2} - 174 T^{3} + 841 T^{4} \))(\( 1 - 29 T^{2} + 841 T^{4} \))(\( 1 - 6 T - 6 T^{2} + 18 T^{3} - 264 T^{4} + 3900 T^{5} - 14429 T^{6} + 113100 T^{7} - 222024 T^{8} + 439002 T^{9} - 4243686 T^{10} - 123066894 T^{11} + 594823321 T^{12} \))(\( 1 - 6 T - 71 T^{2} + 192 T^{3} + 4573 T^{4} - 4224 T^{5} - 186713 T^{6} + 77688 T^{7} + 5509213 T^{8} + 2252952 T^{9} - 157025633 T^{10} - 103019136 T^{11} + 3234396013 T^{12} + 3938140608 T^{13} - 42232455791 T^{14} - 103499257854 T^{15} + 500246412961 T^{16} \))(\( 1 + 6 T + 7 T^{2} - 132 T^{3} - 995 T^{4} - 3828 T^{5} + 5887 T^{6} + 146334 T^{7} + 707281 T^{8} \))(\( 1 - 10 T + 31 T^{2} - 200 T^{3} + 1821 T^{4} - 5800 T^{5} + 26071 T^{6} - 243890 T^{7} + 707281 T^{8} \))(\( 1 + 18 T^{2} + 1683 T^{4} + 10856 T^{6} + 1510005 T^{8} + 9129896 T^{10} + 1190353923 T^{12} + 10706819778 T^{14} + 500246412961 T^{16} \))(\( ( 1 - 29 T^{2} + 841 T^{4} )^{2} \))(\( 1 - 202 T^{2} + 22161 T^{4} - 1720736 T^{6} + 104609393 T^{8} - 5221521276 T^{10} + 219859920283 T^{12} - 7931725055308 T^{14} + 247189558914249 T^{16} - 6670580771514028 T^{18} + 155502744277680523 T^{20} - 3105882626062477596 T^{22} + 52330473610277542673 T^{24} - \)\(72\!\cdots\!36\)\( T^{26} + \)\(78\!\cdots\!01\)\( T^{28} - \)\(60\!\cdots\!62\)\( T^{30} + \)\(25\!\cdots\!21\)\( T^{32} \))(\( 1 + 20 T^{2} + 338 T^{4} + 28080 T^{6} - 44437 T^{8} - 6939980 T^{10} + 33962216 T^{12} - 13624904800 T^{14} - 492015847995 T^{16} - 11458544936800 T^{18} + 24020830094696 T^{20} - 4128061951273580 T^{22} - 22229449852747957 T^{24} + 11813459111069644080 T^{26} + \)\(11\!\cdots\!58\)\( T^{28} + \)\(59\!\cdots\!20\)\( T^{30} + \)\(25\!\cdots\!21\)\( T^{32} \))(\( 1 + 9 T + 74 T^{2} + 129 T^{3} - 54 T^{4} - 8388 T^{5} + 18676 T^{6} + 272682 T^{7} + 3330947 T^{8} + 7907778 T^{9} + 15706516 T^{10} - 204574932 T^{11} - 38193174 T^{12} + 2645938221 T^{13} + 44016925754 T^{14} + 155248886781 T^{15} + 500246412961 T^{16} \))
$31$ (\( 1 - 4 T + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 - 7 T + 31 T^{2} \))(\( ( 1 + 4 T + 31 T^{2} )^{4} \))(\( ( 1 - 4 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) \))(\( 1 + 8 T + 33 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 + T - 30 T^{2} + 31 T^{3} + 961 T^{4} \))(\( 1 - 9 T - 18 T^{2} + 187 T^{3} + 1881 T^{4} - 6768 T^{5} - 31569 T^{6} - 209808 T^{7} + 1807641 T^{8} + 5570917 T^{9} - 16623378 T^{10} - 257662359 T^{11} + 887503681 T^{12} \))(\( 1 - 2 T - 99 T^{2} + 20 T^{3} + 5978 T^{4} + 2478 T^{5} - 249986 T^{6} - 33695 T^{7} + 8127744 T^{8} - 1044545 T^{9} - 240236546 T^{10} + 73822098 T^{11} + 5520808538 T^{12} + 572583020 T^{13} - 87862864419 T^{14} - 55025228222 T^{15} + 852891037441 T^{16} \))(\( 1 + 12 T + 63 T^{2} + 434 T^{3} + 3255 T^{4} + 13454 T^{5} + 60543 T^{6} + 357492 T^{7} + 923521 T^{8} \))(\( 1 - 8 T + 3 T^{2} - 46 T^{3} + 1175 T^{4} - 1426 T^{5} + 2883 T^{6} - 238328 T^{7} + 923521 T^{8} \))(\( ( 1 - 6 T - 15 T^{2} + 206 T^{3} - 561 T^{4} + 6386 T^{5} - 14415 T^{6} - 178746 T^{7} + 923521 T^{8} )^{2} \))(\( ( 1 - 5 T + 31 T^{2} )^{2}( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} ) \))(\( ( 1 + 2 T - 105 T^{2} - 140 T^{3} + 6686 T^{4} + 5712 T^{5} - 296792 T^{6} - 74779 T^{7} + 10300464 T^{8} - 2318149 T^{9} - 285217112 T^{10} + 170166192 T^{11} + 6174661406 T^{12} - 4008081140 T^{13} - 93187886505 T^{14} + 55025228222 T^{15} + 852891037441 T^{16} )^{2} \))(\( ( 1 - 8 T - 24 T^{2} + 88 T^{3} + 1681 T^{4} - 7064 T^{5} + 54924 T^{6} - 168376 T^{7} - 1019363 T^{8} - 5219656 T^{9} + 52781964 T^{10} - 210443624 T^{11} + 1552438801 T^{12} + 2519365288 T^{13} - 21300088344 T^{14} - 220100912888 T^{15} + 852891037441 T^{16} )^{2} \))(\( 1 + 3 T + 36 T^{2} - 23 T^{3} - 84 T^{4} - 5516 T^{5} - 24056 T^{6} - 63114 T^{7} - 303923 T^{8} - 1956534 T^{9} - 23117816 T^{10} - 164327156 T^{11} - 77575764 T^{12} - 658470473 T^{13} + 31950132516 T^{14} + 82537842333 T^{15} + 852891037441 T^{16} \))
$37$ (\( 1 + 6 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 - 3 T + 37 T^{2} \))(\( ( 1 - 8 T + 37 T^{2} )^{4} \))(\( ( 1 - 3 T + 37 T^{2} )^{2} \))(\( ( 1 - 2 T + 37 T^{2} )^{2} \))(\( ( 1 - 3 T + 37 T^{2} )^{2} \))(\( ( 1 + 12 T + 138 T^{2} + 885 T^{3} + 5106 T^{4} + 16428 T^{5} + 50653 T^{6} )^{2} \))(\( ( 1 - 3 T + 67 T^{2} - 189 T^{3} + 2277 T^{4} - 6993 T^{5} + 91723 T^{6} - 151959 T^{7} + 1874161 T^{8} )^{2} \))(\( 1 - 9 T - 6 T^{2} + 307 T^{3} - 1581 T^{4} + 11359 T^{5} - 8214 T^{6} - 455877 T^{7} + 1874161 T^{8} \))(\( 1 + 3 T - 18 T^{2} + 155 T^{3} + 1851 T^{4} + 5735 T^{5} - 24642 T^{6} + 151959 T^{7} + 1874161 T^{8} \))(\( ( 1 + 9 T - 6 T^{2} - 307 T^{3} - 1581 T^{4} - 11359 T^{5} - 8214 T^{6} + 455877 T^{7} + 1874161 T^{8} )^{2} \))(\( ( 1 - 7 T + 12 T^{2} - 259 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 + 7 T + 97 T^{2} + 829 T^{3} + 4471 T^{4} + 30673 T^{5} + 132793 T^{6} + 354571 T^{7} + 1874161 T^{8} )^{4} \))(\( ( 1 + 6 T - 7 T^{2} - 118 T^{3} - 254 T^{4} + 3396 T^{5} + 36665 T^{6} - 93294 T^{7} - 1522501 T^{8} - 3451878 T^{9} + 50194385 T^{10} + 172017588 T^{11} - 476036894 T^{12} - 8182586926 T^{13} - 17960084863 T^{14} + 569591262798 T^{15} + 3512479453921 T^{16} )^{2} \))(\( ( 1 - 12 T + 57 T^{2} - 440 T^{3} + 3921 T^{4} - 16280 T^{5} + 78033 T^{6} - 607836 T^{7} + 1874161 T^{8} )^{2} \))
$41$ (\( 1 + 10 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 10 T + 41 T^{2} \))(\( 1 - 8 T + 41 T^{2} \))(\( ( 1 + 34 T^{2} + 1681 T^{4} )^{2} \))(\( 1 - 2 T - 37 T^{2} - 82 T^{3} + 1681 T^{4} \))(\( 1 - 41 T^{2} + 1681 T^{4} \))(\( 1 - 2 T - 37 T^{2} - 82 T^{3} + 1681 T^{4} \))(\( 1 - 6 T - 6 T^{2} - 202 T^{3} - 108 T^{4} + 9528 T^{5} + 5627 T^{6} + 390648 T^{7} - 181548 T^{8} - 13922042 T^{9} - 16954566 T^{10} - 695137206 T^{11} + 4750104241 T^{12} \))(\( 1 - 2 T - 97 T^{2} + 612 T^{3} + 4493 T^{4} - 38218 T^{5} - 22457 T^{6} + 901512 T^{7} - 2262647 T^{8} + 36961992 T^{9} - 37750217 T^{10} - 2634022778 T^{11} + 12696144173 T^{12} + 70903995012 T^{13} - 460760111377 T^{14} - 389508547762 T^{15} + 7984925229121 T^{16} \))(\( 1 - 3 T - 22 T^{2} - 171 T^{3} + 2215 T^{4} - 7011 T^{5} - 36982 T^{6} - 206763 T^{7} + 2825761 T^{8} \))(\( 1 + 23 T + 208 T^{2} + 961 T^{3} + 3975 T^{4} + 39401 T^{5} + 349648 T^{6} + 1585183 T^{7} + 2825761 T^{8} \))(\( 1 - 87 T^{2} + 2538 T^{4} + 70841 T^{6} - 7729545 T^{8} + 119083721 T^{10} + 7171781418 T^{12} - 413259068967 T^{14} + 7984925229121 T^{16} \))(\( ( 1 - 41 T^{2} + 1681 T^{4} )^{2} \))(\( 1 - 196 T^{2} + 19095 T^{4} - 1280834 T^{6} + 68413043 T^{8} - 3073917978 T^{10} + 120877869925 T^{12} - 4533161979472 T^{14} + 178294470855873 T^{16} - 7620245287492432 T^{18} + 341571970597137925 T^{20} - 14601430823783944698 T^{22} + \)\(54\!\cdots\!03\)\( T^{24} - \)\(17\!\cdots\!34\)\( T^{26} + \)\(43\!\cdots\!95\)\( T^{28} - \)\(74\!\cdots\!56\)\( T^{30} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( 1 - 138 T^{2} + 4581 T^{4} + 242158 T^{6} - 19370244 T^{8} + 47020276 T^{10} + 27362707279 T^{12} - 302286948126 T^{14} - 26002484153453 T^{16} - 508144359799806 T^{18} + 77320471083414319 T^{20} + 223351212440590516 T^{22} - \)\(15\!\cdots\!24\)\( T^{24} + \)\(32\!\cdots\!58\)\( T^{26} + \)\(10\!\cdots\!61\)\( T^{28} - \)\(52\!\cdots\!18\)\( T^{30} + \)\(63\!\cdots\!41\)\( T^{32} \))(\( 1 - 3 T - 59 T^{2} - 42 T^{3} + 1326 T^{4} + 9501 T^{5} + 17474 T^{6} - 345486 T^{7} - 294103 T^{8} - 14164926 T^{9} + 29373794 T^{10} + 654818421 T^{11} + 3746959086 T^{12} - 4865960442 T^{13} - 280256150219 T^{14} - 584262821643 T^{15} + 7984925229121 T^{16} \))
$43$ (\( 1 - 6 T + 43 T^{2} \))(\( 1 + 43 T^{2} \))(\( 1 - 6 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))(\( ( 1 - 80 T^{2} + 1849 T^{4} )^{2} \))(\( 1 + 6 T - 7 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( ( 1 - 5 T + 43 T^{2} )( 1 + 13 T + 43 T^{2} ) \))(\( 1 + 12 T + 101 T^{2} + 516 T^{3} + 1849 T^{4} \))(\( 1 + 3 T + 24 T^{2} + 525 T^{3} + 1725 T^{4} + 13692 T^{5} + 213923 T^{6} + 588756 T^{7} + 3189525 T^{8} + 41741175 T^{9} + 82051224 T^{10} + 441025329 T^{11} + 6321363049 T^{12} \))(\( 1 - 21 T + 113 T^{2} - 516 T^{3} + 15670 T^{4} - 131670 T^{5} + 283958 T^{6} - 4210359 T^{7} + 56707993 T^{8} - 181045437 T^{9} + 525038342 T^{10} - 10468686690 T^{11} + 53572611670 T^{12} - 75856356588 T^{13} + 714314024537 T^{14} - 5708190833247 T^{15} + 11688200277601 T^{16} \))(\( ( 1 + 41 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 8 T + 97 T^{2} - 344 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 8 T + 57 T^{2} + 344 T^{3} + 1849 T^{4} )^{4} \))(\( ( 1 + 43 T^{2} + 1849 T^{4} )^{2} \))(\( 1 + 161 T^{2} + 12045 T^{4} + 451720 T^{6} + 4744646 T^{8} - 258318474 T^{10} + 8737088662 T^{12} + 2425239363077 T^{14} + 153815372427309 T^{16} + 4484267582329373 T^{18} + 29870367454734262 T^{20} - 1632924856417667226 T^{22} + 55456372694318474246 T^{24} + \)\(97\!\cdots\!80\)\( T^{26} + \)\(48\!\cdots\!45\)\( T^{28} + \)\(11\!\cdots\!89\)\( T^{30} + \)\(13\!\cdots\!01\)\( T^{32} \))(\( ( 1 - 180 T^{2} + 12786 T^{4} - 463360 T^{6} + 14361051 T^{8} - 856752640 T^{10} + 43712789586 T^{12} - 1137845348820 T^{14} + 11688200277601 T^{16} )^{2} \))(\( ( 1 - 3 T - 68 T^{2} + 27 T^{3} + 3693 T^{4} + 1161 T^{5} - 125732 T^{6} - 238521 T^{7} + 3418801 T^{8} )^{2} \))
$47$ (\( 1 + 8 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 + 8 T + 47 T^{2} \))(\( ( 1 - 86 T^{2} + 2209 T^{4} )^{2} \))(\( 1 - 7 T + 2 T^{2} - 329 T^{3} + 2209 T^{4} \))(\( 1 + 3 T - 38 T^{2} + 141 T^{3} + 2209 T^{4} \))(\( 1 - 7 T + 2 T^{2} - 329 T^{3} + 2209 T^{4} \))(\( 1 + 12 T + 18 T^{2} - 386 T^{3} - 1434 T^{4} + 3954 T^{5} + 43979 T^{6} + 185838 T^{7} - 3167706 T^{8} - 40075678 T^{9} + 87834258 T^{10} + 2752140084 T^{11} + 10779215329 T^{12} \))(\( 1 - 7 T - 124 T^{2} + 759 T^{3} + 11189 T^{4} - 50870 T^{5} - 638711 T^{6} + 948885 T^{7} + 33885262 T^{8} + 44597595 T^{9} - 1410912599 T^{10} - 5281476010 T^{11} + 54598750709 T^{12} + 174072860313 T^{13} - 1336622700796 T^{14} - 3546361843241 T^{15} + 23811286661761 T^{16} \))(\( 1 + 17 T + 67 T^{2} - 335 T^{3} - 4344 T^{4} - 15745 T^{5} + 148003 T^{6} + 1764991 T^{7} + 4879681 T^{8} \))(\( 1 - 3 T - 43 T^{2} + 45 T^{3} + 2116 T^{4} + 2115 T^{5} - 94987 T^{6} - 311469 T^{7} + 4879681 T^{8} \))(\( 1 - 75 T^{2} + 5541 T^{4} - 375925 T^{6} + 17183556 T^{8} - 830418325 T^{10} + 27038312421 T^{12} - 808441149675 T^{14} + 23811286661761 T^{16} \))(\( ( 1 - 12 T + 47 T^{2} )^{2}( 1 - 12 T + 97 T^{2} - 564 T^{3} + 2209 T^{4} ) \))(\( ( 1 + 15 T + 238 T^{2} + 2445 T^{3} + 25363 T^{4} + 223068 T^{5} + 1824427 T^{6} + 13850433 T^{7} + 95884210 T^{8} + 650970351 T^{9} + 4030159243 T^{10} + 23159588964 T^{11} + 123763349203 T^{12} + 560748542115 T^{13} + 2565453248302 T^{14} + 7599346806945 T^{15} + 23811286661761 T^{16} )^{2} \))(\( 1 + 192 T^{2} + 14115 T^{4} + 332470 T^{6} - 12112005 T^{8} - 594955574 T^{10} + 21788151037 T^{12} + 2123156175840 T^{14} + 93108257741080 T^{16} + 4690051992430560 T^{18} + 106319226640379197 T^{20} - 6413154243334793846 T^{22} - \)\(28\!\cdots\!05\)\( T^{24} + \)\(17\!\cdots\!30\)\( T^{26} + \)\(16\!\cdots\!15\)\( T^{28} + \)\(49\!\cdots\!48\)\( T^{30} + \)\(56\!\cdots\!21\)\( T^{32} \))(\( 1 - 23 T + 327 T^{2} - 2796 T^{3} + 15428 T^{4} - 41679 T^{5} - 80266 T^{6} + 1119532 T^{7} - 8567157 T^{8} + 52618004 T^{9} - 177307594 T^{10} - 4327238817 T^{11} + 75283718468 T^{12} - 641248639572 T^{13} + 3524803412583 T^{14} - 11652331770649 T^{15} + 23811286661761 T^{16} \))
$53$ (\( 1 + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( ( 1 - 8 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 + 9 T + 53 T^{2} )^{2} \))(\( ( 1 - 3 T + 53 T^{2} )^{2} \))(\( ( 1 - 3 T + 53 T^{2} )^{2} \))(\( ( 1 - 3 T + 33 T^{2} - 261 T^{3} + 1749 T^{4} - 8427 T^{5} + 148877 T^{6} )^{2} \))(\( ( 1 + 6 T + 167 T^{2} + 789 T^{3} + 11961 T^{4} + 41817 T^{5} + 469103 T^{6} + 893262 T^{7} + 7890481 T^{8} )^{2} \))(\( 1 + 4 T - 47 T^{2} - 160 T^{3} + 2121 T^{4} - 8480 T^{5} - 132023 T^{6} + 595508 T^{7} + 7890481 T^{8} \))(\( 1 + 6 T + 23 T^{2} - 120 T^{3} - 1319 T^{4} - 6360 T^{5} + 64607 T^{6} + 893262 T^{7} + 7890481 T^{8} \))(\( 1 + 24 T^{2} + 5817 T^{4} - 20908 T^{6} + 15682005 T^{8} - 58730572 T^{10} + 45898927977 T^{12} + 531944667096 T^{14} + 62259690411361 T^{16} \))(\( ( 1 - 6 T - 17 T^{2} - 318 T^{3} + 2809 T^{4} )( 1 + 6 T - 17 T^{2} + 318 T^{3} + 2809 T^{4} ) \))(\( ( 1 - 278 T^{2} + 37843 T^{4} - 3330905 T^{6} + 207574231 T^{8} - 9356512145 T^{10} + 298599472483 T^{12} - 6161692393862 T^{14} + 62259690411361 T^{16} )^{2} \))(\( 1 + 166 T^{2} + 9174 T^{4} - 111674 T^{6} - 30841109 T^{8} - 525703922 T^{10} + 67446933816 T^{12} + 3591171944168 T^{14} + 110175435537457 T^{16} + 10087601991167912 T^{18} + 532188749783405496 T^{20} - 11651891574139647938 T^{22} - \)\(19\!\cdots\!49\)\( T^{24} - \)\(19\!\cdots\!26\)\( T^{26} + \)\(45\!\cdots\!34\)\( T^{28} + \)\(22\!\cdots\!54\)\( T^{30} + \)\(38\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 14 T + 43 T^{2} - 160 T^{3} + 2961 T^{4} - 8480 T^{5} + 120787 T^{6} - 2084278 T^{7} + 7890481 T^{8} )^{2} \))
$59$ (\( 1 - 4 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 + 5 T + 59 T^{2} \))(\( ( 1 + 10 T^{2} + 3481 T^{4} )^{2} \))(\( 1 - 7 T - 10 T^{2} - 413 T^{3} + 3481 T^{4} \))(\( 1 - 59 T^{2} + 3481 T^{4} \))(\( 1 + 11 T + 62 T^{2} + 649 T^{3} + 3481 T^{4} \))(\( 1 + 21 T + 198 T^{2} + 1081 T^{3} + 2481 T^{4} - 40380 T^{5} - 564133 T^{6} - 2382420 T^{7} + 8636361 T^{8} + 222014699 T^{9} + 2399237478 T^{10} + 15013410279 T^{11} + 42180533641 T^{12} \))(\( 1 + 2 T - 211 T^{2} - 180 T^{3} + 27194 T^{4} + 9886 T^{5} - 2406650 T^{6} - 211857 T^{7} + 162461212 T^{8} - 12499563 T^{9} - 8377548650 T^{10} + 2030376794 T^{11} + 329519515034 T^{12} - 128686373820 T^{13} - 8900092598251 T^{14} + 4977302969638 T^{15} + 146830437604321 T^{16} \))(\( 1 - 6 T + 17 T^{2} + 222 T^{3} - 1685 T^{4} + 13098 T^{5} + 59177 T^{6} - 1232274 T^{7} + 12117361 T^{8} \))(\( 1 - 20 T + 131 T^{2} - 530 T^{3} + 3851 T^{4} - 31270 T^{5} + 456011 T^{6} - 4107580 T^{7} + 12117361 T^{8} \))(\( 1 - 72 T^{2} - 327 T^{4} + 271796 T^{6} - 16865475 T^{8} + 946121876 T^{10} - 3962377047 T^{12} - 3036998422152 T^{14} + 146830437604321 T^{16} \))(\( ( 1 - 15 T + 59 T^{2} )^{2}( 1 - 15 T + 166 T^{2} - 885 T^{3} + 3481 T^{4} ) \))(\( ( 1 + 18 T + 307 T^{2} + 3582 T^{3} + 38122 T^{4} + 338940 T^{5} + 2896270 T^{6} + 22582341 T^{7} + 177100792 T^{8} + 1332358119 T^{9} + 10081915870 T^{10} + 69611158260 T^{11} + 461938036042 T^{12} + 2560858839018 T^{13} + 12949423827787 T^{14} + 44795726726742 T^{15} + 146830437604321 T^{16} )^{2} \))(\( 1 + 170 T^{2} + 22518 T^{4} + 2498730 T^{6} + 233218683 T^{8} + 18919071570 T^{10} + 1419551700816 T^{12} + 95367637994400 T^{14} + 5833449282172425 T^{16} + 331974747858506400 T^{18} + 17201220416951466576 T^{20} + \)\(79\!\cdots\!70\)\( T^{22} + \)\(34\!\cdots\!43\)\( T^{24} + \)\(12\!\cdots\!30\)\( T^{26} + \)\(40\!\cdots\!58\)\( T^{28} + \)\(10\!\cdots\!70\)\( T^{30} + \)\(21\!\cdots\!41\)\( T^{32} \))(\( 1 - 3 T + 64 T^{2} + 51 T^{3} - 168 T^{4} + 20412 T^{5} - 184552 T^{6} + 519906 T^{7} - 7825759 T^{8} + 30674454 T^{9} - 642425512 T^{10} + 4192196148 T^{11} - 2035716648 T^{12} + 36461139249 T^{13} + 2699554153024 T^{14} - 7465954454457 T^{15} + 146830437604321 T^{16} \))
$61$ (\( 1 + 6 T + 61 T^{2} \))(\( 1 - 6 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))(\( 1 - 12 T + 61 T^{2} \))(\( ( 1 - 98 T^{2} + 3721 T^{4} )^{2} \))(\( 1 - 61 T^{2} + 3721 T^{4} \))(\( 1 + 8 T + 3 T^{2} + 488 T^{3} + 3721 T^{4} \))(\( 1 - 61 T^{2} + 3721 T^{4} \))(\( 1 - 21 T + 114 T^{2} - 1101 T^{3} + 26439 T^{4} - 183108 T^{5} + 602021 T^{6} - 11169588 T^{7} + 98379519 T^{8} - 249906081 T^{9} + 1578425874 T^{10} - 17736522321 T^{11} + 51520374361 T^{12} \))(\( 1 + 15 T - 97 T^{2} - 990 T^{3} + 28072 T^{4} + 155670 T^{5} - 2089990 T^{6} + 70125 T^{7} + 207502789 T^{8} + 4277625 T^{9} - 7776852790 T^{10} + 35334132270 T^{11} + 388680448552 T^{12} - 836150337990 T^{13} - 4997476313017 T^{14} + 47141142540315 T^{15} + 191707312997281 T^{16} \))(\( 1 + 21 T + 245 T^{2} + 2559 T^{3} + 23404 T^{4} + 156099 T^{5} + 911645 T^{6} + 4766601 T^{7} + 13845841 T^{8} \))(\( 1 - 3 T - 7 T^{2} - 441 T^{3} + 4900 T^{4} - 26901 T^{5} - 26047 T^{6} - 680943 T^{7} + 13845841 T^{8} \))(\( ( 1 - 21 T + 135 T^{2} - 259 T^{3} + 144 T^{4} - 15799 T^{5} + 502335 T^{6} - 4766601 T^{7} + 13845841 T^{8} )^{2} \))(\( ( 1 + 61 T^{2} + 3721 T^{4} )^{2} \))(\( 1 + 11 T^{2} - 10329 T^{4} - 236306 T^{6} + 57256364 T^{8} + 1388511372 T^{10} - 209614040984 T^{12} - 2716193993095 T^{14} + 695408199928701 T^{16} - 10106957848306495 T^{18} - 2902282682831947544 T^{20} + 71536625689945733292 T^{22} + \)\(10\!\cdots\!84\)\( T^{24} - \)\(16\!\cdots\!06\)\( T^{26} - \)\(27\!\cdots\!09\)\( T^{28} + \)\(10\!\cdots\!51\)\( T^{30} + \)\(36\!\cdots\!61\)\( T^{32} \))(\( ( 1 + 83 T^{2} + 420 T^{3} + 3413 T^{4} + 34860 T^{5} + 227941 T^{6} + 4235840 T^{7} + 8009300 T^{8} + 258386240 T^{9} + 848168461 T^{10} + 7912557660 T^{11} + 47255855333 T^{12} + 354730446420 T^{13} + 4276191071963 T^{14} + 191707312997281 T^{16} )^{2} \))(\( 1 - 29 T^{2} - 480 T^{3} - 2160 T^{4} + 21600 T^{5} + 186389 T^{6} - 128880 T^{7} - 11482801 T^{8} - 7861680 T^{9} + 693553469 T^{10} + 4902789600 T^{11} - 29907016560 T^{12} - 405406224480 T^{13} - 1494090856469 T^{14} + 191707312997281 T^{16} \))
$67$ (\( 1 - 8 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 7 T + 67 T^{2} \))(\( ( 1 + 4 T + 67 T^{2} )^{4} \))(\( ( 1 - 5 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} ) \))(\( 1 - 13 T + 102 T^{2} - 871 T^{3} + 4489 T^{4} \))(\( 1 - 4 T - 51 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 + 3 T - 66 T^{2} + 575 T^{3} + 1125 T^{4} - 29808 T^{5} + 214875 T^{6} - 1997136 T^{7} + 5050125 T^{8} + 172938725 T^{9} - 1329973986 T^{10} + 4050375321 T^{11} + 90458382169 T^{12} \))(\( 1 + 14 T - 51 T^{2} - 500 T^{3} + 11354 T^{4} + 6834 T^{5} - 1143698 T^{6} - 2330227 T^{7} + 43235628 T^{8} - 156125209 T^{9} - 5134060322 T^{10} + 2055414342 T^{11} + 228795827834 T^{12} - 675062553500 T^{13} - 4613377490619 T^{14} + 84849962474522 T^{15} + 406067677556641 T^{16} \))(\( ( 1 + 3 T + 125 T^{2} + 201 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 - T + 33 T^{2} - 67 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 - T + 123 T^{2} - 67 T^{3} + 4489 T^{4} )^{4} \))(\( ( 1 + 13 T + 67 T^{2} )^{2}( 1 - 13 T + 102 T^{2} - 871 T^{3} + 4489 T^{4} ) \))(\( ( 1 - 4 T - 165 T^{2} + 1330 T^{3} + 13514 T^{4} - 133584 T^{5} - 335648 T^{6} + 4908017 T^{7} + 931644 T^{8} + 328837139 T^{9} - 1506723872 T^{10} - 40177124592 T^{11} + 272322249194 T^{12} + 1795666392310 T^{13} - 14925633057885 T^{14} - 24242846421292 T^{15} + 406067677556641 T^{16} )^{2} \))(\( ( 1 - 24 T + 429 T^{2} - 5008 T^{3} + 47859 T^{4} - 335536 T^{5} + 1925781 T^{6} - 7218312 T^{7} + 20151121 T^{8} )^{4} \))(\( ( 1 + 6 T - 31 T^{2} + 402 T^{3} + 4489 T^{4} )^{4} \))
$71$ (\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 3 T + 71 T^{2} \))(\( ( 1 - 134 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 - 9 T + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 - 15 T + 71 T^{2} )^{2} \))(\( ( 1 - 12 T + 222 T^{2} - 1593 T^{3} + 15762 T^{4} - 60492 T^{5} + 357911 T^{6} )^{2} \))(\( ( 1 + 3 T + 197 T^{2} + 909 T^{3} + 17697 T^{4} + 64539 T^{5} + 993077 T^{6} + 1073733 T^{7} + 25411681 T^{8} )^{2} \))(\( 1 + 15 T + 119 T^{2} + 1455 T^{3} + 17296 T^{4} + 103305 T^{5} + 599879 T^{6} + 5368665 T^{7} + 25411681 T^{8} \))(\( 1 - 27 T + 253 T^{2} - 819 T^{3} + 100 T^{4} - 58149 T^{5} + 1275373 T^{6} - 9663597 T^{7} + 25411681 T^{8} \))(\( 1 - 117 T^{2} + 273 T^{4} + 566981 T^{6} - 45119220 T^{8} + 2858151221 T^{10} + 6937388913 T^{12} - 14987733218757 T^{14} + 645753531245761 T^{16} \))(\( ( 1 - 3 T - 62 T^{2} - 213 T^{3} + 5041 T^{4} )( 1 + 3 T - 62 T^{2} + 213 T^{3} + 5041 T^{4} ) \))(\( ( 1 - 515 T^{2} + 119305 T^{4} - 16242779 T^{6} + 1421466937 T^{8} - 81879848939 T^{10} + 3031740601705 T^{12} - 65971646219315 T^{14} + 645753531245761 T^{16} )^{2} \))(\( 1 + 338 T^{2} + 50091 T^{4} + 3709542 T^{6} + 63034791 T^{8} - 13931687706 T^{10} - 1397230758891 T^{12} - 60140798780574 T^{14} - 2187888491323968 T^{16} - 303169766652873534 T^{18} - 35505982328326005771 T^{20} - \)\(17\!\cdots\!26\)\( T^{22} + \)\(40\!\cdots\!51\)\( T^{24} + \)\(12\!\cdots\!42\)\( T^{26} + \)\(82\!\cdots\!31\)\( T^{28} + \)\(27\!\cdots\!78\)\( T^{30} + \)\(41\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 21 T + 95 T^{2} + 1371 T^{3} - 21536 T^{4} + 97341 T^{5} + 478895 T^{6} - 7516131 T^{7} + 25411681 T^{8} )^{2} \))
$73$ (\( 1 + 2 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( ( 1 - 73 T^{2} )^{4} \))(\( ( 1 - 4 T + 73 T^{2} )^{2} \))(\( ( 1 - 2 T + 73 T^{2} )^{2} \))(\( ( 1 + 8 T + 73 T^{2} )^{2} \))(\( ( 1 + 6 T + 114 T^{2} + 173 T^{3} + 8322 T^{4} + 31974 T^{5} + 389017 T^{6} )^{2} \))(\( ( 1 - 22 T + 421 T^{2} - 4807 T^{3} + 49780 T^{4} - 350911 T^{5} + 2243509 T^{6} - 8558374 T^{7} + 28398241 T^{8} )^{2} \))(\( 1 - 14 T + 63 T^{2} - 850 T^{3} + 12521 T^{4} - 62050 T^{5} + 335727 T^{6} - 5446238 T^{7} + 28398241 T^{8} \))(\( 1 - 6 T - 57 T^{2} + 130 T^{3} + 4761 T^{4} + 9490 T^{5} - 303753 T^{6} - 2334102 T^{7} + 28398241 T^{8} \))(\( ( 1 - 12 T - 9 T^{2} + 164 T^{3} + 3249 T^{4} + 11972 T^{5} - 47961 T^{6} - 4668204 T^{7} + 28398241 T^{8} )^{2} \))(\( ( 1 - 73 T^{2} )^{4} \))(\( ( 1 - 176 T^{2} + 28675 T^{4} - 2789687 T^{6} + 246500362 T^{8} - 14866242023 T^{10} + 814319560675 T^{12} - 26634823826864 T^{14} + 806460091894081 T^{16} )^{2} \))(\( ( 1 + 10 T + 276 T^{2} + 2170 T^{3} + 24127 T^{4} + 117430 T^{5} - 172242 T^{6} - 4912540 T^{7} - 124201175 T^{8} - 358615420 T^{9} - 917877618 T^{10} + 45682266310 T^{11} + 685164360607 T^{12} + 4498565356810 T^{13} + 41768246455764 T^{14} + 110473985190970 T^{15} + 806460091894081 T^{16} )^{2} \))(\( ( 1 + 4 T - 27 T^{2} + 500 T^{3} + 7301 T^{4} + 36500 T^{5} - 143883 T^{6} + 1556068 T^{7} + 28398241 T^{8} )^{2} \))
$79$ (\( 1 + 10 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( ( 1 - 8 T^{2} + 6241 T^{4} )^{2} \))(\( 1 + 8 T - 15 T^{2} + 632 T^{3} + 6241 T^{4} \))(\( 1 + 2 T - 75 T^{2} + 158 T^{3} + 6241 T^{4} \))(\( 1 - 10 T + 21 T^{2} - 790 T^{3} + 6241 T^{4} \))(\( 1 - 9 T - 180 T^{2} + 533 T^{3} + 34533 T^{4} - 61128 T^{5} - 2824521 T^{6} - 4829112 T^{7} + 215520453 T^{8} + 262789787 T^{9} - 7011014580 T^{10} - 27693507591 T^{11} + 243087455521 T^{12} \))(\( 1 + 11 T - 171 T^{2} - 1952 T^{3} + 23168 T^{4} + 216654 T^{5} - 1770938 T^{6} - 6655723 T^{7} + 156847173 T^{8} - 525802117 T^{9} - 11052424058 T^{10} + 106818871506 T^{11} + 902395476608 T^{12} - 6006414090848 T^{13} - 41567954894091 T^{14} + 211242998847749 T^{15} + 1517108809906561 T^{16} \))(\( 1 + 11 T + 42 T^{2} - 407 T^{3} - 7795 T^{4} - 32153 T^{5} + 262122 T^{6} + 5423429 T^{7} + 38950081 T^{8} \))(\( 1 - 5 T + 6 T^{2} - 715 T^{3} + 9821 T^{4} - 56485 T^{5} + 37446 T^{6} - 2465195 T^{7} + 38950081 T^{8} \))(\( ( 1 - 15 T + 6 T^{2} + 815 T^{3} - 5979 T^{4} + 64385 T^{5} + 37446 T^{6} - 7395585 T^{7} + 38950081 T^{8} )^{2} \))(\( ( 1 + 79 T^{2} + 6241 T^{4} )^{2} \))(\( 1 + 353 T^{2} + 60567 T^{4} + 6638158 T^{6} + 550474730 T^{8} + 44065155330 T^{10} + 4241918300434 T^{12} + 431883347780411 T^{14} + 37912769819643561 T^{16} + 2695383973497545051 T^{18} + \)\(16\!\cdots\!54\)\( T^{20} + \)\(10\!\cdots\!30\)\( T^{22} + \)\(83\!\cdots\!30\)\( T^{24} + \)\(62\!\cdots\!58\)\( T^{26} + \)\(35\!\cdots\!47\)\( T^{28} + \)\(13\!\cdots\!93\)\( T^{30} + \)\(23\!\cdots\!21\)\( T^{32} \))(\( ( 1 + 203 T^{2} - 180 T^{3} + 12338 T^{4} - 36540 T^{5} - 807689 T^{6} - 4199410 T^{7} - 150806725 T^{8} - 331753390 T^{9} - 5040787049 T^{10} - 18015645060 T^{11} + 480566099378 T^{12} - 553870151820 T^{13} + 49346753470763 T^{14} + 1517108809906561 T^{16} )^{2} \))(\( 1 + 22 T + 259 T^{2} + 146 T^{3} - 28378 T^{4} - 420788 T^{5} - 1482397 T^{6} + 19182626 T^{7} + 350855611 T^{8} + 1515427454 T^{9} - 9251639677 T^{10} - 207464894732 T^{11} - 1105325398618 T^{12} + 449250234254 T^{13} + 62959650979939 T^{14} + 422485997695498 T^{15} + 1517108809906561 T^{16} \))
$83$ (\( 1 - 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( ( 1 - 26 T^{2} + 6889 T^{4} )^{2} \))(\( 1 - 12 T + 61 T^{2} - 996 T^{3} + 6889 T^{4} \))(\( 1 - 18 T + 241 T^{2} - 1494 T^{3} + 6889 T^{4} \))(\( 1 + 12 T + 61 T^{2} + 996 T^{3} + 6889 T^{4} \))(\( 1 - 222 T^{2} - 54 T^{3} + 30858 T^{4} + 5994 T^{5} - 2946269 T^{6} + 497502 T^{7} + 212580762 T^{8} - 30876498 T^{9} - 10535747262 T^{10} + 326940373369 T^{12} \))(\( 1 + 18 T - 5 T^{2} - 1620 T^{3} - 2021 T^{4} + 27828 T^{5} - 824807 T^{6} + 4969494 T^{7} + 193494259 T^{8} + 412468002 T^{9} - 5682095423 T^{10} + 15911688636 T^{11} - 95913266741 T^{12} - 6381245841660 T^{13} - 1634701866845 T^{14} + 488448917813286 T^{15} + 2252292232139041 T^{16} \))(\( 1 + 13 T - 14 T^{2} - 421 T^{3} + 1449 T^{4} - 34943 T^{5} - 96446 T^{6} + 7433231 T^{7} + 47458321 T^{8} \))(\( 1 + 21 T + 88 T^{2} - 915 T^{3} - 13199 T^{4} - 75945 T^{5} + 606232 T^{6} + 12007527 T^{7} + 47458321 T^{8} \))(\( 1 - 177 T^{2} + 9810 T^{4} + 724223 T^{6} - 144542001 T^{8} + 4989172247 T^{10} + 465566129010 T^{12} - 57868446086313 T^{14} + 2252292232139041 T^{16} \))(\( ( 1 - 83 T^{2} + 6889 T^{4} )^{2} \))(\( 1 - 370 T^{2} + 62193 T^{4} - 7697168 T^{6} + 924406361 T^{8} - 98104079436 T^{10} + 8874940013659 T^{12} - 811506409257412 T^{14} + 72427176409933185 T^{16} - 5590467653374311268 T^{18} + \)\(42\!\cdots\!39\)\( T^{20} - \)\(32\!\cdots\!84\)\( T^{22} + \)\(20\!\cdots\!01\)\( T^{24} - \)\(11\!\cdots\!32\)\( T^{26} + \)\(66\!\cdots\!73\)\( T^{28} - \)\(27\!\cdots\!30\)\( T^{30} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 - 208 T^{2} + 15045 T^{4} + 774660 T^{6} - 236047260 T^{8} + 17546406456 T^{10} - 74692835973 T^{12} - 112052982977490 T^{14} + 12843285776364315 T^{16} - 771932999731928610 T^{18} - 3544796586006981333 T^{20} + \)\(57\!\cdots\!64\)\( T^{22} - \)\(53\!\cdots\!60\)\( T^{24} + \)\(12\!\cdots\!40\)\( T^{26} + \)\(16\!\cdots\!45\)\( T^{28} - \)\(15\!\cdots\!32\)\( T^{30} + \)\(50\!\cdots\!81\)\( T^{32} \))(\( 1 + 17 T + 213 T^{2} + 3330 T^{3} + 42290 T^{4} + 490473 T^{5} + 4981814 T^{6} + 51032300 T^{7} + 525354219 T^{8} + 4235680900 T^{9} + 34319716646 T^{10} + 280446085251 T^{11} + 2007012395090 T^{12} + 13117005341190 T^{13} + 69638299527597 T^{14} + 461312866823659 T^{15} + 2252292232139041 T^{16} \))
$89$ (\( 1 + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + 89 T^{2} \))(\( 1 + 15 T + 89 T^{2} \))(\( ( 1 - 128 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 - 6 T + 89 T^{2} )^{2} \))(\( ( 1 - 3 T + 89 T^{2} )^{2} \))(\( ( 1 - 3 T + 89 T^{2} )^{2} \))(\( ( 1 + 12 T + 159 T^{2} + 1728 T^{3} + 14151 T^{4} + 95052 T^{5} + 704969 T^{6} )^{2} \))(\( ( 1 + 6 T + 224 T^{2} + 1554 T^{3} + 26094 T^{4} + 138306 T^{5} + 1774304 T^{6} + 4229814 T^{7} + 62742241 T^{8} )^{2} \))(\( ( 1 - 12 T + 209 T^{2} - 1068 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 + 10 T + 183 T^{2} + 890 T^{3} + 7921 T^{4} )^{2} \))(\( ( 1 - 4 T^{2} + 5721 T^{4} - 31684 T^{6} + 62742241 T^{8} )^{2} \))(\( ( 1 - 9 T + 89 T^{2} )^{2}( 1 + 9 T + 89 T^{2} )^{2} \))(\( ( 1 - 404 T^{2} + 80980 T^{4} - 10737836 T^{6} + 1074473494 T^{8} - 85054398956 T^{10} + 5080866676180 T^{12} - 200780441548244 T^{14} + 3936588805702081 T^{16} )^{2} \))(\( ( 1 - 582 T^{2} + 157158 T^{4} - 25689904 T^{6} + 2778331335 T^{8} - 203489729584 T^{10} + 9860445111078 T^{12} - 289243111339302 T^{14} + 3936588805702081 T^{16} )^{2} \))(\( ( 1 + 18 T + 254 T^{2} + 1602 T^{3} + 7921 T^{4} )^{4} \))
$97$ (\( 1 - 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 7 T + 97 T^{2} \))(\( ( 1 + 10 T + 97 T^{2} )^{4} \))(\( ( 1 - 14 T + 97 T^{2} )( 1 - 5 T + 97 T^{2} ) \))(\( 1 + 2 T - 93 T^{2} + 194 T^{3} + 9409 T^{4} \))(\( 1 + 17 T + 192 T^{2} + 1649 T^{3} + 9409 T^{4} \))(\( 1 - 3 T - 141 T^{2} - 724 T^{3} + 8361 T^{4} + 79623 T^{5} - 423066 T^{6} + 7723431 T^{7} + 78668649 T^{8} - 660775252 T^{9} - 12482628621 T^{10} - 25762020771 T^{11} + 832972004929 T^{12} \))(\( 1 + 26 T + 132 T^{2} - 776 T^{3} + 16487 T^{4} + 336432 T^{5} + 568456 T^{6} + 7259774 T^{7} + 271106712 T^{8} + 704198078 T^{9} + 5348602504 T^{10} + 307052402736 T^{11} + 1459582255847 T^{12} - 6663776039432 T^{13} + 109952304650628 T^{14} + 2100755396430938 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 3 T - 43 T^{2} - 765 T^{3} + 11236 T^{4} - 74205 T^{5} - 404587 T^{6} - 2738019 T^{7} + 88529281 T^{8} \))(\( 1 + 33 T + 537 T^{2} + 6655 T^{3} + 71196 T^{4} + 645535 T^{5} + 5052633 T^{6} + 30118209 T^{7} + 88529281 T^{8} \))(\( ( 1 + 27 T + 357 T^{2} + 4325 T^{3} + 49476 T^{4} + 419525 T^{5} + 3359013 T^{6} + 24642171 T^{7} + 88529281 T^{8} )^{2} \))(\( ( 1 - 17 T + 97 T^{2} )^{2}( 1 + 17 T + 192 T^{2} + 1649 T^{3} + 9409 T^{4} ) \))(\( ( 1 + 2 T - 264 T^{2} - 224 T^{3} + 37139 T^{4} + 3000 T^{5} - 3977996 T^{6} + 3110 T^{7} + 379878912 T^{8} + 301670 T^{9} - 37428964364 T^{10} + 2738019000 T^{11} + 3287888967059 T^{12} - 1923564217568 T^{13} - 219904609301256 T^{14} + 161596568956226 T^{15} + 7837433594376961 T^{16} )^{2} \))(\( ( 1 - 30 T + 411 T^{2} - 3150 T^{3} + 11217 T^{4} + 58230 T^{5} - 1794727 T^{6} + 27808950 T^{7} - 324085500 T^{8} + 2697468150 T^{9} - 16886586343 T^{10} + 53144948790 T^{11} + 993032944977 T^{12} - 27050121809550 T^{13} + 342351494025819 T^{14} - 2423948534343390 T^{15} + 7837433594376961 T^{16} )^{2} \))(\( 1 - 6 T + 97 T^{2} - 1530 T^{3} + 9180 T^{4} + 36876 T^{5} + 316511 T^{6} + 9403380 T^{7} - 144949561 T^{8} + 912127860 T^{9} + 2978051999 T^{10} + 33655729548 T^{11} + 812698799580 T^{12} - 13138630593210 T^{13} + 80798284478113 T^{14} - 484789706868678 T^{15} + 7837433594376961 T^{16} \))
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