Properties

Label 403.2
Level 403
Weight 2
Dimension 6305
Nonzero newspaces 30
Newform subspaces 48
Sturm bound 26880
Trace bound 3

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Defining parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Newform subspaces: \( 48 \)
Sturm bound: \(26880\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(403))\).

Total New Old
Modular forms 7080 6945 135
Cusp forms 6361 6305 56
Eisenstein series 719 640 79

Trace form

\( 6305q - 147q^{2} - 150q^{3} - 159q^{4} - 156q^{5} - 174q^{6} - 158q^{7} - 165q^{8} - 161q^{9} + O(q^{10}) \) \( 6305q - 147q^{2} - 150q^{3} - 159q^{4} - 156q^{5} - 174q^{6} - 158q^{7} - 165q^{8} - 161q^{9} - 162q^{10} - 162q^{11} - 170q^{12} - 156q^{13} - 354q^{14} - 186q^{15} - 191q^{16} - 174q^{17} - 189q^{18} - 158q^{19} - 198q^{20} - 172q^{21} - 126q^{22} - 156q^{23} - 78q^{24} - 119q^{25} - 144q^{26} - 264q^{27} - 46q^{28} - 114q^{29} - 60q^{30} - 121q^{31} - 165q^{32} - 138q^{33} - 84q^{34} - 138q^{35} - 83q^{36} - 128q^{37} - 174q^{38} - 162q^{39} - 312q^{40} - 144q^{41} - 186q^{42} - 168q^{43} - 234q^{44} - 222q^{45} - 186q^{46} - 198q^{47} - 204q^{48} - 133q^{49} - 81q^{50} - 18q^{51} - 101q^{52} - 312q^{53} + 36q^{54} - 102q^{55} - 50q^{57} - 48q^{58} - 174q^{59} + 192q^{60} - 69q^{62} - 164q^{63} - 33q^{64} - 63q^{65} - 24q^{66} - 170q^{67} - 60q^{68} - 90q^{69} - 24q^{70} - 114q^{71} - 21q^{72} - 164q^{73} - 84q^{74} - 56q^{75} - 28q^{76} - 96q^{77} + 6q^{78} - 356q^{79} - 6q^{80} - 173q^{81} - 174q^{82} - 24q^{83} - 14q^{84} - 156q^{85} - 42q^{86} - 138q^{87} + 30q^{88} - 66q^{89} + 54q^{90} - 108q^{91} - 132q^{92} - 22q^{93} - 312q^{94} - 42q^{95} + 48q^{96} - 142q^{97} - 3q^{98} - 156q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(403))\)

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
403.2.a \(\chi_{403}(1, \cdot)\) 403.2.a.a 2 1
403.2.a.b 6
403.2.a.c 7
403.2.a.d 8
403.2.a.e 8
403.2.c \(\chi_{403}(311, \cdot)\) 403.2.c.a 2 1
403.2.c.b 32
403.2.e \(\chi_{403}(191, \cdot)\) 403.2.e.a 70 2
403.2.f \(\chi_{403}(94, \cdot)\) 403.2.f.a 2 2
403.2.f.b 34
403.2.f.c 36
403.2.g \(\chi_{403}(87, \cdot)\) 403.2.g.a 70 2
403.2.h \(\chi_{403}(118, \cdot)\) 403.2.h.a 30 2
403.2.h.b 34
403.2.i \(\chi_{403}(216, \cdot)\) 403.2.i.a 68 2
403.2.k \(\chi_{403}(66, \cdot)\) 403.2.k.a 4 4
403.2.k.b 4
403.2.k.c 4
403.2.k.d 48
403.2.k.e 68
403.2.l \(\chi_{403}(25, \cdot)\) 403.2.l.a 2 2
403.2.l.b 2
403.2.l.c 68
403.2.r \(\chi_{403}(218, \cdot)\) 403.2.r.a 68 2
403.2.s \(\chi_{403}(160, \cdot)\) 403.2.s.a 70 2
403.2.v \(\chi_{403}(36, \cdot)\) 403.2.v.a 70 2
403.2.y \(\chi_{403}(64, \cdot)\) 403.2.y.a 136 4
403.2.ba \(\chi_{403}(6, \cdot)\) 403.2.ba.a 140 4
403.2.be \(\chi_{403}(57, \cdot)\) 403.2.be.a 4 4
403.2.be.b 4
403.2.be.c 136
403.2.bf \(\chi_{403}(37, \cdot)\) 403.2.bf.a 140 4
403.2.bg \(\chi_{403}(123, \cdot)\) 403.2.bg.a 144 4
403.2.bi \(\chi_{403}(14, \cdot)\) 403.2.bi.a 120 8
403.2.bi.b 136
403.2.bj \(\chi_{403}(100, \cdot)\) 403.2.bj.a 280 8
403.2.bk \(\chi_{403}(9, \cdot)\) 403.2.bk.a 280 8
403.2.bl \(\chi_{403}(16, \cdot)\) 403.2.bl.a 8 8
403.2.bl.b 280
403.2.bn \(\chi_{403}(60, \cdot)\) 403.2.bn.a 272 8
403.2.bp \(\chi_{403}(10, \cdot)\) 403.2.bp.a 280 8
403.2.bs \(\chi_{403}(4, \cdot)\) 403.2.bs.a 288 8
403.2.bt \(\chi_{403}(82, \cdot)\) 403.2.bt.a 280 8
403.2.bz \(\chi_{403}(38, \cdot)\) 403.2.bz.a 288 8
403.2.cb \(\chi_{403}(15, \cdot)\) 403.2.cb.a 576 16
403.2.cc \(\chi_{403}(24, \cdot)\) 403.2.cc.a 560 16
403.2.cd \(\chi_{403}(21, \cdot)\) 403.2.cd.a 576 16
403.2.ch \(\chi_{403}(11, \cdot)\) 403.2.ch.a 560 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(403))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(403)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 - 3 T + 5 T^{2} - 6 T^{3} + 4 T^{4} \))(\( 1 + 2 T + 5 T^{2} + 7 T^{3} + 10 T^{4} + 9 T^{5} + 13 T^{6} + 18 T^{7} + 40 T^{8} + 56 T^{9} + 80 T^{10} + 64 T^{11} + 64 T^{12} \))(\( 1 - 2 T + 5 T^{2} - 7 T^{3} + 14 T^{4} - 21 T^{5} + 41 T^{6} - 56 T^{7} + 82 T^{8} - 84 T^{9} + 112 T^{10} - 112 T^{11} + 160 T^{12} - 128 T^{13} + 128 T^{14} \))(\( 1 + 5 T + 16 T^{2} + 40 T^{3} + 88 T^{4} + 174 T^{5} + 310 T^{6} + 496 T^{7} + 731 T^{8} + 992 T^{9} + 1240 T^{10} + 1392 T^{11} + 1408 T^{12} + 1280 T^{13} + 1024 T^{14} + 640 T^{15} + 256 T^{16} \))(\( 1 + T + 5 T^{2} + 4 T^{3} + 17 T^{4} + 17 T^{5} + 48 T^{6} + 45 T^{7} + 100 T^{8} + 90 T^{9} + 192 T^{10} + 136 T^{11} + 272 T^{12} + 128 T^{13} + 320 T^{14} + 128 T^{15} + 256 T^{16} \))(\( ( 1 - 2 T^{2} )^{2} \))(\( 1 + T - T^{2} + 2 T^{3} + 4 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 5 T^{3} + 11 T^{4} + 10 T^{5} + 8 T^{6} + 16 T^{7} + 16 T^{8} \))(\( 1 + T - T^{2} - 3 T^{3} - T^{4} - 6 T^{5} - 4 T^{6} + 8 T^{7} + 16 T^{8} \))(\( 1 + T + 4 T^{2} + 2 T^{3} + 9 T^{4} + 4 T^{5} + 16 T^{6} + 8 T^{7} + 16 T^{8} \))(\( 1 - T^{2} + 4 T^{4} \))(\( 1 - T^{2} + 4 T^{4} \))(\( 1 + 2 T + 2 T^{2} + 2 T^{3} + T^{4} + 4 T^{5} + 8 T^{6} + 16 T^{7} + 16 T^{8} \))(\( 1 + 2 T + 2 T^{2} + 2 T^{3} + T^{4} + 4 T^{5} + 8 T^{6} + 16 T^{7} + 16 T^{8} \))(\( ( 1 - T + 4 T^{2} - 2 T^{3} + 9 T^{4} - 4 T^{5} + 16 T^{6} - 8 T^{7} + 16 T^{8} )( 1 + 5 T + 13 T^{2} + 25 T^{3} + 39 T^{4} + 50 T^{5} + 52 T^{6} + 40 T^{7} + 16 T^{8} ) \))
$3$ (\( ( 1 + 2 T + 3 T^{2} )^{2} \))(\( 1 + 5 T + 22 T^{2} + 65 T^{3} + 172 T^{4} + 361 T^{5} + 691 T^{6} + 1083 T^{7} + 1548 T^{8} + 1755 T^{9} + 1782 T^{10} + 1215 T^{11} + 729 T^{12} \))(\( 1 - 5 T + 21 T^{2} - 62 T^{3} + 164 T^{4} - 360 T^{5} + 735 T^{6} - 1306 T^{7} + 2205 T^{8} - 3240 T^{9} + 4428 T^{10} - 5022 T^{11} + 5103 T^{12} - 3645 T^{13} + 2187 T^{14} \))(\( 1 + 3 T + 12 T^{2} + 27 T^{3} + 67 T^{4} + 124 T^{5} + 235 T^{6} + 396 T^{7} + 702 T^{8} + 1188 T^{9} + 2115 T^{10} + 3348 T^{11} + 5427 T^{12} + 6561 T^{13} + 8748 T^{14} + 6561 T^{15} + 6561 T^{16} \))(\( 1 - 7 T + 32 T^{2} - 105 T^{3} + 289 T^{4} - 678 T^{5} + 1449 T^{6} - 2804 T^{7} + 5074 T^{8} - 8412 T^{9} + 13041 T^{10} - 18306 T^{11} + 23409 T^{12} - 25515 T^{13} + 23328 T^{14} - 15309 T^{15} + 6561 T^{16} \))(\( ( 1 - 2 T + 3 T^{2} )^{2} \))(\( ( 1 - 3 T + 3 T^{2} )( 1 + 3 T + 3 T^{2} ) \))(\( 1 + T + 3 T^{2} + 5 T^{3} + 16 T^{4} + 15 T^{5} + 27 T^{6} + 27 T^{7} + 81 T^{8} \))(\( 1 + 2 T + T^{2} - 4 T^{3} - 11 T^{4} - 12 T^{5} + 9 T^{6} + 54 T^{7} + 81 T^{8} \))(\( 1 - 3 T + T^{2} + T^{3} + 4 T^{4} + 3 T^{5} + 9 T^{6} - 81 T^{7} + 81 T^{8} \))(\( 1 - T - 2 T^{2} - 3 T^{3} + 9 T^{4} \))(\( 1 - T - 2 T^{2} - 3 T^{3} + 9 T^{4} \))(\( 1 - 6 T + 20 T^{2} - 48 T^{3} + 91 T^{4} - 144 T^{5} + 180 T^{6} - 162 T^{7} + 81 T^{8} \))(\( 1 - 6 T + 20 T^{2} - 48 T^{3} + 91 T^{4} - 144 T^{5} + 180 T^{6} - 162 T^{7} + 81 T^{8} \))(\( 1 + 5 T + 13 T^{2} + 10 T^{3} - 30 T^{4} - 115 T^{5} - 122 T^{6} + 100 T^{7} + 499 T^{8} + 300 T^{9} - 1098 T^{10} - 3105 T^{11} - 2430 T^{12} + 2430 T^{13} + 9477 T^{14} + 10935 T^{15} + 6561 T^{16} \))
$5$ (\( 1 + 5 T^{2} + 25 T^{4} \))(\( 1 + 9 T + 50 T^{2} + 206 T^{3} + 700 T^{4} + 1979 T^{5} + 4789 T^{6} + 9895 T^{7} + 17500 T^{8} + 25750 T^{9} + 31250 T^{10} + 28125 T^{11} + 15625 T^{12} \))(\( 1 - 11 T + 73 T^{2} - 357 T^{3} + 1400 T^{4} - 4585 T^{5} + 12789 T^{6} - 30754 T^{7} + 63945 T^{8} - 114625 T^{9} + 175000 T^{10} - 223125 T^{11} + 228125 T^{12} - 171875 T^{13} + 78125 T^{14} \))(\( 1 + 15 T + 123 T^{2} + 717 T^{3} + 3289 T^{4} + 12450 T^{5} + 39947 T^{6} + 110340 T^{7} + 264523 T^{8} + 551700 T^{9} + 998675 T^{10} + 1556250 T^{11} + 2055625 T^{12} + 2240625 T^{13} + 1921875 T^{14} + 1171875 T^{15} + 390625 T^{16} \))(\( 1 - 11 T + 72 T^{2} - 350 T^{3} + 1397 T^{4} - 4774 T^{5} + 14277 T^{6} - 37831 T^{7} + 89438 T^{8} - 189155 T^{9} + 356925 T^{10} - 596750 T^{11} + 873125 T^{12} - 1093750 T^{13} + 1125000 T^{14} - 859375 T^{15} + 390625 T^{16} \))(\( ( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} ) \))(\( ( 1 + 3 T + 5 T^{2} )^{2} \))(\( ( 1 + 3 T + 11 T^{2} + 15 T^{3} + 25 T^{4} )^{2} \))(\( ( 1 + 2 T + 6 T^{2} + 10 T^{3} + 25 T^{4} )^{2} \))(\( ( 1 - 3 T + 11 T^{2} - 15 T^{3} + 25 T^{4} )^{2} \))(\( 1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4} \))(\( 1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4} \))(\( ( 1 - 2 T - T^{2} - 10 T^{3} + 25 T^{4} )( 1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4} ) \))(\( ( 1 - 2 T - T^{2} - 10 T^{3} + 25 T^{4} )( 1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4} ) \))(\( ( 1 + 3 T + 5 T^{2} )^{8} \))
$7$ (\( ( 1 - T + 7 T^{2} )^{2} \))(\( 1 + 13 T^{2} - 6 T^{3} + 98 T^{4} - 5 T^{5} + 671 T^{6} - 35 T^{7} + 4802 T^{8} - 2058 T^{9} + 31213 T^{10} + 117649 T^{12} \))(\( 1 - 4 T + 42 T^{2} - 144 T^{3} + 791 T^{4} - 2291 T^{5} + 8715 T^{6} - 20704 T^{7} + 61005 T^{8} - 112259 T^{9} + 271313 T^{10} - 345744 T^{11} + 705894 T^{12} - 470596 T^{13} + 823543 T^{14} \))(\( 1 + 4 T + 36 T^{2} + 108 T^{3} + 578 T^{4} + 1371 T^{5} + 5846 T^{6} + 11754 T^{7} + 45123 T^{8} + 82278 T^{9} + 286454 T^{10} + 470253 T^{11} + 1387778 T^{12} + 1815156 T^{13} + 4235364 T^{14} + 3294172 T^{15} + 5764801 T^{16} \))(\( 1 + 2 T + 17 T^{2} + 56 T^{3} + 261 T^{4} + 773 T^{5} + 2582 T^{6} + 7565 T^{7} + 21254 T^{8} + 52955 T^{9} + 126518 T^{10} + 265139 T^{11} + 626661 T^{12} + 941192 T^{13} + 2000033 T^{14} + 1647086 T^{15} + 5764801 T^{16} \))(\( 1 - 10 T^{2} + 49 T^{4} \))(\( 1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 + 7 T + 27 T^{2} + 95 T^{3} + 296 T^{4} + 665 T^{5} + 1323 T^{6} + 2401 T^{7} + 2401 T^{8} \))(\( 1 - T - T^{2} - 17 T^{3} + 64 T^{4} - 119 T^{5} - 49 T^{6} - 343 T^{7} + 2401 T^{8} \))(\( 1 + 9 T + 29 T^{2} + 33 T^{3} + 4 T^{4} + 231 T^{5} + 1421 T^{6} + 3087 T^{7} + 2401 T^{8} \))(\( ( 1 - T + 7 T^{2} )( 1 + 4 T + 7 T^{2} ) \))(\( ( 1 - 4 T + 7 T^{2} )( 1 + T + 7 T^{2} ) \))(\( ( 1 + 5 T + 7 T^{2} )^{2}( 1 + 2 T^{2} + 49 T^{4} ) \))(\( ( 1 - 4 T + 7 T^{2} )^{2}( 1 + 11 T^{2} + 49 T^{4} ) \))(\( 1 + 3 T + 7 T^{2} + 36 T^{3} + 108 T^{4} + 219 T^{5} + 854 T^{6} + 2628 T^{7} + 5483 T^{8} + 18396 T^{9} + 41846 T^{10} + 75117 T^{11} + 259308 T^{12} + 605052 T^{13} + 823543 T^{14} + 2470629 T^{15} + 5764801 T^{16} \))
$11$ (\( 1 + 2 T^{2} + 121 T^{4} \))(\( 1 + 5 T + 48 T^{2} + 226 T^{3} + 1170 T^{4} + 4357 T^{5} + 16795 T^{6} + 47927 T^{7} + 141570 T^{8} + 300806 T^{9} + 702768 T^{10} + 805255 T^{11} + 1771561 T^{12} \))(\( 1 - 8 T + 74 T^{2} - 429 T^{3} + 2386 T^{4} - 10471 T^{5} + 43268 T^{6} - 147557 T^{7} + 475948 T^{8} - 1266991 T^{9} + 3175766 T^{10} - 6280989 T^{11} + 11917774 T^{12} - 14172488 T^{13} + 19487171 T^{14} \))(\( 1 + 5 T + 32 T^{2} + 76 T^{3} + 397 T^{4} + 704 T^{5} + 4685 T^{6} + 6125 T^{7} + 48318 T^{8} + 67375 T^{9} + 566885 T^{10} + 937024 T^{11} + 5812477 T^{12} + 12239876 T^{13} + 56689952 T^{14} + 97435855 T^{15} + 214358881 T^{16} \))(\( 1 + 2 T + 57 T^{2} + 103 T^{3} + 1580 T^{4} + 2544 T^{5} + 28112 T^{6} + 39952 T^{7} + 359040 T^{8} + 439472 T^{9} + 3401552 T^{10} + 3386064 T^{11} + 23132780 T^{12} + 16588253 T^{13} + 100978977 T^{14} + 38974342 T^{15} + 214358881 T^{16} \))(\( 1 - 21 T^{2} + 121 T^{4} \))(\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 5 T + 4 T^{2} - 25 T^{3} + 201 T^{4} - 275 T^{5} + 484 T^{6} - 6655 T^{7} + 14641 T^{8} \))(\( ( 1 - 9 T + 41 T^{2} - 99 T^{3} + 121 T^{4} )( 1 + 11 T + 51 T^{2} + 121 T^{3} + 121 T^{4} ) \))(\( 1 - 3 T + 8 T^{2} - 51 T^{3} + 265 T^{4} - 561 T^{5} + 968 T^{6} - 3993 T^{7} + 14641 T^{8} \))(\( 1 + 9 T + 38 T^{2} + 99 T^{3} + 121 T^{4} \))(\( 1 - 9 T + 38 T^{2} - 99 T^{3} + 121 T^{4} \))(\( 1 - 6 T + 9 T^{2} + 66 T^{3} - 376 T^{4} + 726 T^{5} + 1089 T^{6} - 7986 T^{7} + 14641 T^{8} \))(\( 1 + 9 T^{2} - 48 T^{3} + 20 T^{4} - 528 T^{5} + 1089 T^{6} + 14641 T^{8} \))(\( 1 + 5 T + 21 T^{2} - 30 T^{3} - 310 T^{4} - 1635 T^{5} - 586 T^{6} + 11900 T^{7} + 83499 T^{8} + 130900 T^{9} - 70906 T^{10} - 2176185 T^{11} - 4538710 T^{12} - 4831530 T^{13} + 37202781 T^{14} + 97435855 T^{15} + 214358881 T^{16} \))
$13$ (\( ( 1 - T )^{2} \))(\( ( 1 - T )^{6} \))(\( ( 1 + T )^{7} \))(\( ( 1 + T )^{8} \))(\( ( 1 - T )^{8} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - T + T^{2} - T^{3} + T^{4} \))(\( 1 - T + T^{2} - T^{3} + T^{4} \))(\( 1 - T + T^{2} - T^{3} + T^{4} \))(\( 1 - 7 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))(\( 1 - 4 T + 3 T^{2} - 52 T^{3} + 169 T^{4} \))(\( 1 + 4 T + 3 T^{2} + 52 T^{3} + 169 T^{4} \))(\( 1 + 5 T + 12 T^{2} - 5 T^{3} - 181 T^{4} - 65 T^{5} + 2028 T^{6} + 10985 T^{7} + 28561 T^{8} \))
$17$ (\( 1 - 6 T + 38 T^{2} - 102 T^{3} + 289 T^{4} \))(\( 1 + 23 T + 296 T^{2} + 2664 T^{3} + 18400 T^{4} + 101871 T^{5} + 462517 T^{6} + 1731807 T^{7} + 5317600 T^{8} + 13088232 T^{9} + 24722216 T^{10} + 32656711 T^{11} + 24137569 T^{12} \))(\( 1 - 7 T + 99 T^{2} - 487 T^{3} + 3936 T^{4} - 14909 T^{5} + 92493 T^{6} - 294386 T^{7} + 1572381 T^{8} - 4308701 T^{9} + 19337568 T^{10} - 40674727 T^{11} + 140565843 T^{12} - 168962983 T^{13} + 410338673 T^{14} \))(\( 1 + 11 T + 126 T^{2} + 996 T^{3} + 7123 T^{4} + 42792 T^{5} + 234463 T^{6} + 1116927 T^{7} + 4923742 T^{8} + 18987759 T^{9} + 67759807 T^{10} + 210237096 T^{11} + 594920083 T^{12} + 1414177572 T^{13} + 3041333694 T^{14} + 4513725403 T^{15} + 6975757441 T^{16} \))(\( 1 - 7 T + 88 T^{2} - 484 T^{3} + 3785 T^{4} - 17682 T^{5} + 105707 T^{6} - 423093 T^{7} + 2094890 T^{8} - 7192581 T^{9} + 30549323 T^{10} - 86871666 T^{11} + 316126985 T^{12} - 687210788 T^{13} + 2124106072 T^{14} - 2872370711 T^{15} + 6975757441 T^{16} \))(\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( 1 + 5 T + 8 T^{2} + 85 T^{3} + 289 T^{4} \))(\( 1 + 15 T + 118 T^{2} + 675 T^{3} + 3079 T^{4} + 11475 T^{5} + 34102 T^{6} + 73695 T^{7} + 83521 T^{8} \))(\( 1 + T - T^{2} - 53 T^{3} + 104 T^{4} - 901 T^{5} - 289 T^{6} + 4913 T^{7} + 83521 T^{8} \))(\( 1 + T - 16 T^{2} - 33 T^{3} + 239 T^{4} - 561 T^{5} - 4624 T^{6} + 4913 T^{7} + 83521 T^{8} \))(\( 1 + 3 T - 8 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 + 3 T - 8 T^{2} + 51 T^{3} + 289 T^{4} \))(\( ( 1 - 17 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 17 T^{2} + 289 T^{4} )^{2} \))(\( 1 + 5 T + 32 T^{2} + 135 T^{3} + 670 T^{4} + 1110 T^{5} + 9032 T^{6} + 10880 T^{7} + 63559 T^{8} + 184960 T^{9} + 2610248 T^{10} + 5453430 T^{11} + 55959070 T^{12} + 191680695 T^{13} + 772402208 T^{14} + 2051693365 T^{15} + 6975757441 T^{16} \))
$19$ (\( ( 1 - T + 19 T^{2} )^{2} \))(\( 1 - 7 T + 37 T^{2} - 205 T^{3} + 878 T^{4} - 4092 T^{5} + 23147 T^{6} - 77748 T^{7} + 316958 T^{8} - 1406095 T^{9} + 4821877 T^{10} - 17332693 T^{11} + 47045881 T^{12} \))(\( 1 - T + 96 T^{2} - 116 T^{3} + 4435 T^{4} - 5215 T^{5} + 127343 T^{6} - 128176 T^{7} + 2419517 T^{8} - 1882615 T^{9} + 30419665 T^{10} - 15117236 T^{11} + 237705504 T^{12} - 47045881 T^{13} + 893871739 T^{14} \))(\( 1 + 9 T + 106 T^{2} + 708 T^{3} + 4938 T^{4} + 25924 T^{5} + 141398 T^{6} + 623397 T^{7} + 3004911 T^{8} + 11844543 T^{9} + 51044678 T^{10} + 177812716 T^{11} + 643525098 T^{12} + 1753078092 T^{13} + 4986863386 T^{14} + 8044845651 T^{15} + 16983563041 T^{16} \))(\( 1 + 5 T + 79 T^{2} + 433 T^{3} + 3319 T^{4} + 17629 T^{5} + 100366 T^{6} + 462785 T^{7} + 2242286 T^{8} + 8792915 T^{9} + 36232126 T^{10} + 120917311 T^{11} + 432535399 T^{12} + 1072150867 T^{13} + 3716624599 T^{14} + 4469358695 T^{15} + 16983563041 T^{16} \))(\( 1 - 34 T^{2} + 361 T^{4} \))(\( 1 + 4 T - 3 T^{2} + 76 T^{3} + 361 T^{4} \))(\( 1 - 2 T - 15 T^{2} + 68 T^{3} + 149 T^{4} + 1292 T^{5} - 5415 T^{6} - 13718 T^{7} + 130321 T^{8} \))(\( 1 - 19 T^{2} + 361 T^{4} - 6859 T^{6} + 130321 T^{8} \))(\( 1 + 10 T + 21 T^{2} - 190 T^{3} - 1519 T^{4} - 3610 T^{5} + 7581 T^{6} + 68590 T^{7} + 130321 T^{8} \))(\( ( 1 - 8 T + 19 T^{2} )( 1 - T + 19 T^{2} ) \))(\( ( 1 + T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( 1 - 6 T + 45 T^{2} - 126 T^{3} + 704 T^{4} - 2394 T^{5} + 16245 T^{6} - 41154 T^{7} + 130321 T^{8} \))(\( 1 - 12 T + 45 T^{2} + 108 T^{3} - 1348 T^{4} + 2052 T^{5} + 16245 T^{6} - 82308 T^{7} + 130321 T^{8} \))(\( 1 + 6 T + 19 T^{2} + 126 T^{3} + 756 T^{4} + 4308 T^{5} + 20501 T^{6} + 90468 T^{7} + 412487 T^{8} + 1718892 T^{9} + 7400861 T^{10} + 29548572 T^{11} + 98522676 T^{12} + 311988474 T^{13} + 893871739 T^{14} + 5363230434 T^{15} + 16983563041 T^{16} \))
$23$ (\( 1 + 6 T + 50 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 + 18 T + 230 T^{2} + 2072 T^{3} + 15500 T^{4} + 94612 T^{5} + 496265 T^{6} + 2176076 T^{7} + 8199500 T^{8} + 25210024 T^{9} + 64363430 T^{10} + 115854174 T^{11} + 148035889 T^{12} \))(\( 1 - 6 T + 85 T^{2} - 436 T^{3} + 3598 T^{4} - 15182 T^{5} + 100343 T^{6} - 386900 T^{7} + 2307889 T^{8} - 8031278 T^{9} + 43776866 T^{10} - 122010676 T^{11} + 547089155 T^{12} - 888215334 T^{13} + 3404825447 T^{14} \))(\( 1 + 98 T^{2} + 84 T^{3} + 4275 T^{4} + 9392 T^{5} + 115707 T^{6} + 424422 T^{7} + 2628074 T^{8} + 9761706 T^{9} + 61209003 T^{10} + 114272464 T^{11} + 1196320275 T^{12} + 540652812 T^{13} + 14507517122 T^{14} + 78310985281 T^{16} \))(\( 1 - 14 T + 186 T^{2} - 1576 T^{3} + 13203 T^{4} - 86804 T^{5} + 558681 T^{6} - 2976046 T^{7} + 15525890 T^{8} - 68449058 T^{9} + 295542249 T^{10} - 1056144268 T^{11} + 3694740723 T^{12} - 10143676568 T^{13} + 27534675354 T^{14} - 47667556258 T^{15} + 78310985281 T^{16} \))(\( ( 1 + 4 T + 23 T^{2} )^{2} \))(\( 1 + 4 T - 7 T^{2} + 92 T^{3} + 529 T^{4} \))(\( 1 + 8 T + T^{2} - 146 T^{3} - 651 T^{4} - 3358 T^{5} + 529 T^{6} + 97336 T^{7} + 279841 T^{8} \))(\( 1 - 2 T + T^{2} - 106 T^{3} + 729 T^{4} - 2438 T^{5} + 529 T^{6} - 24334 T^{7} + 279841 T^{8} \))(\( 1 - 12 T + 41 T^{2} - 36 T^{3} + 49 T^{4} - 828 T^{5} + 21689 T^{6} - 146004 T^{7} + 279841 T^{8} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 + 2 T + 20 T^{2} + 46 T^{3} + 529 T^{4} )^{2} \))(\( ( 1 - 2 T + 20 T^{2} - 46 T^{3} + 529 T^{4} )^{2} \))(\( 1 + 11 T + 93 T^{2} + 798 T^{3} + 5738 T^{4} + 37203 T^{5} + 214886 T^{6} + 1165784 T^{7} + 5972343 T^{8} + 26813032 T^{9} + 113674694 T^{10} + 452648901 T^{11} + 1605727658 T^{12} + 5136201714 T^{13} + 13767337677 T^{14} + 37453079917 T^{15} + 78310985281 T^{16} \))
$29$ (\( 1 - 6 T + 62 T^{2} - 174 T^{3} + 841 T^{4} \))(\( 1 + 18 T + 256 T^{2} + 2385 T^{3} + 19683 T^{4} + 127703 T^{5} + 761621 T^{6} + 3703387 T^{7} + 16553403 T^{8} + 58167765 T^{9} + 181063936 T^{10} + 369200682 T^{11} + 594823321 T^{12} \))(\( 1 + 2 T + 95 T^{2} + 341 T^{3} + 4545 T^{4} + 22874 T^{5} + 158418 T^{6} + 847016 T^{7} + 4594122 T^{8} + 19237034 T^{9} + 110848005 T^{10} + 241182821 T^{11} + 1948559155 T^{12} + 1189646642 T^{13} + 17249876309 T^{14} \))(\( 1 + 12 T + 148 T^{2} + 1103 T^{3} + 8738 T^{4} + 53277 T^{5} + 358535 T^{6} + 1929446 T^{7} + 11586852 T^{8} + 55953934 T^{9} + 301527935 T^{10} + 1299372753 T^{11} + 6180221378 T^{12} + 22623797347 T^{13} + 88033851508 T^{14} + 206998515708 T^{15} + 500246412961 T^{16} \))(\( 1 - 12 T + 218 T^{2} - 1903 T^{3} + 19562 T^{4} - 134879 T^{5} + 1012631 T^{6} - 5780334 T^{7} + 35047928 T^{8} - 167629686 T^{9} + 851622671 T^{10} - 3289563931 T^{11} + 13835830922 T^{12} - 39032716547 T^{13} + 129671483978 T^{14} - 206998515708 T^{15} + 500246412961 T^{16} \))(\( ( 1 - 8 T + 29 T^{2} )^{2} \))(\( 1 + 3 T - 20 T^{2} + 87 T^{3} + 841 T^{4} \))(\( 1 + 8 T + 5 T^{2} - 232 T^{3} - 1711 T^{4} - 6728 T^{5} + 4205 T^{6} + 195112 T^{7} + 707281 T^{8} \))(\( 1 + 10 T + 71 T^{2} + 520 T^{3} + 3641 T^{4} + 15080 T^{5} + 59711 T^{6} + 243890 T^{7} + 707281 T^{8} \))(\( 1 - 10 T + 11 T^{2} + 120 T^{3} - 439 T^{4} + 3480 T^{5} + 9251 T^{6} - 243890 T^{7} + 707281 T^{8} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 - 4 T - 13 T^{2} - 116 T^{3} + 841 T^{4} )( 1 + 4 T - 13 T^{2} + 116 T^{3} + 841 T^{4} ) \))(\( ( 1 - 4 T - 13 T^{2} - 116 T^{3} + 841 T^{4} )( 1 + 4 T - 13 T^{2} + 116 T^{3} + 841 T^{4} ) \))(\( 1 + 7 T + 54 T^{2} + 411 T^{3} + 2762 T^{4} + 11112 T^{5} + 80708 T^{6} + 338866 T^{7} + 1602651 T^{8} + 9827114 T^{9} + 67875428 T^{10} + 271010568 T^{11} + 1953510122 T^{12} + 8430082239 T^{13} + 32120459334 T^{14} + 120749134163 T^{15} + 500246412961 T^{16} \))
$31$ (\( ( 1 + T )^{2} \))(\( ( 1 - T )^{6} \))(\( ( 1 - T )^{7} \))(\( ( 1 + T )^{8} \))(\( ( 1 + T )^{8} \))(\( 1 + T^{2} \))(\( ( 1 + T )^{2} \))(\( 1 + 4 T + 46 T^{2} + 124 T^{3} + 961 T^{4} \))(\( 1 - 4 T + 46 T^{2} - 124 T^{3} + 961 T^{4} \))(\( 1 - 4 T + 46 T^{2} - 124 T^{3} + 961 T^{4} \))(\( 1 - 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))(\( 1 - 13 T^{2} + 961 T^{4} \))(\( ( 1 - 7 T + 31 T^{2} )^{2} \))(\( ( 1 - T - 39 T^{2} - 31 T^{3} + 961 T^{4} )^{2} \))
$37$ (\( 1 + 6 T + 38 T^{2} + 222 T^{3} + 1369 T^{4} \))(\( 1 + 13 T + 167 T^{2} + 1395 T^{3} + 10520 T^{4} + 68826 T^{5} + 424911 T^{6} + 2546562 T^{7} + 14401880 T^{8} + 70660935 T^{9} + 312984887 T^{10} + 901471441 T^{11} + 2565726409 T^{12} \))(\( 1 - 28 T + 543 T^{2} - 7259 T^{3} + 79366 T^{4} - 702049 T^{5} + 5368229 T^{6} - 34835635 T^{7} + 198624473 T^{8} - 961105081 T^{9} + 4020125998 T^{10} - 13604534699 T^{11} + 37653768651 T^{12} - 71840339452 T^{13} + 94931877133 T^{14} \))(\( 1 + 9 T + 165 T^{2} + 991 T^{3} + 12935 T^{4} + 67343 T^{5} + 740502 T^{6} + 3375839 T^{7} + 31495474 T^{8} + 124906043 T^{9} + 1013747238 T^{10} + 3411124979 T^{11} + 24242272535 T^{12} + 68719861387 T^{13} + 423344857485 T^{14} + 854386894197 T^{15} + 3512479453921 T^{16} \))(\( 1 - 2 T + 230 T^{2} - 357 T^{3} + 24787 T^{4} - 30372 T^{5} + 1640477 T^{6} - 1626076 T^{7} + 73077860 T^{8} - 60164812 T^{9} + 2245813013 T^{10} - 1538432916 T^{11} + 46454828707 T^{12} - 24755792649 T^{13} + 590117074070 T^{14} - 189863754266 T^{15} + 3512479453921 T^{16} \))(\( 1 - 65 T^{2} + 1369 T^{4} \))(\( 1 - 5 T - 12 T^{2} - 185 T^{3} + 1369 T^{4} \))(\( ( 1 + 13 T + 105 T^{2} + 481 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 - 2 T + 70 T^{2} - 74 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 + 13 T + 115 T^{2} + 481 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 - 10 T + 37 T^{2} )( 1 + T + 37 T^{2} ) \))(\( ( 1 - T + 37 T^{2} )( 1 + 10 T + 37 T^{2} ) \))(\( 1 + 12 T + 72 T^{2} + 288 T^{3} + 983 T^{4} + 10656 T^{5} + 98568 T^{6} + 607836 T^{7} + 1874161 T^{8} \))(\( 1 + 12 T + 72 T^{2} + 288 T^{3} + 983 T^{4} + 10656 T^{5} + 98568 T^{6} + 607836 T^{7} + 1874161 T^{8} \))(\( ( 1 - 5 T - 24 T^{2} + 125 T^{3} + 107 T^{4} + 4625 T^{5} - 32856 T^{6} - 253265 T^{7} + 1874161 T^{8} )^{2} \))
$41$ (\( 1 + 77 T^{2} + 1681 T^{4} \))(\( 1 + 5 T + 107 T^{2} + 139 T^{3} + 4339 T^{4} - 11907 T^{5} + 124273 T^{6} - 488187 T^{7} + 7293859 T^{8} + 9580019 T^{9} + 302356427 T^{10} + 579281005 T^{11} + 4750104241 T^{12} \))(\( 1 - 3 T + 154 T^{2} - 384 T^{3} + 12246 T^{4} - 27106 T^{5} + 677120 T^{6} - 1349900 T^{7} + 27761920 T^{8} - 45565186 T^{9} + 844006566 T^{10} - 1085092224 T^{11} + 17841854954 T^{12} - 14250312723 T^{13} + 194754273881 T^{14} \))(\( 1 + 25 T + 476 T^{2} + 6372 T^{3} + 72959 T^{4} + 693235 T^{5} + 5892153 T^{6} + 43853249 T^{7} + 297848517 T^{8} + 1797983209 T^{9} + 9904709193 T^{10} + 47778449435 T^{11} + 206164696799 T^{12} + 738235712772 T^{13} + 2261049618716 T^{14} + 4868856847025 T^{15} + 7984925229121 T^{16} \))(\( 1 - 13 T + 257 T^{2} - 2755 T^{3} + 32456 T^{4} - 279296 T^{5} + 2480988 T^{6} - 17390736 T^{7} + 124312468 T^{8} - 713020176 T^{9} + 4170540828 T^{10} - 19249359616 T^{11} + 91712899016 T^{12} - 319183833755 T^{13} + 1220776789937 T^{14} - 2531805560453 T^{15} + 7984925229121 T^{16} \))(\( 1 - 66 T^{2} + 1681 T^{4} \))(\( 1 + 7 T + 8 T^{2} + 287 T^{3} + 1681 T^{4} \))(\( 1 + 19 T + 95 T^{2} - 599 T^{3} - 8776 T^{4} - 24559 T^{5} + 159695 T^{6} + 1309499 T^{7} + 2825761 T^{8} \))(\( 1 - 41 T^{2} + 1681 T^{4} - 68921 T^{6} + 2825761 T^{8} \))(\( 1 - 5 T - 31 T^{2} + 205 T^{3} + 476 T^{4} + 8405 T^{5} - 52111 T^{6} - 344605 T^{7} + 2825761 T^{8} \))(\( 1 - 9 T + 68 T^{2} - 369 T^{3} + 1681 T^{4} \))(\( 1 + 9 T + 68 T^{2} + 369 T^{3} + 1681 T^{4} \))(\( 1 + 20 T + 164 T^{2} + 668 T^{3} + 2335 T^{4} + 27388 T^{5} + 275684 T^{6} + 1378420 T^{7} + 2825761 T^{8} \))(\( 1 - 16 T + 164 T^{2} - 1204 T^{3} + 8239 T^{4} - 49364 T^{5} + 275684 T^{6} - 1102736 T^{7} + 2825761 T^{8} \))(\( 1 - 17 T + 146 T^{2} - 153 T^{3} - 7514 T^{4} + 82824 T^{5} - 245596 T^{6} - 1697654 T^{7} + 23405647 T^{8} - 69603814 T^{9} - 412846876 T^{10} + 5708312904 T^{11} - 21232768154 T^{12} - 17725998753 T^{13} + 693515219186 T^{14} - 3310822655977 T^{15} + 7984925229121 T^{16} \))
$43$ (\( 1 + 10 T + 66 T^{2} + 430 T^{3} + 1849 T^{4} \))(\( 1 + 7 T + 157 T^{2} + 799 T^{3} + 10895 T^{4} + 39897 T^{5} + 515997 T^{6} + 1715571 T^{7} + 20144855 T^{8} + 63526093 T^{9} + 536751757 T^{10} + 1029059101 T^{11} + 6321363049 T^{12} \))(\( 1 + T + 182 T^{2} + 446 T^{3} + 15284 T^{4} + 56610 T^{5} + 839368 T^{6} + 3380702 T^{7} + 36092824 T^{8} + 104671890 T^{9} + 1215184988 T^{10} + 1524785246 T^{11} + 26755536626 T^{12} + 6321363049 T^{13} + 271818611107 T^{14} \))(\( 1 - 7 T + 145 T^{2} - 711 T^{3} + 10108 T^{4} - 44326 T^{5} + 602614 T^{6} - 2834324 T^{7} + 30515756 T^{8} - 121875932 T^{9} + 1114233286 T^{10} - 3524227282 T^{11} + 34557240508 T^{12} - 104523002973 T^{13} + 916597642105 T^{14} - 1902730277749 T^{15} + 11688200277601 T^{16} \))(\( 1 + 5 T + 217 T^{2} + 765 T^{3} + 21840 T^{4} + 54132 T^{5} + 1417198 T^{6} + 2632544 T^{7} + 68767656 T^{8} + 113199392 T^{9} + 2620399102 T^{10} + 4303872924 T^{11} + 74666613840 T^{12} + 112461458895 T^{13} + 1371735781633 T^{14} + 1359093055535 T^{15} + 11688200277601 T^{16} \))(\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( 1 - 2 T - 39 T^{2} - 86 T^{3} + 1849 T^{4} \))(\( 1 - 6 T + 93 T^{2} - 350 T^{3} + 4851 T^{4} - 15050 T^{5} + 171957 T^{6} - 477042 T^{7} + 3418801 T^{8} \))(\( 1 - 18 T + 101 T^{2} - 174 T^{3} + 49 T^{4} - 7482 T^{5} + 186749 T^{6} - 1431126 T^{7} + 3418801 T^{8} \))(\( 1 + 2 T - 19 T^{2} - 254 T^{3} + 619 T^{4} - 10922 T^{5} - 35131 T^{6} + 159014 T^{7} + 3418801 T^{8} \))(\( 1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4} \))(\( 1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4} \))(\( 1 - 2 T - 56 T^{2} + 52 T^{3} + 1579 T^{4} + 2236 T^{5} - 103544 T^{6} - 159014 T^{7} + 3418801 T^{8} \))(\( 1 + 2 T - 56 T^{2} - 52 T^{3} + 1579 T^{4} - 2236 T^{5} - 103544 T^{6} + 159014 T^{7} + 3418801 T^{8} \))(\( 1 + 12 T + 123 T^{2} + 340 T^{3} + 240 T^{4} - 20312 T^{5} + 86989 T^{6} + 1467420 T^{7} + 19111999 T^{8} + 63099060 T^{9} + 160842661 T^{10} - 1614946184 T^{11} + 820512240 T^{12} + 49982870620 T^{13} + 777527655027 T^{14} + 3261823333284 T^{15} + 11688200277601 T^{16} \))
$47$ (\( 1 + 14 T^{2} + 2209 T^{4} \))(\( 1 + 9 T + 187 T^{2} + 1615 T^{3} + 17941 T^{4} + 128543 T^{5} + 1062573 T^{6} + 6041521 T^{7} + 39631669 T^{8} + 167674145 T^{9} + 912500347 T^{10} + 2064105063 T^{11} + 10779215329 T^{12} \))(\( 1 + T + 110 T^{2} + 628 T^{3} + 8078 T^{4} + 51096 T^{5} + 603016 T^{6} + 2275594 T^{7} + 28341752 T^{8} + 112871064 T^{9} + 838682194 T^{10} + 3064439668 T^{11} + 25227950770 T^{12} + 10779215329 T^{13} + 506623120463 T^{14} \))(\( 1 + 17 T + 241 T^{2} + 1981 T^{3} + 14608 T^{4} + 51402 T^{5} + 85212 T^{6} - 2325046 T^{7} - 16365036 T^{8} - 109277162 T^{9} + 188233308 T^{10} + 5336709846 T^{11} + 71282380048 T^{12} + 454332458867 T^{13} + 2597790894289 T^{14} + 8612593047871 T^{15} + 23811286661761 T^{16} \))(\( 1 - 23 T + 461 T^{2} - 6449 T^{3} + 79244 T^{4} - 808340 T^{5} + 7419988 T^{6} - 59462726 T^{7} + 433337284 T^{8} - 2794748122 T^{9} + 16390753492 T^{10} - 83924283820 T^{11} + 386685441164 T^{12} - 1479045950143 T^{13} + 4969218266669 T^{14} - 11652331770649 T^{15} + 23811286661761 T^{16} \))(\( 1 - 90 T^{2} + 2209 T^{4} \))(\( ( 1 + 6 T + 47 T^{2} )^{2} \))(\( 1 - 11 T + 49 T^{2} - 547 T^{3} + 5964 T^{4} - 25709 T^{5} + 108241 T^{6} - 1142053 T^{7} + 4879681 T^{8} \))(\( 1 - 16 T + 59 T^{2} + 738 T^{3} - 9721 T^{4} + 34686 T^{5} + 130331 T^{6} - 1661168 T^{7} + 4879681 T^{8} \))(\( 1 - T + 59 T^{2} - 177 T^{3} + 2264 T^{4} - 8319 T^{5} + 130331 T^{6} - 103823 T^{7} + 4879681 T^{8} \))(\( 1 - 82 T^{2} + 2209 T^{4} \))(\( 1 - 82 T^{2} + 2209 T^{4} \))(\( 1 - 20 T + 200 T^{2} - 1460 T^{3} + 9982 T^{4} - 68620 T^{5} + 441800 T^{6} - 2076460 T^{7} + 4879681 T^{8} \))(\( 1 - 20 T + 200 T^{2} - 1460 T^{3} + 9982 T^{4} - 68620 T^{5} + 441800 T^{6} - 2076460 T^{7} + 4879681 T^{8} \))(\( ( 1 + 14 T + 29 T^{2} - 352 T^{3} - 2851 T^{4} - 16544 T^{5} + 64061 T^{6} + 1453522 T^{7} + 4879681 T^{8} )^{2} \))
$53$ (\( 1 - 18 T + 182 T^{2} - 954 T^{3} + 2809 T^{4} \))(\( 1 + 31 T + 652 T^{2} + 9636 T^{3} + 114432 T^{4} + 1093949 T^{5} + 8760977 T^{6} + 57979297 T^{7} + 321439488 T^{8} + 1434578772 T^{9} + 5144593612 T^{10} + 12964060283 T^{11} + 22164361129 T^{12} \))(\( 1 - 29 T + 591 T^{2} - 8451 T^{3} + 101858 T^{4} - 1016019 T^{5} + 9011455 T^{6} - 69125430 T^{7} + 477607115 T^{8} - 2853997371 T^{9} + 15164313466 T^{10} - 66682454931 T^{11} + 247153536363 T^{12} - 642766472741 T^{13} + 1174711139837 T^{14} \))(\( 1 + 15 T + 424 T^{2} + 4950 T^{3} + 77587 T^{4} + 727866 T^{5} + 8123777 T^{6} + 61843695 T^{7} + 535702502 T^{8} + 3277715835 T^{9} + 22819689593 T^{10} + 108362506482 T^{11} + 612198749347 T^{12} + 2070067690350 T^{13} + 9397689118696 T^{14} + 17620667097555 T^{15} + 62259690411361 T^{16} \))(\( 1 - 25 T + 494 T^{2} - 7208 T^{3} + 90047 T^{4} - 958140 T^{5} + 9122429 T^{6} - 77029789 T^{7} + 592048214 T^{8} - 4082578817 T^{9} + 25624903061 T^{10} - 142645008780 T^{11} + 710514142607 T^{12} - 3014353113544 T^{13} + 10949194397726 T^{14} - 29367778495925 T^{15} + 62259690411361 T^{16} \))(\( ( 1 + 4 T + 53 T^{2} )^{2} \))(\( ( 1 + 9 T + 53 T^{2} )^{2} \))(\( 1 + 6 T + 83 T^{2} + 480 T^{3} + 6481 T^{4} + 25440 T^{5} + 233147 T^{6} + 893262 T^{7} + 7890481 T^{8} \))(\( 1 - 2 T - 49 T^{2} + 204 T^{3} + 2189 T^{4} + 10812 T^{5} - 137641 T^{6} - 297754 T^{7} + 7890481 T^{8} \))(\( 1 + 28 T + 401 T^{2} + 4024 T^{3} + 32129 T^{4} + 213272 T^{5} + 1126409 T^{6} + 4168556 T^{7} + 7890481 T^{8} \))(\( 1 + 3 T - 44 T^{2} + 159 T^{3} + 2809 T^{4} \))(\( 1 + 3 T - 44 T^{2} + 159 T^{3} + 2809 T^{4} \))(\( 1 + 30 T + 477 T^{2} + 5310 T^{3} + 44420 T^{4} + 281430 T^{5} + 1339893 T^{6} + 4466310 T^{7} + 7890481 T^{8} \))(\( 1 + 30 T + 477 T^{2} + 5310 T^{3} + 44420 T^{4} + 281430 T^{5} + 1339893 T^{6} + 4466310 T^{7} + 7890481 T^{8} \))(\( ( 1 - 4 T - 47 T^{2} + 160 T^{3} + 2121 T^{4} + 8480 T^{5} - 132023 T^{6} - 595508 T^{7} + 7890481 T^{8} )^{2} \))
$59$ (\( 1 + 6 T + 107 T^{2} + 354 T^{3} + 3481 T^{4} \))(\( 1 + T + 218 T^{2} + 366 T^{3} + 24064 T^{4} + 38337 T^{5} + 1731235 T^{6} + 2261883 T^{7} + 83766784 T^{8} + 75168714 T^{9} + 2641584698 T^{10} + 714924299 T^{11} + 42180533641 T^{12} \))(\( 1 - 3 T + 105 T^{2} - 407 T^{3} + 5420 T^{4} - 49707 T^{5} + 249413 T^{6} - 4514256 T^{7} + 14715367 T^{8} - 173030067 T^{9} + 1113154180 T^{10} - 4931765927 T^{11} + 75067051395 T^{12} - 126541600923 T^{13} + 2488651484819 T^{14} \))(\( 1 + 15 T + 379 T^{2} + 4031 T^{3} + 62177 T^{4} + 536492 T^{5} + 6357685 T^{6} + 46119098 T^{7} + 447458939 T^{8} + 2721026782 T^{9} + 22131101485 T^{10} + 110184190468 T^{11} + 753421154897 T^{12} + 2881859849269 T^{13} + 15986422249939 T^{14} + 37329772272285 T^{15} + 146830437604321 T^{16} \))(\( 1 + 5 T + 220 T^{2} + 1532 T^{3} + 28399 T^{4} + 212720 T^{5} + 2537683 T^{6} + 18481679 T^{7} + 171856562 T^{8} + 1090419061 T^{9} + 8833674523 T^{10} + 43688220880 T^{11} + 344120935039 T^{12} + 1095264026068 T^{13} + 9279717401020 T^{14} + 12443257424095 T^{15} + 146830437604321 T^{16} \))(\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 6 T - 23 T^{2} - 354 T^{3} + 3481 T^{4} \))(\( 1 + 14 T + 37 T^{2} + 142 T^{3} + 3555 T^{4} + 8378 T^{5} + 128797 T^{6} + 2875306 T^{7} + 12117361 T^{8} \))(\( 1 + 15 T + 41 T^{2} - 45 T^{3} + 1156 T^{4} - 2655 T^{5} + 142721 T^{6} + 3080685 T^{7} + 12117361 T^{8} \))(\( 1 - 49 T^{2} + 270 T^{3} + 3211 T^{4} + 15930 T^{5} - 170569 T^{6} + 12117361 T^{8} \))(\( 1 + 3 T + 62 T^{2} + 177 T^{3} + 3481 T^{4} \))(\( 1 - 3 T + 62 T^{2} - 177 T^{3} + 3481 T^{4} \))(\( 1 + 22 T + 122 T^{2} - 1232 T^{3} - 20033 T^{4} - 72688 T^{5} + 424682 T^{6} + 4518338 T^{7} + 12117361 T^{8} \))(\( 1 - 2 T + 122 T^{2} - 608 T^{3} + 8287 T^{4} - 35872 T^{5} + 424682 T^{6} - 410758 T^{7} + 12117361 T^{8} \))(\( 1 - 4 T - 21 T^{2} - 144 T^{3} + 836 T^{4} + 4008 T^{5} + 237701 T^{6} - 1329022 T^{7} - 10035333 T^{8} - 78412298 T^{9} + 827437181 T^{10} + 823159032 T^{11} + 10130113796 T^{12} - 102949099056 T^{13} - 885791206461 T^{14} - 9954605939276 T^{15} + 146830437604321 T^{16} \))
$61$ (\( 1 - 14 T + 126 T^{2} - 854 T^{3} + 3721 T^{4} \))(\( 1 + 15 T + 272 T^{2} + 2577 T^{3} + 24700 T^{4} + 180103 T^{5} + 1436915 T^{6} + 10986283 T^{7} + 91908700 T^{8} + 584930037 T^{9} + 3766068752 T^{10} + 12668944515 T^{11} + 51520374361 T^{12} \))(\( 1 - 5 T + 315 T^{2} - 1450 T^{3} + 48188 T^{4} - 191734 T^{5} + 4491051 T^{6} - 14924570 T^{7} + 273954111 T^{8} - 713442214 T^{9} + 10937760428 T^{10} - 20076469450 T^{11} + 266047834815 T^{12} - 257601871805 T^{13} + 3142742836021 T^{14} \))(\( 1 - 11 T + 294 T^{2} - 3523 T^{3} + 47281 T^{4} - 506350 T^{5} + 5141323 T^{6} - 44680182 T^{7} + 381642698 T^{8} - 2725491102 T^{9} + 19130862883 T^{10} - 114931829350 T^{11} + 654645208321 T^{12} - 2975512768423 T^{13} + 15146990062134 T^{14} - 34570171196231 T^{15} + 191707312997281 T^{16} \))(\( 1 + 9 T + 248 T^{2} + 2059 T^{3} + 32311 T^{4} + 241390 T^{5} + 2989495 T^{6} + 19910716 T^{7} + 209511118 T^{8} + 1214553676 T^{9} + 11123910895 T^{10} + 54790943590 T^{11} + 447372968551 T^{12} + 1739023783759 T^{13} + 12777052841528 T^{14} + 28284685524189 T^{15} + 191707312997281 T^{16} \))(\( ( 1 - 10 T + 61 T^{2} )^{2} \))(\( ( 1 - 14 T + 61 T^{2} )( 1 + 13 T + 61 T^{2} ) \))(\( ( 1 + 8 T + 133 T^{2} + 488 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 + 23 T + 253 T^{2} + 1403 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 - 11 T + 61 T^{2} )^{4} \))(\( ( 1 - 10 T + 61 T^{2} )^{2} \))(\( ( 1 - 10 T + 61 T^{2} )^{2} \))(\( 1 - 182 T^{2} + 15291 T^{4} - 677222 T^{6} + 13845841 T^{8} \))(\( 1 - 182 T^{2} + 15291 T^{4} - 677222 T^{6} + 13845841 T^{8} \))(\( ( 1 + 3 T - 14 T^{2} - 297 T^{3} - 3741 T^{4} - 18117 T^{5} - 52094 T^{6} + 680943 T^{7} + 13845841 T^{8} )^{2} \))
$67$ (\( ( 1 + 8 T + 67 T^{2} )^{2} \))(\( 1 + 28 T + 566 T^{2} + 7958 T^{3} + 98051 T^{4} + 987149 T^{5} + 8880619 T^{6} + 66138983 T^{7} + 440150939 T^{8} + 2393471954 T^{9} + 11405534486 T^{10} + 37803502996 T^{11} + 90458382169 T^{12} \))(\( 1 + 32 T + 865 T^{2} + 15244 T^{3} + 234085 T^{4} + 2802431 T^{5} + 29745354 T^{6} + 257912236 T^{7} + 1992938718 T^{8} + 12580112759 T^{9} + 70404106855 T^{10} + 307183688524 T^{11} + 1167858217555 T^{12} + 2894668229408 T^{13} + 6060711605323 T^{14} \))(\( 1 - 18 T + 598 T^{2} - 7908 T^{3} + 146860 T^{4} - 1515607 T^{5} + 20041239 T^{6} - 165114013 T^{7} + 1686479924 T^{8} - 11062638871 T^{9} + 89965121871 T^{10} - 455838508141 T^{11} + 2959393630060 T^{12} - 10676789346156 T^{13} + 54094112537062 T^{14} - 109092808895814 T^{15} + 406067677556641 T^{16} \))(\( 1 - 22 T + 438 T^{2} - 5894 T^{3} + 78940 T^{4} - 831393 T^{5} + 8698949 T^{6} - 76822007 T^{7} + 682981360 T^{8} - 5147074469 T^{9} + 39049582061 T^{10} - 250052252859 T^{11} + 1590729491740 T^{12} - 7957637380658 T^{13} + 39620771390022 T^{14} - 133335655317106 T^{15} + 406067677556641 T^{16} \))(\( 1 + 122 T^{2} + 4489 T^{4} \))(\( 1 + 10 T + 33 T^{2} + 670 T^{3} + 4489 T^{4} \))(\( ( 1 - 3 T + 35 T^{2} - 201 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 - 11 T + 163 T^{2} - 737 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 + 9 T + 153 T^{2} + 603 T^{3} + 4489 T^{4} )^{2} \))(\( 1 - 15 T + 142 T^{2} - 1005 T^{3} + 4489 T^{4} \))(\( 1 + 15 T + 142 T^{2} + 1005 T^{3} + 4489 T^{4} \))(\( 1 - 8 T + 137 T^{2} - 1224 T^{3} + 11492 T^{4} - 82008 T^{5} + 614993 T^{6} - 2406104 T^{7} + 20151121 T^{8} \))(\( 1 + 22 T + 137 T^{2} - 834 T^{3} - 16648 T^{4} - 55878 T^{5} + 614993 T^{6} + 6616786 T^{7} + 20151121 T^{8} \))(\( ( 1 + 20 T + 171 T^{2} + 1900 T^{3} + 21152 T^{4} + 127300 T^{5} + 767619 T^{6} + 6015260 T^{7} + 20151121 T^{8} )^{2} \))
$71$ (\( ( 1 - 3 T + 71 T^{2} )^{2} \))(\( 1 - T + 147 T^{2} + 509 T^{3} + 7580 T^{4} + 107146 T^{5} + 310755 T^{6} + 7607366 T^{7} + 38210780 T^{8} + 182176699 T^{9} + 3735517107 T^{10} - 1804229351 T^{11} + 128100283921 T^{12} \))(\( 1 - 5 T + 232 T^{2} - 1756 T^{3} + 29821 T^{4} - 244839 T^{5} + 2745945 T^{6} - 21305042 T^{7} + 194962095 T^{8} - 1234233399 T^{9} + 10673263931 T^{10} - 44622911836 T^{11} + 418581209432 T^{12} - 640501419605 T^{13} + 9095120158391 T^{14} \))(\( 1 + 7 T + 390 T^{2} + 2460 T^{3} + 74246 T^{4} + 409796 T^{5} + 8984378 T^{6} + 42737787 T^{7} + 755659863 T^{8} + 3034382877 T^{9} + 45290249498 T^{10} + 146670496156 T^{11} + 1886715667526 T^{12} + 4438404203460 T^{13} + 49959110729190 T^{14} + 63665841108737 T^{15} + 645753531245761 T^{16} \))(\( 1 + 17 T + 445 T^{2} + 6341 T^{3} + 96767 T^{4} + 1106115 T^{5} + 12767580 T^{6} + 118530765 T^{7} + 1105292078 T^{8} + 8415684315 T^{9} + 64361370780 T^{10} + 395890725765 T^{11} + 2459012135327 T^{12} + 11440618314691 T^{13} + 57004626344845 T^{14} + 154617042692647 T^{15} + 645753531245761 T^{16} \))(\( 1 - 106 T^{2} + 5041 T^{4} \))(\( 1 - 4 T - 55 T^{2} - 284 T^{3} + 5041 T^{4} \))(\( 1 - 34 T + 665 T^{2} - 8926 T^{3} + 86729 T^{4} - 633746 T^{5} + 3352265 T^{6} - 12168974 T^{7} + 25411681 T^{8} \))(\( 1 - 2 T - 67 T^{2} - 74 T^{3} + 5255 T^{4} - 5254 T^{5} - 337747 T^{6} - 715822 T^{7} + 25411681 T^{8} \))(\( 1 - 2 T - 7 T^{2} + 466 T^{3} + 1865 T^{4} + 33086 T^{5} - 35287 T^{6} - 715822 T^{7} + 25411681 T^{8} \))(\( 1 - 15 T + 146 T^{2} - 1065 T^{3} + 5041 T^{4} \))(\( 1 + 15 T + 146 T^{2} + 1065 T^{3} + 5041 T^{4} \))(\( 1 - 16 T + 65 T^{2} + 1016 T^{3} - 15428 T^{4} + 72136 T^{5} + 327665 T^{6} - 5726576 T^{7} + 25411681 T^{8} \))(\( 1 + 2 T + 65 T^{2} + 818 T^{3} + 2464 T^{4} + 58078 T^{5} + 327665 T^{6} + 715822 T^{7} + 25411681 T^{8} \))(\( 1 + 19 T + 291 T^{2} + 4008 T^{3} + 50192 T^{4} + 565539 T^{5} + 5694542 T^{6} + 53394988 T^{7} + 475063971 T^{8} + 3791044148 T^{9} + 28706186222 T^{10} + 202412629029 T^{11} + 1275463092752 T^{12} + 7231351238808 T^{13} + 37277182621011 T^{14} + 172807283009429 T^{15} + 645753531245761 T^{16} \))
$73$ (\( ( 1 - 14 T + 73 T^{2} )^{2} \))(\( 1 + 20 T + 526 T^{2} + 7007 T^{3} + 103261 T^{4} + 998865 T^{5} + 10249753 T^{6} + 72917145 T^{7} + 550277869 T^{8} + 2725842119 T^{9} + 14937474766 T^{10} + 41461431860 T^{11} + 151334226289 T^{12} \))(\( 1 - T + 155 T^{2} + 1727 T^{3} + 10322 T^{4} + 214941 T^{5} + 2026687 T^{6} + 10857629 T^{7} + 147948151 T^{8} + 1145420589 T^{9} + 4015433474 T^{10} + 49043762207 T^{11} + 321326096915 T^{12} - 151334226289 T^{13} + 11047398519097 T^{14} \))(\( 1 - 24 T + 654 T^{2} - 10155 T^{3} + 163680 T^{4} - 1907249 T^{5} + 22776963 T^{6} - 212473704 T^{7} + 2032799812 T^{8} - 15510580392 T^{9} + 121378435827 T^{10} - 741952284233 T^{11} + 4648224086880 T^{12} - 21052042026915 T^{13} + 98972583993006 T^{14} - 265137564458328 T^{15} + 806460091894081 T^{16} \))(\( 1 + 27 T + 644 T^{2} + 9278 T^{3} + 121477 T^{4} + 1137746 T^{5} + 10431667 T^{6} + 75319832 T^{7} + 672560488 T^{8} + 5498347736 T^{9} + 55590353443 T^{10} + 442602535682 T^{11} + 3449733121957 T^{12} + 19233958239854 T^{13} + 97459241730116 T^{14} + 298279760015619 T^{15} + 806460091894081 T^{16} \))(\( 1 - 97 T^{2} + 5329 T^{4} \))(\( ( 1 + 3 T + 73 T^{2} )^{2} \))(\( 1 - 5 T + 12 T^{2} - 655 T^{3} + 8639 T^{4} - 47815 T^{5} + 63948 T^{6} - 1945085 T^{7} + 28398241 T^{8} \))(\( 1 + 14 T + 63 T^{2} + 850 T^{3} + 12521 T^{4} + 62050 T^{5} + 335727 T^{6} + 5446238 T^{7} + 28398241 T^{8} \))(\( 1 - 11 T - 22 T^{2} + 845 T^{3} - 5609 T^{4} + 61685 T^{5} - 117238 T^{6} - 4279187 T^{7} + 28398241 T^{8} \))(\( 1 + 15 T + 148 T^{2} + 1095 T^{3} + 5329 T^{4} \))(\( 1 - 15 T + 148 T^{2} - 1095 T^{3} + 5329 T^{4} \))(\( 1 + 6 T + 90 T^{2} - 564 T^{3} - 97 T^{4} - 41172 T^{5} + 479610 T^{6} + 2334102 T^{7} + 28398241 T^{8} \))(\( 1 - 18 T + 90 T^{2} + 1356 T^{3} - 21121 T^{4} + 98988 T^{5} + 479610 T^{6} - 7002306 T^{7} + 28398241 T^{8} \))(\( ( 1 + 22 T + 171 T^{2} + 1076 T^{3} + 10229 T^{4} + 78548 T^{5} + 911259 T^{6} + 8558374 T^{7} + 28398241 T^{8} )^{2} \))
$79$ (\( ( 1 - 4 T + 79 T^{2} )^{2} \))(\( 1 + 15 T + 391 T^{2} + 4527 T^{3} + 69134 T^{4} + 634850 T^{5} + 7043949 T^{6} + 50153150 T^{7} + 431465294 T^{8} + 2231987553 T^{9} + 15229481671 T^{10} + 46155845985 T^{11} + 243087455521 T^{12} \))(\( 1 + 15 T + 496 T^{2} + 6030 T^{3} + 109559 T^{4} + 1086719 T^{5} + 13935127 T^{6} + 111068090 T^{7} + 1100875033 T^{8} + 6782213279 T^{9} + 54016859801 T^{10} + 234868988430 T^{11} + 1526219973904 T^{12} + 3646311832815 T^{13} + 19203908986159 T^{14} \))(\( 1 - 33 T + 797 T^{2} - 13771 T^{3} + 206359 T^{4} - 2593505 T^{5} + 29672938 T^{6} - 299405543 T^{7} + 2810094306 T^{8} - 23653037897 T^{9} + 185188806058 T^{10} - 1278699111695 T^{11} + 8037699765079 T^{12} - 42374143670629 T^{13} + 193740702050237 T^{14} - 633728996543247 T^{15} + 1517108809906561 T^{16} \))(\( 1 + 23 T + 631 T^{2} + 9223 T^{3} + 151697 T^{4} + 1714229 T^{5} + 21624126 T^{6} + 201926223 T^{7} + 2071566706 T^{8} + 15952171617 T^{9} + 134956170366 T^{10} + 845181751931 T^{11} + 5908610437457 T^{12} + 28379691167977 T^{13} + 153388184433751 T^{14} + 441689906681657 T^{15} + 1517108809906561 T^{16} \))(\( ( 1 + 16 T + 79 T^{2} )^{2} \))(\( ( 1 - 2 T + 79 T^{2} )^{2} \))(\( 1 + 21 T + 162 T^{2} + 1343 T^{3} + 15405 T^{4} + 106097 T^{5} + 1011042 T^{6} + 10353819 T^{7} + 38950081 T^{8} \))(\( 1 - 24 T + 297 T^{2} - 3382 T^{3} + 35205 T^{4} - 267178 T^{5} + 1853577 T^{6} - 11832936 T^{7} + 38950081 T^{8} \))(\( 1 - 9 T - 48 T^{2} + 643 T^{3} - 195 T^{4} + 50797 T^{5} - 299568 T^{6} - 4437351 T^{7} + 38950081 T^{8} \))(\( 1 - 5 T - 54 T^{2} - 395 T^{3} + 6241 T^{4} \))(\( 1 - 5 T - 54 T^{2} - 395 T^{3} + 6241 T^{4} \))(\( 1 + 36 T + 694 T^{2} + 9432 T^{3} + 96531 T^{4} + 745128 T^{5} + 4331254 T^{6} + 17749404 T^{7} + 38950081 T^{8} \))(\( 1 + 36 T + 694 T^{2} + 9432 T^{3} + 96531 T^{4} + 745128 T^{5} + 4331254 T^{6} + 17749404 T^{7} + 38950081 T^{8} \))(\( ( 1 + 27 T + 470 T^{2} + 6117 T^{3} + 61789 T^{4} + 483243 T^{5} + 2933270 T^{6} + 13312053 T^{7} + 38950081 T^{8} )^{2} \))
$83$ (\( 1 - 12 T + 122 T^{2} - 996 T^{3} + 6889 T^{4} \))(\( 1 - T + 425 T^{2} - 363 T^{3} + 80383 T^{4} - 56955 T^{5} + 8627425 T^{6} - 4727265 T^{7} + 553758487 T^{8} - 207558681 T^{9} + 20169786425 T^{10} - 3939040643 T^{11} + 326940373369 T^{12} \))(\( 1 - 17 T + 452 T^{2} - 5040 T^{3} + 77092 T^{4} - 623788 T^{5} + 7666358 T^{6} - 53524394 T^{7} + 636307714 T^{8} - 4297275532 T^{9} + 44080203404 T^{10} - 239189937840 T^{11} + 1780446370636 T^{12} - 5557986347273 T^{13} + 27136050989627 T^{14} \))(\( 1 + 13 T + 473 T^{2} + 5847 T^{3} + 113012 T^{4} + 1228906 T^{5} + 16911750 T^{6} + 156075296 T^{7} + 1700063772 T^{8} + 12954249568 T^{9} + 116505045750 T^{10} + 702672475022 T^{11} + 5363359772852 T^{12} + 23031570639621 T^{13} + 154642796603537 T^{14} + 352768662865151 T^{15} + 2252292232139041 T^{16} \))(\( 1 + 25 T + 601 T^{2} + 10469 T^{3} + 161546 T^{4} + 2131884 T^{5} + 25331676 T^{6} + 268856216 T^{7} + 2572721864 T^{8} + 22315065928 T^{9} + 174509915964 T^{10} + 1218983556708 T^{11} + 7666701924266 T^{12} + 41237816491567 T^{13} + 196491164394769 T^{14} + 678401274740675 T^{15} + 2252292232139041 T^{16} \))(\( 1 - 22 T^{2} + 6889 T^{4} \))(\( ( 1 + 2 T + 83 T^{2} )^{2} \))(\( 1 + 12 T + 61 T^{2} + 1146 T^{3} + 17149 T^{4} + 95118 T^{5} + 420229 T^{6} + 6861444 T^{7} + 47458321 T^{8} \))(\( 1 - T - 67 T^{2} + 515 T^{3} + 5516 T^{4} + 42745 T^{5} - 461563 T^{6} - 571787 T^{7} + 47458321 T^{8} \))(\( 1 + 14 T + 53 T^{2} + 870 T^{3} + 14801 T^{4} + 72210 T^{5} + 365117 T^{6} + 8005018 T^{7} + 47458321 T^{8} \))(\( 1 + 21 T + 230 T^{2} + 1743 T^{3} + 6889 T^{4} \))(\( 1 - 21 T + 230 T^{2} - 1743 T^{3} + 6889 T^{4} \))(\( 1 - 38 T + 650 T^{2} - 6944 T^{3} + 62479 T^{4} - 576352 T^{5} + 4477850 T^{6} - 21727906 T^{7} + 47458321 T^{8} \))(\( 1 - 34 T + 650 T^{2} - 8464 T^{3} + 86383 T^{4} - 702512 T^{5} + 4477850 T^{6} - 19440758 T^{7} + 47458321 T^{8} \))(\( ( 1 + 23 T + 166 T^{2} + 709 T^{3} + 6369 T^{4} + 58847 T^{5} + 1143574 T^{6} + 13151101 T^{7} + 47458321 T^{8} )^{2} \))
$89$ (\( 1 + 6 T + 182 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 + T + 282 T^{2} - 601 T^{3} + 33142 T^{4} - 183391 T^{5} + 2838089 T^{6} - 16321799 T^{7} + 262517782 T^{8} - 423686369 T^{9} + 17693311962 T^{10} + 5584059449 T^{11} + 496981290961 T^{12} \))(\( 1 - 26 T + 730 T^{2} - 11864 T^{3} + 194429 T^{4} - 2319046 T^{5} + 27909218 T^{6} - 261497659 T^{7} + 2483920402 T^{8} - 18369163366 T^{9} + 137066417701 T^{10} - 744373947224 T^{11} + 4076363397770 T^{12} - 12921513564986 T^{13} + 44231334895529 T^{14} \))(\( 1 + 23 T + 618 T^{2} + 10671 T^{3} + 178919 T^{4} + 2353266 T^{5} + 30161411 T^{6} + 320307670 T^{7} + 3279691286 T^{8} + 28507382630 T^{9} + 238908536531 T^{10} + 1658979578754 T^{11} + 11225779017479 T^{12} + 59587498380279 T^{13} + 307134437813898 T^{14} + 1017320702597167 T^{15} + 3936588805702081 T^{16} \))(\( 1 - 2 T + 277 T^{2} + 284 T^{3} + 45671 T^{4} + 80366 T^{5} + 5706761 T^{6} + 13758075 T^{7} + 542670086 T^{8} + 1224468675 T^{9} + 45203253881 T^{10} + 56655538654 T^{11} + 2865500888711 T^{12} + 1585872883516 T^{13} + 137663817596197 T^{14} - 88462669791058 T^{15} + 3936588805702081 T^{16} \))(\( 1 + 47 T^{2} + 7921 T^{4} \))(\( 1 - 6 T - 53 T^{2} - 534 T^{3} + 7921 T^{4} \))(\( 1 + T - 38 T^{2} - 727 T^{3} + 5055 T^{4} - 64703 T^{5} - 300998 T^{6} + 704969 T^{7} + 62742241 T^{8} \))(\( 1 - 4 T - 73 T^{2} + 648 T^{3} + 3905 T^{4} + 57672 T^{5} - 578233 T^{6} - 2819876 T^{7} + 62742241 T^{8} \))(\( 1 + 11 T - 38 T^{2} - 1037 T^{3} - 5625 T^{4} - 92293 T^{5} - 300998 T^{6} + 7754659 T^{7} + 62742241 T^{8} \))(\( 1 - 130 T^{2} + 7921 T^{4} \))(\( 1 - 130 T^{2} + 7921 T^{4} \))(\( 1 + 16 T + 128 T^{2} + 1840 T^{3} + 25774 T^{4} + 163760 T^{5} + 1013888 T^{6} + 11279504 T^{7} + 62742241 T^{8} \))(\( 1 - 16 T + 128 T^{2} - 1840 T^{3} + 25774 T^{4} - 163760 T^{5} + 1013888 T^{6} - 11279504 T^{7} + 62742241 T^{8} \))(\( 1 - 9 T + 134 T^{2} + 51 T^{3} - 1674 T^{4} + 122868 T^{5} - 284444 T^{6} + 806238 T^{7} + 66134807 T^{8} + 71755182 T^{9} - 2253080924 T^{10} + 86618131092 T^{11} - 105030511434 T^{12} + 284787031899 T^{13} + 66595492988774 T^{14} - 398082014059761 T^{15} + 3936588805702081 T^{16} \))
$97$ (\( 1 - 4 T + 153 T^{2} - 388 T^{3} + 9409 T^{4} \))(\( 1 + 5 T + 330 T^{2} + 1813 T^{3} + 59935 T^{4} + 290002 T^{5} + 7241445 T^{6} + 28130194 T^{7} + 563928415 T^{8} + 1654676149 T^{9} + 29214662730 T^{10} + 42936701285 T^{11} + 832972004929 T^{12} \))(\( 1 - 11 T + 339 T^{2} - 1956 T^{3} + 40349 T^{4} - 18067 T^{5} + 2498592 T^{6} + 13581260 T^{7} + 242363424 T^{8} - 169992403 T^{9} + 36825442877 T^{10} - 173163273636 T^{11} + 2911108347123 T^{12} - 9162692054219 T^{13} + 80798284478113 T^{14} \))(\( 1 + 17 T + 651 T^{2} + 8770 T^{3} + 194932 T^{4} + 2156514 T^{5} + 35045998 T^{6} + 321297201 T^{7} + 4144181257 T^{8} + 31165828497 T^{9} + 329747795182 T^{10} + 1968192101922 T^{11} + 17257189803892 T^{12} + 75310974053890 T^{13} + 542264775208779 T^{14} + 1373570836127921 T^{15} + 7837433594376961 T^{16} \))(\( 1 + 15 T + 426 T^{2} + 4739 T^{3} + 84178 T^{4} + 734525 T^{5} + 10845149 T^{6} + 82622183 T^{7} + 1125533024 T^{8} + 8014351751 T^{9} + 102042006941 T^{10} + 670381135325 T^{11} + 7452217816018 T^{12} + 40695405477923 T^{13} + 354846074099754 T^{14} + 1211974267171695 T^{15} + 7837433594376961 T^{16} \))(\( 1 - 190 T^{2} + 9409 T^{4} \))(\( 1 - 18 T + 227 T^{2} - 1746 T^{3} + 9409 T^{4} \))(\( 1 + 8 T + 87 T^{2} + 1270 T^{3} + 19901 T^{4} + 123190 T^{5} + 818583 T^{6} + 7301384 T^{7} + 88529281 T^{8} \))(\( 1 - 28 T + 287 T^{2} - 1970 T^{3} + 17821 T^{4} - 191090 T^{5} + 2700383 T^{6} - 25554844 T^{7} + 88529281 T^{8} \))(\( 1 + 12 T + 47 T^{2} - 600 T^{3} - 11759 T^{4} - 58200 T^{5} + 442223 T^{6} + 10952076 T^{7} + 88529281 T^{8} \))(\( 1 - 146 T^{2} + 9409 T^{4} \))(\( 1 - 146 T^{2} + 9409 T^{4} \))(\( 1 + 20 T + 200 T^{2} + 2460 T^{3} + 29582 T^{4} + 238620 T^{5} + 1881800 T^{6} + 18253460 T^{7} + 88529281 T^{8} \))(\( 1 + 20 T + 200 T^{2} + 2460 T^{3} + 29582 T^{4} + 238620 T^{5} + 1881800 T^{6} + 18253460 T^{7} + 88529281 T^{8} \))(\( 1 + 3 T + 102 T^{2} - 89 T^{3} - 282 T^{4} - 55676 T^{5} - 856316 T^{6} - 2476602 T^{7} - 69420377 T^{8} - 240230394 T^{9} - 8057077244 T^{10} - 50813981948 T^{11} - 24965257242 T^{12} - 764273282873 T^{13} + 84963144502758 T^{14} + 242394853434339 T^{15} + 7837433594376961 T^{16} \))
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