Properties

Label 224.3
Level 224
Weight 3
Dimension 1606
Nonzero newspaces 12
Newform subspaces 26
Sturm bound 9216
Trace bound 13

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Defining parameters

Level: \( N \) = \( 224\( 224 = 2^{5} \cdot 7 \) \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 26 \)
Sturm bound: \(9216\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(224))\).

Total New Old
Modular forms 3264 1706 1558
Cusp forms 2880 1606 1274
Eisenstein series 384 100 284

Trace form

\( 1606q - 16q^{2} - 14q^{3} - 16q^{4} - 24q^{5} - 16q^{6} - 14q^{7} - 40q^{8} + 10q^{9} + O(q^{10}) \) \( 1606q - 16q^{2} - 14q^{3} - 16q^{4} - 24q^{5} - 16q^{6} - 14q^{7} - 40q^{8} + 10q^{9} + 64q^{10} + 18q^{11} + 80q^{12} + 40q^{13} - 4q^{14} - 20q^{15} - 56q^{16} - 88q^{17} - 136q^{18} - 78q^{19} - 176q^{20} - 84q^{21} - 336q^{22} + 118q^{23} - 440q^{24} + 6q^{25} - 216q^{26} + 244q^{27} - 80q^{28} + 16q^{29} - 64q^{30} - 18q^{31} + 24q^{32} - 52q^{33} + 72q^{34} - 110q^{35} + 624q^{36} + 104q^{37} + 768q^{38} - 340q^{39} + 792q^{40} + 120q^{41} + 400q^{42} - 48q^{43} + 352q^{44} + 592q^{45} + 48q^{46} + 286q^{47} - 120q^{48} + 110q^{49} - 664q^{50} - 234q^{51} - 864q^{52} + 136q^{53} - 1208q^{54} - 528q^{55} - 576q^{56} - 584q^{57} - 1080q^{58} - 622q^{59} - 904q^{60} - 504q^{61} - 456q^{62} - 498q^{63} + 416q^{64} - 412q^{65} + 1136q^{66} + 2q^{67} + 712q^{68} - 432q^{69} + 640q^{70} + 292q^{71} + 1472q^{72} - 8q^{73} + 1040q^{74} + 708q^{75} + 1008q^{76} - 180q^{77} + 424q^{78} + 1022q^{79} - 648q^{80} + 282q^{81} - 1296q^{82} + 1272q^{83} - 1016q^{84} - 384q^{85} - 1400q^{86} + 832q^{87} - 1368q^{88} - 200q^{89} - 2632q^{90} - 116q^{91} - 1736q^{92} - 1464q^{93} - 2552q^{94} - 594q^{95} - 3368q^{96} - 1144q^{97} - 1880q^{98} - 1328q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(224))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
224.3.c \(\chi_{224}(97, \cdot)\) 224.3.c.a 8 1
224.3.c.b 8
224.3.d \(\chi_{224}(127, \cdot)\) 224.3.d.a 4 1
224.3.d.b 8
224.3.g \(\chi_{224}(15, \cdot)\) 224.3.g.a 4 1
224.3.g.b 8
224.3.h \(\chi_{224}(209, \cdot)\) 224.3.h.a 2 1
224.3.h.b 2
224.3.h.c 2
224.3.h.d 8
224.3.k \(\chi_{224}(71, \cdot)\) None 0 2
224.3.l \(\chi_{224}(41, \cdot)\) None 0 2
224.3.n \(\chi_{224}(17, \cdot)\) 224.3.n.a 28 2
224.3.o \(\chi_{224}(79, \cdot)\) 224.3.o.a 2 2
224.3.o.b 2
224.3.o.c 12
224.3.o.d 12
224.3.r \(\chi_{224}(95, \cdot)\) 224.3.r.a 4 2
224.3.r.b 4
224.3.r.c 12
224.3.r.d 12
224.3.s \(\chi_{224}(33, \cdot)\) 224.3.s.a 16 2
224.3.s.b 16
224.3.v \(\chi_{224}(13, \cdot)\) 224.3.v.a 8 4
224.3.v.b 240
224.3.w \(\chi_{224}(43, \cdot)\) 224.3.w.a 192 4
224.3.y \(\chi_{224}(23, \cdot)\) None 0 4
224.3.bb \(\chi_{224}(73, \cdot)\) None 0 4
224.3.bc \(\chi_{224}(5, \cdot)\) 224.3.bc.a 496 8
224.3.bf \(\chi_{224}(11, \cdot)\) 224.3.bf.a 496 8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(224))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(224)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 - 31 T^{4} + 256 T^{8} \))
$3$ (\( ( 1 - 4 T^{2} - 18 T^{4} - 324 T^{6} + 6561 T^{8} )^{2} \))(\( ( 1 - 20 T^{2} + 254 T^{4} - 1620 T^{6} + 6561 T^{8} )^{2} \))(\( ( 1 - 14 T^{2} + 81 T^{4} )^{2} \))(\( 1 - 16 T^{2} + 92 T^{4} + 272 T^{6} - 8570 T^{8} + 22032 T^{10} + 603612 T^{12} - 8503056 T^{14} + 43046721 T^{16} \))(\( ( 1 + 4 T + 20 T^{2} + 36 T^{3} + 81 T^{4} )^{2} \))(\( ( 1 - 4 T + 14 T^{2} - 28 T^{3} + 98 T^{4} - 252 T^{5} + 1134 T^{6} - 2916 T^{7} + 6561 T^{8} )^{2} \))(\( ( 1 + 9 T^{2} )^{2} \))(\( 1 - 10 T^{2} + 81 T^{4} \))(\( 1 + 10 T^{2} + 81 T^{4} \))(\( ( 1 + 16 T^{2} + 178 T^{4} + 1296 T^{6} + 6561 T^{8} )^{2} \))(\( 1 - T - 8 T^{2} - 9 T^{3} + 81 T^{4} \))(\( 1 - T - 8 T^{2} - 9 T^{3} + 81 T^{4} \))(\( ( 1 + 3 T - 7 T^{2} - 22 T^{3} + 7 T^{4} - 61 T^{5} - 350 T^{6} - 549 T^{7} + 567 T^{8} - 16038 T^{9} - 45927 T^{10} + 177147 T^{11} + 531441 T^{12} )^{2} \))(\( ( 1 - 3 T + T^{2} + 14 T^{3} - 65 T^{4} + 37 T^{5} + 514 T^{6} + 333 T^{7} - 5265 T^{8} + 10206 T^{9} + 6561 T^{10} - 177147 T^{11} + 531441 T^{12} )^{2} \))(\( 1 - 7 T^{2} - 32 T^{4} - 567 T^{6} + 6561 T^{8} \))(\( 1 + 17 T^{2} + 208 T^{4} + 1377 T^{6} + 6561 T^{8} \))(\( 1 + 11 T^{2} - 117 T^{4} - 884 T^{6} + 18105 T^{8} + 64793 T^{10} - 1253162 T^{12} + 5248233 T^{14} + 118786905 T^{16} - 469793844 T^{18} - 5036466357 T^{20} + 38354628411 T^{22} + 282429536481 T^{24} \))(\( 1 + 27 T^{2} + 411 T^{4} + 2972 T^{6} - 423 T^{8} - 321159 T^{10} - 4031882 T^{12} - 26013879 T^{14} - 2775303 T^{16} + 1579442652 T^{18} + 17692202331 T^{20} + 94143178827 T^{22} + 282429536481 T^{24} \))(\( 1 + 32 T^{2} + 486 T^{4} + 3776 T^{6} + 6841 T^{8} - 164352 T^{10} - 1549098 T^{12} - 1704672 T^{14} + 53230932 T^{16} - 138078432 T^{18} - 10163631978 T^{20} - 87343391232 T^{22} + 294482618361 T^{24} + 13166097898176 T^{26} + 137260754729766 T^{28} + 732057358558752 T^{30} + 1853020188851841 T^{32} \))(\( 1 + 16 T^{2} + 134 T^{4} + 1120 T^{6} + 7897 T^{8} + 73856 T^{10} + 1194422 T^{12} + 13226000 T^{14} + 117489172 T^{16} + 1071306000 T^{18} + 7836602742 T^{20} + 39250106496 T^{22} + 339939955737 T^{24} + 3905198529120 T^{26} + 37845557888454 T^{28} + 366028679279376 T^{30} + 1853020188851841 T^{32} \))(\( ( 1 + 6561 T^{8} )^{2} \))
$5$ (\( ( 1 - 52 T^{2} + 1742 T^{4} - 32500 T^{6} + 390625 T^{8} )^{2} \))(\( ( 1 - 36 T^{2} + 1566 T^{4} - 22500 T^{6} + 390625 T^{8} )^{2} \))(\( ( 1 + 4 T + 26 T^{2} + 100 T^{3} + 625 T^{4} )^{2} \))(\( ( 1 + 24 T^{2} - 224 T^{3} + 78 T^{4} - 5600 T^{5} + 15000 T^{6} + 390625 T^{8} )^{2} \))(\( 1 - 16 T^{2} - 254 T^{4} - 10000 T^{6} + 390625 T^{8} \))(\( 1 - 92 T^{2} + 5464 T^{4} - 211956 T^{6} + 6231214 T^{8} - 132472500 T^{10} + 2134375000 T^{12} - 22460937500 T^{14} + 152587890625 T^{16} \))(\( ( 1 + 25 T^{2} )^{2} \))(\( 1 + 22 T^{2} + 625 T^{4} \))(\( 1 - 22 T^{2} + 625 T^{4} \))(\( ( 1 + 56 T^{2} + 1602 T^{4} + 35000 T^{6} + 390625 T^{8} )^{2} \))(\( 1 + 9 T + 52 T^{2} + 225 T^{3} + 625 T^{4} \))(\( 1 - 9 T + 52 T^{2} - 225 T^{3} + 625 T^{4} \))(\( 1 + 17 T^{2} - 437 T^{4} - 28164 T^{6} - 270975 T^{8} + 5916803 T^{10} + 456152134 T^{12} + 3698001875 T^{14} - 105849609375 T^{16} - 6875976562500 T^{18} - 66680908203125 T^{20} + 1621246337890625 T^{22} + 59604644775390625 T^{24} \))(\( 1 + 121 T^{2} + 7979 T^{4} + 380588 T^{6} + 14474897 T^{8} + 457025259 T^{10} + 12295779174 T^{12} + 285640786875 T^{14} + 5654256640625 T^{16} + 92916992187500 T^{18} + 1217498779296875 T^{20} + 11539459228515625 T^{22} + 59604644775390625 T^{24} \))(\( ( 1 + 9 T + 56 T^{2} + 225 T^{3} + 625 T^{4} )^{2} \))(\( ( 1 + T - 24 T^{2} + 25 T^{3} + 625 T^{4} )^{2} \))(\( ( 1 - T - 29 T^{2} - 132 T^{3} + 201 T^{4} + 2405 T^{5} + 10726 T^{6} + 60125 T^{7} + 125625 T^{8} - 2062500 T^{9} - 11328125 T^{10} - 9765625 T^{11} + 244140625 T^{12} )^{2} \))(\( ( 1 - 9 T + 3 T^{2} + 140 T^{3} + 345 T^{4} - 3363 T^{5} + 5766 T^{6} - 84075 T^{7} + 215625 T^{8} + 2187500 T^{9} + 1171875 T^{10} - 87890625 T^{11} + 244140625 T^{12} )^{2} \))(\( ( 1 + 46 T^{2} + 1073 T^{4} - 5040 T^{5} + 9678 T^{6} - 250320 T^{7} - 145276 T^{8} - 6258000 T^{9} + 6048750 T^{10} - 78750000 T^{11} + 419140625 T^{12} + 11230468750 T^{14} + 152587890625 T^{16} )^{2} \))(\( ( 1 + 30 T^{2} + 321 T^{4} + 1200 T^{5} - 930 T^{6} + 138960 T^{7} - 137884 T^{8} + 3474000 T^{9} - 581250 T^{10} + 18750000 T^{11} + 125390625 T^{12} + 7324218750 T^{14} + 152587890625 T^{16} )^{2} \))(\( ( 1 + 390625 T^{8} )^{2} \))
$7$ (\( 1 - 4 T^{2} + 1862 T^{4} - 9604 T^{6} + 5764801 T^{8} \))(\( 1 - 68 T^{2} + 2758 T^{4} - 163268 T^{6} + 5764801 T^{8} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 + 7 T^{2} )^{4} \))(\( ( 1 + 7 T^{2} )^{2} \))(\( ( 1 + 7 T^{2} )^{4} \))(\( ( 1 + 7 T )^{2} \))(\( ( 1 + 7 T )^{2} \))(\( ( 1 - 7 T )^{2} \))(\( ( 1 - 8 T + 102 T^{2} - 392 T^{3} + 2401 T^{4} )^{2} \))(\( 1 - 2 T + 49 T^{2} \))(\( 1 + 2 T + 49 T^{2} \))(\( 1 + 102 T^{2} + 8463 T^{4} + 426692 T^{6} + 20319663 T^{8} + 588009702 T^{10} + 13841287201 T^{12} \))(\( 1 - 186 T^{2} + 16527 T^{4} - 956284 T^{6} + 39681327 T^{8} - 1072252986 T^{10} + 13841287201 T^{12} \))(\( 1 - 94 T^{2} + 2401 T^{4} \))(\( ( 1 + 49 T^{2} )^{2} \))(\( 1 + 6 T^{2} + 4335 T^{4} + 71444 T^{6} + 10408335 T^{8} + 34588806 T^{10} + 13841287201 T^{12} \))(\( 1 - 90 T^{2} + 7791 T^{4} - 412972 T^{6} + 18706191 T^{8} - 518832090 T^{10} + 13841287201 T^{12} \))(\( 1 + 64 T^{2} + 5084 T^{4} + 338880 T^{6} + 15148742 T^{8} + 813650880 T^{10} + 29308248284 T^{12} + 885842380864 T^{14} + 33232930569601 T^{16} \))(\( 1 - 64 T^{2} + 2268 T^{4} + 3136 T^{6} - 7054138 T^{8} + 7529536 T^{10} + 13074568668 T^{12} - 885842380864 T^{14} + 33232930569601 T^{16} \))(\( ( 1 + 2401 T^{4} )^{2} \))
$11$ (\( ( 1 + 236 T^{2} + 31430 T^{4} + 3455276 T^{6} + 214358881 T^{8} )^{2} \))(\( ( 1 + 12 T^{2} - 12154 T^{4} + 175692 T^{6} + 214358881 T^{8} )^{2} \))(\( 1 - 228 T^{2} + 35110 T^{4} - 3338148 T^{6} + 214358881 T^{8} \))(\( 1 - 296 T^{2} + 72860 T^{4} - 12907416 T^{6} + 1704788486 T^{8} - 188977477656 T^{10} + 15618188069660 T^{12} - 928974799509416 T^{14} + 45949729863572161 T^{16} \))(\( ( 1 + 8 T + 186 T^{2} + 968 T^{3} + 14641 T^{4} )^{2} \))(\( ( 1 - 16 T + 328 T^{2} - 4944 T^{3} + 49230 T^{4} - 598224 T^{5} + 4802248 T^{6} - 28344976 T^{7} + 214358881 T^{8} )^{2} \))(\( ( 1 - 6 T + 121 T^{2} )( 1 + 6 T + 121 T^{2} ) \))(\( ( 1 - 11 T )^{2}( 1 + 11 T )^{2} \))(\( ( 1 - 11 T )^{2}( 1 + 11 T )^{2} \))(\( ( 1 - 364 T^{2} + 59334 T^{4} - 5329324 T^{6} + 214358881 T^{8} )^{2} \))(\( 1 - 17 T + 168 T^{2} - 2057 T^{3} + 14641 T^{4} \))(\( 1 - 17 T + 168 T^{2} - 2057 T^{3} + 14641 T^{4} \))(\( ( 1 - 7 T - 193 T^{2} + 2268 T^{3} + 15415 T^{4} - 171941 T^{5} - 336170 T^{6} - 20804861 T^{7} + 225691015 T^{8} + 4017900348 T^{9} - 41371264033 T^{10} - 181561972207 T^{11} + 3138428376721 T^{12} )^{2} \))(\( ( 1 + 15 T - 129 T^{2} - 924 T^{3} + 35727 T^{4} + 38013 T^{5} - 5198650 T^{6} + 4599573 T^{7} + 523079007 T^{8} - 1636922364 T^{9} - 27652295649 T^{10} + 389061369015 T^{11} + 3138428376721 T^{12} )^{2} \))(\( 1 + 233 T^{2} + 39648 T^{4} + 3411353 T^{6} + 214358881 T^{8} \))(\( 1 - 47 T^{2} - 12432 T^{4} - 688127 T^{6} + 214358881 T^{8} \))(\( 1 + 283 T^{2} + 46555 T^{4} + 3528284 T^{6} - 210042215 T^{8} - 117264051335 T^{10} - 18469284955402 T^{12} - 1716862975595735 T^{14} - 45024414170161415 T^{16} + 11073266626730676764 T^{18} + \)\(21\!\cdots\!55\)\( T^{20} + \)\(19\!\cdots\!83\)\( T^{22} + \)\(98\!\cdots\!41\)\( T^{24} \))(\( 1 + 363 T^{2} + 55851 T^{4} + 5892268 T^{6} + 719654457 T^{8} + 93270469209 T^{10} + 11000493019158 T^{12} + 1365572939688969 T^{14} + 154264324109182617 T^{16} + 18492461094445093228 T^{18} + \)\(25\!\cdots\!11\)\( T^{20} + \)\(24\!\cdots\!63\)\( T^{22} + \)\(98\!\cdots\!41\)\( T^{24} \))(\( 1 - 640 T^{2} + 227030 T^{4} - 52241408 T^{6} + 8348702825 T^{8} - 853428477056 T^{10} + 32116185305766 T^{12} + 6409181104515840 T^{14} - 1320087233250529292 T^{16} + 93836820551216413440 T^{18} + \)\(68\!\cdots\!46\)\( T^{20} - \)\(26\!\cdots\!76\)\( T^{22} + \)\(38\!\cdots\!25\)\( T^{24} - \)\(35\!\cdots\!08\)\( T^{26} + \)\(22\!\cdots\!30\)\( T^{28} - \)\(92\!\cdots\!40\)\( T^{30} + \)\(21\!\cdots\!21\)\( T^{32} \))(\( 1 - 432 T^{2} + 84854 T^{4} - 7780896 T^{6} + 22311049 T^{8} + 70438127616 T^{10} + 144760417670 T^{12} - 2441540782042416 T^{14} + 459119675281580212 T^{16} - 35746598589883012656 T^{18} + 31030681144833827270 T^{20} + \)\(22\!\cdots\!36\)\( T^{22} + \)\(10\!\cdots\!89\)\( T^{24} - \)\(52\!\cdots\!96\)\( T^{26} + \)\(83\!\cdots\!14\)\( T^{28} - \)\(62\!\cdots\!92\)\( T^{30} + \)\(21\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 206 T^{2} + 14641 T^{4} )^{2}( 1 + 13154 T^{4} + 214358881 T^{8} ) \))
$13$ (\( ( 1 - 468 T^{2} + 102862 T^{4} - 13366548 T^{6} + 815730721 T^{8} )^{2} \))(\( ( 1 - 132 T^{2} + 37278 T^{4} - 3770052 T^{6} + 815730721 T^{8} )^{2} \))(\( ( 1 + 4 T + 90 T^{2} + 676 T^{3} + 28561 T^{4} )^{2} \))(\( ( 1 - 16 T + 696 T^{2} - 7536 T^{3} + 176398 T^{4} - 1273584 T^{5} + 19878456 T^{6} - 77228944 T^{7} + 815730721 T^{8} )^{2} \))(\( 1 - 592 T^{2} + 143170 T^{4} - 16908112 T^{6} + 815730721 T^{8} \))(\( 1 - 444 T^{2} + 142936 T^{4} - 35361044 T^{6} + 6575436334 T^{8} - 1009946777684 T^{10} + 116597286336856 T^{12} - 10344349794381564 T^{14} + 665416609183179841 T^{16} \))(\( ( 1 + 169 T^{2} )^{2} \))(\( 1 + 310 T^{2} + 28561 T^{4} \))(\( 1 - 310 T^{2} + 28561 T^{4} \))(\( ( 1 + 344 T^{2} + 86658 T^{4} + 9824984 T^{6} + 815730721 T^{8} )^{2} \))(\( ( 1 - 22 T + 169 T^{2} )( 1 + 22 T + 169 T^{2} ) \))(\( ( 1 - 22 T + 169 T^{2} )( 1 + 22 T + 169 T^{2} ) \))(\( ( 1 - 950 T^{2} + 386271 T^{4} - 85941828 T^{6} + 11032286031 T^{8} - 774944184950 T^{10} + 23298085122481 T^{12} )^{2} \))(\( ( 1 - 86 T^{2} + 60895 T^{4} - 4902788 T^{6} + 1739222095 T^{8} - 70152842006 T^{10} + 23298085122481 T^{12} )^{2} \))(\( ( 1 - 16 T + 169 T^{2} )^{4} \))(\( ( 1 - 24 T + 169 T^{2} )^{4} \))(\( ( 1 + 32 T + 803 T^{2} + 11632 T^{3} + 135707 T^{4} + 913952 T^{5} + 4826809 T^{6} )^{4} \))(\( ( 1 + 339 T^{2} - 784 T^{3} + 57291 T^{4} + 4826809 T^{6} )^{4} \))(\( ( 1 - 192 T^{2} - 16036 T^{4} + 1118400 T^{6} + 1003382406 T^{8} + 31942622400 T^{10} - 13081057841956 T^{12} - 4473232343516352 T^{14} + 665416609183179841 T^{16} )^{2} \))(\( ( 1 - 1056 T^{2} + 510492 T^{4} - 150812640 T^{6} + 30377120006 T^{8} - 4307359811040 T^{10} + 416424007224732 T^{12} - 24602777889339936 T^{14} + 665416609183179841 T^{16} )^{2} \))(\( ( 1 + 815730721 T^{8} )^{2} \))
$17$ (\( ( 1 - 4 T^{2} + 155270 T^{4} - 334084 T^{6} + 6975757441 T^{8} )^{2} \))(\( ( 1 - 644 T^{2} + 270214 T^{4} - 53787524 T^{6} + 6975757441 T^{8} )^{2} \))(\( ( 1 + 28 T + 662 T^{2} + 8092 T^{3} + 83521 T^{4} )^{2} \))(\( ( 1 + 8 T + 428 T^{2} - 1416 T^{3} + 75814 T^{4} - 409224 T^{5} + 35746988 T^{6} + 193100552 T^{7} + 6975757441 T^{8} )^{2} \))(\( ( 1 - 36 T + 870 T^{2} - 10404 T^{3} + 83521 T^{4} )^{2} \))(\( ( 1 + 40 T + 1308 T^{2} + 31512 T^{3} + 588230 T^{4} + 9106968 T^{5} + 109245468 T^{6} + 965502760 T^{7} + 6975757441 T^{8} )^{2} \))(\( ( 1 - 17 T )^{2}( 1 + 17 T )^{2} \))(\( ( 1 - 17 T )^{2}( 1 + 17 T )^{2} \))(\( ( 1 - 17 T )^{2}( 1 + 17 T )^{2} \))(\( ( 1 - 148 T^{2} + 165606 T^{4} - 12361108 T^{6} + 6975757441 T^{8} )^{2} \))(\( 1 - 25 T + 336 T^{2} - 7225 T^{3} + 83521 T^{4} \))(\( 1 - 25 T + 336 T^{2} - 7225 T^{3} + 83521 T^{4} \))(\( ( 1 + 41 T + 471 T^{2} + 5456 T^{3} + 209253 T^{4} + 1462951 T^{5} - 27854634 T^{6} + 422792839 T^{7} + 17477019813 T^{8} + 131694576464 T^{9} + 3285581754711 T^{10} + 82655749918409 T^{11} + 582622237229761 T^{12} )^{2} \))(\( ( 1 - 15 T - 665 T^{2} + 3920 T^{3} + 405365 T^{4} - 1221665 T^{5} - 124870762 T^{6} - 353061185 T^{7} + 33856490165 T^{8} + 94619270480 T^{9} - 4638878698265 T^{10} - 30239908506735 T^{11} + 582622237229761 T^{12} )^{2} \))(\( ( 1 - 7 T - 240 T^{2} - 2023 T^{3} + 83521 T^{4} )^{2} \))(\( ( 1 + T - 288 T^{2} + 289 T^{3} + 83521 T^{4} )^{2} \))(\( ( 1 + 3 T - 181 T^{2} + 11996 T^{3} - 1671 T^{4} - 1164367 T^{5} + 69728918 T^{6} - 336502063 T^{7} - 139563591 T^{8} + 289554277724 T^{9} - 1262612096821 T^{10} + 6047981701347 T^{11} + 582622237229761 T^{12} )^{2} \))(\( ( 1 + 3 T - 261 T^{2} - 5460 T^{3} - 14535 T^{4} + 628833 T^{5} + 36283574 T^{6} + 181732737 T^{7} - 1213977735 T^{8} - 131791126740 T^{9} - 1820672692101 T^{10} + 6047981701347 T^{11} + 582622237229761 T^{12} )^{2} \))(\( ( 1 - 24 T + 766 T^{2} - 13776 T^{3} + 249905 T^{4} - 2407680 T^{5} - 7157346 T^{6} + 486721512 T^{7} - 15232969756 T^{8} + 140662516968 T^{9} - 597788695266 T^{10} - 58115542129920 T^{11} + 1743276663293105 T^{12} - 27772331972585424 T^{13} + 446288633717996926 T^{14} - 4041067837425622296 T^{15} + 48661191875666868481 T^{16} )^{2} \))(\( ( 1 + 24 T + 1022 T^{2} + 19920 T^{3} + 479985 T^{4} + 8829120 T^{5} + 194168350 T^{6} + 3297192024 T^{7} + 67118725988 T^{8} + 952888494936 T^{9} + 16217134760350 T^{10} + 213113493209280 T^{11} + 3348258935318385 T^{12} + 40158598496944080 T^{13} + 595439926448815742 T^{14} + 4041067837425622296 T^{15} + 48661191875666868481 T^{16} )^{2} \))(\( ( 1 + 289 T^{2} )^{8} \))
$19$ (\( ( 1 - 1188 T^{2} + 613294 T^{4} - 154821348 T^{6} + 16983563041 T^{8} )^{2} \))(\( ( 1 - 372 T^{2} + 131646 T^{4} - 48479412 T^{6} + 16983563041 T^{8} )^{2} \))(\( 1 - 348 T^{2} + 111718 T^{4} - 45351708 T^{6} + 16983563041 T^{8} \))(\( 1 - 1936 T^{2} + 1795420 T^{4} - 1065665392 T^{6} + 449725089670 T^{8} - 138878579550832 T^{10} + 30492628755072220 T^{12} - 4284977683312087696 T^{14} + \)\(28\!\cdots\!81\)\( T^{16} \))(\( ( 1 + 4 T + 4 T^{2} + 1444 T^{3} + 130321 T^{4} )^{2} \))(\( ( 1 + 28 T + 1710 T^{2} + 31332 T^{3} + 975266 T^{4} + 11310852 T^{5} + 222848910 T^{6} + 1317284668 T^{7} + 16983563041 T^{8} )^{2} \))(\( ( 1 + 361 T^{2} )^{2} \))(\( 1 - 650 T^{2} + 130321 T^{4} \))(\( 1 + 650 T^{2} + 130321 T^{4} \))(\( ( 1 + 656 T^{2} + 327858 T^{4} + 85490576 T^{6} + 16983563041 T^{8} )^{2} \))(\( 1 + 7 T - 312 T^{2} + 2527 T^{3} + 130321 T^{4} \))(\( 1 + 7 T - 312 T^{2} + 2527 T^{3} + 130321 T^{4} \))(\( ( 1 - 47 T + 487 T^{2} - 8532 T^{3} + 642195 T^{4} - 10028861 T^{5} + 46257550 T^{6} - 3620418821 T^{7} + 83691494595 T^{8} - 401395456692 T^{9} + 8270995200967 T^{10} - 288160114116647 T^{11} + 2213314919066161 T^{12} )^{2} \))(\( ( 1 + 39 T + 151 T^{2} - 3964 T^{3} + 263147 T^{4} + 5820949 T^{5} + 41830430 T^{6} + 2101362589 T^{7} + 34293580187 T^{8} - 186489872284 T^{9} + 2564518019191 T^{10} + 239111584054239 T^{11} + 2213314919066161 T^{12} )^{2} \))(\( ( 1 - 46 T^{2} + 130321 T^{4} )( 1 + 647 T^{2} + 130321 T^{4} ) \))(\( 1 + 673 T^{2} + 322608 T^{4} + 87706033 T^{6} + 16983563041 T^{8} \))(\( 1 + 843 T^{2} + 169755 T^{4} + 10759612 T^{6} + 34418758617 T^{8} + 15878060416809 T^{10} + 3783625584664182 T^{12} + 2069244711578965689 T^{14} + \)\(58\!\cdots\!97\)\( T^{16} + \)\(23\!\cdots\!32\)\( T^{18} + \)\(48\!\cdots\!55\)\( T^{20} + \)\(31\!\cdots\!43\)\( T^{22} + \)\(48\!\cdots\!21\)\( T^{24} \))(\( 1 + 411 T^{2} - 128661 T^{4} - 89218804 T^{6} + 6305474169 T^{8} + 6575128475913 T^{10} + 1202874182390166 T^{12} + 856877318109458073 T^{14} + \)\(10\!\cdots\!29\)\( T^{16} - \)\(19\!\cdots\!44\)\( T^{18} - \)\(37\!\cdots\!41\)\( T^{20} + \)\(15\!\cdots\!11\)\( T^{22} + \)\(48\!\cdots\!21\)\( T^{24} \))(\( 1 + 528 T^{2} + 24262 T^{4} + 11189472 T^{6} + 3728656729 T^{8} - 6420105050688 T^{10} + 940099701135094 T^{12} + 1121910404491838544 T^{14} + \)\(16\!\cdots\!80\)\( T^{16} + \)\(14\!\cdots\!24\)\( T^{18} + \)\(15\!\cdots\!54\)\( T^{20} - \)\(14\!\cdots\!68\)\( T^{22} + \)\(10\!\cdots\!49\)\( T^{24} + \)\(42\!\cdots\!72\)\( T^{26} + \)\(11\!\cdots\!02\)\( T^{28} + \)\(33\!\cdots\!48\)\( T^{30} + \)\(83\!\cdots\!61\)\( T^{32} \))(\( 1 + 1440 T^{2} + 935910 T^{4} + 438945600 T^{6} + 186482707321 T^{8} + 56682302220480 T^{10} + 7723885307690070 T^{12} - 285644590063174560 T^{14} - \)\(25\!\cdots\!40\)\( T^{16} - \)\(37\!\cdots\!60\)\( T^{18} + \)\(13\!\cdots\!70\)\( T^{20} + \)\(12\!\cdots\!80\)\( T^{22} + \)\(53\!\cdots\!01\)\( T^{24} + \)\(16\!\cdots\!00\)\( T^{26} + \)\(45\!\cdots\!10\)\( T^{28} + \)\(91\!\cdots\!40\)\( T^{30} + \)\(83\!\cdots\!61\)\( T^{32} \))(\( ( 1 + 16983563041 T^{8} )^{2} \))
$23$ (\( ( 1 + 1676 T^{2} + 1214822 T^{4} + 469013516 T^{6} + 78310985281 T^{8} )^{2} \))(\( ( 1 + 1004 T^{2} + 516774 T^{4} + 280960364 T^{6} + 78310985281 T^{8} )^{2} \))(\( 1 - 1604 T^{2} + 1138374 T^{4} - 448864964 T^{6} + 78310985281 T^{8} \))(\( 1 - 1928 T^{2} + 2366876 T^{4} - 1917103032 T^{6} + 1186521008582 T^{8} - 536484029577912 T^{10} + 185352391597952156 T^{12} - 42251395904935178888 T^{14} + \)\(61\!\cdots\!61\)\( T^{16} \))(\( 1 - 268 T^{2} + 477286 T^{4} - 74997388 T^{6} + 78310985281 T^{8} \))(\( 1 - 1744 T^{2} + 1272156 T^{4} - 412076080 T^{6} + 99307893702 T^{8} - 115315782303280 T^{10} + 99623789791135836 T^{12} - 38219105009443439824 T^{14} + \)\(61\!\cdots\!61\)\( T^{16} \))(\( ( 1 + 18 T + 529 T^{2} )^{2} \))(\( ( 1 - 10 T + 529 T^{2} )^{2} \))(\( ( 1 - 10 T + 529 T^{2} )^{2} \))(\( ( 1 - 8 T + 642 T^{2} - 4232 T^{3} + 279841 T^{4} )^{4} \))(\( 1 + 9 T + 556 T^{2} + 4761 T^{3} + 279841 T^{4} \))(\( 1 - 9 T + 556 T^{2} - 4761 T^{3} + 279841 T^{4} \))(\( 1 + 2381 T^{2} + 2947123 T^{4} + 2827993812 T^{6} + 2298643835613 T^{8} + 1531108455942719 T^{10} + 862820921151363886 T^{12} + \)\(42\!\cdots\!79\)\( T^{14} + \)\(18\!\cdots\!53\)\( T^{16} + \)\(61\!\cdots\!52\)\( T^{18} + \)\(18\!\cdots\!03\)\( T^{20} + \)\(40\!\cdots\!81\)\( T^{22} + \)\(48\!\cdots\!41\)\( T^{24} \))(\( 1 + 693 T^{2} - 15581 T^{4} - 315659500 T^{6} - 121343121715 T^{8} + 25399919636503 T^{10} + 46081428374834798 T^{12} + 7107938910998636023 T^{14} - \)\(95\!\cdots\!15\)\( T^{16} - \)\(69\!\cdots\!00\)\( T^{18} - \)\(95\!\cdots\!41\)\( T^{20} + \)\(11\!\cdots\!93\)\( T^{22} + \)\(48\!\cdots\!41\)\( T^{24} \))(\( 1 + 697 T^{2} + 205968 T^{4} + 195049177 T^{6} + 78310985281 T^{8} \))(\( 1 + 1009 T^{2} + 738240 T^{4} + 282359569 T^{6} + 78310985281 T^{8} \))(\( 1 + 2659 T^{2} + 3876571 T^{4} + 4127666252 T^{6} + 3503571279769 T^{8} + 2424695206910689 T^{10} + 1397846635041452342 T^{12} + \)\(67\!\cdots\!49\)\( T^{14} + \)\(27\!\cdots\!89\)\( T^{16} + \)\(90\!\cdots\!92\)\( T^{18} + \)\(23\!\cdots\!31\)\( T^{20} + \)\(45\!\cdots\!59\)\( T^{22} + \)\(48\!\cdots\!41\)\( T^{24} \))(\( 1 + 579 T^{2} + 62859 T^{4} - 35156516 T^{6} - 57866315751 T^{8} - 16658355952143 T^{10} + 6113539249932246 T^{12} - 4661690988003649263 T^{14} - \)\(45\!\cdots\!31\)\( T^{16} - \)\(77\!\cdots\!36\)\( T^{18} + \)\(38\!\cdots\!99\)\( T^{20} + \)\(99\!\cdots\!79\)\( T^{22} + \)\(48\!\cdots\!41\)\( T^{24} \))(\( 1 - 928 T^{2} - 110362 T^{4} + 76027072 T^{6} + 161836431161 T^{8} - 2090789193920 T^{10} - 54941991557559978 T^{12} + 14303404978544854944 T^{14} - \)\(12\!\cdots\!04\)\( T^{16} + \)\(40\!\cdots\!04\)\( T^{18} - \)\(43\!\cdots\!18\)\( T^{20} - \)\(45\!\cdots\!20\)\( T^{22} + \)\(99\!\cdots\!21\)\( T^{24} + \)\(13\!\cdots\!72\)\( T^{26} - \)\(53\!\cdots\!42\)\( T^{28} - \)\(12\!\cdots\!68\)\( T^{30} + \)\(37\!\cdots\!21\)\( T^{32} \))(\( 1 - 1648 T^{2} + 1017702 T^{4} - 249312032 T^{6} + 42919392953 T^{8} - 81219467468736 T^{10} + 45669118532829142 T^{12} + 12560582613209435984 T^{14} - \)\(19\!\cdots\!76\)\( T^{16} + \)\(35\!\cdots\!44\)\( T^{18} + \)\(35\!\cdots\!02\)\( T^{20} - \)\(17\!\cdots\!56\)\( T^{22} + \)\(26\!\cdots\!33\)\( T^{24} - \)\(42\!\cdots\!32\)\( T^{26} + \)\(48\!\cdots\!82\)\( T^{28} - \)\(22\!\cdots\!88\)\( T^{30} + \)\(37\!\cdots\!21\)\( T^{32} \))(\( ( 1 + 18 T + 529 T^{2} )^{4}( 1 - 734 T^{2} + 279841 T^{4} )^{2} \))
$29$ (\( ( 1 + 28 T + 1142 T^{2} + 23548 T^{3} + 707281 T^{4} )^{4} \))(\( ( 1 - 4 T + 1398 T^{2} - 3364 T^{3} + 707281 T^{4} )^{4} \))(\( ( 1 - 20 T + 774 T^{2} - 16820 T^{3} + 707281 T^{4} )^{2} \))(\( ( 1 + 40 T + 3660 T^{2} + 100632 T^{3} + 4741126 T^{4} + 84631512 T^{5} + 2588648460 T^{6} + 23792932840 T^{7} + 500246412961 T^{8} )^{2} \))(\( ( 1 - 1178 T^{2} + 707281 T^{4} )^{2} \))(\( 1 - 3384 T^{2} + 6555580 T^{4} - 8754768776 T^{6} + 8490907402822 T^{8} - 6192081614658056 T^{10} + 3279405379878872380 T^{12} - \)\(11\!\cdots\!44\)\( T^{14} + \)\(25\!\cdots\!21\)\( T^{16} \))(\( ( 1 - 54 T + 841 T^{2} )( 1 + 54 T + 841 T^{2} ) \))(\( ( 1 - 29 T )^{2}( 1 + 29 T )^{2} \))(\( ( 1 - 29 T )^{2}( 1 + 29 T )^{2} \))(\( ( 1 - 1444 T^{2} + 1048038 T^{4} - 1021313764 T^{6} + 500246412961 T^{8} )^{2} \))(\( 1 - 1490 T^{2} + 707281 T^{4} \))(\( 1 - 1490 T^{2} + 707281 T^{4} \))(\( ( 1 - 1838 T^{2} + 2723567 T^{4} - 2423469812 T^{6} + 1926327191327 T^{8} - 919452907022318 T^{10} + 353814783205469041 T^{12} )^{2} \))(\( ( 1 - 3662 T^{2} + 6471151 T^{4} - 6858243380 T^{6} + 4576922150431 T^{8} - 1831902364263182 T^{10} + 353814783205469041 T^{12} )^{2} \))(\( ( 1 + 32 T + 841 T^{2} )^{4} \))(\( ( 1 - 24 T + 841 T^{2} )^{4} \))(\( ( 1 - 32 T - 109 T^{2} + 37136 T^{3} - 91669 T^{4} - 22632992 T^{5} + 594823321 T^{6} )^{4} \))(\( ( 1 + 1347 T^{2} - 5488 T^{3} + 1132827 T^{4} + 594823321 T^{6} )^{4} \))(\( ( 1 - 28 T + 1376 T^{2} - 41412 T^{3} + 2055086 T^{4} - 34827492 T^{5} + 973218656 T^{6} - 16655052988 T^{7} + 500246412961 T^{8} )^{4} \))(\( ( 1 + 4 T + 2608 T^{2} + 8572 T^{3} + 2977102 T^{4} + 7209052 T^{5} + 1844588848 T^{6} + 2379293284 T^{7} + 500246412961 T^{8} )^{4} \))(\( ( 1 + 1234 T^{2} + 707281 T^{4} )^{2}( 1 + 108194 T^{4} + 500246412961 T^{8} ) \))
$31$ (\( ( 1 - 2180 T^{2} + 2458118 T^{4} - 2013275780 T^{6} + 852891037441 T^{8} )^{2} \))(\( ( 1 + 252 T^{2} - 435450 T^{4} + 232727292 T^{6} + 852891037441 T^{8} )^{2} \))(\( ( 1 - 1906 T^{2} + 923521 T^{4} )^{2} \))(\( 1 - 3624 T^{2} + 5953500 T^{4} - 5905968152 T^{6} + 5172694104774 T^{8} - 5454285613703192 T^{10} + 5077686791404993500 T^{12} - \)\(28\!\cdots\!64\)\( T^{14} + \)\(72\!\cdots\!81\)\( T^{16} \))(\( 1 - 1380 T^{2} + 1419974 T^{4} - 1274458980 T^{6} + 852891037441 T^{8} \))(\( 1 - 3944 T^{2} + 8438620 T^{4} - 12447428312 T^{6} + 13694235978694 T^{8} - 11495461442126552 T^{10} + 7197223366370371420 T^{12} - \)\(31\!\cdots\!84\)\( T^{14} + \)\(72\!\cdots\!81\)\( T^{16} \))(\( ( 1 - 31 T )^{2}( 1 + 31 T )^{2} \))(\( ( 1 - 31 T )^{2}( 1 + 31 T )^{2} \))(\( ( 1 - 31 T )^{2}( 1 + 31 T )^{2} \))(\( ( 1 + 140 T^{2} + 1206054 T^{4} + 129292940 T^{6} + 852891037441 T^{8} )^{2} \))(\( 1 + 57 T + 2044 T^{2} + 54777 T^{3} + 923521 T^{4} \))(\( 1 - 57 T + 2044 T^{2} - 54777 T^{3} + 923521 T^{4} \))(\( 1 + 3329 T^{2} + 4631887 T^{4} + 6475839496 T^{6} + 10686875408317 T^{8} + 11546553377441207 T^{10} + 9928800654054771830 T^{12} + \)\(10\!\cdots\!47\)\( T^{14} + \)\(91\!\cdots\!97\)\( T^{16} + \)\(51\!\cdots\!56\)\( T^{18} + \)\(33\!\cdots\!47\)\( T^{20} + \)\(22\!\cdots\!29\)\( T^{22} + \)\(62\!\cdots\!21\)\( T^{24} \))(\( 1 + 3561 T^{2} + 5838879 T^{4} + 8280992264 T^{6} + 11856779149293 T^{8} + 13054196823637455 T^{10} + 12193464685853753718 T^{12} + \)\(12\!\cdots\!55\)\( T^{14} + \)\(10\!\cdots\!13\)\( T^{16} + \)\(65\!\cdots\!04\)\( T^{18} + \)\(42\!\cdots\!99\)\( T^{20} + \)\(23\!\cdots\!61\)\( T^{22} + \)\(62\!\cdots\!21\)\( T^{24} \))(\( 1 + 1801 T^{2} + 2320080 T^{4} + 1663261321 T^{6} + 852891037441 T^{8} \))(\( 1 + 241 T^{2} - 865440 T^{4} + 222568561 T^{6} + 852891037441 T^{8} \))(\( 1 + 2963 T^{2} + 4291147 T^{4} + 3752683836 T^{6} + 1856892008697 T^{8} - 613860419386879 T^{10} - 1734915478854125546 T^{12} - \)\(56\!\cdots\!59\)\( T^{14} + \)\(15\!\cdots\!77\)\( T^{16} + \)\(29\!\cdots\!96\)\( T^{18} + \)\(31\!\cdots\!07\)\( T^{20} + \)\(19\!\cdots\!63\)\( T^{22} + \)\(62\!\cdots\!21\)\( T^{24} \))(\( 1 + 5235 T^{2} + 15533691 T^{4} + 32305589068 T^{6} + 51858557764857 T^{8} + 66810392242083729 T^{10} + 70681395526523023542 T^{12} + \)\(61\!\cdots\!09\)\( T^{14} + \)\(44\!\cdots\!37\)\( T^{16} + \)\(25\!\cdots\!48\)\( T^{18} + \)\(11\!\cdots\!71\)\( T^{20} + \)\(35\!\cdots\!35\)\( T^{22} + \)\(62\!\cdots\!21\)\( T^{24} \))(\( 1 + 4480 T^{2} + 9494774 T^{4} + 14306099840 T^{6} + 19217452630025 T^{8} + 24003699927942080 T^{10} + 26963891194383292806 T^{12} + \)\(27\!\cdots\!40\)\( T^{14} + \)\(26\!\cdots\!04\)\( T^{16} + \)\(25\!\cdots\!40\)\( T^{18} + \)\(22\!\cdots\!46\)\( T^{20} + \)\(18\!\cdots\!80\)\( T^{22} + \)\(13\!\cdots\!25\)\( T^{24} + \)\(96\!\cdots\!40\)\( T^{26} + \)\(58\!\cdots\!54\)\( T^{28} + \)\(25\!\cdots\!80\)\( T^{30} + \)\(52\!\cdots\!61\)\( T^{32} \))(\( 1 + 4944 T^{2} + 12401142 T^{4} + 21706728288 T^{6} + 30278528813833 T^{8} + 35431200182034624 T^{10} + 36428088221729894790 T^{12} + \)\(35\!\cdots\!36\)\( T^{14} + \)\(33\!\cdots\!48\)\( T^{16} + \)\(32\!\cdots\!56\)\( T^{18} + \)\(31\!\cdots\!90\)\( T^{20} + \)\(27\!\cdots\!64\)\( T^{22} + \)\(22\!\cdots\!73\)\( T^{24} + \)\(14\!\cdots\!88\)\( T^{26} + \)\(76\!\cdots\!82\)\( T^{28} + \)\(28\!\cdots\!04\)\( T^{30} + \)\(52\!\cdots\!61\)\( T^{32} \))(\( ( 1 - 31 T )^{8}( 1 + 31 T )^{8} \))
$37$ (\( ( 1 - 52 T + 2678 T^{2} - 71188 T^{3} + 1874161 T^{4} )^{4} \))(\( ( 1 + 12 T + 1206 T^{2} + 16428 T^{3} + 1874161 T^{4} )^{4} \))(\( ( 1 - 68 T + 3782 T^{2} - 93092 T^{3} + 1874161 T^{4} )^{2} \))(\( ( 1 + 88 T + 3692 T^{2} + 66024 T^{3} + 510982 T^{4} + 90386856 T^{5} + 6919402412 T^{6} + 225783923992 T^{7} + 3512479453921 T^{8} )^{2} \))(\( 1 - 1780 T^{2} + 2031622 T^{4} - 3336006580 T^{6} + 3512479453921 T^{8} \))(\( 1 - 3512 T^{2} + 9188668 T^{4} - 18622781448 T^{6} + 27544347275206 T^{8} - 34902090701365128 T^{10} + 32275007558901367228 T^{12} - \)\(23\!\cdots\!72\)\( T^{14} + \)\(12\!\cdots\!41\)\( T^{16} \))(\( ( 1 - 38 T + 1369 T^{2} )( 1 + 38 T + 1369 T^{2} ) \))(\( ( 1 - 37 T )^{2}( 1 + 37 T )^{2} \))(\( ( 1 - 37 T )^{2}( 1 + 37 T )^{2} \))(\( ( 1 - 4612 T^{2} + 8955366 T^{4} - 8643630532 T^{6} + 3512479453921 T^{8} )^{2} \))(\( 1 - 15 T + 1444 T^{2} - 20535 T^{3} + 1874161 T^{4} \))(\( 1 + 15 T + 1444 T^{2} + 20535 T^{3} + 1874161 T^{4} \))(\( 1 + 6401 T^{2} + 22091395 T^{4} + 55331146644 T^{6} + 111395987301489 T^{8} + 188098942339055675 T^{10} + \)\(27\!\cdots\!06\)\( T^{12} + \)\(35\!\cdots\!75\)\( T^{14} + \)\(39\!\cdots\!69\)\( T^{16} + \)\(36\!\cdots\!64\)\( T^{18} + \)\(27\!\cdots\!95\)\( T^{20} + \)\(14\!\cdots\!01\)\( T^{22} + \)\(43\!\cdots\!61\)\( T^{24} \))(\( 1 + 5785 T^{2} + 17889827 T^{4} + 38047414052 T^{6} + 62842022068961 T^{8} + 88030006321881747 T^{10} + \)\(11\!\cdots\!14\)\( T^{12} + \)\(16\!\cdots\!67\)\( T^{14} + \)\(22\!\cdots\!81\)\( T^{16} + \)\(25\!\cdots\!12\)\( T^{18} + \)\(22\!\cdots\!07\)\( T^{20} + \)\(13\!\cdots\!85\)\( T^{22} + \)\(43\!\cdots\!61\)\( T^{24} \))(\( ( 1 - T - 1368 T^{2} - 1369 T^{3} + 1874161 T^{4} )^{2} \))(\( ( 1 - 49 T + 1032 T^{2} - 67081 T^{3} + 1874161 T^{4} )^{2} \))(\( ( 1 + 33 T - 1333 T^{2} - 122132 T^{3} - 783591 T^{4} + 87702163 T^{5} + 5266681334 T^{6} + 120064261147 T^{7} - 1468575692151 T^{8} - 313357297783988 T^{9} - 4682135112076693 T^{10} + 158683284289789017 T^{11} + 6582952005840035281 T^{12} )^{2} \))(\( ( 1 + 57 T - 1269 T^{2} - 55332 T^{3} + 5310729 T^{4} + 108467211 T^{5} - 4432135786 T^{6} + 148491611859 T^{7} + 9953161173369 T^{8} - 141966773662788 T^{9} - 4457336427025749 T^{10} + 274089309227817393 T^{11} + 6582952005840035281 T^{12} )^{2} \))(\( ( 1 - 4 T - 2770 T^{2} + 121912 T^{3} + 3850313 T^{4} - 247260872 T^{5} + 4348488942 T^{6} + 233812310196 T^{7} - 10747661313644 T^{8} + 320089052658324 T^{9} + 8149768384027662 T^{10} - 634403749202768648 T^{11} + 13524145303664927273 T^{12} + \)\(58\!\cdots\!88\)\( T^{13} - \)\(18\!\cdots\!70\)\( T^{14} - \)\(36\!\cdots\!56\)\( T^{15} + \)\(12\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 - 36 T - 2658 T^{2} + 179832 T^{3} + 2782297 T^{4} - 349680552 T^{5} + 4944965886 T^{6} + 248707896180 T^{7} - 11947732536204 T^{8} + 340481109870420 T^{9} + 9267662209871646 T^{10} - 897184626980097768 T^{11} + 9772761047206036537 T^{12} + \)\(86\!\cdots\!68\)\( T^{13} - \)\(17\!\cdots\!98\)\( T^{14} - \)\(32\!\cdots\!04\)\( T^{15} + \)\(12\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 - 1294 T^{2} + 1874161 T^{4} )^{2}( 1 - 2073886 T^{4} + 3512479453921 T^{8} ) \))
$41$ (\( ( 1 - 4868 T^{2} + 10725062 T^{4} - 13755804548 T^{6} + 7984925229121 T^{8} )^{2} \))(\( ( 1 - 1988 T^{2} + 1048390 T^{4} - 5617612868 T^{6} + 7984925229121 T^{8} )^{2} \))(\( ( 1 + 60 T + 4150 T^{2} + 100860 T^{3} + 2825761 T^{4} )^{2} \))(\( ( 1 - 72 T + 4364 T^{2} - 180408 T^{3} + 8880422 T^{4} - 303265848 T^{5} + 12331621004 T^{6} - 342007505352 T^{7} + 7984925229121 T^{8} )^{2} \))(\( ( 1 + 20 T + 3174 T^{2} + 33620 T^{3} + 2825761 T^{4} )^{2} \))(\( ( 1 - 64 T + 4956 T^{2} - 221760 T^{3} + 11848326 T^{4} - 372778560 T^{5} + 14004471516 T^{6} - 304006671424 T^{7} + 7984925229121 T^{8} )^{2} \))(\( ( 1 - 41 T )^{2}( 1 + 41 T )^{2} \))(\( ( 1 - 41 T )^{2}( 1 + 41 T )^{2} \))(\( ( 1 - 41 T )^{2}( 1 + 41 T )^{2} \))(\( ( 1 - 5380 T^{2} + 12875334 T^{4} - 15202594180 T^{6} + 7984925229121 T^{8} )^{2} \))(\( ( 1 - 26 T + 1681 T^{2} )^{2} \))(\( ( 1 - 26 T + 1681 T^{2} )^{2} \))(\( ( 1 - 30 T + 4755 T^{2} - 100496 T^{3} + 7993155 T^{4} - 84772830 T^{5} + 4750104241 T^{6} )^{4} \))(\( ( 1 + 58 T + 3139 T^{2} + 88960 T^{3} + 5276659 T^{4} + 163894138 T^{5} + 4750104241 T^{6} )^{4} \))(\( ( 1 + 40 T + 1681 T^{2} )^{4} \))(\( ( 1 + 48 T + 1681 T^{2} )^{4} \))(\( ( 1 - 96 T + 7339 T^{2} - 328752 T^{3} + 12336859 T^{4} - 271273056 T^{5} + 4750104241 T^{6} )^{4} \))(\( ( 1 + 3195 T^{2} + 22736 T^{3} + 5370795 T^{4} + 4750104241 T^{6} )^{4} \))(\( ( 1 - 4384 T^{2} + 14370524 T^{4} - 32104130784 T^{6} + 62557592438726 T^{8} - 90718600708326624 T^{10} + \)\(11\!\cdots\!04\)\( T^{12} - \)\(98\!\cdots\!04\)\( T^{14} + \)\(63\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 - 10816 T^{2} + 53826588 T^{4} - 162742362560 T^{6} + 329722113042758 T^{8} - 459871021169908160 T^{10} + \)\(42\!\cdots\!48\)\( T^{12} - \)\(24\!\cdots\!96\)\( T^{14} + \)\(63\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 + 2825761 T^{4} )^{4} \))
$43$ (\( ( 1 + 2540 T^{2} + 7272902 T^{4} + 8683754540 T^{6} + 11688200277601 T^{8} )^{2} \))(\( ( 1 + 6284 T^{2} + 16414854 T^{4} + 21483745484 T^{6} + 11688200277601 T^{8} )^{2} \))(\( 1 - 1508 T^{2} + 5793318 T^{4} - 5155551908 T^{6} + 11688200277601 T^{8} \))(\( 1 - 4392 T^{2} + 15655580 T^{4} - 32786290584 T^{6} + 70340912004102 T^{8} - 112089803034869784 T^{10} + \)\(18\!\cdots\!80\)\( T^{12} - \)\(17\!\cdots\!92\)\( T^{14} + \)\(13\!\cdots\!01\)\( T^{16} \))(\( ( 1 - 40 T + 4090 T^{2} - 73960 T^{3} + 3418801 T^{4} )^{2} \))(\( ( 1 + 4680 T^{2} + 58016 T^{3} + 10251086 T^{4} + 107271584 T^{5} + 15999988680 T^{6} + 11688200277601 T^{8} )^{2} \))(\( ( 1 - 58 T + 1849 T^{2} )( 1 + 58 T + 1849 T^{2} ) \))(\( ( 1 - 43 T )^{2}( 1 + 43 T )^{2} \))(\( ( 1 - 43 T )^{2}( 1 + 43 T )^{2} \))(\( ( 1 - 1324 T^{2} + 5788998 T^{4} - 4526492524 T^{6} + 11688200277601 T^{8} )^{2} \))(\( ( 1 + 14 T + 1849 T^{2} )^{2} \))(\( ( 1 + 14 T + 1849 T^{2} )^{2} \))(\( ( 1 + 10 T + 3855 T^{2} + 53388 T^{3} + 7127895 T^{4} + 34188010 T^{5} + 6321363049 T^{6} )^{4} \))(\( ( 1 - 50 T + 4047 T^{2} - 107900 T^{3} + 7482903 T^{4} - 170940050 T^{5} + 6321363049 T^{6} )^{4} \))(\( ( 1 - 2098 T^{2} + 3418801 T^{4} )^{2} \))(\( ( 1 - 3122 T^{2} + 3418801 T^{4} )^{2} \))(\( ( 1 - 5206 T^{2} + 17138783 T^{4} - 37018566196 T^{6} + 58594088459183 T^{8} - 60848770645190806 T^{10} + 39959630797262576401 T^{12} )^{2} \))(\( ( 1 - 5718 T^{2} + 18746463 T^{4} - 40352107060 T^{6} + 64090426450863 T^{8} - 66833129187322518 T^{10} + 39959630797262576401 T^{12} )^{2} \))(\( ( 1 + 11176 T^{2} + 58293116 T^{4} + 188186249880 T^{6} + 415246366681670 T^{8} + 643371339275993880 T^{10} + \)\(68\!\cdots\!16\)\( T^{12} + \)\(44\!\cdots\!76\)\( T^{14} + \)\(13\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 + 5992 T^{2} + 25433596 T^{4} + 70773684952 T^{6} + 153071479203142 T^{8} + 241961144887582552 T^{10} + \)\(29\!\cdots\!96\)\( T^{12} + \)\(23\!\cdots\!92\)\( T^{14} + \)\(13\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 + 58 T + 1849 T^{2} )^{4}( 1 - 6726046 T^{4} + 11688200277601 T^{8} ) \))
$47$ (\( ( 1 - 6788 T^{2} + 21266822 T^{4} - 33123274628 T^{6} + 23811286661761 T^{8} )^{2} \))(\( ( 1 - 5892 T^{2} + 16275078 T^{4} - 28751080452 T^{6} + 23811286661761 T^{8} )^{2} \))(\( 1 - 5348 T^{2} + 14587206 T^{4} - 26096533988 T^{6} + 23811286661761 T^{8} \))(\( 1 - 6696 T^{2} + 34041564 T^{4} - 108976927256 T^{6} + 286725887177670 T^{8} - 531772641369485336 T^{10} + \)\(81\!\cdots\!04\)\( T^{12} - \)\(77\!\cdots\!36\)\( T^{14} + \)\(56\!\cdots\!21\)\( T^{16} \))(\( 1 - 7492 T^{2} + 23390470 T^{4} - 36558570052 T^{6} + 23811286661761 T^{8} \))(\( 1 - 8392 T^{2} + 39566748 T^{4} - 127207295352 T^{6} + 316693927920198 T^{8} - 620731022190542712 T^{10} + \)\(94\!\cdots\!28\)\( T^{12} - \)\(97\!\cdots\!72\)\( T^{14} + \)\(56\!\cdots\!21\)\( T^{16} \))(\( ( 1 - 47 T )^{2}( 1 + 47 T )^{2} \))(\( ( 1 - 47 T )^{2}( 1 + 47 T )^{2} \))(\( ( 1 - 47 T )^{2}( 1 + 47 T )^{2} \))(\( ( 1 - 4852 T^{2} + 14998950 T^{4} - 23676212212 T^{6} + 23811286661761 T^{8} )^{2} \))(\( 1 - 87 T + 4732 T^{2} - 192183 T^{3} + 4879681 T^{4} \))(\( 1 + 87 T + 4732 T^{2} + 192183 T^{3} + 4879681 T^{4} \))(\( 1 + 8313 T^{2} + 34702703 T^{4} + 101154992824 T^{6} + 247422958854189 T^{8} + 586359622432093519 T^{10} + \)\(13\!\cdots\!26\)\( T^{12} + \)\(28\!\cdots\!39\)\( T^{14} + \)\(58\!\cdots\!29\)\( T^{16} + \)\(11\!\cdots\!84\)\( T^{18} + \)\(19\!\cdots\!63\)\( T^{20} + \)\(22\!\cdots\!13\)\( T^{22} + \)\(13\!\cdots\!81\)\( T^{24} \))(\( 1 + 3905 T^{2} + 6537087 T^{4} + 2079696952 T^{6} - 28977286497379 T^{8} - 99900087904130553 T^{10} - \)\(24\!\cdots\!46\)\( T^{12} - \)\(48\!\cdots\!93\)\( T^{14} - \)\(68\!\cdots\!19\)\( T^{16} + \)\(24\!\cdots\!32\)\( T^{18} + \)\(37\!\cdots\!27\)\( T^{20} + \)\(10\!\cdots\!05\)\( T^{22} + \)\(13\!\cdots\!81\)\( T^{24} \))(\( 1 - 2807 T^{2} + 2999568 T^{4} - 13697264567 T^{6} + 23811286661761 T^{8} \))(\( 1 + 1393 T^{2} - 2939232 T^{4} + 6797395633 T^{6} + 23811286661761 T^{8} \))(\( 1 + 6995 T^{2} + 22181707 T^{4} + 50014251324 T^{6} + 105476166484281 T^{8} + 174006129657696449 T^{10} + \)\(27\!\cdots\!62\)\( T^{12} + \)\(84\!\cdots\!69\)\( T^{14} + \)\(25\!\cdots\!41\)\( T^{16} + \)\(58\!\cdots\!84\)\( T^{18} + \)\(12\!\cdots\!47\)\( T^{20} + \)\(19\!\cdots\!95\)\( T^{22} + \)\(13\!\cdots\!81\)\( T^{24} \))(\( 1 + 8307 T^{2} + 34424571 T^{4} + 100893075532 T^{6} + 253028343980217 T^{8} + 616841824418715921 T^{10} + \)\(14\!\cdots\!38\)\( T^{12} + \)\(30\!\cdots\!01\)\( T^{14} + \)\(60\!\cdots\!37\)\( T^{16} + \)\(11\!\cdots\!12\)\( T^{18} + \)\(19\!\cdots\!91\)\( T^{20} + \)\(22\!\cdots\!07\)\( T^{22} + \)\(13\!\cdots\!81\)\( T^{24} \))(\( 1 + 7504 T^{2} + 21182918 T^{4} + 37880838368 T^{6} + 100768600793177 T^{8} + 218689095748226816 T^{10} + \)\(22\!\cdots\!70\)\( T^{12} + \)\(76\!\cdots\!12\)\( T^{14} + \)\(29\!\cdots\!24\)\( T^{16} + \)\(37\!\cdots\!72\)\( T^{18} + \)\(52\!\cdots\!70\)\( T^{20} + \)\(25\!\cdots\!56\)\( T^{22} + \)\(57\!\cdots\!17\)\( T^{24} + \)\(10\!\cdots\!68\)\( T^{26} + \)\(28\!\cdots\!58\)\( T^{28} + \)\(49\!\cdots\!44\)\( T^{30} + \)\(32\!\cdots\!41\)\( T^{32} \))(\( 1 + 7200 T^{2} + 21086790 T^{4} + 20987252160 T^{6} - 28679941197479 T^{8} - 70284530432138880 T^{10} + \)\(21\!\cdots\!30\)\( T^{12} + \)\(13\!\cdots\!80\)\( T^{14} + \)\(38\!\cdots\!20\)\( T^{16} + \)\(66\!\cdots\!80\)\( T^{18} + \)\(50\!\cdots\!30\)\( T^{20} - \)\(81\!\cdots\!80\)\( T^{22} - \)\(16\!\cdots\!59\)\( T^{24} + \)\(58\!\cdots\!60\)\( T^{26} + \)\(28\!\cdots\!90\)\( T^{28} + \)\(47\!\cdots\!00\)\( T^{30} + \)\(32\!\cdots\!41\)\( T^{32} \))(\( ( 1 + 2209 T^{2} )^{8} \))
$53$ (\( ( 1 + 30 T + 2809 T^{2} )^{8} \))(\( ( 1 - 68 T + 6262 T^{2} - 191012 T^{3} + 7890481 T^{4} )^{4} \))(\( ( 1 + 140 T + 10070 T^{2} + 393260 T^{3} + 7890481 T^{4} )^{2} \))(\( ( 1 - 24 T + 6108 T^{2} - 242920 T^{3} + 18930726 T^{4} - 682362280 T^{5} + 48195057948 T^{6} - 531944667096 T^{7} + 62259690411361 T^{8} )^{2} \))(\( 1 - 1604 T^{2} - 6155034 T^{4} - 12656331524 T^{6} + 62259690411361 T^{8} \))(\( 1 - 18920 T^{2} + 162796828 T^{4} - 840091728600 T^{6} + 2864724835962118 T^{8} - 6628727822775456600 T^{10} + \)\(10\!\cdots\!08\)\( T^{12} - \)\(92\!\cdots\!20\)\( T^{14} + \)\(38\!\cdots\!21\)\( T^{16} \))(\( ( 1 - 6 T + 2809 T^{2} )( 1 + 6 T + 2809 T^{2} ) \))(\( ( 1 - 53 T )^{2}( 1 + 53 T )^{2} \))(\( ( 1 - 53 T )^{2}( 1 + 53 T )^{2} \))(\( ( 1 - 7780 T^{2} + 30664230 T^{4} - 61387942180 T^{6} + 62259690411361 T^{8} )^{2} \))(\( ( 1 - 53 T )^{2}( 1 - 53 T + 2809 T^{2} ) \))(\( ( 1 + 53 T )^{2}( 1 + 53 T + 2809 T^{2} ) \))(\( 1 + 9273 T^{2} + 34839939 T^{4} + 130830291652 T^{6} + 620089921398753 T^{8} + 1876428047292173523 T^{10} + \)\(44\!\cdots\!94\)\( T^{12} + \)\(14\!\cdots\!63\)\( T^{14} + \)\(38\!\cdots\!33\)\( T^{16} + \)\(64\!\cdots\!32\)\( T^{18} + \)\(13\!\cdots\!19\)\( T^{20} + \)\(28\!\cdots\!73\)\( T^{22} + \)\(24\!\cdots\!81\)\( T^{24} \))(\( 1 + 10561 T^{2} + 59733731 T^{4} + 209884512884 T^{6} + 494098524300977 T^{8} + 757507316642438811 T^{10} + \)\(12\!\cdots\!10\)\( T^{12} + \)\(59\!\cdots\!91\)\( T^{14} + \)\(30\!\cdots\!97\)\( T^{16} + \)\(10\!\cdots\!44\)\( T^{18} + \)\(23\!\cdots\!51\)\( T^{20} + \)\(32\!\cdots\!61\)\( T^{22} + \)\(24\!\cdots\!81\)\( T^{24} \))(\( ( 1 + 7 T - 2760 T^{2} + 19663 T^{3} + 7890481 T^{4} )^{2} \))(\( ( 1 - 25 T - 2184 T^{2} - 70225 T^{3} + 7890481 T^{4} )^{2} \))(\( ( 1 + T - 2837 T^{2} - 53748 T^{3} + 54009 T^{4} + 72242131 T^{5} + 22496954230 T^{6} + 202928145979 T^{7} + 426156988329 T^{8} - 1191290081961492 T^{9} - 176630741697031157 T^{10} + 174887470365513049 T^{11} + \)\(49\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 + 9 T - 2997 T^{2} - 116484 T^{3} + 179145 T^{4} + 137286747 T^{5} + 22274291990 T^{6} + 385638472323 T^{7} + 1413540218745 T^{8} - 2581793441750436 T^{9} - 186592292162848917 T^{10} + 1573987233289617441 T^{11} + \)\(49\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 + 12 T - 5314 T^{2} - 123432 T^{3} + 13289689 T^{4} + 412137720 T^{5} + 8001350174 T^{6} - 662204794044 T^{7} - 79868347316108 T^{8} - 1860133266469596 T^{9} + 63134501522293694 T^{10} + 9134769260962685880 T^{11} + \)\(82\!\cdots\!29\)\( T^{12} - \)\(21\!\cdots\!68\)\( T^{13} - \)\(26\!\cdots\!74\)\( T^{14} + \)\(16\!\cdots\!28\)\( T^{15} + \)\(38\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 - 20 T - 6098 T^{2} + 355352 T^{3} + 15866345 T^{4} - 1398217832 T^{5} + 8057716910 T^{6} + 2171403120260 T^{7} - 80650058761388 T^{8} + 6099471364810340 T^{9} + 63579262181733710 T^{10} - 30990604965455452328 T^{11} + \)\(98\!\cdots\!45\)\( T^{12} + \)\(62\!\cdots\!48\)\( T^{13} - \)\(29\!\cdots\!18\)\( T^{14} - \)\(27\!\cdots\!80\)\( T^{15} + \)\(38\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 - 6 T + 2809 T^{2} )^{4}( 1 + 15377762 T^{4} + 62259690411361 T^{8} ) \))
$59$ (\( ( 1 - 4580 T^{2} + 29037038 T^{4} - 55497513380 T^{6} + 146830437604321 T^{8} )^{2} \))(\( ( 1 - 7860 T^{2} + 33271422 T^{4} - 95242457460 T^{6} + 146830437604321 T^{8} )^{2} \))(\( 1 - 9692 T^{2} + 45396006 T^{4} - 117441462812 T^{6} + 146830437604321 T^{8} \))(\( 1 - 21392 T^{2} + 213726428 T^{4} - 1316320178544 T^{6} + 5495654048256518 T^{8} - 15950326795002102384 T^{10} + \)\(31\!\cdots\!88\)\( T^{12} - \)\(38\!\cdots\!52\)\( T^{14} + \)\(21\!\cdots\!41\)\( T^{16} \))(\( ( 1 + 92 T + 8836 T^{2} + 320252 T^{3} + 12117361 T^{4} )^{2} \))(\( ( 1 + 52 T + 2254 T^{2} - 207508 T^{3} - 19795230 T^{4} - 722335348 T^{5} + 27312531694 T^{6} + 2193387749332 T^{7} + 146830437604321 T^{8} )^{2} \))(\( ( 1 + 3481 T^{2} )^{2} \))(\( 1 - 1130 T^{2} + 12117361 T^{4} \))(\( 1 + 1130 T^{2} + 12117361 T^{4} \))(\( ( 1 + 9200 T^{2} + 44845170 T^{4} + 111479721200 T^{6} + 146830437604321 T^{8} )^{2} \))(\( 1 + 55 T - 456 T^{2} + 191455 T^{3} + 12117361 T^{4} \))(\( 1 + 55 T - 456 T^{2} + 191455 T^{3} + 12117361 T^{4} \))(\( ( 1 + 31 T - 7567 T^{2} - 176030 T^{3} + 36214647 T^{4} + 412965247 T^{5} - 131958052142 T^{6} + 1437532024807 T^{7} + 438825951186567 T^{8} - 7425039336825230 T^{9} - 1111065921351897007 T^{10} + 15844619352319883431 T^{11} + \)\(17\!\cdots\!81\)\( T^{12} )^{2} \))(\( ( 1 - 55 T - 7367 T^{2} + 181142 T^{3} + 51119807 T^{4} - 598293727 T^{5} - 186579818926 T^{6} - 2082660463687 T^{7} + 619437155669327 T^{8} + 7640666224798022 T^{9} - 1081699833831032807 T^{10} - 28111421431535277055 T^{11} + \)\(17\!\cdots\!81\)\( T^{12} )^{2} \))(\( 1 + 4153 T^{2} + 5130048 T^{4} + 50323400233 T^{6} + 146830437604321 T^{8} \))(\( 1 + 6673 T^{2} + 32411568 T^{4} + 80859149953 T^{6} + 146830437604321 T^{8} \))(\( 1 + 18811 T^{2} + 200120491 T^{4} + 1494527327372 T^{6} + 8628303999799801 T^{8} + 40087667805525876841 T^{10} + \)\(15\!\cdots\!62\)\( T^{12} + \)\(48\!\cdots\!01\)\( T^{14} + \)\(12\!\cdots\!21\)\( T^{16} + \)\(26\!\cdots\!32\)\( T^{18} + \)\(43\!\cdots\!31\)\( T^{20} + \)\(49\!\cdots\!11\)\( T^{22} + \)\(31\!\cdots\!61\)\( T^{24} \))(\( 1 + 1707 T^{2} - 9128709 T^{4} - 112178055524 T^{6} - 114189887648679 T^{8} + 551687617569890985 T^{10} + \)\(57\!\cdots\!54\)\( T^{12} + \)\(66\!\cdots\!85\)\( T^{14} - \)\(16\!\cdots\!59\)\( T^{16} - \)\(19\!\cdots\!44\)\( T^{18} - \)\(19\!\cdots\!69\)\( T^{20} + \)\(44\!\cdots\!07\)\( T^{22} + \)\(31\!\cdots\!61\)\( T^{24} \))(\( 1 + 12496 T^{2} + 69591254 T^{4} + 231196127072 T^{6} + 548940902299433 T^{8} + 1224313485336173888 T^{10} + \)\(76\!\cdots\!62\)\( T^{12} - \)\(17\!\cdots\!52\)\( T^{14} - \)\(10\!\cdots\!32\)\( T^{16} - \)\(21\!\cdots\!72\)\( T^{18} + \)\(11\!\cdots\!02\)\( T^{20} + \)\(21\!\cdots\!28\)\( T^{22} + \)\(11\!\cdots\!53\)\( T^{24} + \)\(60\!\cdots\!72\)\( T^{26} + \)\(22\!\cdots\!94\)\( T^{28} + \)\(47\!\cdots\!16\)\( T^{30} + \)\(46\!\cdots\!81\)\( T^{32} \))(\( 1 + 13056 T^{2} + 66899190 T^{4} + 216438091392 T^{6} + 1041428149652041 T^{8} + 6415617182341109568 T^{10} + \)\(27\!\cdots\!66\)\( T^{12} + \)\(85\!\cdots\!44\)\( T^{14} + \)\(25\!\cdots\!80\)\( T^{16} + \)\(10\!\cdots\!84\)\( T^{18} + \)\(41\!\cdots\!86\)\( T^{20} + \)\(11\!\cdots\!08\)\( T^{22} + \)\(22\!\cdots\!81\)\( T^{24} + \)\(56\!\cdots\!92\)\( T^{26} + \)\(21\!\cdots\!90\)\( T^{28} + \)\(50\!\cdots\!76\)\( T^{30} + \)\(46\!\cdots\!81\)\( T^{32} \))(\( ( 1 + 146830437604321 T^{8} )^{2} \))
$61$ (\( ( 1 - 4212 T^{2} + 3996814 T^{4} - 58318682292 T^{6} + 191707312997281 T^{8} )^{2} \))(\( ( 1 - 7140 T^{2} + 40319454 T^{4} - 98859304740 T^{6} + 191707312997281 T^{8} )^{2} \))(\( ( 1 + 4 T + 7194 T^{2} + 14884 T^{3} + 13845841 T^{4} )^{2} \))(\( ( 1 + 96 T + 12728 T^{2} + 895872 T^{3} + 70065870 T^{4} + 3333539712 T^{5} + 176229864248 T^{6} + 4945955938656 T^{7} + 191707312997281 T^{8} )^{2} \))(\( 1 - 13232 T^{2} + 71110338 T^{4} - 183208168112 T^{6} + 191707312997281 T^{8} \))(\( 1 - 16316 T^{2} + 140172120 T^{4} - 816942037524 T^{6} + 3499102878259502 T^{8} - 11311249557773337684 T^{10} + \)\(26\!\cdots\!20\)\( T^{12} - \)\(43\!\cdots\!36\)\( T^{14} + \)\(36\!\cdots\!61\)\( T^{16} \))(\( ( 1 + 3721 T^{2} )^{2} \))(\( 1 - 7370 T^{2} + 13845841 T^{4} \))(\( 1 + 7370 T^{2} + 13845841 T^{4} \))(\( ( 1 + 14840 T^{2} + 82747650 T^{4} + 205472280440 T^{6} + 191707312997281 T^{8} )^{2} \))(\( 1 - 39 T + 4228 T^{2} - 145119 T^{3} + 13845841 T^{4} \))(\( 1 + 39 T + 4228 T^{2} + 145119 T^{3} + 13845841 T^{4} \))(\( 1 - 503 T^{2} - 13520125 T^{4} - 91919186268 T^{6} + 20373908662561 T^{8} + 680714329682975843 T^{10} + \)\(44\!\cdots\!06\)\( T^{12} + \)\(94\!\cdots\!63\)\( T^{14} + \)\(39\!\cdots\!41\)\( T^{16} - \)\(24\!\cdots\!28\)\( T^{18} - \)\(49\!\cdots\!25\)\( T^{20} - \)\(25\!\cdots\!03\)\( T^{22} + \)\(70\!\cdots\!41\)\( T^{24} \))(\( 1 + 9201 T^{2} + 56941411 T^{4} + 154999649300 T^{6} - 75695642240335 T^{8} - 3911957905117164149 T^{10} - \)\(19\!\cdots\!14\)\( T^{12} - \)\(54\!\cdots\!09\)\( T^{14} - \)\(14\!\cdots\!35\)\( T^{16} + \)\(41\!\cdots\!00\)\( T^{18} + \)\(20\!\cdots\!71\)\( T^{20} + \)\(46\!\cdots\!01\)\( T^{22} + \)\(70\!\cdots\!41\)\( T^{24} \))(\( ( 1 + 79 T + 2520 T^{2} + 293959 T^{3} + 13845841 T^{4} )^{2} \))(\( ( 1 - T - 3720 T^{2} - 3721 T^{3} + 13845841 T^{4} )^{2} \))(\( ( 1 + 217 T + 20699 T^{2} + 1814604 T^{3} + 173780089 T^{4} + 12006150107 T^{5} + 685616953942 T^{6} + 44674884548147 T^{7} + 2406131481259849 T^{8} + 93489077396968044 T^{9} + 3968149671730719419 T^{10} + \)\(15\!\cdots\!17\)\( T^{11} + \)\(26\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 - 159 T + 7899 T^{2} - 401828 T^{3} + 49683657 T^{4} - 2161110333 T^{5} + 23418423222 T^{6} - 8041491549093 T^{7} + 687912015120537 T^{8} - 20702328988731908 T^{9} + 1514296065365522619 T^{10} - \)\(11\!\cdots\!59\)\( T^{11} + \)\(26\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 + 180 T + 27726 T^{2} + 3046680 T^{3} + 308297129 T^{4} + 26423205000 T^{5} + 2082233555790 T^{6} + 145145432104140 T^{7} + 9348584465944212 T^{8} + 540086152859504940 T^{9} + 28830274738332969390 T^{10} + \)\(13\!\cdots\!00\)\( T^{11} + \)\(59\!\cdots\!49\)\( T^{12} + \)\(21\!\cdots\!80\)\( T^{13} + \)\(73\!\cdots\!46\)\( T^{14} + \)\(17\!\cdots\!80\)\( T^{15} + \)\(36\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 - 108 T + 15678 T^{2} - 1273320 T^{3} + 112514745 T^{4} - 8281698840 T^{5} + 635104006110 T^{6} - 41916162290292 T^{7} + 2814046950849908 T^{8} - 155970039882176532 T^{9} + 8793549087062088510 T^{10} - \)\(42\!\cdots\!40\)\( T^{11} + \)\(21\!\cdots\!45\)\( T^{12} - \)\(90\!\cdots\!20\)\( T^{13} + \)\(41\!\cdots\!38\)\( T^{14} - \)\(10\!\cdots\!28\)\( T^{15} + \)\(36\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 + 191707312997281 T^{8} )^{2} \))
$67$ (\( ( 1 + 8150 T^{2} + 20151121 T^{4} )^{4} \))(\( ( 1 + 2892 T^{2} + 19813958 T^{4} + 58277041932 T^{6} + 406067677556641 T^{8} )^{2} \))(\( 1 - 11204 T^{2} + 65233446 T^{4} - 225773159684 T^{6} + 406067677556641 T^{8} \))(\( 1 - 16200 T^{2} + 120433884 T^{4} - 596093100152 T^{6} + 2634880977729030 T^{8} - 12011944188428070392 T^{10} + \)\(48\!\cdots\!44\)\( T^{12} - \)\(13\!\cdots\!00\)\( T^{14} + \)\(16\!\cdots\!81\)\( T^{16} \))(\( ( 1 - 112 T + 11602 T^{2} - 502768 T^{3} + 20151121 T^{4} )^{2} \))(\( ( 1 + 152 T + 22224 T^{2} + 2037320 T^{3} + 158433022 T^{4} + 9145529480 T^{5} + 447838513104 T^{6} + 13749674089688 T^{7} + 406067677556641 T^{8} )^{2} \))(\( ( 1 - 118 T + 4489 T^{2} )( 1 + 118 T + 4489 T^{2} ) \))(\( ( 1 - 67 T )^{2}( 1 + 67 T )^{2} \))(\( ( 1 - 67 T )^{2}( 1 + 67 T )^{2} \))(\( ( 1 - 11884 T^{2} + 74122758 T^{4} - 239475921964 T^{6} + 406067677556641 T^{8} )^{2} \))(\( 1 - 17 T - 4200 T^{2} - 76313 T^{3} + 20151121 T^{4} \))(\( 1 - 17 T - 4200 T^{2} - 76313 T^{3} + 20151121 T^{4} \))(\( ( 1 - 89 T - 19 T^{2} + 251662 T^{3} - 15244389 T^{4} + 746405371 T^{5} - 32107721582 T^{6} + 3350613710419 T^{7} - 307191527310069 T^{8} + 22764937373414878 T^{9} - 7715285873576179 T^{10} - \)\(16\!\cdots\!61\)\( T^{11} + \)\(81\!\cdots\!61\)\( T^{12} )^{2} \))(\( ( 1 + 217 T + 18053 T^{2} + 1666970 T^{3} + 209974835 T^{4} + 15078221277 T^{5} + 815515698066 T^{6} + 67686135312453 T^{7} + 4231228307040035 T^{8} + 150791409324257930 T^{9} + 7330739782930039973 T^{10} + \)\(39\!\cdots\!33\)\( T^{11} + \)\(81\!\cdots\!61\)\( T^{12} )^{2} \))(\( 1 + 8857 T^{2} + 58295328 T^{4} + 178478478697 T^{6} + 406067677556641 T^{8} \))(\( 1 + 4753 T^{2} + 2439888 T^{4} + 95778278113 T^{6} + 406067677556641 T^{8} \))(\( 1 + 9899 T^{2} + 24620203 T^{4} - 79278218964 T^{6} - 82489071404871 T^{8} + 4300819315073397209 T^{10} + \)\(30\!\cdots\!86\)\( T^{12} + \)\(86\!\cdots\!89\)\( T^{14} - \)\(33\!\cdots\!11\)\( T^{16} - \)\(64\!\cdots\!04\)\( T^{18} + \)\(40\!\cdots\!43\)\( T^{20} + \)\(32\!\cdots\!99\)\( T^{22} + \)\(66\!\cdots\!21\)\( T^{24} \))(\( 1 + 23547 T^{2} + 312061755 T^{4} + 2891423739964 T^{6} + 20714504811186393 T^{8} + \)\(12\!\cdots\!29\)\( T^{10} + \)\(59\!\cdots\!86\)\( T^{12} + \)\(24\!\cdots\!09\)\( T^{14} + \)\(84\!\cdots\!13\)\( T^{16} + \)\(23\!\cdots\!04\)\( T^{18} + \)\(51\!\cdots\!55\)\( T^{20} + \)\(78\!\cdots\!47\)\( T^{22} + \)\(66\!\cdots\!21\)\( T^{24} \))(\( 1 - 5792 T^{2} - 24227898 T^{4} + 351601426496 T^{6} - 205859799182695 T^{8} - 8707473271916577024 T^{10} + \)\(34\!\cdots\!66\)\( T^{12} + \)\(81\!\cdots\!24\)\( T^{14} - \)\(92\!\cdots\!56\)\( T^{16} + \)\(16\!\cdots\!04\)\( T^{18} + \)\(14\!\cdots\!06\)\( T^{20} - \)\(71\!\cdots\!64\)\( T^{22} - \)\(33\!\cdots\!95\)\( T^{24} + \)\(11\!\cdots\!96\)\( T^{26} - \)\(16\!\cdots\!58\)\( T^{28} - \)\(78\!\cdots\!72\)\( T^{30} + \)\(27\!\cdots\!61\)\( T^{32} \))(\( 1 - 19248 T^{2} + 171825062 T^{4} - 1105279125792 T^{6} + 6322631625605113 T^{8} - 28716244420307792256 T^{10} + \)\(95\!\cdots\!42\)\( T^{12} - \)\(31\!\cdots\!16\)\( T^{14} + \)\(13\!\cdots\!84\)\( T^{16} - \)\(63\!\cdots\!36\)\( T^{18} + \)\(38\!\cdots\!22\)\( T^{20} - \)\(23\!\cdots\!16\)\( T^{22} + \)\(10\!\cdots\!53\)\( T^{24} - \)\(36\!\cdots\!92\)\( T^{26} + \)\(11\!\cdots\!02\)\( T^{28} - \)\(25\!\cdots\!68\)\( T^{30} + \)\(27\!\cdots\!61\)\( T^{32} \))(\( ( 1 + 118 T + 4489 T^{2} )^{4}( 1 - 15839326 T^{4} + 406067677556641 T^{8} ) \))
$71$ (\( ( 1 + 11964 T^{2} + 70047686 T^{4} + 304025351484 T^{6} + 645753531245761 T^{8} )^{2} \))(\( ( 1 + 11516 T^{2} + 65977926 T^{4} + 292640918396 T^{6} + 645753531245761 T^{8} )^{2} \))(\( 1 - 8388 T^{2} + 39052870 T^{4} - 213153180228 T^{6} + 645753531245761 T^{8} \))(\( 1 - 21000 T^{2} + 247457180 T^{4} - 1991232124728 T^{6} + 11615880585488070 T^{8} - 50600555550540147768 T^{10} + \)\(15\!\cdots\!80\)\( T^{12} - \)\(34\!\cdots\!00\)\( T^{14} + \)\(41\!\cdots\!21\)\( T^{16} \))(\( 1 - 9412 T^{2} + 47279686 T^{4} - 239174741572 T^{6} + 645753531245761 T^{8} \))(\( 1 - 9864 T^{2} + 51888284 T^{4} - 294531431096 T^{6} + 1789421441990854 T^{8} - 7484538771485032376 T^{10} + \)\(33\!\cdots\!24\)\( T^{12} - \)\(16\!\cdots\!24\)\( T^{14} + \)\(41\!\cdots\!21\)\( T^{16} \))(\( ( 1 - 114 T + 5041 T^{2} )^{2} \))(\( ( 1 + 110 T + 5041 T^{2} )^{2} \))(\( ( 1 - 110 T + 5041 T^{2} )^{2} \))(\( ( 1 + 136 T + 12678 T^{2} + 685576 T^{3} + 25411681 T^{4} )^{4} \))(\( ( 1 - 71 T )^{2}( 1 + 71 T )^{2} \))(\( ( 1 - 71 T )^{2}( 1 + 71 T )^{2} \))(\( ( 1 - 7830 T^{2} + 72414895 T^{4} - 385201987444 T^{6} + 1840184211388495 T^{8} - 5056250149654308630 T^{10} + \)\(16\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 - 23062 T^{2} + 245626031 T^{4} - 1559141837940 T^{6} + 6241770345068111 T^{8} - 14892367937589740182 T^{10} + \)\(16\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 - 7778 T^{2} + 25411681 T^{4} )^{2} \))(\( ( 1 - 866 T^{2} + 25411681 T^{4} )^{2} \))(\( ( 1 - 12262 T^{2} + 100517039 T^{4} - 635265930196 T^{6} + 2554306930132559 T^{8} - 7918229800135521382 T^{10} + \)\(16\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 - 10086 T^{2} + 56255151 T^{4} - 272956768468 T^{6} + 1429537951818831 T^{8} - 6513070116144745446 T^{10} + \)\(16\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 + 27624 T^{2} + 370534588 T^{4} + 3151580461272 T^{6} + 18747759294515334 T^{8} + 80086957327676918232 T^{10} + \)\(23\!\cdots\!68\)\( T^{12} + \)\(45\!\cdots\!84\)\( T^{14} + \)\(41\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 + 24232 T^{2} + 314425660 T^{4} + 2642217676312 T^{6} + 15735155452974982 T^{8} + 67143192723001800472 T^{10} + \)\(20\!\cdots\!60\)\( T^{12} + \)\(39\!\cdots\!12\)\( T^{14} + \)\(41\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 - 42331966 T^{4} + 645753531245761 T^{8} )^{2} \))
$73$ (\( ( 1 - 8388 T^{2} + 67882822 T^{4} - 238204445508 T^{6} + 806460091894081 T^{8} )^{2} \))(\( ( 1 - 14980 T^{2} + 104177094 T^{4} - 425405650180 T^{6} + 806460091894081 T^{8} )^{2} \))(\( ( 1 + 76 T + 4934 T^{2} + 405004 T^{3} + 28398241 T^{4} )^{2} \))(\( ( 1 - 136 T + 21660 T^{2} - 1811512 T^{3} + 170528390 T^{4} - 9653547448 T^{5} + 615105900060 T^{6} - 20581454775304 T^{7} + 806460091894081 T^{8} )^{2} \))(\( ( 1 - 116 T + 13894 T^{2} - 618164 T^{3} + 28398241 T^{4} )^{2} \))(\( ( 1 + 56 T + 18460 T^{2} + 736008 T^{3} + 138223494 T^{4} + 3922186632 T^{5} + 524231528860 T^{6} + 8474716672184 T^{7} + 806460091894081 T^{8} )^{2} \))(\( ( 1 - 73 T )^{2}( 1 + 73 T )^{2} \))(\( ( 1 - 73 T )^{2}( 1 + 73 T )^{2} \))(\( ( 1 - 73 T )^{2}( 1 + 73 T )^{2} \))(\( ( 1 - 9364 T^{2} + 72904614 T^{4} - 265921128724 T^{6} + 806460091894081 T^{8} )^{2} \))(\( 1 + 119 T + 8832 T^{2} + 634151 T^{3} + 28398241 T^{4} \))(\( 1 + 119 T + 8832 T^{2} + 634151 T^{3} + 28398241 T^{4} \))(\( ( 1 - 27 T - 12877 T^{2} + 216188 T^{3} + 104738937 T^{4} - 821298961 T^{5} - 619422939130 T^{6} - 4376702163169 T^{7} + 2974401575009817 T^{8} + 32716643712966332 T^{9} - 10384786603320081037 T^{10} - \)\(11\!\cdots\!23\)\( T^{11} + \)\(22\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 - 51 T - 9165 T^{2} + 579660 T^{3} + 45654729 T^{4} - 1993134921 T^{5} - 160997144218 T^{6} - 10621415994009 T^{7} + 1296513996931689 T^{8} + 87722397610681740 T^{9} - 7391206742209252365 T^{10} - \)\(21\!\cdots\!99\)\( T^{11} + \)\(22\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 + 46 T + 5329 T^{2} )^{2}( 1 + 97 T + 5329 T^{2} )^{2} \))(\( ( 1 + 95 T + 3696 T^{2} + 506255 T^{3} + 28398241 T^{4} )^{2} \))(\( ( 1 + 5 T - 12813 T^{2} - 167716 T^{3} + 95820777 T^{4} + 946458799 T^{5} - 562891511514 T^{6} + 5043678939871 T^{7} + 2721141518053257 T^{8} - 25381171096285924 T^{9} - 10333173157438859853 T^{10} + 21488129148517788245 T^{11} + \)\(22\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 - 171 T + 4275 T^{2} - 355908 T^{3} + 155672073 T^{4} - 8204564097 T^{5} - 20860196506 T^{6} - 43722122072913 T^{7} + 4420813046023593 T^{8} - 53861061810065412 T^{9} + 3447616892847196275 T^{10} - \)\(73\!\cdots\!79\)\( T^{11} + \)\(22\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 - 36 T + 13374 T^{2} - 465912 T^{3} + 80365289 T^{4} - 3011641896 T^{5} + 480881406846 T^{6} - 17666763587772 T^{7} + 3025613230783092 T^{8} - 94146183159236988 T^{9} + 13656186084031757886 T^{10} - \)\(45\!\cdots\!44\)\( T^{11} + \)\(64\!\cdots\!09\)\( T^{12} - \)\(20\!\cdots\!88\)\( T^{13} + \)\(30\!\cdots\!54\)\( T^{14} - \)\(43\!\cdots\!24\)\( T^{15} + \)\(65\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 + 156 T + 22270 T^{2} + 2208648 T^{3} + 203639977 T^{4} + 17676576216 T^{5} + 1406019151294 T^{6} + 115719264813828 T^{7} + 8350708700464372 T^{8} + 616667962192889412 T^{9} + 39928470709062473854 T^{10} + \)\(26\!\cdots\!24\)\( T^{11} + \)\(16\!\cdots\!37\)\( T^{12} + \)\(94\!\cdots\!52\)\( T^{13} + \)\(51\!\cdots\!70\)\( T^{14} + \)\(19\!\cdots\!04\)\( T^{15} + \)\(65\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 + 28398241 T^{4} )^{4} \))
$79$ (\( ( 1 - 1028 T^{2} + 37863942 T^{4} - 40040683268 T^{6} + 1517108809906561 T^{8} )^{2} \))(\( ( 1 + 7612 T^{2} + 88816006 T^{4} + 296488016572 T^{6} + 1517108809906561 T^{8} )^{2} \))(\( ( 1 - 1282 T^{2} + 38950081 T^{4} )^{2} \))(\( 1 - 26248 T^{2} + 289540636 T^{4} - 1851543245752 T^{6} + 10296312398061382 T^{8} - 72117759397043305912 T^{10} + \)\(43\!\cdots\!96\)\( T^{12} - \)\(15\!\cdots\!68\)\( T^{14} + \)\(23\!\cdots\!21\)\( T^{16} \))(\( 1 - 16900 T^{2} + 142880134 T^{4} - 658256368900 T^{6} + 1517108809906561 T^{8} \))(\( 1 - 24968 T^{2} + 330869788 T^{4} - 3106127956152 T^{6} + 22189846569597766 T^{8} - \)\(12\!\cdots\!12\)\( T^{10} + \)\(50\!\cdots\!68\)\( T^{12} - \)\(14\!\cdots\!88\)\( T^{14} + \)\(23\!\cdots\!21\)\( T^{16} \))(\( ( 1 + 94 T + 6241 T^{2} )^{2} \))(\( ( 1 - 130 T + 6241 T^{2} )^{2} \))(\( ( 1 + 130 T + 6241 T^{2} )^{2} \))(\( ( 1 - 8 T + 11526 T^{2} - 49928 T^{3} + 38950081 T^{4} )^{4} \))(\( 1 + 129 T + 11788 T^{2} + 805089 T^{3} + 38950081 T^{4} \))(\( 1 - 129 T + 11788 T^{2} - 805089 T^{3} + 38950081 T^{4} \))(\( 1 + 27485 T^{2} + 389982499 T^{4} + 4285373244996 T^{6} + 40173777270526125 T^{8} + \)\(31\!\cdots\!47\)\( T^{10} + \)\(20\!\cdots\!50\)\( T^{12} + \)\(12\!\cdots\!07\)\( T^{14} + \)\(60\!\cdots\!25\)\( T^{16} + \)\(25\!\cdots\!36\)\( T^{18} + \)\(89\!\cdots\!79\)\( T^{20} + \)\(24\!\cdots\!85\)\( T^{22} + \)\(34\!\cdots\!81\)\( T^{24} \))(\( 1 + 16693 T^{2} + 149251283 T^{4} + 640487711012 T^{6} - 978609215845699 T^{8} - 44625107831251066425 T^{10} - \)\(37\!\cdots\!74\)\( T^{12} - \)\(17\!\cdots\!25\)\( T^{14} - \)\(14\!\cdots\!39\)\( T^{16} + \)\(37\!\cdots\!92\)\( T^{18} + \)\(34\!\cdots\!43\)\( T^{20} + \)\(14\!\cdots\!93\)\( T^{22} + \)\(34\!\cdots\!81\)\( T^{24} \))(\( 1 + 11257 T^{2} + 87769968 T^{4} + 438461061817 T^{6} + 1517108809906561 T^{8} \))(\( 1 + 10801 T^{2} + 77711520 T^{4} + 420699824881 T^{6} + 1517108809906561 T^{8} \))(\( 1 + 28083 T^{2} + 421723515 T^{4} + 4556484807052 T^{6} + 39635396888713497 T^{8} + \)\(29\!\cdots\!89\)\( T^{10} + \)\(19\!\cdots\!22\)\( T^{12} + \)\(11\!\cdots\!09\)\( T^{14} + \)\(60\!\cdots\!17\)\( T^{16} + \)\(26\!\cdots\!32\)\( T^{18} + \)\(97\!\cdots\!15\)\( T^{20} + \)\(25\!\cdots\!83\)\( T^{22} + \)\(34\!\cdots\!81\)\( T^{24} \))(\( 1 + 16371 T^{2} + 121567851 T^{4} + 486780511900 T^{6} + 101914373627865 T^{8} - 22023984316104222399 T^{10} - \)\(21\!\cdots\!94\)\( T^{12} - \)\(85\!\cdots\!19\)\( T^{14} + \)\(15\!\cdots\!65\)\( T^{16} + \)\(28\!\cdots\!00\)\( T^{18} + \)\(27\!\cdots\!71\)\( T^{20} + \)\(14\!\cdots\!71\)\( T^{22} + \)\(34\!\cdots\!81\)\( T^{24} \))(\( 1 - 10112 T^{2} - 55382202 T^{4} + 565038672512 T^{6} + 4616239476368153 T^{8} - 23803283016229531968 T^{10} - \)\(25\!\cdots\!02\)\( T^{12} + \)\(18\!\cdots\!72\)\( T^{14} + \)\(13\!\cdots\!08\)\( T^{16} + \)\(71\!\cdots\!32\)\( T^{18} - \)\(37\!\cdots\!22\)\( T^{20} - \)\(14\!\cdots\!88\)\( T^{22} + \)\(10\!\cdots\!13\)\( T^{24} + \)\(50\!\cdots\!12\)\( T^{26} - \)\(19\!\cdots\!62\)\( T^{28} - \)\(13\!\cdots\!32\)\( T^{30} + \)\(52\!\cdots\!41\)\( T^{32} \))(\( 1 - 34640 T^{2} + 602988550 T^{4} - 7689396100960 T^{6} + 82922855327705561 T^{8} - \)\(77\!\cdots\!00\)\( T^{10} + \)\(63\!\cdots\!50\)\( T^{12} - \)\(46\!\cdots\!20\)\( T^{14} + \)\(30\!\cdots\!00\)\( T^{16} - \)\(17\!\cdots\!20\)\( T^{18} + \)\(95\!\cdots\!50\)\( T^{20} - \)\(45\!\cdots\!00\)\( T^{22} + \)\(19\!\cdots\!81\)\( T^{24} - \)\(68\!\cdots\!60\)\( T^{26} + \)\(21\!\cdots\!50\)\( T^{28} - \)\(47\!\cdots\!40\)\( T^{30} + \)\(52\!\cdots\!41\)\( T^{32} \))(\( ( 1 - 64606846 T^{4} + 1517108809906561 T^{8} )^{2} \))
$83$ (\( ( 1 - 8132 T^{2} + 106317422 T^{4} - 385931066372 T^{6} + 2252292232139041 T^{8} )^{2} \))(\( ( 1 - 18644 T^{2} + 171328126 T^{4} - 884812936724 T^{6} + 2252292232139041 T^{8} )^{2} \))(\( 1 - 11804 T^{2} + 67754214 T^{4} - 560198021084 T^{6} + 2252292232139041 T^{8} \))(\( 1 - 19280 T^{2} + 168996572 T^{4} - 1078781742000 T^{6} + 6945567152070790 T^{8} - 51197170200775182000 T^{10} + \)\(38\!\cdots\!52\)\( T^{12} - \)\(20\!\cdots\!80\)\( T^{14} + \)\(50\!\cdots\!81\)\( T^{16} \))(\( ( 1 + 44 T + 13924 T^{2} + 303116 T^{3} + 47458321 T^{4} )^{2} \))(\( ( 1 + 36 T + 16478 T^{2} + 177884 T^{3} + 135298114 T^{4} + 1225442876 T^{5} + 782018213438 T^{6} + 11769853441284 T^{7} + 2252292232139041 T^{8} )^{2} \))(\( ( 1 + 6889 T^{2} )^{2} \))(\( 1 - 13130 T^{2} + 47458321 T^{4} \))(\( 1 + 13130 T^{2} + 47458321 T^{4} \))(\( ( 1 + 6608 T^{2} - 3756750 T^{4} + 313604585168 T^{6} + 2252292232139041 T^{8} )^{2} \))(\( ( 1 + 110 T + 6889 T^{2} )^{2} \))(\( ( 1 + 110 T + 6889 T^{2} )^{2} \))(\( ( 1 - 98 T + 12183 T^{2} - 526716 T^{3} + 83928687 T^{4} - 4650915458 T^{5} + 326940373369 T^{6} )^{4} \))(\( ( 1 - 134 T + 22583 T^{2} - 1661172 T^{3} + 155574287 T^{4} - 6359415014 T^{5} + 326940373369 T^{6} )^{4} \))(\( ( 1 - 13714 T^{2} + 47458321 T^{4} )^{2} \))(\( ( 1 - 8594 T^{2} + 47458321 T^{4} )^{2} \))(\( ( 1 - 29238 T^{2} + 396631039 T^{4} - 3342660983284 T^{6} + 18823443167425519 T^{8} - 65852520283281280758 T^{10} + \)\(10\!\cdots\!61\)\( T^{12} )^{2} \))(\( ( 1 - 29238 T^{2} + 403545087 T^{4} - 3424551164404 T^{6} + 19151572276818927 T^{8} - 65852520283281280758 T^{10} + \)\(10\!\cdots\!61\)\( T^{12} )^{2} \))(\( ( 1 - 24232 T^{2} + 235912988 T^{4} - 1035732354840 T^{6} + 3398417338650758 T^{8} - 49154118566082623640 T^{10} + \)\(53\!\cdots\!08\)\( T^{12} - \)\(25\!\cdots\!52\)\( T^{14} + \)\(50\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 - 35368 T^{2} + 588987420 T^{4} - 6301011254168 T^{6} + 49538235115611782 T^{8} - \)\(29\!\cdots\!28\)\( T^{10} + \)\(13\!\cdots\!20\)\( T^{12} - \)\(37\!\cdots\!48\)\( T^{14} + \)\(50\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 + 2252292232139041 T^{8} )^{2} \))
$89$ (\( ( 1 - 30916 T^{2} + 364289990 T^{4} - 1939739122756 T^{6} + 3936588805702081 T^{8} )^{2} \))(\( ( 1 - 18308 T^{2} + 203581510 T^{4} - 1148684948228 T^{6} + 3936588805702081 T^{8} )^{2} \))(\( ( 1 - 68 T + 15206 T^{2} - 538628 T^{3} + 62742241 T^{4} )^{2} \))(\( ( 1 + 40 T + 25916 T^{2} + 837912 T^{3} + 285914566 T^{4} + 6637100952 T^{5} + 1626027917756 T^{6} + 19879251638440 T^{7} + 3936588805702081 T^{8} )^{2} \))(\( ( 1 - 156 T + 20774 T^{2} - 1235676 T^{3} + 62742241 T^{4} )^{2} \))(\( ( 1 + 256 T + 48252 T^{2} + 6269952 T^{3} + 638304966 T^{4} + 49664289792 T^{5} + 3027438612732 T^{6} + 127227210486016 T^{7} + 3936588805702081 T^{8} )^{2} \))(\( ( 1 - 89 T )^{2}( 1 + 89 T )^{2} \))(\( ( 1 - 89 T )^{2}( 1 + 89 T )^{2} \))(\( ( 1 - 89 T )^{2}( 1 + 89 T )^{2} \))(\( ( 1 - 17428 T^{2} + 180509478 T^{4} - 1093471776148 T^{6} + 3936588805702081 T^{8} )^{2} \))(\( 1 + 71 T - 2880 T^{2} + 562391 T^{3} + 62742241 T^{4} \))(\( 1 + 71 T - 2880 T^{2} + 562391 T^{3} + 62742241 T^{4} \))(\( ( 1 + 13 T - 19181 T^{2} - 141748 T^{3} + 218594713 T^{4} + 635752183 T^{5} - 1943770650106 T^{6} + 5035793041543 T^{7} + 13715122164371833 T^{8} - 70446104031139828 T^{9} - 75507709882171615661 T^{10} + \)\(40\!\cdots\!13\)\( T^{11} + \)\(24\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 - 107 T + 1395 T^{2} + 497084 T^{3} - 62702935 T^{4} + 2422278015 T^{5} + 93422604838 T^{6} + 19186864156815 T^{7} - 3934122659177335 T^{8} + 247041448036057724 T^{9} + 5491541383954402995 T^{10} - \)\(33\!\cdots\!07\)\( T^{11} + \)\(24\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 - 97 T + 1488 T^{2} - 768337 T^{3} + 62742241 T^{4} )^{2} \))(\( ( 1 + 95 T + 1104 T^{2} + 752495 T^{3} + 62742241 T^{4} )^{2} \))(\( ( 1 + 261 T + 22931 T^{2} + 2459452 T^{3} + 465950601 T^{4} + 40453273231 T^{5} + 2330338704422 T^{6} + 320430377262751 T^{7} + 29234784902036841 T^{8} + 1222301630016613372 T^{9} + 90269917903554419411 T^{10} + \)\(81\!\cdots\!61\)\( T^{11} + \)\(24\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 - 75 T - 7725 T^{2} + 660828 T^{3} + 10149225 T^{4} + 61763775 T^{5} - 80037126682 T^{6} + 489230861775 T^{7} + 636785120913225 T^{8} + 328419152543175708 T^{9} - 30410148524048575725 T^{10} - \)\(23\!\cdots\!75\)\( T^{11} + \)\(24\!\cdots\!21\)\( T^{12} )^{2} \))(\( ( 1 - 204 T + 42982 T^{2} - 5938440 T^{3} + 800796785 T^{4} - 88063687656 T^{5} + 9449600595510 T^{6} - 894257389252164 T^{7} + 83094368751630116 T^{8} - 7083412780266391044 T^{9} + \)\(59\!\cdots\!10\)\( T^{10} - \)\(43\!\cdots\!16\)\( T^{11} + \)\(31\!\cdots\!85\)\( T^{12} - \)\(18\!\cdots\!40\)\( T^{13} + \)\(10\!\cdots\!22\)\( T^{14} - \)\(39\!\cdots\!64\)\( T^{15} + \)\(15\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 - 12 T + 8678 T^{2} - 103560 T^{3} + 5715441 T^{4} + 150778776 T^{5} - 475047477962 T^{6} + 26903544978684 T^{7} - 3925857799931356 T^{8} + 213102979776155964 T^{9} - 29805543348733992842 T^{10} + 74934230745999443736 T^{11} + \)\(22\!\cdots\!21\)\( T^{12} - \)\(32\!\cdots\!60\)\( T^{13} + \)\(21\!\cdots\!38\)\( T^{14} - \)\(23\!\cdots\!92\)\( T^{15} + \)\(15\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 + 62742241 T^{4} )^{4} \))
$97$ (\( ( 1 - 19204 T^{2} + 268303110 T^{4} - 1700116312324 T^{6} + 7837433594376961 T^{8} )^{2} \))(\( ( 1 - 10628 T^{2} + 166577158 T^{4} - 940889198468 T^{6} + 7837433594376961 T^{8} )^{2} \))(\( ( 1 + 300 T + 41206 T^{2} + 2822700 T^{3} + 88529281 T^{4} )^{2} \))(\( ( 1 - 264 T + 52364 T^{2} - 7260024 T^{3} + 808802534 T^{4} - 68309565816 T^{5} + 4635747270284 T^{6} - 219904609301256 T^{7} + 7837433594376961 T^{8} )^{2} \))(\( ( 1 + 68 T + 3046 T^{2} + 639812 T^{3} + 88529281 T^{4} )^{2} \))(\( ( 1 - 32 T + 19484 T^{2} - 1437536 T^{3} + 199130566 T^{4} - 13525776224 T^{5} + 1724904511004 T^{6} - 26655104157728 T^{7} + 7837433594376961 T^{8} )^{2} \))(\( ( 1 - 97 T )^{2}( 1 + 97 T )^{2} \))(\( ( 1 - 97 T )^{2}( 1 + 97 T )^{2} \))(\( ( 1 - 97 T )^{2}( 1 + 97 T )^{2} \))(\( ( 1 - 13588 T^{2} + 180804198 T^{4} - 1202935870228 T^{6} + 7837433594376961 T^{8} )^{2} \))(\( ( 1 + 22 T + 9409 T^{2} )^{2} \))(\( ( 1 + 22 T + 9409 T^{2} )^{2} \))(\( ( 1 + 46 T + 18423 T^{2} + 458352 T^{3} + 173342007 T^{4} + 4072346926 T^{5} + 832972004929 T^{6} )^{4} \))(\( ( 1 + 38 T + 25191 T^{2} + 597344 T^{3} + 237022119 T^{4} + 3364112678 T^{5} + 832972004929 T^{6} )^{4} \))(\( ( 1 + 88 T + 9409 T^{2} )^{4} \))(\( ( 1 - 144 T + 9409 T^{2} )^{4} \))(\( ( 1 + 192 T + 28555 T^{2} + 2621616 T^{3} + 268673995 T^{4} + 16997621952 T^{5} + 832972004929 T^{6} )^{4} \))(\( ( 1 + 28059 T^{2} - 784 T^{3} + 264007131 T^{4} + 832972004929 T^{6} )^{4} \))(\( ( 1 - 51968 T^{2} + 1305731356 T^{4} - 20766356196608 T^{6} + 230652504659485894 T^{8} - \)\(18\!\cdots\!48\)\( T^{10} + \)\(10\!\cdots\!16\)\( T^{12} - \)\(36\!\cdots\!88\)\( T^{14} + \)\(61\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 - 39520 T^{2} + 789394140 T^{4} - 11378905321376 T^{6} + 124539045704549702 T^{8} - \)\(10\!\cdots\!56\)\( T^{10} + \)\(61\!\cdots\!40\)\( T^{12} - \)\(27\!\cdots\!20\)\( T^{14} + \)\(61\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 - 97 T )^{8}( 1 + 97 T )^{8} \))
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