Properties

Label 324.6
Level 324
Weight 6
Dimension 6664
Nonzero newspaces 8
Sturm bound 34992
Trace bound 1

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Defining parameters

Level: \( N \) = \( 324\( 324 = 2^{2} \cdot 3^{4} \) \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(34992\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(324))\).

Total New Old
Modular forms 14850 6776 8074
Cusp forms 14310 6664 7646
Eisenstein series 540 112 428

Trace form

\( 6664q - 12q^{2} - 20q^{4} + 63q^{5} - 18q^{6} - 87q^{7} - 9q^{8} - 36q^{9} + O(q^{10}) \) \( 6664q - 12q^{2} - 20q^{4} + 63q^{5} - 18q^{6} - 87q^{7} - 9q^{8} - 36q^{9} + 35q^{10} + 1257q^{11} - 18q^{12} - 691q^{13} - 1527q^{14} + 2488q^{16} + 3450q^{17} - 18q^{18} + 522q^{19} - 1251q^{20} - 13779q^{21} - 6576q^{22} - 8403q^{23} - 18q^{24} + 17307q^{25} - 27q^{26} + 17523q^{27} + 13191q^{28} - 11679q^{29} - 18q^{30} - 17145q^{31} - 7242q^{32} - 36783q^{33} - 19234q^{34} - 11184q^{35} - 18q^{36} + 57842q^{37} - 14886q^{38} - 7945q^{40} - 196917q^{41} - 52173q^{42} - 12447q^{43} + 316071q^{44} + 135990q^{45} + 160839q^{46} + 141921q^{47} + 66411q^{48} + 10195q^{49} - 249432q^{50} - 126315q^{51} - 162655q^{52} - 147594q^{53} - 347148q^{54} - 125730q^{55} - 408483q^{56} - 41562q^{57} - 7441q^{58} + 95097q^{59} + 329805q^{60} + 159173q^{61} + 922869q^{62} + 266274q^{63} + 376009q^{64} - 18297q^{65} + 39222q^{66} - 93789q^{67} - 810006q^{68} + 94914q^{69} - 280071q^{70} + 339060q^{71} - 18q^{72} + 149285q^{73} - 20415q^{74} - 56250q^{75} - 107934q^{76} - 563895q^{77} + 2169q^{78} + 54141q^{79} - 455004q^{81} + 45782q^{82} - 263763q^{83} - 2205q^{84} + 193120q^{85} + 279228q^{86} + 405936q^{87} + 319044q^{88} - 445659q^{89} + 856215q^{90} + 141297q^{91} - 106185q^{92} + 1675710q^{93} - 559731q^{94} + 1074756q^{95} - 1285965q^{96} + 490337q^{97} - 2615967q^{98} - 908586q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(324))\)

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
324.6.a \(\chi_{324}(1, \cdot)\) 324.6.a.a 3 1
324.6.a.b 3
324.6.a.c 4
324.6.a.d 5
324.6.a.e 5
324.6.b \(\chi_{324}(323, \cdot)\) n/a 116 1
324.6.e \(\chi_{324}(109, \cdot)\) 324.6.e.a 2 2
324.6.e.b 2
324.6.e.c 2
324.6.e.d 2
324.6.e.e 4
324.6.e.f 4
324.6.e.g 4
324.6.e.h 6
324.6.e.i 6
324.6.e.j 8
324.6.h \(\chi_{324}(107, \cdot)\) n/a 236 2
324.6.i \(\chi_{324}(37, \cdot)\) 324.6.i.a 90 6
324.6.l \(\chi_{324}(35, \cdot)\) n/a 528 6
324.6.m \(\chi_{324}(13, \cdot)\) n/a 810 18
324.6.p \(\chi_{324}(11, \cdot)\) n/a 4824 18

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(324))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(324)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ (\( 1 + 33 T + 4614 T^{2} + 23217 T^{3} + 14418750 T^{4} + 322265625 T^{5} + 30517578125 T^{6} \))(\( 1 - 33 T + 4614 T^{2} - 23217 T^{3} + 14418750 T^{4} - 322265625 T^{5} + 30517578125 T^{6} \))(\( 1 + 4598 T^{2} + 15971451 T^{4} + 44902343750 T^{6} + 95367431640625 T^{8} \))(\( 1 + 21 T + 5644 T^{2} + 319227 T^{3} + 11115175 T^{4} + 1519942932 T^{5} + 34734921875 T^{6} + 3117451171875 T^{7} + 172241210937500 T^{8} + 2002716064453125 T^{9} + 298023223876953125 T^{10} \))(\( 1 - 21 T + 5644 T^{2} - 319227 T^{3} + 11115175 T^{4} - 1519942932 T^{5} + 34734921875 T^{6} - 3117451171875 T^{7} + 172241210937500 T^{8} - 2002716064453125 T^{9} + 298023223876953125 T^{10} \))(\( 1 + 54 T - 209 T^{2} + 168750 T^{3} + 9765625 T^{4} \))(\( 1 - 3125 T^{2} + 9765625 T^{4} \))(\( 1 - 3125 T^{2} + 9765625 T^{4} \))(\( 1 - 54 T - 209 T^{2} - 168750 T^{3} + 9765625 T^{4} \))(\( 1 + 1526 T^{2} - 7436949 T^{4} + 14902343750 T^{6} + 95367431640625 T^{8} \))(\( 1 - 2929 T^{2} - 1186584 T^{4} - 28603515625 T^{6} + 95367431640625 T^{8} \))(\( 1 - 2929 T^{2} - 1186584 T^{4} - 28603515625 T^{6} + 95367431640625 T^{8} \))(\( 1 + 33 T - 3525 T^{2} + 105828 T^{3} + 6104085 T^{4} - 522248637 T^{5} - 15588692786 T^{6} - 1632026990625 T^{7} + 59610205078125 T^{8} + 3229614257812500 T^{9} - 336170196533203125 T^{10} + 9834766387939453125 T^{11} + \)\(93\!\cdots\!25\)\( T^{12} \))(\( 1 - 33 T - 3525 T^{2} - 105828 T^{3} + 6104085 T^{4} + 522248637 T^{5} - 15588692786 T^{6} + 1632026990625 T^{7} + 59610205078125 T^{8} - 3229614257812500 T^{9} - 336170196533203125 T^{10} - 9834766387939453125 T^{11} + \)\(93\!\cdots\!25\)\( T^{12} \))(\( 1 - 4598 T^{2} + 5170153 T^{4} + 16367955802 T^{6} - 46741161157724 T^{8} + 159843318378906250 T^{10} + \)\(49\!\cdots\!25\)\( T^{12} - \)\(42\!\cdots\!50\)\( T^{14} + \)\(90\!\cdots\!25\)\( T^{16} \))
$7$ (\( 1 + 30 T + 6549 T^{2} + 556036 T^{3} + 110069043 T^{4} + 8474257470 T^{5} + 4747561509943 T^{6} \))(\( 1 + 30 T + 6549 T^{2} + 556036 T^{3} + 110069043 T^{4} + 8474257470 T^{5} + 4747561509943 T^{6} \))(\( ( 1 - 88 T + 25722 T^{2} - 1479016 T^{3} + 282475249 T^{4} )^{2} \))(\( 1 + 29 T + 40410 T^{2} + 2467167 T^{3} + 1121022921 T^{4} + 42673614444 T^{5} + 18841032233247 T^{6} + 696913612649583 T^{7} + 191848960616796630 T^{8} + 2313975722630748029 T^{9} + \)\(13\!\cdots\!07\)\( T^{10} \))(\( 1 + 29 T + 40410 T^{2} + 2467167 T^{3} + 1121022921 T^{4} + 42673614444 T^{5} + 18841032233247 T^{6} + 696913612649583 T^{7} + 191848960616796630 T^{8} + 2313975722630748029 T^{9} + \)\(13\!\cdots\!07\)\( T^{10} \))(\( 1 - 88 T - 9063 T^{2} - 1479016 T^{3} + 282475249 T^{4} \))(\( ( 1 + 25 T + 16807 T^{2} )( 1 + 211 T + 16807 T^{2} ) \))(\( ( 1 - 236 T + 16807 T^{2} )( 1 + 211 T + 16807 T^{2} ) \))(\( 1 - 88 T - 9063 T^{2} - 1479016 T^{3} + 282475249 T^{4} \))(\( ( 1 + 29 T - 15966 T^{2} + 487403 T^{3} + 282475249 T^{4} )^{2} \))(\( 1 - 32 T - 2957 T^{2} + 948256 T^{3} - 283837256 T^{4} + 15937338592 T^{5} - 835279311293 T^{6} - 151921968318176 T^{7} + 79792266297612001 T^{8} \))(\( 1 - 32 T - 2957 T^{2} + 948256 T^{3} - 283837256 T^{4} + 15937338592 T^{5} - 835279311293 T^{6} - 151921968318176 T^{7} + 79792266297612001 T^{8} \))(\( 1 - 30 T - 5649 T^{2} + 915602 T^{3} - 83860722 T^{4} - 5511594654 T^{5} + 8829229166475 T^{6} - 92633371349778 T^{7} - 23688578328269778 T^{8} + 4346876813626830686 T^{9} - \)\(45\!\cdots\!49\)\( T^{10} - \)\(40\!\cdots\!10\)\( T^{11} + \)\(22\!\cdots\!49\)\( T^{12} \))(\( 1 - 30 T - 5649 T^{2} + 915602 T^{3} - 83860722 T^{4} - 5511594654 T^{5} + 8829229166475 T^{6} - 92633371349778 T^{7} - 23688578328269778 T^{8} + 4346876813626830686 T^{9} - \)\(45\!\cdots\!49\)\( T^{10} - \)\(40\!\cdots\!10\)\( T^{11} + \)\(22\!\cdots\!49\)\( T^{12} \))(\( ( 1 + 88 T - 17978 T^{2} - 694496 T^{3} + 248992627 T^{4} - 11672394272 T^{5} - 5078340026522 T^{6} + 417785412874984 T^{7} + 79792266297612001 T^{8} )^{2} \))
$11$ (\( 1 - 30 T + 55761 T^{2} + 99601836 T^{3} + 8980364811 T^{4} - 778122738030 T^{5} + 4177248169415651 T^{6} \))(\( 1 + 30 T + 55761 T^{2} - 99601836 T^{3} + 8980364811 T^{4} + 778122738030 T^{5} + 4177248169415651 T^{6} \))(\( 1 + 438068 T^{2} + 92916105558 T^{4} + 11362355720110868 T^{6} + \)\(67\!\cdots\!01\)\( T^{8} \))(\( 1 - 177 T + 427561 T^{2} - 2122014 T^{3} + 77616186361 T^{4} + 7157256911361 T^{5} + 12500164429625411 T^{6} - 55039578127266414 T^{7} + \)\(17\!\cdots\!11\)\( T^{8} - \)\(11\!\cdots\!77\)\( T^{9} + \)\(10\!\cdots\!51\)\( T^{10} \))(\( 1 + 177 T + 427561 T^{2} + 2122014 T^{3} + 77616186361 T^{4} - 7157256911361 T^{5} + 12500164429625411 T^{6} + 55039578127266414 T^{7} + \)\(17\!\cdots\!11\)\( T^{8} + \)\(11\!\cdots\!77\)\( T^{9} + \)\(10\!\cdots\!51\)\( T^{10} \))(\( 1 + 540 T + 130549 T^{2} + 86967540 T^{3} + 25937424601 T^{4} \))(\( 1 - 161051 T^{2} + 25937424601 T^{4} \))(\( 1 - 161051 T^{2} + 25937424601 T^{4} \))(\( 1 - 540 T + 130549 T^{2} - 86967540 T^{3} + 25937424601 T^{4} \))(\( 1 - 314326 T^{2} + 72863409675 T^{4} - 8152806925133926 T^{6} + \)\(67\!\cdots\!01\)\( T^{8} \))(\( 1 + 486 T + 67589 T^{2} - 74598570 T^{3} - 35548706148 T^{4} - 12014174297070 T^{5} + 1753084591356989 T^{6} + 2030142610336006386 T^{7} + \)\(67\!\cdots\!01\)\( T^{8} \))(\( 1 - 486 T + 67589 T^{2} + 74598570 T^{3} - 35548706148 T^{4} + 12014174297070 T^{5} + 1753084591356989 T^{6} - 2030142610336006386 T^{7} + \)\(67\!\cdots\!01\)\( T^{8} \))(\( 1 - 30 T - 54861 T^{2} - 200876502 T^{3} - 2883020610 T^{4} + 5314597127826 T^{5} + 17750924269035127 T^{6} + 855921182033505126 T^{7} - 74778129695004026610 T^{8} - \)\(83\!\cdots\!02\)\( T^{9} - \)\(36\!\cdots\!61\)\( T^{10} - \)\(32\!\cdots\!30\)\( T^{11} + \)\(17\!\cdots\!01\)\( T^{12} \))(\( 1 + 30 T - 54861 T^{2} + 200876502 T^{3} - 2883020610 T^{4} - 5314597127826 T^{5} + 17750924269035127 T^{6} - 855921182033505126 T^{7} - 74778129695004026610 T^{8} + \)\(83\!\cdots\!02\)\( T^{9} - \)\(36\!\cdots\!61\)\( T^{10} + \)\(32\!\cdots\!30\)\( T^{11} + \)\(17\!\cdots\!01\)\( T^{12} \))(\( 1 - 438068 T^{2} + 98987467066 T^{4} - 17978861089360208 T^{6} + \)\(29\!\cdots\!39\)\( T^{8} - \)\(46\!\cdots\!08\)\( T^{10} + \)\(66\!\cdots\!66\)\( T^{12} - \)\(76\!\cdots\!68\)\( T^{14} + \)\(45\!\cdots\!01\)\( T^{16} \))
$13$ (\( 1 + 273 T + 469230 T^{2} + 237041953 T^{3} + 174221814390 T^{4} + 37635368274777 T^{5} + 51185893014090757 T^{6} \))(\( 1 + 273 T + 469230 T^{2} + 237041953 T^{3} + 174221814390 T^{4} + 37635368274777 T^{5} + 51185893014090757 T^{6} \))(\( ( 1 + 686 T + 378663 T^{2} + 254706998 T^{3} + 137858491849 T^{4} )^{2} \))(\( 1 - 181 T + 1045092 T^{2} - 87339735 T^{3} + 629954553255 T^{4} - 52722114809928 T^{5} + 233897715941708715 T^{6} - 12040524145591320015 T^{7} + \)\(53\!\cdots\!44\)\( T^{8} - \)\(34\!\cdots\!81\)\( T^{9} + \)\(70\!\cdots\!93\)\( T^{10} \))(\( 1 - 181 T + 1045092 T^{2} - 87339735 T^{3} + 629954553255 T^{4} - 52722114809928 T^{5} + 233897715941708715 T^{6} - 12040524145591320015 T^{7} + \)\(53\!\cdots\!44\)\( T^{8} - \)\(34\!\cdots\!81\)\( T^{9} + \)\(70\!\cdots\!93\)\( T^{10} \))(\( 1 - 418 T - 196569 T^{2} - 155200474 T^{3} + 137858491849 T^{4} \))(\( ( 1 + 427 T + 371293 T^{2} )( 1 + 775 T + 371293 T^{2} ) \))(\( ( 1 - 1202 T + 371293 T^{2} )( 1 + 775 T + 371293 T^{2} ) \))(\( 1 - 418 T - 196569 T^{2} - 155200474 T^{3} + 137858491849 T^{4} \))(\( ( 1 + 329 T - 263052 T^{2} + 122155397 T^{3} + 137858491849 T^{4} )^{2} \))(\( 1 + 208 T - 231914 T^{2} - 97220864 T^{3} - 78199180517 T^{4} - 36097426257152 T^{5} - 31971314278668986 T^{6} + 10646665746930877456 T^{7} + \)\(19\!\cdots\!01\)\( T^{8} \))(\( 1 + 208 T - 231914 T^{2} - 97220864 T^{3} - 78199180517 T^{4} - 36097426257152 T^{5} - 31971314278668986 T^{6} + 10646665746930877456 T^{7} + \)\(19\!\cdots\!01\)\( T^{8} \))(\( 1 - 273 T - 394701 T^{2} + 345984116 T^{3} - 18757474659 T^{4} - 53737453224027 T^{5} + 66536116005001902 T^{6} - 19952340219908656911 T^{7} - \)\(25\!\cdots\!91\)\( T^{8} + \)\(17\!\cdots\!12\)\( T^{9} - \)\(75\!\cdots\!01\)\( T^{10} - \)\(19\!\cdots\!89\)\( T^{11} + \)\(26\!\cdots\!49\)\( T^{12} \))(\( 1 - 273 T - 394701 T^{2} + 345984116 T^{3} - 18757474659 T^{4} - 53737453224027 T^{5} + 66536116005001902 T^{6} - 19952340219908656911 T^{7} - \)\(25\!\cdots\!91\)\( T^{8} + \)\(17\!\cdots\!12\)\( T^{9} - \)\(75\!\cdots\!01\)\( T^{10} - \)\(19\!\cdots\!89\)\( T^{11} + \)\(26\!\cdots\!49\)\( T^{12} \))(\( ( 1 - 686 T + 91933 T^{2} + 249651178 T^{3} - 169201824908 T^{4} + 92693734833154 T^{5} + 12673744731154117 T^{6} - 35113522607666259302 T^{7} + \)\(19\!\cdots\!01\)\( T^{8} )^{2} \))
$17$ (\( 1 + 543 T + 1400478 T^{2} + 2899206507 T^{3} + 1988478491646 T^{4} + 1094684687943807 T^{5} + 2862423051509815793 T^{6} \))(\( 1 - 543 T + 1400478 T^{2} - 2899206507 T^{3} + 1988478491646 T^{4} - 1094684687943807 T^{5} + 2862423051509815793 T^{6} \))(\( 1 + 2188094 T^{2} + 4213626465219 T^{4} + 4411184157609054206 T^{6} + \)\(40\!\cdots\!01\)\( T^{8} \))(\( 1 + 1140 T + 4980550 T^{2} + 3443850354 T^{3} + 10068870522169 T^{4} + 5069379208548852 T^{5} + 14296356292995309833 T^{6} + \)\(69\!\cdots\!46\)\( T^{7} + \)\(14\!\cdots\!50\)\( T^{8} + \)\(46\!\cdots\!40\)\( T^{9} + \)\(57\!\cdots\!57\)\( T^{10} \))(\( 1 - 1140 T + 4980550 T^{2} - 3443850354 T^{3} + 10068870522169 T^{4} - 5069379208548852 T^{5} + 14296356292995309833 T^{6} - \)\(69\!\cdots\!46\)\( T^{7} + \)\(14\!\cdots\!50\)\( T^{8} - \)\(46\!\cdots\!40\)\( T^{9} + \)\(57\!\cdots\!57\)\( T^{10} \))(\( ( 1 - 594 T + 1419857 T^{2} )^{2} \))(\( ( 1 + 1419857 T^{2} )^{2} \))(\( ( 1 + 1419857 T^{2} )^{2} \))(\( ( 1 + 594 T + 1419857 T^{2} )^{2} \))(\( ( 1 - 2020286 T^{2} + 2015993900449 T^{4} )^{2} \))(\( ( 1 - 1944 T + 2456098 T^{2} - 2760202008 T^{3} + 2015993900449 T^{4} )^{2} \))(\( ( 1 + 1944 T + 2456098 T^{2} + 2760202008 T^{3} + 2015993900449 T^{4} )^{2} \))(\( ( 1 - 543 T + 1400478 T^{2} - 2899206507 T^{3} + 1988478491646 T^{4} - 1094684687943807 T^{5} + 2862423051509815793 T^{6} )^{2} \))(\( ( 1 + 543 T + 1400478 T^{2} + 2899206507 T^{3} + 1988478491646 T^{4} + 1094684687943807 T^{5} + 2862423051509815793 T^{6} )^{2} \))(\( ( 1 + 2188094 T^{2} + 4213626465219 T^{4} + 4411184157609054206 T^{6} + \)\(40\!\cdots\!01\)\( T^{8} )^{2} \))
$19$ (\( 1 - 1410 T + 1123593 T^{2} + 1223470420 T^{3} + 2782127503707 T^{4} - 8644803423499410 T^{5} + 15181127029874798299 T^{6} \))(\( 1 - 1410 T + 1123593 T^{2} + 1223470420 T^{3} + 2782127503707 T^{4} - 8644803423499410 T^{5} + 15181127029874798299 T^{6} \))(\( ( 1 + 1472 T + 3832962 T^{2} + 3644817728 T^{3} + 6131066257801 T^{4} )^{2} \))(\( 1 + 416 T + 5046258 T^{2} + 6215761044 T^{3} + 20272296121125 T^{4} + 15898268281316088 T^{5} + 50196212153221491375 T^{6} + \)\(38\!\cdots\!44\)\( T^{7} + \)\(76\!\cdots\!42\)\( T^{8} + \)\(15\!\cdots\!16\)\( T^{9} + \)\(93\!\cdots\!99\)\( T^{10} \))(\( 1 + 416 T + 5046258 T^{2} + 6215761044 T^{3} + 20272296121125 T^{4} + 15898268281316088 T^{5} + 50196212153221491375 T^{6} + \)\(38\!\cdots\!44\)\( T^{7} + \)\(76\!\cdots\!42\)\( T^{8} + \)\(15\!\cdots\!16\)\( T^{9} + \)\(93\!\cdots\!99\)\( T^{10} \))(\( ( 1 - 836 T + 2476099 T^{2} )^{2} \))(\( ( 1 + 1432 T + 2476099 T^{2} )^{2} \))(\( ( 1 + 1711 T + 2476099 T^{2} )^{2} \))(\( ( 1 - 836 T + 2476099 T^{2} )^{2} \))(\( ( 1 - 1799 T + 2476099 T^{2} )^{4} \))(\( ( 1 + 632 T + 4932498 T^{2} + 1564894568 T^{3} + 6131066257801 T^{4} )^{2} \))(\( ( 1 + 632 T + 4932498 T^{2} + 1564894568 T^{3} + 6131066257801 T^{4} )^{2} \))(\( ( 1 - 1410 T + 1123593 T^{2} + 1223470420 T^{3} + 2782127503707 T^{4} - 8644803423499410 T^{5} + 15181127029874798299 T^{6} )^{2} \))(\( ( 1 - 1410 T + 1123593 T^{2} + 1223470420 T^{3} + 2782127503707 T^{4} - 8644803423499410 T^{5} + 15181127029874798299 T^{6} )^{2} \))(\( ( 1 + 1472 T + 3832962 T^{2} + 3644817728 T^{3} + 6131066257801 T^{4} )^{4} \))
$23$ (\( 1 + 2766 T + 19152933 T^{2} + 33948849540 T^{3} + 123274846244019 T^{4} + 114585730016953134 T^{5} + \)\(26\!\cdots\!07\)\( T^{6} \))(\( 1 - 2766 T + 19152933 T^{2} - 33948849540 T^{3} + 123274846244019 T^{4} - 114585730016953134 T^{5} + \)\(26\!\cdots\!07\)\( T^{6} \))(\( 1 + 19977668 T^{2} + 175780104226854 T^{4} + \)\(82\!\cdots\!32\)\( T^{6} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 - 399 T + 16236442 T^{2} + 15815242731 T^{3} + 114281668162057 T^{4} + 214964375471995932 T^{5} + \)\(73\!\cdots\!51\)\( T^{6} + \)\(65\!\cdots\!19\)\( T^{7} + \)\(43\!\cdots\!94\)\( T^{8} - \)\(68\!\cdots\!99\)\( T^{9} + \)\(11\!\cdots\!43\)\( T^{10} \))(\( 1 + 399 T + 16236442 T^{2} - 15815242731 T^{3} + 114281668162057 T^{4} - 214964375471995932 T^{5} + \)\(73\!\cdots\!51\)\( T^{6} - \)\(65\!\cdots\!19\)\( T^{7} + \)\(43\!\cdots\!94\)\( T^{8} + \)\(68\!\cdots\!99\)\( T^{9} + \)\(11\!\cdots\!43\)\( T^{10} \))(\( 1 - 4104 T + 10406473 T^{2} - 26414751672 T^{3} + 41426511213649 T^{4} \))(\( 1 - 6436343 T^{2} + 41426511213649 T^{4} \))(\( 1 - 6436343 T^{2} + 41426511213649 T^{4} \))(\( 1 + 4104 T + 10406473 T^{2} + 26414751672 T^{3} + 41426511213649 T^{4} \))(\( 1 + 198770 T^{2} - 41387001700749 T^{4} + 8234347633937011730 T^{6} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 + 6804 T + 21901262 T^{2} + 78385264272 T^{3} + 255632710493379 T^{4} + 504514447000237296 T^{5} + \)\(90\!\cdots\!38\)\( T^{6} + \)\(18\!\cdots\!28\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 - 6804 T + 21901262 T^{2} - 78385264272 T^{3} + 255632710493379 T^{4} - 504514447000237296 T^{5} + \)\(90\!\cdots\!38\)\( T^{6} - \)\(18\!\cdots\!28\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 + 2766 T - 11502177 T^{2} - 14920686402 T^{3} + 149657478430830 T^{4} + 82849321261740846 T^{5} - \)\(99\!\cdots\!57\)\( T^{6} + \)\(53\!\cdots\!78\)\( T^{7} + \)\(61\!\cdots\!70\)\( T^{8} - \)\(39\!\cdots\!14\)\( T^{9} - \)\(19\!\cdots\!77\)\( T^{10} + \)\(30\!\cdots\!38\)\( T^{11} + \)\(71\!\cdots\!49\)\( T^{12} \))(\( 1 - 2766 T - 11502177 T^{2} + 14920686402 T^{3} + 149657478430830 T^{4} - 82849321261740846 T^{5} - \)\(99\!\cdots\!57\)\( T^{6} - \)\(53\!\cdots\!78\)\( T^{7} + \)\(61\!\cdots\!70\)\( T^{8} + \)\(39\!\cdots\!14\)\( T^{9} - \)\(19\!\cdots\!77\)\( T^{10} - \)\(30\!\cdots\!38\)\( T^{11} + \)\(71\!\cdots\!49\)\( T^{12} \))(\( 1 - 19977668 T^{2} + 223327114491370 T^{4} - \)\(18\!\cdots\!08\)\( T^{6} + \)\(12\!\cdots\!39\)\( T^{8} - \)\(76\!\cdots\!92\)\( T^{10} + \)\(38\!\cdots\!70\)\( T^{12} - \)\(14\!\cdots\!32\)\( T^{14} + \)\(29\!\cdots\!01\)\( T^{16} \))
$29$ (\( 1 - 3063 T + 45202542 T^{2} - 75644272695 T^{3} + 927156074140758 T^{4} - 1288626255598515663 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} \))(\( 1 + 3063 T + 45202542 T^{2} + 75644272695 T^{3} + 927156074140758 T^{4} + 1288626255598515663 T^{5} + \)\(86\!\cdots\!49\)\( T^{6} \))(\( 1 + 68023478 T^{2} + 1951315900018971 T^{4} + \)\(28\!\cdots\!78\)\( T^{6} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 + 6033 T + 32744932 T^{2} + 82954489011 T^{3} + 288237740873407 T^{4} + 1430006647746298968 T^{5} + \)\(59\!\cdots\!43\)\( T^{6} + \)\(34\!\cdots\!11\)\( T^{7} + \)\(28\!\cdots\!68\)\( T^{8} + \)\(10\!\cdots\!33\)\( T^{9} + \)\(36\!\cdots\!49\)\( T^{10} \))(\( 1 - 6033 T + 32744932 T^{2} - 82954489011 T^{3} + 288237740873407 T^{4} - 1430006647746298968 T^{5} + \)\(59\!\cdots\!43\)\( T^{6} - \)\(34\!\cdots\!11\)\( T^{7} + \)\(28\!\cdots\!68\)\( T^{8} - \)\(10\!\cdots\!33\)\( T^{9} + \)\(36\!\cdots\!49\)\( T^{10} \))(\( 1 - 594 T - 20158313 T^{2} - 12183622506 T^{3} + 420707233300201 T^{4} \))(\( 1 - 20511149 T^{2} + 420707233300201 T^{4} \))(\( 1 - 20511149 T^{2} + 420707233300201 T^{4} \))(\( 1 + 594 T - 20158313 T^{2} + 12183622506 T^{3} + 420707233300201 T^{4} \))(\( 1 - 39031642 T^{2} + 1102761843915963 T^{4} - \)\(16\!\cdots\!42\)\( T^{6} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 + 11664 T + 65809898 T^{2} + 340783588800 T^{3} + 1722290429602299 T^{4} + 6989862966631531200 T^{5} + \)\(27\!\cdots\!98\)\( T^{6} + \)\(10\!\cdots\!36\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 - 11664 T + 65809898 T^{2} - 340783588800 T^{3} + 1722290429602299 T^{4} - 6989862966631531200 T^{5} + \)\(27\!\cdots\!98\)\( T^{6} - \)\(10\!\cdots\!36\)\( T^{7} + \)\(17\!\cdots\!01\)\( T^{8} \))(\( 1 - 3063 T - 35820573 T^{2} + 12833159244 T^{3} + 884415321856221 T^{4} + 971818441032577155 T^{5} - \)\(22\!\cdots\!82\)\( T^{6} + \)\(19\!\cdots\!95\)\( T^{7} + \)\(37\!\cdots\!21\)\( T^{8} + \)\(11\!\cdots\!56\)\( T^{9} - \)\(63\!\cdots\!73\)\( T^{10} - \)\(11\!\cdots\!87\)\( T^{11} + \)\(74\!\cdots\!01\)\( T^{12} \))(\( 1 + 3063 T - 35820573 T^{2} - 12833159244 T^{3} + 884415321856221 T^{4} - 971818441032577155 T^{5} - \)\(22\!\cdots\!82\)\( T^{6} - \)\(19\!\cdots\!95\)\( T^{7} + \)\(37\!\cdots\!21\)\( T^{8} - \)\(11\!\cdots\!56\)\( T^{9} - \)\(63\!\cdots\!73\)\( T^{10} + \)\(11\!\cdots\!87\)\( T^{11} + \)\(74\!\cdots\!01\)\( T^{12} \))(\( 1 - 68023478 T^{2} + 2675877659197513 T^{4} - \)\(75\!\cdots\!82\)\( T^{6} + \)\(16\!\cdots\!56\)\( T^{8} - \)\(31\!\cdots\!82\)\( T^{10} + \)\(47\!\cdots\!13\)\( T^{12} - \)\(50\!\cdots\!78\)\( T^{14} + \)\(31\!\cdots\!01\)\( T^{16} \))
$31$ (\( 1 - 3156 T + 78072333 T^{2} - 162943052312 T^{3} + 2235144610379283 T^{4} - 2586746873711407956 T^{5} + \)\(23\!\cdots\!51\)\( T^{6} \))(\( 1 - 3156 T + 78072333 T^{2} - 162943052312 T^{3} + 2235144610379283 T^{4} - 2586746873711407956 T^{5} + \)\(23\!\cdots\!51\)\( T^{6} \))(\( ( 1 + 2072 T + 57977790 T^{2} + 59319600872 T^{3} + 819628286980801 T^{4} )^{2} \))(\( 1 + 2759 T + 62514558 T^{2} - 8483492775 T^{3} + 1879317626697489 T^{4} - 2373615527060533968 T^{5} + \)\(53\!\cdots\!39\)\( T^{6} - \)\(69\!\cdots\!75\)\( T^{7} + \)\(14\!\cdots\!58\)\( T^{8} + \)\(18\!\cdots\!59\)\( T^{9} + \)\(19\!\cdots\!51\)\( T^{10} \))(\( 1 + 2759 T + 62514558 T^{2} - 8483492775 T^{3} + 1879317626697489 T^{4} - 2373615527060533968 T^{5} + \)\(53\!\cdots\!39\)\( T^{6} - \)\(69\!\cdots\!75\)\( T^{7} + \)\(14\!\cdots\!58\)\( T^{8} + \)\(18\!\cdots\!59\)\( T^{9} + \)\(19\!\cdots\!51\)\( T^{10} \))(\( 1 + 4256 T - 10515615 T^{2} + 121845666656 T^{3} + 819628286980801 T^{4} \))(\( ( 1 - 7601 T + 28629151 T^{2} )( 1 - 2723 T + 28629151 T^{2} ) \))(\( ( 1 - 7601 T + 28629151 T^{2} )( 1 - 2723 T + 28629151 T^{2} ) \))(\( 1 + 4256 T - 10515615 T^{2} + 121845666656 T^{3} + 819628286980801 T^{4} \))(\( ( 1 + 5228 T - 1297167 T^{2} + 149673201428 T^{3} + 819628286980801 T^{4} )^{2} \))(\( 1 + 3328 T - 27162533 T^{2} - 63299175680 T^{3} + 325440737975704 T^{4} - 1812201658718247680 T^{5} - \)\(22\!\cdots\!33\)\( T^{6} + \)\(78\!\cdots\!28\)\( T^{7} + \)\(67\!\cdots\!01\)\( T^{8} \))(\( 1 + 3328 T - 27162533 T^{2} - 63299175680 T^{3} + 325440737975704 T^{4} - 1812201658718247680 T^{5} - \)\(22\!\cdots\!33\)\( T^{6} + \)\(78\!\cdots\!28\)\( T^{7} + \)\(67\!\cdots\!01\)\( T^{8} \))(\( 1 + 3156 T - 68111997 T^{2} - 79489821676 T^{3} + 3345896296586934 T^{4} + 1199858333136257556 T^{5} - \)\(10\!\cdots\!29\)\( T^{6} + \)\(34\!\cdots\!56\)\( T^{7} + \)\(27\!\cdots\!34\)\( T^{8} - \)\(18\!\cdots\!76\)\( T^{9} - \)\(45\!\cdots\!97\)\( T^{10} + \)\(60\!\cdots\!56\)\( T^{11} + \)\(55\!\cdots\!01\)\( T^{12} \))(\( 1 + 3156 T - 68111997 T^{2} - 79489821676 T^{3} + 3345896296586934 T^{4} + 1199858333136257556 T^{5} - \)\(10\!\cdots\!29\)\( T^{6} + \)\(34\!\cdots\!56\)\( T^{7} + \)\(27\!\cdots\!34\)\( T^{8} - \)\(18\!\cdots\!76\)\( T^{9} - \)\(45\!\cdots\!97\)\( T^{10} + \)\(60\!\cdots\!56\)\( T^{11} + \)\(55\!\cdots\!01\)\( T^{12} \))(\( ( 1 - 2072 T - 53684606 T^{2} - 1490779136 T^{3} + 2418885633296515 T^{4} - 42679740992193536 T^{5} - \)\(44\!\cdots\!06\)\( T^{6} - \)\(48\!\cdots\!72\)\( T^{7} + \)\(67\!\cdots\!01\)\( T^{8} )^{2} \))
$37$ (\( 1 - 7143 T + 108119958 T^{2} - 310835233127 T^{3} + 7497465718393806 T^{4} - 34347718172180695407 T^{5} + \)\(33\!\cdots\!93\)\( T^{6} \))(\( 1 - 7143 T + 108119958 T^{2} - 310835233127 T^{3} + 7497465718393806 T^{4} - 34347718172180695407 T^{5} + \)\(33\!\cdots\!93\)\( T^{6} \))(\( ( 1 - 838 T + 86490063 T^{2} - 58110235966 T^{3} + 4808584372417849 T^{4} )^{2} \))(\( 1 + 7586 T + 201201093 T^{2} + 803146672896 T^{3} + 19241810738464926 T^{4} + 60351714230064941916 T^{5} + \)\(13\!\cdots\!82\)\( T^{6} + \)\(38\!\cdots\!04\)\( T^{7} + \)\(67\!\cdots\!49\)\( T^{8} + \)\(17\!\cdots\!86\)\( T^{9} + \)\(16\!\cdots\!57\)\( T^{10} \))(\( 1 + 7586 T + 201201093 T^{2} + 803146672896 T^{3} + 19241810738464926 T^{4} + 60351714230064941916 T^{5} + \)\(13\!\cdots\!82\)\( T^{6} + \)\(38\!\cdots\!04\)\( T^{7} + \)\(67\!\cdots\!49\)\( T^{8} + \)\(17\!\cdots\!86\)\( T^{9} + \)\(16\!\cdots\!57\)\( T^{10} \))(\( ( 1 + 298 T + 69343957 T^{2} )^{2} \))(\( ( 1 - 16550 T + 69343957 T^{2} )^{2} \))(\( ( 1 + 6661 T + 69343957 T^{2} )^{2} \))(\( ( 1 + 298 T + 69343957 T^{2} )^{2} \))(\( ( 1 - 8783 T + 69343957 T^{2} )^{4} \))(\( ( 1 + 9956 T + 151512798 T^{2} + 690388435892 T^{3} + 4808584372417849 T^{4} )^{2} \))(\( ( 1 + 9956 T + 151512798 T^{2} + 690388435892 T^{3} + 4808584372417849 T^{4} )^{2} \))(\( ( 1 - 7143 T + 108119958 T^{2} - 310835233127 T^{3} + 7497465718393806 T^{4} - 34347718172180695407 T^{5} + \)\(33\!\cdots\!93\)\( T^{6} )^{2} \))(\( ( 1 - 7143 T + 108119958 T^{2} - 310835233127 T^{3} + 7497465718393806 T^{4} - 34347718172180695407 T^{5} + \)\(33\!\cdots\!93\)\( T^{6} )^{2} \))(\( ( 1 - 838 T + 86490063 T^{2} - 58110235966 T^{3} + 4808584372417849 T^{4} )^{4} \))
$41$ (\( 1 + 21318 T + 435973047 T^{2} + 4657370441748 T^{3} + 50510180963814447 T^{4} + \)\(28\!\cdots\!18\)\( T^{5} + \)\(15\!\cdots\!01\)\( T^{6} \))(\( 1 - 21318 T + 435973047 T^{2} - 4657370441748 T^{3} + 50510180963814447 T^{4} - \)\(28\!\cdots\!18\)\( T^{5} + \)\(15\!\cdots\!01\)\( T^{6} \))(\( 1 + 451482308 T^{2} + 77787169313251110 T^{4} + \)\(60\!\cdots\!08\)\( T^{6} + \)\(18\!\cdots\!01\)\( T^{8} \))(\( 1 + 18435 T + 457528267 T^{2} + 6389512835910 T^{3} + 92046695080587061 T^{4} + \)\(99\!\cdots\!97\)\( T^{5} + \)\(10\!\cdots\!61\)\( T^{6} + \)\(85\!\cdots\!10\)\( T^{7} + \)\(71\!\cdots\!67\)\( T^{8} + \)\(33\!\cdots\!35\)\( T^{9} + \)\(20\!\cdots\!01\)\( T^{10} \))(\( 1 - 18435 T + 457528267 T^{2} - 6389512835910 T^{3} + 92046695080587061 T^{4} - \)\(99\!\cdots\!97\)\( T^{5} + \)\(10\!\cdots\!61\)\( T^{6} - \)\(85\!\cdots\!10\)\( T^{7} + \)\(71\!\cdots\!67\)\( T^{8} - \)\(33\!\cdots\!35\)\( T^{9} + \)\(20\!\cdots\!01\)\( T^{10} \))(\( 1 + 17226 T + 180878875 T^{2} + 1995738918426 T^{3} + 13422659310152401 T^{4} \))(\( 1 - 115856201 T^{2} + 13422659310152401 T^{4} \))(\( 1 - 115856201 T^{2} + 13422659310152401 T^{4} \))(\( 1 - 17226 T + 180878875 T^{2} - 1995738918426 T^{3} + 13422659310152401 T^{4} \))(\( 1 + 9156974 T^{2} - 13338809137315725 T^{4} + \)\(12\!\cdots\!74\)\( T^{6} + \)\(18\!\cdots\!01\)\( T^{8} \))(\( 1 + 13608 T - 81657310 T^{2} + 477947959776 T^{3} + 36324263378333811 T^{4} + 55373234895348170976 T^{5} - \)\(10\!\cdots\!10\)\( T^{6} + \)\(21\!\cdots\!08\)\( T^{7} + \)\(18\!\cdots\!01\)\( T^{8} \))(\( 1 - 13608 T - 81657310 T^{2} - 477947959776 T^{3} + 36324263378333811 T^{4} - 55373234895348170976 T^{5} - \)\(10\!\cdots\!10\)\( T^{6} - \)\(21\!\cdots\!08\)\( T^{7} + \)\(18\!\cdots\!01\)\( T^{8} \))(\( 1 + 21318 T + 18484077 T^{2} - 20667467550 T^{3} + 40276493669465898 T^{4} + \)\(16\!\cdots\!82\)\( T^{5} - \)\(33\!\cdots\!27\)\( T^{6} + \)\(18\!\cdots\!82\)\( T^{7} + \)\(54\!\cdots\!98\)\( T^{8} - \)\(32\!\cdots\!50\)\( T^{9} + \)\(33\!\cdots\!77\)\( T^{10} + \)\(44\!\cdots\!18\)\( T^{11} + \)\(24\!\cdots\!01\)\( T^{12} \))(\( 1 - 21318 T + 18484077 T^{2} + 20667467550 T^{3} + 40276493669465898 T^{4} - \)\(16\!\cdots\!82\)\( T^{5} - \)\(33\!\cdots\!27\)\( T^{6} - \)\(18\!\cdots\!82\)\( T^{7} + \)\(54\!\cdots\!98\)\( T^{8} + \)\(32\!\cdots\!50\)\( T^{9} + \)\(33\!\cdots\!77\)\( T^{10} - \)\(44\!\cdots\!18\)\( T^{11} + \)\(24\!\cdots\!01\)\( T^{12} \))(\( 1 - 451482308 T^{2} + 126049105123755754 T^{4} - \)\(22\!\cdots\!64\)\( T^{6} + \)\(31\!\cdots\!35\)\( T^{8} - \)\(30\!\cdots\!64\)\( T^{10} + \)\(22\!\cdots\!54\)\( T^{12} - \)\(10\!\cdots\!08\)\( T^{14} + \)\(32\!\cdots\!01\)\( T^{16} \))
$43$ (\( 1 - 18078 T + 490818129 T^{2} - 5010503105108 T^{3} + 72154408940463147 T^{4} - \)\(39\!\cdots\!22\)\( T^{5} + \)\(31\!\cdots\!07\)\( T^{6} \))(\( 1 - 18078 T + 490818129 T^{2} - 5010503105108 T^{3} + 72154408940463147 T^{4} - \)\(39\!\cdots\!22\)\( T^{5} + \)\(31\!\cdots\!07\)\( T^{6} \))(\( ( 1 + 19160 T + 289469058 T^{2} + 2816681767880 T^{3} + 21611482313284249 T^{4} )^{2} \))(\( 1 + 1469 T + 274021497 T^{2} + 2209484086710 T^{3} + 59712901022608185 T^{4} + \)\(32\!\cdots\!87\)\( T^{5} + \)\(87\!\cdots\!55\)\( T^{6} + \)\(47\!\cdots\!90\)\( T^{7} + \)\(87\!\cdots\!79\)\( T^{8} + \)\(68\!\cdots\!69\)\( T^{9} + \)\(68\!\cdots\!43\)\( T^{10} \))(\( 1 + 1469 T + 274021497 T^{2} + 2209484086710 T^{3} + 59712901022608185 T^{4} + \)\(32\!\cdots\!87\)\( T^{5} + \)\(87\!\cdots\!55\)\( T^{6} + \)\(47\!\cdots\!90\)\( T^{7} + \)\(87\!\cdots\!79\)\( T^{8} + \)\(68\!\cdots\!69\)\( T^{9} + \)\(68\!\cdots\!43\)\( T^{10} \))(\( 1 - 12100 T - 598443 T^{2} - 1778802160300 T^{3} + 21611482313284249 T^{4} \))(\( ( 1 - 22475 T + 147008443 T^{2} )( 1 + 19123 T + 147008443 T^{2} ) \))(\( ( 1 - 22475 T + 147008443 T^{2} )( 1 + 19123 T + 147008443 T^{2} ) \))(\( 1 - 12100 T - 598443 T^{2} - 1778802160300 T^{3} + 21611482313284249 T^{4} \))(\( ( 1 + 19976 T + 252032133 T^{2} + 2936640657368 T^{3} + 21611482313284249 T^{4} )^{2} \))(\( 1 + 4960 T - 188409362 T^{2} - 401789383040 T^{3} + 20145544707572395 T^{4} - 59066431614641006720 T^{5} - \)\(40\!\cdots\!38\)\( T^{6} + \)\(15\!\cdots\!20\)\( T^{7} + \)\(46\!\cdots\!01\)\( T^{8} \))(\( 1 + 4960 T - 188409362 T^{2} - 401789383040 T^{3} + 20145544707572395 T^{4} - 59066431614641006720 T^{5} - \)\(40\!\cdots\!38\)\( T^{6} + \)\(15\!\cdots\!20\)\( T^{7} + \)\(46\!\cdots\!01\)\( T^{8} \))(\( 1 + 18078 T - 164004045 T^{2} - 1147996074154 T^{3} + 78168151680455070 T^{4} + \)\(24\!\cdots\!22\)\( T^{5} - \)\(11\!\cdots\!01\)\( T^{6} + \)\(35\!\cdots\!46\)\( T^{7} + \)\(16\!\cdots\!30\)\( T^{8} - \)\(36\!\cdots\!78\)\( T^{9} - \)\(76\!\cdots\!45\)\( T^{10} + \)\(12\!\cdots\!54\)\( T^{11} + \)\(10\!\cdots\!49\)\( T^{12} \))(\( 1 + 18078 T - 164004045 T^{2} - 1147996074154 T^{3} + 78168151680455070 T^{4} + \)\(24\!\cdots\!22\)\( T^{5} - \)\(11\!\cdots\!01\)\( T^{6} + \)\(35\!\cdots\!46\)\( T^{7} + \)\(16\!\cdots\!30\)\( T^{8} - \)\(36\!\cdots\!78\)\( T^{9} - \)\(76\!\cdots\!45\)\( T^{10} + \)\(12\!\cdots\!54\)\( T^{11} + \)\(10\!\cdots\!49\)\( T^{12} \))(\( ( 1 - 19160 T + 77636542 T^{2} + 87136384480 T^{3} + 8213230553542315 T^{4} + 12809784211054164640 T^{5} + \)\(16\!\cdots\!58\)\( T^{6} - \)\(60\!\cdots\!20\)\( T^{7} + \)\(46\!\cdots\!01\)\( T^{8} )^{2} \))
$47$ (\( 1 - 41256 T + 1083114141 T^{2} - 18501711697584 T^{3} + 248406820249443987 T^{4} - \)\(21\!\cdots\!44\)\( T^{5} + \)\(12\!\cdots\!43\)\( T^{6} \))(\( 1 + 41256 T + 1083114141 T^{2} + 18501711697584 T^{3} + 248406820249443987 T^{4} + \)\(21\!\cdots\!44\)\( T^{5} + \)\(12\!\cdots\!43\)\( T^{6} \))(\( 1 + 367391324 T^{2} + 135388412358208134 T^{4} + \)\(19\!\cdots\!76\)\( T^{6} + \)\(27\!\cdots\!01\)\( T^{8} \))(\( 1 + 25155 T + 1034020258 T^{2} + 20179979725617 T^{3} + 464012894081647969 T^{4} + \)\(66\!\cdots\!16\)\( T^{5} + \)\(10\!\cdots\!83\)\( T^{6} + \)\(10\!\cdots\!33\)\( T^{7} + \)\(12\!\cdots\!94\)\( T^{8} + \)\(69\!\cdots\!55\)\( T^{9} + \)\(63\!\cdots\!07\)\( T^{10} \))(\( 1 - 25155 T + 1034020258 T^{2} - 20179979725617 T^{3} + 464012894081647969 T^{4} - \)\(66\!\cdots\!16\)\( T^{5} + \)\(10\!\cdots\!83\)\( T^{6} - \)\(10\!\cdots\!33\)\( T^{7} + \)\(12\!\cdots\!94\)\( T^{8} - \)\(69\!\cdots\!55\)\( T^{9} + \)\(63\!\cdots\!07\)\( T^{10} \))(\( 1 - 1296 T - 227665391 T^{2} - 297231129072 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 229345007 T^{2} + 52599132235830049 T^{4} \))(\( 1 - 229345007 T^{2} + 52599132235830049 T^{4} \))(\( 1 + 1296 T - 227665391 T^{2} + 297231129072 T^{3} + 52599132235830049 T^{4} \))(\( 1 - 341046910 T^{2} + 63713862584718051 T^{4} - \)\(17\!\cdots\!90\)\( T^{6} + \)\(27\!\cdots\!01\)\( T^{8} \))(\( 1 + 18468 T + 28570670 T^{2} - 2699904512880 T^{3} - 33167179979285901 T^{4} - \)\(61\!\cdots\!60\)\( T^{5} + \)\(15\!\cdots\!30\)\( T^{6} + \)\(22\!\cdots\!24\)\( T^{7} + \)\(27\!\cdots\!01\)\( T^{8} \))(\( 1 - 18468 T + 28570670 T^{2} + 2699904512880 T^{3} - 33167179979285901 T^{4} + \)\(61\!\cdots\!60\)\( T^{5} + \)\(15\!\cdots\!30\)\( T^{6} - \)\(22\!\cdots\!24\)\( T^{7} + \)\(27\!\cdots\!01\)\( T^{8} \))(\( 1 - 41256 T + 618943395 T^{2} - 7681533605928 T^{3} + 161422804389198390 T^{4} - \)\(17\!\cdots\!44\)\( T^{5} + \)\(78\!\cdots\!11\)\( T^{6} - \)\(39\!\cdots\!08\)\( T^{7} + \)\(84\!\cdots\!10\)\( T^{8} - \)\(92\!\cdots\!04\)\( T^{9} + \)\(17\!\cdots\!95\)\( T^{10} - \)\(26\!\cdots\!92\)\( T^{11} + \)\(14\!\cdots\!49\)\( T^{12} \))(\( 1 + 41256 T + 618943395 T^{2} + 7681533605928 T^{3} + 161422804389198390 T^{4} + \)\(17\!\cdots\!44\)\( T^{5} + \)\(78\!\cdots\!11\)\( T^{6} + \)\(39\!\cdots\!08\)\( T^{7} + \)\(84\!\cdots\!10\)\( T^{8} + \)\(92\!\cdots\!04\)\( T^{9} + \)\(17\!\cdots\!95\)\( T^{10} + \)\(26\!\cdots\!92\)\( T^{11} + \)\(14\!\cdots\!49\)\( T^{12} \))(\( 1 - 367391324 T^{2} - 412027407735158 T^{4} - \)\(11\!\cdots\!64\)\( T^{6} + \)\(84\!\cdots\!31\)\( T^{8} - \)\(58\!\cdots\!36\)\( T^{10} - \)\(11\!\cdots\!58\)\( T^{12} - \)\(53\!\cdots\!76\)\( T^{14} + \)\(76\!\cdots\!01\)\( T^{16} \))
$53$ (\( 1 - 11874 T + 402605979 T^{2} - 12066273873516 T^{3} + 168368005872652647 T^{4} - \)\(20\!\cdots\!26\)\( T^{5} + \)\(73\!\cdots\!57\)\( T^{6} \))(\( 1 + 11874 T + 402605979 T^{2} + 12066273873516 T^{3} + 168368005872652647 T^{4} + \)\(20\!\cdots\!26\)\( T^{5} + \)\(73\!\cdots\!57\)\( T^{6} \))(\( 1 + 728451284 T^{2} + 478272292253360790 T^{4} + \)\(12\!\cdots\!16\)\( T^{6} + \)\(30\!\cdots\!01\)\( T^{8} \))(\( 1 + 58422 T + 3354568213 T^{2} + 110313236959296 T^{3} + 3390725554692289246 T^{4} + \)\(71\!\cdots\!28\)\( T^{5} + \)\(14\!\cdots\!78\)\( T^{6} + \)\(19\!\cdots\!04\)\( T^{7} + \)\(24\!\cdots\!41\)\( T^{8} + \)\(17\!\cdots\!22\)\( T^{9} + \)\(12\!\cdots\!93\)\( T^{10} \))(\( 1 - 58422 T + 3354568213 T^{2} - 110313236959296 T^{3} + 3390725554692289246 T^{4} - \)\(71\!\cdots\!28\)\( T^{5} + \)\(14\!\cdots\!78\)\( T^{6} - \)\(19\!\cdots\!04\)\( T^{7} + \)\(24\!\cdots\!41\)\( T^{8} - \)\(17\!\cdots\!22\)\( T^{9} + \)\(12\!\cdots\!93\)\( T^{10} \))(\( ( 1 - 19494 T + 418195493 T^{2} )^{2} \))(\( ( 1 + 418195493 T^{2} )^{2} \))(\( ( 1 + 418195493 T^{2} )^{2} \))(\( ( 1 + 19494 T + 418195493 T^{2} )^{2} \))(\( ( 1 - 31068470 T^{2} + 174887470365513049 T^{4} )^{2} \))(\( ( 1 + 11664 T + 484234009 T^{2} + 4877832230352 T^{3} + 174887470365513049 T^{4} )^{2} \))(\( ( 1 - 11664 T + 484234009 T^{2} - 4877832230352 T^{3} + 174887470365513049 T^{4} )^{2} \))(\( ( 1 + 11874 T + 402605979 T^{2} + 12066273873516 T^{3} + 168368005872652647 T^{4} + \)\(20\!\cdots\!26\)\( T^{5} + \)\(73\!\cdots\!57\)\( T^{6} )^{2} \))(\( ( 1 - 11874 T + 402605979 T^{2} - 12066273873516 T^{3} + 168368005872652647 T^{4} - \)\(20\!\cdots\!26\)\( T^{5} + \)\(73\!\cdots\!57\)\( T^{6} )^{2} \))(\( ( 1 + 728451284 T^{2} + 478272292253360790 T^{4} + \)\(12\!\cdots\!16\)\( T^{6} + \)\(30\!\cdots\!01\)\( T^{8} )^{2} \))
$59$ (\( 1 + 92964 T + 4241750433 T^{2} + 131176669224216 T^{3} + 3032530454845471467 T^{4} + \)\(47\!\cdots\!64\)\( T^{5} + \)\(36\!\cdots\!99\)\( T^{6} \))(\( 1 - 92964 T + 4241750433 T^{2} - 131176669224216 T^{3} + 3032530454845471467 T^{4} - \)\(47\!\cdots\!64\)\( T^{5} + \)\(36\!\cdots\!99\)\( T^{6} \))(\( 1 + 1998785708 T^{2} + 1995662264722641366 T^{4} + \)\(10\!\cdots\!08\)\( T^{6} + \)\(26\!\cdots\!01\)\( T^{8} \))(\( 1 + 90537 T + 5365830529 T^{2} + 236000523803862 T^{3} + 8392018437003638425 T^{4} + \)\(24\!\cdots\!43\)\( T^{5} + \)\(59\!\cdots\!75\)\( T^{6} + \)\(12\!\cdots\!62\)\( T^{7} + \)\(19\!\cdots\!71\)\( T^{8} + \)\(23\!\cdots\!37\)\( T^{9} + \)\(18\!\cdots\!99\)\( T^{10} \))(\( 1 - 90537 T + 5365830529 T^{2} - 236000523803862 T^{3} + 8392018437003638425 T^{4} - \)\(24\!\cdots\!43\)\( T^{5} + \)\(59\!\cdots\!75\)\( T^{6} - \)\(12\!\cdots\!62\)\( T^{7} + \)\(19\!\cdots\!71\)\( T^{8} - \)\(23\!\cdots\!37\)\( T^{9} + \)\(18\!\cdots\!99\)\( T^{10} \))(\( 1 - 7668 T - 656126075 T^{2} - 5482039524732 T^{3} + 511116753300641401 T^{4} \))(\( 1 - 714924299 T^{2} + 511116753300641401 T^{4} \))(\( 1 - 714924299 T^{2} + 511116753300641401 T^{4} \))(\( 1 + 7668 T - 656126075 T^{2} + 5482039524732 T^{3} + 511116753300641401 T^{4} \))(\( 1 - 1396994998 T^{2} + 1440478271136378603 T^{4} - \)\(71\!\cdots\!98\)\( T^{6} + \)\(26\!\cdots\!01\)\( T^{8} \))(\( 1 + 1944 T - 957504550 T^{2} - 910890188928 T^{3} + 410247775513479531 T^{4} - \)\(65\!\cdots\!72\)\( T^{5} - \)\(48\!\cdots\!50\)\( T^{6} + \)\(71\!\cdots\!56\)\( T^{7} + \)\(26\!\cdots\!01\)\( T^{8} \))(\( 1 - 1944 T - 957504550 T^{2} + 910890188928 T^{3} + 410247775513479531 T^{4} + \)\(65\!\cdots\!72\)\( T^{5} - \)\(48\!\cdots\!50\)\( T^{6} - \)\(71\!\cdots\!56\)\( T^{7} + \)\(26\!\cdots\!01\)\( T^{8} \))(\( 1 + 92964 T + 4400554863 T^{2} + 131976748804980 T^{3} + 2765208403250199798 T^{4} + \)\(40\!\cdots\!16\)\( T^{5} + \)\(65\!\cdots\!47\)\( T^{6} + \)\(28\!\cdots\!84\)\( T^{7} + \)\(14\!\cdots\!98\)\( T^{8} + \)\(48\!\cdots\!20\)\( T^{9} + \)\(11\!\cdots\!63\)\( T^{10} + \)\(17\!\cdots\!36\)\( T^{11} + \)\(13\!\cdots\!01\)\( T^{12} \))(\( 1 - 92964 T + 4400554863 T^{2} - 131976748804980 T^{3} + 2765208403250199798 T^{4} - \)\(40\!\cdots\!16\)\( T^{5} + \)\(65\!\cdots\!47\)\( T^{6} - \)\(28\!\cdots\!84\)\( T^{7} + \)\(14\!\cdots\!98\)\( T^{8} - \)\(48\!\cdots\!20\)\( T^{9} + \)\(11\!\cdots\!63\)\( T^{10} - \)\(17\!\cdots\!36\)\( T^{11} + \)\(13\!\cdots\!01\)\( T^{12} \))(\( 1 - 1998785708 T^{2} + 1999482041782419898 T^{4} - \)\(19\!\cdots\!12\)\( T^{6} + \)\(16\!\cdots\!91\)\( T^{8} - \)\(99\!\cdots\!12\)\( T^{10} + \)\(52\!\cdots\!98\)\( T^{12} - \)\(26\!\cdots\!08\)\( T^{14} + \)\(68\!\cdots\!01\)\( T^{16} \))
$61$ (\( 1 - 53439 T + 3142629438 T^{2} - 92218187357903 T^{3} + 2654253198748508838 T^{4} - \)\(38\!\cdots\!39\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} \))(\( 1 - 53439 T + 3142629438 T^{2} - 92218187357903 T^{3} + 2654253198748508838 T^{4} - \)\(38\!\cdots\!39\)\( T^{5} + \)\(60\!\cdots\!01\)\( T^{6} \))(\( ( 1 + 60098 T + 2094592503 T^{2} + 50758548497498 T^{3} + 713342911662882601 T^{4} )^{2} \))(\( 1 + 1403 T + 3538874292 T^{2} + 2256100311765 T^{3} + 5454602684103950271 T^{4} + \)\(18\!\cdots\!56\)\( T^{5} + \)\(46\!\cdots\!71\)\( T^{6} + \)\(16\!\cdots\!65\)\( T^{7} + \)\(21\!\cdots\!92\)\( T^{8} + \)\(71\!\cdots\!03\)\( T^{9} + \)\(42\!\cdots\!01\)\( T^{10} \))(\( 1 + 1403 T + 3538874292 T^{2} + 2256100311765 T^{3} + 5454602684103950271 T^{4} + \)\(18\!\cdots\!56\)\( T^{5} + \)\(46\!\cdots\!71\)\( T^{6} + \)\(16\!\cdots\!65\)\( T^{7} + \)\(21\!\cdots\!92\)\( T^{8} + \)\(71\!\cdots\!03\)\( T^{9} + \)\(42\!\cdots\!01\)\( T^{10} \))(\( 1 - 34738 T + 362132343 T^{2} - 29339586304138 T^{3} + 713342911662882601 T^{4} \))(\( ( 1 - 56927 T + 844596301 T^{2} )( 1 + 18301 T + 844596301 T^{2} ) \))(\( ( 1 + 18301 T + 844596301 T^{2} )( 1 + 38626 T + 844596301 T^{2} ) \))(\( 1 - 34738 T + 362132343 T^{2} - 29339586304138 T^{3} + 713342911662882601 T^{4} \))(\( ( 1 - 1069 T - 843453540 T^{2} - 902873445769 T^{3} + 713342911662882601 T^{4} )^{2} \))(\( 1 + 8176 T + 82549030 T^{2} - 13939218707456 T^{3} - 769555065825699461 T^{4} - \)\(11\!\cdots\!56\)\( T^{5} + \)\(58\!\cdots\!30\)\( T^{6} + \)\(49\!\cdots\!76\)\( T^{7} + \)\(50\!\cdots\!01\)\( T^{8} \))(\( 1 + 8176 T + 82549030 T^{2} - 13939218707456 T^{3} - 769555065825699461 T^{4} - \)\(11\!\cdots\!56\)\( T^{5} + \)\(58\!\cdots\!30\)\( T^{6} + \)\(49\!\cdots\!76\)\( T^{7} + \)\(50\!\cdots\!01\)\( T^{8} \))(\( 1 + 53439 T - 286902717 T^{2} - 16497400178524 T^{3} + 2293818871616708589 T^{4} + \)\(44\!\cdots\!89\)\( T^{5} - \)\(66\!\cdots\!54\)\( T^{6} + \)\(37\!\cdots\!89\)\( T^{7} + \)\(16\!\cdots\!89\)\( T^{8} - \)\(99\!\cdots\!24\)\( T^{9} - \)\(14\!\cdots\!17\)\( T^{10} + \)\(22\!\cdots\!39\)\( T^{11} + \)\(36\!\cdots\!01\)\( T^{12} \))(\( 1 + 53439 T - 286902717 T^{2} - 16497400178524 T^{3} + 2293818871616708589 T^{4} + \)\(44\!\cdots\!89\)\( T^{5} - \)\(66\!\cdots\!54\)\( T^{6} + \)\(37\!\cdots\!89\)\( T^{7} + \)\(16\!\cdots\!89\)\( T^{8} - \)\(99\!\cdots\!24\)\( T^{9} - \)\(14\!\cdots\!17\)\( T^{10} + \)\(22\!\cdots\!39\)\( T^{11} + \)\(36\!\cdots\!01\)\( T^{12} \))(\( ( 1 - 60098 T + 1517177101 T^{2} - 24363723250298 T^{3} + 623487594358287604 T^{4} - \)\(20\!\cdots\!98\)\( T^{5} + \)\(10\!\cdots\!01\)\( T^{6} - \)\(36\!\cdots\!98\)\( T^{7} + \)\(50\!\cdots\!01\)\( T^{8} )^{2} \))
$67$ (\( 1 - 53826 T + 1934468313 T^{2} - 45752080329452 T^{3} + 2611774238077234491 T^{4} - \)\(98\!\cdots\!74\)\( T^{5} + \)\(24\!\cdots\!43\)\( T^{6} \))(\( 1 - 53826 T + 1934468313 T^{2} - 45752080329452 T^{3} + 2611774238077234491 T^{4} - \)\(98\!\cdots\!74\)\( T^{5} + \)\(24\!\cdots\!43\)\( T^{6} \))(\( ( 1 + 53648 T + 3394214562 T^{2} + 72431511740336 T^{3} + 1822837804551761449 T^{4} )^{2} \))(\( 1 + 13907 T + 4070090193 T^{2} - 10411373671926 T^{3} + 6695736735425021001 T^{4} - \)\(80\!\cdots\!07\)\( T^{5} + \)\(90\!\cdots\!07\)\( T^{6} - \)\(18\!\cdots\!74\)\( T^{7} + \)\(10\!\cdots\!99\)\( T^{8} + \)\(46\!\cdots\!07\)\( T^{9} + \)\(44\!\cdots\!07\)\( T^{10} \))(\( 1 + 13907 T + 4070090193 T^{2} - 10411373671926 T^{3} + 6695736735425021001 T^{4} - \)\(80\!\cdots\!07\)\( T^{5} + \)\(90\!\cdots\!07\)\( T^{6} - \)\(18\!\cdots\!74\)\( T^{7} + \)\(10\!\cdots\!99\)\( T^{8} + \)\(46\!\cdots\!07\)\( T^{9} + \)\(44\!\cdots\!07\)\( T^{10} \))(\( 1 + 21812 T - 874361763 T^{2} + 29448928833884 T^{3} + 1822837804551761449 T^{4} \))(\( ( 1 - 73475 T + 1350125107 T^{2} )( 1 + 37939 T + 1350125107 T^{2} ) \))(\( ( 1 - 73475 T + 1350125107 T^{2} )( 1 + 35536 T + 1350125107 T^{2} ) \))(\( 1 + 21812 T - 874361763 T^{2} + 29448928833884 T^{3} + 1822837804551761449 T^{4} \))(\( ( 1 - 62077 T + 2503428822 T^{2} - 83811716267239 T^{3} + 1822837804551761449 T^{4} )^{2} \))(\( 1 + 90064 T + 4055895358 T^{2} + 122070811385536 T^{3} + 3673714317894632923 T^{4} + \)\(16\!\cdots\!52\)\( T^{5} + \)\(73\!\cdots\!42\)\( T^{6} + \)\(22\!\cdots\!52\)\( T^{7} + \)\(33\!\cdots\!01\)\( T^{8} \))(\( 1 + 90064 T + 4055895358 T^{2} + 122070811385536 T^{3} + 3673714317894632923 T^{4} + \)\(16\!\cdots\!52\)\( T^{5} + \)\(73\!\cdots\!42\)\( T^{6} + \)\(22\!\cdots\!52\)\( T^{7} + \)\(33\!\cdots\!01\)\( T^{8} \))(\( 1 + 53826 T + 962769963 T^{2} + 12620530756634 T^{3} - 1332258059889251874 T^{4} - \)\(94\!\cdots\!82\)\( T^{5} - \)\(33\!\cdots\!17\)\( T^{6} - \)\(12\!\cdots\!74\)\( T^{7} - \)\(24\!\cdots\!26\)\( T^{8} + \)\(31\!\cdots\!62\)\( T^{9} + \)\(31\!\cdots\!63\)\( T^{10} + \)\(24\!\cdots\!82\)\( T^{11} + \)\(60\!\cdots\!49\)\( T^{12} \))(\( 1 + 53826 T + 962769963 T^{2} + 12620530756634 T^{3} - 1332258059889251874 T^{4} - \)\(94\!\cdots\!82\)\( T^{5} - \)\(33\!\cdots\!17\)\( T^{6} - \)\(12\!\cdots\!74\)\( T^{7} - \)\(24\!\cdots\!26\)\( T^{8} + \)\(31\!\cdots\!62\)\( T^{9} + \)\(31\!\cdots\!63\)\( T^{10} + \)\(24\!\cdots\!82\)\( T^{11} + \)\(60\!\cdots\!49\)\( T^{12} \))(\( ( 1 - 53648 T - 516106658 T^{2} - 37229799341504 T^{3} + 5812048946495544667 T^{4} - \)\(50\!\cdots\!28\)\( T^{5} - \)\(94\!\cdots\!42\)\( T^{6} - \)\(13\!\cdots\!64\)\( T^{7} + \)\(33\!\cdots\!01\)\( T^{8} )^{2} \))
$71$ (\( 1 - 31866 T + 5363863701 T^{2} - 115003148710092 T^{3} + 9677640324107688051 T^{4} - \)\(10\!\cdots\!66\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} \))(\( 1 + 31866 T + 5363863701 T^{2} + 115003148710092 T^{3} + 9677640324107688051 T^{4} + \)\(10\!\cdots\!66\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} \))(\( 1 - 65314012 T^{2} + 4689386407931107110 T^{4} - \)\(21\!\cdots\!12\)\( T^{6} + \)\(10\!\cdots\!01\)\( T^{8} \))(\( 1 + 114684 T + 7758380659 T^{2} + 426246123888336 T^{3} + 19260501229393543450 T^{4} + \)\(77\!\cdots\!40\)\( T^{5} + \)\(34\!\cdots\!50\)\( T^{6} + \)\(13\!\cdots\!36\)\( T^{7} + \)\(45\!\cdots\!09\)\( T^{8} + \)\(12\!\cdots\!84\)\( T^{9} + \)\(19\!\cdots\!51\)\( T^{10} \))(\( 1 - 114684 T + 7758380659 T^{2} - 426246123888336 T^{3} + 19260501229393543450 T^{4} - \)\(77\!\cdots\!40\)\( T^{5} + \)\(34\!\cdots\!50\)\( T^{6} - \)\(13\!\cdots\!36\)\( T^{7} + \)\(45\!\cdots\!09\)\( T^{8} - \)\(12\!\cdots\!84\)\( T^{9} + \)\(19\!\cdots\!51\)\( T^{10} \))(\( ( 1 + 46872 T + 1804229351 T^{2} )^{2} \))(\( ( 1 + 1804229351 T^{2} )^{2} \))(\( ( 1 + 1804229351 T^{2} )^{2} \))(\( ( 1 - 46872 T + 1804229351 T^{2} )^{2} \))(\( ( 1 + 1457026126 T^{2} + 3255243551009881201 T^{4} )^{2} \))(\( ( 1 + 44712 T + 2046094414 T^{2} + 80670702741912 T^{3} + 3255243551009881201 T^{4} )^{2} \))(\( ( 1 - 44712 T + 2046094414 T^{2} - 80670702741912 T^{3} + 3255243551009881201 T^{4} )^{2} \))(\( ( 1 + 31866 T + 5363863701 T^{2} + 115003148710092 T^{3} + 9677640324107688051 T^{4} + \)\(10\!\cdots\!66\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} )^{2} \))(\( ( 1 - 31866 T + 5363863701 T^{2} - 115003148710092 T^{3} + 9677640324107688051 T^{4} - \)\(10\!\cdots\!66\)\( T^{5} + \)\(58\!\cdots\!51\)\( T^{6} )^{2} \))(\( ( 1 - 65314012 T^{2} + 4689386407931107110 T^{4} - \)\(21\!\cdots\!12\)\( T^{6} + \)\(10\!\cdots\!01\)\( T^{8} )^{2} \))
$73$ (\( 1 - 123765 T + 10300430238 T^{2} - 540333156371105 T^{3} + 21353529322076029134 T^{4} - \)\(53\!\cdots\!85\)\( T^{5} + \)\(89\!\cdots\!57\)\( T^{6} \))(\( 1 - 123765 T + 10300430238 T^{2} - 540333156371105 T^{3} + 21353529322076029134 T^{4} - \)\(53\!\cdots\!85\)\( T^{5} + \)\(89\!\cdots\!57\)\( T^{6} \))(\( ( 1 + 46190 T + 3864348579 T^{2} + 95755176880670 T^{3} + 4297625829703557649 T^{4} )^{2} \))(\( 1 - 7600 T + 3606834246 T^{2} - 31056473559714 T^{3} + 12288417972789256281 T^{4} - \)\(80\!\cdots\!84\)\( T^{5} + \)\(25\!\cdots\!33\)\( T^{6} - \)\(13\!\cdots\!86\)\( T^{7} + \)\(32\!\cdots\!22\)\( T^{8} - \)\(14\!\cdots\!00\)\( T^{9} + \)\(38\!\cdots\!93\)\( T^{10} \))(\( 1 - 7600 T + 3606834246 T^{2} - 31056473559714 T^{3} + 12288417972789256281 T^{4} - \)\(80\!\cdots\!84\)\( T^{5} + \)\(25\!\cdots\!33\)\( T^{6} - \)\(13\!\cdots\!86\)\( T^{7} + \)\(32\!\cdots\!22\)\( T^{8} - \)\(14\!\cdots\!00\)\( T^{9} + \)\(38\!\cdots\!93\)\( T^{10} \))(\( ( 1 - 67562 T + 2073071593 T^{2} )^{2} \))(\( ( 1 + 1450 T + 2073071593 T^{2} )^{2} \))(\( ( 1 - 79577 T + 2073071593 T^{2} )^{2} \))(\( ( 1 - 67562 T + 2073071593 T^{2} )^{2} \))(\( ( 1 + 48079 T + 2073071593 T^{2} )^{4} \))(\( ( 1 + 121214 T + 6975764499 T^{2} + 251285300073902 T^{3} + 4297625829703557649 T^{4} )^{2} \))(\( ( 1 + 121214 T + 6975764499 T^{2} + 251285300073902 T^{3} + 4297625829703557649 T^{4} )^{2} \))(\( ( 1 - 123765 T + 10300430238 T^{2} - 540333156371105 T^{3} + 21353529322076029134 T^{4} - \)\(53\!\cdots\!85\)\( T^{5} + \)\(89\!\cdots\!57\)\( T^{6} )^{2} \))(\( ( 1 - 123765 T + 10300430238 T^{2} - 540333156371105 T^{3} + 21353529322076029134 T^{4} - \)\(53\!\cdots\!85\)\( T^{5} + \)\(89\!\cdots\!57\)\( T^{6} )^{2} \))(\( ( 1 + 46190 T + 3864348579 T^{2} + 95755176880670 T^{3} + 4297625829703557649 T^{4} )^{4} \))
$79$ (\( 1 - 129534 T + 12729649965 T^{2} - 811215903905732 T^{3} + 39169850881833376035 T^{4} - \)\(12\!\cdots\!34\)\( T^{5} + \)\(29\!\cdots\!99\)\( T^{6} \))(\( 1 - 129534 T + 12729649965 T^{2} - 811215903905732 T^{3} + 39169850881833376035 T^{4} - \)\(12\!\cdots\!34\)\( T^{5} + \)\(29\!\cdots\!99\)\( T^{6} \))(\( ( 1 - 2512 T - 2000773254 T^{2} - 7729565674288 T^{3} + 9468276082626847201 T^{4} )^{2} \))(\( 1 + 29993 T + 6251931678 T^{2} - 85699438105257 T^{3} + 15422207141619743649 T^{4} - \)\(73\!\cdots\!92\)\( T^{5} + \)\(47\!\cdots\!51\)\( T^{6} - \)\(81\!\cdots\!57\)\( T^{7} + \)\(18\!\cdots\!22\)\( T^{8} + \)\(26\!\cdots\!93\)\( T^{9} + \)\(27\!\cdots\!99\)\( T^{10} \))(\( 1 + 29993 T + 6251931678 T^{2} - 85699438105257 T^{3} + 15422207141619743649 T^{4} - \)\(73\!\cdots\!92\)\( T^{5} + \)\(47\!\cdots\!51\)\( T^{6} - \)\(81\!\cdots\!57\)\( T^{7} + \)\(18\!\cdots\!22\)\( T^{8} + \)\(26\!\cdots\!93\)\( T^{9} + \)\(27\!\cdots\!99\)\( T^{10} \))(\( 1 - 76912 T + 2838399345 T^{2} - 236662561759888 T^{3} + 9468276082626847201 T^{4} \))(\( ( 1 - 90857 T + 3077056399 T^{2} )( 1 - 9707 T + 3077056399 T^{2} ) \))(\( ( 1 - 9707 T + 3077056399 T^{2} )( 1 + 100564 T + 3077056399 T^{2} ) \))(\( 1 - 76912 T + 2838399345 T^{2} - 236662561759888 T^{3} + 9468276082626847201 T^{4} \))(\( ( 1 + 49979 T - 579155958 T^{2} + 153788201765621 T^{3} + 9468276082626847201 T^{4} )^{2} \))(\( 1 + 28768 T - 3190116830 T^{2} - 61459901806592 T^{3} + 4127189778201816739 T^{4} - \)\(18\!\cdots\!08\)\( T^{5} - \)\(30\!\cdots\!30\)\( T^{6} + \)\(83\!\cdots\!32\)\( T^{7} + \)\(89\!\cdots\!01\)\( T^{8} \))(\( 1 + 28768 T - 3190116830 T^{2} - 61459901806592 T^{3} + 4127189778201816739 T^{4} - \)\(18\!\cdots\!08\)\( T^{5} - \)\(30\!\cdots\!30\)\( T^{6} + \)\(83\!\cdots\!32\)\( T^{7} + \)\(89\!\cdots\!01\)\( T^{8} \))(\( 1 + 129534 T + 4049407191 T^{2} + 26490670754846 T^{3} + 17794096453066036302 T^{4} + \)\(14\!\cdots\!34\)\( T^{5} + \)\(58\!\cdots\!91\)\( T^{6} + \)\(43\!\cdots\!66\)\( T^{7} + \)\(16\!\cdots\!02\)\( T^{8} + \)\(77\!\cdots\!54\)\( T^{9} + \)\(36\!\cdots\!91\)\( T^{10} + \)\(35\!\cdots\!66\)\( T^{11} + \)\(84\!\cdots\!01\)\( T^{12} \))(\( 1 + 129534 T + 4049407191 T^{2} + 26490670754846 T^{3} + 17794096453066036302 T^{4} + \)\(14\!\cdots\!34\)\( T^{5} + \)\(58\!\cdots\!91\)\( T^{6} + \)\(43\!\cdots\!66\)\( T^{7} + \)\(16\!\cdots\!02\)\( T^{8} + \)\(77\!\cdots\!54\)\( T^{9} + \)\(36\!\cdots\!91\)\( T^{10} + \)\(35\!\cdots\!66\)\( T^{11} + \)\(84\!\cdots\!01\)\( T^{12} \))(\( ( 1 + 2512 T + 2007083398 T^{2} - 20485073762624 T^{3} - 5484599137678910141 T^{4} - \)\(63\!\cdots\!76\)\( T^{5} + \)\(19\!\cdots\!98\)\( T^{6} + \)\(73\!\cdots\!88\)\( T^{7} + \)\(89\!\cdots\!01\)\( T^{8} )^{2} \))
$83$ (\( 1 - 226584 T + 25210795929 T^{2} - 1851024586107024 T^{3} + 99306349806709942347 T^{4} - \)\(35\!\cdots\!16\)\( T^{5} + \)\(61\!\cdots\!07\)\( T^{6} \))(\( 1 + 226584 T + 25210795929 T^{2} + 1851024586107024 T^{3} + 99306349806709942347 T^{4} + \)\(35\!\cdots\!16\)\( T^{5} + \)\(61\!\cdots\!07\)\( T^{6} \))(\( 1 + 9492423500 T^{2} + 44942056330712675766 T^{4} + \)\(14\!\cdots\!00\)\( T^{6} + \)\(24\!\cdots\!01\)\( T^{8} \))(\( 1 + 228951 T + 31015128418 T^{2} + 2949331181889681 T^{3} + \)\(22\!\cdots\!25\)\( T^{4} + \)\(14\!\cdots\!60\)\( T^{5} + \)\(88\!\cdots\!75\)\( T^{6} + \)\(45\!\cdots\!69\)\( T^{7} + \)\(18\!\cdots\!26\)\( T^{8} + \)\(55\!\cdots\!51\)\( T^{9} + \)\(94\!\cdots\!43\)\( T^{10} \))(\( 1 - 228951 T + 31015128418 T^{2} - 2949331181889681 T^{3} + \)\(22\!\cdots\!25\)\( T^{4} - \)\(14\!\cdots\!60\)\( T^{5} + \)\(88\!\cdots\!75\)\( T^{6} - \)\(45\!\cdots\!69\)\( T^{7} + \)\(18\!\cdots\!26\)\( T^{8} - \)\(55\!\cdots\!51\)\( T^{9} + \)\(94\!\cdots\!43\)\( T^{10} \))(\( 1 + 67716 T + 646416013 T^{2} + 266736076181388 T^{3} + 15516041187205853449 T^{4} \))(\( 1 - 3939040643 T^{2} + 15516041187205853449 T^{4} \))(\( 1 - 3939040643 T^{2} + 15516041187205853449 T^{4} \))(\( 1 - 67716 T + 646416013 T^{2} - 266736076181388 T^{3} + 15516041187205853449 T^{4} \))(\( 1 - 4552161670 T^{2} + 5206134682611335451 T^{4} - \)\(70\!\cdots\!30\)\( T^{6} + \)\(24\!\cdots\!01\)\( T^{8} \))(\( 1 - 15066 T + 2485979765 T^{2} + 152725197486870 T^{3} - 11307081532931957076 T^{4} + \)\(60\!\cdots\!10\)\( T^{5} + \)\(38\!\cdots\!85\)\( T^{6} - \)\(92\!\cdots\!62\)\( T^{7} + \)\(24\!\cdots\!01\)\( T^{8} \))(\( 1 + 15066 T + 2485979765 T^{2} - 152725197486870 T^{3} - 11307081532931957076 T^{4} - \)\(60\!\cdots\!10\)\( T^{5} + \)\(38\!\cdots\!85\)\( T^{6} + \)\(92\!\cdots\!62\)\( T^{7} + \)\(24\!\cdots\!01\)\( T^{8} \))(\( 1 - 226584 T + 26129513127 T^{2} - 2010313812562488 T^{3} + \)\(11\!\cdots\!78\)\( T^{4} - \)\(51\!\cdots\!16\)\( T^{5} + \)\(24\!\cdots\!83\)\( T^{6} - \)\(20\!\cdots\!88\)\( T^{7} + \)\(18\!\cdots\!22\)\( T^{8} - \)\(12\!\cdots\!16\)\( T^{9} + \)\(62\!\cdots\!27\)\( T^{10} - \)\(21\!\cdots\!12\)\( T^{11} + \)\(37\!\cdots\!49\)\( T^{12} \))(\( 1 + 226584 T + 26129513127 T^{2} + 2010313812562488 T^{3} + \)\(11\!\cdots\!78\)\( T^{4} + \)\(51\!\cdots\!16\)\( T^{5} + \)\(24\!\cdots\!83\)\( T^{6} + \)\(20\!\cdots\!88\)\( T^{7} + \)\(18\!\cdots\!22\)\( T^{8} + \)\(12\!\cdots\!16\)\( T^{9} + \)\(62\!\cdots\!27\)\( T^{10} + \)\(21\!\cdots\!12\)\( T^{11} + \)\(37\!\cdots\!49\)\( T^{12} \))(\( 1 - 9492423500 T^{2} + 45164047572639574234 T^{4} - \)\(13\!\cdots\!00\)\( T^{6} + \)\(38\!\cdots\!55\)\( T^{8} - \)\(20\!\cdots\!00\)\( T^{10} + \)\(10\!\cdots\!34\)\( T^{12} - \)\(35\!\cdots\!00\)\( T^{14} + \)\(57\!\cdots\!01\)\( T^{16} \))
$89$ (\( 1 - 45897 T + 3780940614 T^{2} - 499185304837341 T^{3} + 21112997161714561686 T^{4} - \)\(14\!\cdots\!97\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} \))(\( 1 + 45897 T + 3780940614 T^{2} + 499185304837341 T^{3} + 21112997161714561686 T^{4} + \)\(14\!\cdots\!97\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} \))(\( 1 - 680992978 T^{2} + 62238193382785937523 T^{4} - \)\(21\!\cdots\!78\)\( T^{6} + \)\(97\!\cdots\!01\)\( T^{8} \))(\( 1 + 299166 T + 52616244181 T^{2} + 6660261403977288 T^{3} + \)\(67\!\cdots\!10\)\( T^{4} + \)\(55\!\cdots\!64\)\( T^{5} + \)\(37\!\cdots\!90\)\( T^{6} + \)\(20\!\cdots\!88\)\( T^{7} + \)\(91\!\cdots\!69\)\( T^{8} + \)\(29\!\cdots\!66\)\( T^{9} + \)\(54\!\cdots\!49\)\( T^{10} \))(\( 1 - 299166 T + 52616244181 T^{2} - 6660261403977288 T^{3} + \)\(67\!\cdots\!10\)\( T^{4} - \)\(55\!\cdots\!64\)\( T^{5} + \)\(37\!\cdots\!90\)\( T^{6} - \)\(20\!\cdots\!88\)\( T^{7} + \)\(91\!\cdots\!69\)\( T^{8} - \)\(29\!\cdots\!66\)\( T^{9} + \)\(54\!\cdots\!49\)\( T^{10} \))(\( ( 1 - 29754 T + 5584059449 T^{2} )^{2} \))(\( ( 1 + 5584059449 T^{2} )^{2} \))(\( ( 1 + 5584059449 T^{2} )^{2} \))(\( ( 1 + 29754 T + 5584059449 T^{2} )^{2} \))(\( ( 1 + 3438704914 T^{2} + 31181719929966183601 T^{4} )^{2} \))(\( ( 1 + 178848 T + 18739138030 T^{2} + 998697864334752 T^{3} + 31181719929966183601 T^{4} )^{2} \))(\( ( 1 - 178848 T + 18739138030 T^{2} - 998697864334752 T^{3} + 31181719929966183601 T^{4} )^{2} \))(\( ( 1 + 45897 T + 3780940614 T^{2} + 499185304837341 T^{3} + 21112997161714561686 T^{4} + \)\(14\!\cdots\!97\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} )^{2} \))(\( ( 1 - 45897 T + 3780940614 T^{2} - 499185304837341 T^{3} + 21112997161714561686 T^{4} - \)\(14\!\cdots\!97\)\( T^{5} + \)\(17\!\cdots\!49\)\( T^{6} )^{2} \))(\( ( 1 - 680992978 T^{2} + 62238193382785937523 T^{4} - \)\(21\!\cdots\!78\)\( T^{6} + \)\(97\!\cdots\!01\)\( T^{8} )^{2} \))
$97$ (\( 1 - 211290 T + 31141328127 T^{2} - 2965626780069260 T^{3} + \)\(26\!\cdots\!39\)\( T^{4} - \)\(15\!\cdots\!10\)\( T^{5} + \)\(63\!\cdots\!93\)\( T^{6} \))(\( 1 - 211290 T + 31141328127 T^{2} - 2965626780069260 T^{3} + \)\(26\!\cdots\!39\)\( T^{4} - \)\(15\!\cdots\!10\)\( T^{5} + \)\(63\!\cdots\!93\)\( T^{6} \))(\( ( 1 + 165932 T + 24001271142 T^{2} + 1424914543524524 T^{3} + 73742412689492826049 T^{4} )^{2} \))(\( 1 + 40541 T + 19537068819 T^{2} + 1527692999826186 T^{3} + \)\(22\!\cdots\!25\)\( T^{4} + \)\(18\!\cdots\!11\)\( T^{5} + \)\(18\!\cdots\!25\)\( T^{6} + \)\(11\!\cdots\!14\)\( T^{7} + \)\(12\!\cdots\!67\)\( T^{8} + \)\(22\!\cdots\!41\)\( T^{9} + \)\(46\!\cdots\!57\)\( T^{10} \))(\( 1 + 40541 T + 19537068819 T^{2} + 1527692999826186 T^{3} + \)\(22\!\cdots\!25\)\( T^{4} + \)\(18\!\cdots\!11\)\( T^{5} + \)\(18\!\cdots\!25\)\( T^{6} + \)\(11\!\cdots\!14\)\( T^{7} + \)\(12\!\cdots\!67\)\( T^{8} + \)\(22\!\cdots\!41\)\( T^{9} + \)\(46\!\cdots\!57\)\( T^{10} \))(\( 1 - 122398 T + 6393930147 T^{2} - 1051073272776286 T^{3} + 73742412689492826049 T^{4} \))(\( ( 1 - 177725 T + 8587340257 T^{2} )( 1 + 43339 T + 8587340257 T^{2} ) \))(\( ( 1 + 43339 T + 8587340257 T^{2} )( 1 + 134386 T + 8587340257 T^{2} ) \))(\( 1 - 122398 T + 6393930147 T^{2} - 1051073272776286 T^{3} + 73742412689492826049 T^{4} \))(\( ( 1 + 12917 T - 8420491368 T^{2} + 110922674099669 T^{3} + 73742412689492826049 T^{4} )^{2} \))(\( 1 + 88942 T - 5868346127 T^{2} - 302016349055666 T^{3} + 48187435429438608484 T^{4} - \)\(25\!\cdots\!62\)\( T^{5} - \)\(43\!\cdots\!23\)\( T^{6} + \)\(56\!\cdots\!06\)\( T^{7} + \)\(54\!\cdots\!01\)\( T^{8} \))(\( 1 + 88942 T - 5868346127 T^{2} - 302016349055666 T^{3} + 48187435429438608484 T^{4} - \)\(25\!\cdots\!62\)\( T^{5} - \)\(43\!\cdots\!23\)\( T^{6} + \)\(56\!\cdots\!06\)\( T^{7} + \)\(54\!\cdots\!01\)\( T^{8} \))(\( 1 + 211290 T + 13502135973 T^{2} + 648597659815310 T^{3} + 75753854471213874090 T^{4} - \)\(50\!\cdots\!90\)\( T^{5} - \)\(15\!\cdots\!67\)\( T^{6} - \)\(43\!\cdots\!30\)\( T^{7} + \)\(55\!\cdots\!10\)\( T^{8} + \)\(41\!\cdots\!30\)\( T^{9} + \)\(73\!\cdots\!73\)\( T^{10} + \)\(98\!\cdots\!30\)\( T^{11} + \)\(40\!\cdots\!49\)\( T^{12} \))(\( 1 + 211290 T + 13502135973 T^{2} + 648597659815310 T^{3} + 75753854471213874090 T^{4} - \)\(50\!\cdots\!90\)\( T^{5} - \)\(15\!\cdots\!67\)\( T^{6} - \)\(43\!\cdots\!30\)\( T^{7} + \)\(55\!\cdots\!10\)\( T^{8} + \)\(41\!\cdots\!30\)\( T^{9} + \)\(73\!\cdots\!73\)\( T^{10} + \)\(98\!\cdots\!30\)\( T^{11} + \)\(40\!\cdots\!49\)\( T^{12} \))(\( ( 1 - 165932 T + 3532157482 T^{2} - 1132749836085296 T^{3} + \)\(26\!\cdots\!47\)\( T^{4} - \)\(97\!\cdots\!72\)\( T^{5} + \)\(26\!\cdots\!18\)\( T^{6} - \)\(10\!\cdots\!76\)\( T^{7} + \)\(54\!\cdots\!01\)\( T^{8} )^{2} \))
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