Properties

Label 105.3
Level 105
Weight 3
Dimension 476
Nonzero newspaces 12
Newform subspaces 18
Sturm bound 2304
Trace bound 4

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Defining parameters

Level: \( N \) = \( 105\( 105 = 3 \cdot 5 \cdot 7 \) \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 18 \)
Sturm bound: \(2304\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(105))\).

Total New Old
Modular forms 864 540 324
Cusp forms 672 476 196
Eisenstein series 192 64 128

Trace form

\( 476q + 8q^{2} + 8q^{3} + 36q^{4} + 14q^{5} + 4q^{6} - 20q^{7} - 12q^{8} + 4q^{9} + O(q^{10}) \) \( 476q + 8q^{2} + 8q^{3} + 36q^{4} + 14q^{5} + 4q^{6} - 20q^{7} - 12q^{8} + 4q^{9} - 60q^{10} - 44q^{11} - 104q^{12} - 28q^{13} - 48q^{14} - 40q^{15} - 132q^{16} - 16q^{17} - 100q^{18} + 68q^{19} + 72q^{20} + 24q^{21} + 88q^{22} + 80q^{23} - 48q^{24} - 220q^{25} - 308q^{26} - 88q^{27} - 452q^{28} - 216q^{29} - 236q^{30} - 268q^{31} - 292q^{32} - 332q^{33} - 512q^{34} - 98q^{35} - 172q^{36} - 192q^{37} + 228q^{38} + 284q^{39} + 728q^{40} + 448q^{41} + 756q^{42} + 712q^{43} + 1296q^{44} + 430q^{45} + 952q^{46} + 500q^{47} + 592q^{48} + 144q^{49} - 364q^{50} + 40q^{51} - 488q^{52} - 88q^{53} + 124q^{54} - 564q^{55} - 1284q^{56} - 688q^{57} - 1832q^{58} - 1128q^{59} - 1220q^{60} - 1532q^{61} - 1688q^{62} - 336q^{63} - 1308q^{64} - 370q^{65} - 352q^{66} - 308q^{67} - 128q^{68} - 72q^{69} + 516q^{70} + 496q^{71} + 216q^{72} + 1088q^{73} + 1140q^{74} + 296q^{75} + 1656q^{76} + 920q^{77} + 664q^{78} + 628q^{79} + 2000q^{80} + 40q^{81} + 2064q^{82} + 1376q^{83} + 1680q^{84} + 1512q^{85} + 1660q^{86} + 896q^{87} + 1416q^{88} + 120q^{89} + 1496q^{90} + 456q^{91} - 40q^{92} + 1440q^{93} + 1120q^{94} + 150q^{95} + 2828q^{96} + 1432q^{97} + 924q^{98} + 1160q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(105))\)

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
105.3.c \(\chi_{105}(71, \cdot)\) 105.3.c.a 16 1
105.3.e \(\chi_{105}(34, \cdot)\) 105.3.e.a 16 1
105.3.f \(\chi_{105}(29, \cdot)\) 105.3.f.a 24 1
105.3.h \(\chi_{105}(76, \cdot)\) 105.3.h.a 12 1
105.3.k \(\chi_{105}(62, \cdot)\) 105.3.k.a 4 2
105.3.k.b 4
105.3.k.c 16
105.3.k.d 32
105.3.l \(\chi_{105}(22, \cdot)\) 105.3.l.a 24 2
105.3.n \(\chi_{105}(31, \cdot)\) 105.3.n.a 8 2
105.3.n.b 12
105.3.o \(\chi_{105}(44, \cdot)\) 105.3.o.a 16 2
105.3.o.b 40
105.3.r \(\chi_{105}(19, \cdot)\) 105.3.r.a 32 2
105.3.t \(\chi_{105}(11, \cdot)\) 105.3.t.a 8 2
105.3.t.b 36
105.3.v \(\chi_{105}(37, \cdot)\) 105.3.v.a 64 4
105.3.w \(\chi_{105}(17, \cdot)\) 105.3.w.a 112 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(105))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(105)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 - 18 T^{2} + 167 T^{4} - 1116 T^{6} + 6143 T^{8} - 30562 T^{10} + 147193 T^{12} - 678704 T^{14} + 2863008 T^{16} - 10859264 T^{18} + 37681408 T^{20} - 125181952 T^{22} + 402587648 T^{24} - 1170210816 T^{26} + 2801795072 T^{28} - 4831838208 T^{30} + 4294967296 T^{32} \))(\( ( 1 - 8 T^{2} + 34 T^{4} - 56 T^{6} + 13 T^{8} - 896 T^{10} + 8704 T^{12} - 32768 T^{14} + 65536 T^{16} )^{2} \))(\( ( 1 + 2 T + 3 T^{2} + 7 T^{4} + 38 T^{5} + 109 T^{6} + 152 T^{7} + 112 T^{8} + 768 T^{10} + 2048 T^{11} + 4096 T^{12} )^{2} \))(\( 1 + 17 T^{4} + 256 T^{8} \))(\( 1 + 17 T^{4} + 256 T^{8} \))(\( ( 1 + 17 T^{4} + 256 T^{8} )^{4} \))(\( 1 - 2 T - 3 T^{2} + 14 T^{3} - 13 T^{4} - 18 T^{5} + 70 T^{6} - 44 T^{7} - 156 T^{8} - 176 T^{9} + 1120 T^{10} - 1152 T^{11} - 3328 T^{12} + 14336 T^{13} - 12288 T^{14} - 32768 T^{15} + 65536 T^{16} \))(\( 1 - 2 T + T^{2} - 18 T^{3} + 35 T^{4} - 10 T^{5} + 142 T^{6} - 148 T^{7} - 208 T^{8} - 424 T^{9} - 1176 T^{10} + 4080 T^{11} + 144 T^{12} + 16320 T^{13} - 18816 T^{14} - 27136 T^{15} - 53248 T^{16} - 151552 T^{17} + 581632 T^{18} - 163840 T^{19} + 2293760 T^{20} - 4718592 T^{21} + 1048576 T^{22} - 8388608 T^{23} + 16777216 T^{24} \))(\( ( 1 - 6 T^{2} + 10 T^{4} + 36 T^{6} - 156 T^{8} + 576 T^{10} + 2560 T^{12} - 24576 T^{14} + 65536 T^{16} )^{2} \))(\( 1 + 2 T^{2} + 11 T^{4} - 78 T^{6} - 271 T^{8} - 1248 T^{10} + 2816 T^{12} + 8192 T^{14} + 65536 T^{16} \))
$3$ (\( 1 - 8 T + 21 T^{2} + 52 T^{3} - 630 T^{4} + 2116 T^{5} - 1381 T^{6} - 17424 T^{7} + 83754 T^{8} - 156816 T^{9} - 111861 T^{10} + 1542564 T^{11} - 4133430 T^{12} + 3070548 T^{13} + 11160261 T^{14} - 38263752 T^{15} + 43046721 T^{16} \))(\( ( 1 - 3 T^{2} )^{8} \))(\( ( 1 + 3 T^{2} )^{6} \))(\( 1 + 8 T + 32 T^{2} + 72 T^{3} + 81 T^{4} \))(\( 1 - 8 T + 32 T^{2} - 72 T^{3} + 81 T^{4} \))(\( 1 - 224 T^{4} + 23490 T^{8} - 1469664 T^{12} + 43046721 T^{16} \))(\( ( 1 + 3 T + 3 T^{2} )^{4} \))(\( ( 1 - 3 T + 3 T^{2} )^{6} \))(\( 1 + 4 T^{2} + 90 T^{4} - 944 T^{6} - 2381 T^{8} - 76464 T^{10} + 590490 T^{12} + 2125764 T^{14} + 43046721 T^{16} \))(\( 1 + 4 T + 4 T^{2} - 24 T^{3} - 81 T^{4} - 216 T^{5} + 324 T^{6} + 2916 T^{7} + 6561 T^{8} \))
$5$ (\( ( 1 + 5 T^{2} )^{8} \))(\( 1 - 8 T^{2} + 412 T^{4} + 3208 T^{6} - 304250 T^{8} + 2005000 T^{10} + 160937500 T^{12} - 1953125000 T^{14} + 152587890625 T^{16} \))(\( ( 1 + 5 T^{2} )^{6} \))(\( 1 + 48 T^{2} + 625 T^{4} \))(\( 1 + 48 T^{2} + 625 T^{4} \))(\( ( 1 - 56 T^{2} + 2000 T^{4} - 35000 T^{6} + 390625 T^{8} )^{2} \))(\( ( 1 - 5 T^{2} + 25 T^{4} )^{2} \))(\( ( 1 - 5 T^{2} + 25 T^{4} )^{3} \))(\( 1 + 250 T^{4} - 328125 T^{8} + 97656250 T^{12} + 152587890625 T^{16} \))(\( ( 1 - 5 T^{2} + 25 T^{4} )^{2} \))
$7$ (\( ( 1 - 7 T^{2} )^{8} \))(\( 1 + 76 T^{2} + 4372 T^{4} + 256564 T^{6} + 11116630 T^{8} + 616010164 T^{10} + 25203709972 T^{12} + 1051937827276 T^{14} + 33232930569601 T^{16} \))(\( 1 + 8 T + 2 T^{2} + 312 T^{3} + 4255 T^{4} + 13888 T^{5} + 43708 T^{6} + 680512 T^{7} + 10216255 T^{8} + 36706488 T^{9} + 11529602 T^{10} + 2259801992 T^{11} + 13841287201 T^{12} \))(\( ( 1 + 7 T )^{4} \))(\( ( 1 + 49 T^{2} )^{2} \))(\( ( 1 - 16 T + 128 T^{2} - 208 T^{3} - 958 T^{4} - 10192 T^{5} + 307328 T^{6} - 1882384 T^{7} + 5764801 T^{8} )^{2} \))(\( 1 + 16 T + 109 T^{2} + 784 T^{3} + 6664 T^{4} + 38416 T^{5} + 261709 T^{6} + 1882384 T^{7} + 5764801 T^{8} \))(\( 1 - 22 T + 272 T^{2} - 2568 T^{3} + 19600 T^{4} - 138362 T^{5} + 991858 T^{6} - 6779738 T^{7} + 47059600 T^{8} - 302122632 T^{9} + 1568025872 T^{10} - 6214455478 T^{11} + 13841287201 T^{12} \))(\( ( 1 + 52 T^{2} + 4263 T^{4} + 124852 T^{6} + 5764801 T^{8} )^{2} \))(\( ( 1 - 7 T )^{8} \))
$11$ (\( 1 - 634 T^{2} + 247245 T^{4} - 65949338 T^{6} + 13712984198 T^{8} - 2284687822518 T^{10} + 326907972407363 T^{12} - 41733915025260470 T^{14} + 5125952848251765522 T^{16} - \)\(61\!\cdots\!70\)\( T^{18} + \)\(70\!\cdots\!03\)\( T^{20} - \)\(71\!\cdots\!78\)\( T^{22} + \)\(63\!\cdots\!78\)\( T^{24} - \)\(44\!\cdots\!38\)\( T^{26} + \)\(24\!\cdots\!45\)\( T^{28} - \)\(91\!\cdots\!54\)\( T^{30} + \)\(21\!\cdots\!21\)\( T^{32} \))(\( ( 1 + 14 T + 412 T^{2} + 4298 T^{3} + 73702 T^{4} + 520058 T^{5} + 6032092 T^{6} + 24801854 T^{7} + 214358881 T^{8} )^{4} \))(\( ( 1 + 8 T + 198 T^{2} + 1416 T^{3} + 30895 T^{4} + 264944 T^{5} + 5610292 T^{6} + 32058224 T^{7} + 452333695 T^{8} + 2508530376 T^{9} + 42443058438 T^{10} + 207499396808 T^{11} + 3138428376721 T^{12} )^{2} \))(\( ( 1 - 144 T^{2} + 14641 T^{4} )^{2} \))(\( ( 1 - 144 T^{2} + 14641 T^{4} )^{2} \))(\( ( 1 - 284 T^{2} + 40742 T^{4} - 4158044 T^{6} + 214358881 T^{8} )^{4} \))(\( 1 - 20 T - 147 T^{2} + 2960 T^{3} + 57131 T^{4} - 519480 T^{5} - 8882912 T^{6} + 8003440 T^{7} + 1602642534 T^{8} + 968416240 T^{9} - 130054714592 T^{10} - 920290508280 T^{11} + 12246537230411 T^{12} + 76774776818960 T^{13} - 461348971377987 T^{14} - 7594996671664820 T^{15} + 45949729863572161 T^{16} \))(\( 1 - 20 T - 77 T^{2} + 7872 T^{3} - 76264 T^{4} - 640168 T^{5} + 22115011 T^{6} - 150830740 T^{7} - 1492575946 T^{8} + 41825299028 T^{9} - 261075878769 T^{10} - 2649707325072 T^{11} + 64192943543664 T^{12} - 320614586333712 T^{13} - 3822411941056929 T^{14} + 74096068571342708 T^{15} - 319946909592076426 T^{16} - 3912160946263034740 T^{17} + 69406378073897058931 T^{18} - \)\(24\!\cdots\!88\)\( T^{19} - \)\(35\!\cdots\!04\)\( T^{20} + \)\(43\!\cdots\!32\)\( T^{21} - \)\(51\!\cdots\!77\)\( T^{22} - \)\(16\!\cdots\!20\)\( T^{23} + \)\(98\!\cdots\!41\)\( T^{24} \))(\( ( 1 + 334 T^{2} + 57760 T^{4} + 8187676 T^{6} + 1046359339 T^{8} + 119875764316 T^{10} + 12381368966560 T^{12} + 1048235077824814 T^{14} + 45949729863572161 T^{16} )^{2} \))(\( 1 + 358 T^{2} + 70081 T^{4} + 10310758 T^{6} + 1282826884 T^{8} + 150959807878 T^{10} + 15022484739361 T^{12} + 1123557358866118 T^{14} + 45949729863572161 T^{16} \))
$13$ (\( ( 1 + 745 T^{2} + 1452 T^{3} + 296782 T^{4} + 900988 T^{5} + 78625591 T^{6} + 264119992 T^{7} + 15370753026 T^{8} + 44636278648 T^{9} + 2245625504551 T^{10} + 4348896987292 T^{11} + 242094194839822 T^{12} + 200170530164748 T^{13} + 17357073416248345 T^{14} + 665416609183179841 T^{16} )^{2} \))(\( ( 1 + 796 T^{2} + 331060 T^{4} + 90926116 T^{6} + 17935751638 T^{8} + 2596940799076 T^{10} + 270055812494260 T^{12} + 18545275757494876 T^{14} + 665416609183179841 T^{16} )^{2} \))(\( 1 - 852 T^{2} + 436674 T^{4} - 159409348 T^{6} + 45042421839 T^{8} - 10253858128680 T^{10} + 1907667001388316 T^{12} - 292860442013229480 T^{14} + 36742487242313615919 T^{16} - \)\(37\!\cdots\!88\)\( T^{18} + \)\(29\!\cdots\!34\)\( T^{20} - \)\(16\!\cdots\!52\)\( T^{22} + \)\(54\!\cdots\!61\)\( T^{24} \))(\( ( 1 + 16 T + 128 T^{2} + 2704 T^{3} + 28561 T^{4} )^{2} \))(\( ( 1 - 16 T + 128 T^{2} - 2704 T^{3} + 28561 T^{4} )^{2} \))(\( ( 1 - 74400 T^{4} + 2876017858 T^{8} - 60690365642400 T^{12} + 665416609183179841 T^{16} )^{2} \))(\( 1 - 188 T^{2} + 39826 T^{4} - 8798048 T^{6} + 2113175419 T^{8} - 251281048928 T^{10} + 32487291694546 T^{12} - 4380040003026428 T^{14} + 665416609183179841 T^{16} \))(\( 1 - 1050 T^{2} + 558861 T^{4} - 197481550 T^{6} + 52237691370 T^{8} - 11158031023650 T^{10} + 2025783626034165 T^{12} - 318684524066467650 T^{14} + 42611889644625577770 T^{16} - \)\(46\!\cdots\!50\)\( T^{18} + \)\(37\!\cdots\!01\)\( T^{20} - \)\(19\!\cdots\!50\)\( T^{22} + \)\(54\!\cdots\!61\)\( T^{24} \))(\( ( 1 - 188 T^{2} + 20583 T^{4} - 5369468 T^{6} + 815730721 T^{8} )^{4} \))(\( ( 1 - 2 T + 89 T^{2} - 338 T^{3} + 28561 T^{4} )^{4} \))
$17$ (\( 1 - 1918 T^{2} + 1941581 T^{4} - 1392408966 T^{6} + 790147542694 T^{8} - 373036090829946 T^{10} + 150674753302219043 T^{12} - 52956031786998379138 T^{14} + \)\(16\!\cdots\!82\)\( T^{16} - \)\(44\!\cdots\!98\)\( T^{18} + \)\(10\!\cdots\!63\)\( T^{20} - \)\(21\!\cdots\!06\)\( T^{22} + \)\(38\!\cdots\!14\)\( T^{24} - \)\(56\!\cdots\!66\)\( T^{26} + \)\(65\!\cdots\!01\)\( T^{28} - \)\(54\!\cdots\!38\)\( T^{30} + \)\(23\!\cdots\!61\)\( T^{32} \))(\( ( 1 + 844 T^{2} + 436948 T^{4} + 156276148 T^{6} + 48382687318 T^{8} + 13052340157108 T^{10} + 3048043262330068 T^{12} + 491733168221918284 T^{14} + 48661191875666868481 T^{16} )^{2} \))(\( 1 - 2172 T^{2} + 2401794 T^{4} - 1757595148 T^{6} + 941667483759 T^{8} - 387997181982840 T^{10} + 125896935467491356 T^{12} - 32405912636388779640 T^{14} + \)\(65\!\cdots\!19\)\( T^{16} - \)\(10\!\cdots\!28\)\( T^{18} + \)\(11\!\cdots\!14\)\( T^{20} - \)\(88\!\cdots\!72\)\( T^{22} + \)\(33\!\cdots\!21\)\( T^{24} \))(\( 1 - 157438 T^{4} + 6975757441 T^{8} \))(\( 1 - 157438 T^{4} + 6975757441 T^{8} \))(\( ( 1 + 280836 T^{4} + 33000880390 T^{8} + 1959043816700676 T^{12} + 48661191875666868481 T^{16} )^{2} \))(\( 1 + 18 T + 766 T^{2} + 11844 T^{3} + 262438 T^{4} + 1906254 T^{5} + 22625848 T^{6} - 382636314 T^{7} - 5169040877 T^{8} - 110581894746 T^{9} + 1889733450808 T^{10} + 46012337456526 T^{11} + 1830703831301158 T^{12} + 23877431756917956 T^{13} + 446288633717996926 T^{14} + 3030800878069216722 T^{15} + 48661191875666868481 T^{16} \))(\( 1 + 78 T + 3456 T^{2} + 111384 T^{3} + 2892825 T^{4} + 64908048 T^{5} + 1326815384 T^{6} + 25384395654 T^{7} + 459528789294 T^{8} + 7866410803470 T^{9} + 127737192900600 T^{10} + 2033291698334568 T^{11} + 33507834279238509 T^{12} + 587621300818690152 T^{13} + 10668738088251012600 T^{14} + \)\(18\!\cdots\!30\)\( T^{15} + \)\(32\!\cdots\!54\)\( T^{16} + \)\(51\!\cdots\!46\)\( T^{17} + \)\(77\!\cdots\!24\)\( T^{18} + \)\(10\!\cdots\!92\)\( T^{19} + \)\(14\!\cdots\!25\)\( T^{20} + \)\(15\!\cdots\!56\)\( T^{21} + \)\(14\!\cdots\!56\)\( T^{22} + \)\(91\!\cdots\!42\)\( T^{23} + \)\(33\!\cdots\!21\)\( T^{24} \))(\( ( 1 - 906 T^{2} + 463000 T^{4} - 172859364 T^{6} + 52513801899 T^{8} - 14437386940644 T^{10} + 3229775695183000 T^{12} - 527855746930163466 T^{14} + 48661191875666868481 T^{16} )^{2} \))(\( 1 + 512 T^{2} + 32126 T^{4} + 32243712 T^{6} + 24037993859 T^{8} + 2693027069952 T^{10} + 224103183549566 T^{12} + 298302585461637632 T^{14} + 48661191875666868481 T^{16} \))
$19$ (\( ( 1 + 8 T + 860 T^{2} + 16312 T^{3} + 704036 T^{4} + 10691240 T^{5} + 381169188 T^{6} + 5670939160 T^{7} + 156781324406 T^{8} + 2047209036760 T^{9} + 49674349749348 T^{10} + 502978804782440 T^{11} + 11957039789133476 T^{12} + 100009952797249912 T^{13} + 1903450830396898460 T^{14} + 6392053486263072968 T^{15} + \)\(28\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 - 2492 T^{2} + 2811124 T^{4} - 1889002244 T^{6} + 831672508246 T^{8} - 246176661440324 T^{10} + 47742901670068084 T^{12} - 5515580778312873212 T^{14} + \)\(28\!\cdots\!81\)\( T^{16} )^{2} \))(\( 1 - 1404 T^{2} + 1342050 T^{4} - 896154316 T^{6} + 500154418383 T^{8} - 227690692547448 T^{10} + 90028611036772572 T^{12} - 29672878743475970808 T^{14} + \)\(84\!\cdots\!03\)\( T^{16} - \)\(19\!\cdots\!76\)\( T^{18} + \)\(38\!\cdots\!50\)\( T^{20} - \)\(52\!\cdots\!04\)\( T^{22} + \)\(48\!\cdots\!21\)\( T^{24} \))(\( ( 1 - 10 T + 361 T^{2} )^{4} \))(\( ( 1 + 10 T + 361 T^{2} )^{4} \))(\( ( 1 + 696 T^{2} + 371920 T^{4} + 90703416 T^{6} + 16983563041 T^{8} )^{4} \))(\( 1 + 598 T^{2} + 183481 T^{4} - 682560 T^{5} - 48973562 T^{6} - 501474240 T^{7} - 32269961996 T^{8} - 181032200640 T^{9} - 6382283573402 T^{10} - 32111636535360 T^{11} + 3116161130325721 T^{12} + 1323562321601564278 T^{14} + \)\(28\!\cdots\!81\)\( T^{16} \))(\( 1 + 6 T + 1695 T^{2} + 10098 T^{3} + 1583475 T^{4} + 6257352 T^{5} + 993857576 T^{6} + 1495351404 T^{7} + 468684238005 T^{8} - 646226336898 T^{9} + 184440578012361 T^{10} - 649631264996682 T^{11} + 67037012122357518 T^{12} - 234516886663802202 T^{13} + 24036480567148897881 T^{14} - 30402287344769217138 T^{15} + \)\(79\!\cdots\!05\)\( T^{16} + \)\(91\!\cdots\!04\)\( T^{17} + \)\(21\!\cdots\!36\)\( T^{18} + \)\(49\!\cdots\!92\)\( T^{19} + \)\(45\!\cdots\!75\)\( T^{20} + \)\(10\!\cdots\!18\)\( T^{21} + \)\(63\!\cdots\!95\)\( T^{22} + \)\(81\!\cdots\!66\)\( T^{23} + \)\(48\!\cdots\!21\)\( T^{24} \))(\( ( 1 - 12 T - 599 T^{2} - 252 T^{3} + 369744 T^{4} - 90972 T^{5} - 78062279 T^{6} - 564550572 T^{7} + 16983563041 T^{8} )^{4} \))(\( ( 1 - 18 T + 11 T^{2} + 7362 T^{3} - 149316 T^{4} + 2657682 T^{5} + 1433531 T^{6} - 846825858 T^{7} + 16983563041 T^{8} )^{2} \))
$23$ (\( 1 - 4480 T^{2} + 10302200 T^{4} - 16115718144 T^{6} + 19153465500700 T^{8} - 18300056706334464 T^{10} + 14511541318853927624 T^{12} - \)\(97\!\cdots\!40\)\( T^{14} + \)\(55\!\cdots\!30\)\( T^{16} - \)\(27\!\cdots\!40\)\( T^{18} + \)\(11\!\cdots\!44\)\( T^{20} - \)\(40\!\cdots\!44\)\( T^{22} + \)\(11\!\cdots\!00\)\( T^{24} - \)\(27\!\cdots\!44\)\( T^{26} + \)\(49\!\cdots\!00\)\( T^{28} - \)\(60\!\cdots\!80\)\( T^{30} + \)\(37\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 1328 T^{2} + 849580 T^{4} - 574305488 T^{6} + 369064865830 T^{8} - 160714222067408 T^{10} + 66531446875031980 T^{12} - 29102621245722986288 T^{14} + \)\(61\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 + 32 T + 2418 T^{2} + 60144 T^{3} + 2694751 T^{4} + 53735792 T^{5} + 1782680284 T^{6} + 28426233968 T^{7} + 754101814591 T^{8} + 8903470508016 T^{9} + 189355962409458 T^{10} + 1325648358836768 T^{11} + 21914624432020321 T^{12} )^{2} \))(\( 1 - 550078 T^{4} + 78310985281 T^{8} \))(\( 1 - 550078 T^{4} + 78310985281 T^{8} \))(\( ( 1 + 107644 T^{4} - 83134815354 T^{8} + 8429707699587964 T^{12} + \)\(61\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 - 62 T + 1497 T^{2} + 6014 T^{3} - 1196893 T^{4} + 31086552 T^{5} - 143771420 T^{6} - 13896561704 T^{7} + 513552019554 T^{8} - 7351281141416 T^{9} - 40233137944220 T^{10} + 4601925361264728 T^{11} - 93729870105931933 T^{12} + 249139038438885086 T^{13} + 32806192774734420537 T^{14} - \)\(71\!\cdots\!58\)\( T^{15} + \)\(61\!\cdots\!61\)\( T^{16} \))(\( 1 - 2 T - 1961 T^{2} - 16242 T^{3} + 1952552 T^{4} + 28088402 T^{5} - 1236738581 T^{6} - 18913143826 T^{7} + 643866095426 T^{8} + 6409263044018 T^{9} - 382808809220061 T^{10} - 936062983320174 T^{11} + 225254373554835492 T^{12} - 495177318176372046 T^{13} - \)\(10\!\cdots\!01\)\( T^{14} + \)\(94\!\cdots\!02\)\( T^{15} + \)\(50\!\cdots\!06\)\( T^{16} - \)\(78\!\cdots\!74\)\( T^{17} - \)\(27\!\cdots\!01\)\( T^{18} + \)\(32\!\cdots\!18\)\( T^{19} + \)\(11\!\cdots\!72\)\( T^{20} - \)\(52\!\cdots\!98\)\( T^{21} - \)\(33\!\cdots\!61\)\( T^{22} - \)\(18\!\cdots\!58\)\( T^{23} + \)\(48\!\cdots\!41\)\( T^{24} \))(\( ( 1 - 1066 T^{2} + 315400 T^{4} - 278518084 T^{6} + 277658769259 T^{8} - 77940779144644 T^{10} + 24699284757627400 T^{12} - 23360989644533662186 T^{14} + \)\(61\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 + 1082 T^{2} + 328601 T^{4} + 305601162 T^{6} + 303243586964 T^{8} + 85519734775242 T^{10} + 25733068074321881 T^{12} + 23711623635445987322 T^{14} + \)\(61\!\cdots\!61\)\( T^{16} \))
$29$ (\( 1 - 5378 T^{2} + 14503181 T^{4} - 26572841642 T^{6} + 38033992302502 T^{8} - 46226481721014678 T^{10} + 49944592354476620099 T^{12} - \)\(48\!\cdots\!42\)\( T^{14} + \)\(43\!\cdots\!90\)\( T^{16} - \)\(34\!\cdots\!02\)\( T^{18} + \)\(24\!\cdots\!39\)\( T^{20} - \)\(16\!\cdots\!98\)\( T^{22} + \)\(95\!\cdots\!42\)\( T^{24} - \)\(47\!\cdots\!42\)\( T^{26} + \)\(18\!\cdots\!61\)\( T^{28} - \)\(47\!\cdots\!58\)\( T^{30} + \)\(62\!\cdots\!41\)\( T^{32} \))(\( ( 1 + 8 T + 2080 T^{2} + 33800 T^{3} + 2057614 T^{4} + 28425800 T^{5} + 1471144480 T^{6} + 4758586568 T^{7} + 500246412961 T^{8} )^{4} \))(\( ( 1 - 52 T + 3990 T^{2} - 132324 T^{3} + 6311983 T^{4} - 164304136 T^{5} + 6334525012 T^{6} - 138179778376 T^{7} + 4464345648223 T^{8} - 78709401128004 T^{9} + 1995983187714390 T^{10} - 21876776131610452 T^{11} + 353814783205469041 T^{12} )^{2} \))(\( ( 1 + 1664 T^{2} + 707281 T^{4} )^{2} \))(\( ( 1 + 1664 T^{2} + 707281 T^{4} )^{2} \))(\( ( 1 + 2444 T^{2} + 2801222 T^{4} + 1728594764 T^{6} + 500246412961 T^{8} )^{4} \))(\( ( 1 + 50 T + 1234 T^{2} - 15850 T^{3} - 1164374 T^{4} - 13329850 T^{5} + 872784754 T^{6} + 29741166050 T^{7} + 500246412961 T^{8} )^{2} \))(\( ( 1 + 50 T + 4152 T^{2} + 144894 T^{3} + 7271923 T^{4} + 198551984 T^{5} + 7580628328 T^{6} + 166982218544 T^{7} + 5143292971363 T^{8} + 86186330272974 T^{9} + 2077023106614072 T^{10} + 21035361665010050 T^{11} + 353814783205469041 T^{12} )^{2} \))(\( ( 1 - 2394 T^{2} + 2753756 T^{4} - 1693230714 T^{6} + 500246412961 T^{8} )^{4} \))(\( ( 1 - 2624 T^{2} + 3071906 T^{4} - 1855905344 T^{6} + 500246412961 T^{8} )^{2} \))
$31$ (\( ( 1 + 36 T + 5588 T^{2} + 98172 T^{3} + 10424196 T^{4} - 32178444 T^{5} + 7586949868 T^{6} - 323190800532 T^{7} + 3540198882934 T^{8} - 310586359311252 T^{9} + 7006707529045228 T^{10} - 28558487498852364 T^{11} + 8890703340928322436 T^{12} + 80464548189479195772 T^{13} + \)\(44\!\cdots\!68\)\( T^{14} + \)\(27\!\cdots\!56\)\( T^{15} + \)\(72\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 - 3848 T^{2} + 7120156 T^{4} - 9317031800 T^{6} + 9882447105478 T^{8} - 8604474524967800 T^{10} + 6072717237581760796 T^{12} - \)\(30\!\cdots\!28\)\( T^{14} + \)\(72\!\cdots\!81\)\( T^{16} )^{2} \))(\( 1 - 6228 T^{2} + 19622274 T^{4} - 42341564932 T^{6} + 69647410996719 T^{8} - 91080823295899560 T^{10} + 96735996796679061276 T^{12} - \)\(84\!\cdots\!60\)\( T^{14} + \)\(59\!\cdots\!79\)\( T^{16} - \)\(33\!\cdots\!52\)\( T^{18} + \)\(14\!\cdots\!94\)\( T^{20} - \)\(41\!\cdots\!28\)\( T^{22} + \)\(62\!\cdots\!21\)\( T^{24} \))(\( ( 1 - 1726 T^{2} + 923521 T^{4} )^{2} \))(\( ( 1 - 1726 T^{2} + 923521 T^{4} )^{2} \))(\( ( 1 - 2596 T^{2} + 3425222 T^{4} - 2397460516 T^{6} + 852891037441 T^{8} )^{4} \))(\( 1 + 126 T + 9883 T^{2} + 578466 T^{3} + 27206317 T^{4} + 1079090100 T^{5} + 38160094402 T^{6} + 1243487527488 T^{7} + 38998740329170 T^{8} + 1194991513915968 T^{9} + 35241648542229442 T^{10} + 957696435880658100 T^{11} + 23204023931078714797 T^{12} + \)\(47\!\cdots\!66\)\( T^{13} + \)\(77\!\cdots\!63\)\( T^{14} + \)\(95\!\cdots\!46\)\( T^{15} + \)\(72\!\cdots\!81\)\( T^{16} \))(\( 1 - 108 T + 7296 T^{2} - 368064 T^{3} + 14679372 T^{4} - 497355660 T^{5} + 14549964692 T^{6} - 358253632404 T^{7} + 6912430087356 T^{8} - 59089176847584 T^{9} - 2401476398747496 T^{10} + 161517767136947820 T^{11} - 6040783753357557738 T^{12} + \)\(15\!\cdots\!20\)\( T^{13} - \)\(22\!\cdots\!16\)\( T^{14} - \)\(52\!\cdots\!04\)\( T^{15} + \)\(58\!\cdots\!96\)\( T^{16} - \)\(29\!\cdots\!04\)\( T^{17} + \)\(11\!\cdots\!12\)\( T^{18} - \)\(37\!\cdots\!60\)\( T^{19} + \)\(10\!\cdots\!32\)\( T^{20} - \)\(25\!\cdots\!24\)\( T^{21} + \)\(49\!\cdots\!96\)\( T^{22} - \)\(69\!\cdots\!88\)\( T^{23} + \)\(62\!\cdots\!21\)\( T^{24} \))(\( ( 1 - 86 T + 3685 T^{2} - 153854 T^{3} + 5740444 T^{4} - 147853694 T^{5} + 3403174885 T^{6} - 76325316566 T^{7} + 852891037441 T^{8} )^{4} \))(\( ( 1 - 12 T - 1324 T^{2} + 5448 T^{3} + 1093119 T^{4} + 5235528 T^{5} - 1222741804 T^{6} - 10650044172 T^{7} + 852891037441 T^{8} )^{2} \))
$37$ (\( ( 1 + 20 T + 4860 T^{2} + 56172 T^{3} + 13001540 T^{4} + 138784868 T^{5} + 25923379716 T^{6} + 250888407260 T^{7} + 39435511353270 T^{8} + 343466229538940 T^{9} + 48584587251918276 T^{10} + 356084000997179012 T^{11} + 45667642119332038340 T^{12} + \)\(27\!\cdots\!28\)\( T^{13} + \)\(31\!\cdots\!60\)\( T^{14} + \)\(18\!\cdots\!80\)\( T^{15} + \)\(12\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 - 3896 T^{2} + 10011916 T^{4} - 17293616840 T^{6} + 26286367464358 T^{8} - 32411022230471240 T^{10} + 35166649244382922636 T^{12} - \)\(25\!\cdots\!76\)\( T^{14} + \)\(12\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 - 16 T + 4622 T^{2} + 32784 T^{3} + 7136719 T^{4} + 278279680 T^{5} + 7429424740 T^{6} + 380964881920 T^{7} + 13375360417759 T^{8} + 84114774592656 T^{9} + 16234680036022862 T^{10} - 76937349958685584 T^{11} + 6582952005840035281 T^{12} )^{2} \))(\( ( 1 - 60 T + 1800 T^{2} - 82140 T^{3} + 1874161 T^{4} )^{2} \))(\( ( 1 - 60 T + 1800 T^{2} - 82140 T^{3} + 1874161 T^{4} )^{2} \))(\( ( 1 + 96 T + 4608 T^{2} + 183264 T^{3} + 6996962 T^{4} + 250888416 T^{5} + 8636133888 T^{6} + 246309735264 T^{7} + 3512479453921 T^{8} )^{4} \))(\( 1 + 80 T + 1194 T^{2} + 28960 T^{3} + 3461705 T^{4} - 28416960 T^{5} - 6540374054 T^{6} - 198858748720 T^{7} - 6603314864556 T^{8} - 272237626997680 T^{9} - 12257713977418694 T^{10} - 72910144735496640 T^{11} + 12159167688035595305 T^{12} + \)\(13\!\cdots\!40\)\( T^{13} + \)\(78\!\cdots\!14\)\( T^{14} + \)\(72\!\cdots\!20\)\( T^{15} + \)\(12\!\cdots\!41\)\( T^{16} \))(\( 1 + 34 T - 4909 T^{2} - 226690 T^{3} + 12133431 T^{4} + 708409644 T^{5} - 18171294956 T^{6} - 1398986295020 T^{7} + 16325526424229 T^{8} + 1786096223883250 T^{9} - 2380658436212215 T^{10} - 1019433693058130642 T^{11} - 10072912633170313306 T^{12} - \)\(13\!\cdots\!98\)\( T^{13} - \)\(44\!\cdots\!15\)\( T^{14} + \)\(45\!\cdots\!50\)\( T^{15} + \)\(57\!\cdots\!09\)\( T^{16} - \)\(67\!\cdots\!80\)\( T^{17} - \)\(11\!\cdots\!36\)\( T^{18} + \)\(63\!\cdots\!16\)\( T^{19} + \)\(14\!\cdots\!71\)\( T^{20} - \)\(38\!\cdots\!10\)\( T^{21} - \)\(11\!\cdots\!09\)\( T^{22} + \)\(10\!\cdots\!46\)\( T^{23} + \)\(43\!\cdots\!61\)\( T^{24} \))(\( ( 1 + 2468 T^{2} + 1780081 T^{4} + 1388548628 T^{6} + 3656190464464 T^{8} + 2602363685201108 T^{10} + 6252497938815147601 T^{12} + \)\(16\!\cdots\!08\)\( T^{14} + \)\(12\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 + 6 T - 1021 T^{2} - 10086 T^{3} - 806196 T^{4} - 13807734 T^{5} - 1913518381 T^{6} + 15394358454 T^{7} + 3512479453921 T^{8} )^{2} \))
$41$ (\( 1 - 17544 T^{2} + 152048344 T^{4} - 866284444952 T^{6} + 3637613347314524 T^{8} - 11949543415657926792 T^{10} + \)\(31\!\cdots\!80\)\( T^{12} - \)\(69\!\cdots\!84\)\( T^{14} + \)\(12\!\cdots\!02\)\( T^{16} - \)\(19\!\cdots\!24\)\( T^{18} + \)\(25\!\cdots\!80\)\( T^{20} - \)\(26\!\cdots\!52\)\( T^{22} + \)\(23\!\cdots\!84\)\( T^{24} - \)\(15\!\cdots\!52\)\( T^{26} + \)\(77\!\cdots\!84\)\( T^{28} - \)\(25\!\cdots\!24\)\( T^{30} + \)\(40\!\cdots\!81\)\( T^{32} \))(\( ( 1 - 3764 T^{2} + 15157636 T^{4} - 32470435532 T^{6} + 69381130414198 T^{8} - 91753690379339852 T^{10} + \)\(12\!\cdots\!56\)\( T^{12} - \)\(84\!\cdots\!84\)\( T^{14} + \)\(63\!\cdots\!41\)\( T^{16} )^{2} \))(\( 1 - 7524 T^{2} + 32464386 T^{4} - 93240551380 T^{6} + 206850565610415 T^{8} - 379921653079011144 T^{10} + \)\(65\!\cdots\!56\)\( T^{12} - \)\(10\!\cdots\!84\)\( T^{14} + \)\(16\!\cdots\!15\)\( T^{16} - \)\(21\!\cdots\!80\)\( T^{18} + \)\(20\!\cdots\!26\)\( T^{20} - \)\(13\!\cdots\!24\)\( T^{22} + \)\(50\!\cdots\!61\)\( T^{24} \))(\( ( 1 + 2210 T^{2} + 2825761 T^{4} )^{2} \))(\( ( 1 + 2210 T^{2} + 2825761 T^{4} )^{2} \))(\( ( 1 + 5716 T^{2} + 13775622 T^{4} + 16152049876 T^{6} + 7984925229121 T^{8} )^{4} \))(\( 1 - 10106 T^{2} + 48877645 T^{4} - 146585251874 T^{6} + 296639674915264 T^{8} - 414214887920726114 T^{10} + \)\(39\!\cdots\!45\)\( T^{12} - \)\(22\!\cdots\!86\)\( T^{14} + \)\(63\!\cdots\!41\)\( T^{16} \))(\( 1 - 10494 T^{2} + 51364035 T^{4} - 152997660886 T^{6} + 310636210241223 T^{8} - 486286748354299068 T^{10} + \)\(74\!\cdots\!22\)\( T^{12} - \)\(13\!\cdots\!48\)\( T^{14} + \)\(24\!\cdots\!83\)\( T^{16} - \)\(34\!\cdots\!66\)\( T^{18} + \)\(32\!\cdots\!35\)\( T^{20} - \)\(18\!\cdots\!94\)\( T^{22} + \)\(50\!\cdots\!61\)\( T^{24} \))(\( ( 1 - 3054 T^{2} + 6815636 T^{4} - 8629874094 T^{6} + 7984925229121 T^{8} )^{4} \))(\( ( 1 - 2957 T^{2} + 2825761 T^{4} )^{4} \))
$43$ (\( ( 1 - 140 T + 17296 T^{2} - 1328244 T^{3} + 93523420 T^{4} - 4955438268 T^{5} + 256598382768 T^{6} - 10987637195140 T^{7} + 504821370222726 T^{8} - 20316141173813860 T^{9} + 877258807605621168 T^{10} - 31325124358935759132 T^{11} + \)\(10\!\cdots\!20\)\( T^{12} - \)\(28\!\cdots\!56\)\( T^{13} + \)\(69\!\cdots\!96\)\( T^{14} - \)\(10\!\cdots\!60\)\( T^{15} + \)\(13\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 - 12284 T^{2} + 69244228 T^{4} - 235234411460 T^{6} + 528359315216950 T^{8} - 804219641133859460 T^{10} + \)\(80\!\cdots\!28\)\( T^{12} - \)\(49\!\cdots\!84\)\( T^{14} + \)\(13\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 - 76 T + 9590 T^{2} - 631788 T^{3} + 42146383 T^{4} - 2188827368 T^{5} + 102971644948 T^{6} - 4047141803432 T^{7} + 144090096346783 T^{8} - 3993761318001612 T^{9} + 112089840662193590 T^{10} - 1642472655809602924 T^{11} + 39959630797262576401 T^{12} )^{2} \))(\( ( 1 - 72 T + 2592 T^{2} - 133128 T^{3} + 3418801 T^{4} )^{2} \))(\( ( 1 - 72 T + 2592 T^{2} - 133128 T^{3} + 3418801 T^{4} )^{2} \))(\( ( 1 - 16 T + 128 T^{2} - 2896 T^{3} - 2716702 T^{4} - 5354704 T^{5} + 437606528 T^{6} - 101141808784 T^{7} + 11688200277601 T^{8} )^{4} \))(\( ( 1 - 176 T + 17017 T^{2} - 1139948 T^{3} + 56853640 T^{4} - 2107763852 T^{5} + 58177736617 T^{6} - 1112559896624 T^{7} + 11688200277601 T^{8} )^{2} \))(\( ( 1 + 62 T + 7340 T^{2} + 336972 T^{3} + 27181828 T^{4} + 1019437474 T^{5} + 62011212778 T^{6} + 1884939889426 T^{7} + 92929260748228 T^{8} + 2130122349347628 T^{9} + 85791390037591340 T^{10} + 1339911903423623438 T^{11} + 39959630797262576401 T^{12} )^{2} \))(\( ( 1 - 4124 T^{2} + 11073111 T^{4} - 14099135324 T^{6} + 11688200277601 T^{8} )^{4} \))(\( ( 1 - 12 T + 3484 T^{2} - 22188 T^{3} + 3418801 T^{4} )^{4} \))
$47$ (\( 1 - 16494 T^{2} + 133830909 T^{4} - 714029015638 T^{6} + 2855140329276550 T^{8} - 9328199881448227946 T^{10} + \)\(26\!\cdots\!07\)\( T^{12} - \)\(67\!\cdots\!70\)\( T^{14} + \)\(15\!\cdots\!66\)\( T^{16} - \)\(33\!\cdots\!70\)\( T^{18} + \)\(63\!\cdots\!27\)\( T^{20} - \)\(10\!\cdots\!86\)\( T^{22} + \)\(16\!\cdots\!50\)\( T^{24} - \)\(19\!\cdots\!38\)\( T^{26} + \)\(18\!\cdots\!29\)\( T^{28} - \)\(10\!\cdots\!34\)\( T^{30} + \)\(32\!\cdots\!41\)\( T^{32} \))(\( ( 1 + 12796 T^{2} + 80087860 T^{4} + 312929425156 T^{6} + 830307264656278 T^{8} + 1526995770274655236 T^{10} + \)\(19\!\cdots\!60\)\( T^{12} + \)\(14\!\cdots\!36\)\( T^{14} + \)\(56\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 - 6132 T^{2} + 27456354 T^{4} - 92403901348 T^{6} + 277727516070639 T^{8} - 754801362269230440 T^{10} + \)\(17\!\cdots\!96\)\( T^{12} - \)\(36\!\cdots\!40\)\( T^{14} + \)\(66\!\cdots\!79\)\( T^{16} - \)\(10\!\cdots\!68\)\( T^{18} + \)\(15\!\cdots\!34\)\( T^{20} - \)\(16\!\cdots\!32\)\( T^{22} + \)\(13\!\cdots\!81\)\( T^{24} \))(\( 1 + 9442562 T^{4} + 23811286661761 T^{8} \))(\( 1 + 9442562 T^{4} + 23811286661761 T^{8} \))(\( ( 1 - 5511420 T^{4} + 7619082080518 T^{8} - \)\(13\!\cdots\!20\)\( T^{12} + \)\(56\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 + 72 T + 10951 T^{2} + 664056 T^{3} + 65519473 T^{4} + 3342900456 T^{5} + 246192812578 T^{6} + 10750018584384 T^{7} + 651041931981118 T^{8} + 23746791052904256 T^{9} + 1201342389873427618 T^{10} + 36033843838636290024 T^{11} + \)\(15\!\cdots\!53\)\( T^{12} + \)\(34\!\cdots\!44\)\( T^{13} + \)\(12\!\cdots\!91\)\( T^{14} + \)\(18\!\cdots\!68\)\( T^{15} + \)\(56\!\cdots\!21\)\( T^{16} \))(\( 1 - 96 T + 10053 T^{2} - 670176 T^{3} + 37816182 T^{4} - 1580720664 T^{5} + 53466325187 T^{6} - 1308296276496 T^{7} + 51809528884176 T^{8} - 4886895580883496 T^{9} + 455990427411620625 T^{10} - 31230646812310303944 T^{11} + \)\(16\!\cdots\!56\)\( T^{12} - \)\(68\!\cdots\!96\)\( T^{13} + \)\(22\!\cdots\!25\)\( T^{14} - \)\(52\!\cdots\!84\)\( T^{15} + \)\(12\!\cdots\!36\)\( T^{16} - \)\(68\!\cdots\!04\)\( T^{17} + \)\(62\!\cdots\!67\)\( T^{18} - \)\(40\!\cdots\!16\)\( T^{19} + \)\(21\!\cdots\!22\)\( T^{20} - \)\(83\!\cdots\!64\)\( T^{21} + \)\(27\!\cdots\!53\)\( T^{22} - \)\(58\!\cdots\!64\)\( T^{23} + \)\(13\!\cdots\!81\)\( T^{24} \))(\( ( 1 - 7336 T^{2} + 31122250 T^{4} - 94893243424 T^{6} + 228626385513379 T^{8} - 463048756964467744 T^{10} + \)\(74\!\cdots\!50\)\( T^{12} - \)\(85\!\cdots\!76\)\( T^{14} + \)\(56\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 + 4442 T^{2} + 9608921 T^{4} + 1612805802 T^{6} - 17630196388396 T^{8} + 7869977828709162 T^{10} + \)\(22\!\cdots\!81\)\( T^{12} + \)\(51\!\cdots\!22\)\( T^{14} + \)\(56\!\cdots\!21\)\( T^{16} \))
$53$ (\( 1 - 26408 T^{2} + 323575832 T^{4} - 2478395195256 T^{6} + 13692147525400668 T^{8} - 60596495283388870952 T^{10} + \)\(23\!\cdots\!48\)\( T^{12} - \)\(79\!\cdots\!44\)\( T^{14} + \)\(23\!\cdots\!78\)\( T^{16} - \)\(62\!\cdots\!64\)\( T^{18} + \)\(14\!\cdots\!28\)\( T^{20} - \)\(29\!\cdots\!32\)\( T^{22} + \)\(53\!\cdots\!28\)\( T^{24} - \)\(75\!\cdots\!56\)\( T^{26} + \)\(78\!\cdots\!92\)\( T^{28} - \)\(50\!\cdots\!88\)\( T^{30} + \)\(15\!\cdots\!41\)\( T^{32} \))(\( ( 1 - 8000 T^{2} + 42104908 T^{4} - 150562728128 T^{6} + 466968259413286 T^{8} - 1188012345602149568 T^{10} + \)\(26\!\cdots\!88\)\( T^{12} - \)\(39\!\cdots\!00\)\( T^{14} + \)\(38\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 - 88 T + 10434 T^{2} - 574440 T^{3} + 50272015 T^{4} - 2575931008 T^{5} + 181692199804 T^{6} - 7235790201472 T^{7} + 396670379189215 T^{8} - 12732095606942760 T^{9} + 649617609752140674 T^{10} - 15390097392165148312 T^{11} + \)\(49\!\cdots\!41\)\( T^{12} )^{2} \))(\( 1 + 3420962 T^{4} + 62259690411361 T^{8} \))(\( 1 + 3420962 T^{4} + 62259690411361 T^{8} \))(\( ( 1 - 19870076 T^{4} + 198820934324166 T^{8} - \)\(12\!\cdots\!36\)\( T^{12} + \)\(38\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 + 76 T - 3069 T^{2} - 443764 T^{3} + 2229785 T^{4} + 1396117872 T^{5} + 34651196266 T^{6} - 1991894657480 T^{7} - 169369280357850 T^{8} - 5595232092861320 T^{9} + 273414605764143946 T^{10} + 30944060693658997488 T^{11} + \)\(13\!\cdots\!85\)\( T^{12} - \)\(77\!\cdots\!36\)\( T^{13} - \)\(15\!\cdots\!29\)\( T^{14} + \)\(10\!\cdots\!44\)\( T^{15} + \)\(38\!\cdots\!21\)\( T^{16} \))(\( 1 + 76 T - 11231 T^{2} - 724524 T^{3} + 92836166 T^{4} + 4449767804 T^{5} - 540109351793 T^{6} - 16759328047612 T^{7} + 2565935011756424 T^{8} + 43462405312053452 T^{9} - 9681885823291571571 T^{10} - 46904208416898252492 T^{11} + \)\(30\!\cdots\!44\)\( T^{12} - \)\(13\!\cdots\!28\)\( T^{13} - \)\(76\!\cdots\!51\)\( T^{14} + \)\(96\!\cdots\!08\)\( T^{15} + \)\(15\!\cdots\!64\)\( T^{16} - \)\(29\!\cdots\!88\)\( T^{17} - \)\(26\!\cdots\!13\)\( T^{18} + \)\(61\!\cdots\!76\)\( T^{19} + \)\(35\!\cdots\!86\)\( T^{20} - \)\(78\!\cdots\!36\)\( T^{21} - \)\(34\!\cdots\!31\)\( T^{22} + \)\(65\!\cdots\!84\)\( T^{23} + \)\(24\!\cdots\!81\)\( T^{24} \))(\( ( 1 - 7636 T^{2} + 28650250 T^{4} - 105966940624 T^{6} + 357269785558579 T^{8} - 836130131621800144 T^{10} + \)\(17\!\cdots\!50\)\( T^{12} - \)\(37\!\cdots\!76\)\( T^{14} + \)\(38\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 + 4982 T^{2} + 12556241 T^{4} - 17521091178 T^{6} - 107696253516316 T^{8} - 138249837039276618 T^{10} + \)\(78\!\cdots\!01\)\( T^{12} + \)\(24\!\cdots\!62\)\( T^{14} + \)\(38\!\cdots\!21\)\( T^{16} \))
$59$ (\( 1 - 14800 T^{2} + 138468568 T^{4} - 955392890736 T^{6} + 5479095487372636 T^{8} - 27019630879601870800 T^{10} + \)\(12\!\cdots\!12\)\( T^{12} - \)\(48\!\cdots\!04\)\( T^{14} + \)\(17\!\cdots\!62\)\( T^{16} - \)\(58\!\cdots\!44\)\( T^{18} + \)\(17\!\cdots\!52\)\( T^{20} - \)\(48\!\cdots\!00\)\( T^{22} + \)\(11\!\cdots\!76\)\( T^{24} - \)\(24\!\cdots\!36\)\( T^{26} + \)\(43\!\cdots\!48\)\( T^{28} - \)\(56\!\cdots\!00\)\( T^{30} + \)\(46\!\cdots\!81\)\( T^{32} \))(\( ( 1 - 18308 T^{2} + 161406340 T^{4} - 913248530108 T^{6} + 3699369624469174 T^{8} - 11066162122038004988 T^{10} + \)\(23\!\cdots\!40\)\( T^{12} - \)\(32\!\cdots\!48\)\( T^{14} + \)\(21\!\cdots\!41\)\( T^{16} )^{2} \))(\( 1 - 15948 T^{2} + 137050242 T^{4} - 864152710108 T^{6} + 4419517662043791 T^{8} - 18954945757384385304 T^{10} + \)\(70\!\cdots\!16\)\( T^{12} - \)\(22\!\cdots\!44\)\( T^{14} + \)\(64\!\cdots\!11\)\( T^{16} - \)\(15\!\cdots\!48\)\( T^{18} + \)\(29\!\cdots\!22\)\( T^{20} - \)\(41\!\cdots\!48\)\( T^{22} + \)\(31\!\cdots\!61\)\( T^{24} \))(\( ( 1 - 6080 T^{2} + 12117361 T^{4} )^{2} \))(\( ( 1 - 6080 T^{2} + 12117361 T^{4} )^{2} \))(\( ( 1 - 10776 T^{2} + 52783792 T^{4} - 130576682136 T^{6} + 146830437604321 T^{8} )^{4} \))(\( 1 + 54 T + 7198 T^{2} + 336204 T^{3} + 19932742 T^{4} - 202333950 T^{5} - 35478676088 T^{6} - 7641841019598 T^{7} - 385856896323245 T^{8} - 26601248589220638 T^{9} - 429907925960363768 T^{10} - 8534553984691411950 T^{11} + \)\(29\!\cdots\!82\)\( T^{12} + \)\(17\!\cdots\!04\)\( T^{13} + \)\(12\!\cdots\!38\)\( T^{14} + \)\(33\!\cdots\!94\)\( T^{15} + \)\(21\!\cdots\!41\)\( T^{16} \))(\( 1 + 270 T + 48372 T^{2} + 6499440 T^{3} + 729674841 T^{4} + 72198474768 T^{5} + 6488082937652 T^{6} + 539451035302806 T^{7} + 41805568251303822 T^{8} + 3030722232785131878 T^{9} + \)\(20\!\cdots\!28\)\( T^{10} + \)\(13\!\cdots\!68\)\( T^{11} + \)\(80\!\cdots\!17\)\( T^{12} + \)\(46\!\cdots\!08\)\( T^{13} + \)\(25\!\cdots\!08\)\( T^{14} + \)\(12\!\cdots\!98\)\( T^{15} + \)\(61\!\cdots\!62\)\( T^{16} + \)\(27\!\cdots\!06\)\( T^{17} + \)\(11\!\cdots\!12\)\( T^{18} + \)\(44\!\cdots\!48\)\( T^{19} + \)\(15\!\cdots\!81\)\( T^{20} + \)\(48\!\cdots\!40\)\( T^{21} + \)\(12\!\cdots\!72\)\( T^{22} + \)\(24\!\cdots\!70\)\( T^{23} + \)\(31\!\cdots\!61\)\( T^{24} \))(\( ( 1 + 474 T^{2} + 12860200 T^{4} - 17476496604 T^{6} + 10103548950219 T^{8} - 211769018365942044 T^{10} + \)\(18\!\cdots\!00\)\( T^{12} + \)\(84\!\cdots\!94\)\( T^{14} + \)\(21\!\cdots\!41\)\( T^{16} )^{2} \))(\( 1 + 428 T^{2} - 23559094 T^{4} - 210766032 T^{6} + 414645620367539 T^{8} - 2553928096281552 T^{10} - \)\(34\!\cdots\!74\)\( T^{12} + \)\(76\!\cdots\!68\)\( T^{14} + \)\(21\!\cdots\!41\)\( T^{16} \))
$61$ (\( ( 1 + 28 T + 12104 T^{2} + 279684 T^{3} + 87089292 T^{4} + 2698559212 T^{5} + 465312999544 T^{6} + 14439842194996 T^{7} + 1856098427255974 T^{8} + 53730652807580116 T^{9} + 6442649806919296504 T^{10} + \)\(13\!\cdots\!32\)\( T^{11} + \)\(16\!\cdots\!52\)\( T^{12} + \)\(19\!\cdots\!84\)\( T^{13} + \)\(32\!\cdots\!84\)\( T^{14} + \)\(27\!\cdots\!48\)\( T^{15} + \)\(36\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 - 16940 T^{2} + 152924212 T^{4} - 922409219732 T^{6} + 4001805292894678 T^{8} - 12771531393343334612 T^{10} + \)\(29\!\cdots\!72\)\( T^{12} - \)\(44\!\cdots\!40\)\( T^{14} + \)\(36\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 - 13716 T^{2} + 109224834 T^{4} - 648593370628 T^{6} + 3203041286245839 T^{8} - 13994290873734287016 T^{10} + \)\(55\!\cdots\!56\)\( T^{12} - \)\(19\!\cdots\!56\)\( T^{14} + \)\(61\!\cdots\!59\)\( T^{16} - \)\(17\!\cdots\!88\)\( T^{18} + \)\(40\!\cdots\!74\)\( T^{20} - \)\(69\!\cdots\!16\)\( T^{22} + \)\(70\!\cdots\!41\)\( T^{24} \))(\( ( 1 - 7246 T^{2} + 13845841 T^{4} )^{2} \))(\( ( 1 - 7246 T^{2} + 13845841 T^{4} )^{2} \))(\( ( 1 - 8200 T^{2} + 36103376 T^{4} - 113535896200 T^{6} + 191707312997281 T^{8} )^{4} \))(\( 1 + 396 T + 83164 T^{2} + 12233232 T^{3} + 1413738778 T^{4} + 136250283708 T^{5} + 11318984386192 T^{6} + 825650586150588 T^{7} + 53403008176121923 T^{8} + 3072245831066337948 T^{9} + \)\(15\!\cdots\!72\)\( T^{10} + \)\(70\!\cdots\!88\)\( T^{11} + \)\(27\!\cdots\!18\)\( T^{12} + \)\(87\!\cdots\!32\)\( T^{13} + \)\(22\!\cdots\!44\)\( T^{14} + \)\(39\!\cdots\!36\)\( T^{15} + \)\(36\!\cdots\!61\)\( T^{16} \))(\( 1 + 60 T + 13086 T^{2} + 713160 T^{3} + 79444341 T^{4} + 3022528800 T^{5} + 251078089370 T^{6} + 4114433299500 T^{7} + 360604571968890 T^{8} - 6628548155521500 T^{9} + 198447695188114806 T^{10} - 25628280588886519440 T^{11} + \)\(58\!\cdots\!41\)\( T^{12} - \)\(95\!\cdots\!40\)\( T^{13} + \)\(27\!\cdots\!46\)\( T^{14} - \)\(34\!\cdots\!00\)\( T^{15} + \)\(69\!\cdots\!90\)\( T^{16} + \)\(29\!\cdots\!00\)\( T^{17} + \)\(66\!\cdots\!70\)\( T^{18} + \)\(29\!\cdots\!00\)\( T^{19} + \)\(29\!\cdots\!01\)\( T^{20} + \)\(97\!\cdots\!60\)\( T^{21} + \)\(66\!\cdots\!86\)\( T^{22} + \)\(11\!\cdots\!60\)\( T^{23} + \)\(70\!\cdots\!41\)\( T^{24} \))(\( ( 1 + 98 T + 136 T^{2} + 198548 T^{3} + 40060699 T^{4} + 738797108 T^{5} + 1883034376 T^{6} + 5048996687378 T^{7} + 191707312997281 T^{8} )^{4} \))(\( ( 1 - 132 T + 7586 T^{2} - 316272 T^{3} + 18105699 T^{4} - 1176848112 T^{5} + 105034549826 T^{6} - 6800689415652 T^{7} + 191707312997281 T^{8} )^{2} \))
$67$ (\( ( 1 + 60 T + 16740 T^{2} + 1235332 T^{3} + 154240932 T^{4} + 12326585708 T^{5} + 1033583040796 T^{6} + 78720265804692 T^{7} + 5329117931496566 T^{8} + 353375273197262388 T^{9} + 20827856918628132316 T^{10} + \)\(11\!\cdots\!52\)\( T^{11} + \)\(62\!\cdots\!12\)\( T^{12} + \)\(22\!\cdots\!68\)\( T^{13} + \)\(13\!\cdots\!40\)\( T^{14} + \)\(22\!\cdots\!40\)\( T^{15} + \)\(16\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 - 4700 T^{2} + 31619524 T^{4} - 158634829796 T^{6} + 862906917090742 T^{8} - 3196669650033601316 T^{10} + \)\(12\!\cdots\!84\)\( T^{12} - \)\(38\!\cdots\!00\)\( T^{14} + \)\(16\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 - 84 T + 15366 T^{2} - 763540 T^{3} + 102124911 T^{4} - 4033313976 T^{5} + 514098700788 T^{6} - 18105546438264 T^{7} + 2057931438675231 T^{8} - 69068593121318260 T^{9} + 6239635933335345606 T^{10} - \)\(15\!\cdots\!16\)\( T^{11} + \)\(81\!\cdots\!61\)\( T^{12} )^{2} \))(\( ( 1 - 64 T + 2048 T^{2} - 287296 T^{3} + 20151121 T^{4} )^{2} \))(\( ( 1 - 64 T + 2048 T^{2} - 287296 T^{3} + 20151121 T^{4} )^{2} \))(\( ( 1 - 80 T + 3200 T^{2} + 17520 T^{3} - 22069342 T^{4} + 78647280 T^{5} + 64483587200 T^{6} - 7236670573520 T^{7} + 406067677556641 T^{8} )^{4} \))(\( 1 - 184 T + 6231 T^{2} + 140176 T^{3} + 74370665 T^{4} - 7237038408 T^{5} + 24063966106 T^{6} - 15184872524680 T^{7} + 3087140085953070 T^{8} - 68164892763288520 T^{9} + 484915892741904826 T^{10} - \)\(65\!\cdots\!52\)\( T^{11} + \)\(30\!\cdots\!65\)\( T^{12} + \)\(25\!\cdots\!24\)\( T^{13} + \)\(50\!\cdots\!91\)\( T^{14} - \)\(67\!\cdots\!36\)\( T^{15} + \)\(16\!\cdots\!81\)\( T^{16} \))(\( 1 + 18 T - 15576 T^{2} + 716224 T^{3} + 161647428 T^{4} - 11551101282 T^{5} - 593219478248 T^{6} + 115316141768802 T^{7} - 912928968126828 T^{8} - 541451373822575840 T^{9} + 35055175141983029184 T^{10} + \)\(12\!\cdots\!10\)\( T^{11} - \)\(20\!\cdots\!66\)\( T^{12} + \)\(55\!\cdots\!90\)\( T^{13} + \)\(70\!\cdots\!64\)\( T^{14} - \)\(48\!\cdots\!60\)\( T^{15} - \)\(37\!\cdots\!48\)\( T^{16} + \)\(21\!\cdots\!98\)\( T^{17} - \)\(48\!\cdots\!28\)\( T^{18} - \)\(42\!\cdots\!78\)\( T^{19} + \)\(26\!\cdots\!68\)\( T^{20} + \)\(53\!\cdots\!16\)\( T^{21} - \)\(51\!\cdots\!76\)\( T^{22} + \)\(26\!\cdots\!02\)\( T^{23} + \)\(66\!\cdots\!21\)\( T^{24} \))(\( ( 1 + 12548 T^{2} + 81642721 T^{4} + 445546114868 T^{6} + 2168184767444464 T^{8} + 8978253671784967028 T^{10} + \)\(33\!\cdots\!61\)\( T^{12} + \)\(10\!\cdots\!28\)\( T^{14} + \)\(16\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 - 144 T + 6734 T^{2} - 723456 T^{3} + 82820979 T^{4} - 3247593984 T^{5} + 135697648814 T^{6} - 13026007032336 T^{7} + 406067677556641 T^{8} )^{2} \))
$71$ (\( 1 - 17240 T^{2} + 219765336 T^{4} - 2041434479624 T^{6} + 16624899469572444 T^{8} - \)\(11\!\cdots\!96\)\( T^{10} + \)\(74\!\cdots\!40\)\( T^{12} - \)\(43\!\cdots\!72\)\( T^{14} + \)\(22\!\cdots\!98\)\( T^{16} - \)\(10\!\cdots\!32\)\( T^{18} + \)\(48\!\cdots\!40\)\( T^{20} - \)\(19\!\cdots\!36\)\( T^{22} + \)\(69\!\cdots\!24\)\( T^{24} - \)\(21\!\cdots\!24\)\( T^{26} + \)\(59\!\cdots\!16\)\( T^{28} - \)\(11\!\cdots\!40\)\( T^{30} + \)\(17\!\cdots\!41\)\( T^{32} \))(\( ( 1 + 14 T + 11212 T^{2} + 560234 T^{3} + 58945990 T^{4} + 2824139594 T^{5} + 284915767372 T^{6} + 1793403974894 T^{7} + 645753531245761 T^{8} )^{4} \))(\( ( 1 - 16 T + 16698 T^{2} - 42336 T^{3} + 131112895 T^{4} + 1041328304 T^{5} + 716701578892 T^{6} + 5249335980464 T^{7} + 3331799062726495 T^{8} - 5423253620079456 T^{9} + 10782792464741717178 T^{10} - 52083896816158099216 T^{11} + \)\(16\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 - 6554 T^{2} + 25411681 T^{4} )^{2} \))(\( ( 1 - 6554 T^{2} + 25411681 T^{4} )^{2} \))(\( ( 1 - 17504 T^{2} + 126269762 T^{4} - 444806064224 T^{6} + 645753531245761 T^{8} )^{4} \))(\( ( 1 - 82 T + 12166 T^{2} - 846262 T^{3} + 94594474 T^{4} - 4266006742 T^{5} + 309158511046 T^{6} - 10504223281522 T^{7} + 645753531245761 T^{8} )^{2} \))(\( ( 1 + 314 T + 58704 T^{2} + 7369374 T^{3} + 727286203 T^{4} + 59185452824 T^{5} + 4395000293464 T^{6} + 298353867685784 T^{7} + 18481564986337243 T^{8} + 944018901720035454 T^{9} + 37908315298251153744 T^{10} + \)\(10\!\cdots\!14\)\( T^{11} + \)\(16\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 - 13674 T^{2} + 87943916 T^{4} - 347479325994 T^{6} + 645753531245761 T^{8} )^{4} \))(\( ( 1 - 17824 T^{2} + 128951106 T^{4} - 452937802144 T^{6} + 645753531245761 T^{8} )^{2} \))
$73$ (\( ( 1 + 104 T + 24348 T^{2} + 2586552 T^{3} + 336158388 T^{4} + 30976570216 T^{5} + 3043939907492 T^{6} + 241340462677368 T^{7} + 19104376400195478 T^{8} + 1286103325607694072 T^{9} + 86442539082475521572 T^{10} + \)\(46\!\cdots\!24\)\( T^{11} + \)\(27\!\cdots\!28\)\( T^{12} + \)\(11\!\cdots\!48\)\( T^{13} + \)\(55\!\cdots\!08\)\( T^{14} + \)\(12\!\cdots\!36\)\( T^{15} + \)\(65\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 + 29272 T^{2} + 428373724 T^{4} + 3969975503272 T^{6} + 25265454267874246 T^{8} + \)\(11\!\cdots\!52\)\( T^{10} + \)\(34\!\cdots\!44\)\( T^{12} + \)\(67\!\cdots\!12\)\( T^{14} + \)\(65\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 - 19284 T^{2} + 216036930 T^{4} - 1973102936452 T^{6} + 14880325491672495 T^{8} - 96746229105564519336 T^{10} + \)\(55\!\cdots\!08\)\( T^{12} - \)\(27\!\cdots\!76\)\( T^{14} + \)\(12\!\cdots\!95\)\( T^{16} - \)\(45\!\cdots\!92\)\( T^{18} + \)\(14\!\cdots\!30\)\( T^{20} - \)\(35\!\cdots\!84\)\( T^{22} + \)\(52\!\cdots\!41\)\( T^{24} \))(\( ( 1 + 78 T + 3042 T^{2} + 415662 T^{3} + 28398241 T^{4} )^{2} \))(\( ( 1 - 78 T + 3042 T^{2} - 415662 T^{3} + 28398241 T^{4} )^{2} \))(\( ( 1 - 10432892 T^{4} + 418480444620678 T^{8} - \)\(84\!\cdots\!52\)\( T^{12} + \)\(65\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 - 348 T + 68263 T^{2} - 9707460 T^{3} + 1072498525 T^{4} - 96253557984 T^{5} + 7434307414846 T^{6} - 526544361727584 T^{7} + 37365046682274814 T^{8} - 2805954903646295136 T^{9} + \)\(21\!\cdots\!86\)\( T^{10} - \)\(14\!\cdots\!76\)\( T^{11} + \)\(86\!\cdots\!25\)\( T^{12} - \)\(41\!\cdots\!40\)\( T^{13} + \)\(15\!\cdots\!23\)\( T^{14} - \)\(42\!\cdots\!32\)\( T^{15} + \)\(65\!\cdots\!61\)\( T^{16} \))(\( 1 - 234 T + 50280 T^{2} - 7494552 T^{3} + 1045125336 T^{4} - 124045277670 T^{5} + 13798749511760 T^{6} - 1393240344068466 T^{7} + 132320540590792632 T^{8} - 11749990134656584872 T^{9} + \)\(98\!\cdots\!48\)\( T^{10} - \)\(77\!\cdots\!58\)\( T^{11} + \)\(58\!\cdots\!42\)\( T^{12} - \)\(41\!\cdots\!82\)\( T^{13} + \)\(27\!\cdots\!68\)\( T^{14} - \)\(17\!\cdots\!08\)\( T^{15} + \)\(10\!\cdots\!92\)\( T^{16} - \)\(59\!\cdots\!34\)\( T^{17} + \)\(31\!\cdots\!60\)\( T^{18} - \)\(15\!\cdots\!30\)\( T^{19} + \)\(67\!\cdots\!96\)\( T^{20} - \)\(25\!\cdots\!88\)\( T^{21} + \)\(92\!\cdots\!80\)\( T^{22} - \)\(23\!\cdots\!86\)\( T^{23} + \)\(52\!\cdots\!41\)\( T^{24} \))(\( ( 1 + 10828 T^{2} + 58596841 T^{4} + 20056282108 T^{6} - 696353387031776 T^{8} + 569563132866972028 T^{10} + \)\(47\!\cdots\!21\)\( T^{12} + \)\(24\!\cdots\!88\)\( T^{14} + \)\(65\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 + 144 T + 5384 T^{2} + 675936 T^{3} + 96783519 T^{4} + 3602062944 T^{5} + 152896129544 T^{6} + 21792128585616 T^{7} + 806460091894081 T^{8} )^{2} \))
$79$ (\( ( 1 + 102 T + 30141 T^{2} + 2523638 T^{3} + 463628630 T^{4} + 32866476410 T^{5} + 4655301343539 T^{6} + 284411378115370 T^{7} + 33720462322717682 T^{8} + 1775011410818024170 T^{9} + \)\(18\!\cdots\!59\)\( T^{10} + \)\(79\!\cdots\!10\)\( T^{11} + \)\(70\!\cdots\!30\)\( T^{12} + \)\(23\!\cdots\!38\)\( T^{13} + \)\(17\!\cdots\!81\)\( T^{14} + \)\(37\!\cdots\!62\)\( T^{15} + \)\(23\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 - 116 T + 15892 T^{2} - 1623308 T^{3} + 149086294 T^{4} - 10131065228 T^{5} + 618994687252 T^{6} - 28198144840436 T^{7} + 1517108809906561 T^{8} )^{4} \))(\( ( 1 - 60 T + 22242 T^{2} - 662476 T^{3} + 201003183 T^{4} - 1192106616 T^{5} + 1261845815388 T^{6} - 7439937390456 T^{7} + 7829090259107823 T^{8} - 161039605183729996 T^{9} + 33743534149941729762 T^{10} - \)\(56\!\cdots\!60\)\( T^{11} + \)\(59\!\cdots\!41\)\( T^{12} )^{2} \))(\( ( 1 - 9346 T^{2} + 38950081 T^{4} )^{2} \))(\( ( 1 - 9346 T^{2} + 38950081 T^{4} )^{2} \))(\( ( 1 - 6736 T^{2} + 38950081 T^{4} )^{8} \))(\( 1 + 206 T + 5583 T^{2} - 659438 T^{3} + 124066817 T^{4} + 19494076044 T^{5} + 428008398310 T^{6} + 33090623674568 T^{7} + 7605703397631354 T^{8} + 206518582352978888 T^{9} + 16670961782854763110 T^{10} + \)\(47\!\cdots\!24\)\( T^{11} + \)\(18\!\cdots\!37\)\( T^{12} - \)\(62\!\cdots\!38\)\( T^{13} + \)\(32\!\cdots\!03\)\( T^{14} + \)\(75\!\cdots\!86\)\( T^{15} + \)\(23\!\cdots\!21\)\( T^{16} \))(\( 1 - 108 T - 6108 T^{2} + 1752736 T^{3} - 90950172 T^{4} - 3971475972 T^{5} + 1036682005132 T^{6} - 72467068572108 T^{7} - 540849229955460 T^{8} + 549266052938802784 T^{9} - 33282724854561757956 T^{10} - \)\(11\!\cdots\!32\)\( T^{11} + \)\(26\!\cdots\!02\)\( T^{12} - \)\(70\!\cdots\!12\)\( T^{13} - \)\(12\!\cdots\!36\)\( T^{14} + \)\(13\!\cdots\!64\)\( T^{15} - \)\(82\!\cdots\!60\)\( T^{16} - \)\(68\!\cdots\!08\)\( T^{17} + \)\(61\!\cdots\!12\)\( T^{18} - \)\(14\!\cdots\!32\)\( T^{19} - \)\(20\!\cdots\!12\)\( T^{20} + \)\(25\!\cdots\!96\)\( T^{21} - \)\(54\!\cdots\!08\)\( T^{22} - \)\(60\!\cdots\!28\)\( T^{23} + \)\(34\!\cdots\!81\)\( T^{24} \))(\( ( 1 - 152 T + 4981 T^{2} - 857432 T^{3} + 145300984 T^{4} - 5351233112 T^{5} + 194010353461 T^{6} - 36949293239192 T^{7} + 1517108809906561 T^{8} )^{4} \))(\( ( 1 + 172 T + 9796 T^{2} + 1256632 T^{3} + 167981119 T^{4} + 7842640312 T^{5} + 381554993476 T^{6} + 41811042349612 T^{7} + 1517108809906561 T^{8} )^{2} \))
$83$ (\( 1 - 42240 T^{2} + 975418872 T^{4} - 15454190107264 T^{6} + 185929829730979228 T^{8} - \)\(17\!\cdots\!28\)\( T^{10} + \)\(14\!\cdots\!28\)\( T^{12} - \)\(10\!\cdots\!48\)\( T^{14} + \)\(75\!\cdots\!98\)\( T^{16} - \)\(51\!\cdots\!08\)\( T^{18} + \)\(33\!\cdots\!48\)\( T^{20} - \)\(19\!\cdots\!08\)\( T^{22} + \)\(94\!\cdots\!68\)\( T^{24} - \)\(37\!\cdots\!64\)\( T^{26} + \)\(11\!\cdots\!12\)\( T^{28} - \)\(22\!\cdots\!40\)\( T^{30} + \)\(25\!\cdots\!61\)\( T^{32} \))(\( ( 1 - 824 T^{2} + 2185948 T^{4} + 170361875704 T^{6} - 285114310603514 T^{8} + 8085088583322532984 T^{10} + \)\(49\!\cdots\!68\)\( T^{12} - \)\(88\!\cdots\!64\)\( T^{14} + \)\(50\!\cdots\!81\)\( T^{16} )^{2} \))(\( 1 - 45420 T^{2} + 1066844514 T^{4} - 17098817034364 T^{6} + 206563644037003983 T^{8} - \)\(19\!\cdots\!08\)\( T^{10} + \)\(15\!\cdots\!04\)\( T^{12} - \)\(93\!\cdots\!68\)\( T^{14} + \)\(46\!\cdots\!03\)\( T^{16} - \)\(18\!\cdots\!04\)\( T^{18} + \)\(54\!\cdots\!34\)\( T^{20} - \)\(10\!\cdots\!20\)\( T^{22} + \)\(11\!\cdots\!21\)\( T^{24} \))(\( 1 + 27716834 T^{4} + 2252292232139041 T^{8} \))(\( 1 + 27716834 T^{4} + 2252292232139041 T^{8} \))(\( ( 1 - 55419104 T^{4} + 5263624308845250 T^{8} - \)\(12\!\cdots\!64\)\( T^{12} + \)\(50\!\cdots\!81\)\( T^{16} )^{2} \))(\( 1 - 20672 T^{2} + 223804480 T^{4} - 2182268545136 T^{6} + 17948924233578718 T^{8} - \)\(10\!\cdots\!56\)\( T^{10} + \)\(50\!\cdots\!80\)\( T^{12} - \)\(22\!\cdots\!92\)\( T^{14} + \)\(50\!\cdots\!81\)\( T^{16} \))(\( 1 - 52956 T^{2} + 1343643534 T^{4} - 21859222482508 T^{6} + 258399723525197679 T^{8} - \)\(23\!\cdots\!76\)\( T^{10} + \)\(18\!\cdots\!16\)\( T^{12} - \)\(11\!\cdots\!96\)\( T^{14} + \)\(58\!\cdots\!39\)\( T^{16} - \)\(23\!\cdots\!88\)\( T^{18} + \)\(68\!\cdots\!54\)\( T^{20} - \)\(12\!\cdots\!56\)\( T^{22} + \)\(11\!\cdots\!21\)\( T^{24} \))(\( ( 1 + 7386 T^{2} + 83632076 T^{4} + 350527158906 T^{6} + 2252292232139041 T^{8} )^{4} \))(\( ( 1 - 14396 T^{2} + 103463846 T^{4} - 683209989116 T^{6} + 2252292232139041 T^{8} )^{2} \))
$89$ (\( 1 - 33032 T^{2} + 706967320 T^{4} - 12081015642520 T^{6} + 168525587092572636 T^{8} - \)\(20\!\cdots\!04\)\( T^{10} + \)\(21\!\cdots\!16\)\( T^{12} - \)\(20\!\cdots\!76\)\( T^{14} + \)\(16\!\cdots\!54\)\( T^{16} - \)\(12\!\cdots\!16\)\( T^{18} + \)\(84\!\cdots\!96\)\( T^{20} - \)\(50\!\cdots\!84\)\( T^{22} + \)\(26\!\cdots\!96\)\( T^{24} - \)\(11\!\cdots\!20\)\( T^{26} + \)\(43\!\cdots\!20\)\( T^{28} - \)\(12\!\cdots\!92\)\( T^{30} + \)\(24\!\cdots\!21\)\( T^{32} \))(\( ( 1 - 45764 T^{2} + 1024809508 T^{4} - 14337857169596 T^{6} + 136319750978901046 T^{8} - \)\(89\!\cdots\!36\)\( T^{10} + \)\(40\!\cdots\!48\)\( T^{12} - \)\(11\!\cdots\!44\)\( T^{14} + \)\(15\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 - 46020 T^{2} + 1126013634 T^{4} - 19221077499316 T^{6} + 252845241317038383 T^{8} - \)\(26\!\cdots\!72\)\( T^{10} + \)\(23\!\cdots\!84\)\( T^{12} - \)\(16\!\cdots\!52\)\( T^{14} + \)\(99\!\cdots\!23\)\( T^{16} - \)\(47\!\cdots\!36\)\( T^{18} + \)\(17\!\cdots\!74\)\( T^{20} - \)\(44\!\cdots\!20\)\( T^{22} + \)\(61\!\cdots\!41\)\( T^{24} \))(\( ( 1 - 15450 T^{2} + 62742241 T^{4} )^{2} \))(\( ( 1 - 15450 T^{2} + 62742241 T^{4} )^{2} \))(\( ( 1 - 1108 T^{2} - 101931898 T^{4} - 69518403028 T^{6} + 3936588805702081 T^{8} )^{4} \))(\( 1 - 282 T + 59686 T^{2} - 9356196 T^{3} + 1240796086 T^{4} - 138656838366 T^{5} + 14271061565800 T^{6} - 1337157406377822 T^{7} + 121622616146107507 T^{8} - 10591623815918728062 T^{9} + \)\(89\!\cdots\!00\)\( T^{10} - \)\(68\!\cdots\!26\)\( T^{11} + \)\(48\!\cdots\!66\)\( T^{12} - \)\(29\!\cdots\!96\)\( T^{13} + \)\(14\!\cdots\!06\)\( T^{14} - \)\(55\!\cdots\!62\)\( T^{15} + \)\(15\!\cdots\!61\)\( T^{16} \))(\( 1 + 186 T + 44532 T^{2} + 6138000 T^{3} + 889877673 T^{4} + 104389916664 T^{5} + 11976622429892 T^{6} + 1266314492339586 T^{7} + 128180246542580718 T^{8} + 12521360973919319370 T^{9} + \)\(11\!\cdots\!68\)\( T^{10} + \)\(10\!\cdots\!44\)\( T^{11} + \)\(99\!\cdots\!61\)\( T^{12} + \)\(86\!\cdots\!24\)\( T^{13} + \)\(74\!\cdots\!88\)\( T^{14} + \)\(62\!\cdots\!70\)\( T^{15} + \)\(50\!\cdots\!58\)\( T^{16} + \)\(39\!\cdots\!86\)\( T^{17} + \)\(29\!\cdots\!32\)\( T^{18} + \)\(20\!\cdots\!24\)\( T^{19} + \)\(13\!\cdots\!53\)\( T^{20} + \)\(75\!\cdots\!00\)\( T^{21} + \)\(43\!\cdots\!32\)\( T^{22} + \)\(14\!\cdots\!06\)\( T^{23} + \)\(61\!\cdots\!41\)\( T^{24} \))(\( ( 1 - 1586 T^{2} - 121555520 T^{4} + 2241915676 T^{6} + 11299181809334539 T^{8} + 140662813645269916 T^{10} - \)\(47\!\cdots\!20\)\( T^{12} - \)\(39\!\cdots\!06\)\( T^{14} + \)\(15\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 + 28948 T^{2} + 504871786 T^{4} + 6010485861328 T^{6} + 54451796051280979 T^{8} + \)\(37\!\cdots\!48\)\( T^{10} + \)\(19\!\cdots\!66\)\( T^{12} + \)\(71\!\cdots\!08\)\( T^{14} + \)\(15\!\cdots\!61\)\( T^{16} \))
$97$ (\( ( 1 - 364 T + 112297 T^{2} - 23728036 T^{3} + 4389819350 T^{4} - 662305688748 T^{5} + 89325314408919 T^{6} - 10317093604637892 T^{7} + 1074975098720446610 T^{8} - 97073533726037925828 T^{9} + \)\(79\!\cdots\!39\)\( T^{10} - \)\(55\!\cdots\!92\)\( T^{11} + \)\(34\!\cdots\!50\)\( T^{12} - \)\(17\!\cdots\!64\)\( T^{13} + \)\(77\!\cdots\!77\)\( T^{14} - \)\(23\!\cdots\!16\)\( T^{15} + \)\(61\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 + 24808 T^{2} + 234463420 T^{4} + 1188451115032 T^{6} + 6842815259264902 T^{8} + \)\(10\!\cdots\!92\)\( T^{10} + \)\(18\!\cdots\!20\)\( T^{12} + \)\(17\!\cdots\!28\)\( T^{14} + \)\(61\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 - 51924 T^{2} + 1396974978 T^{4} - 26352399780484 T^{6} + 389015604150559215 T^{8} - \)\(47\!\cdots\!84\)\( T^{10} + \)\(48\!\cdots\!52\)\( T^{12} - \)\(41\!\cdots\!04\)\( T^{14} + \)\(30\!\cdots\!15\)\( T^{16} - \)\(18\!\cdots\!44\)\( T^{18} + \)\(85\!\cdots\!38\)\( T^{20} - \)\(28\!\cdots\!24\)\( T^{22} + \)\(48\!\cdots\!81\)\( T^{24} \))(\( ( 1 + 226 T + 25538 T^{2} + 2126434 T^{3} + 88529281 T^{4} )^{2} \))(\( ( 1 - 226 T + 25538 T^{2} - 2126434 T^{3} + 88529281 T^{4} )^{2} \))(\( ( 1 + 284585220 T^{4} + 35721324461420038 T^{8} + \)\(22\!\cdots\!20\)\( T^{12} + \)\(61\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 - 44576 T^{2} + 925514428 T^{4} - 12414040936928 T^{6} + 128325632901816454 T^{8} - \)\(10\!\cdots\!68\)\( T^{10} + \)\(72\!\cdots\!08\)\( T^{12} - \)\(30\!\cdots\!16\)\( T^{14} + \)\(61\!\cdots\!21\)\( T^{16} \))(\( 1 - 64740 T^{2} + 2084566242 T^{4} - 44252577868756 T^{6} + 697286703828717423 T^{8} - \)\(87\!\cdots\!56\)\( T^{10} + \)\(89\!\cdots\!48\)\( T^{12} - \)\(77\!\cdots\!36\)\( T^{14} + \)\(54\!\cdots\!03\)\( T^{16} - \)\(30\!\cdots\!96\)\( T^{18} + \)\(12\!\cdots\!82\)\( T^{20} - \)\(35\!\cdots\!40\)\( T^{22} + \)\(48\!\cdots\!81\)\( T^{24} \))(\( ( 1 - 37448 T^{2} + 527638098 T^{4} - 3315244514888 T^{6} + 7837433594376961 T^{8} )^{4} \))(\( ( 1 + 112 T + 21704 T^{2} + 1053808 T^{3} + 88529281 T^{4} )^{4} \))
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