Properties

Label 210.3
Level 210
Weight 3
Dimension 504
Nonzero newspaces 12
Newform subspaces 17
Sturm bound 6912
Trace bound 5

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Defining parameters

Level: \( N \) = \( 210\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 17 \)
Sturm bound: \(6912\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(210))\).

Total New Old
Modular forms 2496 504 1992
Cusp forms 2112 504 1608
Eisenstein series 384 0 384

Trace form

\( 504q - 8q^{2} - 20q^{3} - 16q^{4} - 12q^{5} + 16q^{6} + 40q^{7} + 16q^{8} + 44q^{9} + O(q^{10}) \) \( 504q - 8q^{2} - 20q^{3} - 16q^{4} - 12q^{5} + 16q^{6} + 40q^{7} + 16q^{8} + 44q^{9} + 72q^{10} + 104q^{11} + 40q^{12} + 112q^{13} + 76q^{15} - 32q^{16} + 8q^{17} - 40q^{18} - 80q^{19} - 16q^{20} - 28q^{21} - 64q^{22} - 64q^{23} - 48q^{24} + 228q^{25} + 144q^{26} - 56q^{27} + 128q^{28} + 240q^{29} + 156q^{30} + 624q^{31} + 32q^{32} + 372q^{33} + 320q^{34} + 100q^{35} + 96q^{36} - 96q^{37} - 304q^{38} - 352q^{39} - 48q^{40} - 736q^{41} - 352q^{42} - 1200q^{43} - 336q^{44} - 666q^{45} - 592q^{46} - 552q^{47} - 32q^{48} + 24q^{49} - 88q^{50} - 124q^{51} + 64q^{52} - 8q^{53} - 192q^{54} + 248q^{55} + 128q^{56} + 680q^{57} + 640q^{58} + 1008q^{59} + 252q^{60} + 1632q^{61} + 160q^{62} - 116q^{63} + 128q^{64} + 564q^{65} - 32q^{66} - 32q^{67} - 16q^{68} - 104q^{69} - 456q^{70} - 704q^{71} - 16q^{72} - 1552q^{73} - 480q^{74} - 298q^{75} - 592q^{76} - 1312q^{77} - 848q^{78} - 1408q^{79} + 48q^{80} - 276q^{81} - 928q^{82} - 1728q^{83} - 216q^{84} - 1568q^{85} + 336q^{86} - 1392q^{87} + 416q^{88} + 144q^{89} - 744q^{90} + 688q^{91} + 160q^{92} - 628q^{93} + 1552q^{94} + 244q^{95} - 32q^{96} + 40q^{97} + 312q^{98} - 1288q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(210))\)

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
210.3.c \(\chi_{210}(29, \cdot)\) 210.3.c.a 24 1
210.3.e \(\chi_{210}(71, \cdot)\) 210.3.e.a 16 1
210.3.f \(\chi_{210}(181, \cdot)\) 210.3.f.a 8 1
210.3.h \(\chi_{210}(139, \cdot)\) 210.3.h.a 16 1
210.3.k \(\chi_{210}(83, \cdot)\) 210.3.k.a 32 2
210.3.k.b 32
210.3.l \(\chi_{210}(43, \cdot)\) 210.3.l.a 8 2
210.3.l.b 16
210.3.o \(\chi_{210}(31, \cdot)\) 210.3.o.a 8 2
210.3.o.b 16
210.3.p \(\chi_{210}(19, \cdot)\) 210.3.p.a 32 2
210.3.q \(\chi_{210}(149, \cdot)\) 210.3.q.a 64 2
210.3.s \(\chi_{210}(11, \cdot)\) 210.3.s.a 40 2
210.3.v \(\chi_{210}(37, \cdot)\) 210.3.v.a 32 4
210.3.v.b 32
210.3.w \(\chi_{210}(17, \cdot)\) 210.3.w.a 64 4
210.3.w.b 64

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(210))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(210)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 + 2 T^{2} )^{8} \))(\( ( 1 - 2 T^{2} )^{4} \))(\( ( 1 + 2 T^{2} )^{8} \))(\( ( 1 - 2 T + 2 T^{2} )^{4} \))(\( ( 1 + 2 T + 2 T^{2} )^{8} \))(\( ( 1 + 2 T^{2} + 4 T^{4} )^{2} \))(\( ( 1 + 2 T^{2} + 4 T^{4} )^{4} \))
$3$ (\( 1 + 8 T + 34 T^{2} + 80 T^{3} + 97 T^{4} + 80 T^{5} + 498 T^{6} + 3288 T^{7} + 11844 T^{8} + 29592 T^{9} + 40338 T^{10} + 58320 T^{11} + 636417 T^{12} + 4723920 T^{13} + 18068994 T^{14} + 38263752 T^{15} + 43046721 T^{16} \))(\( ( 1 + 3 T^{2} )^{4} \))(\( ( 1 - 3 T^{2} )^{8} \))(\( ( 1 + 9 T^{4} )^{2} \))(\( ( 1 + 9 T^{4} )^{4} \))(\( ( 1 - 3 T + 3 T^{2} )^{4} \))(\( ( 1 + 3 T + 3 T^{2} )^{8} \))
$5$ (\( ( 1 + 5 T^{2} )^{8} \))(\( ( 1 + 5 T^{2} )^{4} \))(\( 1 - 12 T^{2} - 376 T^{4} - 3300 T^{6} + 588750 T^{8} - 2062500 T^{10} - 146875000 T^{12} - 2929687500 T^{14} + 152587890625 T^{16} \))(\( 1 + 24 T^{2} + 50 T^{4} + 15000 T^{6} + 390625 T^{8} \))(\( 1 + 16 T + 108 T^{2} + 240 T^{3} - 1736 T^{4} - 15856 T^{5} - 26268 T^{6} + 353520 T^{7} + 2938350 T^{8} + 8838000 T^{9} - 16417500 T^{10} - 247750000 T^{11} - 678125000 T^{12} + 2343750000 T^{13} + 26367187500 T^{14} + 97656250000 T^{15} + 152587890625 T^{16} \))(\( ( 1 - 5 T^{2} + 25 T^{4} )^{2} \))(\( ( 1 - 5 T^{2} + 25 T^{4} )^{4} \))
$7$ (\( ( 1 - 7 T^{2} )^{8} \))(\( 1 + 12 T^{2} - 2842 T^{4} + 28812 T^{6} + 5764801 T^{8} \))(\( 1 - 112 T^{2} + 3932 T^{4} - 24720 T^{6} - 1183546 T^{8} - 59352720 T^{10} + 22667197532 T^{12} - 1550224166512 T^{14} + 33232930569601 T^{16} \))(\( ( 1 + 49 T^{4} )^{2} \))(\( ( 1 + 49 T^{4} )^{4} \))(\( 1 - 78 T^{2} + 5243 T^{4} - 187278 T^{6} + 5764801 T^{8} \))(\( 1 - 4 T + 28 T^{2} - 352 T^{3} + 2898 T^{4} - 16836 T^{5} + 70272 T^{6} - 1158948 T^{7} + 7794283 T^{8} - 56788452 T^{9} + 168723072 T^{10} - 1980738564 T^{11} + 16706393298 T^{12} - 99431287648 T^{13} + 387556041628 T^{14} - 2712892291396 T^{15} + 33232930569601 T^{16} \))
$11$ (\( 1 - 588 T^{2} + 192110 T^{4} - 45729776 T^{6} + 8909879425 T^{8} - 1517060018584 T^{10} + 233462822472086 T^{12} - 32740893640977644 T^{14} + 4166709531307795396 T^{16} - \)\(47\!\cdots\!04\)\( T^{18} + \)\(50\!\cdots\!66\)\( T^{20} - \)\(47\!\cdots\!64\)\( T^{22} + \)\(40\!\cdots\!25\)\( T^{24} - \)\(30\!\cdots\!76\)\( T^{26} + \)\(18\!\cdots\!10\)\( T^{28} - \)\(84\!\cdots\!28\)\( T^{30} + \)\(21\!\cdots\!21\)\( T^{32} \))(\( ( 1 + 8 T + 304 T^{2} + 2120 T^{3} + 45250 T^{4} + 256520 T^{5} + 4450864 T^{6} + 14172488 T^{7} + 214358881 T^{8} )^{2} \))(\( ( 1 - 24 T + 512 T^{2} - 6936 T^{3} + 89778 T^{4} - 839256 T^{5} + 7496192 T^{6} - 42517464 T^{7} + 214358881 T^{8} )^{4} \))(\( ( 1 + 4 T + 120 T^{2} - 964 T^{3} + 9758 T^{4} - 116644 T^{5} + 1756920 T^{6} + 7086244 T^{7} + 214358881 T^{8} )^{2} \))(\( ( 1 - 4 T + 428 T^{2} - 3020 T^{3} + 112132 T^{4} - 750180 T^{5} + 21255892 T^{6} - 132232716 T^{7} + 2897491254 T^{8} - 16000158636 T^{9} + 311207514772 T^{10} - 1328989630980 T^{11} + 24036490044292 T^{12} - 78331022295020 T^{13} + 1343247345236588 T^{14} - 1518999334332964 T^{15} + 45949729863572161 T^{16} )^{2} \))(\( 1 + 4 T - 168 T^{2} + 1928 T^{3} + 16250 T^{4} - 341700 T^{5} + 2353408 T^{6} + 32486668 T^{7} - 296735661 T^{8} + 3930886828 T^{9} + 34456246528 T^{10} - 605342393700 T^{11} + 3483331816250 T^{12} + 50007354630728 T^{13} - 527255967289128 T^{14} + 1518999334332964 T^{15} + 45949729863572161 T^{16} \))(\( 1 + 4 T - 364 T^{2} - 2552 T^{3} + 54108 T^{4} + 655724 T^{5} - 3422504 T^{6} - 97911028 T^{7} - 146055574 T^{8} + 11147160032 T^{9} + 52178728220 T^{10} - 1271915177612 T^{11} - 12776124769680 T^{12} + 140823145942564 T^{13} + 3084355376442156 T^{14} - 7698059096283072 T^{15} - 472018303966569005 T^{16} - 931465150650251712 T^{17} + 45158047066489605996 T^{18} + \)\(24\!\cdots\!04\)\( T^{19} - \)\(27\!\cdots\!80\)\( T^{20} - \)\(32\!\cdots\!12\)\( T^{21} + \)\(16\!\cdots\!20\)\( T^{22} + \)\(42\!\cdots\!12\)\( T^{23} - \)\(67\!\cdots\!14\)\( T^{24} - \)\(54\!\cdots\!68\)\( T^{25} - \)\(23\!\cdots\!04\)\( T^{26} + \)\(53\!\cdots\!04\)\( T^{27} + \)\(53\!\cdots\!28\)\( T^{28} - \)\(30\!\cdots\!72\)\( T^{29} - \)\(52\!\cdots\!84\)\( T^{30} + \)\(69\!\cdots\!04\)\( T^{31} + \)\(21\!\cdots\!21\)\( T^{32} \))
$13$ (\( ( 1 + 494 T^{2} - 456 T^{3} + 146293 T^{4} - 55296 T^{5} + 35813146 T^{6} - 25079880 T^{7} + 6821269256 T^{8} - 4238499720 T^{9} + 1022859262906 T^{10} - 266903230464 T^{11} + 119335694367253 T^{12} - 62863472283144 T^{13} + 11509254050505614 T^{14} + 665416609183179841 T^{16} )^{2} \))(\( 1 - 1088 T^{2} + 557124 T^{4} - 173160640 T^{6} + 35590649030 T^{8} - 4945641039040 T^{10} + 454463162206404 T^{12} - 25348316613259328 T^{14} + 665416609183179841 T^{16} \))(\( ( 1 + 308 T^{2} + 54824 T^{4} + 3243420 T^{6} - 106725490 T^{8} + 92635318620 T^{10} + 44721621048104 T^{12} + 7175810217724148 T^{14} + 665416609183179841 T^{16} )^{2} \))(\( 1 - 8 T + 32 T^{2} - 1000 T^{3} + 57188 T^{4} - 379192 T^{5} + 1703520 T^{6} - 57464472 T^{7} + 1905455878 T^{8} - 9711495768 T^{9} + 48654234720 T^{10} - 1830287358328 T^{11} + 46650008472548 T^{12} - 137858491849000 T^{13} + 745538723919392 T^{14} - 31499011085594312 T^{15} + 665416609183179841 T^{16} \))(\( 1 + 32 T + 512 T^{2} + 12624 T^{3} + 210400 T^{4} + 1218608 T^{5} + 10953344 T^{6} - 12361888 T^{7} - 9595251012 T^{8} - 144909422048 T^{9} - 1442470310272 T^{10} - 30698489798640 T^{11} - 199614992290272 T^{12} + 2586969858854768 T^{13} + 29532641854346496 T^{14} + 799237423444942944 T^{15} + 19007129532539001606 T^{16} + \)\(13\!\cdots\!36\)\( T^{17} + \)\(84\!\cdots\!56\)\( T^{18} + \)\(12\!\cdots\!12\)\( T^{19} - \)\(16\!\cdots\!12\)\( T^{20} - \)\(42\!\cdots\!60\)\( T^{21} - \)\(33\!\cdots\!32\)\( T^{22} - \)\(57\!\cdots\!72\)\( T^{23} - \)\(63\!\cdots\!92\)\( T^{24} - \)\(13\!\cdots\!52\)\( T^{25} + \)\(20\!\cdots\!44\)\( T^{26} + \)\(39\!\cdots\!52\)\( T^{27} + \)\(11\!\cdots\!00\)\( T^{28} + \)\(11\!\cdots\!16\)\( T^{29} + \)\(79\!\cdots\!52\)\( T^{30} + \)\(83\!\cdots\!68\)\( T^{31} + \)\(44\!\cdots\!81\)\( T^{32} \))(\( 1 - 860 T^{2} + 357498 T^{4} - 95438800 T^{6} + 18541152803 T^{8} - 2725827566800 T^{10} + 291622101296058 T^{12} - 20036353205333660 T^{14} + 665416609183179841 T^{16} \))(\( 1 - 1336 T^{2} + 822548 T^{4} - 307870064 T^{6} + 77337463770 T^{8} - 13349067637096 T^{10} + 1484717408181296 T^{12} - 75519988778385192 T^{14} - 843289248891793565 T^{16} - \)\(21\!\cdots\!12\)\( T^{18} + \)\(12\!\cdots\!16\)\( T^{20} - \)\(31\!\cdots\!76\)\( T^{22} + \)\(51\!\cdots\!70\)\( T^{24} - \)\(58\!\cdots\!64\)\( T^{26} + \)\(44\!\cdots\!28\)\( T^{28} - \)\(20\!\cdots\!56\)\( T^{30} + \)\(44\!\cdots\!81\)\( T^{32} \))
$17$ (\( 1 - 2012 T^{2} + 2016998 T^{4} - 1352297560 T^{6} + 695200323953 T^{8} - 299701490294440 T^{10} + 114417537477919350 T^{12} - 39314188029348430308 T^{14} + \)\(12\!\cdots\!52\)\( T^{16} - \)\(32\!\cdots\!68\)\( T^{18} + \)\(79\!\cdots\!50\)\( T^{20} - \)\(17\!\cdots\!40\)\( T^{22} + \)\(33\!\cdots\!93\)\( T^{24} - \)\(54\!\cdots\!60\)\( T^{26} + \)\(68\!\cdots\!58\)\( T^{28} - \)\(57\!\cdots\!92\)\( T^{30} + \)\(23\!\cdots\!61\)\( T^{32} \))(\( ( 1 - 716 T^{2} + 266406 T^{4} - 59801036 T^{6} + 6975757441 T^{8} )^{2} \))(\( ( 1 + 1316 T^{2} + 881960 T^{4} + 398466540 T^{6} + 132906424526 T^{8} + 33280323887340 T^{10} + 6152339032664360 T^{12} + 766730864194365476 T^{14} + 48661191875666868481 T^{16} )^{2} \))(\( 1 + 32 T + 512 T^{2} + 13280 T^{3} + 494308 T^{4} + 9125408 T^{5} + 127106560 T^{6} + 2946229728 T^{7} + 67506528198 T^{8} + 851460391392 T^{9} + 10616066997760 T^{10} + 220265165253152 T^{11} + 3448172709145828 T^{12} + 26772398997962720 T^{13} + 298302585461637632 T^{14} + 5388090449900829728 T^{15} + 48661191875666868481 T^{16} \))(\( 1 - 56 T + 1568 T^{2} - 29832 T^{3} + 267808 T^{4} + 3397960 T^{5} - 165234592 T^{6} + 3465012472 T^{7} - 48572233284 T^{8} + 491667950696 T^{9} - 4716183819232 T^{10} + 39445096533336 T^{11} + 280624802792928 T^{12} - 26208629063564312 T^{13} + 761979769352889696 T^{14} - 15987258252632453928 T^{15} + \)\(28\!\cdots\!74\)\( T^{16} - \)\(46\!\cdots\!92\)\( T^{17} + \)\(63\!\cdots\!16\)\( T^{18} - \)\(63\!\cdots\!28\)\( T^{19} + \)\(19\!\cdots\!48\)\( T^{20} + \)\(79\!\cdots\!64\)\( T^{21} - \)\(27\!\cdots\!52\)\( T^{22} + \)\(82\!\cdots\!84\)\( T^{23} - \)\(23\!\cdots\!04\)\( T^{24} + \)\(48\!\cdots\!48\)\( T^{25} - \)\(67\!\cdots\!92\)\( T^{26} + \)\(39\!\cdots\!40\)\( T^{27} + \)\(90\!\cdots\!68\)\( T^{28} - \)\(29\!\cdots\!08\)\( T^{29} + \)\(44\!\cdots\!88\)\( T^{30} - \)\(45\!\cdots\!44\)\( T^{31} + \)\(23\!\cdots\!61\)\( T^{32} \))(\( 1 - 84 T + 4208 T^{2} - 155904 T^{3} + 4746250 T^{4} - 123749124 T^{5} + 2818194464 T^{6} - 56792172564 T^{7} + 1020121281523 T^{8} - 16412937870996 T^{9} + 235378419827744 T^{10} - 2987003019239556 T^{11} + 33108688754346250 T^{12} - 314301513055600896 T^{13} + 2451674374262834288 T^{14} - 14143737430989678036 T^{15} + 48661191875666868481 T^{16} \))(\( 1 - 12 T + 420 T^{2} - 4464 T^{3} + 92044 T^{4} - 785292 T^{5} + 23989560 T^{6} + 227912772 T^{7} - 3236850998 T^{8} + 177940653384 T^{9} - 2004860299572 T^{10} + 43692613137348 T^{11} - 466147839356624 T^{12} + 8985915182672820 T^{13} - 29797959923559588 T^{14} - 769960022203743096 T^{15} + 34516652247342574675 T^{16} - \)\(22\!\cdots\!44\)\( T^{17} - \)\(24\!\cdots\!48\)\( T^{18} + \)\(21\!\cdots\!80\)\( T^{19} - \)\(32\!\cdots\!84\)\( T^{20} + \)\(88\!\cdots\!52\)\( T^{21} - \)\(11\!\cdots\!92\)\( T^{22} + \)\(29\!\cdots\!36\)\( T^{23} - \)\(15\!\cdots\!38\)\( T^{24} + \)\(32\!\cdots\!48\)\( T^{25} + \)\(97\!\cdots\!60\)\( T^{26} - \)\(92\!\cdots\!88\)\( T^{27} + \)\(31\!\cdots\!24\)\( T^{28} - \)\(43\!\cdots\!16\)\( T^{29} + \)\(11\!\cdots\!20\)\( T^{30} - \)\(98\!\cdots\!88\)\( T^{31} + \)\(23\!\cdots\!61\)\( T^{32} \))
$19$ (\( ( 1 - 24 T + 1612 T^{2} - 39608 T^{3} + 1389160 T^{4} - 32391560 T^{5} + 808980068 T^{6} - 17015640488 T^{7} + 341271444494 T^{8} - 6142646216168 T^{9} + 105427091441828 T^{10} - 1523889477164360 T^{11} + 23592886434035560 T^{12} - 242839272338982008 T^{13} + 3567863649534651532 T^{14} - 19176160458789218904 T^{15} + \)\(28\!\cdots\!81\)\( T^{16} )^{2} \))(\( 1 - 1040 T^{2} + 715428 T^{4} - 373461040 T^{6} + 149925694598 T^{8} - 48669816193840 T^{10} + 12150516539296548 T^{12} - 2301847515828807440 T^{14} + \)\(28\!\cdots\!81\)\( T^{16} \))(\( ( 1 - 1092 T^{2} + 576680 T^{4} - 222586380 T^{6} + 81331407246 T^{8} - 29007679627980 T^{10} + 9794081134483880 T^{12} - 2416939891620247812 T^{14} + \)\(28\!\cdots\!81\)\( T^{16} )^{2} \))(\( 1 - 1632 T^{2} + 1354756 T^{4} - 767600928 T^{6} + 320946269766 T^{8} - 100034520537888 T^{10} + 23008583931172996 T^{12} - 3612129947915974752 T^{14} + \)\(28\!\cdots\!81\)\( T^{16} \))(\( 1 - 2056 T^{2} + 2230944 T^{4} - 1603740248 T^{6} + 819184531004 T^{8} - 297045269538504 T^{10} + 69987022118810464 T^{12} - 7175141044809308632 T^{14} - \)\(43\!\cdots\!46\)\( T^{16} - \)\(93\!\cdots\!72\)\( T^{18} + \)\(11\!\cdots\!24\)\( T^{20} - \)\(65\!\cdots\!44\)\( T^{22} + \)\(23\!\cdots\!24\)\( T^{24} - \)\(60\!\cdots\!48\)\( T^{26} + \)\(10\!\cdots\!24\)\( T^{28} - \)\(13\!\cdots\!96\)\( T^{30} + \)\(83\!\cdots\!61\)\( T^{32} \))(\( 1 - 108 T + 6142 T^{2} - 243432 T^{3} + 7548345 T^{4} - 198492408 T^{5} + 4660679966 T^{6} - 100240172052 T^{7} + 1986343374068 T^{8} - 36186702110772 T^{9} + 607384473849086 T^{10} - 9338250206171448 T^{11} + 128197793162717145 T^{12} - 1492497721269013032 T^{13} + 13594180232904360862 T^{14} - 86292722064551485068 T^{15} + \)\(28\!\cdots\!81\)\( T^{16} \))(\( 1 + 72 T + 3812 T^{2} + 150048 T^{3} + 4883342 T^{4} + 136887912 T^{5} + 3384543112 T^{6} + 75691203624 T^{7} + 1567163213049 T^{8} + 30524546336184 T^{9} + 578634766673960 T^{10} + 10979211701479464 T^{11} + 213751725988675694 T^{12} + 4327693265152902096 T^{13} + 88720456587214840044 T^{14} + \)\(17\!\cdots\!80\)\( T^{15} + \)\(34\!\cdots\!48\)\( T^{16} + \)\(64\!\cdots\!80\)\( T^{17} + \)\(11\!\cdots\!24\)\( T^{18} + \)\(20\!\cdots\!76\)\( T^{19} + \)\(36\!\cdots\!54\)\( T^{20} + \)\(67\!\cdots\!64\)\( T^{21} + \)\(12\!\cdots\!60\)\( T^{22} + \)\(24\!\cdots\!64\)\( T^{23} + \)\(45\!\cdots\!69\)\( T^{24} + \)\(78\!\cdots\!84\)\( T^{25} + \)\(12\!\cdots\!12\)\( T^{26} + \)\(18\!\cdots\!32\)\( T^{27} + \)\(23\!\cdots\!82\)\( T^{28} + \)\(26\!\cdots\!88\)\( T^{29} + \)\(24\!\cdots\!92\)\( T^{30} + \)\(16\!\cdots\!72\)\( T^{31} + \)\(83\!\cdots\!61\)\( T^{32} \))
$23$ (\( 1 - 3856 T^{2} + 7749432 T^{4} - 10915385904 T^{6} + 12001409108892 T^{8} - 10839581553458448 T^{10} + 8275120566094665352 T^{12} - \)\(54\!\cdots\!60\)\( T^{14} + \)\(30\!\cdots\!06\)\( T^{16} - \)\(15\!\cdots\!60\)\( T^{18} + \)\(64\!\cdots\!12\)\( T^{20} - \)\(23\!\cdots\!08\)\( T^{22} + \)\(73\!\cdots\!12\)\( T^{24} - \)\(18\!\cdots\!04\)\( T^{26} + \)\(37\!\cdots\!12\)\( T^{28} - \)\(51\!\cdots\!36\)\( T^{30} + \)\(37\!\cdots\!21\)\( T^{32} \))(\( ( 1 + 780 T^{2} + 15360 T^{3} + 320102 T^{4} + 8125440 T^{5} + 218275980 T^{6} + 78310985281 T^{8} )^{2} \))(\( ( 1 - 1300 T^{2} + 1274456 T^{4} - 947494620 T^{6} + 528617435630 T^{8} - 265147841955420 T^{10} + 99803905057282136 T^{12} - 28489011761626417300 T^{14} + \)\(61\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 + 40 T + 800 T^{2} + 23320 T^{3} + 928156 T^{4} + 22803400 T^{5} + 441522400 T^{6} + 12864455160 T^{7} + 373563445830 T^{8} + 6805296779640 T^{9} + 123556069938400 T^{10} + 3375721591222600 T^{11} + 72684810854471836 T^{12} + 966066241502294680 T^{13} + 17531699545616256800 T^{14} + \)\(46\!\cdots\!60\)\( T^{15} + \)\(61\!\cdots\!61\)\( T^{16} \))(\( 1 - 24 T + 288 T^{2} - 17192 T^{3} + 221472 T^{4} - 2391768 T^{5} + 141400928 T^{6} - 3172207336 T^{7} + 137674628156 T^{8} - 274022502200 T^{9} - 6993233578720 T^{10} - 103772124341000 T^{11} - 60508914798085408 T^{12} + 933592691352233992 T^{13} - 15427273581773601184 T^{14} + \)\(57\!\cdots\!36\)\( T^{15} - \)\(64\!\cdots\!26\)\( T^{16} + \)\(30\!\cdots\!44\)\( T^{17} - \)\(43\!\cdots\!44\)\( T^{18} + \)\(13\!\cdots\!88\)\( T^{19} - \)\(47\!\cdots\!48\)\( T^{20} - \)\(42\!\cdots\!00\)\( T^{21} - \)\(15\!\cdots\!20\)\( T^{22} - \)\(31\!\cdots\!00\)\( T^{23} + \)\(84\!\cdots\!16\)\( T^{24} - \)\(10\!\cdots\!84\)\( T^{25} + \)\(24\!\cdots\!28\)\( T^{26} - \)\(21\!\cdots\!72\)\( T^{27} + \)\(10\!\cdots\!52\)\( T^{28} - \)\(43\!\cdots\!88\)\( T^{29} + \)\(38\!\cdots\!28\)\( T^{30} - \)\(17\!\cdots\!76\)\( T^{31} + \)\(37\!\cdots\!21\)\( T^{32} \))(\( 1 - 12 T - 1512 T^{2} + 15144 T^{3} + 1340890 T^{4} - 9662580 T^{5} - 850652928 T^{6} + 2479269564 T^{7} + 454065720819 T^{8} + 1311533599356 T^{9} - 238047566024448 T^{10} - 1430408620333620 T^{11} + 105006417053440090 T^{12} + 627363085819500456 T^{13} - 33134912141214725352 T^{14} - \)\(13\!\cdots\!08\)\( T^{15} + \)\(61\!\cdots\!61\)\( T^{16} \))(\( 1 + 12 T - 1804 T^{2} - 41256 T^{3} + 1078172 T^{4} + 48109188 T^{5} - 226519400 T^{6} - 29579538300 T^{7} + 68149425194 T^{8} + 16885870838304 T^{9} + 1241401844668 T^{10} - 10296857200481412 T^{11} - 100210062266615184 T^{12} + 3750005340988049388 T^{13} + 80231845600155444876 T^{14} - \)\(51\!\cdots\!40\)\( T^{15} - \)\(38\!\cdots\!85\)\( T^{16} - \)\(27\!\cdots\!60\)\( T^{17} + \)\(22\!\cdots\!16\)\( T^{18} + \)\(55\!\cdots\!32\)\( T^{19} - \)\(78\!\cdots\!04\)\( T^{20} - \)\(42\!\cdots\!88\)\( T^{21} + \)\(27\!\cdots\!28\)\( T^{22} + \)\(19\!\cdots\!36\)\( T^{23} + \)\(41\!\cdots\!34\)\( T^{24} - \)\(95\!\cdots\!00\)\( T^{25} - \)\(38\!\cdots\!00\)\( T^{26} + \)\(43\!\cdots\!52\)\( T^{27} + \)\(51\!\cdots\!52\)\( T^{28} - \)\(10\!\cdots\!84\)\( T^{29} - \)\(24\!\cdots\!24\)\( T^{30} + \)\(85\!\cdots\!88\)\( T^{31} + \)\(37\!\cdots\!21\)\( T^{32} \))
$29$ (\( 1 - 3972 T^{2} + 8120294 T^{4} - 13034144872 T^{6} + 18580208769649 T^{8} - 22683669812342744 T^{10} + 24087258397916480502 T^{12} - \)\(23\!\cdots\!44\)\( T^{14} + \)\(20\!\cdots\!28\)\( T^{16} - \)\(16\!\cdots\!64\)\( T^{18} + \)\(12\!\cdots\!22\)\( T^{20} - \)\(80\!\cdots\!04\)\( T^{22} + \)\(46\!\cdots\!29\)\( T^{24} - \)\(23\!\cdots\!72\)\( T^{26} + \)\(10\!\cdots\!14\)\( T^{28} - \)\(35\!\cdots\!92\)\( T^{30} + \)\(62\!\cdots\!41\)\( T^{32} \))(\( ( 1 + 72 T + 4044 T^{2} + 159480 T^{3} + 5105990 T^{4} + 134122680 T^{5} + 2860244364 T^{6} + 42827279112 T^{7} + 500246412961 T^{8} )^{2} \))(\( ( 1 - 16 T + 1276 T^{2} - 55408 T^{3} + 751270 T^{4} - 46598128 T^{5} + 902490556 T^{6} - 9517173136 T^{7} + 500246412961 T^{8} )^{4} \))(\( 1 - 5816 T^{2} + 15494364 T^{4} - 24578727304 T^{6} + 25344087778310 T^{8} - 17384066826300424 T^{10} + 7751000012112051804 T^{12} - \)\(20\!\cdots\!56\)\( T^{14} + \)\(25\!\cdots\!21\)\( T^{16} \))(\( 1 - 4032 T^{2} + 8105976 T^{4} - 11130637632 T^{6} + 11901856158364 T^{8} - 11208853722734016 T^{10} + 10516466734892486856 T^{12} - \)\(99\!\cdots\!40\)\( T^{14} + \)\(87\!\cdots\!46\)\( T^{16} - \)\(70\!\cdots\!40\)\( T^{18} + \)\(52\!\cdots\!16\)\( T^{20} - \)\(39\!\cdots\!56\)\( T^{22} + \)\(29\!\cdots\!44\)\( T^{24} - \)\(19\!\cdots\!32\)\( T^{26} + \)\(10\!\cdots\!56\)\( T^{28} - \)\(35\!\cdots\!52\)\( T^{30} + \)\(62\!\cdots\!41\)\( T^{32} \))(\( ( 1 - 36 T + 2904 T^{2} - 82956 T^{3} + 3490070 T^{4} - 69765996 T^{5} + 2053944024 T^{6} - 21413639556 T^{7} + 500246412961 T^{8} )^{2} \))(\( ( 1 - 36 T + 1444 T^{2} + 19116 T^{3} - 1274860 T^{4} + 68800452 T^{5} + 84102156 T^{6} - 30035473452 T^{7} + 2426711187974 T^{8} - 25259833173132 T^{9} + 59483856997836 T^{10} + 40924113344941092 T^{11} - 637744142027460460 T^{12} + 8042239471766642316 T^{13} + \)\(51\!\cdots\!04\)\( T^{14} - \)\(10\!\cdots\!16\)\( T^{15} + \)\(25\!\cdots\!21\)\( T^{16} )^{2} \))
$31$ (\( ( 1 + 3684 T^{2} - 19472 T^{3} + 7802120 T^{4} - 58737456 T^{5} + 11372951532 T^{6} - 93476864320 T^{7} + 12493787155086 T^{8} - 89831266611520 T^{9} + 10503159571784172 T^{10} - 52129708412575536 T^{11} + 6654358221039174920 T^{12} - 15959802004090157072 T^{13} + \)\(29\!\cdots\!24\)\( T^{14} + \)\(72\!\cdots\!81\)\( T^{16} )^{2} \))(\( 1 - 5072 T^{2} + 12940644 T^{4} - 21077526640 T^{6} + 23985269180870 T^{8} - 19465538480099440 T^{10} + 11036959286314652004 T^{12} - \)\(39\!\cdots\!92\)\( T^{14} + \)\(72\!\cdots\!81\)\( T^{16} \))(\( ( 1 - 3948 T^{2} + 5903432 T^{4} - 3942646212 T^{6} + 1976573418510 T^{8} - 3641116572352452 T^{10} + 5034984242942397512 T^{12} - \)\(31\!\cdots\!28\)\( T^{14} + \)\(72\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 - 72 T + 4816 T^{2} - 187848 T^{3} + 7076706 T^{4} - 180521928 T^{5} + 4447677136 T^{6} - 63900265032 T^{7} + 852891037441 T^{8} )^{2} \))(\( ( 1 + 56 T + 4484 T^{2} + 186776 T^{3} + 8992264 T^{4} + 304202984 T^{5} + 11800345036 T^{6} + 348556649544 T^{7} + 12266333612430 T^{8} + 334962940211784 T^{9} + 10897866447991756 T^{10} + 269981268071184104 T^{11} + 7669421371903356424 T^{12} + \)\(15\!\cdots\!76\)\( T^{13} + \)\(35\!\cdots\!24\)\( T^{14} + \)\(42\!\cdots\!76\)\( T^{15} + \)\(72\!\cdots\!81\)\( T^{16} )^{2} \))(\( 1 + 132 T + 11278 T^{2} + 722040 T^{3} + 38602473 T^{4} + 1778529960 T^{5} + 72524765390 T^{6} + 2637318955548 T^{7} + 86278260959732 T^{8} + 2534463516281628 T^{9} + 66978143857738190 T^{10} + 1578451886268782760 T^{11} + 32923703244758191593 T^{12} + \)\(59\!\cdots\!40\)\( T^{13} + \)\(88\!\cdots\!58\)\( T^{14} + \)\(99\!\cdots\!72\)\( T^{15} + \)\(72\!\cdots\!81\)\( T^{16} \))(\( 1 - 120 T + 11588 T^{2} - 814560 T^{3} + 49123694 T^{4} - 2488742424 T^{5} + 113293093576 T^{6} - 4558808688792 T^{7} + 170270490089625 T^{8} - 5869377562140936 T^{9} + 196357797692622056 T^{10} - 6377368910762118360 T^{11} + \)\(21\!\cdots\!82\)\( T^{12} - \)\(69\!\cdots\!28\)\( T^{13} + \)\(23\!\cdots\!88\)\( T^{14} - \)\(74\!\cdots\!40\)\( T^{15} + \)\(23\!\cdots\!16\)\( T^{16} - \)\(71\!\cdots\!40\)\( T^{17} + \)\(21\!\cdots\!48\)\( T^{18} - \)\(61\!\cdots\!68\)\( T^{19} + \)\(17\!\cdots\!62\)\( T^{20} - \)\(52\!\cdots\!60\)\( T^{21} + \)\(15\!\cdots\!16\)\( T^{22} - \)\(44\!\cdots\!56\)\( T^{23} + \)\(12\!\cdots\!25\)\( T^{24} - \)\(31\!\cdots\!72\)\( T^{25} + \)\(76\!\cdots\!76\)\( T^{26} - \)\(16\!\cdots\!64\)\( T^{27} + \)\(30\!\cdots\!74\)\( T^{28} - \)\(48\!\cdots\!60\)\( T^{29} + \)\(66\!\cdots\!08\)\( T^{30} - \)\(66\!\cdots\!20\)\( T^{31} + \)\(52\!\cdots\!61\)\( T^{32} \))
$37$ (\( ( 1 - 40 T + 6968 T^{2} - 291512 T^{3} + 25042268 T^{4} - 987943976 T^{5} + 58242343432 T^{6} - 2052793579384 T^{7} + 94406736665478 T^{8} - 2810274410176696 T^{9} + 109155528608860552 T^{10} - 2534793949835662184 T^{11} + 87960451829583332828 T^{12} - \)\(14\!\cdots\!88\)\( T^{13} + \)\(45\!\cdots\!08\)\( T^{14} - \)\(36\!\cdots\!60\)\( T^{15} + \)\(12\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 + 24 T + 2412 T^{2} - 16728 T^{3} + 1972550 T^{4} - 22900632 T^{5} + 4520476332 T^{6} + 61577433816 T^{7} + 3512479453921 T^{8} )^{2} \))(\( ( 1 - 2416 T^{2} + 5835932 T^{4} - 9959371920 T^{6} + 14384225705606 T^{8} - 18665466436959120 T^{10} + 20498591244480089372 T^{12} - \)\(15\!\cdots\!96\)\( T^{14} + \)\(12\!\cdots\!41\)\( T^{16} )^{2} \))(\( 1 - 160 T + 12800 T^{2} - 692576 T^{3} + 28393916 T^{4} - 973559072 T^{5} + 32158084608 T^{6} - 1118111280864 T^{7} + 40611983255110 T^{8} - 1530694343502816 T^{9} + 60269428007013888 T^{10} - 2497886221751932448 T^{11} + 99733046566358744636 T^{12} - \)\(33\!\cdots\!24\)\( T^{13} + \)\(84\!\cdots\!00\)\( T^{14} - \)\(14\!\cdots\!40\)\( T^{15} + \)\(12\!\cdots\!41\)\( T^{16} \))(\( 1 + 152 T + 11552 T^{2} + 598344 T^{3} + 25962168 T^{4} + 1167158904 T^{5} + 56500959840 T^{6} + 2639490056104 T^{7} + 111109511071516 T^{8} + 4242418231122872 T^{9} + 154876079427922976 T^{10} + 5762441784032775208 T^{11} + \)\(22\!\cdots\!72\)\( T^{12} + \)\(89\!\cdots\!08\)\( T^{13} + \)\(32\!\cdots\!12\)\( T^{14} + \)\(10\!\cdots\!40\)\( T^{15} + \)\(37\!\cdots\!46\)\( T^{16} + \)\(14\!\cdots\!60\)\( T^{17} + \)\(60\!\cdots\!32\)\( T^{18} + \)\(22\!\cdots\!72\)\( T^{19} + \)\(79\!\cdots\!12\)\( T^{20} + \)\(27\!\cdots\!92\)\( T^{21} + \)\(10\!\cdots\!56\)\( T^{22} + \)\(38\!\cdots\!08\)\( T^{23} + \)\(13\!\cdots\!56\)\( T^{24} + \)\(44\!\cdots\!16\)\( T^{25} + \)\(13\!\cdots\!40\)\( T^{26} + \)\(36\!\cdots\!76\)\( T^{27} + \)\(11\!\cdots\!48\)\( T^{28} + \)\(35\!\cdots\!96\)\( T^{29} + \)\(93\!\cdots\!92\)\( T^{30} + \)\(16\!\cdots\!48\)\( T^{31} + \)\(15\!\cdots\!81\)\( T^{32} \))(\( 1 + 96 T + 1110 T^{2} - 46464 T^{3} + 7652401 T^{4} + 360085920 T^{5} - 3532027338 T^{6} + 170035213440 T^{7} + 29111429055396 T^{8} + 232778207199360 T^{9} - 6619587887813418 T^{10} + 923881954453061280 T^{11} + 26878901285664514321 T^{12} - \)\(22\!\cdots\!36\)\( T^{13} + \)\(73\!\cdots\!10\)\( T^{14} + \)\(86\!\cdots\!44\)\( T^{15} + \)\(12\!\cdots\!41\)\( T^{16} \))(\( 1 - 44 T - 1956 T^{2} - 11728 T^{3} + 3652806 T^{4} + 242885524 T^{5} - 1534355576 T^{6} - 317275895964 T^{7} - 9605253544351 T^{8} + 75954637404076 T^{9} + 6072970847630504 T^{10} + 248299820626414612 T^{11} + 4168440621293518230 T^{12} + \)\(29\!\cdots\!60\)\( T^{13} + \)\(10\!\cdots\!28\)\( T^{14} - \)\(69\!\cdots\!04\)\( T^{15} - \)\(27\!\cdots\!16\)\( T^{16} - \)\(95\!\cdots\!76\)\( T^{17} + \)\(20\!\cdots\!08\)\( T^{18} + \)\(75\!\cdots\!40\)\( T^{19} + \)\(14\!\cdots\!30\)\( T^{20} + \)\(11\!\cdots\!88\)\( T^{21} + \)\(39\!\cdots\!24\)\( T^{22} + \)\(68\!\cdots\!64\)\( T^{23} - \)\(11\!\cdots\!91\)\( T^{24} - \)\(53\!\cdots\!56\)\( T^{25} - \)\(35\!\cdots\!76\)\( T^{26} + \)\(76\!\cdots\!56\)\( T^{27} + \)\(15\!\cdots\!66\)\( T^{28} - \)\(69\!\cdots\!52\)\( T^{29} - \)\(15\!\cdots\!76\)\( T^{30} - \)\(48\!\cdots\!56\)\( T^{31} + \)\(15\!\cdots\!81\)\( T^{32} \))
$41$ (\( 1 - 10832 T^{2} + 65454200 T^{4} - 277210214128 T^{6} + 920889789641756 T^{8} - 2528312319464856400 T^{10} + \)\(59\!\cdots\!28\)\( T^{12} - \)\(12\!\cdots\!00\)\( T^{14} + \)\(21\!\cdots\!66\)\( T^{16} - \)\(34\!\cdots\!00\)\( T^{18} + \)\(47\!\cdots\!88\)\( T^{20} - \)\(57\!\cdots\!00\)\( T^{22} + \)\(58\!\cdots\!96\)\( T^{24} - \)\(49\!\cdots\!28\)\( T^{26} + \)\(33\!\cdots\!00\)\( T^{28} - \)\(15\!\cdots\!72\)\( T^{30} + \)\(40\!\cdots\!81\)\( T^{32} \))(\( 1 - 11432 T^{2} + 60126684 T^{4} - 189254916760 T^{6} + 389111411703110 T^{8} - 534789162838654360 T^{10} + \)\(48\!\cdots\!64\)\( T^{12} - \)\(25\!\cdots\!92\)\( T^{14} + \)\(63\!\cdots\!41\)\( T^{16} \))(\( ( 1 - 12516 T^{2} + 70001768 T^{4} - 228356671020 T^{6} + 475054496880078 T^{8} - 645281375058146220 T^{10} + \)\(55\!\cdots\!28\)\( T^{12} - \)\(28\!\cdots\!96\)\( T^{14} + \)\(63\!\cdots\!41\)\( T^{16} )^{2} \))(\( ( 1 + 160 T + 11944 T^{2} + 591520 T^{3} + 24800530 T^{4} + 994345120 T^{5} + 33750889384 T^{6} + 760016678560 T^{7} + 7984925229121 T^{8} )^{2} \))(\( ( 1 + 8252 T^{2} - 19936 T^{3} + 34068728 T^{4} - 127251488 T^{5} + 92291784532 T^{6} - 367862933760 T^{7} + 180432835211182 T^{8} - 618377591650560 T^{9} + 260794525350928852 T^{10} - 604457832822360608 T^{11} + \)\(27\!\cdots\!88\)\( T^{12} - \)\(26\!\cdots\!36\)\( T^{13} + \)\(18\!\cdots\!12\)\( T^{14} + \)\(63\!\cdots\!41\)\( T^{16} )^{2} \))(\( 1 - 5456 T^{2} + 19963884 T^{4} - 49821420976 T^{6} + 96897341176550 T^{8} - 140783428358562736 T^{10} + \)\(15\!\cdots\!64\)\( T^{12} - \)\(12\!\cdots\!36\)\( T^{14} + \)\(63\!\cdots\!41\)\( T^{16} \))(\( 1 - 11416 T^{2} + 66218264 T^{4} - 265318066664 T^{6} + 835818107018940 T^{8} - 2208514761298495288 T^{10} + \)\(50\!\cdots\!56\)\( T^{12} - \)\(10\!\cdots\!32\)\( T^{14} + \)\(18\!\cdots\!14\)\( T^{16} - \)\(28\!\cdots\!52\)\( T^{18} + \)\(40\!\cdots\!76\)\( T^{20} - \)\(49\!\cdots\!28\)\( T^{22} + \)\(53\!\cdots\!40\)\( T^{24} - \)\(47\!\cdots\!64\)\( T^{26} + \)\(33\!\cdots\!04\)\( T^{28} - \)\(16\!\cdots\!36\)\( T^{30} + \)\(40\!\cdots\!81\)\( T^{32} \))
$43$ (\( ( 1 + 168 T + 21576 T^{2} + 1867768 T^{3} + 137965244 T^{4} + 8243885160 T^{5} + 447366405624 T^{6} + 21255986843000 T^{7} + 961142451546054 T^{8} + 39302319672707000 T^{9} + 1529456714913736824 T^{10} + 52112591030623452840 T^{11} + \)\(16\!\cdots\!44\)\( T^{12} + \)\(40\!\cdots\!32\)\( T^{13} + \)\(86\!\cdots\!76\)\( T^{14} + \)\(12\!\cdots\!32\)\( T^{15} + \)\(13\!\cdots\!01\)\( T^{16} )^{2} \))(\( ( 1 + 32 T + 3396 T^{2} + 140128 T^{3} + 8375270 T^{4} + 259096672 T^{5} + 11610248196 T^{6} + 202283617568 T^{7} + 11688200277601 T^{8} )^{2} \))(\( ( 1 - 1912 T^{2} + 2635964 T^{4} - 3280241736 T^{6} + 4054697588678 T^{8} - 11214493727278536 T^{10} + 30809675156546242364 T^{12} - \)\(76\!\cdots\!12\)\( T^{14} + \)\(13\!\cdots\!01\)\( T^{16} )^{2} \))(\( 1 + 32 T + 512 T^{2} - 44896 T^{3} - 2147132 T^{4} + 116117984 T^{5} + 5822932480 T^{6} + 160684182624 T^{7} + 3183857489478 T^{8} + 297105053671776 T^{9} + 19907447385556480 T^{10} + 734023933381973216 T^{11} - 25096108838445990332 T^{12} - \)\(97\!\cdots\!04\)\( T^{13} + \)\(20\!\cdots\!12\)\( T^{14} + \)\(23\!\cdots\!68\)\( T^{15} + \)\(13\!\cdots\!01\)\( T^{16} \))(\( 1 - 158592 T^{3} + 2725896 T^{4} - 61004160 T^{5} + 12575711232 T^{6} - 618250768128 T^{7} + 18017190018460 T^{8} - 968512496926464 T^{9} + 65630298643144704 T^{10} - 3092793950726971008 T^{11} + \)\(10\!\cdots\!80\)\( T^{12} - \)\(37\!\cdots\!52\)\( T^{13} + \)\(33\!\cdots\!64\)\( T^{14} - \)\(12\!\cdots\!48\)\( T^{15} + \)\(20\!\cdots\!26\)\( T^{16} - \)\(22\!\cdots\!52\)\( T^{17} + \)\(11\!\cdots\!64\)\( T^{18} - \)\(23\!\cdots\!48\)\( T^{19} + \)\(11\!\cdots\!80\)\( T^{20} - \)\(66\!\cdots\!92\)\( T^{21} + \)\(26\!\cdots\!04\)\( T^{22} - \)\(71\!\cdots\!36\)\( T^{23} + \)\(24\!\cdots\!60\)\( T^{24} - \)\(15\!\cdots\!72\)\( T^{25} + \)\(58\!\cdots\!32\)\( T^{26} - \)\(52\!\cdots\!40\)\( T^{27} + \)\(43\!\cdots\!96\)\( T^{28} - \)\(46\!\cdots\!08\)\( T^{29} + \)\(18\!\cdots\!01\)\( T^{32} \))(\( ( 1 + 56 T + 5082 T^{2} + 180688 T^{3} + 11078435 T^{4} + 334092112 T^{5} + 17374346682 T^{6} + 353996330744 T^{7} + 11688200277601 T^{8} )^{2} \))(\( ( 1 + 28 T + 5732 T^{2} + 194288 T^{3} + 21755610 T^{4} + 646615948 T^{5} + 59916131504 T^{6} + 1611056221164 T^{7} + 122468758030675 T^{8} + 2978842952932236 T^{9} + 204841330302006704 T^{10} + 4087494160581305452 T^{11} + \)\(25\!\cdots\!10\)\( T^{12} + \)\(41\!\cdots\!12\)\( T^{13} + \)\(22\!\cdots\!32\)\( T^{14} + \)\(20\!\cdots\!72\)\( T^{15} + \)\(13\!\cdots\!01\)\( T^{16} )^{2} \))
$47$ (\( 1 - 18860 T^{2} + 165198086 T^{4} - 880812409480 T^{6} + 3099424527294161 T^{8} - 7043887723434328360 T^{10} + \)\(79\!\cdots\!02\)\( T^{12} + \)\(68\!\cdots\!80\)\( T^{14} - \)\(40\!\cdots\!04\)\( T^{16} + \)\(33\!\cdots\!80\)\( T^{18} + \)\(18\!\cdots\!22\)\( T^{20} - \)\(81\!\cdots\!60\)\( T^{22} + \)\(17\!\cdots\!81\)\( T^{24} - \)\(24\!\cdots\!80\)\( T^{26} + \)\(22\!\cdots\!66\)\( T^{28} - \)\(12\!\cdots\!60\)\( T^{30} + \)\(32\!\cdots\!41\)\( T^{32} \))(\( 1 - 9656 T^{2} + 49532316 T^{4} - 174004173832 T^{6} + 446973571058246 T^{8} - 849084860968707592 T^{10} + \)\(11\!\cdots\!76\)\( T^{12} - \)\(11\!\cdots\!96\)\( T^{14} + \)\(56\!\cdots\!21\)\( T^{16} \))(\( ( 1 + 6768 T^{2} + 28283420 T^{4} + 81813152400 T^{6} + 198252999971526 T^{8} + 399222085316384400 T^{10} + \)\(67\!\cdots\!20\)\( T^{12} + \)\(78\!\cdots\!88\)\( T^{14} + \)\(56\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 + 144 T + 10368 T^{2} + 613776 T^{3} + 40380676 T^{4} + 2550145200 T^{5} + 136914549120 T^{6} + 6692132733360 T^{7} + 317421876290310 T^{8} + 14782921207992240 T^{9} + 668099323964430720 T^{10} + 27488564231015770800 T^{11} + \)\(96\!\cdots\!36\)\( T^{12} + \)\(32\!\cdots\!24\)\( T^{13} + \)\(12\!\cdots\!88\)\( T^{14} + \)\(36\!\cdots\!36\)\( T^{15} + \)\(56\!\cdots\!21\)\( T^{16} \))(\( 1 - 80 T + 3200 T^{2} - 185424 T^{3} + 10961416 T^{4} - 416599088 T^{5} + 15442425728 T^{6} - 918151881776 T^{7} + 40326873674268 T^{8} - 452413353633424 T^{9} - 5098985333045632 T^{10} + 1563817770500267376 T^{11} - \)\(31\!\cdots\!76\)\( T^{12} + \)\(17\!\cdots\!60\)\( T^{13} - \)\(66\!\cdots\!16\)\( T^{14} + \)\(36\!\cdots\!52\)\( T^{15} - \)\(19\!\cdots\!38\)\( T^{16} + \)\(79\!\cdots\!68\)\( T^{17} - \)\(32\!\cdots\!96\)\( T^{18} + \)\(19\!\cdots\!40\)\( T^{19} - \)\(75\!\cdots\!36\)\( T^{20} + \)\(82\!\cdots\!24\)\( T^{21} - \)\(59\!\cdots\!12\)\( T^{22} - \)\(11\!\cdots\!56\)\( T^{23} + \)\(22\!\cdots\!28\)\( T^{24} - \)\(11\!\cdots\!64\)\( T^{25} + \)\(42\!\cdots\!28\)\( T^{26} - \)\(25\!\cdots\!92\)\( T^{27} + \)\(14\!\cdots\!96\)\( T^{28} - \)\(55\!\cdots\!96\)\( T^{29} + \)\(21\!\cdots\!00\)\( T^{30} - \)\(11\!\cdots\!20\)\( T^{31} + \)\(32\!\cdots\!41\)\( T^{32} \))(\( 1 + 24 T + 3580 T^{2} + 81312 T^{3} + 3430986 T^{4} + 200307384 T^{5} + 5424417392 T^{6} + 942687331128 T^{7} + 25778360177363 T^{8} + 2082396314461752 T^{9} + 26469426483811952 T^{10} + 2159156424124689336 T^{11} + 81696191178488726346 T^{12} + \)\(42\!\cdots\!88\)\( T^{13} + \)\(41\!\cdots\!80\)\( T^{14} + \)\(61\!\cdots\!56\)\( T^{15} + \)\(56\!\cdots\!21\)\( T^{16} \))(\( 1 + 24 T + 10040 T^{2} + 236352 T^{3} + 48191588 T^{4} + 529473000 T^{5} + 142018937488 T^{6} - 1533668366952 T^{7} + 289429105887690 T^{8} - 11114511768111792 T^{9} + 616929826339364168 T^{10} - 28449623988679606104 T^{11} + \)\(19\!\cdots\!48\)\( T^{12} - \)\(39\!\cdots\!52\)\( T^{13} + \)\(60\!\cdots\!84\)\( T^{14} - \)\(28\!\cdots\!36\)\( T^{15} + \)\(14\!\cdots\!27\)\( T^{16} - \)\(62\!\cdots\!24\)\( T^{17} + \)\(29\!\cdots\!04\)\( T^{18} - \)\(42\!\cdots\!08\)\( T^{19} + \)\(46\!\cdots\!28\)\( T^{20} - \)\(14\!\cdots\!96\)\( T^{21} + \)\(71\!\cdots\!88\)\( T^{22} - \)\(28\!\cdots\!48\)\( T^{23} + \)\(16\!\cdots\!90\)\( T^{24} - \)\(19\!\cdots\!28\)\( T^{25} + \)\(39\!\cdots\!88\)\( T^{26} + \)\(32\!\cdots\!00\)\( T^{27} + \)\(65\!\cdots\!28\)\( T^{28} + \)\(70\!\cdots\!08\)\( T^{29} + \)\(66\!\cdots\!40\)\( T^{30} + \)\(34\!\cdots\!76\)\( T^{31} + \)\(32\!\cdots\!41\)\( T^{32} \))
$53$ (\( 1 - 15704 T^{2} + 138921152 T^{4} - 871766999944 T^{6} + 4342207935569660 T^{8} - 18113936181752364376 T^{10} + \)\(65\!\cdots\!52\)\( T^{12} - \)\(21\!\cdots\!64\)\( T^{14} + \)\(62\!\cdots\!50\)\( T^{16} - \)\(16\!\cdots\!84\)\( T^{18} + \)\(40\!\cdots\!72\)\( T^{20} - \)\(88\!\cdots\!16\)\( T^{22} + \)\(16\!\cdots\!60\)\( T^{24} - \)\(26\!\cdots\!44\)\( T^{26} + \)\(33\!\cdots\!12\)\( T^{28} - \)\(29\!\cdots\!44\)\( T^{30} + \)\(15\!\cdots\!41\)\( T^{32} \))(\( ( 1 - 64 T + 6168 T^{2} - 270464 T^{3} + 22592978 T^{4} - 759733376 T^{5} + 48668486808 T^{6} - 1418519112256 T^{7} + 62259690411361 T^{8} )^{2} \))(\( ( 1 - 6868 T^{2} + 39779480 T^{4} - 162177493980 T^{6} + 501674308076846 T^{8} - 1279658434876804380 T^{10} + \)\(24\!\cdots\!80\)\( T^{12} - \)\(33\!\cdots\!88\)\( T^{14} + \)\(38\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 + 200 T + 20000 T^{2} + 1719464 T^{3} + 146284516 T^{4} + 10449435128 T^{5} + 642474929248 T^{6} + 39041749119576 T^{7} + 2230315686063750 T^{8} + 109668273276888984 T^{9} + 5069436222207688288 T^{10} + \)\(23\!\cdots\!12\)\( T^{11} + \)\(91\!\cdots\!76\)\( T^{12} + \)\(30\!\cdots\!36\)\( T^{13} + \)\(98\!\cdots\!00\)\( T^{14} + \)\(27\!\cdots\!00\)\( T^{15} + \)\(38\!\cdots\!21\)\( T^{16} \))(\( 1 - 48 T + 1152 T^{2} - 172480 T^{3} + 14460640 T^{4} - 33746752 T^{5} - 164137984 T^{6} + 7272556080 T^{7} - 144052676687940 T^{8} + 6754246786116880 T^{9} - 156566570729557248 T^{10} + 21067810577807322688 T^{11} - \)\(28\!\cdots\!60\)\( T^{12} - \)\(50\!\cdots\!00\)\( T^{13} + \)\(11\!\cdots\!80\)\( T^{14} - \)\(15\!\cdots\!88\)\( T^{15} + \)\(20\!\cdots\!78\)\( T^{16} - \)\(43\!\cdots\!92\)\( T^{17} + \)\(90\!\cdots\!80\)\( T^{18} - \)\(11\!\cdots\!00\)\( T^{19} - \)\(17\!\cdots\!60\)\( T^{20} + \)\(36\!\cdots\!12\)\( T^{21} - \)\(76\!\cdots\!68\)\( T^{22} + \)\(93\!\cdots\!20\)\( T^{23} - \)\(55\!\cdots\!40\)\( T^{24} + \)\(79\!\cdots\!20\)\( T^{25} - \)\(50\!\cdots\!84\)\( T^{26} - \)\(28\!\cdots\!68\)\( T^{27} + \)\(34\!\cdots\!40\)\( T^{28} - \)\(11\!\cdots\!20\)\( T^{29} + \)\(21\!\cdots\!72\)\( T^{30} - \)\(25\!\cdots\!52\)\( T^{31} + \)\(15\!\cdots\!41\)\( T^{32} \))(\( 1 - 32 T - 3572 T^{2} + 570944 T^{3} - 366070 T^{4} - 2018388320 T^{5} + 123180800432 T^{6} + 3809526158624 T^{7} - 445561676340941 T^{8} + 10700958979574816 T^{9} + 971955765373487792 T^{10} - 44736287623035613280 T^{11} - 22791404868886921270 T^{12} + \)\(99\!\cdots\!56\)\( T^{13} - \)\(17\!\cdots\!52\)\( T^{14} - \)\(44\!\cdots\!08\)\( T^{15} + \)\(38\!\cdots\!21\)\( T^{16} \))(\( 1 - 32 T - 12072 T^{2} + 345280 T^{3} + 71529764 T^{4} - 1574568864 T^{5} - 290206976304 T^{6} + 2770742930720 T^{7} + 1006589576083018 T^{8} + 3889510628997504 T^{9} - 3360408915215254232 T^{10} - 25194864185334307040 T^{11} + \)\(10\!\cdots\!32\)\( T^{12} + \)\(34\!\cdots\!88\)\( T^{13} - \)\(28\!\cdots\!00\)\( T^{14} - \)\(63\!\cdots\!04\)\( T^{15} + \)\(75\!\cdots\!55\)\( T^{16} - \)\(17\!\cdots\!36\)\( T^{17} - \)\(22\!\cdots\!00\)\( T^{18} + \)\(75\!\cdots\!52\)\( T^{19} + \)\(64\!\cdots\!52\)\( T^{20} - \)\(44\!\cdots\!60\)\( T^{21} - \)\(16\!\cdots\!12\)\( T^{22} + \)\(53\!\cdots\!76\)\( T^{23} + \)\(39\!\cdots\!78\)\( T^{24} + \)\(30\!\cdots\!80\)\( T^{25} - \)\(88\!\cdots\!04\)\( T^{26} - \)\(13\!\cdots\!76\)\( T^{27} + \)\(17\!\cdots\!84\)\( T^{28} + \)\(23\!\cdots\!20\)\( T^{29} - \)\(22\!\cdots\!92\)\( T^{30} - \)\(17\!\cdots\!68\)\( T^{31} + \)\(15\!\cdots\!41\)\( T^{32} \))
$59$ (\( 1 - 26768 T^{2} + 368873336 T^{4} - 3501619664560 T^{6} + 25676127920457884 T^{8} - \)\(15\!\cdots\!96\)\( T^{10} + \)\(77\!\cdots\!60\)\( T^{12} - \)\(33\!\cdots\!08\)\( T^{14} + \)\(12\!\cdots\!58\)\( T^{16} - \)\(40\!\cdots\!88\)\( T^{18} + \)\(11\!\cdots\!60\)\( T^{20} - \)\(27\!\cdots\!76\)\( T^{22} + \)\(55\!\cdots\!44\)\( T^{24} - \)\(91\!\cdots\!60\)\( T^{26} + \)\(11\!\cdots\!96\)\( T^{28} - \)\(10\!\cdots\!28\)\( T^{30} + \)\(46\!\cdots\!81\)\( T^{32} \))(\( 1 - 13672 T^{2} + 87440284 T^{4} - 360721973080 T^{6} + 1260995942842630 T^{8} - 4370998368442641880 T^{10} + \)\(12\!\cdots\!64\)\( T^{12} - \)\(24\!\cdots\!32\)\( T^{14} + \)\(21\!\cdots\!41\)\( T^{16} \))(\( ( 1 - 11736 T^{2} + 79787516 T^{4} - 412369170408 T^{6} + 1633889740528710 T^{8} - 4996826103104253288 T^{10} + \)\(11\!\cdots\!36\)\( T^{12} - \)\(20\!\cdots\!16\)\( T^{14} + \)\(21\!\cdots\!41\)\( T^{16} )^{2} \))(\( 1 - 616 T^{2} + 1419676 T^{4} + 5207600552 T^{6} - 204890323221242 T^{8} + 63102375832383272 T^{10} + \)\(20\!\cdots\!96\)\( T^{12} - \)\(10\!\cdots\!96\)\( T^{14} + \)\(21\!\cdots\!41\)\( T^{16} \))(\( 1 - 14320 T^{2} + 157767608 T^{4} - 1244890527696 T^{6} + 8207935216533276 T^{8} - 45520264315988706288 T^{10} + \)\(21\!\cdots\!36\)\( T^{12} - \)\(91\!\cdots\!96\)\( T^{14} + \)\(33\!\cdots\!38\)\( T^{16} - \)\(11\!\cdots\!56\)\( T^{18} + \)\(32\!\cdots\!56\)\( T^{20} - \)\(80\!\cdots\!28\)\( T^{22} + \)\(17\!\cdots\!16\)\( T^{24} - \)\(32\!\cdots\!96\)\( T^{26} + \)\(49\!\cdots\!88\)\( T^{28} - \)\(54\!\cdots\!20\)\( T^{30} + \)\(46\!\cdots\!81\)\( T^{32} \))(\( 1 - 132 T + 15632 T^{2} - 1296768 T^{3} + 88851370 T^{4} - 4629146772 T^{5} + 218386477856 T^{6} - 7743785317668 T^{7} + 393482793133843 T^{8} - 26956116690802308 T^{9} + 2646267789699658016 T^{10} - \)\(19\!\cdots\!52\)\( T^{11} + \)\(13\!\cdots\!70\)\( T^{12} - \)\(66\!\cdots\!68\)\( T^{13} + \)\(27\!\cdots\!92\)\( T^{14} - \)\(81\!\cdots\!52\)\( T^{15} + \)\(21\!\cdots\!41\)\( T^{16} \))(\( 1 - 132 T + 9660 T^{2} - 508464 T^{3} + 17070268 T^{4} - 1368116580 T^{5} + 85370423112 T^{6} - 5735724829716 T^{7} + 274189008275050 T^{8} - 2776853544451464 T^{9} + 245103035882958612 T^{10} + 4667418467579246988 T^{11} + \)\(23\!\cdots\!68\)\( T^{12} - \)\(15\!\cdots\!44\)\( T^{13} + \)\(45\!\cdots\!16\)\( T^{14} - \)\(18\!\cdots\!68\)\( T^{15} - \)\(23\!\cdots\!33\)\( T^{16} - \)\(62\!\cdots\!08\)\( T^{17} + \)\(55\!\cdots\!76\)\( T^{18} - \)\(65\!\cdots\!04\)\( T^{19} + \)\(34\!\cdots\!28\)\( T^{20} + \)\(23\!\cdots\!88\)\( T^{21} + \)\(43\!\cdots\!72\)\( T^{22} - \)\(17\!\cdots\!04\)\( T^{23} + \)\(59\!\cdots\!50\)\( T^{24} - \)\(43\!\cdots\!36\)\( T^{25} + \)\(22\!\cdots\!12\)\( T^{26} - \)\(12\!\cdots\!80\)\( T^{27} + \)\(54\!\cdots\!48\)\( T^{28} - \)\(56\!\cdots\!24\)\( T^{29} + \)\(37\!\cdots\!60\)\( T^{30} - \)\(17\!\cdots\!32\)\( T^{31} + \)\(46\!\cdots\!81\)\( T^{32} \))
$61$ (\( ( 1 - 56 T + 11072 T^{2} - 269288 T^{3} + 50054524 T^{4} - 711106488 T^{5} + 247917300928 T^{6} - 7112512171688 T^{7} + 1188015110923334 T^{8} - 26465657790851048 T^{9} + 3432623529798240448 T^{10} - 36636472472295954168 T^{11} + \)\(95\!\cdots\!44\)\( T^{12} - \)\(19\!\cdots\!88\)\( T^{13} + \)\(29\!\cdots\!12\)\( T^{14} - \)\(55\!\cdots\!96\)\( T^{15} + \)\(36\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 - 5096 T^{2} + 58282524 T^{4} - 205728528856 T^{6} + 1227606280747910 T^{8} - 2848484499704087896 T^{10} + \)\(11\!\cdots\!44\)\( T^{12} - \)\(13\!\cdots\!16\)\( T^{14} + \)\(36\!\cdots\!61\)\( T^{16} \))(\( ( 1 - 15944 T^{2} + 96425692 T^{4} - 269693317496 T^{6} + 596407807846918 T^{8} - 3734130792812134136 T^{10} + \)\(18\!\cdots\!52\)\( T^{12} - \)\(42\!\cdots\!24\)\( T^{14} + \)\(36\!\cdots\!61\)\( T^{16} )^{2} \))(\( ( 1 - 144 T + 14124 T^{2} - 1141872 T^{3} + 82373126 T^{4} - 4248905712 T^{5} + 195558658284 T^{6} - 7418933907984 T^{7} + 191707312997281 T^{8} )^{2} \))(\( ( 1 - 48 T + 22640 T^{2} - 673936 T^{3} + 215932124 T^{4} - 3175993520 T^{5} + 1217381291920 T^{6} - 6110146782096 T^{7} + 5029652273881990 T^{8} - 22735856176179216 T^{9} + 16855667804298904720 T^{10} - \)\(16\!\cdots\!20\)\( T^{11} + \)\(41\!\cdots\!44\)\( T^{12} - \)\(48\!\cdots\!36\)\( T^{13} + \)\(60\!\cdots\!40\)\( T^{14} - \)\(47\!\cdots\!68\)\( T^{15} + \)\(36\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 - 96 T + 11380 T^{2} - 797568 T^{3} + 60840138 T^{4} - 3862327392 T^{5} + 197844384848 T^{6} - 13588740778464 T^{7} + 649379857320947 T^{8} - 50563704436664544 T^{9} + 2739321895348217168 T^{10} - \)\(19\!\cdots\!12\)\( T^{11} + \)\(11\!\cdots\!78\)\( T^{12} - \)\(56\!\cdots\!68\)\( T^{13} + \)\(30\!\cdots\!80\)\( T^{14} - \)\(94\!\cdots\!36\)\( T^{15} + \)\(36\!\cdots\!61\)\( T^{16} \))(\( 1 - 96 T + 17624 T^{2} - 1396992 T^{3} + 159354980 T^{4} - 12864972960 T^{5} + 1094820209872 T^{6} - 90213896412000 T^{7} + 6336184490820426 T^{8} - 516522392725304640 T^{9} + 33635567216910203432 T^{10} - \)\(25\!\cdots\!96\)\( T^{11} + \)\(16\!\cdots\!12\)\( T^{12} - \)\(10\!\cdots\!72\)\( T^{13} + \)\(72\!\cdots\!12\)\( T^{14} - \)\(43\!\cdots\!24\)\( T^{15} + \)\(28\!\cdots\!43\)\( T^{16} - \)\(16\!\cdots\!04\)\( T^{17} + \)\(10\!\cdots\!92\)\( T^{18} - \)\(56\!\cdots\!92\)\( T^{19} + \)\(31\!\cdots\!72\)\( T^{20} - \)\(18\!\cdots\!96\)\( T^{21} + \)\(89\!\cdots\!72\)\( T^{22} - \)\(51\!\cdots\!40\)\( T^{23} + \)\(23\!\cdots\!86\)\( T^{24} - \)\(12\!\cdots\!00\)\( T^{25} + \)\(55\!\cdots\!72\)\( T^{26} - \)\(24\!\cdots\!60\)\( T^{27} + \)\(11\!\cdots\!80\)\( T^{28} - \)\(36\!\cdots\!12\)\( T^{29} + \)\(17\!\cdots\!44\)\( T^{30} - \)\(34\!\cdots\!96\)\( T^{31} + \)\(13\!\cdots\!21\)\( T^{32} \))
$67$ (\( ( 1 - 120 T + 21032 T^{2} - 1363784 T^{3} + 159985756 T^{4} - 7095679000 T^{5} + 808761061016 T^{6} - 25648223522216 T^{7} + 3474267779595526 T^{8} - 115134875391227624 T^{9} + 16297442000621798936 T^{10} - \)\(64\!\cdots\!00\)\( T^{11} + \)\(64\!\cdots\!96\)\( T^{12} - \)\(24\!\cdots\!16\)\( T^{13} + \)\(17\!\cdots\!52\)\( T^{14} - \)\(44\!\cdots\!80\)\( T^{15} + \)\(16\!\cdots\!81\)\( T^{16} )^{2} \))(\( ( 1 + 96 T + 14188 T^{2} + 794016 T^{3} + 79706118 T^{4} + 3564337824 T^{5} + 285904104748 T^{6} + 8684004688224 T^{7} + 406067677556641 T^{8} )^{2} \))(\( ( 1 - 18688 T^{2} + 141351740 T^{4} - 579001624320 T^{6} + 2070725817126086 T^{8} - 11667531790868862720 T^{10} + \)\(57\!\cdots\!40\)\( T^{12} - \)\(15\!\cdots\!68\)\( T^{14} + \)\(16\!\cdots\!81\)\( T^{16} )^{2} \))(\( 1 - 80 T + 3200 T^{2} - 105296 T^{3} - 42100604 T^{4} + 2558251408 T^{5} - 64394556032 T^{6} - 2106545111664 T^{7} + 886628492165190 T^{8} - 9456281006259696 T^{9} - 1297622490342111872 T^{10} + \)\(23\!\cdots\!52\)\( T^{11} - \)\(17\!\cdots\!64\)\( T^{12} - \)\(19\!\cdots\!04\)\( T^{13} + \)\(26\!\cdots\!00\)\( T^{14} - \)\(29\!\cdots\!20\)\( T^{15} + \)\(16\!\cdots\!81\)\( T^{16} \))(\( 1 + 80 T + 3200 T^{2} - 609968 T^{3} - 25803832 T^{4} + 2674348464 T^{5} + 482550620032 T^{6} + 12521071726512 T^{7} - 1529742891382500 T^{8} - 116256625005179504 T^{9} + 3984919157383710336 T^{10} + \)\(89\!\cdots\!92\)\( T^{11} + \)\(25\!\cdots\!88\)\( T^{12} - \)\(21\!\cdots\!76\)\( T^{13} - \)\(18\!\cdots\!68\)\( T^{14} + \)\(71\!\cdots\!08\)\( T^{15} + \)\(10\!\cdots\!46\)\( T^{16} + \)\(31\!\cdots\!12\)\( T^{17} - \)\(38\!\cdots\!28\)\( T^{18} - \)\(19\!\cdots\!44\)\( T^{19} + \)\(10\!\cdots\!08\)\( T^{20} + \)\(16\!\cdots\!08\)\( T^{21} + \)\(32\!\cdots\!96\)\( T^{22} - \)\(42\!\cdots\!16\)\( T^{23} - \)\(25\!\cdots\!00\)\( T^{24} + \)\(92\!\cdots\!08\)\( T^{25} + \)\(16\!\cdots\!32\)\( T^{26} + \)\(39\!\cdots\!96\)\( T^{27} - \)\(17\!\cdots\!72\)\( T^{28} - \)\(18\!\cdots\!92\)\( T^{29} + \)\(43\!\cdots\!00\)\( T^{30} + \)\(48\!\cdots\!20\)\( T^{31} + \)\(27\!\cdots\!61\)\( T^{32} \))(\( 1 + 120 T - 4522 T^{2} - 749040 T^{3} + 46360561 T^{4} + 4026690720 T^{5} - 240439443082 T^{6} - 2848051223400 T^{7} + 1781423144538724 T^{8} - 12784901941842600 T^{9} - 4845124310717994922 T^{10} + \)\(36\!\cdots\!80\)\( T^{11} + \)\(18\!\cdots\!01\)\( T^{12} - \)\(13\!\cdots\!60\)\( T^{13} - \)\(37\!\cdots\!42\)\( T^{14} + \)\(44\!\cdots\!80\)\( T^{15} + \)\(16\!\cdots\!81\)\( T^{16} \))(\( 1 + 164 T - 6340 T^{2} - 2597968 T^{3} - 31915482 T^{4} + 22697073892 T^{5} + 967634972296 T^{6} - 123392891205548 T^{7} - 9455087268413407 T^{8} + 333882071018564764 T^{9} + 51639925158822741896 T^{10} + \)\(26\!\cdots\!32\)\( T^{11} - \)\(16\!\cdots\!86\)\( T^{12} - \)\(60\!\cdots\!36\)\( T^{13} + \)\(18\!\cdots\!60\)\( T^{14} + \)\(15\!\cdots\!28\)\( T^{15} + \)\(54\!\cdots\!88\)\( T^{16} + \)\(70\!\cdots\!92\)\( T^{17} + \)\(36\!\cdots\!60\)\( T^{18} - \)\(55\!\cdots\!84\)\( T^{19} - \)\(67\!\cdots\!26\)\( T^{20} + \)\(47\!\cdots\!68\)\( T^{21} + \)\(42\!\cdots\!56\)\( T^{22} + \)\(12\!\cdots\!56\)\( T^{23} - \)\(15\!\cdots\!67\)\( T^{24} - \)\(91\!\cdots\!32\)\( T^{25} + \)\(32\!\cdots\!96\)\( T^{26} + \)\(33\!\cdots\!88\)\( T^{27} - \)\(21\!\cdots\!22\)\( T^{28} - \)\(78\!\cdots\!92\)\( T^{29} - \)\(85\!\cdots\!40\)\( T^{30} + \)\(99\!\cdots\!36\)\( T^{31} + \)\(27\!\cdots\!61\)\( T^{32} \))
$71$ (\( 1 - 58328 T^{2} + 1630496768 T^{4} - 29214173879944 T^{6} + 378588472445657852 T^{8} - \)\(37\!\cdots\!40\)\( T^{10} + \)\(30\!\cdots\!12\)\( T^{12} - \)\(20\!\cdots\!48\)\( T^{14} + \)\(11\!\cdots\!90\)\( T^{16} - \)\(51\!\cdots\!88\)\( T^{18} + \)\(19\!\cdots\!32\)\( T^{20} - \)\(62\!\cdots\!40\)\( T^{22} + \)\(15\!\cdots\!92\)\( T^{24} - \)\(30\!\cdots\!44\)\( T^{26} + \)\(43\!\cdots\!08\)\( T^{28} - \)\(39\!\cdots\!08\)\( T^{30} + \)\(17\!\cdots\!41\)\( T^{32} \))(\( ( 1 - 88 T + 8304 T^{2} - 522200 T^{3} + 58604450 T^{4} - 2632410200 T^{5} + 211018599024 T^{6} - 11272824985048 T^{7} + 645753531245761 T^{8} )^{2} \))(\( ( 1 + 96 T + 14048 T^{2} + 646080 T^{3} + 72093138 T^{4} + 3256889280 T^{5} + 356983294688 T^{6} + 12297627256416 T^{7} + 645753531245761 T^{8} )^{4} \))(\( ( 1 + 140 T + 26424 T^{2} + 2214100 T^{3} + 216062270 T^{4} + 11161278100 T^{5} + 671478258744 T^{6} + 17934039748940 T^{7} + 645753531245761 T^{8} )^{2} \))(\( ( 1 - 268 T + 44204 T^{2} - 5071044 T^{3} + 471192708 T^{4} - 37316092140 T^{5} + 2755016710036 T^{6} - 195026045020868 T^{7} + 13901563235868662 T^{8} - 983126292950195588 T^{9} + 70009605785104330516 T^{10} - \)\(47\!\cdots\!40\)\( T^{11} + \)\(30\!\cdots\!88\)\( T^{12} - \)\(16\!\cdots\!44\)\( T^{13} + \)\(72\!\cdots\!64\)\( T^{14} - \)\(22\!\cdots\!08\)\( T^{15} + \)\(41\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 - 4 T + 13176 T^{2} - 338828 T^{3} + 79144886 T^{4} - 1708031948 T^{5} + 334824308856 T^{6} - 512401135684 T^{7} + 645753531245761 T^{8} )^{2} \))(\( ( 1 + 68 T + 26092 T^{2} + 2195028 T^{3} + 351820772 T^{4} + 28773766364 T^{5} + 3188424927972 T^{6} + 217589962697708 T^{7} + 19655929349959526 T^{8} + 1096871001959146028 T^{9} + 81023237162072440932 T^{10} + \)\(36\!\cdots\!44\)\( T^{11} + \)\(22\!\cdots\!92\)\( T^{12} + \)\(71\!\cdots\!28\)\( T^{13} + \)\(42\!\cdots\!72\)\( T^{14} + \)\(56\!\cdots\!08\)\( T^{15} + \)\(41\!\cdots\!21\)\( T^{16} )^{2} \))
$73$ (\( ( 1 - 24 T + 15156 T^{2} + 137320 T^{3} + 133090184 T^{4} + 1190310168 T^{5} + 1034805205980 T^{6} + 7023266129048 T^{7} + 5908298409616782 T^{8} + 37426985201696792 T^{9} + 29386647627474681180 T^{10} + \)\(18\!\cdots\!52\)\( T^{11} + \)\(10\!\cdots\!04\)\( T^{12} + \)\(59\!\cdots\!80\)\( T^{13} + \)\(34\!\cdots\!76\)\( T^{14} - \)\(29\!\cdots\!16\)\( T^{15} + \)\(65\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 - 18048 T^{2} + 179971204 T^{4} - 1281534583680 T^{6} + 7286987478858630 T^{8} - 36393327957179306880 T^{10} + \)\(14\!\cdots\!24\)\( T^{12} - \)\(41\!\cdots\!08\)\( T^{14} + \)\(65\!\cdots\!61\)\( T^{16} \))(\( ( 1 + 18612 T^{2} + 177429992 T^{4} + 1152928560348 T^{6} + 6336699932034510 T^{8} + 32741143112545547868 T^{10} + \)\(14\!\cdots\!52\)\( T^{12} + \)\(42\!\cdots\!52\)\( T^{14} + \)\(65\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 - 312 T + 48672 T^{2} - 5493144 T^{3} + 450793636 T^{4} - 23206886280 T^{5} + 386836170336 T^{6} + 68692339480344 T^{7} - 8375186112407610 T^{8} + 366061477090753176 T^{9} + 10985466792718778976 T^{10} - \)\(35\!\cdots\!20\)\( T^{11} + \)\(36\!\cdots\!16\)\( T^{12} - \)\(23\!\cdots\!56\)\( T^{13} + \)\(11\!\cdots\!12\)\( T^{14} - \)\(38\!\cdots\!08\)\( T^{15} + \)\(65\!\cdots\!61\)\( T^{16} \))(\( 1 - 638960 T^{3} - 86919200 T^{4} - 369113360 T^{5} + 204134940800 T^{6} + 33110468899200 T^{7} + 5206311620706876 T^{8} + 26720496193596800 T^{9} - 3344897125184227200 T^{10} - \)\(13\!\cdots\!20\)\( T^{11} - \)\(22\!\cdots\!00\)\( T^{12} - \)\(53\!\cdots\!20\)\( T^{13} + \)\(75\!\cdots\!00\)\( T^{14} + \)\(36\!\cdots\!00\)\( T^{15} + \)\(78\!\cdots\!66\)\( T^{16} + \)\(19\!\cdots\!00\)\( T^{17} + \)\(21\!\cdots\!00\)\( T^{18} - \)\(80\!\cdots\!80\)\( T^{19} - \)\(17\!\cdots\!00\)\( T^{20} - \)\(59\!\cdots\!80\)\( T^{21} - \)\(76\!\cdots\!00\)\( T^{22} + \)\(32\!\cdots\!00\)\( T^{23} + \)\(33\!\cdots\!36\)\( T^{24} + \)\(11\!\cdots\!00\)\( T^{25} + \)\(37\!\cdots\!00\)\( T^{26} - \)\(36\!\cdots\!40\)\( T^{27} - \)\(45\!\cdots\!00\)\( T^{28} - \)\(17\!\cdots\!40\)\( T^{29} + \)\(42\!\cdots\!21\)\( T^{32} \))(\( 1 - 24 T + 9630 T^{2} - 226512 T^{3} + 47274361 T^{4} + 2709573216 T^{5} - 18252715698 T^{6} + 34150744827912 T^{7} - 1287593588654412 T^{8} + 181989319187943048 T^{9} - 518345019296287218 T^{10} + \)\(41\!\cdots\!24\)\( T^{11} + \)\(38\!\cdots\!41\)\( T^{12} - \)\(97\!\cdots\!88\)\( T^{13} + \)\(22\!\cdots\!30\)\( T^{14} - \)\(29\!\cdots\!16\)\( T^{15} + \)\(65\!\cdots\!61\)\( T^{16} \))(\( 1 + 348 T + 82708 T^{2} + 14734320 T^{3} + 2214323678 T^{4} + 290251205388 T^{5} + 34312832193656 T^{6} + 3733330194438684 T^{7} + 379285162573239545 T^{8} + 36467064302261366820 T^{9} + \)\(33\!\cdots\!56\)\( T^{10} + \)\(29\!\cdots\!16\)\( T^{11} + \)\(24\!\cdots\!70\)\( T^{12} + \)\(20\!\cdots\!16\)\( T^{13} + \)\(16\!\cdots\!72\)\( T^{14} + \)\(12\!\cdots\!12\)\( T^{15} + \)\(91\!\cdots\!12\)\( T^{16} + \)\(65\!\cdots\!48\)\( T^{17} + \)\(45\!\cdots\!52\)\( T^{18} + \)\(30\!\cdots\!24\)\( T^{19} + \)\(20\!\cdots\!70\)\( T^{20} + \)\(12\!\cdots\!84\)\( T^{21} + \)\(76\!\cdots\!76\)\( T^{22} + \)\(44\!\cdots\!80\)\( T^{23} + \)\(24\!\cdots\!45\)\( T^{24} + \)\(12\!\cdots\!96\)\( T^{25} + \)\(63\!\cdots\!56\)\( T^{26} + \)\(28\!\cdots\!52\)\( T^{27} + \)\(11\!\cdots\!98\)\( T^{28} + \)\(41\!\cdots\!80\)\( T^{29} + \)\(12\!\cdots\!48\)\( T^{30} + \)\(27\!\cdots\!52\)\( T^{31} + \)\(42\!\cdots\!21\)\( T^{32} \))
$79$ (\( ( 1 - 4 T + 21374 T^{2} - 1216 T^{3} + 230456449 T^{4} + 2685965400 T^{5} + 1772108711446 T^{6} + 44455008585260 T^{7} + 11672772046344164 T^{8} + 277443708580607660 T^{9} + 69023777851627327126 T^{10} + \)\(65\!\cdots\!00\)\( T^{11} + \)\(34\!\cdots\!89\)\( T^{12} - \)\(11\!\cdots\!16\)\( T^{13} + \)\(12\!\cdots\!34\)\( T^{14} - \)\(14\!\cdots\!24\)\( T^{15} + \)\(23\!\cdots\!21\)\( T^{16} )^{2} \))(\( ( 1 + 144 T + 27876 T^{2} + 2532528 T^{3} + 267406406 T^{4} + 15805507248 T^{5} + 1085772457956 T^{6} + 35004593595024 T^{7} + 1517108809906561 T^{8} )^{2} \))(\( ( 1 + 152 T + 28916 T^{2} + 2541000 T^{3} + 270417254 T^{4} + 15858381000 T^{5} + 1126280542196 T^{6} + 36949293239192 T^{7} + 1517108809906561 T^{8} )^{4} \))(\( 1 - 2856 T^{2} - 59627684 T^{4} + 132589015272 T^{6} + 2412904555054278 T^{8} + 5164352884554637032 T^{10} - \)\(90\!\cdots\!24\)\( T^{12} - \)\(16\!\cdots\!96\)\( T^{14} + \)\(23\!\cdots\!21\)\( T^{16} \))(\( 1 - 52208 T^{2} + 1391680568 T^{4} - 25119513250000 T^{6} + 343967562165562012 T^{8} - \)\(37\!\cdots\!72\)\( T^{10} + \)\(34\!\cdots\!24\)\( T^{12} - \)\(27\!\cdots\!40\)\( T^{14} + \)\(18\!\cdots\!30\)\( T^{16} - \)\(10\!\cdots\!40\)\( T^{18} + \)\(52\!\cdots\!64\)\( T^{20} - \)\(22\!\cdots\!52\)\( T^{22} + \)\(79\!\cdots\!52\)\( T^{24} - \)\(22\!\cdots\!00\)\( T^{26} + \)\(48\!\cdots\!08\)\( T^{28} - \)\(71\!\cdots\!88\)\( T^{30} + \)\(52\!\cdots\!41\)\( T^{32} \))(\( 1 - 12 T - 2418 T^{2} + 386472 T^{3} - 58917335 T^{4} - 324907032 T^{5} + 66125106126 T^{6} - 10581169939908 T^{7} + 1991860414252788 T^{8} - 66037081594965828 T^{9} + 2575578239741296206 T^{10} - 78980823689760123672 T^{11} - \)\(89\!\cdots\!35\)\( T^{12} + \)\(36\!\cdots\!72\)\( T^{13} - \)\(14\!\cdots\!38\)\( T^{14} - \)\(44\!\cdots\!72\)\( T^{15} + \)\(23\!\cdots\!21\)\( T^{16} \))(\( 1 - 280 T + 14532 T^{2} + 1622944 T^{3} + 35326638 T^{4} - 30655524856 T^{5} + 55399514824 T^{6} + 161497193433480 T^{7} + 10355496367899353 T^{8} - 1123575678148193512 T^{9} - 61265347082641448728 T^{10} + \)\(14\!\cdots\!40\)\( T^{11} + \)\(44\!\cdots\!62\)\( T^{12} - \)\(73\!\cdots\!60\)\( T^{13} + \)\(53\!\cdots\!92\)\( T^{14} - \)\(10\!\cdots\!56\)\( T^{15} + \)\(35\!\cdots\!48\)\( T^{16} - \)\(66\!\cdots\!96\)\( T^{17} + \)\(20\!\cdots\!52\)\( T^{18} - \)\(17\!\cdots\!60\)\( T^{19} + \)\(67\!\cdots\!82\)\( T^{20} + \)\(13\!\cdots\!40\)\( T^{21} - \)\(36\!\cdots\!48\)\( T^{22} - \)\(41\!\cdots\!72\)\( T^{23} + \)\(23\!\cdots\!13\)\( T^{24} + \)\(23\!\cdots\!80\)\( T^{25} + \)\(49\!\cdots\!24\)\( T^{26} - \)\(17\!\cdots\!96\)\( T^{27} + \)\(12\!\cdots\!78\)\( T^{28} + \)\(35\!\cdots\!24\)\( T^{29} + \)\(19\!\cdots\!52\)\( T^{30} - \)\(23\!\cdots\!80\)\( T^{31} + \)\(52\!\cdots\!41\)\( T^{32} \))
$83$ (\( 1 - 26752 T^{2} + 559157880 T^{4} - 7483229844864 T^{6} + 85634770716597660 T^{8} - \)\(74\!\cdots\!16\)\( T^{10} + \)\(60\!\cdots\!76\)\( T^{12} - \)\(41\!\cdots\!76\)\( T^{14} + \)\(29\!\cdots\!06\)\( T^{16} - \)\(19\!\cdots\!96\)\( T^{18} + \)\(13\!\cdots\!16\)\( T^{20} - \)\(80\!\cdots\!76\)\( T^{22} + \)\(43\!\cdots\!60\)\( T^{24} - \)\(18\!\cdots\!64\)\( T^{26} + \)\(63\!\cdots\!80\)\( T^{28} - \)\(14\!\cdots\!32\)\( T^{30} + \)\(25\!\cdots\!61\)\( T^{32} \))(\( 1 - 37880 T^{2} + 719278428 T^{4} - 8629223884360 T^{6} + 71063717963313158 T^{8} - \)\(40\!\cdots\!60\)\( T^{10} + \)\(16\!\cdots\!48\)\( T^{12} - \)\(40\!\cdots\!80\)\( T^{14} + \)\(50\!\cdots\!81\)\( T^{16} \))(\( ( 1 + 39632 T^{2} + 756012572 T^{4} + 9074582537520 T^{6} + 74694570513655814 T^{8} + \)\(43\!\cdots\!20\)\( T^{10} + \)\(17\!\cdots\!52\)\( T^{12} + \)\(42\!\cdots\!52\)\( T^{14} + \)\(50\!\cdots\!81\)\( T^{16} )^{2} \))(\( 1 + 320 T + 51200 T^{2} + 5915840 T^{3} + 553217092 T^{4} + 45528000320 T^{5} + 3742826444800 T^{6} + 317655699460800 T^{7} + 26711748349549254 T^{8} + 2188330113585451200 T^{9} + \)\(17\!\cdots\!00\)\( T^{10} + \)\(14\!\cdots\!80\)\( T^{11} + \)\(12\!\cdots\!72\)\( T^{12} + \)\(91\!\cdots\!60\)\( T^{13} + \)\(54\!\cdots\!00\)\( T^{14} + \)\(23\!\cdots\!80\)\( T^{15} + \)\(50\!\cdots\!81\)\( T^{16} \))(\( 1 + 256 T + 32768 T^{2} + 2489472 T^{3} + 78882184 T^{4} + 642592896 T^{5} + 678427795456 T^{6} + 150782876556800 T^{7} + 17212084280490396 T^{8} + 1275723698299503616 T^{9} + 84640034952293916672 T^{10} + \)\(62\!\cdots\!76\)\( T^{11} + \)\(45\!\cdots\!48\)\( T^{12} + \)\(40\!\cdots\!04\)\( T^{13} + \)\(47\!\cdots\!44\)\( T^{14} + \)\(59\!\cdots\!24\)\( T^{15} + \)\(59\!\cdots\!02\)\( T^{16} + \)\(41\!\cdots\!36\)\( T^{17} + \)\(22\!\cdots\!24\)\( T^{18} + \)\(13\!\cdots\!76\)\( T^{19} + \)\(10\!\cdots\!68\)\( T^{20} + \)\(96\!\cdots\!24\)\( T^{21} + \)\(90\!\cdots\!92\)\( T^{22} + \)\(93\!\cdots\!64\)\( T^{23} + \)\(87\!\cdots\!76\)\( T^{24} + \)\(52\!\cdots\!00\)\( T^{25} + \)\(16\!\cdots\!56\)\( T^{26} + \)\(10\!\cdots\!44\)\( T^{27} + \)\(90\!\cdots\!64\)\( T^{28} + \)\(19\!\cdots\!68\)\( T^{29} + \)\(17\!\cdots\!88\)\( T^{30} + \)\(95\!\cdots\!44\)\( T^{31} + \)\(25\!\cdots\!61\)\( T^{32} \))(\( 1 - 2384 T^{2} + 54393900 T^{4} - 170213772976 T^{6} + 3204332319622694 T^{8} - 8078059876516133296 T^{10} + \)\(12\!\cdots\!00\)\( T^{12} - \)\(25\!\cdots\!24\)\( T^{14} + \)\(50\!\cdots\!81\)\( T^{16} \))(\( 1 - 66184 T^{2} + 2113671608 T^{4} - 43986302935160 T^{6} + 678322851950602236 T^{8} - \)\(83\!\cdots\!72\)\( T^{10} + \)\(84\!\cdots\!60\)\( T^{12} - \)\(72\!\cdots\!04\)\( T^{14} + \)\(53\!\cdots\!06\)\( T^{16} - \)\(34\!\cdots\!84\)\( T^{18} + \)\(19\!\cdots\!60\)\( T^{20} - \)\(88\!\cdots\!92\)\( T^{22} + \)\(34\!\cdots\!16\)\( T^{24} - \)\(10\!\cdots\!60\)\( T^{26} + \)\(24\!\cdots\!68\)\( T^{28} - \)\(35\!\cdots\!44\)\( T^{30} + \)\(25\!\cdots\!61\)\( T^{32} \))
$89$ (\( 1 - 71136 T^{2} + 2535583160 T^{4} - 60654761408672 T^{6} + 1094469962087760028 T^{8} - \)\(15\!\cdots\!12\)\( T^{10} + \)\(18\!\cdots\!28\)\( T^{12} - \)\(19\!\cdots\!80\)\( T^{14} + \)\(16\!\cdots\!02\)\( T^{16} - \)\(11\!\cdots\!80\)\( T^{18} + \)\(74\!\cdots\!68\)\( T^{20} - \)\(39\!\cdots\!52\)\( T^{22} + \)\(16\!\cdots\!08\)\( T^{24} - \)\(58\!\cdots\!72\)\( T^{26} + \)\(15\!\cdots\!60\)\( T^{28} - \)\(27\!\cdots\!16\)\( T^{30} + \)\(24\!\cdots\!21\)\( T^{32} \))(\( 1 - 20024 T^{2} + 352120860 T^{4} - 3746723082376 T^{6} + 35814387700257734 T^{8} - \)\(23\!\cdots\!16\)\( T^{10} + \)\(13\!\cdots\!60\)\( T^{12} - \)\(49\!\cdots\!04\)\( T^{14} + \)\(15\!\cdots\!61\)\( T^{16} \))(\( ( 1 - 38508 T^{2} + 778838024 T^{4} - 10318651040964 T^{6} + 96273467949842958 T^{8} - \)\(64\!\cdots\!24\)\( T^{10} + \)\(30\!\cdots\!44\)\( T^{12} - \)\(95\!\cdots\!68\)\( T^{14} + \)\(15\!\cdots\!61\)\( T^{16} )^{2} \))(\( 1 - 26800 T^{2} + 323387236 T^{4} - 2700009379600 T^{6} + 20962417894146886 T^{8} - \)\(16\!\cdots\!00\)\( T^{10} + \)\(12\!\cdots\!16\)\( T^{12} - \)\(66\!\cdots\!00\)\( T^{14} + \)\(15\!\cdots\!61\)\( T^{16} \))(\( 1 - 60568 T^{2} + 1632136448 T^{4} - 25689569431240 T^{6} + 260052896713761532 T^{8} - \)\(17\!\cdots\!32\)\( T^{10} + \)\(70\!\cdots\!24\)\( T^{12} - \)\(68\!\cdots\!20\)\( T^{14} - \)\(92\!\cdots\!90\)\( T^{16} - \)\(43\!\cdots\!20\)\( T^{18} + \)\(27\!\cdots\!44\)\( T^{20} - \)\(42\!\cdots\!72\)\( T^{22} + \)\(40\!\cdots\!52\)\( T^{24} - \)\(24\!\cdots\!40\)\( T^{26} + \)\(99\!\cdots\!68\)\( T^{28} - \)\(23\!\cdots\!08\)\( T^{30} + \)\(24\!\cdots\!21\)\( T^{32} \))(\( 1 - 492 T + 137248 T^{2} - 27827520 T^{3} + 4512312618 T^{4} - 615183153660 T^{5} + 72837035721440 T^{6} - 7634393359602348 T^{7} + 716618506839255347 T^{8} - 60472029801410198508 T^{9} + \)\(45\!\cdots\!40\)\( T^{10} - \)\(30\!\cdots\!60\)\( T^{11} + \)\(17\!\cdots\!58\)\( T^{12} - \)\(86\!\cdots\!20\)\( T^{13} + \)\(33\!\cdots\!08\)\( T^{14} - \)\(96\!\cdots\!72\)\( T^{15} + \)\(15\!\cdots\!61\)\( T^{16} \))(\( 1 + 300 T + 54668 T^{2} + 7400400 T^{3} + 757620572 T^{4} + 53632718700 T^{5} + 870152589352 T^{6} - 480156239482500 T^{7} - 98736006237054870 T^{8} - 12632355432189921000 T^{9} - \)\(12\!\cdots\!92\)\( T^{10} - \)\(89\!\cdots\!00\)\( T^{11} - \)\(37\!\cdots\!44\)\( T^{12} + \)\(17\!\cdots\!40\)\( T^{13} + \)\(60\!\cdots\!12\)\( T^{14} + \)\(83\!\cdots\!20\)\( T^{15} + \)\(83\!\cdots\!23\)\( T^{16} + \)\(66\!\cdots\!20\)\( T^{17} + \)\(37\!\cdots\!92\)\( T^{18} + \)\(84\!\cdots\!40\)\( T^{19} - \)\(14\!\cdots\!64\)\( T^{20} - \)\(27\!\cdots\!00\)\( T^{21} - \)\(30\!\cdots\!32\)\( T^{22} - \)\(24\!\cdots\!00\)\( T^{23} - \)\(15\!\cdots\!70\)\( T^{24} - \)\(58\!\cdots\!00\)\( T^{25} + \)\(84\!\cdots\!52\)\( T^{26} + \)\(41\!\cdots\!00\)\( T^{27} + \)\(46\!\cdots\!52\)\( T^{28} + \)\(35\!\cdots\!00\)\( T^{29} + \)\(20\!\cdots\!08\)\( T^{30} + \)\(90\!\cdots\!00\)\( T^{31} + \)\(24\!\cdots\!21\)\( T^{32} \))
$97$ (\( ( 1 + 96 T + 62878 T^{2} + 5357144 T^{3} + 1785824677 T^{4} + 133941251648 T^{5} + 30441979716138 T^{6} + 1968996759462584 T^{7} + 345736614004039176 T^{8} + 18526290509783452856 T^{9} + \)\(26\!\cdots\!78\)\( T^{10} + \)\(11\!\cdots\!92\)\( T^{11} + \)\(13\!\cdots\!97\)\( T^{12} + \)\(39\!\cdots\!56\)\( T^{13} + \)\(43\!\cdots\!98\)\( T^{14} + \)\(62\!\cdots\!24\)\( T^{15} + \)\(61\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 - 40128 T^{2} + 785762308 T^{4} - 10615096489536 T^{6} + 111881094946850310 T^{8} - \)\(93\!\cdots\!16\)\( T^{10} + \)\(61\!\cdots\!88\)\( T^{12} - \)\(27\!\cdots\!48\)\( T^{14} + \)\(61\!\cdots\!21\)\( T^{16} \))(\( ( 1 + 54804 T^{2} + 1439825768 T^{4} + 23691050976252 T^{6} + 266516143722806094 T^{8} + \)\(20\!\cdots\!12\)\( T^{10} + \)\(11\!\cdots\!48\)\( T^{12} + \)\(38\!\cdots\!64\)\( T^{14} + \)\(61\!\cdots\!21\)\( T^{16} )^{2} \))(\( 1 + 24 T + 288 T^{2} + 197496 T^{3} - 223582556 T^{4} - 4223145048 T^{5} - 17461370016 T^{6} + 856985885448 T^{7} + 24034841148321606 T^{8} + 8063380196180232 T^{9} - 1545842532791438496 T^{10} - \)\(35\!\cdots\!92\)\( T^{11} - \)\(17\!\cdots\!16\)\( T^{12} + \)\(14\!\cdots\!04\)\( T^{13} + \)\(19\!\cdots\!08\)\( T^{14} + \)\(15\!\cdots\!56\)\( T^{15} + \)\(61\!\cdots\!21\)\( T^{16} \))(\( 1 - 688 T + 236672 T^{2} - 56991072 T^{3} + 10854023776 T^{4} - 1693042723360 T^{5} + 219961022412800 T^{6} - 24020408470599760 T^{7} + 2158083026478171708 T^{8} - \)\(14\!\cdots\!44\)\( T^{9} + \)\(52\!\cdots\!16\)\( T^{10} + \)\(44\!\cdots\!04\)\( T^{11} - \)\(12\!\cdots\!36\)\( T^{12} + \)\(17\!\cdots\!52\)\( T^{13} - \)\(20\!\cdots\!48\)\( T^{14} + \)\(21\!\cdots\!08\)\( T^{15} - \)\(20\!\cdots\!18\)\( T^{16} + \)\(19\!\cdots\!72\)\( T^{17} - \)\(18\!\cdots\!88\)\( T^{18} + \)\(14\!\cdots\!08\)\( T^{19} - \)\(97\!\cdots\!96\)\( T^{20} + \)\(32\!\cdots\!96\)\( T^{21} + \)\(36\!\cdots\!56\)\( T^{22} - \)\(96\!\cdots\!36\)\( T^{23} + \)\(13\!\cdots\!68\)\( T^{24} - \)\(13\!\cdots\!40\)\( T^{25} + \)\(11\!\cdots\!00\)\( T^{26} - \)\(86\!\cdots\!40\)\( T^{27} + \)\(52\!\cdots\!56\)\( T^{28} - \)\(25\!\cdots\!88\)\( T^{29} + \)\(10\!\cdots\!92\)\( T^{30} - \)\(27\!\cdots\!12\)\( T^{31} + \)\(37\!\cdots\!41\)\( T^{32} \))(\( 1 - 35880 T^{2} + 724155484 T^{4} - 9811041724440 T^{6} + 103976225413471686 T^{8} - \)\(86\!\cdots\!40\)\( T^{10} + \)\(56\!\cdots\!24\)\( T^{12} - \)\(24\!\cdots\!80\)\( T^{14} + \)\(61\!\cdots\!21\)\( T^{16} \))(\( 1 - 70448 T^{2} + 2604307832 T^{4} - 66719407643536 T^{6} + 1323480529449253148 T^{8} - \)\(21\!\cdots\!72\)\( T^{10} + \)\(29\!\cdots\!68\)\( T^{12} - \)\(34\!\cdots\!84\)\( T^{14} + \)\(34\!\cdots\!38\)\( T^{16} - \)\(30\!\cdots\!04\)\( T^{18} + \)\(23\!\cdots\!48\)\( T^{20} - \)\(14\!\cdots\!52\)\( T^{22} + \)\(81\!\cdots\!08\)\( T^{24} - \)\(36\!\cdots\!36\)\( T^{26} + \)\(12\!\cdots\!92\)\( T^{28} - \)\(30\!\cdots\!28\)\( T^{30} + \)\(37\!\cdots\!41\)\( T^{32} \))
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