LMFDB - Space of modular forms of level 5, weight 9, and Character 5.c

Defining parameters

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	5.c (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$ 5 $
Character field:			$\Q(i)$
Newform subspaces:			$ 1 $
Sturm bound:			$4$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{9}(5, [\chi])$.

	Total	New
Modular forms	10	10
Cusp forms	6	6
Eisenstein series	4	4

Trace form

$ 6q - 2q^{2} - 72q^{3} + 220q^{5} + 1752q^{6} - 2352q^{7} - 8220q^{8} + O(q^{10}) $

\( 6q - 2q^{2} - 72q^{3} + 220q^{5} + 1752q^{6} - 2352q^{7} - 8220q^{8} + 30870q^{10} + 23192q^{11} - 45912q^{12} - 119142q^{13} + 241440q^{15} + 218616q^{16} - 265502q^{17} - 454062q^{18} + 412260q^{20} + 231672q^{21} - 35664q^{22} + 28888q^{23} - 340350q^{25} - 801388q^{26} + 392040q^{27} + 1305192q^{28} - 2549760q^{30} - 747648q^{31} + 3033928q^{32} + 4269096q^{33} - 4971680q^{35} - 3972804q^{36} - 454002q^{37} + 1443720q^{38} + 2683500q^{40} + 2489432q^{41} + 4223856q^{42} + 792648q^{43} + 210690q^{45} - 3149928q^{46} - 15313352q^{47} - 21677712q^{48} + 29537650q^{50} + 35567712q^{51} - 735732q^{52} - 13509122q^{53} + 4448040q^{55} - 18454800q^{56} - 34625520q^{57} - 23903520q^{58} + 13688520q^{60} + 24111192q^{61} + 53913416q^{62} + 44837688q^{63} - 30943610q^{65} - 55047936q^{66} - 32827752q^{67} + 8118692q^{68} - 44156280q^{70} - 13992928q^{71} + 82596420q^{72} + 111859638q^{73} - 126793200q^{75} - 56470800q^{76} + 26260136q^{77} + 31125576q^{78} + 23045920q^{80} + 65834226q^{81} + 38023056q^{82} - 14768432q^{83} - 19713030q^{85} - 135560008q^{86} - 133207680q^{87} - 44555040q^{88} + 135147990q^{90} + 167542032q^{91} + 69931048q^{92} - 96798024q^{93} + 239661000q^{95} + 184867872q^{96} - 186656202q^{97} - 345959698q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of $S_{9}^{\mathrm{new}}(5, [\chi])$ into newform subspaces

Label	Dim.	$A$	Field	CM	Traces				$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	$q$-expansion
5.9.c.a	$6$	$2.037$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$-2$	$-72$	$220$	$-2352$	$q-\beta _{3}q^{2}+(-12-12\beta _{1}-\beta _{2}-\beta _{5})q^{3}+\cdots$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ 1 + 2 T + 2 T^{2} + 2912 T^{3} - 51136 T^{4} - 1135744 T^{5} + 2070656 T^{6} - 290750464 T^{7} - 3351248896 T^{8} + 48855252992 T^{9} + 8589934592 T^{10} + 2199023255552 T^{11} + 281474976710656 T^{12} $
$3$	$ 1 + 72 T + 2592 T^{2} + 88992 T^{3} - 43043121 T^{4} - 3659977224 T^{5} - 147990802464 T^{6} - 24013110566664 T^{7} - 1852865220656241 T^{8} + 25133969310517152 T^{9} + 4803028329503971872 T^{10} + $$87\!\cdots\!72$$ T^{11} + $$79\!\cdots\!61$$ T^{12} $
$5$	$ 1 - 220 T + 194375 T^{2} - 199375000 T^{3} + 75927734375 T^{4} - 33569335937500 T^{5} + 59604644775390625 T^{6} $
$7$	$ 1 + 2352 T + 2765952 T^{2} - 2361533048 T^{3} + 6289666320399 T^{4} + 128493496173721896 T^{5} + $$28\!\cdots\!96$$ T^{6} + $$74\!\cdots\!96$$ T^{7} + $$20\!\cdots\!99$$ T^{8} - $$45\!\cdots\!48$$ T^{9} + $$30\!\cdots\!52$$ T^{10} + $$14\!\cdots\!52$$ T^{11} + $$36\!\cdots\!01$$ T^{12} $
$11$	$ ( 1 - 11596 T + 493098215 T^{2} - 5106545516920 T^{3} + 105699981590497415 T^{4} - $$53\!\cdots\!56$$ T^{5} + $$98\!\cdots\!41$$ T^{6} )^{2} $
$13$	$ 1 + 119142 T + 7097408082 T^{2} + 332686420223782 T^{3} + 13680551086291514559 T^{4} + $$46\!\cdots\!56$$ T^{5} + $$13\!\cdots\!76$$ T^{6} + $$38\!\cdots\!76$$ T^{7} + $$91\!\cdots\!19$$ T^{8} + $$18\!\cdots\!02$$ T^{9} + $$31\!\cdots\!42$$ T^{10} + $$43\!\cdots\!42$$ T^{11} + $$29\!\cdots\!21$$ T^{12} $
$17$	$ 1 + 265502 T + 35245656002 T^{2} + 3505767378301982 T^{3} + $$37\!\cdots\!19$$ T^{4} + $$40\!\cdots\!76$$ T^{5} + $$37\!\cdots\!76$$ T^{6} + $$28\!\cdots\!16$$ T^{7} + $$18\!\cdots\!39$$ T^{8} + $$11\!\cdots\!22$$ T^{9} + $$83\!\cdots\!22$$ T^{10} + $$43\!\cdots\!02$$ T^{11} + $$11\!\cdots\!41$$ T^{12} $
$19$	$ 1 - 66391003446 T^{2} + $$21\!\cdots\!15$$ T^{4} - $$42\!\cdots\!20$$ T^{6} + $$60\!\cdots\!15$$ T^{8} - $$55\!\cdots\!06$$ T^{10} + $$23\!\cdots\!41$$ T^{12} $
$23$	$ 1 - 28888 T + 417258272 T^{2} - 2207314762520128 T^{3} + $$86\!\cdots\!39$$ T^{4} - $$83\!\cdots\!64$$ T^{5} + $$12\!\cdots\!16$$ T^{6} - $$65\!\cdots\!84$$ T^{7} + $$52\!\cdots\!79$$ T^{8} - $$10\!\cdots\!48$$ T^{9} + $$15\!\cdots\!12$$ T^{10} - $$85\!\cdots\!88$$ T^{11} + $$23\!\cdots\!81$$ T^{12} $
$29$	$ 1 - 1726260912966 T^{2} + $$13\!\cdots\!15$$ T^{4} - $$77\!\cdots\!20$$ T^{6} + $$34\!\cdots\!15$$ T^{8} - $$10\!\cdots\!06$$ T^{10} + $$15\!\cdots\!61$$ T^{12} $
$31$	$ ( 1 + 373824 T + 1438821265815 T^{2} + 103488660558742480 T^{3} + $$12\!\cdots\!15$$ T^{4} + $$27\!\cdots\!44$$ T^{5} + $$62\!\cdots\!21$$ T^{6} )^{2} $
$37$	$ 1 + 454002 T + 103058908002 T^{2} + 1591257258997412242 T^{3} + $$36\!\cdots\!59$$ T^{4} + $$11\!\cdots\!36$$ T^{5} + $$25\!\cdots\!36$$ T^{6} + $$39\!\cdots\!56$$ T^{7} + $$45\!\cdots\!19$$ T^{8} + $$68\!\cdots\!62$$ T^{9} + $$15\!\cdots\!62$$ T^{10} + $$24\!\cdots\!02$$ T^{11} + $$18\!\cdots\!21$$ T^{12} $
$41$	$ ( 1 - 1244716 T + 19779856453415 T^{2} - 17348876621060070520 T^{3} + $$15\!\cdots\!15$$ T^{4} - $$79\!\cdots\!56$$ T^{5} + $$50\!\cdots\!61$$ T^{6} )^{2} $
$43$	$ 1 - 792648 T + 314145425952 T^{2} - 6701894073526462448 T^{3} + $$27\!\cdots\!99$$ T^{4} - $$18\!\cdots\!04$$ T^{5} + $$86\!\cdots\!96$$ T^{6} - $$22\!\cdots\!04$$ T^{7} + $$37\!\cdots\!99$$ T^{8} - $$10\!\cdots\!48$$ T^{9} + $$58\!\cdots\!52$$ T^{10} - $$17\!\cdots\!48$$ T^{11} + $$25\!\cdots\!01$$ T^{12} $
$47$	$ 1 + 15313352 T + 117249374737952 T^{2} + $$85\!\cdots\!72$$ T^{3} + $$63\!\cdots\!79$$ T^{4} + $$35\!\cdots\!16$$ T^{5} + $$17\!\cdots\!16$$ T^{6} + $$85\!\cdots\!76$$ T^{7} + $$36\!\cdots\!59$$ T^{8} + $$11\!\cdots\!32$$ T^{9} + $$37\!\cdots\!32$$ T^{10} + $$11\!\cdots\!52$$ T^{11} + $$18\!\cdots\!61$$ T^{12} $
$53$	$ 1 + 13509122 T + 91248188605442 T^{2} + $$98\!\cdots\!42$$ T^{3} + $$11\!\cdots\!79$$ T^{4} + $$81\!\cdots\!76$$ T^{5} + $$50\!\cdots\!36$$ T^{6} + $$51\!\cdots\!36$$ T^{7} + $$46\!\cdots\!59$$ T^{8} + $$23\!\cdots\!02$$ T^{9} + $$13\!\cdots\!22$$ T^{10} + $$12\!\cdots\!22$$ T^{11} + $$58\!\cdots\!61$$ T^{12} $
$59$	$ 1 - 413223229068726 T^{2} + $$98\!\cdots\!15$$ T^{4} - $$17\!\cdots\!20$$ T^{6} + $$21\!\cdots\!15$$ T^{8} - $$19\!\cdots\!06$$ T^{10} + $$10\!\cdots\!21$$ T^{12} $
$61$	$ ( 1 - 12055596 T + 200152007609415 T^{2} + $$24\!\cdots\!80$$ T^{3} + $$38\!\cdots\!15$$ T^{4} - $$44\!\cdots\!56$$ T^{5} + $$70\!\cdots\!41$$ T^{6} )^{2} $
$67$	$ 1 + 32827752 T + 538830650686752 T^{2} + $$16\!\cdots\!32$$ T^{3} + $$54\!\cdots\!19$$ T^{4} + $$88\!\cdots\!76$$ T^{5} + $$12\!\cdots\!76$$ T^{6} + $$36\!\cdots\!16$$ T^{7} + $$90\!\cdots\!39$$ T^{8} + $$10\!\cdots\!72$$ T^{9} + $$14\!\cdots\!72$$ T^{10} + $$36\!\cdots\!52$$ T^{11} + $$44\!\cdots\!41$$ T^{12} $
$71$	$ ( 1 + 6996464 T + 1071469029384215 T^{2} + $$14\!\cdots\!80$$ T^{3} + $$69\!\cdots\!15$$ T^{4} + $$29\!\cdots\!44$$ T^{5} + $$26\!\cdots\!81$$ T^{6} )^{2} $
$73$	$ 1 - 111859638 T + 6256289306745522 T^{2} - $$29\!\cdots\!78$$ T^{3} + $$12\!\cdots\!39$$ T^{4} - $$42\!\cdots\!64$$ T^{5} + $$12\!\cdots\!16$$ T^{6} - $$33\!\cdots\!84$$ T^{7} + $$79\!\cdots\!79$$ T^{8} - $$15\!\cdots\!98$$ T^{9} + $$26\!\cdots\!62$$ T^{10} - $$38\!\cdots\!38$$ T^{11} + $$27\!\cdots\!81$$ T^{12} $
$79$	$ 1 - 4185433961698566 T^{2} + $$55\!\cdots\!15$$ T^{4} - $$46\!\cdots\!20$$ T^{6} + $$12\!\cdots\!15$$ T^{8} - $$22\!\cdots\!06$$ T^{10} + $$12\!\cdots\!61$$ T^{12} $
$83$	$ 1 + 14768432 T + 109053291869312 T^{2} + $$28\!\cdots\!12$$ T^{3} + $$10\!\cdots\!19$$ T^{4} + $$10\!\cdots\!16$$ T^{5} + $$83\!\cdots\!56$$ T^{6} + $$23\!\cdots\!56$$ T^{7} + $$51\!\cdots\!39$$ T^{8} + $$32\!\cdots\!52$$ T^{9} + $$28\!\cdots\!32$$ T^{10} + $$85\!\cdots\!32$$ T^{11} + $$13\!\cdots\!41$$ T^{12} $
$89$	$ 1 - 8165894455313286 T^{2} + $$62\!\cdots\!15$$ T^{4} - $$26\!\cdots\!20$$ T^{6} + $$97\!\cdots\!15$$ T^{8} - $$19\!\cdots\!06$$ T^{10} + $$37\!\cdots\!81$$ T^{12} $
$97$	$ 1 + 186656202 T + 17420268872532402 T^{2} + $$93\!\cdots\!22$$ T^{3} + $$66\!\cdots\!79$$ T^{4} + $$11\!\cdots\!16$$ T^{5} + $$13\!\cdots\!16$$ T^{6} + $$87\!\cdots\!76$$ T^{7} + $$41\!\cdots\!59$$ T^{8} + $$45\!\cdots\!82$$ T^{9} + $$65\!\cdots\!82$$ T^{10} + $$55\!\cdots\!02$$ T^{11} + $$23\!\cdots\!61$$ T^{12} $
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Overview	Features
Universe	Knowledge

Degree 1	Degree 2
Degree 3	Degree 4
$\zeta$ zeros

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(4\)
Trace bound:			\(0\)

Introduction

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{9}^{\mathrm{new}}(5, [\chi])\) into newform subspaces

Hecke characteristic polynomials

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	5.9.c

Level	5
Weight	9
Character orbit	c
Rep. character	\(\chi_{5}(2,\cdot)\)
Character field	\(\Q(\zeta_{4})\)
Dimension	6
Newform subspaces	1
Sturm bound	4
Trace bound	0

Label	Dim.	\(A\)	Field	CM	Traces				$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	$q$-expansion
5.9.c.a	\(6\)	\(2.037\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(-2\)	\(-72\)	\(220\)	\(-2352\)	\(q-\beta _{3}q^{2}+(-12-12\beta _{1}-\beta _{2}-\beta _{5})q^{3}+\cdots\)

$p$	$F_p(T)$
$2$	\( 1 + 2 T + 2 T^{2} + 2912 T^{3} - 51136 T^{4} - 1135744 T^{5} + 2070656 T^{6} - 290750464 T^{7} - 3351248896 T^{8} + 48855252992 T^{9} + 8589934592 T^{10} + 2199023255552 T^{11} + 281474976710656 T^{12} \)
$3$	\( 1 + 72 T + 2592 T^{2} + 88992 T^{3} - 43043121 T^{4} - 3659977224 T^{5} - 147990802464 T^{6} - 24013110566664 T^{7} - 1852865220656241 T^{8} + 25133969310517152 T^{9} + 4803028329503971872 T^{10} + \)\(87\!\cdots\!72\)\( T^{11} + \)\(79\!\cdots\!61\)\( T^{12} \)
$5$	\( 1 - 220 T + 194375 T^{2} - 199375000 T^{3} + 75927734375 T^{4} - 33569335937500 T^{5} + 59604644775390625 T^{6} \)
$7$	\( 1 + 2352 T + 2765952 T^{2} - 2361533048 T^{3} + 6289666320399 T^{4} + 128493496173721896 T^{5} + \)\(28\!\cdots\!96\)\( T^{6} + \)\(74\!\cdots\!96\)\( T^{7} + \)\(20\!\cdots\!99\)\( T^{8} - \)\(45\!\cdots\!48\)\( T^{9} + \)\(30\!\cdots\!52\)\( T^{10} + \)\(14\!\cdots\!52\)\( T^{11} + \)\(36\!\cdots\!01\)\( T^{12} \)
$11$	\( ( 1 - 11596 T + 493098215 T^{2} - 5106545516920 T^{3} + 105699981590497415 T^{4} - \)\(53\!\cdots\!56\)\( T^{5} + \)\(98\!\cdots\!41\)\( T^{6} )^{2} \)
$13$	\( 1 + 119142 T + 7097408082 T^{2} + 332686420223782 T^{3} + 13680551086291514559 T^{4} + \)\(46\!\cdots\!56\)\( T^{5} + \)\(13\!\cdots\!76\)\( T^{6} + \)\(38\!\cdots\!76\)\( T^{7} + \)\(91\!\cdots\!19\)\( T^{8} + \)\(18\!\cdots\!02\)\( T^{9} + \)\(31\!\cdots\!42\)\( T^{10} + \)\(43\!\cdots\!42\)\( T^{11} + \)\(29\!\cdots\!21\)\( T^{12} \)
$17$	\( 1 + 265502 T + 35245656002 T^{2} + 3505767378301982 T^{3} + \)\(37\!\cdots\!19\)\( T^{4} + \)\(40\!\cdots\!76\)\( T^{5} + \)\(37\!\cdots\!76\)\( T^{6} + \)\(28\!\cdots\!16\)\( T^{7} + \)\(18\!\cdots\!39\)\( T^{8} + \)\(11\!\cdots\!22\)\( T^{9} + \)\(83\!\cdots\!22\)\( T^{10} + \)\(43\!\cdots\!02\)\( T^{11} + \)\(11\!\cdots\!41\)\( T^{12} \)
$19$	\( 1 - 66391003446 T^{2} + \)\(21\!\cdots\!15\)\( T^{4} - \)\(42\!\cdots\!20\)\( T^{6} + \)\(60\!\cdots\!15\)\( T^{8} - \)\(55\!\cdots\!06\)\( T^{10} + \)\(23\!\cdots\!41\)\( T^{12} \)
$23$	\( 1 - 28888 T + 417258272 T^{2} - 2207314762520128 T^{3} + \)\(86\!\cdots\!39\)\( T^{4} - \)\(83\!\cdots\!64\)\( T^{5} + \)\(12\!\cdots\!16\)\( T^{6} - \)\(65\!\cdots\!84\)\( T^{7} + \)\(52\!\cdots\!79\)\( T^{8} - \)\(10\!\cdots\!48\)\( T^{9} + \)\(15\!\cdots\!12\)\( T^{10} - \)\(85\!\cdots\!88\)\( T^{11} + \)\(23\!\cdots\!81\)\( T^{12} \)
$29$	\( 1 - 1726260912966 T^{2} + \)\(13\!\cdots\!15\)\( T^{4} - \)\(77\!\cdots\!20\)\( T^{6} + \)\(34\!\cdots\!15\)\( T^{8} - \)\(10\!\cdots\!06\)\( T^{10} + \)\(15\!\cdots\!61\)\( T^{12} \)
$31$	\( ( 1 + 373824 T + 1438821265815 T^{2} + 103488660558742480 T^{3} + \)\(12\!\cdots\!15\)\( T^{4} + \)\(27\!\cdots\!44\)\( T^{5} + \)\(62\!\cdots\!21\)\( T^{6} )^{2} \)
$37$	\( 1 + 454002 T + 103058908002 T^{2} + 1591257258997412242 T^{3} + \)\(36\!\cdots\!59\)\( T^{4} + \)\(11\!\cdots\!36\)\( T^{5} + \)\(25\!\cdots\!36\)\( T^{6} + \)\(39\!\cdots\!56\)\( T^{7} + \)\(45\!\cdots\!19\)\( T^{8} + \)\(68\!\cdots\!62\)\( T^{9} + \)\(15\!\cdots\!62\)\( T^{10} + \)\(24\!\cdots\!02\)\( T^{11} + \)\(18\!\cdots\!21\)\( T^{12} \)
$41$	\( ( 1 - 1244716 T + 19779856453415 T^{2} - 17348876621060070520 T^{3} + \)\(15\!\cdots\!15\)\( T^{4} - \)\(79\!\cdots\!56\)\( T^{5} + \)\(50\!\cdots\!61\)\( T^{6} )^{2} \)
$43$	\( 1 - 792648 T + 314145425952 T^{2} - 6701894073526462448 T^{3} + \)\(27\!\cdots\!99\)\( T^{4} - \)\(18\!\cdots\!04\)\( T^{5} + \)\(86\!\cdots\!96\)\( T^{6} - \)\(22\!\cdots\!04\)\( T^{7} + \)\(37\!\cdots\!99\)\( T^{8} - \)\(10\!\cdots\!48\)\( T^{9} + \)\(58\!\cdots\!52\)\( T^{10} - \)\(17\!\cdots\!48\)\( T^{11} + \)\(25\!\cdots\!01\)\( T^{12} \)
$47$	\( 1 + 15313352 T + 117249374737952 T^{2} + \)\(85\!\cdots\!72\)\( T^{3} + \)\(63\!\cdots\!79\)\( T^{4} + \)\(35\!\cdots\!16\)\( T^{5} + \)\(17\!\cdots\!16\)\( T^{6} + \)\(85\!\cdots\!76\)\( T^{7} + \)\(36\!\cdots\!59\)\( T^{8} + \)\(11\!\cdots\!32\)\( T^{9} + \)\(37\!\cdots\!32\)\( T^{10} + \)\(11\!\cdots\!52\)\( T^{11} + \)\(18\!\cdots\!61\)\( T^{12} \)
$53$	\( 1 + 13509122 T + 91248188605442 T^{2} + \)\(98\!\cdots\!42\)\( T^{3} + \)\(11\!\cdots\!79\)\( T^{4} + \)\(81\!\cdots\!76\)\( T^{5} + \)\(50\!\cdots\!36\)\( T^{6} + \)\(51\!\cdots\!36\)\( T^{7} + \)\(46\!\cdots\!59\)\( T^{8} + \)\(23\!\cdots\!02\)\( T^{9} + \)\(13\!\cdots\!22\)\( T^{10} + \)\(12\!\cdots\!22\)\( T^{11} + \)\(58\!\cdots\!61\)\( T^{12} \)
$59$	\( 1 - 413223229068726 T^{2} + \)\(98\!\cdots\!15\)\( T^{4} - \)\(17\!\cdots\!20\)\( T^{6} + \)\(21\!\cdots\!15\)\( T^{8} - \)\(19\!\cdots\!06\)\( T^{10} + \)\(10\!\cdots\!21\)\( T^{12} \)
$61$	\( ( 1 - 12055596 T + 200152007609415 T^{2} + \)\(24\!\cdots\!80\)\( T^{3} + \)\(38\!\cdots\!15\)\( T^{4} - \)\(44\!\cdots\!56\)\( T^{5} + \)\(70\!\cdots\!41\)\( T^{6} )^{2} \)
$67$	\( 1 + 32827752 T + 538830650686752 T^{2} + \)\(16\!\cdots\!32\)\( T^{3} + \)\(54\!\cdots\!19\)\( T^{4} + \)\(88\!\cdots\!76\)\( T^{5} + \)\(12\!\cdots\!76\)\( T^{6} + \)\(36\!\cdots\!16\)\( T^{7} + \)\(90\!\cdots\!39\)\( T^{8} + \)\(10\!\cdots\!72\)\( T^{9} + \)\(14\!\cdots\!72\)\( T^{10} + \)\(36\!\cdots\!52\)\( T^{11} + \)\(44\!\cdots\!41\)\( T^{12} \)
$71$	\( ( 1 + 6996464 T + 1071469029384215 T^{2} + \)\(14\!\cdots\!80\)\( T^{3} + \)\(69\!\cdots\!15\)\( T^{4} + \)\(29\!\cdots\!44\)\( T^{5} + \)\(26\!\cdots\!81\)\( T^{6} )^{2} \)
$73$	\( 1 - 111859638 T + 6256289306745522 T^{2} - \)\(29\!\cdots\!78\)\( T^{3} + \)\(12\!\cdots\!39\)\( T^{4} - \)\(42\!\cdots\!64\)\( T^{5} + \)\(12\!\cdots\!16\)\( T^{6} - \)\(33\!\cdots\!84\)\( T^{7} + \)\(79\!\cdots\!79\)\( T^{8} - \)\(15\!\cdots\!98\)\( T^{9} + \)\(26\!\cdots\!62\)\( T^{10} - \)\(38\!\cdots\!38\)\( T^{11} + \)\(27\!\cdots\!81\)\( T^{12} \)
$79$	\( 1 - 4185433961698566 T^{2} + \)\(55\!\cdots\!15\)\( T^{4} - \)\(46\!\cdots\!20\)\( T^{6} + \)\(12\!\cdots\!15\)\( T^{8} - \)\(22\!\cdots\!06\)\( T^{10} + \)\(12\!\cdots\!61\)\( T^{12} \)
$83$	\( 1 + 14768432 T + 109053291869312 T^{2} + \)\(28\!\cdots\!12\)\( T^{3} + \)\(10\!\cdots\!19\)\( T^{4} + \)\(10\!\cdots\!16\)\( T^{5} + \)\(83\!\cdots\!56\)\( T^{6} + \)\(23\!\cdots\!56\)\( T^{7} + \)\(51\!\cdots\!39\)\( T^{8} + \)\(32\!\cdots\!52\)\( T^{9} + \)\(28\!\cdots\!32\)\( T^{10} + \)\(85\!\cdots\!32\)\( T^{11} + \)\(13\!\cdots\!41\)\( T^{12} \)
$89$	\( 1 - 8165894455313286 T^{2} + \)\(62\!\cdots\!15\)\( T^{4} - \)\(26\!\cdots\!20\)\( T^{6} + \)\(97\!\cdots\!15\)\( T^{8} - \)\(19\!\cdots\!06\)\( T^{10} + \)\(37\!\cdots\!81\)\( T^{12} \)
$97$	\( 1 + 186656202 T + 17420268872532402 T^{2} + \)\(93\!\cdots\!22\)\( T^{3} + \)\(66\!\cdots\!79\)\( T^{4} + \)\(11\!\cdots\!16\)\( T^{5} + \)\(13\!\cdots\!16\)\( T^{6} + \)\(87\!\cdots\!76\)\( T^{7} + \)\(41\!\cdots\!59\)\( T^{8} + \)\(45\!\cdots\!82\)\( T^{9} + \)\(65\!\cdots\!82\)\( T^{10} + \)\(55\!\cdots\!02\)\( T^{11} + \)\(23\!\cdots\!61\)\( T^{12} \)
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