LMFDB - Group of Dirichlet characters of modulus 100315

Show commands: PariGP / SageMath

sage: H = DirichletGroup(100315)

pari: g = idealstar(,100315,2)

Character group

sage: G.order() pari: g.no
Order	=	80248
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{40124}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{100315}(40127,\cdot)$, $\chi_{100315}(40131,\cdot)$

First 32 of 80248 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{100315}(1,\cdot)$	100315.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{100315}(2,\cdot)$	100315.r	5732	yes	$-1$	$1$	$e\left(\frac{3265}{5732}\right)$	$e\left(\frac{5379}{5732}\right)$	$e\left(\frac{399}{2866}\right)$	$e\left(\frac{728}{1433}\right)$	$e\left(\frac{2113}{5732}\right)$	$e\left(\frac{4063}{5732}\right)$	$e\left(\frac{2513}{2866}\right)$	$e\left(\frac{1263}{1433}\right)$	$e\left(\frac{445}{5732}\right)$	$e\left(\frac{4251}{5732}\right)$
$\chi_{100315}(3,\cdot)$	100315.w	40124	yes	$-1$	$1$	$e\left(\frac{5379}{5732}\right)$	$e\left(\frac{33511}{40124}\right)$	$e\left(\frac{2513}{2866}\right)$	$e\left(\frac{7760}{10031}\right)$	$e\left(\frac{4965}{40124}\right)$	$e\left(\frac{4673}{5732}\right)$	$e\left(\frac{13449}{20062}\right)$	$e\left(\frac{4849}{10031}\right)$	$e\left(\frac{28569}{40124}\right)$	$e\left(\frac{34463}{40124}\right)$
$\chi_{100315}(4,\cdot)$	100315.p	2866	yes	$1$	$1$	$e\left(\frac{399}{2866}\right)$	$e\left(\frac{2513}{2866}\right)$	$e\left(\frac{399}{1433}\right)$	$e\left(\frac{23}{1433}\right)$	$e\left(\frac{2113}{2866}\right)$	$e\left(\frac{1197}{2866}\right)$	$e\left(\frac{1080}{1433}\right)$	$e\left(\frac{1093}{1433}\right)$	$e\left(\frac{445}{2866}\right)$	$e\left(\frac{1385}{2866}\right)$
$\chi_{100315}(6,\cdot)$	100315.s	10031	no	$1$	$1$	$e\left(\frac{728}{1433}\right)$	$e\left(\frac{7760}{10031}\right)$	$e\left(\frac{23}{1433}\right)$	$e\left(\frac{2825}{10031}\right)$	$e\left(\frac{4939}{10031}\right)$	$e\left(\frac{751}{1433}\right)$	$e\left(\frac{5489}{10031}\right)$	$e\left(\frac{3659}{10031}\right)$	$e\left(\frac{7921}{10031}\right)$	$e\left(\frac{6024}{10031}\right)$
$\chi_{100315}(7,\cdot)$	100315.x	40124	yes	$1$	$1$	$e\left(\frac{2113}{5732}\right)$	$e\left(\frac{4965}{40124}\right)$	$e\left(\frac{2113}{2866}\right)$	$e\left(\frac{4939}{10031}\right)$	$e\left(\frac{35289}{40124}\right)$	$e\left(\frac{607}{5732}\right)$	$e\left(\frac{4965}{20062}\right)$	$e\left(\frac{7299}{10031}\right)$	$e\left(\frac{34547}{40124}\right)$	$e\left(\frac{17453}{40124}\right)$
$\chi_{100315}(8,\cdot)$	100315.r	5732	yes	$-1$	$1$	$e\left(\frac{4063}{5732}\right)$	$e\left(\frac{4673}{5732}\right)$	$e\left(\frac{1197}{2866}\right)$	$e\left(\frac{751}{1433}\right)$	$e\left(\frac{607}{5732}\right)$	$e\left(\frac{725}{5732}\right)$	$e\left(\frac{1807}{2866}\right)$	$e\left(\frac{923}{1433}\right)$	$e\left(\frac{1335}{5732}\right)$	$e\left(\frac{1289}{5732}\right)$
$\chi_{100315}(9,\cdot)$	100315.u	20062	yes	$1$	$1$	$e\left(\frac{2513}{2866}\right)$	$e\left(\frac{13449}{20062}\right)$	$e\left(\frac{1080}{1433}\right)$	$e\left(\frac{5489}{10031}\right)$	$e\left(\frac{4965}{20062}\right)$	$e\left(\frac{1807}{2866}\right)$	$e\left(\frac{3418}{10031}\right)$	$e\left(\frac{9698}{10031}\right)$	$e\left(\frac{8507}{20062}\right)$	$e\left(\frac{14401}{20062}\right)$
$\chi_{100315}(11,\cdot)$	100315.s	10031	no	$1$	$1$	$e\left(\frac{1263}{1433}\right)$	$e\left(\frac{4849}{10031}\right)$	$e\left(\frac{1093}{1433}\right)$	$e\left(\frac{3659}{10031}\right)$	$e\left(\frac{7299}{10031}\right)$	$e\left(\frac{923}{1433}\right)$	$e\left(\frac{9698}{10031}\right)$	$e\left(\frac{8464}{10031}\right)$	$e\left(\frac{2469}{10031}\right)$	$e\left(\frac{1727}{10031}\right)$
$\chi_{100315}(12,\cdot)$	100315.w	40124	yes	$-1$	$1$	$e\left(\frac{445}{5732}\right)$	$e\left(\frac{28569}{40124}\right)$	$e\left(\frac{445}{2866}\right)$	$e\left(\frac{7921}{10031}\right)$	$e\left(\frac{34547}{40124}\right)$	$e\left(\frac{1335}{5732}\right)$	$e\left(\frac{8507}{20062}\right)$	$e\left(\frac{2469}{10031}\right)$	$e\left(\frac{34799}{40124}\right)$	$e\left(\frac{13729}{40124}\right)$
$\chi_{100315}(13,\cdot)$	100315.w	40124	yes	$-1$	$1$	$e\left(\frac{4251}{5732}\right)$	$e\left(\frac{34463}{40124}\right)$	$e\left(\frac{1385}{2866}\right)$	$e\left(\frac{6024}{10031}\right)$	$e\left(\frac{17453}{40124}\right)$	$e\left(\frac{1289}{5732}\right)$	$e\left(\frac{14401}{20062}\right)$	$e\left(\frac{1727}{10031}\right)$	$e\left(\frac{13729}{40124}\right)$	$e\left(\frac{8563}{40124}\right)$
$\chi_{100315}(14,\cdot)$	100315.v	20062	yes	$-1$	$1$	$e\left(\frac{2689}{2866}\right)$	$e\left(\frac{1247}{20062}\right)$	$e\left(\frac{1256}{1433}\right)$	$e\left(\frac{4}{10031}\right)$	$e\left(\frac{2489}{10031}\right)$	$e\left(\frac{2335}{2866}\right)$	$e\left(\frac{1247}{10031}\right)$	$e\left(\frac{6109}{10031}\right)$	$e\left(\frac{18831}{20062}\right)$	$e\left(\frac{3543}{20062}\right)$
$\chi_{100315}(16,\cdot)$	100315.m	1433	no	$1$	$1$	$e\left(\frac{399}{1433}\right)$	$e\left(\frac{1080}{1433}\right)$	$e\left(\frac{798}{1433}\right)$	$e\left(\frac{46}{1433}\right)$	$e\left(\frac{680}{1433}\right)$	$e\left(\frac{1197}{1433}\right)$	$e\left(\frac{727}{1433}\right)$	$e\left(\frac{753}{1433}\right)$	$e\left(\frac{445}{1433}\right)$	$e\left(\frac{1385}{1433}\right)$
$\chi_{100315}(17,\cdot)$	100315.x	40124	yes	$1$	$1$	$e\left(\frac{3525}{5732}\right)$	$e\left(\frac{19953}{40124}\right)$	$e\left(\frac{659}{2866}\right)$	$e\left(\frac{1126}{10031}\right)$	$e\left(\frac{3965}{40124}\right)$	$e\left(\frac{4843}{5732}\right)$	$e\left(\frac{19953}{20062}\right)$	$e\left(\frac{9398}{10031}\right)$	$e\left(\frac{29179}{40124}\right)$	$e\left(\frac{28633}{40124}\right)$
$\chi_{100315}(18,\cdot)$	100315.w	40124	yes	$-1$	$1$	$e\left(\frac{2559}{5732}\right)$	$e\left(\frac{24427}{40124}\right)$	$e\left(\frac{2559}{2866}\right)$	$e\left(\frac{554}{10031}\right)$	$e\left(\frac{24721}{40124}\right)$	$e\left(\frac{1945}{5732}\right)$	$e\left(\frac{4365}{20062}\right)$	$e\left(\frac{8508}{10031}\right)$	$e\left(\frac{20129}{40124}\right)$	$e\left(\frac{18435}{40124}\right)$
$\chi_{100315}(19,\cdot)$	100315.u	20062	yes	$1$	$1$	$e\left(\frac{2385}{2866}\right)$	$e\left(\frac{9817}{20062}\right)$	$e\left(\frac{952}{1433}\right)$	$e\left(\frac{3225}{10031}\right)$	$e\left(\frac{16159}{20062}\right)$	$e\left(\frac{1423}{2866}\right)$	$e\left(\frac{9817}{10031}\right)$	$e\left(\frac{2668}{10031}\right)$	$e\left(\frac{3083}{20062}\right)$	$e\left(\frac{15263}{20062}\right)$
$\chi_{100315}(21,\cdot)$	100315.t	20062	no	$-1$	$1$	$e\left(\frac{440}{1433}\right)$	$e\left(\frac{9619}{10031}\right)$	$e\left(\frac{880}{1433}\right)$	$e\left(\frac{2668}{10031}\right)$	$e\left(\frac{65}{20062}\right)$	$e\left(\frac{1320}{1433}\right)$	$e\left(\frac{9207}{10031}\right)$	$e\left(\frac{2117}{10031}\right)$	$e\left(\frac{5748}{10031}\right)$	$e\left(\frac{2948}{10031}\right)$
$\chi_{100315}(22,\cdot)$	100315.w	40124	yes	$-1$	$1$	$e\left(\frac{2585}{5732}\right)$	$e\left(\frac{16925}{40124}\right)$	$e\left(\frac{2585}{2866}\right)$	$e\left(\frac{8755}{10031}\right)$	$e\left(\frac{3863}{40124}\right)$	$e\left(\frac{2023}{5732}\right)$	$e\left(\frac{16925}{20062}\right)$	$e\left(\frac{7274}{10031}\right)$	$e\left(\frac{12991}{40124}\right)$	$e\left(\frac{36665}{40124}\right)$
$\chi_{100315}(23,\cdot)$	100315.w	40124	yes	$-1$	$1$	$e\left(\frac{2947}{5732}\right)$	$e\left(\frac{10359}{40124}\right)$	$e\left(\frac{81}{2866}\right)$	$e\left(\frac{7747}{10031}\right)$	$e\left(\frac{2701}{40124}\right)$	$e\left(\frac{3109}{5732}\right)$	$e\left(\frac{10359}{20062}\right)$	$e\left(\frac{2549}{10031}\right)$	$e\left(\frac{11493}{40124}\right)$	$e\left(\frac{36511}{40124}\right)$
$\chi_{100315}(24,\cdot)$	100315.u	20062	yes	$1$	$1$	$e\left(\frac{1855}{2866}\right)$	$e\left(\frac{13049}{20062}\right)$	$e\left(\frac{422}{1433}\right)$	$e\left(\frac{2986}{10031}\right)$	$e\left(\frac{4607}{20062}\right)$	$e\left(\frac{2699}{2866}\right)$	$e\left(\frac{3018}{10031}\right)$	$e\left(\frac{1279}{10031}\right)$	$e\left(\frac{18957}{20062}\right)$	$e\left(\frac{1681}{20062}\right)$
$\chi_{100315}(26,\cdot)$	100315.s	10031	no	$1$	$1$	$e\left(\frac{446}{1433}\right)$	$e\left(\frac{7998}{10031}\right)$	$e\left(\frac{892}{1433}\right)$	$e\left(\frac{1089}{10031}\right)$	$e\left(\frac{8061}{10031}\right)$	$e\left(\frac{1338}{1433}\right)$	$e\left(\frac{5965}{10031}\right)$	$e\left(\frac{537}{10031}\right)$	$e\left(\frac{4211}{10031}\right)$	$e\left(\frac{9580}{10031}\right)$
$\chi_{100315}(27,\cdot)$	100315.w	40124	yes	$-1$	$1$	$e\left(\frac{4673}{5732}\right)$	$e\left(\frac{20285}{40124}\right)$	$e\left(\frac{1807}{2866}\right)$	$e\left(\frac{3218}{10031}\right)$	$e\left(\frac{14895}{40124}\right)$	$e\left(\frac{2555}{5732}\right)$	$e\left(\frac{223}{20062}\right)$	$e\left(\frac{4516}{10031}\right)$	$e\left(\frac{5459}{40124}\right)$	$e\left(\frac{23141}{40124}\right)$
$\chi_{100315}(28,\cdot)$	100315.x	40124	yes	$1$	$1$	$e\left(\frac{2911}{5732}\right)$	$e\left(\frac{23}{40124}\right)$	$e\left(\frac{45}{2866}\right)$	$e\left(\frac{5100}{10031}\right)$	$e\left(\frac{24747}{40124}\right)$	$e\left(\frac{3001}{5732}\right)$	$e\left(\frac{23}{20062}\right)$	$e\left(\frac{4919}{10031}\right)$	$e\left(\frac{653}{40124}\right)$	$e\left(\frac{36843}{40124}\right)$
$\chi_{100315}(29,\cdot)$	100315.u	20062	yes	$1$	$1$	$e\left(\frac{2315}{2866}\right)$	$e\left(\frac{8189}{20062}\right)$	$e\left(\frac{882}{1433}\right)$	$e\left(\frac{2166}{10031}\right)$	$e\left(\frac{7279}{20062}\right)$	$e\left(\frac{1213}{2866}\right)$	$e\left(\frac{8189}{10031}\right)$	$e\left(\frac{2809}{10031}\right)$	$e\left(\frac{475}{20062}\right)$	$e\left(\frac{7629}{20062}\right)$
$\chi_{100315}(31,\cdot)$	100315.s	10031	no	$1$	$1$	$e\left(\frac{1055}{1433}\right)$	$e\left(\frac{8978}{10031}\right)$	$e\left(\frac{677}{1433}\right)$	$e\left(\frac{6332}{10031}\right)$	$e\left(\frac{7935}{10031}\right)$	$e\left(\frac{299}{1433}\right)$	$e\left(\frac{7925}{10031}\right)$	$e\left(\frac{663}{10031}\right)$	$e\left(\frac{3686}{10031}\right)$	$e\left(\frac{620}{10031}\right)$
$\chi_{100315}(32,\cdot)$	100315.r	5732	yes	$-1$	$1$	$e\left(\frac{4861}{5732}\right)$	$e\left(\frac{3967}{5732}\right)$	$e\left(\frac{1995}{2866}\right)$	$e\left(\frac{774}{1433}\right)$	$e\left(\frac{4833}{5732}\right)$	$e\left(\frac{3119}{5732}\right)$	$e\left(\frac{1101}{2866}\right)$	$e\left(\frac{583}{1433}\right)$	$e\left(\frac{2225}{5732}\right)$	$e\left(\frac{4059}{5732}\right)$
$\chi_{100315}(33,\cdot)$	100315.w	40124	yes	$-1$	$1$	$e\left(\frac{4699}{5732}\right)$	$e\left(\frac{12783}{40124}\right)$	$e\left(\frac{1833}{2866}\right)$	$e\left(\frac{1388}{10031}\right)$	$e\left(\frac{34161}{40124}\right)$	$e\left(\frac{2633}{5732}\right)$	$e\left(\frac{12783}{20062}\right)$	$e\left(\frac{3282}{10031}\right)$	$e\left(\frac{38445}{40124}\right)$	$e\left(\frac{1247}{40124}\right)$
$\chi_{100315}(34,\cdot)$	100315.v	20062	yes	$-1$	$1$	$e\left(\frac{529}{2866}\right)$	$e\left(\frac{8741}{20062}\right)$	$e\left(\frac{529}{1433}\right)$	$e\left(\frac{6222}{10031}\right)$	$e\left(\frac{4689}{10031}\right)$	$e\left(\frac{1587}{2866}\right)$	$e\left(\frac{8741}{10031}\right)$	$e\left(\frac{8208}{10031}\right)$	$e\left(\frac{16147}{20062}\right)$	$e\left(\frac{9133}{20062}\right)$
$\chi_{100315}(36,\cdot)$	100315.s	10031	no	$1$	$1$	$e\left(\frac{23}{1433}\right)$	$e\left(\frac{5489}{10031}\right)$	$e\left(\frac{46}{1433}\right)$	$e\left(\frac{5650}{10031}\right)$	$e\left(\frac{9878}{10031}\right)$	$e\left(\frac{69}{1433}\right)$	$e\left(\frac{947}{10031}\right)$	$e\left(\frac{7318}{10031}\right)$	$e\left(\frac{5811}{10031}\right)$	$e\left(\frac{2017}{10031}\right)$
$\chi_{100315}(37,\cdot)$	100315.w	40124	yes	$-1$	$1$	$e\left(\frac{17}{5732}\right)$	$e\left(\frac{22873}{40124}\right)$	$e\left(\frac{17}{2866}\right)$	$e\left(\frac{5748}{10031}\right)$	$e\left(\frac{32659}{40124}\right)$	$e\left(\frac{51}{5732}\right)$	$e\left(\frac{2811}{20062}\right)$	$e\left(\frac{1508}{10031}\right)$	$e\left(\frac{23111}{40124}\right)$	$e\left(\frac{1117}{40124}\right)$
$\chi_{100315}(38,\cdot)$	100315.w	40124	yes	$-1$	$1$	$e\left(\frac{2303}{5732}\right)$	$e\left(\frac{17163}{40124}\right)$	$e\left(\frac{2303}{2866}\right)$	$e\left(\frac{8321}{10031}\right)$	$e\left(\frac{6985}{40124}\right)$	$e\left(\frac{1177}{5732}\right)$	$e\left(\frac{17163}{20062}\right)$	$e\left(\frac{1478}{10031}\right)$	$e\left(\frac{9281}{40124}\right)$	$e\left(\frac{20159}{40124}\right)$
$\chi_{100315}(39,\cdot)$	100315.u	20062	yes	$1$	$1$	$e\left(\frac{1949}{2866}\right)$	$e\left(\frac{13925}{20062}\right)$	$e\left(\frac{516}{1433}\right)$	$e\left(\frac{3753}{10031}\right)$	$e\left(\frac{11209}{20062}\right)$	$e\left(\frac{115}{2866}\right)$	$e\left(\frac{3894}{10031}\right)$	$e\left(\frac{6576}{10031}\right)$	$e\left(\frac{1087}{20062}\right)$	$e\left(\frac{1451}{20062}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Modulus	$100315$
Structure	\(C_{2}\times C_{40124}\)
Order	$80248$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{100315}(1,\cdot)\)	100315.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{100315}(2,\cdot)\)	100315.r	5732	yes	\(-1\)	\(1\)	\(e\left(\frac{3265}{5732}\right)\)	\(e\left(\frac{5379}{5732}\right)\)	\(e\left(\frac{399}{2866}\right)\)	\(e\left(\frac{728}{1433}\right)\)	\(e\left(\frac{2113}{5732}\right)\)	\(e\left(\frac{4063}{5732}\right)\)	\(e\left(\frac{2513}{2866}\right)\)	\(e\left(\frac{1263}{1433}\right)\)	\(e\left(\frac{445}{5732}\right)\)	\(e\left(\frac{4251}{5732}\right)\)
\(\chi_{100315}(3,\cdot)\)	100315.w	40124	yes	\(-1\)	\(1\)	\(e\left(\frac{5379}{5732}\right)\)	\(e\left(\frac{33511}{40124}\right)\)	\(e\left(\frac{2513}{2866}\right)\)	\(e\left(\frac{7760}{10031}\right)\)	\(e\left(\frac{4965}{40124}\right)\)	\(e\left(\frac{4673}{5732}\right)\)	\(e\left(\frac{13449}{20062}\right)\)	\(e\left(\frac{4849}{10031}\right)\)	\(e\left(\frac{28569}{40124}\right)\)	\(e\left(\frac{34463}{40124}\right)\)
\(\chi_{100315}(4,\cdot)\)	100315.p	2866	yes	\(1\)	\(1\)	\(e\left(\frac{399}{2866}\right)\)	\(e\left(\frac{2513}{2866}\right)\)	\(e\left(\frac{399}{1433}\right)\)	\(e\left(\frac{23}{1433}\right)\)	\(e\left(\frac{2113}{2866}\right)\)	\(e\left(\frac{1197}{2866}\right)\)	\(e\left(\frac{1080}{1433}\right)\)	\(e\left(\frac{1093}{1433}\right)\)	\(e\left(\frac{445}{2866}\right)\)	\(e\left(\frac{1385}{2866}\right)\)
\(\chi_{100315}(6,\cdot)\)	100315.s	10031	no	\(1\)	\(1\)	\(e\left(\frac{728}{1433}\right)\)	\(e\left(\frac{7760}{10031}\right)\)	\(e\left(\frac{23}{1433}\right)\)	\(e\left(\frac{2825}{10031}\right)\)	\(e\left(\frac{4939}{10031}\right)\)	\(e\left(\frac{751}{1433}\right)\)	\(e\left(\frac{5489}{10031}\right)\)	\(e\left(\frac{3659}{10031}\right)\)	\(e\left(\frac{7921}{10031}\right)\)	\(e\left(\frac{6024}{10031}\right)\)
\(\chi_{100315}(7,\cdot)\)	100315.x	40124	yes	\(1\)	\(1\)	\(e\left(\frac{2113}{5732}\right)\)	\(e\left(\frac{4965}{40124}\right)\)	\(e\left(\frac{2113}{2866}\right)\)	\(e\left(\frac{4939}{10031}\right)\)	\(e\left(\frac{35289}{40124}\right)\)	\(e\left(\frac{607}{5732}\right)\)	\(e\left(\frac{4965}{20062}\right)\)	\(e\left(\frac{7299}{10031}\right)\)	\(e\left(\frac{34547}{40124}\right)\)	\(e\left(\frac{17453}{40124}\right)\)
\(\chi_{100315}(8,\cdot)\)	100315.r	5732	yes	\(-1\)	\(1\)	\(e\left(\frac{4063}{5732}\right)\)	\(e\left(\frac{4673}{5732}\right)\)	\(e\left(\frac{1197}{2866}\right)\)	\(e\left(\frac{751}{1433}\right)\)	\(e\left(\frac{607}{5732}\right)\)	\(e\left(\frac{725}{5732}\right)\)	\(e\left(\frac{1807}{2866}\right)\)	\(e\left(\frac{923}{1433}\right)\)	\(e\left(\frac{1335}{5732}\right)\)	\(e\left(\frac{1289}{5732}\right)\)
\(\chi_{100315}(9,\cdot)\)	100315.u	20062	yes	\(1\)	\(1\)	\(e\left(\frac{2513}{2866}\right)\)	\(e\left(\frac{13449}{20062}\right)\)	\(e\left(\frac{1080}{1433}\right)\)	\(e\left(\frac{5489}{10031}\right)\)	\(e\left(\frac{4965}{20062}\right)\)	\(e\left(\frac{1807}{2866}\right)\)	\(e\left(\frac{3418}{10031}\right)\)	\(e\left(\frac{9698}{10031}\right)\)	\(e\left(\frac{8507}{20062}\right)\)	\(e\left(\frac{14401}{20062}\right)\)
\(\chi_{100315}(11,\cdot)\)	100315.s	10031	no	\(1\)	\(1\)	\(e\left(\frac{1263}{1433}\right)\)	\(e\left(\frac{4849}{10031}\right)\)	\(e\left(\frac{1093}{1433}\right)\)	\(e\left(\frac{3659}{10031}\right)\)	\(e\left(\frac{7299}{10031}\right)\)	\(e\left(\frac{923}{1433}\right)\)	\(e\left(\frac{9698}{10031}\right)\)	\(e\left(\frac{8464}{10031}\right)\)	\(e\left(\frac{2469}{10031}\right)\)	\(e\left(\frac{1727}{10031}\right)\)
\(\chi_{100315}(12,\cdot)\)	100315.w	40124	yes	\(-1\)	\(1\)	\(e\left(\frac{445}{5732}\right)\)	\(e\left(\frac{28569}{40124}\right)\)	\(e\left(\frac{445}{2866}\right)\)	\(e\left(\frac{7921}{10031}\right)\)	\(e\left(\frac{34547}{40124}\right)\)	\(e\left(\frac{1335}{5732}\right)\)	\(e\left(\frac{8507}{20062}\right)\)	\(e\left(\frac{2469}{10031}\right)\)	\(e\left(\frac{34799}{40124}\right)\)	\(e\left(\frac{13729}{40124}\right)\)
\(\chi_{100315}(13,\cdot)\)	100315.w	40124	yes	\(-1\)	\(1\)	\(e\left(\frac{4251}{5732}\right)\)	\(e\left(\frac{34463}{40124}\right)\)	\(e\left(\frac{1385}{2866}\right)\)	\(e\left(\frac{6024}{10031}\right)\)	\(e\left(\frac{17453}{40124}\right)\)	\(e\left(\frac{1289}{5732}\right)\)	\(e\left(\frac{14401}{20062}\right)\)	\(e\left(\frac{1727}{10031}\right)\)	\(e\left(\frac{13729}{40124}\right)\)	\(e\left(\frac{8563}{40124}\right)\)
\(\chi_{100315}(14,\cdot)\)	100315.v	20062	yes	\(-1\)	\(1\)	\(e\left(\frac{2689}{2866}\right)\)	\(e\left(\frac{1247}{20062}\right)\)	\(e\left(\frac{1256}{1433}\right)\)	\(e\left(\frac{4}{10031}\right)\)	\(e\left(\frac{2489}{10031}\right)\)	\(e\left(\frac{2335}{2866}\right)\)	\(e\left(\frac{1247}{10031}\right)\)	\(e\left(\frac{6109}{10031}\right)\)	\(e\left(\frac{18831}{20062}\right)\)	\(e\left(\frac{3543}{20062}\right)\)
\(\chi_{100315}(16,\cdot)\)	100315.m	1433	no	\(1\)	\(1\)	\(e\left(\frac{399}{1433}\right)\)	\(e\left(\frac{1080}{1433}\right)\)	\(e\left(\frac{798}{1433}\right)\)	\(e\left(\frac{46}{1433}\right)\)	\(e\left(\frac{680}{1433}\right)\)	\(e\left(\frac{1197}{1433}\right)\)	\(e\left(\frac{727}{1433}\right)\)	\(e\left(\frac{753}{1433}\right)\)	\(e\left(\frac{445}{1433}\right)\)	\(e\left(\frac{1385}{1433}\right)\)
\(\chi_{100315}(17,\cdot)\)	100315.x	40124	yes	\(1\)	\(1\)	\(e\left(\frac{3525}{5732}\right)\)	\(e\left(\frac{19953}{40124}\right)\)	\(e\left(\frac{659}{2866}\right)\)	\(e\left(\frac{1126}{10031}\right)\)	\(e\left(\frac{3965}{40124}\right)\)	\(e\left(\frac{4843}{5732}\right)\)	\(e\left(\frac{19953}{20062}\right)\)	\(e\left(\frac{9398}{10031}\right)\)	\(e\left(\frac{29179}{40124}\right)\)	\(e\left(\frac{28633}{40124}\right)\)
\(\chi_{100315}(18,\cdot)\)	100315.w	40124	yes	\(-1\)	\(1\)	\(e\left(\frac{2559}{5732}\right)\)	\(e\left(\frac{24427}{40124}\right)\)	\(e\left(\frac{2559}{2866}\right)\)	\(e\left(\frac{554}{10031}\right)\)	\(e\left(\frac{24721}{40124}\right)\)	\(e\left(\frac{1945}{5732}\right)\)	\(e\left(\frac{4365}{20062}\right)\)	\(e\left(\frac{8508}{10031}\right)\)	\(e\left(\frac{20129}{40124}\right)\)	\(e\left(\frac{18435}{40124}\right)\)
\(\chi_{100315}(19,\cdot)\)	100315.u	20062	yes	\(1\)	\(1\)	\(e\left(\frac{2385}{2866}\right)\)	\(e\left(\frac{9817}{20062}\right)\)	\(e\left(\frac{952}{1433}\right)\)	\(e\left(\frac{3225}{10031}\right)\)	\(e\left(\frac{16159}{20062}\right)\)	\(e\left(\frac{1423}{2866}\right)\)	\(e\left(\frac{9817}{10031}\right)\)	\(e\left(\frac{2668}{10031}\right)\)	\(e\left(\frac{3083}{20062}\right)\)	\(e\left(\frac{15263}{20062}\right)\)
\(\chi_{100315}(21,\cdot)\)	100315.t	20062	no	\(-1\)	\(1\)	\(e\left(\frac{440}{1433}\right)\)	\(e\left(\frac{9619}{10031}\right)\)	\(e\left(\frac{880}{1433}\right)\)	\(e\left(\frac{2668}{10031}\right)\)	\(e\left(\frac{65}{20062}\right)\)	\(e\left(\frac{1320}{1433}\right)\)	\(e\left(\frac{9207}{10031}\right)\)	\(e\left(\frac{2117}{10031}\right)\)	\(e\left(\frac{5748}{10031}\right)\)	\(e\left(\frac{2948}{10031}\right)\)
\(\chi_{100315}(22,\cdot)\)	100315.w	40124	yes	\(-1\)	\(1\)	\(e\left(\frac{2585}{5732}\right)\)	\(e\left(\frac{16925}{40124}\right)\)	\(e\left(\frac{2585}{2866}\right)\)	\(e\left(\frac{8755}{10031}\right)\)	\(e\left(\frac{3863}{40124}\right)\)	\(e\left(\frac{2023}{5732}\right)\)	\(e\left(\frac{16925}{20062}\right)\)	\(e\left(\frac{7274}{10031}\right)\)	\(e\left(\frac{12991}{40124}\right)\)	\(e\left(\frac{36665}{40124}\right)\)
\(\chi_{100315}(23,\cdot)\)	100315.w	40124	yes	\(-1\)	\(1\)	\(e\left(\frac{2947}{5732}\right)\)	\(e\left(\frac{10359}{40124}\right)\)	\(e\left(\frac{81}{2866}\right)\)	\(e\left(\frac{7747}{10031}\right)\)	\(e\left(\frac{2701}{40124}\right)\)	\(e\left(\frac{3109}{5732}\right)\)	\(e\left(\frac{10359}{20062}\right)\)	\(e\left(\frac{2549}{10031}\right)\)	\(e\left(\frac{11493}{40124}\right)\)	\(e\left(\frac{36511}{40124}\right)\)
\(\chi_{100315}(24,\cdot)\)	100315.u	20062	yes	\(1\)	\(1\)	\(e\left(\frac{1855}{2866}\right)\)	\(e\left(\frac{13049}{20062}\right)\)	\(e\left(\frac{422}{1433}\right)\)	\(e\left(\frac{2986}{10031}\right)\)	\(e\left(\frac{4607}{20062}\right)\)	\(e\left(\frac{2699}{2866}\right)\)	\(e\left(\frac{3018}{10031}\right)\)	\(e\left(\frac{1279}{10031}\right)\)	\(e\left(\frac{18957}{20062}\right)\)	\(e\left(\frac{1681}{20062}\right)\)
\(\chi_{100315}(26,\cdot)\)	100315.s	10031	no	\(1\)	\(1\)	\(e\left(\frac{446}{1433}\right)\)	\(e\left(\frac{7998}{10031}\right)\)	\(e\left(\frac{892}{1433}\right)\)	\(e\left(\frac{1089}{10031}\right)\)	\(e\left(\frac{8061}{10031}\right)\)	\(e\left(\frac{1338}{1433}\right)\)	\(e\left(\frac{5965}{10031}\right)\)	\(e\left(\frac{537}{10031}\right)\)	\(e\left(\frac{4211}{10031}\right)\)	\(e\left(\frac{9580}{10031}\right)\)
\(\chi_{100315}(27,\cdot)\)	100315.w	40124	yes	\(-1\)	\(1\)	\(e\left(\frac{4673}{5732}\right)\)	\(e\left(\frac{20285}{40124}\right)\)	\(e\left(\frac{1807}{2866}\right)\)	\(e\left(\frac{3218}{10031}\right)\)	\(e\left(\frac{14895}{40124}\right)\)	\(e\left(\frac{2555}{5732}\right)\)	\(e\left(\frac{223}{20062}\right)\)	\(e\left(\frac{4516}{10031}\right)\)	\(e\left(\frac{5459}{40124}\right)\)	\(e\left(\frac{23141}{40124}\right)\)
\(\chi_{100315}(28,\cdot)\)	100315.x	40124	yes	\(1\)	\(1\)	\(e\left(\frac{2911}{5732}\right)\)	\(e\left(\frac{23}{40124}\right)\)	\(e\left(\frac{45}{2866}\right)\)	\(e\left(\frac{5100}{10031}\right)\)	\(e\left(\frac{24747}{40124}\right)\)	\(e\left(\frac{3001}{5732}\right)\)	\(e\left(\frac{23}{20062}\right)\)	\(e\left(\frac{4919}{10031}\right)\)	\(e\left(\frac{653}{40124}\right)\)	\(e\left(\frac{36843}{40124}\right)\)
\(\chi_{100315}(29,\cdot)\)	100315.u	20062	yes	\(1\)	\(1\)	\(e\left(\frac{2315}{2866}\right)\)	\(e\left(\frac{8189}{20062}\right)\)	\(e\left(\frac{882}{1433}\right)\)	\(e\left(\frac{2166}{10031}\right)\)	\(e\left(\frac{7279}{20062}\right)\)	\(e\left(\frac{1213}{2866}\right)\)	\(e\left(\frac{8189}{10031}\right)\)	\(e\left(\frac{2809}{10031}\right)\)	\(e\left(\frac{475}{20062}\right)\)	\(e\left(\frac{7629}{20062}\right)\)
\(\chi_{100315}(31,\cdot)\)	100315.s	10031	no	\(1\)	\(1\)	\(e\left(\frac{1055}{1433}\right)\)	\(e\left(\frac{8978}{10031}\right)\)	\(e\left(\frac{677}{1433}\right)\)	\(e\left(\frac{6332}{10031}\right)\)	\(e\left(\frac{7935}{10031}\right)\)	\(e\left(\frac{299}{1433}\right)\)	\(e\left(\frac{7925}{10031}\right)\)	\(e\left(\frac{663}{10031}\right)\)	\(e\left(\frac{3686}{10031}\right)\)	\(e\left(\frac{620}{10031}\right)\)
\(\chi_{100315}(32,\cdot)\)	100315.r	5732	yes	\(-1\)	\(1\)	\(e\left(\frac{4861}{5732}\right)\)	\(e\left(\frac{3967}{5732}\right)\)	\(e\left(\frac{1995}{2866}\right)\)	\(e\left(\frac{774}{1433}\right)\)	\(e\left(\frac{4833}{5732}\right)\)	\(e\left(\frac{3119}{5732}\right)\)	\(e\left(\frac{1101}{2866}\right)\)	\(e\left(\frac{583}{1433}\right)\)	\(e\left(\frac{2225}{5732}\right)\)	\(e\left(\frac{4059}{5732}\right)\)
\(\chi_{100315}(33,\cdot)\)	100315.w	40124	yes	\(-1\)	\(1\)	\(e\left(\frac{4699}{5732}\right)\)	\(e\left(\frac{12783}{40124}\right)\)	\(e\left(\frac{1833}{2866}\right)\)	\(e\left(\frac{1388}{10031}\right)\)	\(e\left(\frac{34161}{40124}\right)\)	\(e\left(\frac{2633}{5732}\right)\)	\(e\left(\frac{12783}{20062}\right)\)	\(e\left(\frac{3282}{10031}\right)\)	\(e\left(\frac{38445}{40124}\right)\)	\(e\left(\frac{1247}{40124}\right)\)
\(\chi_{100315}(34,\cdot)\)	100315.v	20062	yes	\(-1\)	\(1\)	\(e\left(\frac{529}{2866}\right)\)	\(e\left(\frac{8741}{20062}\right)\)	\(e\left(\frac{529}{1433}\right)\)	\(e\left(\frac{6222}{10031}\right)\)	\(e\left(\frac{4689}{10031}\right)\)	\(e\left(\frac{1587}{2866}\right)\)	\(e\left(\frac{8741}{10031}\right)\)	\(e\left(\frac{8208}{10031}\right)\)	\(e\left(\frac{16147}{20062}\right)\)	\(e\left(\frac{9133}{20062}\right)\)
\(\chi_{100315}(36,\cdot)\)	100315.s	10031	no	\(1\)	\(1\)	\(e\left(\frac{23}{1433}\right)\)	\(e\left(\frac{5489}{10031}\right)\)	\(e\left(\frac{46}{1433}\right)\)	\(e\left(\frac{5650}{10031}\right)\)	\(e\left(\frac{9878}{10031}\right)\)	\(e\left(\frac{69}{1433}\right)\)	\(e\left(\frac{947}{10031}\right)\)	\(e\left(\frac{7318}{10031}\right)\)	\(e\left(\frac{5811}{10031}\right)\)	\(e\left(\frac{2017}{10031}\right)\)
\(\chi_{100315}(37,\cdot)\)	100315.w	40124	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{5732}\right)\)	\(e\left(\frac{22873}{40124}\right)\)	\(e\left(\frac{17}{2866}\right)\)	\(e\left(\frac{5748}{10031}\right)\)	\(e\left(\frac{32659}{40124}\right)\)	\(e\left(\frac{51}{5732}\right)\)	\(e\left(\frac{2811}{20062}\right)\)	\(e\left(\frac{1508}{10031}\right)\)	\(e\left(\frac{23111}{40124}\right)\)	\(e\left(\frac{1117}{40124}\right)\)
\(\chi_{100315}(38,\cdot)\)	100315.w	40124	yes	\(-1\)	\(1\)	\(e\left(\frac{2303}{5732}\right)\)	\(e\left(\frac{17163}{40124}\right)\)	\(e\left(\frac{2303}{2866}\right)\)	\(e\left(\frac{8321}{10031}\right)\)	\(e\left(\frac{6985}{40124}\right)\)	\(e\left(\frac{1177}{5732}\right)\)	\(e\left(\frac{17163}{20062}\right)\)	\(e\left(\frac{1478}{10031}\right)\)	\(e\left(\frac{9281}{40124}\right)\)	\(e\left(\frac{20159}{40124}\right)\)
\(\chi_{100315}(39,\cdot)\)	100315.u	20062	yes	\(1\)	\(1\)	\(e\left(\frac{1949}{2866}\right)\)	\(e\left(\frac{13925}{20062}\right)\)	\(e\left(\frac{516}{1433}\right)\)	\(e\left(\frac{3753}{10031}\right)\)	\(e\left(\frac{11209}{20062}\right)\)	\(e\left(\frac{115}{2866}\right)\)	\(e\left(\frac{3894}{10031}\right)\)	\(e\left(\frac{6576}{10031}\right)\)	\(e\left(\frac{1087}{20062}\right)\)	\(e\left(\frac{1451}{20062}\right)\)

Introduction

L-functions

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