LMFDB - Group of Dirichlet characters of modulus 10060

Show commands: PariGP / SageMath

sage: H = DirichletGroup(10060)

pari: g = idealstar(,10060,2)

Character group

sage: G.order() pari: g.no
Order	=	4016
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{1004}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{10060}(5031,\cdot)$, $\chi_{10060}(6037,\cdot)$, $\chi_{10060}(6041,\cdot)$

First 32 of 4016 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{10060}(1,\cdot)$	10060.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{10060}(3,\cdot)$	10060.w	1004	yes	$1$	$1$	$e\left(\frac{229}{1004}\right)$	$e\left(\frac{979}{1004}\right)$	$e\left(\frac{229}{502}\right)$	$e\left(\frac{277}{502}\right)$	$e\left(\frac{787}{1004}\right)$	$e\left(\frac{917}{1004}\right)$	$e\left(\frac{163}{251}\right)$	$e\left(\frac{51}{251}\right)$	$e\left(\frac{405}{1004}\right)$	$e\left(\frac{687}{1004}\right)$
$\chi_{10060}(7,\cdot)$	10060.w	1004	yes	$1$	$1$	$e\left(\frac{979}{1004}\right)$	$e\left(\frac{485}{1004}\right)$	$e\left(\frac{477}{502}\right)$	$e\left(\frac{349}{502}\right)$	$e\left(\frac{997}{1004}\right)$	$e\left(\frac{483}{1004}\right)$	$e\left(\frac{151}{251}\right)$	$e\left(\frac{115}{251}\right)$	$e\left(\frac{175}{1004}\right)$	$e\left(\frac{929}{1004}\right)$
$\chi_{10060}(9,\cdot)$	10060.r	502	no	$1$	$1$	$e\left(\frac{229}{502}\right)$	$e\left(\frac{477}{502}\right)$	$e\left(\frac{229}{251}\right)$	$e\left(\frac{26}{251}\right)$	$e\left(\frac{285}{502}\right)$	$e\left(\frac{415}{502}\right)$	$e\left(\frac{75}{251}\right)$	$e\left(\frac{102}{251}\right)$	$e\left(\frac{405}{502}\right)$	$e\left(\frac{185}{502}\right)$
$\chi_{10060}(11,\cdot)$	10060.s	502	no	$-1$	$1$	$e\left(\frac{277}{502}\right)$	$e\left(\frac{349}{502}\right)$	$e\left(\frac{26}{251}\right)$	$e\left(\frac{7}{502}\right)$	$e\left(\frac{94}{251}\right)$	$e\left(\frac{40}{251}\right)$	$e\left(\frac{165}{502}\right)$	$e\left(\frac{62}{251}\right)$	$e\left(\frac{69}{502}\right)$	$e\left(\frac{329}{502}\right)$
$\chi_{10060}(13,\cdot)$	10060.v	1004	no	$-1$	$1$	$e\left(\frac{787}{1004}\right)$	$e\left(\frac{997}{1004}\right)$	$e\left(\frac{285}{502}\right)$	$e\left(\frac{94}{251}\right)$	$e\left(\frac{883}{1004}\right)$	$e\left(\frac{317}{1004}\right)$	$e\left(\frac{21}{502}\right)$	$e\left(\frac{195}{251}\right)$	$e\left(\frac{515}{1004}\right)$	$e\left(\frac{353}{1004}\right)$
$\chi_{10060}(17,\cdot)$	10060.u	1004	no	$1$	$1$	$e\left(\frac{917}{1004}\right)$	$e\left(\frac{483}{1004}\right)$	$e\left(\frac{415}{502}\right)$	$e\left(\frac{40}{251}\right)$	$e\left(\frac{317}{1004}\right)$	$e\left(\frac{717}{1004}\right)$	$e\left(\frac{154}{251}\right)$	$e\left(\frac{99}{251}\right)$	$e\left(\frac{609}{1004}\right)$	$e\left(\frac{743}{1004}\right)$
$\chi_{10060}(19,\cdot)$	10060.o	502	yes	$1$	$1$	$e\left(\frac{163}{251}\right)$	$e\left(\frac{151}{251}\right)$	$e\left(\frac{75}{251}\right)$	$e\left(\frac{165}{502}\right)$	$e\left(\frac{21}{502}\right)$	$e\left(\frac{154}{251}\right)$	$e\left(\frac{98}{251}\right)$	$e\left(\frac{63}{251}\right)$	$e\left(\frac{114}{251}\right)$	$e\left(\frac{238}{251}\right)$
$\chi_{10060}(21,\cdot)$	10060.m	251	no	$1$	$1$	$e\left(\frac{51}{251}\right)$	$e\left(\frac{115}{251}\right)$	$e\left(\frac{102}{251}\right)$	$e\left(\frac{62}{251}\right)$	$e\left(\frac{195}{251}\right)$	$e\left(\frac{99}{251}\right)$	$e\left(\frac{63}{251}\right)$	$e\left(\frac{166}{251}\right)$	$e\left(\frac{145}{251}\right)$	$e\left(\frac{153}{251}\right)$
$\chi_{10060}(23,\cdot)$	10060.w	1004	yes	$1$	$1$	$e\left(\frac{405}{1004}\right)$	$e\left(\frac{175}{1004}\right)$	$e\left(\frac{405}{502}\right)$	$e\left(\frac{69}{502}\right)$	$e\left(\frac{515}{1004}\right)$	$e\left(\frac{609}{1004}\right)$	$e\left(\frac{114}{251}\right)$	$e\left(\frac{145}{251}\right)$	$e\left(\frac{177}{1004}\right)$	$e\left(\frac{211}{1004}\right)$
$\chi_{10060}(27,\cdot)$	10060.w	1004	yes	$1$	$1$	$e\left(\frac{687}{1004}\right)$	$e\left(\frac{929}{1004}\right)$	$e\left(\frac{185}{502}\right)$	$e\left(\frac{329}{502}\right)$	$e\left(\frac{353}{1004}\right)$	$e\left(\frac{743}{1004}\right)$	$e\left(\frac{238}{251}\right)$	$e\left(\frac{153}{251}\right)$	$e\left(\frac{211}{1004}\right)$	$e\left(\frac{53}{1004}\right)$
$\chi_{10060}(29,\cdot)$	10060.q	502	no	$-1$	$1$	$e\left(\frac{211}{502}\right)$	$e\left(\frac{23}{502}\right)$	$e\left(\frac{211}{251}\right)$	$e\left(\frac{207}{251}\right)$	$e\left(\frac{39}{502}\right)$	$e\left(\frac{35}{251}\right)$	$e\left(\frac{113}{502}\right)$	$e\left(\frac{117}{251}\right)$	$e\left(\frac{29}{502}\right)$	$e\left(\frac{131}{502}\right)$
$\chi_{10060}(31,\cdot)$	10060.t	502	no	$1$	$1$	$e\left(\frac{67}{502}\right)$	$e\left(\frac{407}{502}\right)$	$e\left(\frac{67}{251}\right)$	$e\left(\frac{47}{502}\right)$	$e\left(\frac{165}{251}\right)$	$e\left(\frac{71}{502}\right)$	$e\left(\frac{34}{251}\right)$	$e\left(\frac{237}{251}\right)$	$e\left(\frac{33}{502}\right)$	$e\left(\frac{201}{502}\right)$
$\chi_{10060}(33,\cdot)$	10060.v	1004	no	$-1$	$1$	$e\left(\frac{783}{1004}\right)$	$e\left(\frac{673}{1004}\right)$	$e\left(\frac{281}{502}\right)$	$e\left(\frac{142}{251}\right)$	$e\left(\frac{159}{1004}\right)$	$e\left(\frac{73}{1004}\right)$	$e\left(\frac{491}{502}\right)$	$e\left(\frac{113}{251}\right)$	$e\left(\frac{543}{1004}\right)$	$e\left(\frac{341}{1004}\right)$
$\chi_{10060}(37,\cdot)$	10060.u	1004	no	$1$	$1$	$e\left(\frac{41}{1004}\right)$	$e\left(\frac{811}{1004}\right)$	$e\left(\frac{41}{502}\right)$	$e\left(\frac{10}{251}\right)$	$e\left(\frac{393}{1004}\right)$	$e\left(\frac{493}{1004}\right)$	$e\left(\frac{164}{251}\right)$	$e\left(\frac{213}{251}\right)$	$e\left(\frac{717}{1004}\right)$	$e\left(\frac{123}{1004}\right)$
$\chi_{10060}(39,\cdot)$	10060.p	502	yes	$-1$	$1$	$e\left(\frac{3}{251}\right)$	$e\left(\frac{243}{251}\right)$	$e\left(\frac{6}{251}\right)$	$e\left(\frac{465}{502}\right)$	$e\left(\frac{333}{502}\right)$	$e\left(\frac{115}{502}\right)$	$e\left(\frac{347}{502}\right)$	$e\left(\frac{246}{251}\right)$	$e\left(\frac{230}{251}\right)$	$e\left(\frac{9}{251}\right)$
$\chi_{10060}(41,\cdot)$	10060.n	502	no	$-1$	$1$	$e\left(\frac{7}{251}\right)$	$e\left(\frac{65}{251}\right)$	$e\left(\frac{14}{251}\right)$	$e\left(\frac{166}{251}\right)$	$e\left(\frac{12}{251}\right)$	$e\left(\frac{101}{502}\right)$	$e\left(\frac{475}{502}\right)$	$e\left(\frac{72}{251}\right)$	$e\left(\frac{202}{251}\right)$	$e\left(\frac{21}{251}\right)$
$\chi_{10060}(43,\cdot)$	10060.w	1004	yes	$1$	$1$	$e\left(\frac{261}{1004}\right)$	$e\left(\frac{559}{1004}\right)$	$e\left(\frac{261}{502}\right)$	$e\left(\frac{11}{502}\right)$	$e\left(\frac{555}{1004}\right)$	$e\left(\frac{861}{1004}\right)$	$e\left(\frac{40}{251}\right)$	$e\left(\frac{205}{251}\right)$	$e\left(\frac{181}{1004}\right)$	$e\left(\frac{783}{1004}\right)$
$\chi_{10060}(47,\cdot)$	10060.w	1004	yes	$1$	$1$	$e\left(\frac{699}{1004}\right)$	$e\left(\frac{897}{1004}\right)$	$e\left(\frac{197}{502}\right)$	$e\left(\frac{41}{502}\right)$	$e\left(\frac{517}{1004}\right)$	$e\left(\frac{471}{1004}\right)$	$e\left(\frac{35}{251}\right)$	$e\left(\frac{148}{251}\right)$	$e\left(\frac{127}{1004}\right)$	$e\left(\frac{89}{1004}\right)$
$\chi_{10060}(49,\cdot)$	10060.r	502	no	$1$	$1$	$e\left(\frac{477}{502}\right)$	$e\left(\frac{485}{502}\right)$	$e\left(\frac{226}{251}\right)$	$e\left(\frac{98}{251}\right)$	$e\left(\frac{495}{502}\right)$	$e\left(\frac{483}{502}\right)$	$e\left(\frac{51}{251}\right)$	$e\left(\frac{230}{251}\right)$	$e\left(\frac{175}{502}\right)$	$e\left(\frac{427}{502}\right)$
$\chi_{10060}(51,\cdot)$	10060.t	502	no	$1$	$1$	$e\left(\frac{71}{502}\right)$	$e\left(\frac{229}{502}\right)$	$e\left(\frac{71}{251}\right)$	$e\left(\frac{357}{502}\right)$	$e\left(\frac{25}{251}\right)$	$e\left(\frac{315}{502}\right)$	$e\left(\frac{66}{251}\right)$	$e\left(\frac{150}{251}\right)$	$e\left(\frac{5}{502}\right)$	$e\left(\frac{213}{502}\right)$
$\chi_{10060}(53,\cdot)$	10060.u	1004	no	$1$	$1$	$e\left(\frac{603}{1004}\right)$	$e\left(\frac{149}{1004}\right)$	$e\left(\frac{101}{502}\right)$	$e\left(\frac{43}{251}\right)$	$e\left(\frac{711}{1004}\right)$	$e\left(\frac{639}{1004}\right)$	$e\left(\frac{153}{251}\right)$	$e\left(\frac{188}{251}\right)$	$e\left(\frac{799}{1004}\right)$	$e\left(\frac{805}{1004}\right)$
$\chi_{10060}(57,\cdot)$	10060.u	1004	no	$1$	$1$	$e\left(\frac{881}{1004}\right)$	$e\left(\frac{579}{1004}\right)$	$e\left(\frac{379}{502}\right)$	$e\left(\frac{221}{251}\right)$	$e\left(\frac{829}{1004}\right)$	$e\left(\frac{529}{1004}\right)$	$e\left(\frac{10}{251}\right)$	$e\left(\frac{114}{251}\right)$	$e\left(\frac{861}{1004}\right)$	$e\left(\frac{635}{1004}\right)$
$\chi_{10060}(59,\cdot)$	10060.p	502	yes	$-1$	$1$	$e\left(\frac{79}{251}\right)$	$e\left(\frac{124}{251}\right)$	$e\left(\frac{158}{251}\right)$	$e\left(\frac{197}{502}\right)$	$e\left(\frac{235}{502}\right)$	$e\left(\frac{351}{502}\right)$	$e\left(\frac{269}{502}\right)$	$e\left(\frac{203}{251}\right)$	$e\left(\frac{200}{251}\right)$	$e\left(\frac{237}{251}\right)$
$\chi_{10060}(61,\cdot)$	10060.m	251	no	$1$	$1$	$e\left(\frac{118}{251}\right)$	$e\left(\frac{20}{251}\right)$	$e\left(\frac{236}{251}\right)$	$e\left(\frac{109}{251}\right)$	$e\left(\frac{23}{251}\right)$	$e\left(\frac{170}{251}\right)$	$e\left(\frac{131}{251}\right)$	$e\left(\frac{138}{251}\right)$	$e\left(\frac{178}{251}\right)$	$e\left(\frac{103}{251}\right)$
$\chi_{10060}(63,\cdot)$	10060.w	1004	yes	$1$	$1$	$e\left(\frac{433}{1004}\right)$	$e\left(\frac{435}{1004}\right)$	$e\left(\frac{433}{502}\right)$	$e\left(\frac{401}{502}\right)$	$e\left(\frac{563}{1004}\right)$	$e\left(\frac{309}{1004}\right)$	$e\left(\frac{226}{251}\right)$	$e\left(\frac{217}{251}\right)$	$e\left(\frac{985}{1004}\right)$	$e\left(\frac{295}{1004}\right)$
$\chi_{10060}(67,\cdot)$	10060.w	1004	yes	$1$	$1$	$e\left(\frac{463}{1004}\right)$	$e\left(\frac{857}{1004}\right)$	$e\left(\frac{463}{502}\right)$	$e\left(\frac{183}{502}\right)$	$e\left(\frac{973}{1004}\right)$	$e\left(\frac{131}{1004}\right)$	$e\left(\frac{95}{251}\right)$	$e\left(\frac{79}{251}\right)$	$e\left(\frac{775}{1004}\right)$	$e\left(\frac{385}{1004}\right)$
$\chi_{10060}(69,\cdot)$	10060.r	502	no	$1$	$1$	$e\left(\frac{317}{502}\right)$	$e\left(\frac{75}{502}\right)$	$e\left(\frac{66}{251}\right)$	$e\left(\frac{173}{251}\right)$	$e\left(\frac{149}{502}\right)$	$e\left(\frac{261}{502}\right)$	$e\left(\frac{26}{251}\right)$	$e\left(\frac{196}{251}\right)$	$e\left(\frac{291}{502}\right)$	$e\left(\frac{449}{502}\right)$
$\chi_{10060}(71,\cdot)$	10060.t	502	no	$1$	$1$	$e\left(\frac{13}{502}\right)$	$e\left(\frac{49}{502}\right)$	$e\left(\frac{13}{251}\right)$	$e\left(\frac{129}{502}\right)$	$e\left(\frac{47}{251}\right)$	$e\left(\frac{291}{502}\right)$	$e\left(\frac{104}{251}\right)$	$e\left(\frac{31}{251}\right)$	$e\left(\frac{411}{502}\right)$	$e\left(\frac{39}{502}\right)$
$\chi_{10060}(73,\cdot)$	10060.v	1004	no	$-1$	$1$	$e\left(\frac{847}{1004}\right)$	$e\left(\frac{837}{1004}\right)$	$e\left(\frac{345}{502}\right)$	$e\left(\frac{127}{251}\right)$	$e\left(\frac{699}{1004}\right)$	$e\left(\frac{965}{1004}\right)$	$e\left(\frac{501}{502}\right)$	$e\left(\frac{170}{251}\right)$	$e\left(\frac{95}{1004}\right)$	$e\left(\frac{533}{1004}\right)$
$\chi_{10060}(77,\cdot)$	10060.v	1004	no	$-1$	$1$	$e\left(\frac{529}{1004}\right)$	$e\left(\frac{179}{1004}\right)$	$e\left(\frac{27}{502}\right)$	$e\left(\frac{178}{251}\right)$	$e\left(\frac{369}{1004}\right)$	$e\left(\frac{643}{1004}\right)$	$e\left(\frac{467}{502}\right)$	$e\left(\frac{177}{251}\right)$	$e\left(\frac{313}{1004}\right)$	$e\left(\frac{583}{1004}\right)$
$\chi_{10060}(79,\cdot)$	10060.p	502	yes	$-1$	$1$	$e\left(\frac{168}{251}\right)$	$e\left(\frac{54}{251}\right)$	$e\left(\frac{85}{251}\right)$	$e\left(\frac{187}{502}\right)$	$e\left(\frac{325}{502}\right)$	$e\left(\frac{165}{502}\right)$	$e\left(\frac{105}{502}\right)$	$e\left(\frac{222}{251}\right)$	$e\left(\frac{79}{251}\right)$	$e\left(\frac{2}{251}\right)$

Click here to search among the remaining 3984 characters.

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	$10060$
Structure	\(C_{2}\times C_{2}\times C_{1004}\)
Order	$4016$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{10060}(1,\cdot)\)	10060.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{10060}(3,\cdot)\)	10060.w	1004	yes	\(1\)	\(1\)	\(e\left(\frac{229}{1004}\right)\)	\(e\left(\frac{979}{1004}\right)\)	\(e\left(\frac{229}{502}\right)\)	\(e\left(\frac{277}{502}\right)\)	\(e\left(\frac{787}{1004}\right)\)	\(e\left(\frac{917}{1004}\right)\)	\(e\left(\frac{163}{251}\right)\)	\(e\left(\frac{51}{251}\right)\)	\(e\left(\frac{405}{1004}\right)\)	\(e\left(\frac{687}{1004}\right)\)
\(\chi_{10060}(7,\cdot)\)	10060.w	1004	yes	\(1\)	\(1\)	\(e\left(\frac{979}{1004}\right)\)	\(e\left(\frac{485}{1004}\right)\)	\(e\left(\frac{477}{502}\right)\)	\(e\left(\frac{349}{502}\right)\)	\(e\left(\frac{997}{1004}\right)\)	\(e\left(\frac{483}{1004}\right)\)	\(e\left(\frac{151}{251}\right)\)	\(e\left(\frac{115}{251}\right)\)	\(e\left(\frac{175}{1004}\right)\)	\(e\left(\frac{929}{1004}\right)\)
\(\chi_{10060}(9,\cdot)\)	10060.r	502	no	\(1\)	\(1\)	\(e\left(\frac{229}{502}\right)\)	\(e\left(\frac{477}{502}\right)\)	\(e\left(\frac{229}{251}\right)\)	\(e\left(\frac{26}{251}\right)\)	\(e\left(\frac{285}{502}\right)\)	\(e\left(\frac{415}{502}\right)\)	\(e\left(\frac{75}{251}\right)\)	\(e\left(\frac{102}{251}\right)\)	\(e\left(\frac{405}{502}\right)\)	\(e\left(\frac{185}{502}\right)\)
\(\chi_{10060}(11,\cdot)\)	10060.s	502	no	\(-1\)	\(1\)	\(e\left(\frac{277}{502}\right)\)	\(e\left(\frac{349}{502}\right)\)	\(e\left(\frac{26}{251}\right)\)	\(e\left(\frac{7}{502}\right)\)	\(e\left(\frac{94}{251}\right)\)	\(e\left(\frac{40}{251}\right)\)	\(e\left(\frac{165}{502}\right)\)	\(e\left(\frac{62}{251}\right)\)	\(e\left(\frac{69}{502}\right)\)	\(e\left(\frac{329}{502}\right)\)
\(\chi_{10060}(13,\cdot)\)	10060.v	1004	no	\(-1\)	\(1\)	\(e\left(\frac{787}{1004}\right)\)	\(e\left(\frac{997}{1004}\right)\)	\(e\left(\frac{285}{502}\right)\)	\(e\left(\frac{94}{251}\right)\)	\(e\left(\frac{883}{1004}\right)\)	\(e\left(\frac{317}{1004}\right)\)	\(e\left(\frac{21}{502}\right)\)	\(e\left(\frac{195}{251}\right)\)	\(e\left(\frac{515}{1004}\right)\)	\(e\left(\frac{353}{1004}\right)\)
\(\chi_{10060}(17,\cdot)\)	10060.u	1004	no	\(1\)	\(1\)	\(e\left(\frac{917}{1004}\right)\)	\(e\left(\frac{483}{1004}\right)\)	\(e\left(\frac{415}{502}\right)\)	\(e\left(\frac{40}{251}\right)\)	\(e\left(\frac{317}{1004}\right)\)	\(e\left(\frac{717}{1004}\right)\)	\(e\left(\frac{154}{251}\right)\)	\(e\left(\frac{99}{251}\right)\)	\(e\left(\frac{609}{1004}\right)\)	\(e\left(\frac{743}{1004}\right)\)
\(\chi_{10060}(19,\cdot)\)	10060.o	502	yes	\(1\)	\(1\)	\(e\left(\frac{163}{251}\right)\)	\(e\left(\frac{151}{251}\right)\)	\(e\left(\frac{75}{251}\right)\)	\(e\left(\frac{165}{502}\right)\)	\(e\left(\frac{21}{502}\right)\)	\(e\left(\frac{154}{251}\right)\)	\(e\left(\frac{98}{251}\right)\)	\(e\left(\frac{63}{251}\right)\)	\(e\left(\frac{114}{251}\right)\)	\(e\left(\frac{238}{251}\right)\)
\(\chi_{10060}(21,\cdot)\)	10060.m	251	no	\(1\)	\(1\)	\(e\left(\frac{51}{251}\right)\)	\(e\left(\frac{115}{251}\right)\)	\(e\left(\frac{102}{251}\right)\)	\(e\left(\frac{62}{251}\right)\)	\(e\left(\frac{195}{251}\right)\)	\(e\left(\frac{99}{251}\right)\)	\(e\left(\frac{63}{251}\right)\)	\(e\left(\frac{166}{251}\right)\)	\(e\left(\frac{145}{251}\right)\)	\(e\left(\frac{153}{251}\right)\)
\(\chi_{10060}(23,\cdot)\)	10060.w	1004	yes	\(1\)	\(1\)	\(e\left(\frac{405}{1004}\right)\)	\(e\left(\frac{175}{1004}\right)\)	\(e\left(\frac{405}{502}\right)\)	\(e\left(\frac{69}{502}\right)\)	\(e\left(\frac{515}{1004}\right)\)	\(e\left(\frac{609}{1004}\right)\)	\(e\left(\frac{114}{251}\right)\)	\(e\left(\frac{145}{251}\right)\)	\(e\left(\frac{177}{1004}\right)\)	\(e\left(\frac{211}{1004}\right)\)
\(\chi_{10060}(27,\cdot)\)	10060.w	1004	yes	\(1\)	\(1\)	\(e\left(\frac{687}{1004}\right)\)	\(e\left(\frac{929}{1004}\right)\)	\(e\left(\frac{185}{502}\right)\)	\(e\left(\frac{329}{502}\right)\)	\(e\left(\frac{353}{1004}\right)\)	\(e\left(\frac{743}{1004}\right)\)	\(e\left(\frac{238}{251}\right)\)	\(e\left(\frac{153}{251}\right)\)	\(e\left(\frac{211}{1004}\right)\)	\(e\left(\frac{53}{1004}\right)\)
\(\chi_{10060}(29,\cdot)\)	10060.q	502	no	\(-1\)	\(1\)	\(e\left(\frac{211}{502}\right)\)	\(e\left(\frac{23}{502}\right)\)	\(e\left(\frac{211}{251}\right)\)	\(e\left(\frac{207}{251}\right)\)	\(e\left(\frac{39}{502}\right)\)	\(e\left(\frac{35}{251}\right)\)	\(e\left(\frac{113}{502}\right)\)	\(e\left(\frac{117}{251}\right)\)	\(e\left(\frac{29}{502}\right)\)	\(e\left(\frac{131}{502}\right)\)
\(\chi_{10060}(31,\cdot)\)	10060.t	502	no	\(1\)	\(1\)	\(e\left(\frac{67}{502}\right)\)	\(e\left(\frac{407}{502}\right)\)	\(e\left(\frac{67}{251}\right)\)	\(e\left(\frac{47}{502}\right)\)	\(e\left(\frac{165}{251}\right)\)	\(e\left(\frac{71}{502}\right)\)	\(e\left(\frac{34}{251}\right)\)	\(e\left(\frac{237}{251}\right)\)	\(e\left(\frac{33}{502}\right)\)	\(e\left(\frac{201}{502}\right)\)
\(\chi_{10060}(33,\cdot)\)	10060.v	1004	no	\(-1\)	\(1\)	\(e\left(\frac{783}{1004}\right)\)	\(e\left(\frac{673}{1004}\right)\)	\(e\left(\frac{281}{502}\right)\)	\(e\left(\frac{142}{251}\right)\)	\(e\left(\frac{159}{1004}\right)\)	\(e\left(\frac{73}{1004}\right)\)	\(e\left(\frac{491}{502}\right)\)	\(e\left(\frac{113}{251}\right)\)	\(e\left(\frac{543}{1004}\right)\)	\(e\left(\frac{341}{1004}\right)\)
\(\chi_{10060}(37,\cdot)\)	10060.u	1004	no	\(1\)	\(1\)	\(e\left(\frac{41}{1004}\right)\)	\(e\left(\frac{811}{1004}\right)\)	\(e\left(\frac{41}{502}\right)\)	\(e\left(\frac{10}{251}\right)\)	\(e\left(\frac{393}{1004}\right)\)	\(e\left(\frac{493}{1004}\right)\)	\(e\left(\frac{164}{251}\right)\)	\(e\left(\frac{213}{251}\right)\)	\(e\left(\frac{717}{1004}\right)\)	\(e\left(\frac{123}{1004}\right)\)
\(\chi_{10060}(39,\cdot)\)	10060.p	502	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{251}\right)\)	\(e\left(\frac{243}{251}\right)\)	\(e\left(\frac{6}{251}\right)\)	\(e\left(\frac{465}{502}\right)\)	\(e\left(\frac{333}{502}\right)\)	\(e\left(\frac{115}{502}\right)\)	\(e\left(\frac{347}{502}\right)\)	\(e\left(\frac{246}{251}\right)\)	\(e\left(\frac{230}{251}\right)\)	\(e\left(\frac{9}{251}\right)\)
\(\chi_{10060}(41,\cdot)\)	10060.n	502	no	\(-1\)	\(1\)	\(e\left(\frac{7}{251}\right)\)	\(e\left(\frac{65}{251}\right)\)	\(e\left(\frac{14}{251}\right)\)	\(e\left(\frac{166}{251}\right)\)	\(e\left(\frac{12}{251}\right)\)	\(e\left(\frac{101}{502}\right)\)	\(e\left(\frac{475}{502}\right)\)	\(e\left(\frac{72}{251}\right)\)	\(e\left(\frac{202}{251}\right)\)	\(e\left(\frac{21}{251}\right)\)
\(\chi_{10060}(43,\cdot)\)	10060.w	1004	yes	\(1\)	\(1\)	\(e\left(\frac{261}{1004}\right)\)	\(e\left(\frac{559}{1004}\right)\)	\(e\left(\frac{261}{502}\right)\)	\(e\left(\frac{11}{502}\right)\)	\(e\left(\frac{555}{1004}\right)\)	\(e\left(\frac{861}{1004}\right)\)	\(e\left(\frac{40}{251}\right)\)	\(e\left(\frac{205}{251}\right)\)	\(e\left(\frac{181}{1004}\right)\)	\(e\left(\frac{783}{1004}\right)\)
\(\chi_{10060}(47,\cdot)\)	10060.w	1004	yes	\(1\)	\(1\)	\(e\left(\frac{699}{1004}\right)\)	\(e\left(\frac{897}{1004}\right)\)	\(e\left(\frac{197}{502}\right)\)	\(e\left(\frac{41}{502}\right)\)	\(e\left(\frac{517}{1004}\right)\)	\(e\left(\frac{471}{1004}\right)\)	\(e\left(\frac{35}{251}\right)\)	\(e\left(\frac{148}{251}\right)\)	\(e\left(\frac{127}{1004}\right)\)	\(e\left(\frac{89}{1004}\right)\)
\(\chi_{10060}(49,\cdot)\)	10060.r	502	no	\(1\)	\(1\)	\(e\left(\frac{477}{502}\right)\)	\(e\left(\frac{485}{502}\right)\)	\(e\left(\frac{226}{251}\right)\)	\(e\left(\frac{98}{251}\right)\)	\(e\left(\frac{495}{502}\right)\)	\(e\left(\frac{483}{502}\right)\)	\(e\left(\frac{51}{251}\right)\)	\(e\left(\frac{230}{251}\right)\)	\(e\left(\frac{175}{502}\right)\)	\(e\left(\frac{427}{502}\right)\)
\(\chi_{10060}(51,\cdot)\)	10060.t	502	no	\(1\)	\(1\)	\(e\left(\frac{71}{502}\right)\)	\(e\left(\frac{229}{502}\right)\)	\(e\left(\frac{71}{251}\right)\)	\(e\left(\frac{357}{502}\right)\)	\(e\left(\frac{25}{251}\right)\)	\(e\left(\frac{315}{502}\right)\)	\(e\left(\frac{66}{251}\right)\)	\(e\left(\frac{150}{251}\right)\)	\(e\left(\frac{5}{502}\right)\)	\(e\left(\frac{213}{502}\right)\)
\(\chi_{10060}(53,\cdot)\)	10060.u	1004	no	\(1\)	\(1\)	\(e\left(\frac{603}{1004}\right)\)	\(e\left(\frac{149}{1004}\right)\)	\(e\left(\frac{101}{502}\right)\)	\(e\left(\frac{43}{251}\right)\)	\(e\left(\frac{711}{1004}\right)\)	\(e\left(\frac{639}{1004}\right)\)	\(e\left(\frac{153}{251}\right)\)	\(e\left(\frac{188}{251}\right)\)	\(e\left(\frac{799}{1004}\right)\)	\(e\left(\frac{805}{1004}\right)\)
\(\chi_{10060}(57,\cdot)\)	10060.u	1004	no	\(1\)	\(1\)	\(e\left(\frac{881}{1004}\right)\)	\(e\left(\frac{579}{1004}\right)\)	\(e\left(\frac{379}{502}\right)\)	\(e\left(\frac{221}{251}\right)\)	\(e\left(\frac{829}{1004}\right)\)	\(e\left(\frac{529}{1004}\right)\)	\(e\left(\frac{10}{251}\right)\)	\(e\left(\frac{114}{251}\right)\)	\(e\left(\frac{861}{1004}\right)\)	\(e\left(\frac{635}{1004}\right)\)
\(\chi_{10060}(59,\cdot)\)	10060.p	502	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{251}\right)\)	\(e\left(\frac{124}{251}\right)\)	\(e\left(\frac{158}{251}\right)\)	\(e\left(\frac{197}{502}\right)\)	\(e\left(\frac{235}{502}\right)\)	\(e\left(\frac{351}{502}\right)\)	\(e\left(\frac{269}{502}\right)\)	\(e\left(\frac{203}{251}\right)\)	\(e\left(\frac{200}{251}\right)\)	\(e\left(\frac{237}{251}\right)\)
\(\chi_{10060}(61,\cdot)\)	10060.m	251	no	\(1\)	\(1\)	\(e\left(\frac{118}{251}\right)\)	\(e\left(\frac{20}{251}\right)\)	\(e\left(\frac{236}{251}\right)\)	\(e\left(\frac{109}{251}\right)\)	\(e\left(\frac{23}{251}\right)\)	\(e\left(\frac{170}{251}\right)\)	\(e\left(\frac{131}{251}\right)\)	\(e\left(\frac{138}{251}\right)\)	\(e\left(\frac{178}{251}\right)\)	\(e\left(\frac{103}{251}\right)\)
\(\chi_{10060}(63,\cdot)\)	10060.w	1004	yes	\(1\)	\(1\)	\(e\left(\frac{433}{1004}\right)\)	\(e\left(\frac{435}{1004}\right)\)	\(e\left(\frac{433}{502}\right)\)	\(e\left(\frac{401}{502}\right)\)	\(e\left(\frac{563}{1004}\right)\)	\(e\left(\frac{309}{1004}\right)\)	\(e\left(\frac{226}{251}\right)\)	\(e\left(\frac{217}{251}\right)\)	\(e\left(\frac{985}{1004}\right)\)	\(e\left(\frac{295}{1004}\right)\)
\(\chi_{10060}(67,\cdot)\)	10060.w	1004	yes	\(1\)	\(1\)	\(e\left(\frac{463}{1004}\right)\)	\(e\left(\frac{857}{1004}\right)\)	\(e\left(\frac{463}{502}\right)\)	\(e\left(\frac{183}{502}\right)\)	\(e\left(\frac{973}{1004}\right)\)	\(e\left(\frac{131}{1004}\right)\)	\(e\left(\frac{95}{251}\right)\)	\(e\left(\frac{79}{251}\right)\)	\(e\left(\frac{775}{1004}\right)\)	\(e\left(\frac{385}{1004}\right)\)
\(\chi_{10060}(69,\cdot)\)	10060.r	502	no	\(1\)	\(1\)	\(e\left(\frac{317}{502}\right)\)	\(e\left(\frac{75}{502}\right)\)	\(e\left(\frac{66}{251}\right)\)	\(e\left(\frac{173}{251}\right)\)	\(e\left(\frac{149}{502}\right)\)	\(e\left(\frac{261}{502}\right)\)	\(e\left(\frac{26}{251}\right)\)	\(e\left(\frac{196}{251}\right)\)	\(e\left(\frac{291}{502}\right)\)	\(e\left(\frac{449}{502}\right)\)
\(\chi_{10060}(71,\cdot)\)	10060.t	502	no	\(1\)	\(1\)	\(e\left(\frac{13}{502}\right)\)	\(e\left(\frac{49}{502}\right)\)	\(e\left(\frac{13}{251}\right)\)	\(e\left(\frac{129}{502}\right)\)	\(e\left(\frac{47}{251}\right)\)	\(e\left(\frac{291}{502}\right)\)	\(e\left(\frac{104}{251}\right)\)	\(e\left(\frac{31}{251}\right)\)	\(e\left(\frac{411}{502}\right)\)	\(e\left(\frac{39}{502}\right)\)
\(\chi_{10060}(73,\cdot)\)	10060.v	1004	no	\(-1\)	\(1\)	\(e\left(\frac{847}{1004}\right)\)	\(e\left(\frac{837}{1004}\right)\)	\(e\left(\frac{345}{502}\right)\)	\(e\left(\frac{127}{251}\right)\)	\(e\left(\frac{699}{1004}\right)\)	\(e\left(\frac{965}{1004}\right)\)	\(e\left(\frac{501}{502}\right)\)	\(e\left(\frac{170}{251}\right)\)	\(e\left(\frac{95}{1004}\right)\)	\(e\left(\frac{533}{1004}\right)\)
\(\chi_{10060}(77,\cdot)\)	10060.v	1004	no	\(-1\)	\(1\)	\(e\left(\frac{529}{1004}\right)\)	\(e\left(\frac{179}{1004}\right)\)	\(e\left(\frac{27}{502}\right)\)	\(e\left(\frac{178}{251}\right)\)	\(e\left(\frac{369}{1004}\right)\)	\(e\left(\frac{643}{1004}\right)\)	\(e\left(\frac{467}{502}\right)\)	\(e\left(\frac{177}{251}\right)\)	\(e\left(\frac{313}{1004}\right)\)	\(e\left(\frac{583}{1004}\right)\)
\(\chi_{10060}(79,\cdot)\)	10060.p	502	yes	\(-1\)	\(1\)	\(e\left(\frac{168}{251}\right)\)	\(e\left(\frac{54}{251}\right)\)	\(e\left(\frac{85}{251}\right)\)	\(e\left(\frac{187}{502}\right)\)	\(e\left(\frac{325}{502}\right)\)	\(e\left(\frac{165}{502}\right)\)	\(e\left(\frac{105}{502}\right)\)	\(e\left(\frac{222}{251}\right)\)	\(e\left(\frac{79}{251}\right)\)	\(e\left(\frac{2}{251}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 4016 characters

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