LMFDB - Group of Dirichlet characters of modulus 3089

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3089)

pari: g = idealstar(,3089,2)

Character group

sage: G.order() pari: g.no
Order	=	3088
sage: H.invariants() pari: g.cyc
Structure	=	$C_{3088}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{3089}(3,\cdot)$

First 32 of 3088 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{3089}(1,\cdot)$	3089.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3089}(2,\cdot)$	3089.h	772	yes	$1$	$1$	$e\left(\frac{23}{193}\right)$	$e\left(\frac{315}{772}\right)$	$e\left(\frac{46}{193}\right)$	$e\left(\frac{313}{386}\right)$	$e\left(\frac{407}{772}\right)$	$e\left(\frac{39}{386}\right)$	$e\left(\frac{69}{193}\right)$	$e\left(\frac{315}{386}\right)$	$e\left(\frac{359}{386}\right)$	$e\left(\frac{211}{386}\right)$
$\chi_{3089}(3,\cdot)$	3089.j	3088	yes	$-1$	$1$	$e\left(\frac{315}{772}\right)$	$e\left(\frac{1}{3088}\right)$	$e\left(\frac{315}{386}\right)$	$e\left(\frac{561}{1544}\right)$	$e\left(\frac{1261}{3088}\right)$	$e\left(\frac{467}{1544}\right)$	$e\left(\frac{173}{772}\right)$	$e\left(\frac{1}{1544}\right)$	$e\left(\frac{1191}{1544}\right)$	$e\left(\frac{943}{1544}\right)$
$\chi_{3089}(4,\cdot)$	3089.g	386	yes	$1$	$1$	$e\left(\frac{46}{193}\right)$	$e\left(\frac{315}{386}\right)$	$e\left(\frac{92}{193}\right)$	$e\left(\frac{120}{193}\right)$	$e\left(\frac{21}{386}\right)$	$e\left(\frac{39}{193}\right)$	$e\left(\frac{138}{193}\right)$	$e\left(\frac{122}{193}\right)$	$e\left(\frac{166}{193}\right)$	$e\left(\frac{18}{193}\right)$
$\chi_{3089}(5,\cdot)$	3089.i	1544	yes	$1$	$1$	$e\left(\frac{313}{386}\right)$	$e\left(\frac{561}{1544}\right)$	$e\left(\frac{120}{193}\right)$	$e\left(\frac{517}{772}\right)$	$e\left(\frac{269}{1544}\right)$	$e\left(\frac{279}{772}\right)$	$e\left(\frac{167}{386}\right)$	$e\left(\frac{561}{772}\right)$	$e\left(\frac{371}{772}\right)$	$e\left(\frac{203}{772}\right)$
$\chi_{3089}(6,\cdot)$	3089.j	3088	yes	$-1$	$1$	$e\left(\frac{407}{772}\right)$	$e\left(\frac{1261}{3088}\right)$	$e\left(\frac{21}{386}\right)$	$e\left(\frac{269}{1544}\right)$	$e\left(\frac{2889}{3088}\right)$	$e\left(\frac{623}{1544}\right)$	$e\left(\frac{449}{772}\right)$	$e\left(\frac{1261}{1544}\right)$	$e\left(\frac{1083}{1544}\right)$	$e\left(\frac{243}{1544}\right)$
$\chi_{3089}(7,\cdot)$	3089.i	1544	yes	$1$	$1$	$e\left(\frac{39}{386}\right)$	$e\left(\frac{467}{1544}\right)$	$e\left(\frac{39}{193}\right)$	$e\left(\frac{279}{772}\right)$	$e\left(\frac{623}{1544}\right)$	$e\left(\frac{385}{772}\right)$	$e\left(\frac{117}{386}\right)$	$e\left(\frac{467}{772}\right)$	$e\left(\frac{357}{772}\right)$	$e\left(\frac{341}{772}\right)$
$\chi_{3089}(8,\cdot)$	3089.h	772	yes	$1$	$1$	$e\left(\frac{69}{193}\right)$	$e\left(\frac{173}{772}\right)$	$e\left(\frac{138}{193}\right)$	$e\left(\frac{167}{386}\right)$	$e\left(\frac{449}{772}\right)$	$e\left(\frac{117}{386}\right)$	$e\left(\frac{14}{193}\right)$	$e\left(\frac{173}{386}\right)$	$e\left(\frac{305}{386}\right)$	$e\left(\frac{247}{386}\right)$
$\chi_{3089}(9,\cdot)$	3089.i	1544	yes	$1$	$1$	$e\left(\frac{315}{386}\right)$	$e\left(\frac{1}{1544}\right)$	$e\left(\frac{122}{193}\right)$	$e\left(\frac{561}{772}\right)$	$e\left(\frac{1261}{1544}\right)$	$e\left(\frac{467}{772}\right)$	$e\left(\frac{173}{386}\right)$	$e\left(\frac{1}{772}\right)$	$e\left(\frac{419}{772}\right)$	$e\left(\frac{171}{772}\right)$
$\chi_{3089}(10,\cdot)$	3089.i	1544	yes	$1$	$1$	$e\left(\frac{359}{386}\right)$	$e\left(\frac{1191}{1544}\right)$	$e\left(\frac{166}{193}\right)$	$e\left(\frac{371}{772}\right)$	$e\left(\frac{1083}{1544}\right)$	$e\left(\frac{357}{772}\right)$	$e\left(\frac{305}{386}\right)$	$e\left(\frac{419}{772}\right)$	$e\left(\frac{317}{772}\right)$	$e\left(\frac{625}{772}\right)$
$\chi_{3089}(11,\cdot)$	3089.i	1544	yes	$1$	$1$	$e\left(\frac{211}{386}\right)$	$e\left(\frac{943}{1544}\right)$	$e\left(\frac{18}{193}\right)$	$e\left(\frac{203}{772}\right)$	$e\left(\frac{243}{1544}\right)$	$e\left(\frac{341}{772}\right)$	$e\left(\frac{247}{386}\right)$	$e\left(\frac{171}{772}\right)$	$e\left(\frac{625}{772}\right)$	$e\left(\frac{677}{772}\right)$
$\chi_{3089}(12,\cdot)$	3089.j	3088	yes	$-1$	$1$	$e\left(\frac{499}{772}\right)$	$e\left(\frac{2521}{3088}\right)$	$e\left(\frac{113}{386}\right)$	$e\left(\frac{1521}{1544}\right)$	$e\left(\frac{1429}{3088}\right)$	$e\left(\frac{779}{1544}\right)$	$e\left(\frac{725}{772}\right)$	$e\left(\frac{977}{1544}\right)$	$e\left(\frac{975}{1544}\right)$	$e\left(\frac{1087}{1544}\right)$
$\chi_{3089}(13,\cdot)$	3089.j	3088	yes	$-1$	$1$	$e\left(\frac{765}{772}\right)$	$e\left(\frac{223}{3088}\right)$	$e\left(\frac{379}{386}\right)$	$e\left(\frac{39}{1544}\right)$	$e\left(\frac{195}{3088}\right)$	$e\left(\frac{693}{1544}\right)$	$e\left(\frac{751}{772}\right)$	$e\left(\frac{223}{1544}\right)$	$e\left(\frac{25}{1544}\right)$	$e\left(\frac{305}{1544}\right)$
$\chi_{3089}(14,\cdot)$	3089.i	1544	yes	$1$	$1$	$e\left(\frac{85}{386}\right)$	$e\left(\frac{1097}{1544}\right)$	$e\left(\frac{85}{193}\right)$	$e\left(\frac{133}{772}\right)$	$e\left(\frac{1437}{1544}\right)$	$e\left(\frac{463}{772}\right)$	$e\left(\frac{255}{386}\right)$	$e\left(\frac{325}{772}\right)$	$e\left(\frac{303}{772}\right)$	$e\left(\frac{763}{772}\right)$
$\chi_{3089}(15,\cdot)$	3089.j	3088	yes	$-1$	$1$	$e\left(\frac{169}{772}\right)$	$e\left(\frac{1123}{3088}\right)$	$e\left(\frac{169}{386}\right)$	$e\left(\frac{51}{1544}\right)$	$e\left(\frac{1799}{3088}\right)$	$e\left(\frac{1025}{1544}\right)$	$e\left(\frac{507}{772}\right)$	$e\left(\frac{1123}{1544}\right)$	$e\left(\frac{389}{1544}\right)$	$e\left(\frac{1349}{1544}\right)$
$\chi_{3089}(16,\cdot)$	3089.f	193	yes	$1$	$1$	$e\left(\frac{92}{193}\right)$	$e\left(\frac{122}{193}\right)$	$e\left(\frac{184}{193}\right)$	$e\left(\frac{47}{193}\right)$	$e\left(\frac{21}{193}\right)$	$e\left(\frac{78}{193}\right)$	$e\left(\frac{83}{193}\right)$	$e\left(\frac{51}{193}\right)$	$e\left(\frac{139}{193}\right)$	$e\left(\frac{36}{193}\right)$
$\chi_{3089}(17,\cdot)$	3089.j	3088	yes	$-1$	$1$	$e\left(\frac{463}{772}\right)$	$e\left(\frac{1793}{3088}\right)$	$e\left(\frac{77}{386}\right)$	$e\left(\frac{729}{1544}\right)$	$e\left(\frac{557}{3088}\right)$	$e\left(\frac{483}{1544}\right)$	$e\left(\frac{617}{772}\right)$	$e\left(\frac{249}{1544}\right)$	$e\left(\frac{111}{1544}\right)$	$e\left(\frac{119}{1544}\right)$
$\chi_{3089}(18,\cdot)$	3089.i	1544	yes	$1$	$1$	$e\left(\frac{361}{386}\right)$	$e\left(\frac{631}{1544}\right)$	$e\left(\frac{168}{193}\right)$	$e\left(\frac{415}{772}\right)$	$e\left(\frac{531}{1544}\right)$	$e\left(\frac{545}{772}\right)$	$e\left(\frac{311}{386}\right)$	$e\left(\frac{631}{772}\right)$	$e\left(\frac{365}{772}\right)$	$e\left(\frac{593}{772}\right)$
$\chi_{3089}(19,\cdot)$	3089.i	1544	yes	$1$	$1$	$e\left(\frac{307}{386}\right)$	$e\left(\frac{1083}{1544}\right)$	$e\left(\frac{114}{193}\right)$	$e\left(\frac{771}{772}\right)$	$e\left(\frac{767}{1544}\right)$	$e\left(\frac{101}{772}\right)$	$e\left(\frac{149}{386}\right)$	$e\left(\frac{311}{772}\right)$	$e\left(\frac{613}{772}\right)$	$e\left(\frac{685}{772}\right)$
$\chi_{3089}(20,\cdot)$	3089.i	1544	yes	$1$	$1$	$e\left(\frac{19}{386}\right)$	$e\left(\frac{277}{1544}\right)$	$e\left(\frac{19}{193}\right)$	$e\left(\frac{225}{772}\right)$	$e\left(\frac{353}{1544}\right)$	$e\left(\frac{435}{772}\right)$	$e\left(\frac{57}{386}\right)$	$e\left(\frac{277}{772}\right)$	$e\left(\frac{263}{772}\right)$	$e\left(\frac{275}{772}\right)$
$\chi_{3089}(21,\cdot)$	3089.j	3088	yes	$-1$	$1$	$e\left(\frac{393}{772}\right)$	$e\left(\frac{935}{3088}\right)$	$e\left(\frac{7}{386}\right)$	$e\left(\frac{1119}{1544}\right)$	$e\left(\frac{2507}{3088}\right)$	$e\left(\frac{1237}{1544}\right)$	$e\left(\frac{407}{772}\right)$	$e\left(\frac{935}{1544}\right)$	$e\left(\frac{361}{1544}\right)$	$e\left(\frac{81}{1544}\right)$
$\chi_{3089}(22,\cdot)$	3089.i	1544	yes	$1$	$1$	$e\left(\frac{257}{386}\right)$	$e\left(\frac{29}{1544}\right)$	$e\left(\frac{64}{193}\right)$	$e\left(\frac{57}{772}\right)$	$e\left(\frac{1057}{1544}\right)$	$e\left(\frac{419}{772}\right)$	$e\left(\frac{385}{386}\right)$	$e\left(\frac{29}{772}\right)$	$e\left(\frac{571}{772}\right)$	$e\left(\frac{327}{772}\right)$
$\chi_{3089}(23,\cdot)$	3089.j	3088	yes	$-1$	$1$	$e\left(\frac{341}{772}\right)$	$e\left(\frac{827}{3088}\right)$	$e\left(\frac{341}{386}\right)$	$e\left(\frac{747}{1544}\right)$	$e\left(\frac{2191}{3088}\right)$	$e\left(\frac{209}{1544}\right)$	$e\left(\frac{251}{772}\right)$	$e\left(\frac{827}{1544}\right)$	$e\left(\frac{1429}{1544}\right)$	$e\left(\frac{141}{1544}\right)$
$\chi_{3089}(24,\cdot)$	3089.j	3088	yes	$-1$	$1$	$e\left(\frac{591}{772}\right)$	$e\left(\frac{693}{3088}\right)$	$e\left(\frac{205}{386}\right)$	$e\left(\frac{1229}{1544}\right)$	$e\left(\frac{3057}{3088}\right)$	$e\left(\frac{935}{1544}\right)$	$e\left(\frac{229}{772}\right)$	$e\left(\frac{693}{1544}\right)$	$e\left(\frac{867}{1544}\right)$	$e\left(\frac{387}{1544}\right)$
$\chi_{3089}(25,\cdot)$	3089.h	772	yes	$1$	$1$	$e\left(\frac{120}{193}\right)$	$e\left(\frac{561}{772}\right)$	$e\left(\frac{47}{193}\right)$	$e\left(\frac{131}{386}\right)$	$e\left(\frac{269}{772}\right)$	$e\left(\frac{279}{386}\right)$	$e\left(\frac{167}{193}\right)$	$e\left(\frac{175}{386}\right)$	$e\left(\frac{371}{386}\right)$	$e\left(\frac{203}{386}\right)$
$\chi_{3089}(26,\cdot)$	3089.j	3088	yes	$-1$	$1$	$e\left(\frac{85}{772}\right)$	$e\left(\frac{1483}{3088}\right)$	$e\left(\frac{85}{386}\right)$	$e\left(\frac{1291}{1544}\right)$	$e\left(\frac{1823}{3088}\right)$	$e\left(\frac{849}{1544}\right)$	$e\left(\frac{255}{772}\right)$	$e\left(\frac{1483}{1544}\right)$	$e\left(\frac{1461}{1544}\right)$	$e\left(\frac{1149}{1544}\right)$
$\chi_{3089}(27,\cdot)$	3089.j	3088	yes	$-1$	$1$	$e\left(\frac{173}{772}\right)$	$e\left(\frac{3}{3088}\right)$	$e\left(\frac{173}{386}\right)$	$e\left(\frac{139}{1544}\right)$	$e\left(\frac{695}{3088}\right)$	$e\left(\frac{1401}{1544}\right)$	$e\left(\frac{519}{772}\right)$	$e\left(\frac{3}{1544}\right)$	$e\left(\frac{485}{1544}\right)$	$e\left(\frac{1285}{1544}\right)$
$\chi_{3089}(28,\cdot)$	3089.i	1544	yes	$1$	$1$	$e\left(\frac{131}{386}\right)$	$e\left(\frac{183}{1544}\right)$	$e\left(\frac{131}{193}\right)$	$e\left(\frac{759}{772}\right)$	$e\left(\frac{707}{1544}\right)$	$e\left(\frac{541}{772}\right)$	$e\left(\frac{7}{386}\right)$	$e\left(\frac{183}{772}\right)$	$e\left(\frac{249}{772}\right)$	$e\left(\frac{413}{772}\right)$
$\chi_{3089}(29,\cdot)$	3089.j	3088	yes	$-1$	$1$	$e\left(\frac{359}{772}\right)$	$e\left(\frac{805}{3088}\right)$	$e\left(\frac{359}{386}\right)$	$e\left(\frac{757}{1544}\right)$	$e\left(\frac{2241}{3088}\right)$	$e\left(\frac{743}{1544}\right)$	$e\left(\frac{305}{772}\right)$	$e\left(\frac{805}{1544}\right)$	$e\left(\frac{1475}{1544}\right)$	$e\left(\frac{1011}{1544}\right)$
$\chi_{3089}(30,\cdot)$	3089.j	3088	yes	$-1$	$1$	$e\left(\frac{261}{772}\right)$	$e\left(\frac{2383}{3088}\right)$	$e\left(\frac{261}{386}\right)$	$e\left(\frac{1303}{1544}\right)$	$e\left(\frac{339}{3088}\right)$	$e\left(\frac{1181}{1544}\right)$	$e\left(\frac{11}{772}\right)$	$e\left(\frac{839}{1544}\right)$	$e\left(\frac{281}{1544}\right)$	$e\left(\frac{649}{1544}\right)$
$\chi_{3089}(31,\cdot)$	3089.i	1544	yes	$1$	$1$	$e\left(\frac{265}{386}\right)$	$e\left(\frac{105}{1544}\right)$	$e\left(\frac{72}{193}\right)$	$e\left(\frac{233}{772}\right)$	$e\left(\frac{1165}{1544}\right)$	$e\left(\frac{399}{772}\right)$	$e\left(\frac{23}{386}\right)$	$e\left(\frac{105}{772}\right)$	$e\left(\frac{763}{772}\right)$	$e\left(\frac{199}{772}\right)$
$\chi_{3089}(32,\cdot)$	3089.h	772	yes	$1$	$1$	$e\left(\frac{115}{193}\right)$	$e\left(\frac{31}{772}\right)$	$e\left(\frac{37}{193}\right)$	$e\left(\frac{21}{386}\right)$	$e\left(\frac{491}{772}\right)$	$e\left(\frac{195}{386}\right)$	$e\left(\frac{152}{193}\right)$	$e\left(\frac{31}{386}\right)$	$e\left(\frac{251}{386}\right)$	$e\left(\frac{283}{386}\right)$

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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	$3089$
Structure	\(C_{3088}\)
Order	$3088$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{3089}(1,\cdot)\)	3089.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3089}(2,\cdot)\)	3089.h	772	yes	\(1\)	\(1\)	\(e\left(\frac{23}{193}\right)\)	\(e\left(\frac{315}{772}\right)\)	\(e\left(\frac{46}{193}\right)\)	\(e\left(\frac{313}{386}\right)\)	\(e\left(\frac{407}{772}\right)\)	\(e\left(\frac{39}{386}\right)\)	\(e\left(\frac{69}{193}\right)\)	\(e\left(\frac{315}{386}\right)\)	\(e\left(\frac{359}{386}\right)\)	\(e\left(\frac{211}{386}\right)\)
\(\chi_{3089}(3,\cdot)\)	3089.j	3088	yes	\(-1\)	\(1\)	\(e\left(\frac{315}{772}\right)\)	\(e\left(\frac{1}{3088}\right)\)	\(e\left(\frac{315}{386}\right)\)	\(e\left(\frac{561}{1544}\right)\)	\(e\left(\frac{1261}{3088}\right)\)	\(e\left(\frac{467}{1544}\right)\)	\(e\left(\frac{173}{772}\right)\)	\(e\left(\frac{1}{1544}\right)\)	\(e\left(\frac{1191}{1544}\right)\)	\(e\left(\frac{943}{1544}\right)\)
\(\chi_{3089}(4,\cdot)\)	3089.g	386	yes	\(1\)	\(1\)	\(e\left(\frac{46}{193}\right)\)	\(e\left(\frac{315}{386}\right)\)	\(e\left(\frac{92}{193}\right)\)	\(e\left(\frac{120}{193}\right)\)	\(e\left(\frac{21}{386}\right)\)	\(e\left(\frac{39}{193}\right)\)	\(e\left(\frac{138}{193}\right)\)	\(e\left(\frac{122}{193}\right)\)	\(e\left(\frac{166}{193}\right)\)	\(e\left(\frac{18}{193}\right)\)
\(\chi_{3089}(5,\cdot)\)	3089.i	1544	yes	\(1\)	\(1\)	\(e\left(\frac{313}{386}\right)\)	\(e\left(\frac{561}{1544}\right)\)	\(e\left(\frac{120}{193}\right)\)	\(e\left(\frac{517}{772}\right)\)	\(e\left(\frac{269}{1544}\right)\)	\(e\left(\frac{279}{772}\right)\)	\(e\left(\frac{167}{386}\right)\)	\(e\left(\frac{561}{772}\right)\)	\(e\left(\frac{371}{772}\right)\)	\(e\left(\frac{203}{772}\right)\)
\(\chi_{3089}(6,\cdot)\)	3089.j	3088	yes	\(-1\)	\(1\)	\(e\left(\frac{407}{772}\right)\)	\(e\left(\frac{1261}{3088}\right)\)	\(e\left(\frac{21}{386}\right)\)	\(e\left(\frac{269}{1544}\right)\)	\(e\left(\frac{2889}{3088}\right)\)	\(e\left(\frac{623}{1544}\right)\)	\(e\left(\frac{449}{772}\right)\)	\(e\left(\frac{1261}{1544}\right)\)	\(e\left(\frac{1083}{1544}\right)\)	\(e\left(\frac{243}{1544}\right)\)
\(\chi_{3089}(7,\cdot)\)	3089.i	1544	yes	\(1\)	\(1\)	\(e\left(\frac{39}{386}\right)\)	\(e\left(\frac{467}{1544}\right)\)	\(e\left(\frac{39}{193}\right)\)	\(e\left(\frac{279}{772}\right)\)	\(e\left(\frac{623}{1544}\right)\)	\(e\left(\frac{385}{772}\right)\)	\(e\left(\frac{117}{386}\right)\)	\(e\left(\frac{467}{772}\right)\)	\(e\left(\frac{357}{772}\right)\)	\(e\left(\frac{341}{772}\right)\)
\(\chi_{3089}(8,\cdot)\)	3089.h	772	yes	\(1\)	\(1\)	\(e\left(\frac{69}{193}\right)\)	\(e\left(\frac{173}{772}\right)\)	\(e\left(\frac{138}{193}\right)\)	\(e\left(\frac{167}{386}\right)\)	\(e\left(\frac{449}{772}\right)\)	\(e\left(\frac{117}{386}\right)\)	\(e\left(\frac{14}{193}\right)\)	\(e\left(\frac{173}{386}\right)\)	\(e\left(\frac{305}{386}\right)\)	\(e\left(\frac{247}{386}\right)\)
\(\chi_{3089}(9,\cdot)\)	3089.i	1544	yes	\(1\)	\(1\)	\(e\left(\frac{315}{386}\right)\)	\(e\left(\frac{1}{1544}\right)\)	\(e\left(\frac{122}{193}\right)\)	\(e\left(\frac{561}{772}\right)\)	\(e\left(\frac{1261}{1544}\right)\)	\(e\left(\frac{467}{772}\right)\)	\(e\left(\frac{173}{386}\right)\)	\(e\left(\frac{1}{772}\right)\)	\(e\left(\frac{419}{772}\right)\)	\(e\left(\frac{171}{772}\right)\)
\(\chi_{3089}(10,\cdot)\)	3089.i	1544	yes	\(1\)	\(1\)	\(e\left(\frac{359}{386}\right)\)	\(e\left(\frac{1191}{1544}\right)\)	\(e\left(\frac{166}{193}\right)\)	\(e\left(\frac{371}{772}\right)\)	\(e\left(\frac{1083}{1544}\right)\)	\(e\left(\frac{357}{772}\right)\)	\(e\left(\frac{305}{386}\right)\)	\(e\left(\frac{419}{772}\right)\)	\(e\left(\frac{317}{772}\right)\)	\(e\left(\frac{625}{772}\right)\)
\(\chi_{3089}(11,\cdot)\)	3089.i	1544	yes	\(1\)	\(1\)	\(e\left(\frac{211}{386}\right)\)	\(e\left(\frac{943}{1544}\right)\)	\(e\left(\frac{18}{193}\right)\)	\(e\left(\frac{203}{772}\right)\)	\(e\left(\frac{243}{1544}\right)\)	\(e\left(\frac{341}{772}\right)\)	\(e\left(\frac{247}{386}\right)\)	\(e\left(\frac{171}{772}\right)\)	\(e\left(\frac{625}{772}\right)\)	\(e\left(\frac{677}{772}\right)\)
\(\chi_{3089}(12,\cdot)\)	3089.j	3088	yes	\(-1\)	\(1\)	\(e\left(\frac{499}{772}\right)\)	\(e\left(\frac{2521}{3088}\right)\)	\(e\left(\frac{113}{386}\right)\)	\(e\left(\frac{1521}{1544}\right)\)	\(e\left(\frac{1429}{3088}\right)\)	\(e\left(\frac{779}{1544}\right)\)	\(e\left(\frac{725}{772}\right)\)	\(e\left(\frac{977}{1544}\right)\)	\(e\left(\frac{975}{1544}\right)\)	\(e\left(\frac{1087}{1544}\right)\)
\(\chi_{3089}(13,\cdot)\)	3089.j	3088	yes	\(-1\)	\(1\)	\(e\left(\frac{765}{772}\right)\)	\(e\left(\frac{223}{3088}\right)\)	\(e\left(\frac{379}{386}\right)\)	\(e\left(\frac{39}{1544}\right)\)	\(e\left(\frac{195}{3088}\right)\)	\(e\left(\frac{693}{1544}\right)\)	\(e\left(\frac{751}{772}\right)\)	\(e\left(\frac{223}{1544}\right)\)	\(e\left(\frac{25}{1544}\right)\)	\(e\left(\frac{305}{1544}\right)\)
\(\chi_{3089}(14,\cdot)\)	3089.i	1544	yes	\(1\)	\(1\)	\(e\left(\frac{85}{386}\right)\)	\(e\left(\frac{1097}{1544}\right)\)	\(e\left(\frac{85}{193}\right)\)	\(e\left(\frac{133}{772}\right)\)	\(e\left(\frac{1437}{1544}\right)\)	\(e\left(\frac{463}{772}\right)\)	\(e\left(\frac{255}{386}\right)\)	\(e\left(\frac{325}{772}\right)\)	\(e\left(\frac{303}{772}\right)\)	\(e\left(\frac{763}{772}\right)\)
\(\chi_{3089}(15,\cdot)\)	3089.j	3088	yes	\(-1\)	\(1\)	\(e\left(\frac{169}{772}\right)\)	\(e\left(\frac{1123}{3088}\right)\)	\(e\left(\frac{169}{386}\right)\)	\(e\left(\frac{51}{1544}\right)\)	\(e\left(\frac{1799}{3088}\right)\)	\(e\left(\frac{1025}{1544}\right)\)	\(e\left(\frac{507}{772}\right)\)	\(e\left(\frac{1123}{1544}\right)\)	\(e\left(\frac{389}{1544}\right)\)	\(e\left(\frac{1349}{1544}\right)\)
\(\chi_{3089}(16,\cdot)\)	3089.f	193	yes	\(1\)	\(1\)	\(e\left(\frac{92}{193}\right)\)	\(e\left(\frac{122}{193}\right)\)	\(e\left(\frac{184}{193}\right)\)	\(e\left(\frac{47}{193}\right)\)	\(e\left(\frac{21}{193}\right)\)	\(e\left(\frac{78}{193}\right)\)	\(e\left(\frac{83}{193}\right)\)	\(e\left(\frac{51}{193}\right)\)	\(e\left(\frac{139}{193}\right)\)	\(e\left(\frac{36}{193}\right)\)
\(\chi_{3089}(17,\cdot)\)	3089.j	3088	yes	\(-1\)	\(1\)	\(e\left(\frac{463}{772}\right)\)	\(e\left(\frac{1793}{3088}\right)\)	\(e\left(\frac{77}{386}\right)\)	\(e\left(\frac{729}{1544}\right)\)	\(e\left(\frac{557}{3088}\right)\)	\(e\left(\frac{483}{1544}\right)\)	\(e\left(\frac{617}{772}\right)\)	\(e\left(\frac{249}{1544}\right)\)	\(e\left(\frac{111}{1544}\right)\)	\(e\left(\frac{119}{1544}\right)\)
\(\chi_{3089}(18,\cdot)\)	3089.i	1544	yes	\(1\)	\(1\)	\(e\left(\frac{361}{386}\right)\)	\(e\left(\frac{631}{1544}\right)\)	\(e\left(\frac{168}{193}\right)\)	\(e\left(\frac{415}{772}\right)\)	\(e\left(\frac{531}{1544}\right)\)	\(e\left(\frac{545}{772}\right)\)	\(e\left(\frac{311}{386}\right)\)	\(e\left(\frac{631}{772}\right)\)	\(e\left(\frac{365}{772}\right)\)	\(e\left(\frac{593}{772}\right)\)
\(\chi_{3089}(19,\cdot)\)	3089.i	1544	yes	\(1\)	\(1\)	\(e\left(\frac{307}{386}\right)\)	\(e\left(\frac{1083}{1544}\right)\)	\(e\left(\frac{114}{193}\right)\)	\(e\left(\frac{771}{772}\right)\)	\(e\left(\frac{767}{1544}\right)\)	\(e\left(\frac{101}{772}\right)\)	\(e\left(\frac{149}{386}\right)\)	\(e\left(\frac{311}{772}\right)\)	\(e\left(\frac{613}{772}\right)\)	\(e\left(\frac{685}{772}\right)\)
\(\chi_{3089}(20,\cdot)\)	3089.i	1544	yes	\(1\)	\(1\)	\(e\left(\frac{19}{386}\right)\)	\(e\left(\frac{277}{1544}\right)\)	\(e\left(\frac{19}{193}\right)\)	\(e\left(\frac{225}{772}\right)\)	\(e\left(\frac{353}{1544}\right)\)	\(e\left(\frac{435}{772}\right)\)	\(e\left(\frac{57}{386}\right)\)	\(e\left(\frac{277}{772}\right)\)	\(e\left(\frac{263}{772}\right)\)	\(e\left(\frac{275}{772}\right)\)
\(\chi_{3089}(21,\cdot)\)	3089.j	3088	yes	\(-1\)	\(1\)	\(e\left(\frac{393}{772}\right)\)	\(e\left(\frac{935}{3088}\right)\)	\(e\left(\frac{7}{386}\right)\)	\(e\left(\frac{1119}{1544}\right)\)	\(e\left(\frac{2507}{3088}\right)\)	\(e\left(\frac{1237}{1544}\right)\)	\(e\left(\frac{407}{772}\right)\)	\(e\left(\frac{935}{1544}\right)\)	\(e\left(\frac{361}{1544}\right)\)	\(e\left(\frac{81}{1544}\right)\)
\(\chi_{3089}(22,\cdot)\)	3089.i	1544	yes	\(1\)	\(1\)	\(e\left(\frac{257}{386}\right)\)	\(e\left(\frac{29}{1544}\right)\)	\(e\left(\frac{64}{193}\right)\)	\(e\left(\frac{57}{772}\right)\)	\(e\left(\frac{1057}{1544}\right)\)	\(e\left(\frac{419}{772}\right)\)	\(e\left(\frac{385}{386}\right)\)	\(e\left(\frac{29}{772}\right)\)	\(e\left(\frac{571}{772}\right)\)	\(e\left(\frac{327}{772}\right)\)
\(\chi_{3089}(23,\cdot)\)	3089.j	3088	yes	\(-1\)	\(1\)	\(e\left(\frac{341}{772}\right)\)	\(e\left(\frac{827}{3088}\right)\)	\(e\left(\frac{341}{386}\right)\)	\(e\left(\frac{747}{1544}\right)\)	\(e\left(\frac{2191}{3088}\right)\)	\(e\left(\frac{209}{1544}\right)\)	\(e\left(\frac{251}{772}\right)\)	\(e\left(\frac{827}{1544}\right)\)	\(e\left(\frac{1429}{1544}\right)\)	\(e\left(\frac{141}{1544}\right)\)
\(\chi_{3089}(24,\cdot)\)	3089.j	3088	yes	\(-1\)	\(1\)	\(e\left(\frac{591}{772}\right)\)	\(e\left(\frac{693}{3088}\right)\)	\(e\left(\frac{205}{386}\right)\)	\(e\left(\frac{1229}{1544}\right)\)	\(e\left(\frac{3057}{3088}\right)\)	\(e\left(\frac{935}{1544}\right)\)	\(e\left(\frac{229}{772}\right)\)	\(e\left(\frac{693}{1544}\right)\)	\(e\left(\frac{867}{1544}\right)\)	\(e\left(\frac{387}{1544}\right)\)
\(\chi_{3089}(25,\cdot)\)	3089.h	772	yes	\(1\)	\(1\)	\(e\left(\frac{120}{193}\right)\)	\(e\left(\frac{561}{772}\right)\)	\(e\left(\frac{47}{193}\right)\)	\(e\left(\frac{131}{386}\right)\)	\(e\left(\frac{269}{772}\right)\)	\(e\left(\frac{279}{386}\right)\)	\(e\left(\frac{167}{193}\right)\)	\(e\left(\frac{175}{386}\right)\)	\(e\left(\frac{371}{386}\right)\)	\(e\left(\frac{203}{386}\right)\)
\(\chi_{3089}(26,\cdot)\)	3089.j	3088	yes	\(-1\)	\(1\)	\(e\left(\frac{85}{772}\right)\)	\(e\left(\frac{1483}{3088}\right)\)	\(e\left(\frac{85}{386}\right)\)	\(e\left(\frac{1291}{1544}\right)\)	\(e\left(\frac{1823}{3088}\right)\)	\(e\left(\frac{849}{1544}\right)\)	\(e\left(\frac{255}{772}\right)\)	\(e\left(\frac{1483}{1544}\right)\)	\(e\left(\frac{1461}{1544}\right)\)	\(e\left(\frac{1149}{1544}\right)\)
\(\chi_{3089}(27,\cdot)\)	3089.j	3088	yes	\(-1\)	\(1\)	\(e\left(\frac{173}{772}\right)\)	\(e\left(\frac{3}{3088}\right)\)	\(e\left(\frac{173}{386}\right)\)	\(e\left(\frac{139}{1544}\right)\)	\(e\left(\frac{695}{3088}\right)\)	\(e\left(\frac{1401}{1544}\right)\)	\(e\left(\frac{519}{772}\right)\)	\(e\left(\frac{3}{1544}\right)\)	\(e\left(\frac{485}{1544}\right)\)	\(e\left(\frac{1285}{1544}\right)\)
\(\chi_{3089}(28,\cdot)\)	3089.i	1544	yes	\(1\)	\(1\)	\(e\left(\frac{131}{386}\right)\)	\(e\left(\frac{183}{1544}\right)\)	\(e\left(\frac{131}{193}\right)\)	\(e\left(\frac{759}{772}\right)\)	\(e\left(\frac{707}{1544}\right)\)	\(e\left(\frac{541}{772}\right)\)	\(e\left(\frac{7}{386}\right)\)	\(e\left(\frac{183}{772}\right)\)	\(e\left(\frac{249}{772}\right)\)	\(e\left(\frac{413}{772}\right)\)
\(\chi_{3089}(29,\cdot)\)	3089.j	3088	yes	\(-1\)	\(1\)	\(e\left(\frac{359}{772}\right)\)	\(e\left(\frac{805}{3088}\right)\)	\(e\left(\frac{359}{386}\right)\)	\(e\left(\frac{757}{1544}\right)\)	\(e\left(\frac{2241}{3088}\right)\)	\(e\left(\frac{743}{1544}\right)\)	\(e\left(\frac{305}{772}\right)\)	\(e\left(\frac{805}{1544}\right)\)	\(e\left(\frac{1475}{1544}\right)\)	\(e\left(\frac{1011}{1544}\right)\)
\(\chi_{3089}(30,\cdot)\)	3089.j	3088	yes	\(-1\)	\(1\)	\(e\left(\frac{261}{772}\right)\)	\(e\left(\frac{2383}{3088}\right)\)	\(e\left(\frac{261}{386}\right)\)	\(e\left(\frac{1303}{1544}\right)\)	\(e\left(\frac{339}{3088}\right)\)	\(e\left(\frac{1181}{1544}\right)\)	\(e\left(\frac{11}{772}\right)\)	\(e\left(\frac{839}{1544}\right)\)	\(e\left(\frac{281}{1544}\right)\)	\(e\left(\frac{649}{1544}\right)\)
\(\chi_{3089}(31,\cdot)\)	3089.i	1544	yes	\(1\)	\(1\)	\(e\left(\frac{265}{386}\right)\)	\(e\left(\frac{105}{1544}\right)\)	\(e\left(\frac{72}{193}\right)\)	\(e\left(\frac{233}{772}\right)\)	\(e\left(\frac{1165}{1544}\right)\)	\(e\left(\frac{399}{772}\right)\)	\(e\left(\frac{23}{386}\right)\)	\(e\left(\frac{105}{772}\right)\)	\(e\left(\frac{763}{772}\right)\)	\(e\left(\frac{199}{772}\right)\)
\(\chi_{3089}(32,\cdot)\)	3089.h	772	yes	\(1\)	\(1\)	\(e\left(\frac{115}{193}\right)\)	\(e\left(\frac{31}{772}\right)\)	\(e\left(\frac{37}{193}\right)\)	\(e\left(\frac{21}{386}\right)\)	\(e\left(\frac{491}{772}\right)\)	\(e\left(\frac{195}{386}\right)\)	\(e\left(\frac{152}{193}\right)\)	\(e\left(\frac{31}{386}\right)\)	\(e\left(\frac{251}{386}\right)\)	\(e\left(\frac{283}{386}\right)\)

Introduction

L-functions

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Character group

First 32 of 3088 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.