LMFDB - Group of Dirichlet characters of modulus 1113

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1113)

pari: g = idealstar(,1113,2)

Character group

sage: G.order() pari: g.no
Order	=	624
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{156}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1113}(743,\cdot)$, $\chi_{1113}(955,\cdot)$, $\chi_{1113}(1009,\cdot)$

First 32 of 624 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{1113}(1,\cdot)$	1113.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1113}(2,\cdot)$	1113.bv	156	yes	$1$	$1$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{59}{156}\right)$
$\chi_{1113}(4,\cdot)$	1113.bm	78	no	$1$	$1$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{59}{78}\right)$
$\chi_{1113}(5,\cdot)$	1113.bt	156	yes	$-1$	$1$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{95}{156}\right)$
$\chi_{1113}(8,\cdot)$	1113.bh	52	no	$1$	$1$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{7}{52}\right)$
$\chi_{1113}(10,\cdot)$	1113.bq	78	no	$-1$	$1$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{77}{78}\right)$
$\chi_{1113}(11,\cdot)$	1113.br	78	yes	$-1$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{47}{78}\right)$
$\chi_{1113}(13,\cdot)$	1113.ba	26	no	$-1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{1113}(16,\cdot)$	1113.bg	39	no	$1$	$1$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{20}{39}\right)$
$\chi_{1113}(17,\cdot)$	1113.bp	78	yes	$1$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{37}{39}\right)$
$\chi_{1113}(19,\cdot)$	1113.bs	156	no	$1$	$1$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{77}{156}\right)$
$\chi_{1113}(20,\cdot)$	1113.bj	52	yes	$-1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{19}{52}\right)$
$\chi_{1113}(22,\cdot)$	1113.bi	52	no	$-1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{51}{52}\right)$
$\chi_{1113}(23,\cdot)$	1113.u	12	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{1113}(25,\cdot)$	1113.bm	78	no	$1$	$1$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{17}{78}\right)$
$\chi_{1113}(26,\cdot)$	1113.bt	156	yes	$-1$	$1$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{149}{156}\right)$
$\chi_{1113}(29,\cdot)$	1113.z	26	no	$-1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{1113}(31,\cdot)$	1113.bs	156	no	$1$	$1$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{49}{156}\right)$
$\chi_{1113}(32,\cdot)$	1113.bv	156	yes	$1$	$1$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{139}{156}\right)$
$\chi_{1113}(34,\cdot)$	1113.bk	52	no	$1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{17}{52}\right)$
$\chi_{1113}(37,\cdot)$	1113.bm	78	no	$1$	$1$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{1}{78}\right)$
$\chi_{1113}(38,\cdot)$	1113.bp	78	yes	$1$	$1$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{34}{39}\right)$
$\chi_{1113}(40,\cdot)$	1113.bo	78	no	$-1$	$1$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{29}{39}\right)$
$\chi_{1113}(41,\cdot)$	1113.bj	52	yes	$-1$	$1$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{27}{52}\right)$
$\chi_{1113}(43,\cdot)$	1113.be	26	no	$1$	$1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{1113}(44,\cdot)$	1113.bl	78	yes	$-1$	$1$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{14}{39}\right)$
$\chi_{1113}(46,\cdot)$	1113.bg	39	no	$1$	$1$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{31}{39}\right)$
$\chi_{1113}(47,\cdot)$	1113.bn	78	yes	$1$	$1$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{37}{78}\right)$
$\chi_{1113}(50,\cdot)$	1113.bh	52	no	$1$	$1$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{31}{52}\right)$
$\chi_{1113}(52,\cdot)$	1113.q	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1113}(55,\cdot)$	1113.bk	52	no	$1$	$1$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{11}{52}\right)$
$\chi_{1113}(58,\cdot)$	1113.bu	156	no	$-1$	$1$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{17}{156}\right)$

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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	$1113$
Structure	\(C_{2}\times C_{2}\times C_{156}\)
Order	$624$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{1113}(1,\cdot)\)	1113.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1113}(2,\cdot)\)	1113.bv	156	yes	\(1\)	\(1\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{59}{156}\right)\)
\(\chi_{1113}(4,\cdot)\)	1113.bm	78	no	\(1\)	\(1\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{59}{78}\right)\)
\(\chi_{1113}(5,\cdot)\)	1113.bt	156	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{95}{156}\right)\)
\(\chi_{1113}(8,\cdot)\)	1113.bh	52	no	\(1\)	\(1\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{7}{52}\right)\)
\(\chi_{1113}(10,\cdot)\)	1113.bq	78	no	\(-1\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)
\(\chi_{1113}(11,\cdot)\)	1113.br	78	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)
\(\chi_{1113}(13,\cdot)\)	1113.ba	26	no	\(-1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{1113}(16,\cdot)\)	1113.bg	39	no	\(1\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)
\(\chi_{1113}(17,\cdot)\)	1113.bp	78	yes	\(1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)
\(\chi_{1113}(19,\cdot)\)	1113.bs	156	no	\(1\)	\(1\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{77}{156}\right)\)
\(\chi_{1113}(20,\cdot)\)	1113.bj	52	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{19}{52}\right)\)
\(\chi_{1113}(22,\cdot)\)	1113.bi	52	no	\(-1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{51}{52}\right)\)
\(\chi_{1113}(23,\cdot)\)	1113.u	12	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1113}(25,\cdot)\)	1113.bm	78	no	\(1\)	\(1\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{17}{78}\right)\)
\(\chi_{1113}(26,\cdot)\)	1113.bt	156	yes	\(-1\)	\(1\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{149}{156}\right)\)
\(\chi_{1113}(29,\cdot)\)	1113.z	26	no	\(-1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{1113}(31,\cdot)\)	1113.bs	156	no	\(1\)	\(1\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{49}{156}\right)\)
\(\chi_{1113}(32,\cdot)\)	1113.bv	156	yes	\(1\)	\(1\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{139}{156}\right)\)
\(\chi_{1113}(34,\cdot)\)	1113.bk	52	no	\(1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{17}{52}\right)\)
\(\chi_{1113}(37,\cdot)\)	1113.bm	78	no	\(1\)	\(1\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{1}{78}\right)\)
\(\chi_{1113}(38,\cdot)\)	1113.bp	78	yes	\(1\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)
\(\chi_{1113}(40,\cdot)\)	1113.bo	78	no	\(-1\)	\(1\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{29}{39}\right)\)
\(\chi_{1113}(41,\cdot)\)	1113.bj	52	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{27}{52}\right)\)
\(\chi_{1113}(43,\cdot)\)	1113.be	26	no	\(1\)	\(1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{1113}(44,\cdot)\)	1113.bl	78	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{14}{39}\right)\)
\(\chi_{1113}(46,\cdot)\)	1113.bg	39	no	\(1\)	\(1\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)
\(\chi_{1113}(47,\cdot)\)	1113.bn	78	yes	\(1\)	\(1\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{37}{78}\right)\)
\(\chi_{1113}(50,\cdot)\)	1113.bh	52	no	\(1\)	\(1\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{31}{52}\right)\)
\(\chi_{1113}(52,\cdot)\)	1113.q	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1113}(55,\cdot)\)	1113.bk	52	no	\(1\)	\(1\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{11}{52}\right)\)
\(\chi_{1113}(58,\cdot)\)	1113.bu	156	no	\(-1\)	\(1\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{17}{156}\right)\)

Introduction

L-functions

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Character group

First 32 of 624 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.