LMFDB - Group of Dirichlet characters of modulus 845

sage:H = DirichletGroup(845)

pari:g = idealstar(,845,2)

Character group

sage:G.order() pari:g.no
Order	=	624
sage:H.invariants() pari:g.cyc
Structure	=	$C_{4}\times C_{156}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{845}(677,\cdot)$, $\chi_{845}(171,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$14$
$\chi_{845}(1,\cdot)$	845.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{845}(2,\cdot)$	845.bn	156	yes	$1$	$1$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{845}(3,\cdot)$	845.bl	156	yes	$-1$	$1$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{845}(4,\cdot)$	845.bh	78	yes	$1$	$1$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{845}(6,\cdot)$	845.bm	156	no	$-1$	$1$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{845}(7,\cdot)$	845.bi	156	yes	$1$	$1$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{845}(8,\cdot)$	845.z	52	yes	$1$	$1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{845}(9,\cdot)$	845.bf	78	yes	$1$	$1$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{845}(11,\cdot)$	845.bm	156	no	$-1$	$1$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{845}(12,\cdot)$	845.bc	52	yes	$-1$	$1$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{845}(14,\cdot)$	845.x	26	yes	$1$	$1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{845}(16,\cdot)$	845.y	39	no	$1$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{845}(17,\cdot)$	845.bk	156	yes	$-1$	$1$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{845}(18,\cdot)$	845.be	52	yes	$1$	$1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{845}(19,\cdot)$	845.s	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$1$
$\chi_{845}(21,\cdot)$	845.ba	52	no	$-1$	$1$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{845}(22,\cdot)$	845.q	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$-1$
$\chi_{845}(23,\cdot)$	845.r	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$-1$
$\chi_{845}(24,\cdot)$	845.bj	156	yes	$-1$	$1$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{845}(27,\cdot)$	845.bb	52	yes	$-1$	$1$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{845}(28,\cdot)$	845.bi	156	yes	$1$	$1$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{845}(29,\cdot)$	845.bf	78	yes	$1$	$1$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{845}(31,\cdot)$	845.ba	52	no	$-1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{845}(32,\cdot)$	845.bn	156	yes	$1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{845}(33,\cdot)$	845.bn	156	yes	$1$	$1$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{845}(34,\cdot)$	845.bd	52	yes	$-1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{845}(36,\cdot)$	845.bg	78	no	$1$	$1$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{845}(37,\cdot)$	845.bi	156	yes	$1$	$1$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{1}{26}\right)$
$\chi_{845}(38,\cdot)$	845.bc	52	yes	$-1$	$1$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{845}(41,\cdot)$	845.bm	156	no	$-1$	$1$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{845}(42,\cdot)$	845.bl	156	yes	$-1$	$1$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{845}(43,\cdot)$	845.bk	156	yes	$-1$	$1$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{25}{26}\right)$

Click here to search among the remaining 592 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 $\F_{q}$
Belyi maps

Modulus	$845$
Structure	\(C_{4}\times C_{156}\)
Order	$624$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(14\)
\(\chi_{845}(1,\cdot)\)	845.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{845}(2,\cdot)\)	845.bn	156	yes	\(1\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{845}(3,\cdot)\)	845.bl	156	yes	\(-1\)	\(1\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{845}(4,\cdot)\)	845.bh	78	yes	\(1\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{845}(6,\cdot)\)	845.bm	156	no	\(-1\)	\(1\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{845}(7,\cdot)\)	845.bi	156	yes	\(1\)	\(1\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{845}(8,\cdot)\)	845.z	52	yes	\(1\)	\(1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{845}(9,\cdot)\)	845.bf	78	yes	\(1\)	\(1\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{845}(11,\cdot)\)	845.bm	156	no	\(-1\)	\(1\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{845}(12,\cdot)\)	845.bc	52	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{845}(14,\cdot)\)	845.x	26	yes	\(1\)	\(1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{845}(16,\cdot)\)	845.y	39	no	\(1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{845}(17,\cdot)\)	845.bk	156	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{845}(18,\cdot)\)	845.be	52	yes	\(1\)	\(1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)
\(\chi_{845}(19,\cdot)\)	845.s	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(1\)
\(\chi_{845}(21,\cdot)\)	845.ba	52	no	\(-1\)	\(1\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{845}(22,\cdot)\)	845.q	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(-1\)
\(\chi_{845}(23,\cdot)\)	845.r	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(-1\)
\(\chi_{845}(24,\cdot)\)	845.bj	156	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{845}(27,\cdot)\)	845.bb	52	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)
\(\chi_{845}(28,\cdot)\)	845.bi	156	yes	\(1\)	\(1\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{845}(29,\cdot)\)	845.bf	78	yes	\(1\)	\(1\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{845}(31,\cdot)\)	845.ba	52	no	\(-1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{845}(32,\cdot)\)	845.bn	156	yes	\(1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{845}(33,\cdot)\)	845.bn	156	yes	\(1\)	\(1\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{845}(34,\cdot)\)	845.bd	52	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{845}(36,\cdot)\)	845.bg	78	no	\(1\)	\(1\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{845}(37,\cdot)\)	845.bi	156	yes	\(1\)	\(1\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)
\(\chi_{845}(38,\cdot)\)	845.bc	52	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{845}(41,\cdot)\)	845.bm	156	no	\(-1\)	\(1\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{845}(42,\cdot)\)	845.bl	156	yes	\(-1\)	\(1\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{845}(43,\cdot)\)	845.bk	156	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

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.