LMFDB - Group of Dirichlet characters of modulus 4312

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4312)

pari: g = idealstar(,4312,2)

Character group

sage: G.order() pari: g.no
Order	=	1680
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{210}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4312}(1079,\cdot)$, $\chi_{4312}(2157,\cdot)$, $\chi_{4312}(3433,\cdot)$, $\chi_{4312}(3137,\cdot)$

First 32 of 1680 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	$-1$	$1$	$3$	$5$	$9$	$13$	$15$	$17$	$19$	$23$	$25$	$27$
$\chi_{4312}(1,\cdot)$	4312.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4312}(3,\cdot)$	4312.et	210	yes	$1$	$1$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{19}{70}\right)$
$\chi_{4312}(5,\cdot)$	4312.el	210	yes	$-1$	$1$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{6}{35}\right)$
$\chi_{4312}(9,\cdot)$	4312.ei	105	no	$1$	$1$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{19}{35}\right)$
$\chi_{4312}(13,\cdot)$	4312.eg	70	yes	$1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{9}{35}\right)$
$\chi_{4312}(15,\cdot)$	4312.ea	70	no	$-1$	$1$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{31}{70}\right)$
$\chi_{4312}(17,\cdot)$	4312.ew	210	no	$1$	$1$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{27}{70}\right)$
$\chi_{4312}(19,\cdot)$	4312.cv	30	no	$-1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{4312}(23,\cdot)$	4312.dj	42	no	$-1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{4312}(25,\cdot)$	4312.ei	105	no	$1$	$1$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{12}{35}\right)$
$\chi_{4312}(27,\cdot)$	4312.dz	70	yes	$1$	$1$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{57}{70}\right)$
$\chi_{4312}(29,\cdot)$	4312.dv	70	yes	$-1$	$1$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{41}{70}\right)$
$\chi_{4312}(31,\cdot)$	4312.cy	30	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{4312}(37,\cdot)$	4312.eu	210	yes	$1$	$1$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{41}{70}\right)$
$\chi_{4312}(39,\cdot)$	4312.er	210	no	$1$	$1$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{37}{70}\right)$
$\chi_{4312}(41,\cdot)$	4312.dw	70	no	$1$	$1$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{19}{70}\right)$
$\chi_{4312}(43,\cdot)$	4312.cb	14	yes	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{14}\right)$	$-1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{4312}(45,\cdot)$	4312.dq	42	no	$-1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{4312}(47,\cdot)$	4312.en	210	no	$1$	$1$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{137}{210}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{4312}(51,\cdot)$	4312.ep	210	yes	$1$	$1$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{4312}(53,\cdot)$	4312.eu	210	yes	$1$	$1$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{43}{70}\right)$
$\chi_{4312}(57,\cdot)$	4312.ef	70	no	$-1$	$1$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{34}{35}\right)$
$\chi_{4312}(59,\cdot)$	4312.et	210	yes	$1$	$1$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{51}{70}\right)$
$\chi_{4312}(61,\cdot)$	4312.ej	210	yes	$1$	$1$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{31}{35}\right)$
$\chi_{4312}(65,\cdot)$	4312.dr	42	no	$-1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{4312}(67,\cdot)$	4312.v	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{4312}(69,\cdot)$	4312.eh	70	yes	$-1$	$1$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{4312}(71,\cdot)$	4312.ea	70	no	$-1$	$1$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{57}{70}\right)$
$\chi_{4312}(73,\cdot)$	4312.ew	210	no	$1$	$1$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{31}{70}\right)$
$\chi_{4312}(75,\cdot)$	4312.et	210	yes	$1$	$1$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{43}{70}\right)$
$\chi_{4312}(79,\cdot)$	4312.cu	30	no	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{4312}(81,\cdot)$	4312.ei	105	no	$1$	$1$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{3}{35}\right)$

Click here to search among the remaining 1648 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	$4312$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{210}\)
Order	$1680$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{4312}(1,\cdot)\)	4312.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4312}(3,\cdot)\)	4312.et	210	yes	\(1\)	\(1\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{19}{70}\right)\)
\(\chi_{4312}(5,\cdot)\)	4312.el	210	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{6}{35}\right)\)
\(\chi_{4312}(9,\cdot)\)	4312.ei	105	no	\(1\)	\(1\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{19}{35}\right)\)
\(\chi_{4312}(13,\cdot)\)	4312.eg	70	yes	\(1\)	\(1\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)
\(\chi_{4312}(15,\cdot)\)	4312.ea	70	no	\(-1\)	\(1\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)
\(\chi_{4312}(17,\cdot)\)	4312.ew	210	no	\(1\)	\(1\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{27}{70}\right)\)
\(\chi_{4312}(19,\cdot)\)	4312.cv	30	no	\(-1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{4312}(23,\cdot)\)	4312.dj	42	no	\(-1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{4312}(25,\cdot)\)	4312.ei	105	no	\(1\)	\(1\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)
\(\chi_{4312}(27,\cdot)\)	4312.dz	70	yes	\(1\)	\(1\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)
\(\chi_{4312}(29,\cdot)\)	4312.dv	70	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)
\(\chi_{4312}(31,\cdot)\)	4312.cy	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{4312}(37,\cdot)\)	4312.eu	210	yes	\(1\)	\(1\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{41}{70}\right)\)
\(\chi_{4312}(39,\cdot)\)	4312.er	210	no	\(1\)	\(1\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{37}{70}\right)\)
\(\chi_{4312}(41,\cdot)\)	4312.dw	70	no	\(1\)	\(1\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{19}{70}\right)\)
\(\chi_{4312}(43,\cdot)\)	4312.cb	14	yes	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{4312}(45,\cdot)\)	4312.dq	42	no	\(-1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{4312}(47,\cdot)\)	4312.en	210	no	\(1\)	\(1\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{4312}(51,\cdot)\)	4312.ep	210	yes	\(1\)	\(1\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{4312}(53,\cdot)\)	4312.eu	210	yes	\(1\)	\(1\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{43}{70}\right)\)
\(\chi_{4312}(57,\cdot)\)	4312.ef	70	no	\(-1\)	\(1\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)
\(\chi_{4312}(59,\cdot)\)	4312.et	210	yes	\(1\)	\(1\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)
\(\chi_{4312}(61,\cdot)\)	4312.ej	210	yes	\(1\)	\(1\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{31}{35}\right)\)
\(\chi_{4312}(65,\cdot)\)	4312.dr	42	no	\(-1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{4312}(67,\cdot)\)	4312.v	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{4312}(69,\cdot)\)	4312.eh	70	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{4312}(71,\cdot)\)	4312.ea	70	no	\(-1\)	\(1\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)
\(\chi_{4312}(73,\cdot)\)	4312.ew	210	no	\(1\)	\(1\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{31}{70}\right)\)
\(\chi_{4312}(75,\cdot)\)	4312.et	210	yes	\(1\)	\(1\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{43}{70}\right)\)
\(\chi_{4312}(79,\cdot)\)	4312.cu	30	no	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{4312}(81,\cdot)\)	4312.ei	105	no	\(1\)	\(1\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 1680 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.