LMFDB - Group of Dirichlet characters of modulus 392

Show commands: PariGP / SageMath

sage: H = DirichletGroup(392)

pari: g = idealstar(,392,2)

Character group

sage: G.order() pari: g.no
Order	=	168
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{42}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{392}(295,\cdot)$, $\chi_{392}(197,\cdot)$, $\chi_{392}(297,\cdot)$

First 32 of 168 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{392}(1,\cdot)$	392.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{392}(3,\cdot)$	392.bc	42	yes	$1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{392}(5,\cdot)$	392.bf	42	yes	$-1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{392}(9,\cdot)$	392.y	21	no	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{392}(11,\cdot)$	392.be	42	yes	$-1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{392}(13,\cdot)$	392.r	14	yes	$-1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{392}(15,\cdot)$	392.v	14	no	$-1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$-1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{392}(17,\cdot)$	392.ba	42	no	$-1$	$1$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{392}(19,\cdot)$	392.m	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{392}(23,\cdot)$	392.bb	42	no	$-1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{392}(25,\cdot)$	392.y	21	no	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{392}(27,\cdot)$	392.u	14	yes	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{14}\right)$	$-1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{392}(29,\cdot)$	392.x	14	yes	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$-1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{392}(31,\cdot)$	392.l	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{392}(33,\cdot)$	392.ba	42	no	$-1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{392}(37,\cdot)$	392.z	42	yes	$1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{392}(39,\cdot)$	392.bb	42	no	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{392}(41,\cdot)$	392.w	14	no	$-1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$-1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{392}(43,\cdot)$	392.s	14	yes	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{392}(45,\cdot)$	392.bf	42	yes	$-1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{392}(47,\cdot)$	392.bd	42	no	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{392}(51,\cdot)$	392.be	42	yes	$-1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{392}(53,\cdot)$	392.z	42	yes	$1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{392}(55,\cdot)$	392.t	14	no	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{14}\right)$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{392}(57,\cdot)$	392.q	7	no	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{392}(59,\cdot)$	392.bc	42	yes	$1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{392}(61,\cdot)$	392.bf	42	yes	$-1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{392}(65,\cdot)$	392.y	21	no	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{392}(67,\cdot)$	392.k	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{392}(69,\cdot)$	392.r	14	yes	$-1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{14}\right)$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{392}(71,\cdot)$	392.v	14	no	$-1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$-1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{392}(73,\cdot)$	392.ba	42	no	$-1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$

Click here to search among the remaining 136 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	$392$
Structure	\(C_{2}\times C_{2}\times C_{42}\)
Order	$168$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{392}(1,\cdot)\)	392.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{392}(3,\cdot)\)	392.bc	42	yes	\(1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{392}(5,\cdot)\)	392.bf	42	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{392}(9,\cdot)\)	392.y	21	no	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{392}(11,\cdot)\)	392.be	42	yes	\(-1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{392}(13,\cdot)\)	392.r	14	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{392}(15,\cdot)\)	392.v	14	no	\(-1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(-1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{392}(17,\cdot)\)	392.ba	42	no	\(-1\)	\(1\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{392}(19,\cdot)\)	392.m	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{392}(23,\cdot)\)	392.bb	42	no	\(-1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{392}(25,\cdot)\)	392.y	21	no	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{392}(27,\cdot)\)	392.u	14	yes	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(-1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{392}(29,\cdot)\)	392.x	14	yes	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(-1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{392}(31,\cdot)\)	392.l	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{392}(33,\cdot)\)	392.ba	42	no	\(-1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{392}(37,\cdot)\)	392.z	42	yes	\(1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{392}(39,\cdot)\)	392.bb	42	no	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{392}(41,\cdot)\)	392.w	14	no	\(-1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{392}(43,\cdot)\)	392.s	14	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{392}(45,\cdot)\)	392.bf	42	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{392}(47,\cdot)\)	392.bd	42	no	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{392}(51,\cdot)\)	392.be	42	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{392}(53,\cdot)\)	392.z	42	yes	\(1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{392}(55,\cdot)\)	392.t	14	no	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{392}(57,\cdot)\)	392.q	7	no	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{392}(59,\cdot)\)	392.bc	42	yes	\(1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{392}(61,\cdot)\)	392.bf	42	yes	\(-1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{392}(65,\cdot)\)	392.y	21	no	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{392}(67,\cdot)\)	392.k	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{392}(69,\cdot)\)	392.r	14	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{392}(71,\cdot)\)	392.v	14	no	\(-1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(-1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{392}(73,\cdot)\)	392.ba	42	no	\(-1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 168 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.