LMFDB - Group of Dirichlet characters of modulus 714

Show commands: PariGP / SageMath

sage: H = DirichletGroup(714)

pari: g = idealstar(,714,2)

Character group

sage: G.order() pari: g.no
Order	=	192
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{48}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{714}(239,\cdot)$, $\chi_{714}(409,\cdot)$, $\chi_{714}(547,\cdot)$

First 32 of 192 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	$-1$	$1$	$5$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{714}(1,\cdot)$	714.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{714}(5,\cdot)$	714.bn	48	no	$-1$	$1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{1}{48}\right)$	$-i$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{714}(11,\cdot)$	714.bk	48	no	$1$	$1$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{11}{48}\right)$	$-i$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{714}(13,\cdot)$	714.j	4	no	$-1$	$1$	$-i$	$-i$	$-1$	$1$	$-i$	$-1$	$i$	$-i$	$i$	$i$
$\chi_{714}(19,\cdot)$	714.bi	24	no	$-1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{24}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{714}(23,\cdot)$	714.bk	48	no	$1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{19}{48}\right)$	$-i$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{714}(25,\cdot)$	714.bh	24	no	$1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{24}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{714}(29,\cdot)$	714.bf	16	no	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{714}(31,\cdot)$	714.bl	48	no	$1$	$1$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{29}{48}\right)$	$-i$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{714}(37,\cdot)$	714.bm	48	no	$-1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{37}{48}\right)$	$i$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{714}(41,\cdot)$	714.bc	16	no	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{714}(43,\cdot)$	714.u	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$-i$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{714}(47,\cdot)$	714.y	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-i$
$\chi_{714}(53,\cdot)$	714.bg	24	no	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{714}(55,\cdot)$	714.j	4	no	$-1$	$1$	$i$	$i$	$-1$	$1$	$i$	$-1$	$-i$	$i$	$-i$	$-i$
$\chi_{714}(59,\cdot)$	714.bj	24	no	$1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{24}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{714}(61,\cdot)$	714.bl	48	no	$1$	$1$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{31}{48}\right)$	$i$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{714}(65,\cdot)$	714.bk	48	no	$1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{37}{48}\right)$	$i$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{714}(67,\cdot)$	714.t	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$
$\chi_{714}(71,\cdot)$	714.bf	16	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{16}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{714}(73,\cdot)$	714.bl	48	no	$1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{41}{48}\right)$	$-i$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{714}(79,\cdot)$	714.bm	48	no	$-1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{19}{48}\right)$	$-i$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{714}(83,\cdot)$	714.w	8	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$-i$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{714}(89,\cdot)$	714.y	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$i$
$\chi_{714}(95,\cdot)$	714.bk	48	no	$1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{23}{48}\right)$	$-i$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{714}(97,\cdot)$	714.be	16	no	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{714}(101,\cdot)$	714.q	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$
$\chi_{714}(103,\cdot)$	714.r	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$
$\chi_{714}(107,\cdot)$	714.bk	48	no	$1$	$1$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{1}{48}\right)$	$i$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{714}(109,\cdot)$	714.bm	48	no	$-1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{23}{48}\right)$	$-i$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{714}(113,\cdot)$	714.bf	16	no	$1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{714}(115,\cdot)$	714.z	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$i$

Click here to search among the remaining 160 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	$714$
Structure	\(C_{2}\times C_{2}\times C_{48}\)
Order	$192$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{714}(1,\cdot)\)	714.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{714}(5,\cdot)\)	714.bn	48	no	\(-1\)	\(1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(-i\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{714}(11,\cdot)\)	714.bk	48	no	\(1\)	\(1\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(-i\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{714}(13,\cdot)\)	714.j	4	no	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(-i\)	\(i\)	\(i\)
\(\chi_{714}(19,\cdot)\)	714.bi	24	no	\(-1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{714}(23,\cdot)\)	714.bk	48	no	\(1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(-i\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{714}(25,\cdot)\)	714.bh	24	no	\(1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{714}(29,\cdot)\)	714.bf	16	no	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{714}(31,\cdot)\)	714.bl	48	no	\(1\)	\(1\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(-i\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{714}(37,\cdot)\)	714.bm	48	no	\(-1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(i\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{714}(41,\cdot)\)	714.bc	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{714}(43,\cdot)\)	714.u	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{714}(47,\cdot)\)	714.y	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)
\(\chi_{714}(53,\cdot)\)	714.bg	24	no	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{714}(55,\cdot)\)	714.j	4	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(i\)	\(-i\)	\(-i\)
\(\chi_{714}(59,\cdot)\)	714.bj	24	no	\(1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{714}(61,\cdot)\)	714.bl	48	no	\(1\)	\(1\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(i\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{714}(65,\cdot)\)	714.bk	48	no	\(1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(i\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{714}(67,\cdot)\)	714.t	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)
\(\chi_{714}(71,\cdot)\)	714.bf	16	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{714}(73,\cdot)\)	714.bl	48	no	\(1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(-i\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{714}(79,\cdot)\)	714.bm	48	no	\(-1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(-i\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{714}(83,\cdot)\)	714.w	8	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{714}(89,\cdot)\)	714.y	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)
\(\chi_{714}(95,\cdot)\)	714.bk	48	no	\(1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(-i\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{714}(97,\cdot)\)	714.be	16	no	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{714}(101,\cdot)\)	714.q	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)
\(\chi_{714}(103,\cdot)\)	714.r	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)
\(\chi_{714}(107,\cdot)\)	714.bk	48	no	\(1\)	\(1\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(i\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{714}(109,\cdot)\)	714.bm	48	no	\(-1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(-i\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{714}(113,\cdot)\)	714.bf	16	no	\(1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{714}(115,\cdot)\)	714.z	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 192 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.