LMFDB - Group of Dirichlet characters of modulus 624

Show commands: PariGP / SageMath

sage: H = DirichletGroup(624)

pari: g = idealstar(,624,2)

Character group

sage: G.order() pari: g.no
Order	=	192
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{12}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{624}(79,\cdot)$, $\chi_{624}(469,\cdot)$, $\chi_{624}(209,\cdot)$, $\chi_{624}(145,\cdot)$

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	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{624}(1,\cdot)$	624.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{624}(5,\cdot)$	624.u	4	yes	$1$	$1$	$-1$	$-i$	$1$	$1$	$-1$	$-1$	$1$	$i$	$-i$	$i$
$\chi_{624}(7,\cdot)$	624.cr	12	no	$1$	$1$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{624}(11,\cdot)$	624.cy	12	yes	$-1$	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{5}{12}\right)$
$\chi_{624}(17,\cdot)$	624.cb	6	no	$-1$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{624}(19,\cdot)$	624.ch	12	no	$1$	$1$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{1}{12}\right)$
$\chi_{624}(23,\cdot)$	624.bq	6	no	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{624}(25,\cdot)$	624.m	2	no	$1$	$1$	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$
$\chi_{624}(29,\cdot)$	624.cw	12	yes	$-1$	$1$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{5}{12}\right)$
$\chi_{624}(31,\cdot)$	624.bc	4	no	$1$	$1$	$-i$	$-i$	$-i$	$-1$	$i$	$1$	$-1$	$1$	$i$	$-1$
$\chi_{624}(35,\cdot)$	624.cl	12	yes	$1$	$1$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{7}{12}\right)$
$\chi_{624}(37,\cdot)$	624.cf	12	no	$-1$	$1$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{5}{12}\right)$
$\chi_{624}(41,\cdot)$	624.cm	12	no	$1$	$1$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{2}{3}\right)$
$\chi_{624}(43,\cdot)$	624.cu	12	no	$-1$	$1$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{7}{12}\right)$
$\chi_{624}(47,\cdot)$	624.bd	4	no	$-1$	$1$	$-i$	$i$	$-i$	$1$	$-i$	$-1$	$-1$	$-1$	$-i$	$1$
$\chi_{624}(49,\cdot)$	624.bv	6	no	$1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{624}(53,\cdot)$	624.w	4	no	$-1$	$1$	$-i$	$-1$	$-i$	$-1$	$-i$	$1$	$-1$	$i$	$1$	$i$
$\chi_{624}(55,\cdot)$	624.bt	6	no	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{624}(59,\cdot)$	624.cy	12	yes	$-1$	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{1}{12}\right)$
$\chi_{624}(61,\cdot)$	624.cv	12	no	$1$	$1$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{7}{12}\right)$
$\chi_{624}(67,\cdot)$	624.ch	12	no	$1$	$1$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{5}{12}\right)$
$\chi_{624}(71,\cdot)$	624.co	12	no	$-1$	$1$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{624}(73,\cdot)$	624.z	4	no	$-1$	$1$	$-i$	$-i$	$i$	$-1$	$-i$	$-1$	$-1$	$-1$	$i$	$-1$
$\chi_{624}(77,\cdot)$	624.bi	4	yes	$-1$	$1$	$-i$	$1$	$-i$	$-1$	$-i$	$1$	$-1$	$-i$	$-1$	$-i$
$\chi_{624}(79,\cdot)$	624.k	2	no	$-1$	$1$	$1$	$-1$	$-1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$
$\chi_{624}(83,\cdot)$	624.bo	4	yes	$-1$	$1$	$1$	$i$	$1$	$1$	$-1$	$1$	$1$	$-i$	$i$	$i$
$\chi_{624}(85,\cdot)$	624.cf	12	no	$-1$	$1$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{1}{12}\right)$
$\chi_{624}(89,\cdot)$	624.cm	12	no	$1$	$1$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{2}{3}\right)$
$\chi_{624}(95,\cdot)$	624.bz	6	no	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{624}(97,\cdot)$	624.cs	12	no	$-1$	$1$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{624}(101,\cdot)$	624.ck	12	yes	$-1$	$1$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{11}{12}\right)$
$\chi_{624}(103,\cdot)$	624.o	2	no	$-1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$-1$	$1$	$-1$	$1$	$1$

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	$624$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{12}\)
Order	$192$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{624}(1,\cdot)\)	624.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{624}(5,\cdot)\)	624.u	4	yes	\(1\)	\(1\)	\(-1\)	\(-i\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(i\)	\(-i\)	\(i\)
\(\chi_{624}(7,\cdot)\)	624.cr	12	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{624}(11,\cdot)\)	624.cy	12	yes	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{624}(17,\cdot)\)	624.cb	6	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{624}(19,\cdot)\)	624.ch	12	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{624}(23,\cdot)\)	624.bq	6	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{624}(25,\cdot)\)	624.m	2	no	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)
\(\chi_{624}(29,\cdot)\)	624.cw	12	yes	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{624}(31,\cdot)\)	624.bc	4	no	\(1\)	\(1\)	\(-i\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(1\)	\(-1\)	\(1\)	\(i\)	\(-1\)
\(\chi_{624}(35,\cdot)\)	624.cl	12	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{624}(37,\cdot)\)	624.cf	12	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{624}(41,\cdot)\)	624.cm	12	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{624}(43,\cdot)\)	624.cu	12	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{624}(47,\cdot)\)	624.bd	4	no	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(-1\)	\(-i\)	\(1\)
\(\chi_{624}(49,\cdot)\)	624.bv	6	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{624}(53,\cdot)\)	624.w	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(-1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(1\)	\(i\)
\(\chi_{624}(55,\cdot)\)	624.bt	6	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{624}(59,\cdot)\)	624.cy	12	yes	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{624}(61,\cdot)\)	624.cv	12	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{624}(67,\cdot)\)	624.ch	12	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{624}(71,\cdot)\)	624.co	12	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{624}(73,\cdot)\)	624.z	4	no	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(i\)	\(-1\)	\(-i\)	\(-1\)	\(-1\)	\(-1\)	\(i\)	\(-1\)
\(\chi_{624}(77,\cdot)\)	624.bi	4	yes	\(-1\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(1\)	\(-1\)	\(-i\)	\(-1\)	\(-i\)
\(\chi_{624}(79,\cdot)\)	624.k	2	no	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{624}(83,\cdot)\)	624.bo	4	yes	\(-1\)	\(1\)	\(1\)	\(i\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-i\)	\(i\)	\(i\)
\(\chi_{624}(85,\cdot)\)	624.cf	12	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{624}(89,\cdot)\)	624.cm	12	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{624}(95,\cdot)\)	624.bz	6	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{624}(97,\cdot)\)	624.cs	12	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{624}(101,\cdot)\)	624.ck	12	yes	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{624}(103,\cdot)\)	624.o	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)

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.