LMFDB - Group of Dirichlet characters of modulus 960

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(960)

pari: g = idealstar(,960,2)

Character group

sage: G.order() pari: g.no
Order	=	256
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{16}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{960}(511,\cdot)$, $\chi_{960}(901,\cdot)$, $\chi_{960}(641,\cdot)$, $\chi_{960}(577,\cdot)$

First 32 of 256 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{960}(1,\cdot)$	960.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{960}(7,\cdot)$	960.cc	8	no	$1$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$-i$
$\chi_{960}(11,\cdot)$	960.cn	16	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{16}\right)$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{960}(13,\cdot)$	960.cq	16	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$-1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{960}(17,\cdot)$	960.bf	4	no	$1$	$1$	$-i$	$i$	$1$	$-i$	$-i$	$-i$	$i$	$1$	$1$	$1$
$\chi_{960}(19,\cdot)$	960.co	16	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{16}\right)$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{960}(23,\cdot)$	960.ca	8	no	$-1$	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$-i$
$\chi_{960}(29,\cdot)$	960.cl	16	yes	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{16}\right)$	$-1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{960}(31,\cdot)$	960.g	2	no	$-1$	$1$	$-1$	$1$	$-1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$
$\chi_{960}(37,\cdot)$	960.cq	16	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$-1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{960}(41,\cdot)$	960.bz	8	no	$-1$	$1$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$-i$
$\chi_{960}(43,\cdot)$	960.cg	16	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$-1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{960}(47,\cdot)$	960.bd	4	no	$-1$	$1$	$i$	$-i$	$1$	$-i$	$i$	$i$	$i$	$-1$	$1$	$1$
$\chi_{960}(49,\cdot)$	960.bl	4	no	$1$	$1$	$1$	$i$	$i$	$-1$	$-i$	$1$	$-i$	$1$	$-i$	$-1$
$\chi_{960}(53,\cdot)$	960.cr	16	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$-1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{960}(59,\cdot)$	960.cp	16	yes	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$-i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{16}\right)$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{960}(61,\cdot)$	960.ci	16	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{16}\right)$	$-1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{960}(67,\cdot)$	960.cg	16	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{960}(71,\cdot)$	960.bx	8	no	$1$	$1$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$i$
$\chi_{960}(73,\cdot)$	960.bp	8	no	$-1$	$1$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$i$
$\chi_{960}(77,\cdot)$	960.cr	16	yes	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$	$-1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{960}(79,\cdot)$	960.q	4	no	$-1$	$1$	$-1$	$-i$	$i$	$-1$	$i$	$-1$	$-i$	$-1$	$-i$	$-1$
$\chi_{960}(83,\cdot)$	960.ch	16	yes	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$-1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{960}(89,\cdot)$	960.bu	8	no	$-1$	$1$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$i$
$\chi_{960}(91,\cdot)$	960.cm	16	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$-i$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{16}\right)$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{960}(97,\cdot)$	960.x	4	no	$-1$	$1$	$i$	$-1$	$i$	$i$	$1$	$-i$	$1$	$1$	$-i$	$1$
$\chi_{960}(101,\cdot)$	960.cj	16	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{16}\right)$	$-1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{960}(103,\cdot)$	960.bo	8	no	$1$	$1$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$-i$
$\chi_{960}(107,\cdot)$	960.ch	16	yes	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$-1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{960}(109,\cdot)$	960.ck	16	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-i$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$-1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{960}(113,\cdot)$	960.bf	4	no	$1$	$1$	$i$	$-i$	$1$	$i$	$i$	$i$	$-i$	$1$	$1$	$1$
$\chi_{960}(119,\cdot)$	960.bs	8	no	$1$	$1$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$-i$

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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	$960$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{16}\)
Order	$256$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{960}(1,\cdot)\)	960.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{960}(7,\cdot)\)	960.cc	8	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)
\(\chi_{960}(11,\cdot)\)	960.cn	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{960}(13,\cdot)\)	960.cq	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{960}(17,\cdot)\)	960.bf	4	no	\(1\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(-i\)	\(-i\)	\(-i\)	\(i\)	\(1\)	\(1\)	\(1\)
\(\chi_{960}(19,\cdot)\)	960.co	16	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{960}(23,\cdot)\)	960.ca	8	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)
\(\chi_{960}(29,\cdot)\)	960.cl	16	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{960}(31,\cdot)\)	960.g	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{960}(37,\cdot)\)	960.cq	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{960}(41,\cdot)\)	960.bz	8	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)
\(\chi_{960}(43,\cdot)\)	960.cg	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{960}(47,\cdot)\)	960.bd	4	no	\(-1\)	\(1\)	\(i\)	\(-i\)	\(1\)	\(-i\)	\(i\)	\(i\)	\(i\)	\(-1\)	\(1\)	\(1\)
\(\chi_{960}(49,\cdot)\)	960.bl	4	no	\(1\)	\(1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(-i\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-1\)
\(\chi_{960}(53,\cdot)\)	960.cr	16	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{960}(59,\cdot)\)	960.cp	16	yes	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{960}(61,\cdot)\)	960.ci	16	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{960}(67,\cdot)\)	960.cg	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{960}(71,\cdot)\)	960.bx	8	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)
\(\chi_{960}(73,\cdot)\)	960.bp	8	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)
\(\chi_{960}(77,\cdot)\)	960.cr	16	yes	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{960}(79,\cdot)\)	960.q	4	no	\(-1\)	\(1\)	\(-1\)	\(-i\)	\(i\)	\(-1\)	\(i\)	\(-1\)	\(-i\)	\(-1\)	\(-i\)	\(-1\)
\(\chi_{960}(83,\cdot)\)	960.ch	16	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{960}(89,\cdot)\)	960.bu	8	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)
\(\chi_{960}(91,\cdot)\)	960.cm	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-i\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{960}(97,\cdot)\)	960.x	4	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(i\)	\(i\)	\(1\)	\(-i\)	\(1\)	\(1\)	\(-i\)	\(1\)
\(\chi_{960}(101,\cdot)\)	960.cj	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{960}(103,\cdot)\)	960.bo	8	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)
\(\chi_{960}(107,\cdot)\)	960.ch	16	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{960}(109,\cdot)\)	960.ck	16	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{960}(113,\cdot)\)	960.bf	4	no	\(1\)	\(1\)	\(i\)	\(-i\)	\(1\)	\(i\)	\(i\)	\(i\)	\(-i\)	\(1\)	\(1\)	\(1\)
\(\chi_{960}(119,\cdot)\)	960.bs	8	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 256 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.