LMFDB - Group of Dirichlet characters of modulus 195

Show commands: PariGP / SageMath

sage: H = DirichletGroup(195)

pari: g = idealstar(,195,2)

Character group

sage: G.order() pari: g.no
Order	=	96
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{12}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{195}(131,\cdot)$, $\chi_{195}(157,\cdot)$, $\chi_{195}(106,\cdot)$

First 32 of 96 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$14$	$16$	$17$	$19$	$22$
$\chi_{195}(1,\cdot)$	195.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{195}(2,\cdot)$	195.bn	12	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{195}(4,\cdot)$	195.v	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{195}(7,\cdot)$	195.bm	12	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{195}(8,\cdot)$	195.j	4	yes	$-1$	$1$	$-1$	$1$	$-1$	$-1$	$i$	$1$	$1$	$-i$	$-i$	$-i$
$\chi_{195}(11,\cdot)$	195.bg	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{195}(14,\cdot)$	195.f	2	no	$-1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$-1$
$\chi_{195}(16,\cdot)$	195.i	3	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{195}(17,\cdot)$	195.bf	12	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{195}(19,\cdot)$	195.bi	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{195}(22,\cdot)$	195.be	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{195}(23,\cdot)$	195.bf	12	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{195}(28,\cdot)$	195.bm	12	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{195}(29,\cdot)$	195.x	6	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{195}(31,\cdot)$	195.p	4	no	$-1$	$1$	$-i$	$-1$	$i$	$i$	$i$	$1$	$1$	$-1$	$-i$	$1$
$\chi_{195}(32,\cdot)$	195.bn	12	yes	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{195}(34,\cdot)$	195.q	4	no	$-1$	$1$	$-i$	$-1$	$i$	$i$	$-i$	$1$	$1$	$1$	$i$	$-1$
$\chi_{195}(37,\cdot)$	195.bm	12	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{195}(38,\cdot)$	195.s	4	yes	$1$	$1$	$-i$	$-1$	$i$	$i$	$1$	$1$	$1$	$i$	$1$	$-i$
$\chi_{195}(41,\cdot)$	195.bg	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{195}(43,\cdot)$	195.bk	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{195}(44,\cdot)$	195.n	4	yes	$1$	$1$	$-i$	$-1$	$-i$	$i$	$-i$	$-1$	$1$	$-1$	$-i$	$-1$
$\chi_{195}(46,\cdot)$	195.bj	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{195}(47,\cdot)$	195.u	4	yes	$-1$	$1$	$1$	$1$	$1$	$1$	$i$	$1$	$1$	$i$	$-i$	$i$
$\chi_{195}(49,\cdot)$	195.v	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{195}(53,\cdot)$	195.m	4	no	$1$	$1$	$i$	$-1$	$-i$	$-i$	$-1$	$1$	$1$	$i$	$-1$	$-i$
$\chi_{195}(56,\cdot)$	195.w	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{195}(58,\cdot)$	195.bm	12	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{195}(59,\cdot)$	195.bh	12	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{195}(61,\cdot)$	195.i	3	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{195}(62,\cdot)$	195.bf	12	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{195}(64,\cdot)$	195.h	2	no	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$-1$	$-1$

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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	$195$
Structure	\(C_{2}\times C_{4}\times C_{12}\)
Order	$96$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(14\)	\(16\)	\(17\)	\(19\)	\(22\)
\(\chi_{195}(1,\cdot)\)	195.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{195}(2,\cdot)\)	195.bn	12	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{195}(4,\cdot)\)	195.v	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{195}(7,\cdot)\)	195.bm	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{195}(8,\cdot)\)	195.j	4	yes	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(i\)	\(1\)	\(1\)	\(-i\)	\(-i\)	\(-i\)
\(\chi_{195}(11,\cdot)\)	195.bg	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{195}(14,\cdot)\)	195.f	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)
\(\chi_{195}(16,\cdot)\)	195.i	3	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{195}(17,\cdot)\)	195.bf	12	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{195}(19,\cdot)\)	195.bi	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{195}(22,\cdot)\)	195.be	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{195}(23,\cdot)\)	195.bf	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{195}(28,\cdot)\)	195.bm	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{195}(29,\cdot)\)	195.x	6	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{195}(31,\cdot)\)	195.p	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(i\)	\(i\)	\(1\)	\(1\)	\(-1\)	\(-i\)	\(1\)
\(\chi_{195}(32,\cdot)\)	195.bn	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{195}(34,\cdot)\)	195.q	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(i\)	\(-i\)	\(1\)	\(1\)	\(1\)	\(i\)	\(-1\)
\(\chi_{195}(37,\cdot)\)	195.bm	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{195}(38,\cdot)\)	195.s	4	yes	\(1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(i\)	\(1\)	\(1\)	\(1\)	\(i\)	\(1\)	\(-i\)
\(\chi_{195}(41,\cdot)\)	195.bg	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{195}(43,\cdot)\)	195.bk	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{195}(44,\cdot)\)	195.n	4	yes	\(1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(-1\)	\(-i\)	\(-1\)
\(\chi_{195}(46,\cdot)\)	195.bj	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{195}(47,\cdot)\)	195.u	4	yes	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(i\)	\(1\)	\(1\)	\(i\)	\(-i\)	\(i\)
\(\chi_{195}(49,\cdot)\)	195.v	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{195}(53,\cdot)\)	195.m	4	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(1\)	\(1\)	\(i\)	\(-1\)	\(-i\)
\(\chi_{195}(56,\cdot)\)	195.w	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{195}(58,\cdot)\)	195.bm	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{195}(59,\cdot)\)	195.bh	12	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{195}(61,\cdot)\)	195.i	3	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{195}(62,\cdot)\)	195.bf	12	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{195}(64,\cdot)\)	195.h	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

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Character group

First 32 of 96 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.