LMFDB - Group of Dirichlet characters of modulus 1040

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1040)

pari: g = idealstar(,1040,2)

Character group

sage: G.order() pari: g.no
Order	=	384
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{4}\times C_{12}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1040}(911,\cdot)$, $\chi_{1040}(261,\cdot)$, $\chi_{1040}(417,\cdot)$, $\chi_{1040}(561,\cdot)$

First 32 of 384 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	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{1040}(1,\cdot)$	1040.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1040}(3,\cdot)$	1040.dp	12	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{1}{12}\right)$
$\chi_{1040}(7,\cdot)$	1040.ex	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$
$\chi_{1040}(9,\cdot)$	1040.db	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{1040}(11,\cdot)$	1040.et	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{1}{12}\right)$
$\chi_{1040}(17,\cdot)$	1040.ep	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{1}{6}\right)$
$\chi_{1040}(19,\cdot)$	1040.en	12	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{11}{12}\right)$
$\chi_{1040}(21,\cdot)$	1040.bu	4	no	$-1$	$1$	$-i$	$i$	$-1$	$1$	$-1$	$1$	$1$	$1$	$i$	$-i$
$\chi_{1040}(23,\cdot)$	1040.eq	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{1040}(27,\cdot)$	1040.cn	4	no	$1$	$1$	$1$	$i$	$1$	$-i$	$i$	$-i$	$i$	$-i$	$1$	$i$
$\chi_{1040}(29,\cdot)$	1040.ec	12	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{7}{12}\right)$
$\chi_{1040}(31,\cdot)$	1040.u	4	no	$1$	$1$	$-1$	$-i$	$1$	$-i$	$-1$	$i$	$i$	$1$	$-1$	$1$
$\chi_{1040}(33,\cdot)$	1040.ey	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{1040}(37,\cdot)$	1040.fm	12	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{7}{12}\right)$
$\chi_{1040}(41,\cdot)$	1040.fl	12	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{1040}(43,\cdot)$	1040.fi	12	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{11}{12}\right)$
$\chi_{1040}(47,\cdot)$	1040.bf	4	no	$-1$	$1$	$i$	$-1$	$-1$	$i$	$-i$	$i$	$-i$	$-i$	$-i$	$-1$
$\chi_{1040}(49,\cdot)$	1040.df	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{1040}(51,\cdot)$	1040.bk	4	no	$-1$	$1$	$-i$	$-1$	$-1$	$-i$	$1$	$i$	$i$	$1$	$i$	$i$
$\chi_{1040}(53,\cdot)$	1040.cp	4	no	$-1$	$1$	$1$	$i$	$1$	$i$	$-i$	$i$	$i$	$-i$	$1$	$i$
$\chi_{1040}(57,\cdot)$	1040.bi	4	no	$1$	$1$	$i$	$-1$	$-1$	$-i$	$-i$	$-i$	$-i$	$i$	$-i$	$1$
$\chi_{1040}(59,\cdot)$	1040.en	12	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{5}{12}\right)$
$\chi_{1040}(61,\cdot)$	1040.ev	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{11}{12}\right)$
$\chi_{1040}(63,\cdot)$	1040.ea	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{1040}(67,\cdot)$	1040.fn	12	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{1}{12}\right)$
$\chi_{1040}(69,\cdot)$	1040.fa	12	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{5}{12}\right)$
$\chi_{1040}(71,\cdot)$	1040.ds	12	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{1040}(73,\cdot)$	1040.bi	4	no	$1$	$1$	$-i$	$-1$	$-1$	$i$	$i$	$i$	$i$	$-i$	$i$	$1$
$\chi_{1040}(77,\cdot)$	1040.co	4	yes	$-1$	$1$	$1$	$i$	$1$	$i$	$i$	$i$	$i$	$i$	$1$	$-i$
$\chi_{1040}(79,\cdot)$	1040.n	2	no	$-1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$
$\chi_{1040}(81,\cdot)$	1040.q	3	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{1040}(83,\cdot)$	1040.ct	4	yes	$-1$	$1$	$1$	$1$	$1$	$-1$	$i$	$1$	$1$	$-i$	$1$	$-i$

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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	$1040$
Structure	\(C_{2}\times C_{4}\times C_{4}\times C_{12}\)
Order	$384$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{1040}(1,\cdot)\)	1040.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1040}(3,\cdot)\)	1040.dp	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1040}(7,\cdot)\)	1040.ex	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1040}(9,\cdot)\)	1040.db	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1040}(11,\cdot)\)	1040.et	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1040}(17,\cdot)\)	1040.ep	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1040}(19,\cdot)\)	1040.en	12	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1040}(21,\cdot)\)	1040.bu	4	no	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(i\)	\(-i\)
\(\chi_{1040}(23,\cdot)\)	1040.eq	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1040}(27,\cdot)\)	1040.cn	4	no	\(1\)	\(1\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(i\)	\(-i\)	\(i\)	\(-i\)	\(1\)	\(i\)
\(\chi_{1040}(29,\cdot)\)	1040.ec	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1040}(31,\cdot)\)	1040.u	4	no	\(1\)	\(1\)	\(-1\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(i\)	\(1\)	\(-1\)	\(1\)
\(\chi_{1040}(33,\cdot)\)	1040.ey	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1040}(37,\cdot)\)	1040.fm	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1040}(41,\cdot)\)	1040.fl	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1040}(43,\cdot)\)	1040.fi	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1040}(47,\cdot)\)	1040.bf	4	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(-i\)	\(i\)	\(-i\)	\(-i\)	\(-i\)	\(-1\)
\(\chi_{1040}(49,\cdot)\)	1040.df	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1040}(51,\cdot)\)	1040.bk	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(1\)	\(i\)	\(i\)	\(1\)	\(i\)	\(i\)
\(\chi_{1040}(53,\cdot)\)	1040.cp	4	no	\(-1\)	\(1\)	\(1\)	\(i\)	\(1\)	\(i\)	\(-i\)	\(i\)	\(i\)	\(-i\)	\(1\)	\(i\)
\(\chi_{1040}(57,\cdot)\)	1040.bi	4	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(-i\)	\(-i\)	\(-i\)	\(-i\)	\(i\)	\(-i\)	\(1\)
\(\chi_{1040}(59,\cdot)\)	1040.en	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1040}(61,\cdot)\)	1040.ev	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1040}(63,\cdot)\)	1040.ea	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1040}(67,\cdot)\)	1040.fn	12	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1040}(69,\cdot)\)	1040.fa	12	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1040}(71,\cdot)\)	1040.ds	12	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1040}(73,\cdot)\)	1040.bi	4	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(i\)	\(i\)	\(i\)	\(-i\)	\(i\)	\(1\)
\(\chi_{1040}(77,\cdot)\)	1040.co	4	yes	\(-1\)	\(1\)	\(1\)	\(i\)	\(1\)	\(i\)	\(i\)	\(i\)	\(i\)	\(i\)	\(1\)	\(-i\)
\(\chi_{1040}(79,\cdot)\)	1040.n	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1040}(81,\cdot)\)	1040.q	3	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1040}(83,\cdot)\)	1040.ct	4	yes	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(i\)	\(1\)	\(1\)	\(-i\)	\(1\)	\(-i\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 384 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.