LMFDB - Group of Dirichlet characters of modulus 585

Show commands: PariGP / SageMath

sage: H = DirichletGroup(585)

pari: g = idealstar(,585,2)

Character group

sage: G.order() pari: g.no
Order	=	288
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{12}\times C_{12}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{585}(326,\cdot)$, $\chi_{585}(352,\cdot)$, $\chi_{585}(496,\cdot)$

First 32 of 288 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$14$	$16$	$17$	$19$	$22$
$\chi_{585}(1,\cdot)$	585.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{585}(2,\cdot)$	585.cb	12	yes	$-1$	$1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$-i$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$i$
$\chi_{585}(4,\cdot)$	585.bx	6	yes	$1$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$
$\chi_{585}(7,\cdot)$	585.dt	12	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{585}(8,\cdot)$	585.m	4	no	$-1$	$1$	$-1$	$1$	$-1$	$-1$	$i$	$1$	$1$	$-i$	$-i$	$-i$
$\chi_{585}(11,\cdot)$	585.cm	12	no	$1$	$1$	$-i$	$-1$	$e\left(\frac{1}{12}\right)$	$i$	$i$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$1$
$\chi_{585}(14,\cdot)$	585.bj	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{585}(16,\cdot)$	585.l	3	no	$1$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{585}(17,\cdot)$	585.cv	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{585}(19,\cdot)$	585.dg	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{585}(22,\cdot)$	585.cp	12	yes	$-1$	$1$	$i$	$-1$	$e\left(\frac{11}{12}\right)$	$-i$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$
$\chi_{585}(23,\cdot)$	585.cr	12	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{585}(28,\cdot)$	585.dp	12	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{585}(29,\cdot)$	585.by	6	yes	$-1$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$
$\chi_{585}(31,\cdot)$	585.cy	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$-i$	$e\left(\frac{2}{3}\right)$
$\chi_{585}(32,\cdot)$	585.cb	12	yes	$-1$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$-i$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$i$
$\chi_{585}(34,\cdot)$	585.db	12	yes	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{585}(37,\cdot)$	585.dp	12	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{585}(38,\cdot)$	585.cs	12	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$1$	$e\left(\frac{1}{12}\right)$
$\chi_{585}(41,\cdot)$	585.dd	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{585}(43,\cdot)$	585.dl	12	yes	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{585}(44,\cdot)$	585.q	4	no	$1$	$1$	$-i$	$-1$	$-i$	$i$	$-i$	$-1$	$1$	$-1$	$-i$	$-1$
$\chi_{585}(46,\cdot)$	585.dh	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{585}(47,\cdot)$	585.cd	12	yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$-i$	$e\left(\frac{7}{12}\right)$
$\chi_{585}(49,\cdot)$	585.bk	6	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{585}(53,\cdot)$	585.p	4	no	$1$	$1$	$i$	$-1$	$-i$	$-i$	$-1$	$1$	$1$	$i$	$-1$	$-i$
$\chi_{585}(56,\cdot)$	585.bc	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{585}(58,\cdot)$	585.ca	12	yes	$1$	$1$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$i$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-i$
$\chi_{585}(59,\cdot)$	585.cn	12	yes	$1$	$1$	$i$	$-1$	$e\left(\frac{11}{12}\right)$	$-i$	$i$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-1$
$\chi_{585}(61,\cdot)$	585.k	3	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{585}(62,\cdot)$	585.cv	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{585}(64,\cdot)$	585.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	$585$
Structure	\(C_{2}\times C_{12}\times C_{12}\)
Order	$288$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(14\)	\(16\)	\(17\)	\(19\)	\(22\)
\(\chi_{585}(1,\cdot)\)	585.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{585}(2,\cdot)\)	585.cb	12	yes	\(-1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)
\(\chi_{585}(4,\cdot)\)	585.bx	6	yes	\(1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)
\(\chi_{585}(7,\cdot)\)	585.dt	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{585}(8,\cdot)\)	585.m	4	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(i\)	\(1\)	\(1\)	\(-i\)	\(-i\)	\(-i\)
\(\chi_{585}(11,\cdot)\)	585.cm	12	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)
\(\chi_{585}(14,\cdot)\)	585.bj	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{585}(16,\cdot)\)	585.l	3	no	\(1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{585}(17,\cdot)\)	585.cv	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{585}(19,\cdot)\)	585.dg	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{585}(22,\cdot)\)	585.cp	12	yes	\(-1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)
\(\chi_{585}(23,\cdot)\)	585.cr	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{585}(28,\cdot)\)	585.dp	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{585}(29,\cdot)\)	585.by	6	yes	\(-1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)
\(\chi_{585}(31,\cdot)\)	585.cy	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{585}(32,\cdot)\)	585.cb	12	yes	\(-1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)
\(\chi_{585}(34,\cdot)\)	585.db	12	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{585}(37,\cdot)\)	585.dp	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{585}(38,\cdot)\)	585.cs	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(1\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{585}(41,\cdot)\)	585.dd	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{585}(43,\cdot)\)	585.dl	12	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{585}(44,\cdot)\)	585.q	4	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(-1\)	\(-i\)	\(-1\)
\(\chi_{585}(46,\cdot)\)	585.dh	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{585}(47,\cdot)\)	585.cd	12	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{585}(49,\cdot)\)	585.bk	6	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{585}(53,\cdot)\)	585.p	4	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(1\)	\(1\)	\(i\)	\(-1\)	\(-i\)
\(\chi_{585}(56,\cdot)\)	585.bc	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{585}(58,\cdot)\)	585.ca	12	yes	\(1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)
\(\chi_{585}(59,\cdot)\)	585.cn	12	yes	\(1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)
\(\chi_{585}(61,\cdot)\)	585.k	3	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{585}(62,\cdot)\)	585.cv	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{585}(64,\cdot)\)	585.h	2	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)

Introduction

L-functions

Modular forms

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Fields

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Properties

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Character group

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.