LMFDB - Group of Dirichlet characters of modulus 588

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(588)

pari: g = idealstar(,588,2)

Character group

sage: G.order() pari: g.no
Order	=	168
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{42}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{588}(295,\cdot)$, $\chi_{588}(197,\cdot)$, $\chi_{588}(493,\cdot)$

First 32 of 168 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	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{588}(1,\cdot)$	588.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{588}(5,\cdot)$	588.be	42	no	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{588}(11,\cdot)$	588.bb	42	yes	$1$	$1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{588}(13,\cdot)$	588.v	14	no	$-1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{14}\right)$	$-1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$-1$	$e\left(\frac{1}{7}\right)$
$\chi_{588}(17,\cdot)$	588.be	42	no	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{588}(19,\cdot)$	588.o	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{588}(23,\cdot)$	588.bb	42	yes	$1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{588}(25,\cdot)$	588.y	21	no	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{588}(29,\cdot)$	588.w	14	no	$-1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{14}\right)$	$1$	$e\left(\frac{5}{7}\right)$
$\chi_{588}(31,\cdot)$	588.o	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{588}(37,\cdot)$	588.y	21	no	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{588}(41,\cdot)$	588.t	14	no	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{7}\right)$	$-1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$-1$	$e\left(\frac{3}{7}\right)$
$\chi_{588}(43,\cdot)$	588.s	14	no	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$-1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$-1$	$e\left(\frac{4}{7}\right)$
$\chi_{588}(47,\cdot)$	588.bf	42	yes	$-1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{588}(53,\cdot)$	588.z	42	no	$-1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{588}(55,\cdot)$	588.x	14	no	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{14}\right)$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$1$	$e\left(\frac{4}{7}\right)$
$\chi_{588}(59,\cdot)$	588.bf	42	yes	$-1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{588}(61,\cdot)$	588.bc	42	no	$-1$	$1$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{588}(65,\cdot)$	588.z	42	no	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{588}(67,\cdot)$	588.l	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{588}(71,\cdot)$	588.u	14	yes	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{14}\right)$	$-1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$	$-1$	$e\left(\frac{2}{7}\right)$
$\chi_{588}(73,\cdot)$	588.bc	42	no	$-1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{588}(79,\cdot)$	588.l	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{588}(83,\cdot)$	588.r	14	yes	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{6}{7}\right)$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$	$1$	$e\left(\frac{6}{7}\right)$
$\chi_{588}(85,\cdot)$	588.q	7	no	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$1$	$e\left(\frac{1}{7}\right)$
$\chi_{588}(89,\cdot)$	588.be	42	no	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{588}(95,\cdot)$	588.bb	42	yes	$1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{588}(97,\cdot)$	588.d	2	no	$-1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$-1$	$1$
$\chi_{588}(101,\cdot)$	588.be	42	no	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{588}(103,\cdot)$	588.ba	42	no	$1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{588}(107,\cdot)$	588.bb	42	yes	$1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{588}(109,\cdot)$	588.y	21	no	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{10}{21}\right)$

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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	$588$
Structure	\(C_{2}\times C_{2}\times C_{42}\)
Order	$168$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)
\(\chi_{588}(1,\cdot)\)	588.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{588}(5,\cdot)\)	588.be	42	no	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{588}(11,\cdot)\)	588.bb	42	yes	\(1\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{588}(13,\cdot)\)	588.v	14	no	\(-1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(-1\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{588}(17,\cdot)\)	588.be	42	no	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{588}(19,\cdot)\)	588.o	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{588}(23,\cdot)\)	588.bb	42	yes	\(1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{588}(25,\cdot)\)	588.y	21	no	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{588}(29,\cdot)\)	588.w	14	no	\(-1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(1\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{588}(31,\cdot)\)	588.o	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{588}(37,\cdot)\)	588.y	21	no	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{588}(41,\cdot)\)	588.t	14	no	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-1\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{588}(43,\cdot)\)	588.s	14	no	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(-1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(-1\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{588}(47,\cdot)\)	588.bf	42	yes	\(-1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{588}(53,\cdot)\)	588.z	42	no	\(-1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{588}(55,\cdot)\)	588.x	14	no	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{588}(59,\cdot)\)	588.bf	42	yes	\(-1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{588}(61,\cdot)\)	588.bc	42	no	\(-1\)	\(1\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{588}(65,\cdot)\)	588.z	42	no	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{588}(67,\cdot)\)	588.l	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{588}(71,\cdot)\)	588.u	14	yes	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(-1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(-1\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{588}(73,\cdot)\)	588.bc	42	no	\(-1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{588}(79,\cdot)\)	588.l	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{588}(83,\cdot)\)	588.r	14	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(1\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{588}(85,\cdot)\)	588.q	7	no	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(1\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{588}(89,\cdot)\)	588.be	42	no	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{588}(95,\cdot)\)	588.bb	42	yes	\(1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{588}(97,\cdot)\)	588.d	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{588}(101,\cdot)\)	588.be	42	no	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{588}(103,\cdot)\)	588.ba	42	no	\(1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{588}(107,\cdot)\)	588.bb	42	yes	\(1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{588}(109,\cdot)\)	588.y	21	no	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{10}{21}\right)\)

Introduction

L-functions

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First 32 of 168 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.