LMFDB - Group of Dirichlet characters of modulus 231

sage:H = DirichletGroup(231)

pari:g = idealstar(,231,2)

Character group

sage:G.order() pari:g.no
Order	=	120
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{30}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{231}(155,\cdot)$, $\chi_{231}(199,\cdot)$, $\chi_{231}(211,\cdot)$

First 32 of 120 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{231}(1,\cdot)$	231.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{231}(2,\cdot)$	231.be	30	yes	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{231}(4,\cdot)$	231.y	15	no	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{231}(5,\cdot)$	231.bc	30	yes	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{231}(8,\cdot)$	231.s	10	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{231}(10,\cdot)$	231.p	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{231}(13,\cdot)$	231.w	10	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{231}(16,\cdot)$	231.y	15	no	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{231}(17,\cdot)$	231.bf	30	yes	$-1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{231}(19,\cdot)$	231.ba	30	no	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{231}(20,\cdot)$	231.u	10	yes	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{231}(23,\cdot)$	231.q	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$
$\chi_{231}(25,\cdot)$	231.y	15	no	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{231}(26,\cdot)$	231.bc	30	yes	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{231}(29,\cdot)$	231.s	10	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{231}(31,\cdot)$	231.bd	30	no	$-1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{231}(32,\cdot)$	231.l	6	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$
$\chi_{231}(34,\cdot)$	231.f	2	no	$-1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$-1$	$1$	$-1$	$-1$	$-1$
$\chi_{231}(37,\cdot)$	231.y	15	no	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{231}(38,\cdot)$	231.bc	30	yes	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{231}(40,\cdot)$	231.ba	30	no	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{231}(41,\cdot)$	231.r	10	yes	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{231}(43,\cdot)$	231.d	2	no	$-1$	$1$	$-1$	$1$	$1$	$-1$	$-1$	$-1$	$1$	$-1$	$-1$	$1$
$\chi_{231}(46,\cdot)$	231.bb	30	no	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{231}(47,\cdot)$	231.bc	30	yes	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{231}(50,\cdot)$	231.s	10	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{231}(52,\cdot)$	231.ba	30	no	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{231}(53,\cdot)$	231.z	30	yes	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{231}(58,\cdot)$	231.y	15	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{231}(59,\cdot)$	231.bc	30	yes	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{231}(61,\cdot)$	231.ba	30	no	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{231}(62,\cdot)$	231.r	10	yes	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$231$
Structure	\(C_{2}\times C_{2}\times C_{30}\)
Order	$120$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\(\chi_{231}(1,\cdot)\)	231.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{231}(2,\cdot)\)	231.be	30	yes	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{231}(4,\cdot)\)	231.y	15	no	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{231}(5,\cdot)\)	231.bc	30	yes	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{231}(8,\cdot)\)	231.s	10	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{231}(10,\cdot)\)	231.p	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{231}(13,\cdot)\)	231.w	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{231}(16,\cdot)\)	231.y	15	no	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{231}(17,\cdot)\)	231.bf	30	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{231}(19,\cdot)\)	231.ba	30	no	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{231}(20,\cdot)\)	231.u	10	yes	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{231}(23,\cdot)\)	231.q	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)
\(\chi_{231}(25,\cdot)\)	231.y	15	no	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{231}(26,\cdot)\)	231.bc	30	yes	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{231}(29,\cdot)\)	231.s	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{231}(31,\cdot)\)	231.bd	30	no	\(-1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{231}(32,\cdot)\)	231.l	6	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)
\(\chi_{231}(34,\cdot)\)	231.f	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)
\(\chi_{231}(37,\cdot)\)	231.y	15	no	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{231}(38,\cdot)\)	231.bc	30	yes	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{231}(40,\cdot)\)	231.ba	30	no	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{231}(41,\cdot)\)	231.r	10	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{231}(43,\cdot)\)	231.d	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{231}(46,\cdot)\)	231.bb	30	no	\(-1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{231}(47,\cdot)\)	231.bc	30	yes	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{231}(50,\cdot)\)	231.s	10	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{231}(52,\cdot)\)	231.ba	30	no	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{231}(53,\cdot)\)	231.z	30	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{231}(58,\cdot)\)	231.y	15	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{231}(59,\cdot)\)	231.bc	30	yes	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{231}(61,\cdot)\)	231.ba	30	no	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{231}(62,\cdot)\)	231.r	10	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)

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L-functions

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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.