LMFDB - Group of Dirichlet characters of modulus 2310

sage:H = DirichletGroup(2310)

pari:g = idealstar(,2310,2)

Character group

sage:G.order() pari:g.no
Order	=	480
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{60}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{2310}(1541,\cdot)$, $\chi_{2310}(1387,\cdot)$, $\chi_{2310}(661,\cdot)$, $\chi_{2310}(211,\cdot)$

First 32 of 480 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	$-1$	$1$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{2310}(1,\cdot)$	2310.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2310}(13,\cdot)$	2310.cs	20	no	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$	$-i$	$e\left(\frac{1}{20}\right)$
$\chi_{2310}(17,\cdot)$	2310.dm	60	no	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{7}{10}\right)$	$i$	$e\left(\frac{47}{60}\right)$
$\chi_{2310}(19,\cdot)$	2310.df	30	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{1}{15}\right)$
$\chi_{2310}(23,\cdot)$	2310.ck	12	no	$1$	$1$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$i$	$e\left(\frac{11}{12}\right)$
$\chi_{2310}(29,\cdot)$	2310.bu	10	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{3}{5}\right)$
$\chi_{2310}(31,\cdot)$	2310.dc	30	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{19}{30}\right)$
$\chi_{2310}(37,\cdot)$	2310.dn	60	no	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{3}{5}\right)$	$-i$	$e\left(\frac{31}{60}\right)$
$\chi_{2310}(41,\cdot)$	2310.bs	10	no	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{2}{5}\right)$
$\chi_{2310}(43,\cdot)$	2310.y	4	no	$1$	$1$	$-i$	$i$	$1$	$i$	$1$	$1$	$-i$	$-1$	$-i$	$-i$
$\chi_{2310}(47,\cdot)$	2310.do	60	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{2}{5}\right)$	$-i$	$e\left(\frac{19}{60}\right)$
$\chi_{2310}(53,\cdot)$	2310.dl	60	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{23}{60}\right)$
$\chi_{2310}(59,\cdot)$	2310.cw	30	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{13}{30}\right)$
$\chi_{2310}(61,\cdot)$	2310.db	30	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{11}{30}\right)$
$\chi_{2310}(67,\cdot)$	2310.ci	12	no	$-1$	$1$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$-i$	$e\left(\frac{7}{12}\right)$
$\chi_{2310}(71,\cdot)$	2310.bt	10	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{7}{10}\right)$
$\chi_{2310}(73,\cdot)$	2310.dk	60	no	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{3}{5}\right)$	$-i$	$e\left(\frac{11}{60}\right)$
$\chi_{2310}(79,\cdot)$	2310.da	30	no	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{29}{30}\right)$
$\chi_{2310}(83,\cdot)$	2310.cu	20	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-i$	$e\left(\frac{19}{20}\right)$
$\chi_{2310}(89,\cdot)$	2310.bn	6	no	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{2310}(97,\cdot)$	2310.cq	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$-i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-i$	$e\left(\frac{11}{20}\right)$
$\chi_{2310}(101,\cdot)$	2310.cx	30	no	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{2}{15}\right)$
$\chi_{2310}(103,\cdot)$	2310.dq	60	no	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{10}\right)$	$i$	$e\left(\frac{31}{60}\right)$
$\chi_{2310}(107,\cdot)$	2310.dr	60	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{2}{5}\right)$	$i$	$e\left(\frac{49}{60}\right)$
$\chi_{2310}(109,\cdot)$	2310.bj	6	no	$-1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{2310}(113,\cdot)$	2310.cr	20	no	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{10}\right)$	$i$	$e\left(\frac{13}{20}\right)$
$\chi_{2310}(127,\cdot)$	2310.cn	20	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$-i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{10}\right)$	$i$	$e\left(\frac{9}{20}\right)$
$\chi_{2310}(131,\cdot)$	2310.bm	6	no	$-1$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{2310}(137,\cdot)$	2310.dl	60	no	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{7}{10}\right)$	$-i$	$e\left(\frac{17}{60}\right)$
$\chi_{2310}(139,\cdot)$	2310.cb	10	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{3}{5}\right)$
$\chi_{2310}(149,\cdot)$	2310.cv	30	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{13}{15}\right)$
$\chi_{2310}(151,\cdot)$	2310.dd	30	no	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{11}{15}\right)$

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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	$2310$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{60}\)
Order	$480$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{2310}(1,\cdot)\)	2310.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2310}(13,\cdot)\)	2310.cs	20	no	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{2310}(17,\cdot)\)	2310.dm	60	no	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(e\left(\frac{47}{60}\right)\)
\(\chi_{2310}(19,\cdot)\)	2310.df	30	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{2310}(23,\cdot)\)	2310.ck	12	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{2310}(29,\cdot)\)	2310.bu	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{2310}(31,\cdot)\)	2310.dc	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{2310}(37,\cdot)\)	2310.dn	60	no	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)	\(e\left(\frac{31}{60}\right)\)
\(\chi_{2310}(41,\cdot)\)	2310.bs	10	no	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{2310}(43,\cdot)\)	2310.y	4	no	\(1\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(i\)	\(1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)
\(\chi_{2310}(47,\cdot)\)	2310.do	60	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-i\)	\(e\left(\frac{19}{60}\right)\)
\(\chi_{2310}(53,\cdot)\)	2310.dl	60	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(i\)	\(e\left(\frac{23}{60}\right)\)
\(\chi_{2310}(59,\cdot)\)	2310.cw	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{2310}(61,\cdot)\)	2310.db	30	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{2310}(67,\cdot)\)	2310.ci	12	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{2310}(71,\cdot)\)	2310.bt	10	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{2310}(73,\cdot)\)	2310.dk	60	no	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)	\(e\left(\frac{11}{60}\right)\)
\(\chi_{2310}(79,\cdot)\)	2310.da	30	no	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{2310}(83,\cdot)\)	2310.cu	20	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{2310}(89,\cdot)\)	2310.bn	6	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2310}(97,\cdot)\)	2310.cq	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{2310}(101,\cdot)\)	2310.cx	30	no	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{2310}(103,\cdot)\)	2310.dq	60	no	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(i\)	\(e\left(\frac{31}{60}\right)\)
\(\chi_{2310}(107,\cdot)\)	2310.dr	60	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(i\)	\(e\left(\frac{49}{60}\right)\)
\(\chi_{2310}(109,\cdot)\)	2310.bj	6	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2310}(113,\cdot)\)	2310.cr	20	no	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(i\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{2310}(127,\cdot)\)	2310.cn	20	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{2310}(131,\cdot)\)	2310.bm	6	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2310}(137,\cdot)\)	2310.dl	60	no	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)	\(e\left(\frac{17}{60}\right)\)
\(\chi_{2310}(139,\cdot)\)	2310.cb	10	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{2310}(149,\cdot)\)	2310.cv	30	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{2310}(151,\cdot)\)	2310.dd	30	no	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(e\left(\frac{11}{15}\right)\)

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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.