LMFDB - Group of Dirichlet characters of modulus 616

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(616)

gp:g = idealstar(,616,2)

magma:G = FullDirichletGroup(616);

Character group

Order	=	240	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{30}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{616}(463,\cdot)$, $\chi_{616}(309,\cdot)$, $\chi_{616}(353,\cdot)$, $\chi_{616}(57,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 240 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	$-1$	$1$	$3$	$5$	$9$	$13$	$15$	$17$	$19$	$23$	$25$	$27$
$\chi_{616}(1,\cdot)$	616.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{616}(3,\cdot)$	616.cb	30	yes	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{616}(5,\cdot)$	616.cj	30	yes	$-1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{616}(9,\cdot)$	616.bw	15	no	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{616}(13,\cdot)$	616.bi	10	yes	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{616}(15,\cdot)$	616.bo	10	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{616}(17,\cdot)$	616.by	30	no	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{616}(19,\cdot)$	616.ce	30	yes	$-1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{616}(23,\cdot)$	616.bb	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{616}(25,\cdot)$	616.bw	15	no	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{616}(27,\cdot)$	616.bp	10	yes	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{616}(29,\cdot)$	616.bt	10	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{616}(31,\cdot)$	616.ch	30	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{616}(37,\cdot)$	616.ca	30	yes	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{616}(39,\cdot)$	616.cd	30	no	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{616}(41,\cdot)$	616.bs	10	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{616}(43,\cdot)$	616.l	2	no	$1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$
$\chi_{616}(45,\cdot)$	616.u	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{616}(47,\cdot)$	616.ch	30	no	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{616}(51,\cdot)$	616.cf	30	yes	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{616}(53,\cdot)$	616.ca	30	yes	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{616}(57,\cdot)$	616.bj	10	no	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{616}(59,\cdot)$	616.cb	30	yes	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{616}(61,\cdot)$	616.cl	30	yes	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{616}(65,\cdot)$	616.t	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{616}(67,\cdot)$	616.v	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{616}(69,\cdot)$	616.bh	10	yes	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{616}(71,\cdot)$	616.bo	10	no	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{616}(73,\cdot)$	616.by	30	no	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{616}(75,\cdot)$	616.cb	30	yes	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{616}(79,\cdot)$	616.cd	30	no	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{616}(81,\cdot)$	616.bw	15	no	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{5}\right)$

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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	$616$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{30}\)
Order	$240$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{616}(1,\cdot)\)	616.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{616}(3,\cdot)\)	616.cb	30	yes	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{616}(5,\cdot)\)	616.cj	30	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{616}(9,\cdot)\)	616.bw	15	no	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{616}(13,\cdot)\)	616.bi	10	yes	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{616}(15,\cdot)\)	616.bo	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{616}(17,\cdot)\)	616.by	30	no	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{616}(19,\cdot)\)	616.ce	30	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{616}(23,\cdot)\)	616.bb	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{616}(25,\cdot)\)	616.bw	15	no	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{616}(27,\cdot)\)	616.bp	10	yes	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{616}(29,\cdot)\)	616.bt	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{616}(31,\cdot)\)	616.ch	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{616}(37,\cdot)\)	616.ca	30	yes	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{616}(39,\cdot)\)	616.cd	30	no	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{616}(41,\cdot)\)	616.bs	10	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{616}(43,\cdot)\)	616.l	2	no	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)
\(\chi_{616}(45,\cdot)\)	616.u	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{616}(47,\cdot)\)	616.ch	30	no	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{616}(51,\cdot)\)	616.cf	30	yes	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{616}(53,\cdot)\)	616.ca	30	yes	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{616}(57,\cdot)\)	616.bj	10	no	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{616}(59,\cdot)\)	616.cb	30	yes	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{616}(61,\cdot)\)	616.cl	30	yes	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{616}(65,\cdot)\)	616.t	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{616}(67,\cdot)\)	616.v	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{616}(69,\cdot)\)	616.bh	10	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{616}(71,\cdot)\)	616.bo	10	no	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{616}(73,\cdot)\)	616.by	30	no	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{616}(75,\cdot)\)	616.cb	30	yes	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{616}(79,\cdot)\)	616.cd	30	no	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{616}(81,\cdot)\)	616.bw	15	no	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)

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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.