LMFDB - Group of Dirichlet characters of modulus 861

Show commands: PariGP / SageMath

sage: H = DirichletGroup(861)

pari: g = idealstar(,861,2)

Character group

sage: G.order() pari: g.no
Order	=	480
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{120}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{861}(575,\cdot)$, $\chi_{861}(493,\cdot)$, $\chi_{861}(211,\cdot)$

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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{861}(1,\cdot)$	861.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{861}(2,\cdot)$	861.ch	60	yes	$-1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{31}{60}\right)$
$\chi_{861}(4,\cdot)$	861.bz	30	no	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{861}(5,\cdot)$	861.cg	60	yes	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{60}\right)$
$\chi_{861}(8,\cdot)$	861.bl	20	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{861}(10,\cdot)$	861.by	30	no	$-1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{861}(11,\cdot)$	861.cl	120	yes	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{1}{120}\right)$
$\chi_{861}(13,\cdot)$	861.cd	40	no	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{19}{40}\right)$
$\chi_{861}(16,\cdot)$	861.bk	15	no	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{861}(17,\cdot)$	861.cj	120	yes	$-1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{31}{120}\right)$
$\chi_{861}(19,\cdot)$	861.ci	120	no	$1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{23}{120}\right)$
$\chi_{861}(20,\cdot)$	861.bm	20	yes	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{861}(22,\cdot)$	861.cb	40	no	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{21}{40}\right)$
$\chi_{861}(23,\cdot)$	861.bu	30	yes	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{861}(25,\cdot)$	861.bz	30	no	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{861}(26,\cdot)$	861.cj	120	yes	$-1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{119}{120}\right)$
$\chi_{861}(29,\cdot)$	861.ca	40	no	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{23}{40}\right)$
$\chi_{861}(31,\cdot)$	861.bx	30	no	$-1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{861}(32,\cdot)$	861.bg	12	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{861}(34,\cdot)$	861.cd	40	no	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{31}{40}\right)$
$\chi_{861}(37,\cdot)$	861.bk	15	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{861}(38,\cdot)$	861.br	24	yes	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{861}(40,\cdot)$	861.q	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{861}(43,\cdot)$	861.bo	20	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{861}(44,\cdot)$	861.bp	24	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{861}(46,\cdot)$	861.ce	60	no	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{17}{60}\right)$
$\chi_{861}(47,\cdot)$	861.cj	120	yes	$-1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{47}{120}\right)$
$\chi_{861}(50,\cdot)$	861.m	4	no	$-1$	$1$	$1$	$1$	$1$	$1$	$1$	$-i$	$i$	$1$	$i$	$-i$
$\chi_{861}(52,\cdot)$	861.ci	120	no	$1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{61}{120}\right)$
$\chi_{861}(53,\cdot)$	861.cl	120	yes	$1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{49}{120}\right)$
$\chi_{861}(55,\cdot)$	861.v	8	no	$1$	$1$	$i$	$-1$	$i$	$-i$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{861}(58,\cdot)$	861.ck	120	no	$-1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{11}{120}\right)$

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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	$861$
Structure	\(C_{2}\times C_{2}\times C_{120}\)
Order	$480$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{861}(1,\cdot)\)	861.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{861}(2,\cdot)\)	861.ch	60	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)
\(\chi_{861}(4,\cdot)\)	861.bz	30	no	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{861}(5,\cdot)\)	861.cg	60	yes	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)
\(\chi_{861}(8,\cdot)\)	861.bl	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{861}(10,\cdot)\)	861.by	30	no	\(-1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{861}(11,\cdot)\)	861.cl	120	yes	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{1}{120}\right)\)
\(\chi_{861}(13,\cdot)\)	861.cd	40	no	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)
\(\chi_{861}(16,\cdot)\)	861.bk	15	no	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{861}(17,\cdot)\)	861.cj	120	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{31}{120}\right)\)
\(\chi_{861}(19,\cdot)\)	861.ci	120	no	\(1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{23}{120}\right)\)
\(\chi_{861}(20,\cdot)\)	861.bm	20	yes	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{861}(22,\cdot)\)	861.cb	40	no	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)
\(\chi_{861}(23,\cdot)\)	861.bu	30	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{861}(25,\cdot)\)	861.bz	30	no	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{861}(26,\cdot)\)	861.cj	120	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{119}{120}\right)\)
\(\chi_{861}(29,\cdot)\)	861.ca	40	no	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)
\(\chi_{861}(31,\cdot)\)	861.bx	30	no	\(-1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{861}(32,\cdot)\)	861.bg	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{861}(34,\cdot)\)	861.cd	40	no	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)
\(\chi_{861}(37,\cdot)\)	861.bk	15	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{861}(38,\cdot)\)	861.br	24	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{861}(40,\cdot)\)	861.q	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{861}(43,\cdot)\)	861.bo	20	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{861}(44,\cdot)\)	861.bp	24	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{861}(46,\cdot)\)	861.ce	60	no	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)
\(\chi_{861}(47,\cdot)\)	861.cj	120	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{47}{120}\right)\)
\(\chi_{861}(50,\cdot)\)	861.m	4	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(i\)	\(-i\)
\(\chi_{861}(52,\cdot)\)	861.ci	120	no	\(1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{61}{120}\right)\)
\(\chi_{861}(53,\cdot)\)	861.cl	120	yes	\(1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{49}{120}\right)\)
\(\chi_{861}(55,\cdot)\)	861.v	8	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(i\)	\(-i\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{861}(58,\cdot)\)	861.ck	120	no	\(-1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{11}{120}\right)\)

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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.