LMFDB - Group of Dirichlet characters of modulus 882

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(882)

gp:g = idealstar(,882,2)

magma:G = FullDirichletGroup(882);

Character group

Order	=	252	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{6}\times C_{42}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{882}(785,\cdot)$, $\chi_{882}(199,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 252 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	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{882}(1,\cdot)$	882.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{882}(5,\cdot)$	882.bk	42	no	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{11}{42}\right)$	$-1$	$e\left(\frac{2}{21}\right)$
$\chi_{882}(11,\cdot)$	882.be	42	no	$-1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{13}{42}\right)$	$1$	$e\left(\frac{10}{21}\right)$
$\chi_{882}(13,\cdot)$	882.bh	42	no	$-1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{9}{14}\right)$	$-1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{882}(17,\cdot)$	882.bl	42	no	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{882}(19,\cdot)$	882.n	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{882}(23,\cdot)$	882.be	42	no	$-1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{42}\right)$	$1$	$e\left(\frac{20}{21}\right)$
$\chi_{882}(25,\cdot)$	882.bb	21	no	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{11}{21}\right)$	$1$	$e\left(\frac{4}{21}\right)$
$\chi_{882}(29,\cdot)$	882.bf	42	no	$-1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{3}{14}\right)$	$1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{882}(31,\cdot)$	882.j	6	no	$-1$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{882}(37,\cdot)$	882.z	21	no	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{882}(41,\cdot)$	882.bj	42	no	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{3}{7}\right)$	$-1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{882}(43,\cdot)$	882.ba	21	no	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{4}{7}\right)$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{882}(47,\cdot)$	882.bc	42	no	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{882}(53,\cdot)$	882.bd	42	no	$-1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{882}(55,\cdot)$	882.w	14	no	$-1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{14}\right)$	$-1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$-1$	$e\left(\frac{4}{7}\right)$
$\chi_{882}(59,\cdot)$	882.bc	42	no	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{882}(61,\cdot)$	882.bm	42	no	$-1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{882}(65,\cdot)$	882.bn	42	no	$-1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{882}(67,\cdot)$	882.h	3	no	$1$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{882}(71,\cdot)$	882.x	14	no	$-1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{14}\right)$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$	$1$	$e\left(\frac{2}{7}\right)$
$\chi_{882}(73,\cdot)$	882.bi	42	no	$-1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{882}(79,\cdot)$	882.h	3	no	$1$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{882}(83,\cdot)$	882.bj	42	no	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{6}{7}\right)$	$-1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{882}(85,\cdot)$	882.ba	21	no	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{7}\right)$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{882}(89,\cdot)$	882.bl	42	no	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{882}(95,\cdot)$	882.bn	42	no	$-1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{882}(97,\cdot)$	882.o	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$
$\chi_{882}(101,\cdot)$	882.bk	42	no	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{25}{42}\right)$	$-1$	$e\left(\frac{16}{21}\right)$
$\chi_{882}(103,\cdot)$	882.bg	42	no	$-1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{16}{21}\right)$	$-1$	$e\left(\frac{2}{21}\right)$
$\chi_{882}(107,\cdot)$	882.bd	42	no	$-1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{882}(109,\cdot)$	882.z	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 $\F_{q}$
Belyi maps

Modulus	$882$
Structure	\(C_{6}\times C_{42}\)
Order	$252$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)
\(\chi_{882}(1,\cdot)\)	882.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{882}(5,\cdot)\)	882.bk	42	no	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(-1\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{882}(11,\cdot)\)	882.be	42	no	\(-1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(1\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{882}(13,\cdot)\)	882.bh	42	no	\(-1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{882}(17,\cdot)\)	882.bl	42	no	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{882}(19,\cdot)\)	882.n	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{882}(23,\cdot)\)	882.be	42	no	\(-1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(1\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{882}(25,\cdot)\)	882.bb	21	no	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(1\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{882}(29,\cdot)\)	882.bf	42	no	\(-1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{882}(31,\cdot)\)	882.j	6	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{882}(37,\cdot)\)	882.z	21	no	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{882}(41,\cdot)\)	882.bj	42	no	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{882}(43,\cdot)\)	882.ba	21	no	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{882}(47,\cdot)\)	882.bc	42	no	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{882}(53,\cdot)\)	882.bd	42	no	\(-1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{882}(55,\cdot)\)	882.w	14	no	\(-1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(-1\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{882}(59,\cdot)\)	882.bc	42	no	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{882}(61,\cdot)\)	882.bm	42	no	\(-1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{882}(65,\cdot)\)	882.bn	42	no	\(-1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{882}(67,\cdot)\)	882.h	3	no	\(1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{882}(71,\cdot)\)	882.x	14	no	\(-1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(1\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{882}(73,\cdot)\)	882.bi	42	no	\(-1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{882}(79,\cdot)\)	882.h	3	no	\(1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{882}(83,\cdot)\)	882.bj	42	no	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(-1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{882}(85,\cdot)\)	882.ba	21	no	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{882}(89,\cdot)\)	882.bl	42	no	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{882}(95,\cdot)\)	882.bn	42	no	\(-1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{882}(97,\cdot)\)	882.o	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)
\(\chi_{882}(101,\cdot)\)	882.bk	42	no	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(-1\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{882}(103,\cdot)\)	882.bg	42	no	\(-1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(-1\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{882}(107,\cdot)\)	882.bd	42	no	\(-1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{882}(109,\cdot)\)	882.z	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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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.