LMFDB - Group of Dirichlet characters of modulus 2842

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2842)

pari: g = idealstar(,2842,2)

Character group

sage: G.order() pari: g.no
Order	=	1176
sage: H.invariants() pari: g.cyc
Structure	=	$C_{14}\times C_{84}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2842}(1277,\cdot)$, $\chi_{2842}(785,\cdot)$

First 32 of 1176 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{2842}(1,\cdot)$	2842.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2842}(3,\cdot)$	2842.ec	84	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{2842}(5,\cdot)$	2842.dj	42	no	$-1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{2842}(9,\cdot)$	2842.dn	42	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{2842}(11,\cdot)$	2842.dv	84	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{2842}(13,\cdot)$	2842.br	14	no	$-1$	$1$	$1$	$e\left(\frac{13}{14}\right)$	$1$	$-1$	$-1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{2842}(15,\cdot)$	2842.cn	28	no	$-1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{2842}(17,\cdot)$	2842.ea	84	no	$1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{2842}(19,\cdot)$	2842.dx	84	no	$1$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{2842}(23,\cdot)$	2842.bw	21	no	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{2842}(25,\cdot)$	2842.by	21	no	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{2842}(27,\cdot)$	2842.cb	28	no	$1$	$1$	$-i$	$e\left(\frac{6}{7}\right)$	$-1$	$i$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{2842}(31,\cdot)$	2842.dx	84	no	$1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{2842}(33,\cdot)$	2842.cq	42	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{2842}(37,\cdot)$	2842.dt	84	no	$-1$	$1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{1}{14}\right)$	$-i$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{2842}(39,\cdot)$	2842.dv	84	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{2842}(41,\cdot)$	2842.ce	28	no	$1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{28}\right)$	$-i$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{2842}(43,\cdot)$	2842.cm	28	no	$-1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{2842}(45,\cdot)$	2842.cx	42	no	$-1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{14}\right)$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{2842}(47,\cdot)$	2842.ec	84	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{2842}(51,\cdot)$	2842.da	42	no	$1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{2842}(53,\cdot)$	2842.bs	21	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{2842}(55,\cdot)$	2842.ch	28	no	$1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{17}{28}\right)$	$1$	$e\left(\frac{1}{7}\right)$
$\chi_{2842}(57,\cdot)$	2842.bg	14	no	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{13}{14}\right)$	$-1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{2842}(59,\cdot)$	2842.cv	42	no	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{2842}(61,\cdot)$	2842.eb	84	no	$1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{2842}(65,\cdot)$	2842.bw	21	no	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{2842}(67,\cdot)$	2842.dd	42	no	$1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{2842}(69,\cdot)$	2842.cf	28	no	$1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{2842}(71,\cdot)$	2842.be	14	no	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{7}\right)$	$-1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{2842}(73,\cdot)$	2842.eb	84	no	$1$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{2842}(75,\cdot)$	2842.ea	84	no	$1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{10}{21}\right)$

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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 $\F_{q}$

Modulus	$2842$
Structure	\(C_{14}\times C_{84}\)
Order	$1176$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{2842}(1,\cdot)\)	2842.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2842}(3,\cdot)\)	2842.ec	84	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{2842}(5,\cdot)\)	2842.dj	42	no	\(-1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{2842}(9,\cdot)\)	2842.dn	42	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{2842}(11,\cdot)\)	2842.dv	84	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{2842}(13,\cdot)\)	2842.br	14	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(1\)	\(-1\)	\(-1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{2842}(15,\cdot)\)	2842.cn	28	no	\(-1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{2842}(17,\cdot)\)	2842.ea	84	no	\(1\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{2842}(19,\cdot)\)	2842.dx	84	no	\(1\)	\(1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{2842}(23,\cdot)\)	2842.bw	21	no	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{2842}(25,\cdot)\)	2842.by	21	no	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{2842}(27,\cdot)\)	2842.cb	28	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{6}{7}\right)\)	\(-1\)	\(i\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{2842}(31,\cdot)\)	2842.dx	84	no	\(1\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{2842}(33,\cdot)\)	2842.cq	42	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{2842}(37,\cdot)\)	2842.dt	84	no	\(-1\)	\(1\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-i\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{2842}(39,\cdot)\)	2842.dv	84	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{2842}(41,\cdot)\)	2842.ce	28	no	\(1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(-i\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{2842}(43,\cdot)\)	2842.cm	28	no	\(-1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{2842}(45,\cdot)\)	2842.cx	42	no	\(-1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{2842}(47,\cdot)\)	2842.ec	84	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{2842}(51,\cdot)\)	2842.da	42	no	\(1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{2842}(53,\cdot)\)	2842.bs	21	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{2842}(55,\cdot)\)	2842.ch	28	no	\(1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(1\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{2842}(57,\cdot)\)	2842.bg	14	no	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{2842}(59,\cdot)\)	2842.cv	42	no	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{2842}(61,\cdot)\)	2842.eb	84	no	\(1\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{2842}(65,\cdot)\)	2842.bw	21	no	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{2842}(67,\cdot)\)	2842.dd	42	no	\(1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{2842}(69,\cdot)\)	2842.cf	28	no	\(1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{2842}(71,\cdot)\)	2842.be	14	no	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{2842}(73,\cdot)\)	2842.eb	84	no	\(1\)	\(1\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{2842}(75,\cdot)\)	2842.ea	84	no	\(1\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)

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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.