LMFDB - Group of Dirichlet characters of modulus 2352

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2352)

pari: g = idealstar(,2352,2)

Character group

sage: G.order() pari: g.no
Order	=	672
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{84}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2352}(1471,\cdot)$, $\chi_{2352}(1765,\cdot)$, $\chi_{2352}(785,\cdot)$, $\chi_{2352}(2257,\cdot)$

First 32 of 672 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	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{2352}(1,\cdot)$	2352.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2352}(5,\cdot)$	2352.dr	84	yes	$1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{84}\right)$
$\chi_{2352}(11,\cdot)$	2352.dl	84	yes	$1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{61}{84}\right)$
$\chi_{2352}(13,\cdot)$	2352.cu	28	no	$-1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{9}{14}\right)$	$-i$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{28}\right)$	$-1$	$e\left(\frac{25}{28}\right)$
$\chi_{2352}(17,\cdot)$	2352.dg	42	no	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{2352}(19,\cdot)$	2352.bt	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{2352}(23,\cdot)$	2352.df	42	no	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{42}\right)$
$\chi_{2352}(25,\cdot)$	2352.cy	42	no	$1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{42}\right)$
$\chi_{2352}(29,\cdot)$	2352.cs	28	yes	$-1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{3}{14}\right)$	$i$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{28}\right)$	$1$	$e\left(\frac{13}{28}\right)$
$\chi_{2352}(31,\cdot)$	2352.bl	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2352}(37,\cdot)$	2352.dp	84	no	$1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{53}{84}\right)$
$\chi_{2352}(41,\cdot)$	2352.ce	14	no	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$-1$	$e\left(\frac{13}{14}\right)$
$\chi_{2352}(43,\cdot)$	2352.co	28	no	$-1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{4}{7}\right)$	$i$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{9}{28}\right)$	$-1$	$e\left(\frac{23}{28}\right)$
$\chi_{2352}(47,\cdot)$	2352.dj	42	no	$-1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{2352}(53,\cdot)$	2352.dm	84	yes	$-1$	$1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{2352}(55,\cdot)$	2352.bx	14	no	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{14}\right)$	$-1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$	$1$	$e\left(\frac{1}{14}\right)$
$\chi_{2352}(59,\cdot)$	2352.do	84	yes	$-1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{2352}(61,\cdot)$	2352.dk	84	no	$-1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{2352}(65,\cdot)$	2352.cv	42	no	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{2352}(67,\cdot)$	2352.bq	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{2352}(71,\cdot)$	2352.cd	14	no	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{14}\right)$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$-1$	$e\left(\frac{11}{14}\right)$
$\chi_{2352}(73,\cdot)$	2352.dd	42	no	$-1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{42}\right)$
$\chi_{2352}(79,\cdot)$	2352.be	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{2352}(83,\cdot)$	2352.cq	28	yes	$-1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{6}{7}\right)$	$i$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{17}{28}\right)$	$1$	$e\left(\frac{17}{28}\right)$
$\chi_{2352}(85,\cdot)$	2352.cp	28	no	$1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{7}\right)$	$-i$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{25}{28}\right)$	$1$	$e\left(\frac{11}{28}\right)$
$\chi_{2352}(89,\cdot)$	2352.da	42	no	$1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{42}\right)$
$\chi_{2352}(95,\cdot)$	2352.cz	42	no	$1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{2352}(97,\cdot)$	2352.f	2	no	$-1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$-1$	$1$
$\chi_{2352}(101,\cdot)$	2352.dr	84	yes	$1$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{2352}(103,\cdot)$	2352.dh	42	no	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{42}\right)$
$\chi_{2352}(107,\cdot)$	2352.dl	84	yes	$1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{2352}(109,\cdot)$	2352.dp	84	no	$1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{84}\right)$

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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	$2352$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{84}\)
Order	$672$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)
\(\chi_{2352}(1,\cdot)\)	2352.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2352}(5,\cdot)\)	2352.dr	84	yes	\(1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{84}\right)\)
\(\chi_{2352}(11,\cdot)\)	2352.dl	84	yes	\(1\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{61}{84}\right)\)
\(\chi_{2352}(13,\cdot)\)	2352.cu	28	no	\(-1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-i\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(-1\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{2352}(17,\cdot)\)	2352.dg	42	no	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{2352}(19,\cdot)\)	2352.bt	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{2352}(23,\cdot)\)	2352.df	42	no	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{42}\right)\)
\(\chi_{2352}(25,\cdot)\)	2352.cy	42	no	\(1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{42}\right)\)
\(\chi_{2352}(29,\cdot)\)	2352.cs	28	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(i\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(1\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{2352}(31,\cdot)\)	2352.bl	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2352}(37,\cdot)\)	2352.dp	84	no	\(1\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{53}{84}\right)\)
\(\chi_{2352}(41,\cdot)\)	2352.ce	14	no	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{2352}(43,\cdot)\)	2352.co	28	no	\(-1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(i\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(-1\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{2352}(47,\cdot)\)	2352.dj	42	no	\(-1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{2352}(53,\cdot)\)	2352.dm	84	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{2352}(55,\cdot)\)	2352.bx	14	no	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(1\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{2352}(59,\cdot)\)	2352.do	84	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{2352}(61,\cdot)\)	2352.dk	84	no	\(-1\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{84}\right)\)
\(\chi_{2352}(65,\cdot)\)	2352.cv	42	no	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{2352}(67,\cdot)\)	2352.bq	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{2352}(71,\cdot)\)	2352.cd	14	no	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(-1\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{2352}(73,\cdot)\)	2352.dd	42	no	\(-1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{29}{42}\right)\)
\(\chi_{2352}(79,\cdot)\)	2352.be	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2352}(83,\cdot)\)	2352.cq	28	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(i\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(1\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{2352}(85,\cdot)\)	2352.cp	28	no	\(1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(-i\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(1\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{2352}(89,\cdot)\)	2352.da	42	no	\(1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{42}\right)\)
\(\chi_{2352}(95,\cdot)\)	2352.cz	42	no	\(1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{2352}(97,\cdot)\)	2352.f	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{2352}(101,\cdot)\)	2352.dr	84	yes	\(1\)	\(1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{84}\right)\)
\(\chi_{2352}(103,\cdot)\)	2352.dh	42	no	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{25}{42}\right)\)
\(\chi_{2352}(107,\cdot)\)	2352.dl	84	yes	\(1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{2352}(109,\cdot)\)	2352.dp	84	no	\(1\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{84}\right)\)

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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.