LMFDB - Group of Dirichlet characters of modulus 1584

sage:H = DirichletGroup(1584)

pari:g = idealstar(,1584,2)

Character group

sage:G.order() pari:g.no
Order	=	480
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{60}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{1584}(991,\cdot)$, $\chi_{1584}(1189,\cdot)$, $\chi_{1584}(353,\cdot)$, $\chi_{1584}(145,\cdot)$

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	$-1$	$1$	$5$	$7$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{1584}(1,\cdot)$	1584.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1584}(5,\cdot)$	1584.dn	60	yes	$-1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{1584}(7,\cdot)$	1584.dc	30	no	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1584}(13,\cdot)$	1584.dr	60	yes	$-1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{1584}(17,\cdot)$	1584.cd	10	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1584}(19,\cdot)$	1584.cu	20	no	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{1584}(23,\cdot)$	1584.bg	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$
$\chi_{1584}(25,\cdot)$	1584.da	30	no	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1584}(29,\cdot)$	1584.dp	60	yes	$1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{1584}(31,\cdot)$	1584.dg	30	no	$-1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{1584}(35,\cdot)$	1584.cs	20	no	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{1584}(37,\cdot)$	1584.cr	20	no	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$-1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{1584}(41,\cdot)$	1584.df	30	no	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1584}(43,\cdot)$	1584.cj	12	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$
$\chi_{1584}(47,\cdot)$	1584.cy	30	no	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1584}(49,\cdot)$	1584.cm	15	no	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1584}(53,\cdot)$	1584.ct	20	no	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{20}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{1584}(59,\cdot)$	1584.dq	60	yes	$1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{1584}(61,\cdot)$	1584.dr	60	yes	$-1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1584}(65,\cdot)$	1584.bn	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{1584}(67,\cdot)$	1584.ch	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$
$\chi_{1584}(71,\cdot)$	1584.bu	10	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{1584}(73,\cdot)$	1584.ca	10	no	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1584}(79,\cdot)$	1584.dh	30	no	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1584}(83,\cdot)$	1584.dk	60	yes	$-1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1584}(85,\cdot)$	1584.dr	60	yes	$-1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{1584}(89,\cdot)$	1584.n	2	no	$-1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$
$\chi_{1584}(91,\cdot)$	1584.co	20	no	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{20}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{1584}(95,\cdot)$	1584.cz	30	no	$-1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1584}(97,\cdot)$	1584.cm	15	no	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1584}(101,\cdot)$	1584.dp	60	yes	$1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{1584}(103,\cdot)$	1584.cv	30	no	$-1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{5}\right)$

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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	$1584$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{60}\)
Order	$480$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{1584}(1,\cdot)\)	1584.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1584}(5,\cdot)\)	1584.dn	60	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{1584}(7,\cdot)\)	1584.dc	30	no	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1584}(13,\cdot)\)	1584.dr	60	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{1584}(17,\cdot)\)	1584.cd	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1584}(19,\cdot)\)	1584.cu	20	no	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{1584}(23,\cdot)\)	1584.bg	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)
\(\chi_{1584}(25,\cdot)\)	1584.da	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1584}(29,\cdot)\)	1584.dp	60	yes	\(1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{1584}(31,\cdot)\)	1584.dg	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{1584}(35,\cdot)\)	1584.cs	20	no	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{1584}(37,\cdot)\)	1584.cr	20	no	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{1584}(41,\cdot)\)	1584.df	30	no	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1584}(43,\cdot)\)	1584.cj	12	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)
\(\chi_{1584}(47,\cdot)\)	1584.cy	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1584}(49,\cdot)\)	1584.cm	15	no	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1584}(53,\cdot)\)	1584.ct	20	no	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{1584}(59,\cdot)\)	1584.dq	60	yes	\(1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{1584}(61,\cdot)\)	1584.dr	60	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{1584}(65,\cdot)\)	1584.bn	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{1584}(67,\cdot)\)	1584.ch	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)
\(\chi_{1584}(71,\cdot)\)	1584.bu	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{1584}(73,\cdot)\)	1584.ca	10	no	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1584}(79,\cdot)\)	1584.dh	30	no	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1584}(83,\cdot)\)	1584.dk	60	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{1584}(85,\cdot)\)	1584.dr	60	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{1584}(89,\cdot)\)	1584.n	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1584}(91,\cdot)\)	1584.co	20	no	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{1584}(95,\cdot)\)	1584.cz	30	no	\(-1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1584}(97,\cdot)\)	1584.cm	15	no	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1584}(101,\cdot)\)	1584.dp	60	yes	\(1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{1584}(103,\cdot)\)	1584.cv	30	no	\(-1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)

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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.