LMFDB - Group of Dirichlet characters of modulus 1575

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1575)

pari: g = idealstar(,1575,2)

Character group

sage: G.order() pari: g.no
Order	=	720
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{60}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1575}(1226,\cdot)$, $\chi_{1575}(127,\cdot)$, $\chi_{1575}(451,\cdot)$

First 32 of 720 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	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$17$	$19$	$22$	$23$
$\chi_{1575}(1,\cdot)$	1575.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1575}(2,\cdot)$	1575.ek	60	yes	$1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{1575}(4,\cdot)$	1575.db	30	yes	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{1575}(8,\cdot)$	1575.cx	20	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1575}(11,\cdot)$	1575.dx	30	yes	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{1575}(13,\cdot)$	1575.eg	60	yes	$1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{60}\right)$
$\chi_{1575}(16,\cdot)$	1575.cr	15	yes	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1575}(17,\cdot)$	1575.ee	60	no	$-1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{59}{60}\right)$
$\chi_{1575}(19,\cdot)$	1575.dh	30	no	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{1575}(22,\cdot)$	1575.ej	60	no	$-1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{60}\right)$
$\chi_{1575}(23,\cdot)$	1575.em	60	yes	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{53}{60}\right)$
$\chi_{1575}(26,\cdot)$	1575.bk	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{1575}(29,\cdot)$	1575.dp	30	no	$-1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{1575}(31,\cdot)$	1575.dn	30	yes	$-1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1575}(32,\cdot)$	1575.cf	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$i$
$\chi_{1575}(34,\cdot)$	1575.dj	30	yes	$-1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{1575}(37,\cdot)$	1575.eh	60	no	$-1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{37}{60}\right)$
$\chi_{1575}(38,\cdot)$	1575.en	60	yes	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{37}{60}\right)$
$\chi_{1575}(41,\cdot)$	1575.de	30	yes	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{1575}(43,\cdot)$	1575.cg	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{1575}(44,\cdot)$	1575.dr	30	no	$-1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{1575}(46,\cdot)$	1575.cs	15	no	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{1575}(47,\cdot)$	1575.el	60	yes	$-1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{1575}(52,\cdot)$	1575.ep	60	yes	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{13}{60}\right)$
$\chi_{1575}(53,\cdot)$	1575.ed	60	no	$1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{41}{60}\right)$
$\chi_{1575}(58,\cdot)$	1575.eo	60	yes	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{59}{60}\right)$
$\chi_{1575}(59,\cdot)$	1575.dv	30	yes	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1575}(61,\cdot)$	1575.dn	30	yes	$-1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1575}(62,\cdot)$	1575.cw	20	no	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{1575}(64,\cdot)$	1575.bx	10	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1575}(67,\cdot)$	1575.ea	60	yes	$-1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{1575}(68,\cdot)$	1575.cc	12	no	$-1$	$1$	$i$	$-1$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$

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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	$1575$
Structure	\(C_{2}\times C_{6}\times C_{60}\)
Order	$720$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)	\(22\)	\(23\)
\(\chi_{1575}(1,\cdot)\)	1575.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1575}(2,\cdot)\)	1575.ek	60	yes	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{1575}(4,\cdot)\)	1575.db	30	yes	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{1575}(8,\cdot)\)	1575.cx	20	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{1575}(11,\cdot)\)	1575.dx	30	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{1575}(13,\cdot)\)	1575.eg	60	yes	\(1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)
\(\chi_{1575}(16,\cdot)\)	1575.cr	15	yes	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1575}(17,\cdot)\)	1575.ee	60	no	\(-1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{59}{60}\right)\)
\(\chi_{1575}(19,\cdot)\)	1575.dh	30	no	\(-1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{1575}(22,\cdot)\)	1575.ej	60	no	\(-1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)
\(\chi_{1575}(23,\cdot)\)	1575.em	60	yes	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)
\(\chi_{1575}(26,\cdot)\)	1575.bk	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1575}(29,\cdot)\)	1575.dp	30	no	\(-1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{1575}(31,\cdot)\)	1575.dn	30	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1575}(32,\cdot)\)	1575.cf	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)
\(\chi_{1575}(34,\cdot)\)	1575.dj	30	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{1575}(37,\cdot)\)	1575.eh	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{37}{60}\right)\)
\(\chi_{1575}(38,\cdot)\)	1575.en	60	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)
\(\chi_{1575}(41,\cdot)\)	1575.de	30	yes	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{1575}(43,\cdot)\)	1575.cg	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1575}(44,\cdot)\)	1575.dr	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{1575}(46,\cdot)\)	1575.cs	15	no	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{1575}(47,\cdot)\)	1575.el	60	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{1575}(52,\cdot)\)	1575.ep	60	yes	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)
\(\chi_{1575}(53,\cdot)\)	1575.ed	60	no	\(1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{41}{60}\right)\)
\(\chi_{1575}(58,\cdot)\)	1575.eo	60	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)
\(\chi_{1575}(59,\cdot)\)	1575.dv	30	yes	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1575}(61,\cdot)\)	1575.dn	30	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1575}(62,\cdot)\)	1575.cw	20	no	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{1575}(64,\cdot)\)	1575.bx	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1575}(67,\cdot)\)	1575.ea	60	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{1575}(68,\cdot)\)	1575.cc	12	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)

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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.