LMFDB - Group of Dirichlet characters of modulus 764

Show commands: PariGP / SageMath

sage: H = DirichletGroup(764)

pari: g = idealstar(,764,2)

Character group

sage: G.order() pari: g.no
Order	=	380
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{190}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{764}(383,\cdot)$, $\chi_{764}(401,\cdot)$

First 32 of 380 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{764}(1,\cdot)$	764.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{764}(3,\cdot)$	764.o	190	yes	$-1$	$1$	$e\left(\frac{61}{190}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{61}{95}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{36}{95}\right)$	$e\left(\frac{161}{190}\right)$	$e\left(\frac{79}{95}\right)$	$e\left(\frac{21}{190}\right)$	$e\left(\frac{21}{95}\right)$
$\chi_{764}(5,\cdot)$	764.i	19	no	$1$	$1$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{3}{19}\right)$	$1$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{10}{19}\right)$
$\chi_{764}(7,\cdot)$	764.g	10	yes	$1$	$1$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{764}(9,\cdot)$	764.m	95	no	$1$	$1$	$e\left(\frac{61}{95}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{27}{95}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{72}{95}\right)$	$e\left(\frac{66}{95}\right)$	$e\left(\frac{63}{95}\right)$	$e\left(\frac{21}{95}\right)$	$e\left(\frac{42}{95}\right)$
$\chi_{764}(11,\cdot)$	764.l	38	yes	$1$	$1$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{7}{19}\right)$	$1$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{15}{38}\right)$
$\chi_{764}(13,\cdot)$	764.m	95	no	$1$	$1$	$e\left(\frac{36}{95}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{72}{95}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{2}{95}\right)$	$e\left(\frac{81}{95}\right)$	$e\left(\frac{73}{95}\right)$	$e\left(\frac{56}{95}\right)$	$e\left(\frac{17}{95}\right)$
$\chi_{764}(15,\cdot)$	764.o	190	yes	$-1$	$1$	$e\left(\frac{161}{190}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{66}{95}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{81}{95}\right)$	$e\left(\frac{101}{190}\right)$	$e\left(\frac{59}{95}\right)$	$e\left(\frac{71}{190}\right)$	$e\left(\frac{71}{95}\right)$
$\chi_{764}(17,\cdot)$	764.m	95	no	$1$	$1$	$e\left(\frac{79}{95}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{63}{95}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{73}{95}\right)$	$e\left(\frac{59}{95}\right)$	$e\left(\frac{52}{95}\right)$	$e\left(\frac{49}{95}\right)$	$e\left(\frac{3}{95}\right)$
$\chi_{764}(19,\cdot)$	764.n	190	yes	$1$	$1$	$e\left(\frac{21}{190}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{21}{95}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{56}{95}\right)$	$e\left(\frac{71}{190}\right)$	$e\left(\frac{49}{95}\right)$	$e\left(\frac{48}{95}\right)$	$e\left(\frac{97}{190}\right)$
$\chi_{764}(21,\cdot)$	764.p	190	no	$-1$	$1$	$e\left(\frac{21}{95}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{42}{95}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{17}{95}\right)$	$e\left(\frac{71}{95}\right)$	$e\left(\frac{3}{95}\right)$	$e\left(\frac{97}{190}\right)$	$e\left(\frac{99}{190}\right)$
$\chi_{764}(23,\cdot)$	764.o	190	yes	$-1$	$1$	$e\left(\frac{59}{190}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{59}{95}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{94}{95}\right)$	$e\left(\frac{109}{190}\right)$	$e\left(\frac{11}{95}\right)$	$e\left(\frac{39}{190}\right)$	$e\left(\frac{39}{95}\right)$
$\chi_{764}(25,\cdot)$	764.i	19	no	$1$	$1$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{6}{19}\right)$	$1$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{1}{19}\right)$
$\chi_{764}(27,\cdot)$	764.o	190	yes	$-1$	$1$	$e\left(\frac{183}{190}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{88}{95}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{13}{95}\right)$	$e\left(\frac{103}{190}\right)$	$e\left(\frac{47}{95}\right)$	$e\left(\frac{63}{190}\right)$	$e\left(\frac{63}{95}\right)$
$\chi_{764}(29,\cdot)$	764.p	190	no	$-1$	$1$	$e\left(\frac{14}{95}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{28}{95}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{43}{95}\right)$	$e\left(\frac{79}{95}\right)$	$e\left(\frac{2}{95}\right)$	$e\left(\frac{33}{190}\right)$	$e\left(\frac{161}{190}\right)$
$\chi_{764}(31,\cdot)$	764.l	38	yes	$1$	$1$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{1}{19}\right)$	$1$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{13}{38}\right)$
$\chi_{764}(33,\cdot)$	764.p	190	no	$-1$	$1$	$e\left(\frac{68}{95}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{41}{95}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{46}{95}\right)$	$e\left(\frac{58}{95}\right)$	$e\left(\frac{64}{95}\right)$	$e\left(\frac{11}{190}\right)$	$e\left(\frac{117}{190}\right)$
$\chi_{764}(35,\cdot)$	764.n	190	yes	$1$	$1$	$e\left(\frac{81}{190}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{81}{95}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{26}{95}\right)$	$e\left(\frac{111}{190}\right)$	$e\left(\frac{94}{95}\right)$	$e\left(\frac{63}{95}\right)$	$e\left(\frac{157}{190}\right)$
$\chi_{764}(37,\cdot)$	764.j	38	no	$-1$	$1$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{18}{19}\right)$	$-1$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{25}{38}\right)$
$\chi_{764}(39,\cdot)$	764.h	10	yes	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{764}(41,\cdot)$	764.j	38	no	$-1$	$1$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{8}{19}\right)$	$-1$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{9}{38}\right)$
$\chi_{764}(43,\cdot)$	764.o	190	yes	$-1$	$1$	$e\left(\frac{73}{190}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{73}{95}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{68}{95}\right)$	$e\left(\frac{93}{190}\right)$	$e\left(\frac{12}{95}\right)$	$e\left(\frac{103}{190}\right)$	$e\left(\frac{8}{95}\right)$
$\chi_{764}(45,\cdot)$	764.m	95	no	$1$	$1$	$e\left(\frac{16}{95}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{32}{95}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{22}{95}\right)$	$e\left(\frac{36}{95}\right)$	$e\left(\frac{43}{95}\right)$	$e\left(\frac{46}{95}\right)$	$e\left(\frac{92}{95}\right)$
$\chi_{764}(47,\cdot)$	764.n	190	yes	$1$	$1$	$e\left(\frac{113}{190}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{18}{95}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{48}{95}\right)$	$e\left(\frac{183}{190}\right)$	$e\left(\frac{42}{95}\right)$	$e\left(\frac{14}{95}\right)$	$e\left(\frac{151}{190}\right)$
$\chi_{764}(49,\cdot)$	764.e	5	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{764}(51,\cdot)$	764.o	190	yes	$-1$	$1$	$e\left(\frac{29}{190}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{95}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{14}{95}\right)$	$e\left(\frac{89}{190}\right)$	$e\left(\frac{36}{95}\right)$	$e\left(\frac{119}{190}\right)$	$e\left(\frac{24}{95}\right)$
$\chi_{764}(53,\cdot)$	764.p	190	no	$-1$	$1$	$e\left(\frac{47}{95}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{94}{95}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{29}{95}\right)$	$e\left(\frac{82}{95}\right)$	$e\left(\frac{61}{95}\right)$	$e\left(\frac{9}{190}\right)$	$e\left(\frac{113}{190}\right)$
$\chi_{764}(55,\cdot)$	764.l	38	yes	$1$	$1$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{10}{19}\right)$	$1$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{35}{38}\right)$
$\chi_{764}(57,\cdot)$	764.p	190	no	$-1$	$1$	$e\left(\frac{41}{95}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{82}{95}\right)$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{92}{95}\right)$	$e\left(\frac{21}{95}\right)$	$e\left(\frac{33}{95}\right)$	$e\left(\frac{117}{190}\right)$	$e\left(\frac{139}{190}\right)$
$\chi_{764}(59,\cdot)$	764.o	190	yes	$-1$	$1$	$e\left(\frac{179}{190}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{84}{95}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{34}{95}\right)$	$e\left(\frac{189}{190}\right)$	$e\left(\frac{6}{95}\right)$	$e\left(\frac{99}{190}\right)$	$e\left(\frac{4}{95}\right)$
$\chi_{764}(61,\cdot)$	764.p	190	no	$-1$	$1$	$e\left(\frac{73}{95}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{51}{95}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{41}{95}\right)$	$e\left(\frac{93}{95}\right)$	$e\left(\frac{24}{95}\right)$	$e\left(\frac{111}{190}\right)$	$e\left(\frac{127}{190}\right)$
$\chi_{764}(63,\cdot)$	764.n	190	yes	$1$	$1$	$e\left(\frac{103}{190}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{95}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{53}{95}\right)$	$e\left(\frac{113}{190}\right)$	$e\left(\frac{82}{95}\right)$	$e\left(\frac{59}{95}\right)$	$e\left(\frac{141}{190}\right)$

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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	$764$
Structure	\(C_{2}\times C_{190}\)
Order	$380$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{764}(1,\cdot)\)	764.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{764}(3,\cdot)\)	764.o	190	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{190}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{61}{95}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{36}{95}\right)\)	\(e\left(\frac{161}{190}\right)\)	\(e\left(\frac{79}{95}\right)\)	\(e\left(\frac{21}{190}\right)\)	\(e\left(\frac{21}{95}\right)\)
\(\chi_{764}(5,\cdot)\)	764.i	19	no	\(1\)	\(1\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(1\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)
\(\chi_{764}(7,\cdot)\)	764.g	10	yes	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{764}(9,\cdot)\)	764.m	95	no	\(1\)	\(1\)	\(e\left(\frac{61}{95}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{27}{95}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{72}{95}\right)\)	\(e\left(\frac{66}{95}\right)\)	\(e\left(\frac{63}{95}\right)\)	\(e\left(\frac{21}{95}\right)\)	\(e\left(\frac{42}{95}\right)\)
\(\chi_{764}(11,\cdot)\)	764.l	38	yes	\(1\)	\(1\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(1\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{15}{38}\right)\)
\(\chi_{764}(13,\cdot)\)	764.m	95	no	\(1\)	\(1\)	\(e\left(\frac{36}{95}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{72}{95}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{2}{95}\right)\)	\(e\left(\frac{81}{95}\right)\)	\(e\left(\frac{73}{95}\right)\)	\(e\left(\frac{56}{95}\right)\)	\(e\left(\frac{17}{95}\right)\)
\(\chi_{764}(15,\cdot)\)	764.o	190	yes	\(-1\)	\(1\)	\(e\left(\frac{161}{190}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{66}{95}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{81}{95}\right)\)	\(e\left(\frac{101}{190}\right)\)	\(e\left(\frac{59}{95}\right)\)	\(e\left(\frac{71}{190}\right)\)	\(e\left(\frac{71}{95}\right)\)
\(\chi_{764}(17,\cdot)\)	764.m	95	no	\(1\)	\(1\)	\(e\left(\frac{79}{95}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{63}{95}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{73}{95}\right)\)	\(e\left(\frac{59}{95}\right)\)	\(e\left(\frac{52}{95}\right)\)	\(e\left(\frac{49}{95}\right)\)	\(e\left(\frac{3}{95}\right)\)
\(\chi_{764}(19,\cdot)\)	764.n	190	yes	\(1\)	\(1\)	\(e\left(\frac{21}{190}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{21}{95}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{56}{95}\right)\)	\(e\left(\frac{71}{190}\right)\)	\(e\left(\frac{49}{95}\right)\)	\(e\left(\frac{48}{95}\right)\)	\(e\left(\frac{97}{190}\right)\)
\(\chi_{764}(21,\cdot)\)	764.p	190	no	\(-1\)	\(1\)	\(e\left(\frac{21}{95}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{42}{95}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{17}{95}\right)\)	\(e\left(\frac{71}{95}\right)\)	\(e\left(\frac{3}{95}\right)\)	\(e\left(\frac{97}{190}\right)\)	\(e\left(\frac{99}{190}\right)\)
\(\chi_{764}(23,\cdot)\)	764.o	190	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{190}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{59}{95}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{94}{95}\right)\)	\(e\left(\frac{109}{190}\right)\)	\(e\left(\frac{11}{95}\right)\)	\(e\left(\frac{39}{190}\right)\)	\(e\left(\frac{39}{95}\right)\)
\(\chi_{764}(25,\cdot)\)	764.i	19	no	\(1\)	\(1\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(1\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{1}{19}\right)\)
\(\chi_{764}(27,\cdot)\)	764.o	190	yes	\(-1\)	\(1\)	\(e\left(\frac{183}{190}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{88}{95}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{13}{95}\right)\)	\(e\left(\frac{103}{190}\right)\)	\(e\left(\frac{47}{95}\right)\)	\(e\left(\frac{63}{190}\right)\)	\(e\left(\frac{63}{95}\right)\)
\(\chi_{764}(29,\cdot)\)	764.p	190	no	\(-1\)	\(1\)	\(e\left(\frac{14}{95}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{28}{95}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{43}{95}\right)\)	\(e\left(\frac{79}{95}\right)\)	\(e\left(\frac{2}{95}\right)\)	\(e\left(\frac{33}{190}\right)\)	\(e\left(\frac{161}{190}\right)\)
\(\chi_{764}(31,\cdot)\)	764.l	38	yes	\(1\)	\(1\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(1\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{13}{38}\right)\)
\(\chi_{764}(33,\cdot)\)	764.p	190	no	\(-1\)	\(1\)	\(e\left(\frac{68}{95}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{41}{95}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{46}{95}\right)\)	\(e\left(\frac{58}{95}\right)\)	\(e\left(\frac{64}{95}\right)\)	\(e\left(\frac{11}{190}\right)\)	\(e\left(\frac{117}{190}\right)\)
\(\chi_{764}(35,\cdot)\)	764.n	190	yes	\(1\)	\(1\)	\(e\left(\frac{81}{190}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{81}{95}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{26}{95}\right)\)	\(e\left(\frac{111}{190}\right)\)	\(e\left(\frac{94}{95}\right)\)	\(e\left(\frac{63}{95}\right)\)	\(e\left(\frac{157}{190}\right)\)
\(\chi_{764}(37,\cdot)\)	764.j	38	no	\(-1\)	\(1\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(-1\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{25}{38}\right)\)
\(\chi_{764}(39,\cdot)\)	764.h	10	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{764}(41,\cdot)\)	764.j	38	no	\(-1\)	\(1\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(-1\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{9}{38}\right)\)
\(\chi_{764}(43,\cdot)\)	764.o	190	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{190}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{73}{95}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{68}{95}\right)\)	\(e\left(\frac{93}{190}\right)\)	\(e\left(\frac{12}{95}\right)\)	\(e\left(\frac{103}{190}\right)\)	\(e\left(\frac{8}{95}\right)\)
\(\chi_{764}(45,\cdot)\)	764.m	95	no	\(1\)	\(1\)	\(e\left(\frac{16}{95}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{32}{95}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{22}{95}\right)\)	\(e\left(\frac{36}{95}\right)\)	\(e\left(\frac{43}{95}\right)\)	\(e\left(\frac{46}{95}\right)\)	\(e\left(\frac{92}{95}\right)\)
\(\chi_{764}(47,\cdot)\)	764.n	190	yes	\(1\)	\(1\)	\(e\left(\frac{113}{190}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{18}{95}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{48}{95}\right)\)	\(e\left(\frac{183}{190}\right)\)	\(e\left(\frac{42}{95}\right)\)	\(e\left(\frac{14}{95}\right)\)	\(e\left(\frac{151}{190}\right)\)
\(\chi_{764}(49,\cdot)\)	764.e	5	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{764}(51,\cdot)\)	764.o	190	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{190}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{29}{95}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{14}{95}\right)\)	\(e\left(\frac{89}{190}\right)\)	\(e\left(\frac{36}{95}\right)\)	\(e\left(\frac{119}{190}\right)\)	\(e\left(\frac{24}{95}\right)\)
\(\chi_{764}(53,\cdot)\)	764.p	190	no	\(-1\)	\(1\)	\(e\left(\frac{47}{95}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{94}{95}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{29}{95}\right)\)	\(e\left(\frac{82}{95}\right)\)	\(e\left(\frac{61}{95}\right)\)	\(e\left(\frac{9}{190}\right)\)	\(e\left(\frac{113}{190}\right)\)
\(\chi_{764}(55,\cdot)\)	764.l	38	yes	\(1\)	\(1\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(1\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{35}{38}\right)\)
\(\chi_{764}(57,\cdot)\)	764.p	190	no	\(-1\)	\(1\)	\(e\left(\frac{41}{95}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{82}{95}\right)\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{92}{95}\right)\)	\(e\left(\frac{21}{95}\right)\)	\(e\left(\frac{33}{95}\right)\)	\(e\left(\frac{117}{190}\right)\)	\(e\left(\frac{139}{190}\right)\)
\(\chi_{764}(59,\cdot)\)	764.o	190	yes	\(-1\)	\(1\)	\(e\left(\frac{179}{190}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{84}{95}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{34}{95}\right)\)	\(e\left(\frac{189}{190}\right)\)	\(e\left(\frac{6}{95}\right)\)	\(e\left(\frac{99}{190}\right)\)	\(e\left(\frac{4}{95}\right)\)
\(\chi_{764}(61,\cdot)\)	764.p	190	no	\(-1\)	\(1\)	\(e\left(\frac{73}{95}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{51}{95}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{41}{95}\right)\)	\(e\left(\frac{93}{95}\right)\)	\(e\left(\frac{24}{95}\right)\)	\(e\left(\frac{111}{190}\right)\)	\(e\left(\frac{127}{190}\right)\)
\(\chi_{764}(63,\cdot)\)	764.n	190	yes	\(1\)	\(1\)	\(e\left(\frac{103}{190}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{95}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{53}{95}\right)\)	\(e\left(\frac{113}{190}\right)\)	\(e\left(\frac{82}{95}\right)\)	\(e\left(\frac{59}{95}\right)\)	\(e\left(\frac{141}{190}\right)\)

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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.