LMFDB - Group of Dirichlet characters of modulus 987

Show commands: PariGP / SageMath

sage: H = DirichletGroup(987)

pari: g = idealstar(,987,2)

Character group

sage: G.order() pari: g.no
Order	=	552
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{138}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{987}(659,\cdot)$, $\chi_{987}(283,\cdot)$, $\chi_{987}(757,\cdot)$

First 32 of 552 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{987}(1,\cdot)$	987.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{987}(2,\cdot)$	987.z	138	yes	$-1$	$1$	$e\left(\frac{29}{138}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{77}{138}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{19}{69}\right)$
$\chi_{987}(4,\cdot)$	987.y	69	no	$1$	$1$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{38}{69}\right)$
$\chi_{987}(5,\cdot)$	987.ba	138	yes	$-1$	$1$	$e\left(\frac{77}{138}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{95}{138}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{10}{69}\right)$
$\chi_{987}(8,\cdot)$	987.x	46	no	$-1$	$1$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{19}{23}\right)$
$\chi_{987}(10,\cdot)$	987.bf	138	no	$1$	$1$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{77}{138}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{107}{138}\right)$	$e\left(\frac{29}{69}\right)$
$\chi_{987}(11,\cdot)$	987.bc	138	yes	$1$	$1$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{77}{138}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{83}{138}\right)$	$e\left(\frac{25}{138}\right)$
$\chi_{987}(13,\cdot)$	987.r	46	no	$1$	$1$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{6}{23}\right)$
$\chi_{987}(16,\cdot)$	987.y	69	no	$1$	$1$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{7}{69}\right)$
$\chi_{987}(17,\cdot)$	987.bb	138	yes	$1$	$1$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{107}{138}\right)$	$e\left(\frac{83}{138}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{67}{138}\right)$
$\chi_{987}(19,\cdot)$	987.bf	138	no	$1$	$1$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{13}{69}\right)$
$\chi_{987}(20,\cdot)$	987.w	46	yes	$-1$	$1$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{16}{23}\right)$
$\chi_{987}(22,\cdot)$	987.t	46	no	$-1$	$1$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{21}{46}\right)$
$\chi_{987}(23,\cdot)$	987.bc	138	yes	$1$	$1$	$e\left(\frac{17}{138}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{55}{138}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{77}{138}\right)$
$\chi_{987}(25,\cdot)$	987.y	69	no	$1$	$1$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{20}{69}\right)$
$\chi_{987}(26,\cdot)$	987.ba	138	yes	$-1$	$1$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{37}{69}\right)$
$\chi_{987}(29,\cdot)$	987.u	46	no	$1$	$1$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{11}{46}\right)$
$\chi_{987}(31,\cdot)$	987.bf	138	no	$1$	$1$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{17}{138}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{29}{138}\right)$	$e\left(\frac{53}{69}\right)$
$\chi_{987}(32,\cdot)$	987.z	138	yes	$-1$	$1$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{109}{138}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{119}{138}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{65}{138}\right)$	$e\left(\frac{26}{69}\right)$
$\chi_{987}(34,\cdot)$	987.s	46	no	$-1$	$1$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{35}{46}\right)$
$\chi_{987}(37,\cdot)$	987.y	69	no	$1$	$1$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{52}{69}\right)$
$\chi_{987}(38,\cdot)$	987.ba	138	yes	$-1$	$1$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{97}{138}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{32}{69}\right)$
$\chi_{987}(40,\cdot)$	987.bf	138	no	$1$	$1$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{97}{138}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{133}{138}\right)$	$e\left(\frac{67}{69}\right)$
$\chi_{987}(41,\cdot)$	987.w	46	yes	$-1$	$1$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{4}{23}\right)$
$\chi_{987}(43,\cdot)$	987.t	46	no	$-1$	$1$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{33}{46}\right)$
$\chi_{987}(44,\cdot)$	987.bc	138	yes	$1$	$1$	$e\left(\frac{137}{138}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{13}{138}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{109}{138}\right)$	$e\left(\frac{101}{138}\right)$
$\chi_{987}(46,\cdot)$	987.l	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{987}(50,\cdot)$	987.x	46	no	$-1$	$1$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{13}{23}\right)$
$\chi_{987}(52,\cdot)$	987.bf	138	no	$1$	$1$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{113}{138}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{56}{69}\right)$
$\chi_{987}(53,\cdot)$	987.z	138	yes	$-1$	$1$	$e\left(\frac{97}{138}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{91}{138}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{131}{138}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{53}{138}\right)$	$e\left(\frac{35}{69}\right)$
$\chi_{987}(55,\cdot)$	987.s	46	no	$-1$	$1$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{15}{46}\right)$
$\chi_{987}(58,\cdot)$	987.bd	138	no	$-1$	$1$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{56}{69}\right)$	$e\left(\frac{113}{138}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{31}{138}\right)$	$e\left(\frac{55}{138}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{71}{138}\right)$

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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	$987$
Structure	\(C_{2}\times C_{2}\times C_{138}\)
Order	$552$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{987}(1,\cdot)\)	987.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{987}(2,\cdot)\)	987.z	138	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{138}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{77}{138}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{19}{69}\right)\)
\(\chi_{987}(4,\cdot)\)	987.y	69	no	\(1\)	\(1\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{38}{69}\right)\)
\(\chi_{987}(5,\cdot)\)	987.ba	138	yes	\(-1\)	\(1\)	\(e\left(\frac{77}{138}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{95}{138}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{10}{69}\right)\)
\(\chi_{987}(8,\cdot)\)	987.x	46	no	\(-1\)	\(1\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{19}{23}\right)\)
\(\chi_{987}(10,\cdot)\)	987.bf	138	no	\(1\)	\(1\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{77}{138}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{107}{138}\right)\)	\(e\left(\frac{29}{69}\right)\)
\(\chi_{987}(11,\cdot)\)	987.bc	138	yes	\(1\)	\(1\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{77}{138}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{83}{138}\right)\)	\(e\left(\frac{25}{138}\right)\)
\(\chi_{987}(13,\cdot)\)	987.r	46	no	\(1\)	\(1\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{6}{23}\right)\)
\(\chi_{987}(16,\cdot)\)	987.y	69	no	\(1\)	\(1\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{7}{69}\right)\)
\(\chi_{987}(17,\cdot)\)	987.bb	138	yes	\(1\)	\(1\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{107}{138}\right)\)	\(e\left(\frac{83}{138}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{67}{138}\right)\)
\(\chi_{987}(19,\cdot)\)	987.bf	138	no	\(1\)	\(1\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{13}{69}\right)\)
\(\chi_{987}(20,\cdot)\)	987.w	46	yes	\(-1\)	\(1\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{16}{23}\right)\)
\(\chi_{987}(22,\cdot)\)	987.t	46	no	\(-1\)	\(1\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{21}{46}\right)\)
\(\chi_{987}(23,\cdot)\)	987.bc	138	yes	\(1\)	\(1\)	\(e\left(\frac{17}{138}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{55}{138}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{77}{138}\right)\)
\(\chi_{987}(25,\cdot)\)	987.y	69	no	\(1\)	\(1\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{20}{69}\right)\)
\(\chi_{987}(26,\cdot)\)	987.ba	138	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{37}{69}\right)\)
\(\chi_{987}(29,\cdot)\)	987.u	46	no	\(1\)	\(1\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{11}{46}\right)\)
\(\chi_{987}(31,\cdot)\)	987.bf	138	no	\(1\)	\(1\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{17}{138}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{29}{138}\right)\)	\(e\left(\frac{53}{69}\right)\)
\(\chi_{987}(32,\cdot)\)	987.z	138	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{109}{138}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{119}{138}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{65}{138}\right)\)	\(e\left(\frac{26}{69}\right)\)
\(\chi_{987}(34,\cdot)\)	987.s	46	no	\(-1\)	\(1\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{35}{46}\right)\)
\(\chi_{987}(37,\cdot)\)	987.y	69	no	\(1\)	\(1\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{52}{69}\right)\)
\(\chi_{987}(38,\cdot)\)	987.ba	138	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{97}{138}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{32}{69}\right)\)
\(\chi_{987}(40,\cdot)\)	987.bf	138	no	\(1\)	\(1\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{97}{138}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{133}{138}\right)\)	\(e\left(\frac{67}{69}\right)\)
\(\chi_{987}(41,\cdot)\)	987.w	46	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)
\(\chi_{987}(43,\cdot)\)	987.t	46	no	\(-1\)	\(1\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)
\(\chi_{987}(44,\cdot)\)	987.bc	138	yes	\(1\)	\(1\)	\(e\left(\frac{137}{138}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{13}{138}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{109}{138}\right)\)	\(e\left(\frac{101}{138}\right)\)
\(\chi_{987}(46,\cdot)\)	987.l	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{987}(50,\cdot)\)	987.x	46	no	\(-1\)	\(1\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{13}{23}\right)\)
\(\chi_{987}(52,\cdot)\)	987.bf	138	no	\(1\)	\(1\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{113}{138}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{56}{69}\right)\)
\(\chi_{987}(53,\cdot)\)	987.z	138	yes	\(-1\)	\(1\)	\(e\left(\frac{97}{138}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{91}{138}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{131}{138}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{53}{138}\right)\)	\(e\left(\frac{35}{69}\right)\)
\(\chi_{987}(55,\cdot)\)	987.s	46	no	\(-1\)	\(1\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{15}{46}\right)\)
\(\chi_{987}(58,\cdot)\)	987.bd	138	no	\(-1\)	\(1\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{56}{69}\right)\)	\(e\left(\frac{113}{138}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{31}{138}\right)\)	\(e\left(\frac{55}{138}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{71}{138}\right)\)

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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.