LMFDB - Group of Dirichlet characters of modulus 1316

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1316)

pari: g = idealstar(,1316,2)

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	=	$\chi_{1316}(659,\cdot)$, $\chi_{1316}(941,\cdot)$, $\chi_{1316}(757,\cdot)$

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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{1316}(1,\cdot)$	1316.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1316}(3,\cdot)$	1316.bd	138	yes	$1$	$1$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{37}{138}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{29}{138}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{17}{138}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{1}{138}\right)$	$e\left(\frac{37}{69}\right)$
$\chi_{1316}(5,\cdot)$	1316.bb	138	no	$1$	$1$	$e\left(\frac{37}{138}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{107}{138}\right)$	$e\left(\frac{26}{69}\right)$
$\chi_{1316}(9,\cdot)$	1316.y	69	no	$1$	$1$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{5}{69}\right)$
$\chi_{1316}(11,\cdot)$	1316.ba	138	yes	$1$	$1$	$e\left(\frac{29}{138}\right)$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{67}{69}\right)$
$\chi_{1316}(13,\cdot)$	1316.v	46	no	$1$	$1$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{11}{23}\right)$
$\chi_{1316}(15,\cdot)$	1316.w	46	no	$1$	$1$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{21}{23}\right)$
$\chi_{1316}(17,\cdot)$	1316.z	138	no	$-1$	$1$	$e\left(\frac{17}{138}\right)$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{101}{138}\right)$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{25}{69}\right)$
$\chi_{1316}(19,\cdot)$	1316.bf	138	yes	$-1$	$1$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{95}{138}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{20}{69}\right)$
$\chi_{1316}(23,\cdot)$	1316.ba	138	yes	$1$	$1$	$e\left(\frac{1}{138}\right)$	$e\left(\frac{107}{138}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{49}{69}\right)$	$e\left(\frac{38}{69}\right)$
$\chi_{1316}(25,\cdot)$	1316.y	69	no	$1$	$1$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{52}{69}\right)$
$\chi_{1316}(27,\cdot)$	1316.t	46	yes	$1$	$1$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{14}{23}\right)$
$\chi_{1316}(29,\cdot)$	1316.s	46	no	$-1$	$1$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{12}{23}\right)$
$\chi_{1316}(31,\cdot)$	1316.bf	138	yes	$-1$	$1$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{29}{138}\right)$	$e\left(\frac{37}{138}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{55}{69}\right)$
$\chi_{1316}(33,\cdot)$	1316.bb	138	no	$1$	$1$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{61}{138}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{31}{138}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{83}{138}\right)$	$e\left(\frac{35}{69}\right)$
$\chi_{1316}(37,\cdot)$	1316.y	69	no	$1$	$1$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{11}{69}\right)$
$\chi_{1316}(39,\cdot)$	1316.ba	138	yes	$1$	$1$	$e\left(\frac{89}{138}\right)$	$e\left(\frac{1}{138}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{1}{69}\right)$
$\chi_{1316}(41,\cdot)$	1316.v	46	no	$1$	$1$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{15}{23}\right)$
$\chi_{1316}(43,\cdot)$	1316.w	46	no	$1$	$1$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{13}{23}\right)$
$\chi_{1316}(45,\cdot)$	1316.bb	138	no	$1$	$1$	$e\left(\frac{137}{138}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{125}{138}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{109}{138}\right)$	$e\left(\frac{31}{69}\right)$
$\chi_{1316}(51,\cdot)$	1316.bc	138	yes	$-1$	$1$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{43}{138}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{53}{138}\right)$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{62}{69}\right)$
$\chi_{1316}(53,\cdot)$	1316.y	69	no	$1$	$1$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{22}{69}\right)$
$\chi_{1316}(55,\cdot)$	1316.t	46	yes	$1$	$1$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{8}{23}\right)$
$\chi_{1316}(57,\cdot)$	1316.s	46	no	$-1$	$1$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{19}{23}\right)$
$\chi_{1316}(59,\cdot)$	1316.bd	138	yes	$1$	$1$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{95}{138}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{89}{138}\right)$	$e\left(\frac{8}{69}\right)$	$e\left(\frac{127}{138}\right)$	$e\left(\frac{7}{69}\right)$
$\chi_{1316}(61,\cdot)$	1316.z	138	no	$-1$	$1$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{31}{138}\right)$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{35}{69}\right)$
$\chi_{1316}(65,\cdot)$	1316.y	69	no	$1$	$1$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{59}{69}\right)$
$\chi_{1316}(67,\cdot)$	1316.ba	138	yes	$1$	$1$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{19}{138}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{19}{69}\right)$
$\chi_{1316}(69,\cdot)$	1316.v	46	no	$1$	$1$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{2}{23}\right)$
$\chi_{1316}(71,\cdot)$	1316.u	46	no	$-1$	$1$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{5}{23}\right)$
$\chi_{1316}(73,\cdot)$	1316.bb	138	no	$1$	$1$	$e\left(\frac{107}{138}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{64}{69}\right)$
$\chi_{1316}(75,\cdot)$	1316.bd	138	yes	$1$	$1$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{89}{138}\right)$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{77}{138}\right)$	$e\left(\frac{20}{69}\right)$

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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	$1316$
Structure	\(C_{2}\times C_{2}\times C_{138}\)
Order	$552$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{1316}(1,\cdot)\)	1316.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1316}(3,\cdot)\)	1316.bd	138	yes	\(1\)	\(1\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{37}{138}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{29}{138}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{17}{138}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{1}{138}\right)\)	\(e\left(\frac{37}{69}\right)\)
\(\chi_{1316}(5,\cdot)\)	1316.bb	138	no	\(1\)	\(1\)	\(e\left(\frac{37}{138}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{107}{138}\right)\)	\(e\left(\frac{26}{69}\right)\)
\(\chi_{1316}(9,\cdot)\)	1316.y	69	no	\(1\)	\(1\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{5}{69}\right)\)
\(\chi_{1316}(11,\cdot)\)	1316.ba	138	yes	\(1\)	\(1\)	\(e\left(\frac{29}{138}\right)\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{67}{69}\right)\)
\(\chi_{1316}(13,\cdot)\)	1316.v	46	no	\(1\)	\(1\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{11}{23}\right)\)
\(\chi_{1316}(15,\cdot)\)	1316.w	46	no	\(1\)	\(1\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)
\(\chi_{1316}(17,\cdot)\)	1316.z	138	no	\(-1\)	\(1\)	\(e\left(\frac{17}{138}\right)\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{101}{138}\right)\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{25}{69}\right)\)
\(\chi_{1316}(19,\cdot)\)	1316.bf	138	yes	\(-1\)	\(1\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{95}{138}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{20}{69}\right)\)
\(\chi_{1316}(23,\cdot)\)	1316.ba	138	yes	\(1\)	\(1\)	\(e\left(\frac{1}{138}\right)\)	\(e\left(\frac{107}{138}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{49}{69}\right)\)	\(e\left(\frac{38}{69}\right)\)
\(\chi_{1316}(25,\cdot)\)	1316.y	69	no	\(1\)	\(1\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{52}{69}\right)\)
\(\chi_{1316}(27,\cdot)\)	1316.t	46	yes	\(1\)	\(1\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{14}{23}\right)\)
\(\chi_{1316}(29,\cdot)\)	1316.s	46	no	\(-1\)	\(1\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{12}{23}\right)\)
\(\chi_{1316}(31,\cdot)\)	1316.bf	138	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{29}{138}\right)\)	\(e\left(\frac{37}{138}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{55}{69}\right)\)
\(\chi_{1316}(33,\cdot)\)	1316.bb	138	no	\(1\)	\(1\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{61}{138}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{31}{138}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{83}{138}\right)\)	\(e\left(\frac{35}{69}\right)\)
\(\chi_{1316}(37,\cdot)\)	1316.y	69	no	\(1\)	\(1\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{11}{69}\right)\)
\(\chi_{1316}(39,\cdot)\)	1316.ba	138	yes	\(1\)	\(1\)	\(e\left(\frac{89}{138}\right)\)	\(e\left(\frac{1}{138}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{1}{69}\right)\)
\(\chi_{1316}(41,\cdot)\)	1316.v	46	no	\(1\)	\(1\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{15}{23}\right)\)
\(\chi_{1316}(43,\cdot)\)	1316.w	46	no	\(1\)	\(1\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)
\(\chi_{1316}(45,\cdot)\)	1316.bb	138	no	\(1\)	\(1\)	\(e\left(\frac{137}{138}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{125}{138}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{109}{138}\right)\)	\(e\left(\frac{31}{69}\right)\)
\(\chi_{1316}(51,\cdot)\)	1316.bc	138	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{43}{138}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{53}{138}\right)\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{62}{69}\right)\)
\(\chi_{1316}(53,\cdot)\)	1316.y	69	no	\(1\)	\(1\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{22}{69}\right)\)
\(\chi_{1316}(55,\cdot)\)	1316.t	46	yes	\(1\)	\(1\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{8}{23}\right)\)
\(\chi_{1316}(57,\cdot)\)	1316.s	46	no	\(-1\)	\(1\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{19}{23}\right)\)
\(\chi_{1316}(59,\cdot)\)	1316.bd	138	yes	\(1\)	\(1\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{95}{138}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{89}{138}\right)\)	\(e\left(\frac{8}{69}\right)\)	\(e\left(\frac{127}{138}\right)\)	\(e\left(\frac{7}{69}\right)\)
\(\chi_{1316}(61,\cdot)\)	1316.z	138	no	\(-1\)	\(1\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{31}{138}\right)\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{35}{69}\right)\)
\(\chi_{1316}(65,\cdot)\)	1316.y	69	no	\(1\)	\(1\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{59}{69}\right)\)
\(\chi_{1316}(67,\cdot)\)	1316.ba	138	yes	\(1\)	\(1\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{19}{138}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{19}{69}\right)\)
\(\chi_{1316}(69,\cdot)\)	1316.v	46	no	\(1\)	\(1\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{2}{23}\right)\)
\(\chi_{1316}(71,\cdot)\)	1316.u	46	no	\(-1\)	\(1\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{5}{23}\right)\)
\(\chi_{1316}(73,\cdot)\)	1316.bb	138	no	\(1\)	\(1\)	\(e\left(\frac{107}{138}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{64}{69}\right)\)
\(\chi_{1316}(75,\cdot)\)	1316.bd	138	yes	\(1\)	\(1\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{89}{138}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{77}{138}\right)\)	\(e\left(\frac{20}{69}\right)\)

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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.