LMFDB - Group of Dirichlet characters of modulus 316

Show commands: PariGP / SageMath

sage: H = DirichletGroup(316)

pari: g = idealstar(,316,2)

Character group

sage: G.order() pari: g.no
Order	=	156
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{78}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{316}(159,\cdot)$, $\chi_{316}(161,\cdot)$

First 32 of 156 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{316}(1,\cdot)$	316.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{316}(3,\cdot)$	316.p	78	yes	$1$	$1$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{316}(5,\cdot)$	316.m	39	no	$1$	$1$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{316}(7,\cdot)$	316.p	78	yes	$1$	$1$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{316}(9,\cdot)$	316.m	39	no	$1$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{316}(11,\cdot)$	316.n	78	yes	$-1$	$1$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{316}(13,\cdot)$	316.m	39	no	$1$	$1$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{316}(15,\cdot)$	316.j	26	yes	$1$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{316}(17,\cdot)$	316.k	26	no	$-1$	$1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{316}(19,\cdot)$	316.n	78	yes	$-1$	$1$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{316}(21,\cdot)$	316.i	13	no	$1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{316}(23,\cdot)$	316.h	6	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$1$
$\chi_{316}(25,\cdot)$	316.m	39	no	$1$	$1$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{316}(27,\cdot)$	316.j	26	yes	$1$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{316}(29,\cdot)$	316.o	78	no	$-1$	$1$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{316}(31,\cdot)$	316.n	78	yes	$-1$	$1$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{316}(33,\cdot)$	316.k	26	no	$-1$	$1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{316}(35,\cdot)$	316.p	78	yes	$1$	$1$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{316}(37,\cdot)$	316.o	78	no	$-1$	$1$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{316}(39,\cdot)$	316.p	78	yes	$1$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{316}(41,\cdot)$	316.k	26	no	$-1$	$1$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{316}(43,\cdot)$	316.p	78	yes	$1$	$1$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{316}(45,\cdot)$	316.m	39	no	$1$	$1$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{316}(47,\cdot)$	316.p	78	yes	$1$	$1$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{316}(49,\cdot)$	316.m	39	no	$1$	$1$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{316}(51,\cdot)$	316.n	78	yes	$-1$	$1$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{316}(53,\cdot)$	316.o	78	no	$-1$	$1$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{316}(55,\cdot)$	316.h	6	yes	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$1$
$\chi_{316}(57,\cdot)$	316.k	26	no	$-1$	$1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{316}(59,\cdot)$	316.p	78	yes	$1$	$1$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{316}(61,\cdot)$	316.k	26	no	$-1$	$1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{316}(63,\cdot)$	316.p	78	yes	$1$	$1$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{1}{13}\right)$

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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	$316$
Structure	\(C_{2}\times C_{78}\)
Order	$156$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{316}(1,\cdot)\)	316.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{316}(3,\cdot)\)	316.p	78	yes	\(1\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{316}(5,\cdot)\)	316.m	39	no	\(1\)	\(1\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{316}(7,\cdot)\)	316.p	78	yes	\(1\)	\(1\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{316}(9,\cdot)\)	316.m	39	no	\(1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{316}(11,\cdot)\)	316.n	78	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{316}(13,\cdot)\)	316.m	39	no	\(1\)	\(1\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{316}(15,\cdot)\)	316.j	26	yes	\(1\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{316}(17,\cdot)\)	316.k	26	no	\(-1\)	\(1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{316}(19,\cdot)\)	316.n	78	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{316}(21,\cdot)\)	316.i	13	no	\(1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{316}(23,\cdot)\)	316.h	6	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)
\(\chi_{316}(25,\cdot)\)	316.m	39	no	\(1\)	\(1\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{316}(27,\cdot)\)	316.j	26	yes	\(1\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{316}(29,\cdot)\)	316.o	78	no	\(-1\)	\(1\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{316}(31,\cdot)\)	316.n	78	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{316}(33,\cdot)\)	316.k	26	no	\(-1\)	\(1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{316}(35,\cdot)\)	316.p	78	yes	\(1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{316}(37,\cdot)\)	316.o	78	no	\(-1\)	\(1\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{316}(39,\cdot)\)	316.p	78	yes	\(1\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{316}(41,\cdot)\)	316.k	26	no	\(-1\)	\(1\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{316}(43,\cdot)\)	316.p	78	yes	\(1\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{316}(45,\cdot)\)	316.m	39	no	\(1\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{316}(47,\cdot)\)	316.p	78	yes	\(1\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{316}(49,\cdot)\)	316.m	39	no	\(1\)	\(1\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{316}(51,\cdot)\)	316.n	78	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{316}(53,\cdot)\)	316.o	78	no	\(-1\)	\(1\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{316}(55,\cdot)\)	316.h	6	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)
\(\chi_{316}(57,\cdot)\)	316.k	26	no	\(-1\)	\(1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{316}(59,\cdot)\)	316.p	78	yes	\(1\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{316}(61,\cdot)\)	316.k	26	no	\(-1\)	\(1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{316}(63,\cdot)\)	316.p	78	yes	\(1\)	\(1\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)

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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.