LMFDB - Group of Dirichlet characters of modulus 319

Show commands: PariGP / SageMath

sage: H = DirichletGroup(319)

pari: g = idealstar(,319,2)

Character group

sage: G.order() pari: g.no
Order	=	280
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{140}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{319}(233,\cdot)$, $\chi_{319}(89,\cdot)$

First 32 of 280 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{319}(1,\cdot)$	319.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{319}(2,\cdot)$	319.x	140	yes	$1$	$1$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{9}{28}\right)$	$i$
$\chi_{319}(3,\cdot)$	319.w	140	yes	$-1$	$1$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{3}{28}\right)$	$i$
$\chi_{319}(4,\cdot)$	319.t	70	yes	$1$	$1$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{9}{14}\right)$	$-1$
$\chi_{319}(5,\cdot)$	319.t	70	yes	$1$	$1$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{1}{14}\right)$	$-1$
$\chi_{319}(6,\cdot)$	319.v	70	yes	$-1$	$1$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{3}{7}\right)$	$-1$
$\chi_{319}(7,\cdot)$	319.u	70	yes	$-1$	$1$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{5}{14}\right)$	$1$
$\chi_{319}(8,\cdot)$	319.x	140	yes	$1$	$1$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{27}{28}\right)$	$-i$
$\chi_{319}(9,\cdot)$	319.t	70	yes	$1$	$1$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{3}{14}\right)$	$-1$
$\chi_{319}(10,\cdot)$	319.q	28	yes	$1$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{28}\right)$	$-i$
$\chi_{319}(12,\cdot)$	319.e	4	no	$-1$	$1$	$i$	$i$	$-1$	$-1$	$-1$	$1$	$-i$	$-1$	$-i$	$-i$
$\chi_{319}(13,\cdot)$	319.v	70	yes	$-1$	$1$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{2}{7}\right)$	$-1$
$\chi_{319}(14,\cdot)$	319.w	140	yes	$-1$	$1$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{19}{28}\right)$	$i$
$\chi_{319}(15,\cdot)$	319.w	140	yes	$-1$	$1$	$e\left(\frac{23}{140}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{69}{140}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{5}{28}\right)$	$-i$
$\chi_{319}(16,\cdot)$	319.s	35	yes	$1$	$1$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{2}{7}\right)$	$1$
$\chi_{319}(17,\cdot)$	319.o	20	yes	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-i$	$i$
$\chi_{319}(18,\cdot)$	319.x	140	yes	$1$	$1$	$e\left(\frac{13}{140}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{15}{28}\right)$	$-i$
$\chi_{319}(19,\cdot)$	319.x	140	yes	$1$	$1$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{25}{28}\right)$	$i$
$\chi_{319}(20,\cdot)$	319.s	35	yes	$1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{5}{7}\right)$	$1$
$\chi_{319}(21,\cdot)$	319.q	28	yes	$1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{28}\right)$	$i$
$\chi_{319}(23,\cdot)$	319.h	7	no	$1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$	$1$
$\chi_{319}(24,\cdot)$	319.u	70	yes	$-1$	$1$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{1}{14}\right)$	$1$
$\chi_{319}(25,\cdot)$	319.s	35	yes	$1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{1}{7}\right)$	$1$
$\chi_{319}(26,\cdot)$	319.w	140	yes	$-1$	$1$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{17}{28}\right)$	$-i$
$\chi_{319}(27,\cdot)$	319.w	140	yes	$-1$	$1$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{9}{28}\right)$	$-i$
$\chi_{319}(28,\cdot)$	319.i	10	yes	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$-1$
$\chi_{319}(30,\cdot)$	319.j	10	no	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$1$
$\chi_{319}(31,\cdot)$	319.w	140	yes	$-1$	$1$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{23}{28}\right)$	$i$
$\chi_{319}(32,\cdot)$	319.q	28	yes	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{17}{28}\right)$	$i$
$\chi_{319}(34,\cdot)$	319.n	14	no	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$-1$
$\chi_{319}(35,\cdot)$	319.v	70	yes	$-1$	$1$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{3}{7}\right)$	$-1$
$\chi_{319}(36,\cdot)$	319.s	35	yes	$1$	$1$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{6}{7}\right)$	$1$

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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	$319$
Structure	\(C_{2}\times C_{140}\)
Order	$280$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{319}(1,\cdot)\)	319.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{319}(2,\cdot)\)	319.x	140	yes	\(1\)	\(1\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(i\)
\(\chi_{319}(3,\cdot)\)	319.w	140	yes	\(-1\)	\(1\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(i\)
\(\chi_{319}(4,\cdot)\)	319.t	70	yes	\(1\)	\(1\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-1\)
\(\chi_{319}(5,\cdot)\)	319.t	70	yes	\(1\)	\(1\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)
\(\chi_{319}(6,\cdot)\)	319.v	70	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)
\(\chi_{319}(7,\cdot)\)	319.u	70	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(1\)
\(\chi_{319}(8,\cdot)\)	319.x	140	yes	\(1\)	\(1\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(-i\)
\(\chi_{319}(9,\cdot)\)	319.t	70	yes	\(1\)	\(1\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(-1\)
\(\chi_{319}(10,\cdot)\)	319.q	28	yes	\(1\)	\(1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(-i\)
\(\chi_{319}(12,\cdot)\)	319.e	4	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)
\(\chi_{319}(13,\cdot)\)	319.v	70	yes	\(-1\)	\(1\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(-1\)
\(\chi_{319}(14,\cdot)\)	319.w	140	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(i\)
\(\chi_{319}(15,\cdot)\)	319.w	140	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{140}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{69}{140}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(-i\)
\(\chi_{319}(16,\cdot)\)	319.s	35	yes	\(1\)	\(1\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(1\)
\(\chi_{319}(17,\cdot)\)	319.o	20	yes	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)	\(i\)
\(\chi_{319}(18,\cdot)\)	319.x	140	yes	\(1\)	\(1\)	\(e\left(\frac{13}{140}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(-i\)
\(\chi_{319}(19,\cdot)\)	319.x	140	yes	\(1\)	\(1\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(i\)
\(\chi_{319}(20,\cdot)\)	319.s	35	yes	\(1\)	\(1\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(1\)
\(\chi_{319}(21,\cdot)\)	319.q	28	yes	\(1\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(i\)
\(\chi_{319}(23,\cdot)\)	319.h	7	no	\(1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(1\)
\(\chi_{319}(24,\cdot)\)	319.u	70	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(1\)
\(\chi_{319}(25,\cdot)\)	319.s	35	yes	\(1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(1\)
\(\chi_{319}(26,\cdot)\)	319.w	140	yes	\(-1\)	\(1\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(-i\)
\(\chi_{319}(27,\cdot)\)	319.w	140	yes	\(-1\)	\(1\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(-i\)
\(\chi_{319}(28,\cdot)\)	319.i	10	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(-1\)
\(\chi_{319}(30,\cdot)\)	319.j	10	no	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(1\)
\(\chi_{319}(31,\cdot)\)	319.w	140	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(i\)
\(\chi_{319}(32,\cdot)\)	319.q	28	yes	\(1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(i\)
\(\chi_{319}(34,\cdot)\)	319.n	14	no	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)
\(\chi_{319}(35,\cdot)\)	319.v	70	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)
\(\chi_{319}(36,\cdot)\)	319.s	35	yes	\(1\)	\(1\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)

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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.