LMFDB - Group of Dirichlet characters of modulus 1078

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1078)

pari: g = idealstar(,1078,2)

Character group

sage: G.order() pari: g.no
Order	=	420
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{210}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1078}(199,\cdot)$, $\chi_{1078}(981,\cdot)$

First 32 of 420 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	$-1$	$1$	$3$	$5$	$9$	$13$	$15$	$17$	$19$	$23$	$25$	$27$
$\chi_{1078}(1,\cdot)$	1078.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1078}(3,\cdot)$	1078.be	210	no	$-1$	$1$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{19}{70}\right)$
$\chi_{1078}(5,\cdot)$	1078.be	210	no	$-1$	$1$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{47}{70}\right)$
$\chi_{1078}(9,\cdot)$	1078.bc	105	no	$1$	$1$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{19}{35}\right)$
$\chi_{1078}(13,\cdot)$	1078.ba	70	no	$1$	$1$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{53}{70}\right)$
$\chi_{1078}(15,\cdot)$	1078.v	35	no	$1$	$1$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{33}{35}\right)$
$\chi_{1078}(17,\cdot)$	1078.bf	210	no	$1$	$1$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{27}{70}\right)$
$\chi_{1078}(19,\cdot)$	1078.s	30	no	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1078}(23,\cdot)$	1078.r	21	no	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{1078}(25,\cdot)$	1078.bc	105	no	$1$	$1$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{12}{35}\right)$
$\chi_{1078}(27,\cdot)$	1078.z	70	no	$-1$	$1$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{57}{70}\right)$
$\chi_{1078}(29,\cdot)$	1078.bb	70	no	$-1$	$1$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{1078}(31,\cdot)$	1078.t	30	no	$-1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{1078}(37,\cdot)$	1078.bc	105	no	$1$	$1$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{1078}(39,\cdot)$	1078.bd	210	no	$-1$	$1$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{1078}(41,\cdot)$	1078.ba	70	no	$1$	$1$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{19}{70}\right)$
$\chi_{1078}(43,\cdot)$	1078.n	14	no	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$	$-1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{1078}(45,\cdot)$	1078.x	42	no	$-1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{1078}(47,\cdot)$	1078.be	210	no	$-1$	$1$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{137}{210}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{39}{70}\right)$
$\chi_{1078}(51,\cdot)$	1078.bd	210	no	$-1$	$1$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{1078}(53,\cdot)$	1078.bc	105	no	$1$	$1$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{1078}(57,\cdot)$	1078.bb	70	no	$-1$	$1$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{34}{35}\right)$
$\chi_{1078}(59,\cdot)$	1078.be	210	no	$-1$	$1$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{51}{70}\right)$
$\chi_{1078}(61,\cdot)$	1078.bf	210	no	$1$	$1$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{41}{210}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{27}{70}\right)$
$\chi_{1078}(65,\cdot)$	1078.y	42	no	$-1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{1078}(67,\cdot)$	1078.e	3	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{1078}(69,\cdot)$	1078.z	70	no	$-1$	$1$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{69}{70}\right)$
$\chi_{1078}(71,\cdot)$	1078.v	35	no	$1$	$1$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{1078}(73,\cdot)$	1078.bf	210	no	$1$	$1$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{31}{70}\right)$
$\chi_{1078}(75,\cdot)$	1078.be	210	no	$-1$	$1$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{29}{210}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{43}{70}\right)$
$\chi_{1078}(79,\cdot)$	1078.u	30	no	$-1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1078}(81,\cdot)$	1078.bc	105	no	$1$	$1$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{3}{35}\right)$

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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	$1078$
Structure	\(C_{2}\times C_{210}\)
Order	$420$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{1078}(1,\cdot)\)	1078.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1078}(3,\cdot)\)	1078.be	210	no	\(-1\)	\(1\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{19}{70}\right)\)
\(\chi_{1078}(5,\cdot)\)	1078.be	210	no	\(-1\)	\(1\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{47}{70}\right)\)
\(\chi_{1078}(9,\cdot)\)	1078.bc	105	no	\(1\)	\(1\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{19}{35}\right)\)
\(\chi_{1078}(13,\cdot)\)	1078.ba	70	no	\(1\)	\(1\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)
\(\chi_{1078}(15,\cdot)\)	1078.v	35	no	\(1\)	\(1\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)
\(\chi_{1078}(17,\cdot)\)	1078.bf	210	no	\(1\)	\(1\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{27}{70}\right)\)
\(\chi_{1078}(19,\cdot)\)	1078.s	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1078}(23,\cdot)\)	1078.r	21	no	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{1078}(25,\cdot)\)	1078.bc	105	no	\(1\)	\(1\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)
\(\chi_{1078}(27,\cdot)\)	1078.z	70	no	\(-1\)	\(1\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)
\(\chi_{1078}(29,\cdot)\)	1078.bb	70	no	\(-1\)	\(1\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{1078}(31,\cdot)\)	1078.t	30	no	\(-1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{1078}(37,\cdot)\)	1078.bc	105	no	\(1\)	\(1\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{1078}(39,\cdot)\)	1078.bd	210	no	\(-1\)	\(1\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{1078}(41,\cdot)\)	1078.ba	70	no	\(1\)	\(1\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{19}{70}\right)\)
\(\chi_{1078}(43,\cdot)\)	1078.n	14	no	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{1078}(45,\cdot)\)	1078.x	42	no	\(-1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{1078}(47,\cdot)\)	1078.be	210	no	\(-1\)	\(1\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{39}{70}\right)\)
\(\chi_{1078}(51,\cdot)\)	1078.bd	210	no	\(-1\)	\(1\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{1078}(53,\cdot)\)	1078.bc	105	no	\(1\)	\(1\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{1078}(57,\cdot)\)	1078.bb	70	no	\(-1\)	\(1\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)
\(\chi_{1078}(59,\cdot)\)	1078.be	210	no	\(-1\)	\(1\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)
\(\chi_{1078}(61,\cdot)\)	1078.bf	210	no	\(1\)	\(1\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{41}{210}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{27}{70}\right)\)
\(\chi_{1078}(65,\cdot)\)	1078.y	42	no	\(-1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{1078}(67,\cdot)\)	1078.e	3	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{1078}(69,\cdot)\)	1078.z	70	no	\(-1\)	\(1\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)
\(\chi_{1078}(71,\cdot)\)	1078.v	35	no	\(1\)	\(1\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{1078}(73,\cdot)\)	1078.bf	210	no	\(1\)	\(1\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{31}{70}\right)\)
\(\chi_{1078}(75,\cdot)\)	1078.be	210	no	\(-1\)	\(1\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{29}{210}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{43}{70}\right)\)
\(\chi_{1078}(79,\cdot)\)	1078.u	30	no	\(-1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1078}(81,\cdot)\)	1078.bc	105	no	\(1\)	\(1\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)

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First 32 of 420 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.