LMFDB - Group of Dirichlet characters of modulus 639

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(639)

pari: g = idealstar(,639,2)

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	=	$\chi_{639}(569,\cdot)$, $\chi_{639}(433,\cdot)$

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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{639}(1,\cdot)$	639.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{639}(2,\cdot)$	639.be	210	yes	$-1$	$1$	$e\left(\frac{143}{210}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{76}{105}\right)$
$\chi_{639}(4,\cdot)$	639.bc	105	yes	$1$	$1$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{47}{105}\right)$
$\chi_{639}(5,\cdot)$	639.t	30	yes	$-1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{639}(7,\cdot)$	639.bd	210	yes	$-1$	$1$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{143}{210}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{23}{210}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{105}\right)$
$\chi_{639}(8,\cdot)$	639.ba	70	no	$-1$	$1$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{6}{35}\right)$
$\chi_{639}(10,\cdot)$	639.v	35	no	$1$	$1$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{639}(11,\cdot)$	639.bf	210	yes	$1$	$1$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{210}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{31}{105}\right)$
$\chi_{639}(13,\cdot)$	639.bd	210	yes	$-1$	$1$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{74}{105}\right)$
$\chi_{639}(14,\cdot)$	639.s	30	yes	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{639}(16,\cdot)$	639.bc	105	yes	$1$	$1$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{94}{105}\right)$
$\chi_{639}(17,\cdot)$	639.m	10	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{639}(19,\cdot)$	639.v	35	no	$1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{639}(20,\cdot)$	639.x	42	yes	$-1$	$1$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{639}(22,\cdot)$	639.bd	210	yes	$-1$	$1$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{105}\right)$
$\chi_{639}(23,\cdot)$	639.w	42	yes	$1$	$1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{639}(25,\cdot)$	639.q	15	yes	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{639}(26,\cdot)$	639.p	14	no	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$-1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{14}\right)$	$1$	$e\left(\frac{3}{7}\right)$
$\chi_{639}(28,\cdot)$	639.bb	70	no	$-1$	$1$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{16}{35}\right)$
$\chi_{639}(29,\cdot)$	639.be	210	yes	$-1$	$1$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{103}{105}\right)$
$\chi_{639}(31,\cdot)$	639.bd	210	yes	$-1$	$1$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{105}\right)$
$\chi_{639}(32,\cdot)$	639.x	42	yes	$-1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{639}(34,\cdot)$	639.y	42	yes	$-1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{639}(35,\cdot)$	639.z	70	no	$1$	$1$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{33}{35}\right)$
$\chi_{639}(37,\cdot)$	639.j	7	no	$1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$1$	$e\left(\frac{6}{7}\right)$
$\chi_{639}(38,\cdot)$	639.be	210	yes	$-1$	$1$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{22}{105}\right)$
$\chi_{639}(40,\cdot)$	639.bc	105	yes	$1$	$1$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{105}\right)$
$\chi_{639}(41,\cdot)$	639.w	42	yes	$1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{639}(43,\cdot)$	639.bc	105	yes	$1$	$1$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{105}\right)$
$\chi_{639}(44,\cdot)$	639.z	70	no	$1$	$1$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{639}(46,\cdot)$	639.k	10	no	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{639}(47,\cdot)$	639.bf	210	yes	$1$	$1$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{79}{105}\right)$

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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	$639$
Structure	\(C_{2}\times C_{210}\)
Order	$420$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{639}(1,\cdot)\)	639.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{639}(2,\cdot)\)	639.be	210	yes	\(-1\)	\(1\)	\(e\left(\frac{143}{210}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{76}{105}\right)\)
\(\chi_{639}(4,\cdot)\)	639.bc	105	yes	\(1\)	\(1\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{47}{105}\right)\)
\(\chi_{639}(5,\cdot)\)	639.t	30	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{639}(7,\cdot)\)	639.bd	210	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{143}{210}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{23}{210}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{105}\right)\)
\(\chi_{639}(8,\cdot)\)	639.ba	70	no	\(-1\)	\(1\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{6}{35}\right)\)
\(\chi_{639}(10,\cdot)\)	639.v	35	no	\(1\)	\(1\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{639}(11,\cdot)\)	639.bf	210	yes	\(1\)	\(1\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{210}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{31}{105}\right)\)
\(\chi_{639}(13,\cdot)\)	639.bd	210	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{74}{105}\right)\)
\(\chi_{639}(14,\cdot)\)	639.s	30	yes	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{639}(16,\cdot)\)	639.bc	105	yes	\(1\)	\(1\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{94}{105}\right)\)
\(\chi_{639}(17,\cdot)\)	639.m	10	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{639}(19,\cdot)\)	639.v	35	no	\(1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{639}(20,\cdot)\)	639.x	42	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{639}(22,\cdot)\)	639.bd	210	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{105}\right)\)
\(\chi_{639}(23,\cdot)\)	639.w	42	yes	\(1\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{639}(25,\cdot)\)	639.q	15	yes	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{639}(26,\cdot)\)	639.p	14	no	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(-1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(1\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{639}(28,\cdot)\)	639.bb	70	no	\(-1\)	\(1\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{16}{35}\right)\)
\(\chi_{639}(29,\cdot)\)	639.be	210	yes	\(-1\)	\(1\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{103}{105}\right)\)
\(\chi_{639}(31,\cdot)\)	639.bd	210	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{105}\right)\)
\(\chi_{639}(32,\cdot)\)	639.x	42	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{639}(34,\cdot)\)	639.y	42	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{639}(35,\cdot)\)	639.z	70	no	\(1\)	\(1\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{33}{35}\right)\)
\(\chi_{639}(37,\cdot)\)	639.j	7	no	\(1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(1\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{639}(38,\cdot)\)	639.be	210	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{22}{105}\right)\)
\(\chi_{639}(40,\cdot)\)	639.bc	105	yes	\(1\)	\(1\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{105}\right)\)
\(\chi_{639}(41,\cdot)\)	639.w	42	yes	\(1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{639}(43,\cdot)\)	639.bc	105	yes	\(1\)	\(1\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{105}\right)\)
\(\chi_{639}(44,\cdot)\)	639.z	70	no	\(1\)	\(1\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{639}(46,\cdot)\)	639.k	10	no	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{639}(47,\cdot)\)	639.bf	210	yes	\(1\)	\(1\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{79}{105}\right)\)

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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.