LMFDB - Group of Dirichlet characters of modulus 497

sage:H = DirichletGroup(497)

pari:g = idealstar(,497,2)

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	=	$\chi_{497}(143,\cdot)$, $\chi_{497}(78,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{497}(1,\cdot)$	497.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{497}(2,\cdot)$	497.bc	105	yes	$1$	$1$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{97}{105}\right)$
$\chi_{497}(3,\cdot)$	497.be	210	yes	$-1$	$1$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{199}{210}\right)$
$\chi_{497}(4,\cdot)$	497.bc	105	yes	$1$	$1$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{89}{105}\right)$
$\chi_{497}(5,\cdot)$	497.t	30	yes	$-1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{497}(6,\cdot)$	497.ba	70	yes	$-1$	$1$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{61}{70}\right)$
$\chi_{497}(8,\cdot)$	497.v	35	no	$1$	$1$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{27}{35}\right)$
$\chi_{497}(9,\cdot)$	497.bc	105	yes	$1$	$1$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{94}{105}\right)$
$\chi_{497}(10,\cdot)$	497.be	210	yes	$-1$	$1$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{143}{210}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{61}{210}\right)$
$\chi_{497}(11,\cdot)$	497.bd	210	yes	$-1$	$1$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{17}{105}\right)$
$\chi_{497}(12,\cdot)$	497.be	210	yes	$-1$	$1$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{167}{210}\right)$
$\chi_{497}(13,\cdot)$	497.z	70	yes	$1$	$1$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{47}{70}\right)$
$\chi_{497}(15,\cdot)$	497.v	35	no	$1$	$1$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{497}(16,\cdot)$	497.bc	105	yes	$1$	$1$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{73}{105}\right)$
$\chi_{497}(17,\cdot)$	497.s	30	yes	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{497}(18,\cdot)$	497.bc	105	yes	$1$	$1$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{86}{105}\right)$
$\chi_{497}(19,\cdot)$	497.be	210	yes	$-1$	$1$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{179}{210}\right)$
$\chi_{497}(20,\cdot)$	497.o	14	yes	$-1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$	$-1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{497}(22,\cdot)$	497.bb	70	no	$-1$	$1$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{497}(23,\cdot)$	497.y	42	yes	$-1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{497}(24,\cdot)$	497.be	210	yes	$-1$	$1$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{151}{210}\right)$
$\chi_{497}(25,\cdot)$	497.q	15	yes	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{497}(26,\cdot)$	497.w	42	yes	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{25}{42}\right)$
$\chi_{497}(27,\cdot)$	497.ba	70	yes	$-1$	$1$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{59}{70}\right)$
$\chi_{497}(29,\cdot)$	497.v	35	no	$1$	$1$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{32}{35}\right)$
$\chi_{497}(30,\cdot)$	497.r	21	yes	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{497}(31,\cdot)$	497.bf	210	yes	$1$	$1$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{169}{210}\right)$
$\chi_{497}(32,\cdot)$	497.r	21	yes	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{497}(33,\cdot)$	497.bf	210	yes	$1$	$1$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{23}{210}\right)$
$\chi_{497}(34,\cdot)$	497.p	14	yes	$1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{7}\right)$	$-1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{497}(36,\cdot)$	497.v	35	no	$1$	$1$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{497}(37,\cdot)$	497.r	21	yes	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{11}{21}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$497$
Structure	\(C_{2}\times C_{210}\)
Order	$420$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{497}(1,\cdot)\)	497.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{497}(2,\cdot)\)	497.bc	105	yes	\(1\)	\(1\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)
\(\chi_{497}(3,\cdot)\)	497.be	210	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{199}{210}\right)\)
\(\chi_{497}(4,\cdot)\)	497.bc	105	yes	\(1\)	\(1\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)
\(\chi_{497}(5,\cdot)\)	497.t	30	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{497}(6,\cdot)\)	497.ba	70	yes	\(-1\)	\(1\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)
\(\chi_{497}(8,\cdot)\)	497.v	35	no	\(1\)	\(1\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)
\(\chi_{497}(9,\cdot)\)	497.bc	105	yes	\(1\)	\(1\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)
\(\chi_{497}(10,\cdot)\)	497.be	210	yes	\(-1\)	\(1\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{143}{210}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{61}{210}\right)\)
\(\chi_{497}(11,\cdot)\)	497.bd	210	yes	\(-1\)	\(1\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{17}{105}\right)\)
\(\chi_{497}(12,\cdot)\)	497.be	210	yes	\(-1\)	\(1\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{167}{210}\right)\)
\(\chi_{497}(13,\cdot)\)	497.z	70	yes	\(1\)	\(1\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{47}{70}\right)\)
\(\chi_{497}(15,\cdot)\)	497.v	35	no	\(1\)	\(1\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{497}(16,\cdot)\)	497.bc	105	yes	\(1\)	\(1\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)
\(\chi_{497}(17,\cdot)\)	497.s	30	yes	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{497}(18,\cdot)\)	497.bc	105	yes	\(1\)	\(1\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)
\(\chi_{497}(19,\cdot)\)	497.be	210	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{179}{210}\right)\)
\(\chi_{497}(20,\cdot)\)	497.o	14	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(-1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{497}(22,\cdot)\)	497.bb	70	no	\(-1\)	\(1\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{497}(23,\cdot)\)	497.y	42	yes	\(-1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{497}(24,\cdot)\)	497.be	210	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{151}{210}\right)\)
\(\chi_{497}(25,\cdot)\)	497.q	15	yes	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{497}(26,\cdot)\)	497.w	42	yes	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)
\(\chi_{497}(27,\cdot)\)	497.ba	70	yes	\(-1\)	\(1\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{59}{70}\right)\)
\(\chi_{497}(29,\cdot)\)	497.v	35	no	\(1\)	\(1\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)
\(\chi_{497}(30,\cdot)\)	497.r	21	yes	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{497}(31,\cdot)\)	497.bf	210	yes	\(1\)	\(1\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{169}{210}\right)\)
\(\chi_{497}(32,\cdot)\)	497.r	21	yes	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{497}(33,\cdot)\)	497.bf	210	yes	\(1\)	\(1\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{23}{210}\right)\)
\(\chi_{497}(34,\cdot)\)	497.p	14	yes	\(1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{497}(36,\cdot)\)	497.v	35	no	\(1\)	\(1\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{497}(37,\cdot)\)	497.r	21	yes	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)

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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.