LMFDB - Group of Dirichlet characters of modulus 669

Show commands: PariGP / SageMath

sage: H = DirichletGroup(669)

pari: g = idealstar(,669,2)

Character group

sage: G.order() pari: g.no
Order	=	444
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{222}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{669}(224,\cdot)$, $\chi_{669}(226,\cdot)$

First 32 of 444 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{669}(1,\cdot)$	669.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{669}(2,\cdot)$	669.l	74	yes	$-1$	$1$	$e\left(\frac{33}{74}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{49}{74}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{25}{74}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{19}{74}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{53}{74}\right)$	$e\left(\frac{29}{37}\right)$
$\chi_{669}(4,\cdot)$	669.i	37	no	$1$	$1$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{21}{37}\right)$
$\chi_{669}(5,\cdot)$	669.p	222	yes	$1$	$1$	$e\left(\frac{49}{74}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{20}{111}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{73}{74}\right)$	$e\left(\frac{187}{222}\right)$	$e\left(\frac{44}{111}\right)$	$e\left(\frac{69}{74}\right)$	$e\left(\frac{63}{74}\right)$	$e\left(\frac{24}{37}\right)$
$\chi_{669}(7,\cdot)$	669.i	37	no	$1$	$1$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{3}{37}\right)$
$\chi_{669}(8,\cdot)$	669.l	74	yes	$-1$	$1$	$e\left(\frac{25}{74}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{73}{74}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{1}{74}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{57}{74}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{11}{74}\right)$	$e\left(\frac{13}{37}\right)$
$\chi_{669}(10,\cdot)$	669.n	222	no	$-1$	$1$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{187}{222}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{211}{222}\right)$	$e\left(\frac{145}{222}\right)$	$e\left(\frac{9}{74}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{16}{37}\right)$
$\chi_{669}(11,\cdot)$	669.p	222	yes	$1$	$1$	$e\left(\frac{19}{74}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{44}{111}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{57}{74}\right)$	$e\left(\frac{145}{222}\right)$	$e\left(\frac{8}{111}\right)$	$e\left(\frac{63}{74}\right)$	$e\left(\frac{35}{74}\right)$	$e\left(\frac{1}{37}\right)$
$\chi_{669}(13,\cdot)$	669.j	74	no	$-1$	$1$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{69}{74}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{9}{74}\right)$	$e\left(\frac{63}{74}\right)$	$e\left(\frac{25}{74}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{28}{37}\right)$
$\chi_{669}(14,\cdot)$	669.l	74	yes	$-1$	$1$	$e\left(\frac{53}{74}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{63}{74}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{11}{74}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{35}{74}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{47}{74}\right)$	$e\left(\frac{32}{37}\right)$
$\chi_{669}(16,\cdot)$	669.i	37	no	$1$	$1$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{5}{37}\right)$
$\chi_{669}(17,\cdot)$	669.l	74	yes	$-1$	$1$	$e\left(\frac{19}{74}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{17}{74}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{57}{74}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{67}{74}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{35}{74}\right)$	$e\left(\frac{1}{37}\right)$
$\chi_{669}(19,\cdot)$	669.m	111	no	$1$	$1$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{106}{111}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{46}{111}\right)$	$e\left(\frac{100}{111}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{31}{37}\right)$
$\chi_{669}(20,\cdot)$	669.p	222	yes	$1$	$1$	$e\left(\frac{41}{74}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{56}{111}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{49}{74}\right)$	$e\left(\frac{13}{222}\right)$	$e\left(\frac{101}{111}\right)$	$e\left(\frac{23}{74}\right)$	$e\left(\frac{21}{74}\right)$	$e\left(\frac{8}{37}\right)$
$\chi_{669}(22,\cdot)$	669.n	222	no	$-1$	$1$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{13}{222}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{169}{222}\right)$	$e\left(\frac{73}{222}\right)$	$e\left(\frac{3}{74}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{30}{37}\right)$
$\chi_{669}(23,\cdot)$	669.p	222	yes	$1$	$1$	$e\left(\frac{49}{74}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{94}{111}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{73}{74}\right)$	$e\left(\frac{113}{222}\right)$	$e\left(\frac{7}{111}\right)$	$e\left(\frac{69}{74}\right)$	$e\left(\frac{63}{74}\right)$	$e\left(\frac{24}{37}\right)$
$\chi_{669}(25,\cdot)$	669.m	111	no	$1$	$1$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{40}{111}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{76}{111}\right)$	$e\left(\frac{88}{111}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{11}{37}\right)$
$\chi_{669}(26,\cdot)$	669.k	74	yes	$1$	$1$	$e\left(\frac{47}{74}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{67}{74}\right)$	$e\left(\frac{17}{74}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{39}{74}\right)$	$e\left(\frac{71}{74}\right)$	$e\left(\frac{20}{37}\right)$
$\chi_{669}(28,\cdot)$	669.i	37	no	$1$	$1$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{24}{37}\right)$
$\chi_{669}(29,\cdot)$	669.o	222	yes	$-1$	$1$	$e\left(\frac{21}{74}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{181}{222}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{63}{74}\right)$	$e\left(\frac{11}{111}\right)$	$e\left(\frac{43}{222}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{27}{74}\right)$	$e\left(\frac{5}{37}\right)$
$\chi_{669}(31,\cdot)$	669.m	111	no	$1$	$1$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{97}{111}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{40}{111}\right)$	$e\left(\frac{58}{111}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{35}{37}\right)$
$\chi_{669}(32,\cdot)$	669.l	74	yes	$-1$	$1$	$e\left(\frac{17}{74}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{23}{74}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{51}{74}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{21}{74}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{43}{74}\right)$	$e\left(\frac{34}{37}\right)$
$\chi_{669}(34,\cdot)$	669.i	37	no	$1$	$1$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{30}{37}\right)$
$\chi_{669}(35,\cdot)$	669.p	222	yes	$1$	$1$	$e\left(\frac{69}{74}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{41}{111}\right)$	$e\left(\frac{31}{37}\right)$	$e\left(\frac{59}{74}\right)$	$e\left(\frac{67}{222}\right)$	$e\left(\frac{68}{111}\right)$	$e\left(\frac{73}{74}\right)$	$e\left(\frac{57}{74}\right)$	$e\left(\frac{27}{37}\right)$
$\chi_{669}(37,\cdot)$	669.m	111	no	$1$	$1$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{104}{111}\right)$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{20}{111}\right)$	$e\left(\frac{29}{111}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{36}{37}\right)$
$\chi_{669}(38,\cdot)$	669.o	222	yes	$-1$	$1$	$e\left(\frac{67}{74}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{137}{222}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{53}{74}\right)$	$e\left(\frac{58}{111}\right)$	$e\left(\frac{35}{222}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{65}{74}\right)$	$e\left(\frac{23}{37}\right)$
$\chi_{669}(40,\cdot)$	669.h	6	no	$-1$	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$1$
$\chi_{669}(41,\cdot)$	669.l	74	yes	$-1$	$1$	$e\left(\frac{67}{74}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{21}{74}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{53}{74}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{61}{74}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{65}{74}\right)$	$e\left(\frac{23}{37}\right)$
$\chi_{669}(43,\cdot)$	669.m	111	no	$1$	$1$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{34}{111}\right)$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{109}{111}\right)$	$e\left(\frac{97}{111}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{26}{37}\right)$
$\chi_{669}(44,\cdot)$	669.p	222	yes	$1$	$1$	$e\left(\frac{11}{74}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{80}{111}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{33}{74}\right)$	$e\left(\frac{193}{222}\right)$	$e\left(\frac{65}{111}\right)$	$e\left(\frac{17}{74}\right)$	$e\left(\frac{67}{74}\right)$	$e\left(\frac{22}{37}\right)$
$\chi_{669}(46,\cdot)$	669.n	222	no	$-1$	$1$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{113}{222}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{137}{222}\right)$	$e\left(\frac{71}{222}\right)$	$e\left(\frac{9}{74}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{16}{37}\right)$
$\chi_{669}(47,\cdot)$	669.o	222	yes	$-1$	$1$	$e\left(\frac{3}{74}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{121}{222}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{9}{74}\right)$	$e\left(\frac{65}{111}\right)$	$e\left(\frac{133}{222}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{25}{74}\right)$	$e\left(\frac{6}{37}\right)$

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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	$669$
Structure	\(C_{2}\times C_{222}\)
Order	$444$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{669}(1,\cdot)\)	669.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{669}(2,\cdot)\)	669.l	74	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{74}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{49}{74}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{25}{74}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{19}{74}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{53}{74}\right)\)	\(e\left(\frac{29}{37}\right)\)
\(\chi_{669}(4,\cdot)\)	669.i	37	no	\(1\)	\(1\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{21}{37}\right)\)
\(\chi_{669}(5,\cdot)\)	669.p	222	yes	\(1\)	\(1\)	\(e\left(\frac{49}{74}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{20}{111}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{73}{74}\right)\)	\(e\left(\frac{187}{222}\right)\)	\(e\left(\frac{44}{111}\right)\)	\(e\left(\frac{69}{74}\right)\)	\(e\left(\frac{63}{74}\right)\)	\(e\left(\frac{24}{37}\right)\)
\(\chi_{669}(7,\cdot)\)	669.i	37	no	\(1\)	\(1\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{3}{37}\right)\)
\(\chi_{669}(8,\cdot)\)	669.l	74	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{74}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{73}{74}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{1}{74}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{57}{74}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{11}{74}\right)\)	\(e\left(\frac{13}{37}\right)\)
\(\chi_{669}(10,\cdot)\)	669.n	222	no	\(-1\)	\(1\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{187}{222}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{211}{222}\right)\)	\(e\left(\frac{145}{222}\right)\)	\(e\left(\frac{9}{74}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)
\(\chi_{669}(11,\cdot)\)	669.p	222	yes	\(1\)	\(1\)	\(e\left(\frac{19}{74}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{44}{111}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{57}{74}\right)\)	\(e\left(\frac{145}{222}\right)\)	\(e\left(\frac{8}{111}\right)\)	\(e\left(\frac{63}{74}\right)\)	\(e\left(\frac{35}{74}\right)\)	\(e\left(\frac{1}{37}\right)\)
\(\chi_{669}(13,\cdot)\)	669.j	74	no	\(-1\)	\(1\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{69}{74}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{9}{74}\right)\)	\(e\left(\frac{63}{74}\right)\)	\(e\left(\frac{25}{74}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{28}{37}\right)\)
\(\chi_{669}(14,\cdot)\)	669.l	74	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{74}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{63}{74}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{11}{74}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{35}{74}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{47}{74}\right)\)	\(e\left(\frac{32}{37}\right)\)
\(\chi_{669}(16,\cdot)\)	669.i	37	no	\(1\)	\(1\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)
\(\chi_{669}(17,\cdot)\)	669.l	74	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{74}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{17}{74}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{57}{74}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{67}{74}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{35}{74}\right)\)	\(e\left(\frac{1}{37}\right)\)
\(\chi_{669}(19,\cdot)\)	669.m	111	no	\(1\)	\(1\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{106}{111}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{46}{111}\right)\)	\(e\left(\frac{100}{111}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{31}{37}\right)\)
\(\chi_{669}(20,\cdot)\)	669.p	222	yes	\(1\)	\(1\)	\(e\left(\frac{41}{74}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{56}{111}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{49}{74}\right)\)	\(e\left(\frac{13}{222}\right)\)	\(e\left(\frac{101}{111}\right)\)	\(e\left(\frac{23}{74}\right)\)	\(e\left(\frac{21}{74}\right)\)	\(e\left(\frac{8}{37}\right)\)
\(\chi_{669}(22,\cdot)\)	669.n	222	no	\(-1\)	\(1\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{13}{222}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{169}{222}\right)\)	\(e\left(\frac{73}{222}\right)\)	\(e\left(\frac{3}{74}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)
\(\chi_{669}(23,\cdot)\)	669.p	222	yes	\(1\)	\(1\)	\(e\left(\frac{49}{74}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{94}{111}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{73}{74}\right)\)	\(e\left(\frac{113}{222}\right)\)	\(e\left(\frac{7}{111}\right)\)	\(e\left(\frac{69}{74}\right)\)	\(e\left(\frac{63}{74}\right)\)	\(e\left(\frac{24}{37}\right)\)
\(\chi_{669}(25,\cdot)\)	669.m	111	no	\(1\)	\(1\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{40}{111}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{76}{111}\right)\)	\(e\left(\frac{88}{111}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{11}{37}\right)\)
\(\chi_{669}(26,\cdot)\)	669.k	74	yes	\(1\)	\(1\)	\(e\left(\frac{47}{74}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{67}{74}\right)\)	\(e\left(\frac{17}{74}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{39}{74}\right)\)	\(e\left(\frac{71}{74}\right)\)	\(e\left(\frac{20}{37}\right)\)
\(\chi_{669}(28,\cdot)\)	669.i	37	no	\(1\)	\(1\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)
\(\chi_{669}(29,\cdot)\)	669.o	222	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{74}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{181}{222}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{63}{74}\right)\)	\(e\left(\frac{11}{111}\right)\)	\(e\left(\frac{43}{222}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{27}{74}\right)\)	\(e\left(\frac{5}{37}\right)\)
\(\chi_{669}(31,\cdot)\)	669.m	111	no	\(1\)	\(1\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{97}{111}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{40}{111}\right)\)	\(e\left(\frac{58}{111}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{35}{37}\right)\)
\(\chi_{669}(32,\cdot)\)	669.l	74	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{74}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{23}{74}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{51}{74}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{21}{74}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{43}{74}\right)\)	\(e\left(\frac{34}{37}\right)\)
\(\chi_{669}(34,\cdot)\)	669.i	37	no	\(1\)	\(1\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)
\(\chi_{669}(35,\cdot)\)	669.p	222	yes	\(1\)	\(1\)	\(e\left(\frac{69}{74}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{41}{111}\right)\)	\(e\left(\frac{31}{37}\right)\)	\(e\left(\frac{59}{74}\right)\)	\(e\left(\frac{67}{222}\right)\)	\(e\left(\frac{68}{111}\right)\)	\(e\left(\frac{73}{74}\right)\)	\(e\left(\frac{57}{74}\right)\)	\(e\left(\frac{27}{37}\right)\)
\(\chi_{669}(37,\cdot)\)	669.m	111	no	\(1\)	\(1\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{104}{111}\right)\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{20}{111}\right)\)	\(e\left(\frac{29}{111}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{36}{37}\right)\)
\(\chi_{669}(38,\cdot)\)	669.o	222	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{74}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{137}{222}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{53}{74}\right)\)	\(e\left(\frac{58}{111}\right)\)	\(e\left(\frac{35}{222}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{65}{74}\right)\)	\(e\left(\frac{23}{37}\right)\)
\(\chi_{669}(40,\cdot)\)	669.h	6	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(1\)	\(1\)
\(\chi_{669}(41,\cdot)\)	669.l	74	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{74}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{21}{74}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{53}{74}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{61}{74}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{65}{74}\right)\)	\(e\left(\frac{23}{37}\right)\)
\(\chi_{669}(43,\cdot)\)	669.m	111	no	\(1\)	\(1\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{34}{111}\right)\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{109}{111}\right)\)	\(e\left(\frac{97}{111}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{26}{37}\right)\)
\(\chi_{669}(44,\cdot)\)	669.p	222	yes	\(1\)	\(1\)	\(e\left(\frac{11}{74}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{80}{111}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{33}{74}\right)\)	\(e\left(\frac{193}{222}\right)\)	\(e\left(\frac{65}{111}\right)\)	\(e\left(\frac{17}{74}\right)\)	\(e\left(\frac{67}{74}\right)\)	\(e\left(\frac{22}{37}\right)\)
\(\chi_{669}(46,\cdot)\)	669.n	222	no	\(-1\)	\(1\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{113}{222}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{137}{222}\right)\)	\(e\left(\frac{71}{222}\right)\)	\(e\left(\frac{9}{74}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)
\(\chi_{669}(47,\cdot)\)	669.o	222	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{74}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{121}{222}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{9}{74}\right)\)	\(e\left(\frac{65}{111}\right)\)	\(e\left(\frac{133}{222}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{25}{74}\right)\)	\(e\left(\frac{6}{37}\right)\)

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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.