LMFDB - Group of Dirichlet characters of modulus 690

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(690)

gp:g = idealstar(,690,2)

magma:G = FullDirichletGroup(690);

Character group

Order	=	176	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{44}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{690}(461,\cdot)$, $\chi_{690}(277,\cdot)$, $\chi_{690}(511,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 176 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$29$	$31$	$37$	$41$	$43$
$\chi_{690}(1,\cdot)$	690.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{690}(7,\cdot)$	690.w	44	no	$1$	$1$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{44}\right)$
$\chi_{690}(11,\cdot)$	690.q	22	no	$1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{690}(13,\cdot)$	690.v	44	no	$-1$	$1$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{690}(17,\cdot)$	690.u	44	no	$-1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{44}\right)$
$\chi_{690}(19,\cdot)$	690.p	22	no	$-1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{690}(29,\cdot)$	690.t	22	no	$-1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{690}(31,\cdot)$	690.m	11	no	$1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{690}(37,\cdot)$	690.w	44	no	$1$	$1$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{690}(41,\cdot)$	690.o	22	no	$-1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{690}(43,\cdot)$	690.w	44	no	$1$	$1$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{44}\right)$
$\chi_{690}(47,\cdot)$	690.i	4	no	$1$	$1$	$i$	$-1$	$-i$	$-i$	$-1$	$1$	$1$	$i$	$-1$	$-i$
$\chi_{690}(49,\cdot)$	690.r	22	no	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{690}(53,\cdot)$	690.u	44	no	$-1$	$1$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{25}{44}\right)$
$\chi_{690}(59,\cdot)$	690.t	22	no	$-1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{690}(61,\cdot)$	690.s	22	no	$-1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{690}(67,\cdot)$	690.w	44	no	$1$	$1$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{31}{44}\right)$
$\chi_{690}(71,\cdot)$	690.o	22	no	$-1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{690}(73,\cdot)$	690.v	44	no	$-1$	$1$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{44}\right)$
$\chi_{690}(77,\cdot)$	690.x	44	no	$1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{44}\right)$
$\chi_{690}(79,\cdot)$	690.p	22	no	$-1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{690}(83,\cdot)$	690.u	44	no	$-1$	$1$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{44}\right)$
$\chi_{690}(89,\cdot)$	690.n	22	no	$1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{690}(91,\cdot)$	690.c	2	no	$-1$	$1$	$-1$	$-1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$1$	$-1$
$\chi_{690}(97,\cdot)$	690.w	44	no	$1$	$1$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{43}{44}\right)$
$\chi_{690}(101,\cdot)$	690.o	22	no	$-1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{690}(103,\cdot)$	690.w	44	no	$1$	$1$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{44}\right)$
$\chi_{690}(107,\cdot)$	690.u	44	no	$-1$	$1$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{27}{44}\right)$
$\chi_{690}(109,\cdot)$	690.p	22	no	$-1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{690}(113,\cdot)$	690.u	44	no	$-1$	$1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{690}(119,\cdot)$	690.t	22	no	$-1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{690}(121,\cdot)$	690.m	11	no	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{11}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$690$
Structure	\(C_{2}\times C_{2}\times C_{44}\)
Order	$176$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{690}(1,\cdot)\)	690.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{690}(7,\cdot)\)	690.w	44	no	\(1\)	\(1\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{44}\right)\)
\(\chi_{690}(11,\cdot)\)	690.q	22	no	\(1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{690}(13,\cdot)\)	690.v	44	no	\(-1\)	\(1\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{690}(17,\cdot)\)	690.u	44	no	\(-1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{44}\right)\)
\(\chi_{690}(19,\cdot)\)	690.p	22	no	\(-1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{690}(29,\cdot)\)	690.t	22	no	\(-1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{690}(31,\cdot)\)	690.m	11	no	\(1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{690}(37,\cdot)\)	690.w	44	no	\(1\)	\(1\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{690}(41,\cdot)\)	690.o	22	no	\(-1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{690}(43,\cdot)\)	690.w	44	no	\(1\)	\(1\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{44}\right)\)
\(\chi_{690}(47,\cdot)\)	690.i	4	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(1\)	\(1\)	\(i\)	\(-1\)	\(-i\)
\(\chi_{690}(49,\cdot)\)	690.r	22	no	\(1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{690}(53,\cdot)\)	690.u	44	no	\(-1\)	\(1\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)
\(\chi_{690}(59,\cdot)\)	690.t	22	no	\(-1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{690}(61,\cdot)\)	690.s	22	no	\(-1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{690}(67,\cdot)\)	690.w	44	no	\(1\)	\(1\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{31}{44}\right)\)
\(\chi_{690}(71,\cdot)\)	690.o	22	no	\(-1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{690}(73,\cdot)\)	690.v	44	no	\(-1\)	\(1\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)
\(\chi_{690}(77,\cdot)\)	690.x	44	no	\(1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)
\(\chi_{690}(79,\cdot)\)	690.p	22	no	\(-1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{690}(83,\cdot)\)	690.u	44	no	\(-1\)	\(1\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{44}\right)\)
\(\chi_{690}(89,\cdot)\)	690.n	22	no	\(1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{690}(91,\cdot)\)	690.c	2	no	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)
\(\chi_{690}(97,\cdot)\)	690.w	44	no	\(1\)	\(1\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)
\(\chi_{690}(101,\cdot)\)	690.o	22	no	\(-1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{690}(103,\cdot)\)	690.w	44	no	\(1\)	\(1\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)
\(\chi_{690}(107,\cdot)\)	690.u	44	no	\(-1\)	\(1\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{27}{44}\right)\)
\(\chi_{690}(109,\cdot)\)	690.p	22	no	\(-1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{690}(113,\cdot)\)	690.u	44	no	\(-1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{690}(119,\cdot)\)	690.t	22	no	\(-1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{690}(121,\cdot)\)	690.m	11	no	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)

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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.