LMFDB - Group of Dirichlet characters of modulus 460

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(460)

gp:g = idealstar(,460,2)

magma:G = FullDirichletGroup(460);

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	=	$\chi_{460}(231,\cdot)$, $\chi_{460}(277,\cdot)$, $\chi_{460}(281,\cdot)$	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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$27$	$29$
$\chi_{460}(1,\cdot)$	460.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{460}(3,\cdot)$	460.w	44	yes	$1$	$1$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{460}(7,\cdot)$	460.v	44	yes	$-1$	$1$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{460}(9,\cdot)$	460.s	22	no	$1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{460}(11,\cdot)$	460.q	22	no	$1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{460}(13,\cdot)$	460.u	44	no	$-1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{460}(17,\cdot)$	460.x	44	no	$1$	$1$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{460}(19,\cdot)$	460.o	22	yes	$1$	$1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{460}(21,\cdot)$	460.p	22	no	$-1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{460}(27,\cdot)$	460.w	44	yes	$1$	$1$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{460}(29,\cdot)$	460.s	22	no	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{460}(31,\cdot)$	460.t	22	no	$-1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{460}(33,\cdot)$	460.x	44	no	$1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{460}(37,\cdot)$	460.x	44	no	$1$	$1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{460}(39,\cdot)$	460.n	22	yes	$-1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{460}(41,\cdot)$	460.m	11	no	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{460}(43,\cdot)$	460.v	44	yes	$-1$	$1$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{460}(47,\cdot)$	460.j	4	no	$1$	$1$	$i$	$-i$	$-1$	$-1$	$-i$	$i$	$1$	$1$	$-i$	$-1$
$\chi_{460}(49,\cdot)$	460.s	22	no	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{460}(51,\cdot)$	460.q	22	no	$1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{460}(53,\cdot)$	460.x	44	no	$1$	$1$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{460}(57,\cdot)$	460.x	44	no	$1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{460}(59,\cdot)$	460.n	22	yes	$-1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{460}(61,\cdot)$	460.p	22	no	$-1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{460}(63,\cdot)$	460.v	44	yes	$-1$	$1$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{460}(67,\cdot)$	460.v	44	yes	$-1$	$1$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{460}(71,\cdot)$	460.t	22	no	$-1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{460}(73,\cdot)$	460.u	44	no	$-1$	$1$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{460}(77,\cdot)$	460.u	44	no	$-1$	$1$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{460}(79,\cdot)$	460.o	22	yes	$1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{460}(81,\cdot)$	460.m	11	no	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{460}(83,\cdot)$	460.v	44	yes	$-1$	$1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{15}{22}\right)$

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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	$460$
Structure	\(C_{2}\times C_{2}\times C_{44}\)
Order	$176$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(27\)	\(29\)
\(\chi_{460}(1,\cdot)\)	460.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{460}(3,\cdot)\)	460.w	44	yes	\(1\)	\(1\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{460}(7,\cdot)\)	460.v	44	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{460}(9,\cdot)\)	460.s	22	no	\(1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{460}(11,\cdot)\)	460.q	22	no	\(1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{460}(13,\cdot)\)	460.u	44	no	\(-1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{460}(17,\cdot)\)	460.x	44	no	\(1\)	\(1\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{460}(19,\cdot)\)	460.o	22	yes	\(1\)	\(1\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{460}(21,\cdot)\)	460.p	22	no	\(-1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{460}(27,\cdot)\)	460.w	44	yes	\(1\)	\(1\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{460}(29,\cdot)\)	460.s	22	no	\(1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{460}(31,\cdot)\)	460.t	22	no	\(-1\)	\(1\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{460}(33,\cdot)\)	460.x	44	no	\(1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{460}(37,\cdot)\)	460.x	44	no	\(1\)	\(1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{460}(39,\cdot)\)	460.n	22	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{460}(41,\cdot)\)	460.m	11	no	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{460}(43,\cdot)\)	460.v	44	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{460}(47,\cdot)\)	460.j	4	no	\(1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(i\)	\(1\)	\(1\)	\(-i\)	\(-1\)
\(\chi_{460}(49,\cdot)\)	460.s	22	no	\(1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{460}(51,\cdot)\)	460.q	22	no	\(1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{460}(53,\cdot)\)	460.x	44	no	\(1\)	\(1\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{460}(57,\cdot)\)	460.x	44	no	\(1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{460}(59,\cdot)\)	460.n	22	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{460}(61,\cdot)\)	460.p	22	no	\(-1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{460}(63,\cdot)\)	460.v	44	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{460}(67,\cdot)\)	460.v	44	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{460}(71,\cdot)\)	460.t	22	no	\(-1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{460}(73,\cdot)\)	460.u	44	no	\(-1\)	\(1\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{460}(77,\cdot)\)	460.u	44	no	\(-1\)	\(1\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{460}(79,\cdot)\)	460.o	22	yes	\(1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{460}(81,\cdot)\)	460.m	11	no	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{460}(83,\cdot)\)	460.v	44	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)

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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.