LMFDB - Group of Dirichlet characters of modulus 522

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(522)

gp:g = idealstar(,522,2)

magma:G := FullDirichletGroup(522);

Character group

Order	=	168	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{84}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(AbelianGroup(G));
Generators	=	$\chi_{522}(407,\cdot)$, $\chi_{522}(379,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 168 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$31$	$35$
$\chi_{522}(1,\cdot)$	522.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{522}(5,\cdot)$	522.u	42	no	$-1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{17}{21}\right)$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{522}(7,\cdot)$	522.q	21	no	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{21}\right)$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{522}(11,\cdot)$	522.x	84	no	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{17}{42}\right)$	$i$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{522}(13,\cdot)$	522.v	42	no	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{5}{21}\right)$	$-1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{522}(17,\cdot)$	522.g	4	no	$1$	$1$	$1$	$1$	$i$	$-1$	$i$	$-i$	$-1$	$1$	$-i$	$1$
$\chi_{522}(19,\cdot)$	522.s	28	no	$-1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{11}{14}\right)$	$-i$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{522}(23,\cdot)$	522.t	42	no	$-1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{11}{21}\right)$	$-1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{522}(25,\cdot)$	522.q	21	no	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{13}{21}\right)$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{522}(31,\cdot)$	522.w	84	no	$-1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{13}{42}\right)$	$-i$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{522}(35,\cdot)$	522.o	14	no	$-1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{522}(37,\cdot)$	522.s	28	no	$-1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{13}{14}\right)$	$i$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{522}(41,\cdot)$	522.l	12	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$1$
$\chi_{522}(43,\cdot)$	522.w	84	no	$-1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{29}{42}\right)$	$-i$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{522}(47,\cdot)$	522.x	84	no	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{17}{42}\right)$	$-i$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{522}(49,\cdot)$	522.q	21	no	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{21}\right)$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{522}(53,\cdot)$	522.p	14	no	$-1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$-1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{522}(55,\cdot)$	522.s	28	no	$-1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{3}{14}\right)$	$i$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{522}(59,\cdot)$	522.j	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$
$\chi_{522}(61,\cdot)$	522.w	84	no	$-1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{23}{42}\right)$	$-i$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{522}(65,\cdot)$	522.t	42	no	$-1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{21}\right)$	$-1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{522}(67,\cdot)$	522.v	42	no	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{2}{21}\right)$	$-1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{522}(71,\cdot)$	522.o	14	no	$-1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{7}\right)$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{522}(73,\cdot)$	522.s	28	no	$-1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{5}{14}\right)$	$i$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{522}(77,\cdot)$	522.x	84	no	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{19}{42}\right)$	$i$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{522}(79,\cdot)$	522.w	84	no	$-1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{11}{42}\right)$	$-i$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{522}(83,\cdot)$	522.t	42	no	$-1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{13}{21}\right)$	$-1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{522}(85,\cdot)$	522.w	84	no	$-1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{13}{42}\right)$	$i$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{522}(89,\cdot)$	522.r	28	no	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{9}{14}\right)$	$i$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{522}(91,\cdot)$	522.n	14	no	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$	$-1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{522}(95,\cdot)$	522.x	84	no	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{25}{42}\right)$	$-i$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{522}(97,\cdot)$	522.w	84	no	$-1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{5}{42}\right)$	$i$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{13}{14}\right)$

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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	$522$
Structure	\(C_{2}\times C_{84}\)
Order	$168$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(31\)	\(35\)
\(\chi_{522}(1,\cdot)\)	522.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{522}(5,\cdot)\)	522.u	42	no	\(-1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{522}(7,\cdot)\)	522.q	21	no	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{522}(11,\cdot)\)	522.x	84	no	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(i\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{522}(13,\cdot)\)	522.v	42	no	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(-1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{522}(17,\cdot)\)	522.g	4	no	\(1\)	\(1\)	\(1\)	\(1\)	\(i\)	\(-1\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(-i\)	\(1\)
\(\chi_{522}(19,\cdot)\)	522.s	28	no	\(-1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(-i\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{522}(23,\cdot)\)	522.t	42	no	\(-1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(-1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{522}(25,\cdot)\)	522.q	21	no	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{522}(31,\cdot)\)	522.w	84	no	\(-1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(-i\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{522}(35,\cdot)\)	522.o	14	no	\(-1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{522}(37,\cdot)\)	522.s	28	no	\(-1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(i\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{522}(41,\cdot)\)	522.l	12	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)
\(\chi_{522}(43,\cdot)\)	522.w	84	no	\(-1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(-i\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{522}(47,\cdot)\)	522.x	84	no	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(-i\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{522}(49,\cdot)\)	522.q	21	no	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{522}(53,\cdot)\)	522.p	14	no	\(-1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(-1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{522}(55,\cdot)\)	522.s	28	no	\(-1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(i\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{522}(59,\cdot)\)	522.j	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)
\(\chi_{522}(61,\cdot)\)	522.w	84	no	\(-1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(-i\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{522}(65,\cdot)\)	522.t	42	no	\(-1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(-1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{522}(67,\cdot)\)	522.v	42	no	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(-1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{522}(71,\cdot)\)	522.o	14	no	\(-1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{522}(73,\cdot)\)	522.s	28	no	\(-1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(i\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{522}(77,\cdot)\)	522.x	84	no	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(i\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{522}(79,\cdot)\)	522.w	84	no	\(-1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(-i\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{522}(83,\cdot)\)	522.t	42	no	\(-1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(-1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{522}(85,\cdot)\)	522.w	84	no	\(-1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(i\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{522}(89,\cdot)\)	522.r	28	no	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(i\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{522}(91,\cdot)\)	522.n	14	no	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(-1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{522}(95,\cdot)\)	522.x	84	no	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(-i\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{522}(97,\cdot)\)	522.w	84	no	\(-1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(i\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{13}{14}\right)\)

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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.