LMFDB - Group of Dirichlet characters of modulus 536

Show commands: PariGP / SageMath

sage: H = DirichletGroup(536)

pari: g = idealstar(,536,2)

Character group

sage: G.order() pari: g.no
Order	=	264
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{66}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{536}(135,\cdot)$, $\chi_{536}(269,\cdot)$, $\chi_{536}(337,\cdot)$

First 32 of 264 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{536}(1,\cdot)$	536.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{536}(3,\cdot)$	536.u	22	yes	$1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{536}(5,\cdot)$	536.r	22	yes	$-1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{536}(7,\cdot)$	536.bb	66	no	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{20}{33}\right)$
$\chi_{536}(9,\cdot)$	536.q	11	no	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{536}(11,\cdot)$	536.bd	66	yes	$1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{61}{66}\right)$
$\chi_{536}(13,\cdot)$	536.z	66	yes	$-1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{23}{66}\right)$
$\chi_{536}(15,\cdot)$	536.v	22	no	$-1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{536}(17,\cdot)$	536.y	33	no	$1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{4}{33}\right)$
$\chi_{536}(19,\cdot)$	536.ba	66	yes	$-1$	$1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{59}{66}\right)$
$\chi_{536}(21,\cdot)$	536.bf	66	yes	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{49}{66}\right)$
$\chi_{536}(23,\cdot)$	536.bc	66	no	$-1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{10}{33}\right)$
$\chi_{536}(25,\cdot)$	536.q	11	no	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{536}(27,\cdot)$	536.u	22	yes	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{536}(29,\cdot)$	536.j	6	yes	$1$	$1$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{536}(31,\cdot)$	536.bb	66	no	$1$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{5}{33}\right)$
$\chi_{536}(33,\cdot)$	536.y	33	no	$1$	$1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{2}{33}\right)$
$\chi_{536}(35,\cdot)$	536.ba	66	yes	$-1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{13}{66}\right)$
$\chi_{536}(37,\cdot)$	536.j	6	yes	$1$	$1$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{536}(39,\cdot)$	536.bc	66	no	$-1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{16}{33}\right)$
$\chi_{536}(41,\cdot)$	536.be	66	no	$-1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{26}{33}\right)$
$\chi_{536}(43,\cdot)$	536.u	22	yes	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{536}(45,\cdot)$	536.r	22	yes	$-1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{536}(47,\cdot)$	536.bc	66	no	$-1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{32}{33}\right)$
$\chi_{536}(49,\cdot)$	536.y	33	no	$1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{7}{33}\right)$
$\chi_{536}(51,\cdot)$	536.bd	66	yes	$1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{17}{66}\right)$
$\chi_{536}(53,\cdot)$	536.r	22	yes	$-1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{536}(55,\cdot)$	536.bc	66	no	$-1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{17}{33}\right)$
$\chi_{536}(57,\cdot)$	536.be	66	no	$-1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{1}{33}\right)$
$\chi_{536}(59,\cdot)$	536.t	22	yes	$-1$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{536}(61,\cdot)$	536.z	66	yes	$-1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{5}{66}\right)$
$\chi_{536}(63,\cdot)$	536.bb	66	no	$1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{29}{33}\right)$

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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	$536$
Structure	\(C_{2}\times C_{2}\times C_{66}\)
Order	$264$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{536}(1,\cdot)\)	536.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{536}(3,\cdot)\)	536.u	22	yes	\(1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{536}(5,\cdot)\)	536.r	22	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{536}(7,\cdot)\)	536.bb	66	no	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)
\(\chi_{536}(9,\cdot)\)	536.q	11	no	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{536}(11,\cdot)\)	536.bd	66	yes	\(1\)	\(1\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{61}{66}\right)\)
\(\chi_{536}(13,\cdot)\)	536.z	66	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{23}{66}\right)\)
\(\chi_{536}(15,\cdot)\)	536.v	22	no	\(-1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{536}(17,\cdot)\)	536.y	33	no	\(1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)
\(\chi_{536}(19,\cdot)\)	536.ba	66	yes	\(-1\)	\(1\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{59}{66}\right)\)
\(\chi_{536}(21,\cdot)\)	536.bf	66	yes	\(1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{49}{66}\right)\)
\(\chi_{536}(23,\cdot)\)	536.bc	66	no	\(-1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)
\(\chi_{536}(25,\cdot)\)	536.q	11	no	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{536}(27,\cdot)\)	536.u	22	yes	\(1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{536}(29,\cdot)\)	536.j	6	yes	\(1\)	\(1\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{536}(31,\cdot)\)	536.bb	66	no	\(1\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)
\(\chi_{536}(33,\cdot)\)	536.y	33	no	\(1\)	\(1\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)
\(\chi_{536}(35,\cdot)\)	536.ba	66	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)
\(\chi_{536}(37,\cdot)\)	536.j	6	yes	\(1\)	\(1\)	\(-1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{536}(39,\cdot)\)	536.bc	66	no	\(-1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)
\(\chi_{536}(41,\cdot)\)	536.be	66	no	\(-1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)
\(\chi_{536}(43,\cdot)\)	536.u	22	yes	\(1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{536}(45,\cdot)\)	536.r	22	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{536}(47,\cdot)\)	536.bc	66	no	\(-1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)
\(\chi_{536}(49,\cdot)\)	536.y	33	no	\(1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)
\(\chi_{536}(51,\cdot)\)	536.bd	66	yes	\(1\)	\(1\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)
\(\chi_{536}(53,\cdot)\)	536.r	22	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{536}(55,\cdot)\)	536.bc	66	no	\(-1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{17}{33}\right)\)
\(\chi_{536}(57,\cdot)\)	536.be	66	no	\(-1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)
\(\chi_{536}(59,\cdot)\)	536.t	22	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{536}(61,\cdot)\)	536.z	66	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{5}{66}\right)\)
\(\chi_{536}(63,\cdot)\)	536.bb	66	no	\(1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)

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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.