LMFDB - Group of Dirichlet characters of modulus 469

Show commands: PariGP / SageMath

sage: H = DirichletGroup(469)

pari: g = idealstar(,469,2)

Character group

sage: G.order() pari: g.no
Order	=	396
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{66}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{469}(269,\cdot)$, $\chi_{469}(337,\cdot)$

First 32 of 396 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{469}(1,\cdot)$	469.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{469}(2,\cdot)$	469.bm	66	yes	$-1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{19}{66}\right)$
$\chi_{469}(3,\cdot)$	469.bh	66	yes	$1$	$1$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{2}{33}\right)$
$\chi_{469}(4,\cdot)$	469.y	33	yes	$1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{19}{33}\right)$
$\chi_{469}(5,\cdot)$	469.bh	66	yes	$1$	$1$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{16}{33}\right)$
$\chi_{469}(6,\cdot)$	469.bl	66	yes	$-1$	$1$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{23}{66}\right)$
$\chi_{469}(8,\cdot)$	469.x	22	no	$-1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{469}(9,\cdot)$	469.ba	33	yes	$1$	$1$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{4}{33}\right)$
$\chi_{469}(10,\cdot)$	469.bj	66	yes	$-1$	$1$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{469}(11,\cdot)$	469.bm	66	yes	$-1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{65}{66}\right)$
$\chi_{469}(12,\cdot)$	469.bg	66	yes	$1$	$1$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{469}(13,\cdot)$	469.bd	66	yes	$1$	$1$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{10}{33}\right)$
$\chi_{469}(15,\cdot)$	469.u	11	no	$1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{469}(16,\cdot)$	469.y	33	yes	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{33}\right)$
$\chi_{469}(17,\cdot)$	469.bj	66	yes	$-1$	$1$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{469}(18,\cdot)$	469.bf	66	yes	$-1$	$1$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{469}(19,\cdot)$	469.bc	66	yes	$-1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{25}{66}\right)$
$\chi_{469}(20,\cdot)$	469.bd	66	yes	$1$	$1$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{2}{33}\right)$
$\chi_{469}(22,\cdot)$	469.u	11	no	$1$	$1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{469}(23,\cdot)$	469.y	33	yes	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{33}\right)$
$\chi_{469}(24,\cdot)$	469.bk	66	yes	$-1$	$1$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{61}{66}\right)$
$\chi_{469}(25,\cdot)$	469.ba	33	yes	$1$	$1$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{32}{33}\right)$
$\chi_{469}(26,\cdot)$	469.bj	66	yes	$-1$	$1$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{469}(27,\cdot)$	469.w	22	yes	$1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{469}(29,\cdot)$	469.g	3	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{469}(30,\cdot)$	469.j	6	yes	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{469}(31,\cdot)$	469.bn	66	yes	$1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{33}\right)$
$\chi_{469}(32,\cdot)$	469.bm	66	yes	$-1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{29}{66}\right)$
$\chi_{469}(33,\cdot)$	469.bj	66	yes	$-1$	$1$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{469}(34,\cdot)$	469.bd	66	yes	$1$	$1$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{29}{33}\right)$
$\chi_{469}(36,\cdot)$	469.z	33	no	$1$	$1$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{23}{33}\right)$
$\chi_{469}(37,\cdot)$	469.h	3	yes	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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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	$469$
Structure	\(C_{6}\times C_{66}\)
Order	$396$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{469}(1,\cdot)\)	469.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{469}(2,\cdot)\)	469.bm	66	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{19}{66}\right)\)
\(\chi_{469}(3,\cdot)\)	469.bh	66	yes	\(1\)	\(1\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)
\(\chi_{469}(4,\cdot)\)	469.y	33	yes	\(1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{19}{33}\right)\)
\(\chi_{469}(5,\cdot)\)	469.bh	66	yes	\(1\)	\(1\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)
\(\chi_{469}(6,\cdot)\)	469.bl	66	yes	\(-1\)	\(1\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{23}{66}\right)\)
\(\chi_{469}(8,\cdot)\)	469.x	22	no	\(-1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{469}(9,\cdot)\)	469.ba	33	yes	\(1\)	\(1\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)
\(\chi_{469}(10,\cdot)\)	469.bj	66	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{469}(11,\cdot)\)	469.bm	66	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{65}{66}\right)\)
\(\chi_{469}(12,\cdot)\)	469.bg	66	yes	\(1\)	\(1\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{469}(13,\cdot)\)	469.bd	66	yes	\(1\)	\(1\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)
\(\chi_{469}(15,\cdot)\)	469.u	11	no	\(1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{469}(16,\cdot)\)	469.y	33	yes	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{33}\right)\)
\(\chi_{469}(17,\cdot)\)	469.bj	66	yes	\(-1\)	\(1\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{469}(18,\cdot)\)	469.bf	66	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{469}(19,\cdot)\)	469.bc	66	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{25}{66}\right)\)
\(\chi_{469}(20,\cdot)\)	469.bd	66	yes	\(1\)	\(1\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)
\(\chi_{469}(22,\cdot)\)	469.u	11	no	\(1\)	\(1\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{469}(23,\cdot)\)	469.y	33	yes	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{33}\right)\)
\(\chi_{469}(24,\cdot)\)	469.bk	66	yes	\(-1\)	\(1\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{61}{66}\right)\)
\(\chi_{469}(25,\cdot)\)	469.ba	33	yes	\(1\)	\(1\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)
\(\chi_{469}(26,\cdot)\)	469.bj	66	yes	\(-1\)	\(1\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{469}(27,\cdot)\)	469.w	22	yes	\(1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{469}(29,\cdot)\)	469.g	3	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{469}(30,\cdot)\)	469.j	6	yes	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{469}(31,\cdot)\)	469.bn	66	yes	\(1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{33}\right)\)
\(\chi_{469}(32,\cdot)\)	469.bm	66	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{29}{66}\right)\)
\(\chi_{469}(33,\cdot)\)	469.bj	66	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{469}(34,\cdot)\)	469.bd	66	yes	\(1\)	\(1\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)
\(\chi_{469}(36,\cdot)\)	469.z	33	no	\(1\)	\(1\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)
\(\chi_{469}(37,\cdot)\)	469.h	3	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)

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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.