LMFDB - Group of Dirichlet characters of modulus 567

Show commands: PariGP / SageMath

sage: H = DirichletGroup(567)

pari: g = idealstar(,567,2)

Character group

sage: G.order() pari: g.no
Order	=	324
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{54}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{567}(407,\cdot)$, $\chi_{567}(325,\cdot)$

First 32 of 324 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{567}(1,\cdot)$	567.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{567}(2,\cdot)$	567.bq	54	yes	$-1$	$1$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{567}(4,\cdot)$	567.bg	27	yes	$1$	$1$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{567}(5,\cdot)$	567.br	54	yes	$1$	$1$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{567}(8,\cdot)$	567.bb	18	no	$-1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{567}(10,\cdot)$	567.z	18	no	$-1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{567}(11,\cdot)$	567.bj	54	yes	$-1$	$1$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{567}(13,\cdot)$	567.bn	54	yes	$-1$	$1$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{567}(16,\cdot)$	567.bg	27	yes	$1$	$1$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{567}(17,\cdot)$	567.bd	18	no	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{567}(19,\cdot)$	567.z	18	no	$-1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{567}(20,\cdot)$	567.bm	54	yes	$1$	$1$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{567}(22,\cdot)$	567.bh	27	no	$1$	$1$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{567}(23,\cdot)$	567.bj	54	yes	$-1$	$1$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{567}(25,\cdot)$	567.bi	27	yes	$1$	$1$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{567}(26,\cdot)$	567.s	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{567}(29,\cdot)$	567.bp	54	no	$-1$	$1$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{567}(31,\cdot)$	567.bo	54	yes	$-1$	$1$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{567}(32,\cdot)$	567.bq	54	yes	$-1$	$1$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{567}(34,\cdot)$	567.bn	54	yes	$-1$	$1$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{567}(37,\cdot)$	567.w	9	no	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{9}\right)$	$1$	$1$
$\chi_{567}(38,\cdot)$	567.br	54	yes	$1$	$1$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{567}(40,\cdot)$	567.bk	54	yes	$-1$	$1$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{567}(41,\cdot)$	567.bm	54	yes	$1$	$1$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{567}(43,\cdot)$	567.bh	27	no	$1$	$1$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{567}(44,\cdot)$	567.bf	18	no	$-1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{9}\right)$	$-1$	$1$
$\chi_{567}(46,\cdot)$	567.w	9	no	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$1$	$1$
$\chi_{567}(47,\cdot)$	567.bl	54	yes	$1$	$1$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{567}(50,\cdot)$	567.bp	54	no	$-1$	$1$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{567}(52,\cdot)$	567.bk	54	yes	$-1$	$1$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{567}(53,\cdot)$	567.n	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{567}(55,\cdot)$	567.l	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$

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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	$567$
Structure	\(C_{6}\times C_{54}\)
Order	$324$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{567}(1,\cdot)\)	567.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{567}(2,\cdot)\)	567.bq	54	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{567}(4,\cdot)\)	567.bg	27	yes	\(1\)	\(1\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{567}(5,\cdot)\)	567.br	54	yes	\(1\)	\(1\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{567}(8,\cdot)\)	567.bb	18	no	\(-1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{567}(10,\cdot)\)	567.z	18	no	\(-1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{567}(11,\cdot)\)	567.bj	54	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{567}(13,\cdot)\)	567.bn	54	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{567}(16,\cdot)\)	567.bg	27	yes	\(1\)	\(1\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{567}(17,\cdot)\)	567.bd	18	no	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{567}(19,\cdot)\)	567.z	18	no	\(-1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{567}(20,\cdot)\)	567.bm	54	yes	\(1\)	\(1\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{567}(22,\cdot)\)	567.bh	27	no	\(1\)	\(1\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{567}(23,\cdot)\)	567.bj	54	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{567}(25,\cdot)\)	567.bi	27	yes	\(1\)	\(1\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{567}(26,\cdot)\)	567.s	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{567}(29,\cdot)\)	567.bp	54	no	\(-1\)	\(1\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{567}(31,\cdot)\)	567.bo	54	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{567}(32,\cdot)\)	567.bq	54	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{567}(34,\cdot)\)	567.bn	54	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{567}(37,\cdot)\)	567.w	9	no	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(1\)	\(1\)
\(\chi_{567}(38,\cdot)\)	567.br	54	yes	\(1\)	\(1\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{567}(40,\cdot)\)	567.bk	54	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{567}(41,\cdot)\)	567.bm	54	yes	\(1\)	\(1\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{567}(43,\cdot)\)	567.bh	27	no	\(1\)	\(1\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{567}(44,\cdot)\)	567.bf	18	no	\(-1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(-1\)	\(1\)
\(\chi_{567}(46,\cdot)\)	567.w	9	no	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(1\)	\(1\)
\(\chi_{567}(47,\cdot)\)	567.bl	54	yes	\(1\)	\(1\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{567}(50,\cdot)\)	567.bp	54	no	\(-1\)	\(1\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{567}(52,\cdot)\)	567.bk	54	yes	\(-1\)	\(1\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{567}(53,\cdot)\)	567.n	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{567}(55,\cdot)\)	567.l	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(-1\)

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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.