LMFDB - Group of Dirichlet characters of modulus 2268

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2268)

pari: g = idealstar(,2268,2)

Character group

sage: G.order() pari: g.no
Order	=	648
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{54}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2268}(1135,\cdot)$, $\chi_{2268}(1541,\cdot)$, $\chi_{2268}(325,\cdot)$

First 32 of 648 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	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{2268}(1,\cdot)$	2268.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2268}(5,\cdot)$	2268.cr	54	no	$1$	$1$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{2268}(11,\cdot)$	2268.cs	54	yes	$1$	$1$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{2268}(13,\cdot)$	2268.cw	54	no	$-1$	$1$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{2268}(17,\cdot)$	2268.ca	18	no	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{18}\right)$	$1$
$\chi_{2268}(19,\cdot)$	2268.cd	18	no	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{9}\right)$	$1$
$\chi_{2268}(23,\cdot)$	2268.cs	54	yes	$1$	$1$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{2268}(25,\cdot)$	2268.co	27	no	$1$	$1$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{2268}(29,\cdot)$	2268.dc	54	no	$-1$	$1$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{2268}(31,\cdot)$	2268.cu	54	yes	$1$	$1$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{2268}(37,\cdot)$	2268.bq	9	no	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{9}\right)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2268}(41,\cdot)$	2268.dg	54	no	$1$	$1$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{2268}(43,\cdot)$	2268.cx	54	no	$-1$	$1$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{2268}(47,\cdot)$	2268.da	54	yes	$-1$	$1$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{2268}(53,\cdot)$	2268.m	6	no	$-1$	$1$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2268}(55,\cdot)$	2268.bi	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{2268}(59,\cdot)$	2268.da	54	yes	$-1$	$1$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{2268}(61,\cdot)$	2268.cv	54	no	$-1$	$1$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{2268}(65,\cdot)$	2268.db	54	no	$-1$	$1$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{2268}(67,\cdot)$	2268.cy	54	yes	$-1$	$1$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{2268}(71,\cdot)$	2268.cf	18	no	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{2268}(73,\cdot)$	2268.br	18	no	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{18}\right)$	$-1$	$-1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{2268}(79,\cdot)$	2268.cy	54	yes	$-1$	$1$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{2268}(83,\cdot)$	2268.cz	54	yes	$-1$	$1$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{2268}(85,\cdot)$	2268.cn	27	no	$1$	$1$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{2268}(89,\cdot)$	2268.ca	18	no	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{17}{18}\right)$	$1$
$\chi_{2268}(95,\cdot)$	2268.de	54	yes	$1$	$1$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{2268}(97,\cdot)$	2268.cw	54	no	$-1$	$1$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{2268}(101,\cdot)$	2268.cr	54	no	$1$	$1$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{2268}(103,\cdot)$	2268.dh	54	yes	$1$	$1$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{2268}(107,\cdot)$	2268.o	6	no	$1$	$1$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{2268}(109,\cdot)$	2268.l	3	no	$1$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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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	$2268$
Structure	\(C_{2}\times C_{6}\times C_{54}\)
Order	$648$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)
\(\chi_{2268}(1,\cdot)\)	2268.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2268}(5,\cdot)\)	2268.cr	54	no	\(1\)	\(1\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{2268}(11,\cdot)\)	2268.cs	54	yes	\(1\)	\(1\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{2268}(13,\cdot)\)	2268.cw	54	no	\(-1\)	\(1\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{2268}(17,\cdot)\)	2268.ca	18	no	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(1\)
\(\chi_{2268}(19,\cdot)\)	2268.cd	18	no	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(1\)
\(\chi_{2268}(23,\cdot)\)	2268.cs	54	yes	\(1\)	\(1\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{2268}(25,\cdot)\)	2268.co	27	no	\(1\)	\(1\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{2268}(29,\cdot)\)	2268.dc	54	no	\(-1\)	\(1\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{2268}(31,\cdot)\)	2268.cu	54	yes	\(1\)	\(1\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{2268}(37,\cdot)\)	2268.bq	9	no	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2268}(41,\cdot)\)	2268.dg	54	no	\(1\)	\(1\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{2268}(43,\cdot)\)	2268.cx	54	no	\(-1\)	\(1\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{2268}(47,\cdot)\)	2268.da	54	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{2268}(53,\cdot)\)	2268.m	6	no	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2268}(55,\cdot)\)	2268.bi	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{2268}(59,\cdot)\)	2268.da	54	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{2268}(61,\cdot)\)	2268.cv	54	no	\(-1\)	\(1\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{2268}(65,\cdot)\)	2268.db	54	no	\(-1\)	\(1\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{2268}(67,\cdot)\)	2268.cy	54	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{2268}(71,\cdot)\)	2268.cf	18	no	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2268}(73,\cdot)\)	2268.br	18	no	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2268}(79,\cdot)\)	2268.cy	54	yes	\(-1\)	\(1\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{2268}(83,\cdot)\)	2268.cz	54	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{2268}(85,\cdot)\)	2268.cn	27	no	\(1\)	\(1\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{2268}(89,\cdot)\)	2268.ca	18	no	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(1\)
\(\chi_{2268}(95,\cdot)\)	2268.de	54	yes	\(1\)	\(1\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{2268}(97,\cdot)\)	2268.cw	54	no	\(-1\)	\(1\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{2268}(101,\cdot)\)	2268.cr	54	no	\(1\)	\(1\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{2268}(103,\cdot)\)	2268.dh	54	yes	\(1\)	\(1\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{2268}(107,\cdot)\)	2268.o	6	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2268}(109,\cdot)\)	2268.l	3	no	\(1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)

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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.