LMFDB - Group of Dirichlet characters of modulus 4368

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4368)

pari: g = idealstar(,4368,2)

Character group

sage: G.order() pari: g.no
Order	=	1152
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{12}\times C_{12}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4368}(3823,\cdot)$, $\chi_{4368}(1093,\cdot)$, $\chi_{4368}(1457,\cdot)$, $\chi_{4368}(1249,\cdot)$, $\chi_{4368}(2017,\cdot)$

First 32 of 1152 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	$-1$	$1$	$5$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{4368}(1,\cdot)$	4368.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4368}(5,\cdot)$	4368.ir	12	yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$
$\chi_{4368}(11,\cdot)$	4368.jc	12	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{4368}(17,\cdot)$	4368.gl	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{4368}(19,\cdot)$	4368.ii	12	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{4368}(23,\cdot)$	4368.fx	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{4368}(25,\cdot)$	4368.ej	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{4368}(29,\cdot)$	4368.lw	12	no	$-1$	$1$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{4368}(31,\cdot)$	4368.kt	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$i$
$\chi_{4368}(37,\cdot)$	4368.oj	12	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{1}{12}\right)$
$\chi_{4368}(41,\cdot)$	4368.lt	12	no	$-1$	$1$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{4368}(43,\cdot)$	4368.kb	12	no	$-1$	$1$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{4368}(47,\cdot)$	4368.mz	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$i$
$\chi_{4368}(53,\cdot)$	4368.mh	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$1$
$\chi_{4368}(55,\cdot)$	4368.hr	6	no	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{4368}(59,\cdot)$	4368.oi	12	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{5}{12}\right)$
$\chi_{4368}(61,\cdot)$	4368.nh	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{4368}(67,\cdot)$	4368.oh	12	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{4368}(71,\cdot)$	4368.ku	12	no	$-1$	$1$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{4368}(73,\cdot)$	4368.lc	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-i$
$\chi_{4368}(79,\cdot)$	4368.ez	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{4368}(83,\cdot)$	4368.bo	4	yes	$1$	$1$	$-1$	$1$	$-1$	$1$	$1$	$1$	$-i$	$-i$	$1$	$i$
$\chi_{4368}(85,\cdot)$	4368.ic	12	no	$-1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{4368}(89,\cdot)$	4368.jo	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{7}{12}\right)$
$\chi_{4368}(95,\cdot)$	4368.eu	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{4368}(97,\cdot)$	4368.kv	12	no	$1$	$1$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{4368}(101,\cdot)$	4368.kj	12	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{4368}(103,\cdot)$	4368.gw	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{4368}(107,\cdot)$	4368.jk	12	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{4368}(109,\cdot)$	4368.om	12	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$i$
$\chi_{4368}(113,\cdot)$	4368.dv	6	no	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{4368}(115,\cdot)$	4368.oz	12	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$

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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	$4368$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{12}\times C_{12}\)
Order	$1152$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{4368}(1,\cdot)\)	4368.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4368}(5,\cdot)\)	4368.ir	12	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)
\(\chi_{4368}(11,\cdot)\)	4368.jc	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{4368}(17,\cdot)\)	4368.gl	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{4368}(19,\cdot)\)	4368.ii	12	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{4368}(23,\cdot)\)	4368.fx	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{4368}(25,\cdot)\)	4368.ej	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{4368}(29,\cdot)\)	4368.lw	12	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{4368}(31,\cdot)\)	4368.kt	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)
\(\chi_{4368}(37,\cdot)\)	4368.oj	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{4368}(41,\cdot)\)	4368.lt	12	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{4368}(43,\cdot)\)	4368.kb	12	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{4368}(47,\cdot)\)	4368.mz	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)
\(\chi_{4368}(53,\cdot)\)	4368.mh	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)
\(\chi_{4368}(55,\cdot)\)	4368.hr	6	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{4368}(59,\cdot)\)	4368.oi	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{4368}(61,\cdot)\)	4368.nh	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{4368}(67,\cdot)\)	4368.oh	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{4368}(71,\cdot)\)	4368.ku	12	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{4368}(73,\cdot)\)	4368.lc	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)
\(\chi_{4368}(79,\cdot)\)	4368.ez	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{4368}(83,\cdot)\)	4368.bo	4	yes	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(i\)
\(\chi_{4368}(85,\cdot)\)	4368.ic	12	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{4368}(89,\cdot)\)	4368.jo	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{4368}(95,\cdot)\)	4368.eu	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{4368}(97,\cdot)\)	4368.kv	12	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{4368}(101,\cdot)\)	4368.kj	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{4368}(103,\cdot)\)	4368.gw	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{4368}(107,\cdot)\)	4368.jk	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{4368}(109,\cdot)\)	4368.om	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)
\(\chi_{4368}(113,\cdot)\)	4368.dv	6	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{4368}(115,\cdot)\)	4368.oz	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)

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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.