LMFDB - Group of Dirichlet characters of modulus 560

Show commands: PariGP / SageMath

sage: H = DirichletGroup(560)

pari: g = idealstar(,560,2)

Character group

sage: G.order() pari: g.no
Order	=	192
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{12}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{560}(351,\cdot)$, $\chi_{560}(421,\cdot)$, $\chi_{560}(337,\cdot)$, $\chi_{560}(241,\cdot)$

First 32 of 192 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	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{560}(1,\cdot)$	560.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{560}(3,\cdot)$	560.da	12	yes	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$-i$	$e\left(\frac{2}{3}\right)$
$\chi_{560}(9,\cdot)$	560.bv	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{560}(11,\cdot)$	560.cm	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{560}(13,\cdot)$	560.bn	4	yes	$1$	$1$	$1$	$1$	$-i$	$1$	$i$	$i$	$-i$	$1$	$-i$	$-1$
$\chi_{560}(17,\cdot)$	560.ci	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{560}(19,\cdot)$	560.co	12	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{560}(23,\cdot)$	560.cl	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{560}(27,\cdot)$	560.u	4	yes	$-1$	$1$	$-1$	$1$	$-i$	$1$	$-i$	$i$	$-i$	$-1$	$i$	$1$
$\chi_{560}(29,\cdot)$	560.bb	4	no	$1$	$1$	$-i$	$-1$	$-i$	$-i$	$-1$	$i$	$1$	$i$	$i$	$1$
$\chi_{560}(31,\cdot)$	560.bs	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{560}(33,\cdot)$	560.ci	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{560}(37,\cdot)$	560.cy	12	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{560}(39,\cdot)$	560.by	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{560}(41,\cdot)$	560.m	2	no	$-1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$1$	$1$	$-1$	$-1$
$\chi_{560}(43,\cdot)$	560.t	4	no	$1$	$1$	$-1$	$1$	$-i$	$1$	$-i$	$-i$	$i$	$-1$	$i$	$-1$
$\chi_{560}(47,\cdot)$	560.cw	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{560}(51,\cdot)$	560.cm	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{560}(53,\cdot)$	560.cg	12	yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$i$	$e\left(\frac{2}{3}\right)$
$\chi_{560}(57,\cdot)$	560.y	4	no	$-1$	$1$	$i$	$-1$	$-1$	$i$	$i$	$1$	$-i$	$-i$	$1$	$1$
$\chi_{560}(59,\cdot)$	560.co	12	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$-i$	$e\left(\frac{2}{3}\right)$
$\chi_{560}(61,\cdot)$	560.ct	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{560}(67,\cdot)$	560.db	12	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{560}(69,\cdot)$	560.bf	4	yes	$-1$	$1$	$-i$	$-1$	$i$	$-i$	$1$	$i$	$1$	$i$	$-i$	$-1$
$\chi_{560}(71,\cdot)$	560.o	2	no	$-1$	$1$	$1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$1$	$-1$	$-1$
$\chi_{560}(73,\cdot)$	560.cx	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{560}(79,\cdot)$	560.bt	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{560}(81,\cdot)$	560.q	3	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{560}(83,\cdot)$	560.u	4	yes	$-1$	$1$	$-1$	$1$	$i$	$1$	$i$	$-i$	$i$	$-1$	$-i$	$1$
$\chi_{560}(87,\cdot)$	560.cj	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{560}(89,\cdot)$	560.ca	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{560}(93,\cdot)$	560.cy	12	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$-i$	$e\left(\frac{1}{3}\right)$

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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	$560$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{12}\)
Order	$192$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{560}(1,\cdot)\)	560.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{560}(3,\cdot)\)	560.da	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{560}(9,\cdot)\)	560.bv	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{560}(11,\cdot)\)	560.cm	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{560}(13,\cdot)\)	560.bn	4	yes	\(1\)	\(1\)	\(1\)	\(1\)	\(-i\)	\(1\)	\(i\)	\(i\)	\(-i\)	\(1\)	\(-i\)	\(-1\)
\(\chi_{560}(17,\cdot)\)	560.ci	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{560}(19,\cdot)\)	560.co	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{560}(23,\cdot)\)	560.cl	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{560}(27,\cdot)\)	560.u	4	yes	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(i\)	\(-i\)	\(-1\)	\(i\)	\(1\)
\(\chi_{560}(29,\cdot)\)	560.bb	4	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(1\)	\(i\)	\(i\)	\(1\)
\(\chi_{560}(31,\cdot)\)	560.bs	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{560}(33,\cdot)\)	560.ci	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{560}(37,\cdot)\)	560.cy	12	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{560}(39,\cdot)\)	560.by	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{560}(41,\cdot)\)	560.m	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{560}(43,\cdot)\)	560.t	4	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-i\)	\(i\)	\(-1\)	\(i\)	\(-1\)
\(\chi_{560}(47,\cdot)\)	560.cw	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{560}(51,\cdot)\)	560.cm	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{560}(53,\cdot)\)	560.cg	12	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{560}(57,\cdot)\)	560.y	4	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(i\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(1\)
\(\chi_{560}(59,\cdot)\)	560.co	12	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{560}(61,\cdot)\)	560.ct	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{560}(67,\cdot)\)	560.db	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{560}(69,\cdot)\)	560.bf	4	yes	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(-i\)	\(1\)	\(i\)	\(1\)	\(i\)	\(-i\)	\(-1\)
\(\chi_{560}(71,\cdot)\)	560.o	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{560}(73,\cdot)\)	560.cx	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{560}(79,\cdot)\)	560.bt	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{560}(81,\cdot)\)	560.q	3	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{560}(83,\cdot)\)	560.u	4	yes	\(-1\)	\(1\)	\(-1\)	\(1\)	\(i\)	\(1\)	\(i\)	\(-i\)	\(i\)	\(-1\)	\(-i\)	\(1\)
\(\chi_{560}(87,\cdot)\)	560.cj	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{560}(89,\cdot)\)	560.ca	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{560}(93,\cdot)\)	560.cy	12	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)

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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.