LMFDB - Group of Dirichlet characters of modulus 1680

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1680)

pari: g = idealstar(,1680,2)

Character group

sage: G.order() pari: g.no
Order	=	384
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{12}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1680}(1471,\cdot)$, $\chi_{1680}(421,\cdot)$, $\chi_{1680}(1121,\cdot)$, $\chi_{1680}(337,\cdot)$, $\chi_{1680}(241,\cdot)$

First 32 of 384 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	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{1680}(1,\cdot)$	1680.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1680}(11,\cdot)$	1680.fm	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$-i$
$\chi_{1680}(13,\cdot)$	1680.co	4	no	$1$	$1$	$-i$	$1$	$i$	$i$	$-i$	$-i$	$-1$	$-1$	$1$	$1$
$\chi_{1680}(17,\cdot)$	1680.fz	12	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$-i$
$\chi_{1680}(19,\cdot)$	1680.ff	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$-i$
$\chi_{1680}(23,\cdot)$	1680.gb	12	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$i$
$\chi_{1680}(29,\cdot)$	1680.ci	4	no	$-1$	$1$	$i$	$-i$	$1$	$i$	$-1$	$-i$	$1$	$i$	$1$	$i$
$\chi_{1680}(31,\cdot)$	1680.dx	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$
$\chi_{1680}(37,\cdot)$	1680.es	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$
$\chi_{1680}(41,\cdot)$	1680.bf	2	no	$1$	$1$	$1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$-1$	$1$	$-1$
$\chi_{1680}(43,\cdot)$	1680.cp	4	no	$1$	$1$	$-i$	$1$	$-i$	$-i$	$i$	$i$	$-1$	$1$	$-1$	$1$
$\chi_{1680}(47,\cdot)$	1680.eo	12	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$i$
$\chi_{1680}(53,\cdot)$	1680.fp	12	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$
$\chi_{1680}(59,\cdot)$	1680.fg	12	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$i$
$\chi_{1680}(61,\cdot)$	1680.fn	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$-i$
$\chi_{1680}(67,\cdot)$	1680.fs	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$
$\chi_{1680}(71,\cdot)$	1680.e	2	no	$1$	$1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$1$
$\chi_{1680}(73,\cdot)$	1680.gd	12	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$-i$
$\chi_{1680}(79,\cdot)$	1680.dy	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$1$
$\chi_{1680}(83,\cdot)$	1680.cr	4	yes	$1$	$1$	$-i$	$1$	$-i$	$-i$	$-i$	$i$	$1$	$-1$	$-1$	$-1$
$\chi_{1680}(89,\cdot)$	1680.dh	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$
$\chi_{1680}(97,\cdot)$	1680.cz	4	no	$1$	$1$	$1$	$i$	$-i$	$1$	$-i$	$-1$	$-1$	$i$	$-1$	$-i$
$\chi_{1680}(101,\cdot)$	1680.ey	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$i$
$\chi_{1680}(103,\cdot)$	1680.ek	12	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$i$
$\chi_{1680}(107,\cdot)$	1680.ex	12	yes	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$
$\chi_{1680}(109,\cdot)$	1680.fh	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$i$
$\chi_{1680}(113,\cdot)$	1680.bk	4	no	$1$	$1$	$-1$	$i$	$i$	$-1$	$-i$	$1$	$1$	$-i$	$-1$	$i$
$\chi_{1680}(121,\cdot)$	1680.du	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$
$\chi_{1680}(127,\cdot)$	1680.bl	4	no	$1$	$1$	$-1$	$-i$	$i$	$1$	$i$	$-1$	$-1$	$i$	$1$	$i$
$\chi_{1680}(131,\cdot)$	1680.fd	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$i$
$\chi_{1680}(137,\cdot)$	1680.ei	12	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$i$
$\chi_{1680}(139,\cdot)$	1680.ch	4	no	$1$	$1$	$-i$	$-i$	$1$	$-i$	$-1$	$-i$	$1$	$-i$	$1$	$i$

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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	$1680$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{12}\)
Order	$384$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{1680}(1,\cdot)\)	1680.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1680}(11,\cdot)\)	1680.fm	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(-i\)
\(\chi_{1680}(13,\cdot)\)	1680.co	4	no	\(1\)	\(1\)	\(-i\)	\(1\)	\(i\)	\(i\)	\(-i\)	\(-i\)	\(-1\)	\(-1\)	\(1\)	\(1\)
\(\chi_{1680}(17,\cdot)\)	1680.fz	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(-i\)
\(\chi_{1680}(19,\cdot)\)	1680.ff	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(-i\)
\(\chi_{1680}(23,\cdot)\)	1680.gb	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(i\)
\(\chi_{1680}(29,\cdot)\)	1680.ci	4	no	\(-1\)	\(1\)	\(i\)	\(-i\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(1\)	\(i\)	\(1\)	\(i\)
\(\chi_{1680}(31,\cdot)\)	1680.dx	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(-1\)
\(\chi_{1680}(37,\cdot)\)	1680.es	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(1\)
\(\chi_{1680}(41,\cdot)\)	1680.bf	2	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)
\(\chi_{1680}(43,\cdot)\)	1680.cp	4	no	\(1\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-i\)	\(i\)	\(i\)	\(-1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{1680}(47,\cdot)\)	1680.eo	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(i\)
\(\chi_{1680}(53,\cdot)\)	1680.fp	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(-1\)
\(\chi_{1680}(59,\cdot)\)	1680.fg	12	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(i\)
\(\chi_{1680}(61,\cdot)\)	1680.fn	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(-i\)
\(\chi_{1680}(67,\cdot)\)	1680.fs	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)
\(\chi_{1680}(71,\cdot)\)	1680.e	2	no	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{1680}(73,\cdot)\)	1680.gd	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(-i\)
\(\chi_{1680}(79,\cdot)\)	1680.dy	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(1\)
\(\chi_{1680}(83,\cdot)\)	1680.cr	4	yes	\(1\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-i\)	\(-i\)	\(i\)	\(1\)	\(-1\)	\(-1\)	\(-1\)
\(\chi_{1680}(89,\cdot)\)	1680.dh	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)
\(\chi_{1680}(97,\cdot)\)	1680.cz	4	no	\(1\)	\(1\)	\(1\)	\(i\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(-1\)	\(-i\)
\(\chi_{1680}(101,\cdot)\)	1680.ey	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(i\)
\(\chi_{1680}(103,\cdot)\)	1680.ek	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(i\)
\(\chi_{1680}(107,\cdot)\)	1680.ex	12	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-1\)
\(\chi_{1680}(109,\cdot)\)	1680.fh	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(i\)
\(\chi_{1680}(113,\cdot)\)	1680.bk	4	no	\(1\)	\(1\)	\(-1\)	\(i\)	\(i\)	\(-1\)	\(-i\)	\(1\)	\(1\)	\(-i\)	\(-1\)	\(i\)
\(\chi_{1680}(121,\cdot)\)	1680.du	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-1\)
\(\chi_{1680}(127,\cdot)\)	1680.bl	4	no	\(1\)	\(1\)	\(-1\)	\(-i\)	\(i\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(1\)	\(i\)
\(\chi_{1680}(131,\cdot)\)	1680.fd	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(i\)
\(\chi_{1680}(137,\cdot)\)	1680.ei	12	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(i\)
\(\chi_{1680}(139,\cdot)\)	1680.ch	4	no	\(1\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(1\)	\(-i\)	\(1\)	\(i\)

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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.