LMFDB - Group of Dirichlet characters of modulus 3360

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3360)

pari: g = idealstar(,3360,2)

Character group

sage: G.order() pari: g.no
Order	=	768
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{24}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{3360}(1471,\cdot)$, $\chi_{3360}(421,\cdot)$, $\chi_{3360}(1121,\cdot)$, $\chi_{3360}(2017,\cdot)$, $\chi_{3360}(1921,\cdot)$

First 32 of 768 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	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{3360}(1,\cdot)$	3360.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3360}(11,\cdot)$	3360.hr	24	no	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{24}\right)$	$i$	$e\left(\frac{5}{8}\right)$
$\chi_{3360}(13,\cdot)$	3360.et	8	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$
$\chi_{3360}(17,\cdot)$	3360.ft	12	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$i$
$\chi_{3360}(19,\cdot)$	3360.ij	24	no	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{24}\right)$	$-i$	$e\left(\frac{3}{8}\right)$
$\chi_{3360}(23,\cdot)$	3360.gd	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$
$\chi_{3360}(29,\cdot)$	3360.em	8	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$
$\chi_{3360}(31,\cdot)$	3360.dx	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$
$\chi_{3360}(37,\cdot)$	3360.ic	24	no	$-1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{24}\right)$	$-i$	$e\left(\frac{3}{8}\right)$
$\chi_{3360}(41,\cdot)$	3360.ck	4	no	$1$	$1$	$i$	$-i$	$1$	$-i$	$1$	$-i$	$-1$	$-i$	$-1$	$-i$
$\chi_{3360}(43,\cdot)$	3360.es	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$
$\chi_{3360}(47,\cdot)$	3360.hc	12	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$-i$
$\chi_{3360}(53,\cdot)$	3360.ia	24	yes	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{24}\right)$	$i$	$e\left(\frac{3}{8}\right)$
$\chi_{3360}(59,\cdot)$	3360.hn	24	yes	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{24}\right)$	$-i$	$e\left(\frac{5}{8}\right)$
$\chi_{3360}(61,\cdot)$	3360.ho	24	no	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{24}\right)$	$-i$	$e\left(\frac{7}{8}\right)$
$\chi_{3360}(67,\cdot)$	3360.if	24	no	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{24}\right)$	$i$	$e\left(\frac{1}{8}\right)$
$\chi_{3360}(71,\cdot)$	3360.ca	4	no	$1$	$1$	$i$	$-i$	$-1$	$i$	$-1$	$i$	$-1$	$i$	$1$	$-i$
$\chi_{3360}(73,\cdot)$	3360.hb	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$1$
$\chi_{3360}(79,\cdot)$	3360.do	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$
$\chi_{3360}(83,\cdot)$	3360.ew	8	yes	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$
$\chi_{3360}(89,\cdot)$	3360.gr	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$-i$
$\chi_{3360}(97,\cdot)$	3360.cz	4	no	$1$	$1$	$1$	$i$	$-i$	$1$	$-i$	$-1$	$-1$	$i$	$-1$	$-i$
$\chi_{3360}(101,\cdot)$	3360.io	24	no	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{24}\right)$	$-i$	$e\left(\frac{5}{8}\right)$
$\chi_{3360}(103,\cdot)$	3360.fx	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$
$\chi_{3360}(107,\cdot)$	3360.ih	24	yes	$-1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{24}\right)$	$i$	$e\left(\frac{3}{8}\right)$
$\chi_{3360}(109,\cdot)$	3360.hk	24	no	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{24}\right)$	$i$	$e\left(\frac{7}{8}\right)$
$\chi_{3360}(113,\cdot)$	3360.da	4	no	$1$	$1$	$1$	$-i$	$i$	$1$	$-i$	$-1$	$1$	$i$	$-1$	$-i$
$\chi_{3360}(121,\cdot)$	3360.gi	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$i$
$\chi_{3360}(127,\cdot)$	3360.bl	4	no	$1$	$1$	$-1$	$-i$	$i$	$1$	$i$	$-1$	$-1$	$i$	$1$	$i$
$\chi_{3360}(131,\cdot)$	3360.ii	24	no	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{24}\right)$	$i$	$e\left(\frac{3}{8}\right)$
$\chi_{3360}(137,\cdot)$	3360.gv	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$
$\chi_{3360}(139,\cdot)$	3360.ep	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$

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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	$3360$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{24}\)
Order	$768$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{3360}(1,\cdot)\)	3360.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3360}(11,\cdot)\)	3360.hr	24	no	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{3360}(13,\cdot)\)	3360.et	8	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{3360}(17,\cdot)\)	3360.ft	12	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(i\)
\(\chi_{3360}(19,\cdot)\)	3360.ij	24	no	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{3360}(23,\cdot)\)	3360.gd	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-1\)
\(\chi_{3360}(29,\cdot)\)	3360.em	8	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{3360}(31,\cdot)\)	3360.dx	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(-1\)
\(\chi_{3360}(37,\cdot)\)	3360.ic	24	no	\(-1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{3360}(41,\cdot)\)	3360.ck	4	no	\(1\)	\(1\)	\(i\)	\(-i\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(-1\)	\(-i\)
\(\chi_{3360}(43,\cdot)\)	3360.es	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{3360}(47,\cdot)\)	3360.hc	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(-i\)
\(\chi_{3360}(53,\cdot)\)	3360.ia	24	yes	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{3360}(59,\cdot)\)	3360.hn	24	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{3360}(61,\cdot)\)	3360.ho	24	no	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{3360}(67,\cdot)\)	3360.if	24	no	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{3360}(71,\cdot)\)	3360.ca	4	no	\(1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(i\)	\(-1\)	\(i\)	\(-1\)	\(i\)	\(1\)	\(-i\)
\(\chi_{3360}(73,\cdot)\)	3360.hb	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(1\)
\(\chi_{3360}(79,\cdot)\)	3360.do	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(-1\)
\(\chi_{3360}(83,\cdot)\)	3360.ew	8	yes	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{3360}(89,\cdot)\)	3360.gr	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(-i\)
\(\chi_{3360}(97,\cdot)\)	3360.cz	4	no	\(1\)	\(1\)	\(1\)	\(i\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(-1\)	\(-i\)
\(\chi_{3360}(101,\cdot)\)	3360.io	24	no	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{3360}(103,\cdot)\)	3360.fx	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)
\(\chi_{3360}(107,\cdot)\)	3360.ih	24	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{3360}(109,\cdot)\)	3360.hk	24	no	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{3360}(113,\cdot)\)	3360.da	4	no	\(1\)	\(1\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(-1\)	\(-i\)
\(\chi_{3360}(121,\cdot)\)	3360.gi	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(i\)
\(\chi_{3360}(127,\cdot)\)	3360.bl	4	no	\(1\)	\(1\)	\(-1\)	\(-i\)	\(i\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(1\)	\(i\)
\(\chi_{3360}(131,\cdot)\)	3360.ii	24	no	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{3360}(137,\cdot)\)	3360.gv	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(-1\)
\(\chi_{3360}(139,\cdot)\)	3360.ep	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)

Introduction

L-functions

Modular forms

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Fields

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Properties

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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.