LMFDB - Group of Dirichlet characters of modulus 2880

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2880)

pari: g = idealstar(,2880,2)

Character group

sage: G.order() pari: g.no
Order	=	768
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{48}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2880}(2431,\cdot)$, $\chi_{2880}(901,\cdot)$, $\chi_{2880}(641,\cdot)$, $\chi_{2880}(577,\cdot)$

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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{2880}(1,\cdot)$	2880.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2880}(7,\cdot)$	2880.ej	24	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{24}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{2880}(11,\cdot)$	2880.ff	48	no	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{1}{48}\right)$	$i$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{2880}(13,\cdot)$	2880.fm	48	yes	$-1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{47}{48}\right)$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{2880}(17,\cdot)$	2880.bg	4	no	$1$	$1$	$-i$	$i$	$1$	$-i$	$-i$	$-i$	$i$	$1$	$1$	$1$
$\chi_{2880}(19,\cdot)$	2880.ec	16	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{16}\right)$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{2880}(23,\cdot)$	2880.el	24	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{24}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{2880}(29,\cdot)$	2880.fh	48	yes	$-1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{7}{48}\right)$	$i$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{2880}(31,\cdot)$	2880.bz	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{2880}(37,\cdot)$	2880.ee	16	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$-1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{2880}(41,\cdot)$	2880.eq	24	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{19}{24}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{2880}(43,\cdot)$	2880.ey	48	yes	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{37}{48}\right)$	$-1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{2880}(47,\cdot)$	2880.de	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{2880}(49,\cdot)$	2880.cu	12	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{2880}(53,\cdot)$	2880.ef	16	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$-1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{2880}(59,\cdot)$	2880.fd	48	yes	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{5}{48}\right)$	$-i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{2880}(61,\cdot)$	2880.fi	48	no	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{7}{48}\right)$	$i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{2880}(67,\cdot)$	2880.ey	48	yes	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{11}{48}\right)$	$-1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{2880}(71,\cdot)$	2880.cn	8	no	$1$	$1$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$i$
$\chi_{2880}(73,\cdot)$	2880.cf	8	no	$-1$	$1$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$i$
$\chi_{2880}(77,\cdot)$	2880.fn	48	yes	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{23}{48}\right)$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{2880}(79,\cdot)$	2880.dp	12	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{5}{6}\right)$
$\chi_{2880}(83,\cdot)$	2880.ez	48	yes	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{7}{48}\right)$	$-1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{2880}(89,\cdot)$	2880.ck	8	no	$-1$	$1$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$i$
$\chi_{2880}(91,\cdot)$	2880.ea	16	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$-i$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{16}\right)$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{2880}(97,\cdot)$	2880.dm	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{2880}(101,\cdot)$	2880.fj	48	no	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{37}{48}\right)$	$i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{2880}(103,\cdot)$	2880.ex	24	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{19}{24}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{2880}(107,\cdot)$	2880.dv	16	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$-1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{2880}(109,\cdot)$	2880.dy	16	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-i$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$-1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{2880}(113,\cdot)$	2880.dc	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{2880}(119,\cdot)$	2880.ep	24	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{24}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{12}\right)$

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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	$2880$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{48}\)
Order	$768$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{2880}(1,\cdot)\)	2880.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2880}(7,\cdot)\)	2880.ej	24	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{2880}(11,\cdot)\)	2880.ff	48	no	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(i\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{2880}(13,\cdot)\)	2880.fm	48	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{2880}(17,\cdot)\)	2880.bg	4	no	\(1\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(-i\)	\(-i\)	\(-i\)	\(i\)	\(1\)	\(1\)	\(1\)
\(\chi_{2880}(19,\cdot)\)	2880.ec	16	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{2880}(23,\cdot)\)	2880.el	24	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{2880}(29,\cdot)\)	2880.fh	48	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(i\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{2880}(31,\cdot)\)	2880.bz	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2880}(37,\cdot)\)	2880.ee	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{2880}(41,\cdot)\)	2880.eq	24	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{2880}(43,\cdot)\)	2880.ey	48	yes	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(-1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{2880}(47,\cdot)\)	2880.de	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2880}(49,\cdot)\)	2880.cu	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2880}(53,\cdot)\)	2880.ef	16	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{2880}(59,\cdot)\)	2880.fd	48	yes	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(-i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{2880}(61,\cdot)\)	2880.fi	48	no	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{2880}(67,\cdot)\)	2880.ey	48	yes	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(-1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{2880}(71,\cdot)\)	2880.cn	8	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)
\(\chi_{2880}(73,\cdot)\)	2880.cf	8	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)
\(\chi_{2880}(77,\cdot)\)	2880.fn	48	yes	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{2880}(79,\cdot)\)	2880.dp	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2880}(83,\cdot)\)	2880.ez	48	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(-1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{2880}(89,\cdot)\)	2880.ck	8	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)
\(\chi_{2880}(91,\cdot)\)	2880.ea	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-i\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{2880}(97,\cdot)\)	2880.dm	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2880}(101,\cdot)\)	2880.fj	48	no	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{2880}(103,\cdot)\)	2880.ex	24	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{2880}(107,\cdot)\)	2880.dv	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{2880}(109,\cdot)\)	2880.dy	16	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{2880}(113,\cdot)\)	2880.dc	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2880}(119,\cdot)\)	2880.ep	24	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)

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L-functions

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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.