LMFDB - Group of Dirichlet characters of modulus 2240

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2240)

pari: g = idealstar(,2240,2)

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	=	$\chi_{2240}(1471,\cdot)$, $\chi_{2240}(1541,\cdot)$, $\chi_{2240}(897,\cdot)$, $\chi_{2240}(1921,\cdot)$

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	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{2240}(1,\cdot)$	2240.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2240}(3,\cdot)$	2240.fm	48	yes	$-1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2240}(9,\cdot)$	2240.ei	24	no	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2240}(11,\cdot)$	2240.fe	48	no	$-1$	$1$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{2240}(13,\cdot)$	2240.du	16	yes	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$-1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$1$
$\chi_{2240}(17,\cdot)$	2240.dp	12	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{2240}(19,\cdot)$	2240.fj	48	yes	$1$	$1$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2240}(23,\cdot)$	2240.eo	24	no	$1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2240}(27,\cdot)$	2240.dt	16	yes	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$-1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$-1$
$\chi_{2240}(29,\cdot)$	2240.dz	16	no	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{16}\right)$	$-i$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-1$
$\chi_{2240}(31,\cdot)$	2240.bz	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{2240}(33,\cdot)$	2240.dn	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{2240}(37,\cdot)$	2240.fa	48	yes	$-1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2240}(39,\cdot)$	2240.el	24	no	$-1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2240}(41,\cdot)$	2240.cr	8	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$
$\chi_{2240}(43,\cdot)$	2240.dv	16	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$-1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$1$
$\chi_{2240}(47,\cdot)$	2240.cu	12	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{2240}(51,\cdot)$	2240.fe	48	no	$-1$	$1$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2240}(53,\cdot)$	2240.fn	48	yes	$-1$	$1$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2240}(57,\cdot)$	2240.ck	8	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$
$\chi_{2240}(59,\cdot)$	2240.fj	48	yes	$1$	$1$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2240}(61,\cdot)$	2240.fd	48	no	$-1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2240}(67,\cdot)$	2240.fk	48	yes	$1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{2240}(69,\cdot)$	2240.ea	16	yes	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$-i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$1$
$\chi_{2240}(71,\cdot)$	2240.cf	8	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$
$\chi_{2240}(73,\cdot)$	2240.es	24	no	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2240}(79,\cdot)$	2240.di	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$-i$	$e\left(\frac{5}{6}\right)$
$\chi_{2240}(81,\cdot)$	2240.df	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$i$	$e\left(\frac{2}{3}\right)$
$\chi_{2240}(83,\cdot)$	2240.dt	16	yes	$-1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-1$
$\chi_{2240}(87,\cdot)$	2240.er	24	no	$-1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{2240}(89,\cdot)$	2240.ex	24	no	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2240}(93,\cdot)$	2240.fa	48	yes	$-1$	$1$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{6}\right)$

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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	$2240$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{48}\)
Order	$768$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{2240}(1,\cdot)\)	2240.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2240}(3,\cdot)\)	2240.fm	48	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2240}(9,\cdot)\)	2240.ei	24	no	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2240}(11,\cdot)\)	2240.fe	48	no	\(-1\)	\(1\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2240}(13,\cdot)\)	2240.du	16	yes	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(1\)
\(\chi_{2240}(17,\cdot)\)	2240.dp	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2240}(19,\cdot)\)	2240.fj	48	yes	\(1\)	\(1\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2240}(23,\cdot)\)	2240.eo	24	no	\(1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2240}(27,\cdot)\)	2240.dt	16	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)
\(\chi_{2240}(29,\cdot)\)	2240.dz	16	no	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-i\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)
\(\chi_{2240}(31,\cdot)\)	2240.bz	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2240}(33,\cdot)\)	2240.dn	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2240}(37,\cdot)\)	2240.fa	48	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2240}(39,\cdot)\)	2240.el	24	no	\(-1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2240}(41,\cdot)\)	2240.cr	8	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)
\(\chi_{2240}(43,\cdot)\)	2240.dv	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(1\)
\(\chi_{2240}(47,\cdot)\)	2240.cu	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2240}(51,\cdot)\)	2240.fe	48	no	\(-1\)	\(1\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2240}(53,\cdot)\)	2240.fn	48	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2240}(57,\cdot)\)	2240.ck	8	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)
\(\chi_{2240}(59,\cdot)\)	2240.fj	48	yes	\(1\)	\(1\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2240}(61,\cdot)\)	2240.fd	48	no	\(-1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2240}(67,\cdot)\)	2240.fk	48	yes	\(1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2240}(69,\cdot)\)	2240.ea	16	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(1\)
\(\chi_{2240}(71,\cdot)\)	2240.cf	8	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)
\(\chi_{2240}(73,\cdot)\)	2240.es	24	no	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2240}(79,\cdot)\)	2240.di	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2240}(81,\cdot)\)	2240.df	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2240}(83,\cdot)\)	2240.dt	16	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)
\(\chi_{2240}(87,\cdot)\)	2240.er	24	no	\(-1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2240}(89,\cdot)\)	2240.ex	24	no	\(-1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2240}(93,\cdot)\)	2240.fa	48	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{6}\right)\)

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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.