LMFDB - Group of Dirichlet characters of modulus 2320

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2320)

pari: g = idealstar(,2320,2)

Character group

sage: G.order() pari: g.no
Order	=	896
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{4}\times C_{28}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2320}(2031,\cdot)$, $\chi_{2320}(581,\cdot)$, $\chi_{2320}(1857,\cdot)$, $\chi_{2320}(321,\cdot)$

First 32 of 896 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{2320}(1,\cdot)$	2320.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2320}(3,\cdot)$	2320.ee	28	yes	$-1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$-1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{2320}(7,\cdot)$	2320.ej	28	no	$1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{27}{28}\right)$	$i$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{2320}(9,\cdot)$	2320.dg	14	no	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{7}\right)$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{2320}(11,\cdot)$	2320.dl	28	no	$1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{23}{28}\right)$	$-i$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{2320}(13,\cdot)$	2320.ds	28	yes	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{1}{14}\right)$	$i$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{2320}(17,\cdot)$	2320.w	4	no	$1$	$1$	$-1$	$i$	$1$	$-i$	$i$	$1$	$i$	$-i$	$-i$	$-1$
$\chi_{2320}(19,\cdot)$	2320.du	28	yes	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{15}{28}\right)$	$i$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{2320}(21,\cdot)$	2320.fm	28	no	$-1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{19}{28}\right)$	$-i$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{2320}(23,\cdot)$	2320.ej	28	no	$1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{28}\right)$	$-i$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{2320}(27,\cdot)$	2320.ee	28	yes	$-1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{7}\right)$	$-1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{2320}(31,\cdot)$	2320.fb	28	no	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{9}{14}\right)$	$-i$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{2320}(33,\cdot)$	2320.er	28	no	$-1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{15}{28}\right)$	$i$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{2320}(37,\cdot)$	2320.em	28	yes	$1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{7}\right)$	$-1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{2320}(39,\cdot)$	2320.ec	28	no	$1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{11}{14}\right)$	$-i$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{2320}(41,\cdot)$	2320.cg	4	no	$-1$	$1$	$-i$	$1$	$-1$	$-i$	$1$	$i$	$-i$	$-i$	$1$	$i$
$\chi_{2320}(43,\cdot)$	2320.es	28	yes	$-1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{14}\right)$	$-1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{2320}(47,\cdot)$	2320.fg	28	no	$-1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{23}{28}\right)$	$-1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{2320}(49,\cdot)$	2320.dh	14	no	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{14}\right)$	$-1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{2320}(51,\cdot)$	2320.dy	28	no	$-1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{27}{28}\right)$	$-1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{28}\right)$
$\chi_{2320}(53,\cdot)$	2320.dm	28	yes	$-1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{7}\right)$	$-i$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{2320}(57,\cdot)$	2320.bw	4	no	$-1$	$1$	$-i$	$i$	$-1$	$1$	$i$	$-i$	$-1$	$1$	$-i$	$i$
$\chi_{2320}(59,\cdot)$	2320.be	4	no	$-1$	$1$	$-i$	$-1$	$-1$	$-i$	$i$	$-1$	$i$	$i$	$-1$	$i$
$\chi_{2320}(61,\cdot)$	2320.dv	28	no	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{13}{28}\right)$	$-i$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{2320}(63,\cdot)$	2320.ei	28	no	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{28}\right)$	$i$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{2320}(67,\cdot)$	2320.dn	28	yes	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{3}{7}\right)$	$-i$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{2320}(69,\cdot)$	2320.dk	28	yes	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{28}\right)$	$i$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{2320}(71,\cdot)$	2320.dj	14	no	$-1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{14}\right)$	$-1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{2320}(73,\cdot)$	2320.dq	28	no	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{28}\right)$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{2320}(77,\cdot)$	2320.et	28	yes	$1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{14}\right)$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{2320}(79,\cdot)$	2320.dw	28	no	$1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{3}{7}\right)$	$i$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{2320}(81,\cdot)$	2320.cu	7	no	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$

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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	$2320$
Structure	\(C_{2}\times C_{4}\times C_{4}\times C_{28}\)
Order	$896$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{2320}(1,\cdot)\)	2320.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2320}(3,\cdot)\)	2320.ee	28	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(-1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{2320}(7,\cdot)\)	2320.ej	28	no	\(1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(i\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{2320}(9,\cdot)\)	2320.dg	14	no	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{2320}(11,\cdot)\)	2320.dl	28	no	\(1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(-i\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{2320}(13,\cdot)\)	2320.ds	28	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(i\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{2320}(17,\cdot)\)	2320.w	4	no	\(1\)	\(1\)	\(-1\)	\(i\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(i\)	\(-i\)	\(-i\)	\(-1\)
\(\chi_{2320}(19,\cdot)\)	2320.du	28	yes	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(i\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{2320}(21,\cdot)\)	2320.fm	28	no	\(-1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(-i\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{2320}(23,\cdot)\)	2320.ej	28	no	\(1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(-i\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{2320}(27,\cdot)\)	2320.ee	28	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(-1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{2320}(31,\cdot)\)	2320.fb	28	no	\(1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-i\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{2320}(33,\cdot)\)	2320.er	28	no	\(-1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(i\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{2320}(37,\cdot)\)	2320.em	28	yes	\(1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{2320}(39,\cdot)\)	2320.ec	28	no	\(1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(-i\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{2320}(41,\cdot)\)	2320.cg	4	no	\(-1\)	\(1\)	\(-i\)	\(1\)	\(-1\)	\(-i\)	\(1\)	\(i\)	\(-i\)	\(-i\)	\(1\)	\(i\)
\(\chi_{2320}(43,\cdot)\)	2320.es	28	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(-1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{2320}(47,\cdot)\)	2320.fg	28	no	\(-1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(-1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{2320}(49,\cdot)\)	2320.dh	14	no	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(-1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{2320}(51,\cdot)\)	2320.dy	28	no	\(-1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(-1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{2320}(53,\cdot)\)	2320.dm	28	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(-i\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{2320}(57,\cdot)\)	2320.bw	4	no	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(-i\)	\(i\)
\(\chi_{2320}(59,\cdot)\)	2320.be	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(i\)	\(-1\)	\(i\)	\(i\)	\(-1\)	\(i\)
\(\chi_{2320}(61,\cdot)\)	2320.dv	28	no	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(-i\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{2320}(63,\cdot)\)	2320.ei	28	no	\(1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(i\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{2320}(67,\cdot)\)	2320.dn	28	yes	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-i\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{2320}(69,\cdot)\)	2320.dk	28	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(i\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{2320}(71,\cdot)\)	2320.dj	14	no	\(-1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{2320}(73,\cdot)\)	2320.dq	28	no	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{2320}(77,\cdot)\)	2320.et	28	yes	\(1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{2320}(79,\cdot)\)	2320.dw	28	no	\(1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(i\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{2320}(81,\cdot)\)	2320.cu	7	no	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)

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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.