LMFDB - Group of Dirichlet characters of modulus 2368

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2368)

pari: g = idealstar(,2368,2)

Character group

sage: G.order() pari: g.no
Order	=	1152
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{144}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2368}(1407,\cdot)$, $\chi_{2368}(1925,\cdot)$, $\chi_{2368}(705,\cdot)$

First 32 of 1152 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{2368}(1,\cdot)$	2368.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2368}(3,\cdot)$	2368.dx	144	yes	$-1$	$1$	$e\left(\frac{121}{144}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{13}{144}\right)$	$e\left(\frac{47}{144}\right)$
$\chi_{2368}(5,\cdot)$	2368.dy	144	yes	$-1$	$1$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{139}{144}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{125}{144}\right)$
$\chi_{2368}(7,\cdot)$	2368.dq	72	no	$-1$	$1$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{49}{72}\right)$
$\chi_{2368}(9,\cdot)$	2368.dt	72	no	$1$	$1$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{47}{72}\right)$
$\chi_{2368}(11,\cdot)$	2368.di	48	yes	$-1$	$1$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{19}{48}\right)$
$\chi_{2368}(13,\cdot)$	2368.dz	144	yes	$-1$	$1$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{139}{144}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{131}{144}\right)$
$\chi_{2368}(15,\cdot)$	2368.cy	36	no	$1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{2368}(17,\cdot)$	2368.cz	36	no	$-1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{2368}(19,\cdot)$	2368.eb	144	yes	$1$	$1$	$e\left(\frac{13}{144}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{85}{144}\right)$	$e\left(\frac{11}{144}\right)$
$\chi_{2368}(21,\cdot)$	2368.ec	144	yes	$1$	$1$	$e\left(\frac{47}{144}\right)$	$e\left(\frac{125}{144}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{131}{144}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{1}{144}\right)$
$\chi_{2368}(23,\cdot)$	2368.cr	24	no	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{2368}(25,\cdot)$	2368.dr	72	no	$1$	$1$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{53}{72}\right)$
$\chi_{2368}(27,\cdot)$	2368.di	48	yes	$-1$	$1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{47}{48}\right)$
$\chi_{2368}(29,\cdot)$	2368.dg	48	yes	$-1$	$1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{37}{48}\right)$
$\chi_{2368}(31,\cdot)$	2368.j	4	no	$1$	$1$	$-1$	$i$	$-1$	$1$	$-1$	$i$	$-i$	$-i$	$-i$	$1$
$\chi_{2368}(33,\cdot)$	2368.ci	18	no	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{2368}(35,\cdot)$	2368.eb	144	yes	$1$	$1$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{113}{144}\right)$	$e\left(\frac{79}{144}\right)$
$\chi_{2368}(39,\cdot)$	2368.do	72	no	$1$	$1$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{17}{72}\right)$
$\chi_{2368}(41,\cdot)$	2368.dr	72	no	$1$	$1$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{43}{72}\right)$
$\chi_{2368}(43,\cdot)$	2368.by	16	yes	$1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{2368}(45,\cdot)$	2368.dn	48	yes	$-1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{25}{48}\right)$
$\chi_{2368}(47,\cdot)$	2368.bq	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{2368}(49,\cdot)$	2368.dc	36	no	$1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{2368}(51,\cdot)$	2368.dm	48	yes	$1$	$1$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{17}{48}\right)$
$\chi_{2368}(53,\cdot)$	2368.dw	144	yes	$1$	$1$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{125}{144}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{131}{144}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{73}{144}\right)$
$\chi_{2368}(55,\cdot)$	2368.du	72	no	$1$	$1$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{19}{72}\right)$
$\chi_{2368}(57,\cdot)$	2368.dv	72	no	$-1$	$1$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{29}{72}\right)$
$\chi_{2368}(59,\cdot)$	2368.ea	144	yes	$1$	$1$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{125}{144}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{109}{144}\right)$
$\chi_{2368}(61,\cdot)$	2368.dy	144	yes	$-1$	$1$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{103}{144}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{23}{144}\right)$
$\chi_{2368}(63,\cdot)$	2368.z	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2368}(65,\cdot)$	2368.cg	18	no	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$

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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	$2368$
Structure	\(C_{2}\times C_{4}\times C_{144}\)
Order	$1152$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{2368}(1,\cdot)\)	2368.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2368}(3,\cdot)\)	2368.dx	144	yes	\(-1\)	\(1\)	\(e\left(\frac{121}{144}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{47}{144}\right)\)
\(\chi_{2368}(5,\cdot)\)	2368.dy	144	yes	\(-1\)	\(1\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{139}{144}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{125}{144}\right)\)
\(\chi_{2368}(7,\cdot)\)	2368.dq	72	no	\(-1\)	\(1\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{49}{72}\right)\)
\(\chi_{2368}(9,\cdot)\)	2368.dt	72	no	\(1\)	\(1\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{47}{72}\right)\)
\(\chi_{2368}(11,\cdot)\)	2368.di	48	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)
\(\chi_{2368}(13,\cdot)\)	2368.dz	144	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{139}{144}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{131}{144}\right)\)
\(\chi_{2368}(15,\cdot)\)	2368.cy	36	no	\(1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{2368}(17,\cdot)\)	2368.cz	36	no	\(-1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{2368}(19,\cdot)\)	2368.eb	144	yes	\(1\)	\(1\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{85}{144}\right)\)	\(e\left(\frac{11}{144}\right)\)
\(\chi_{2368}(21,\cdot)\)	2368.ec	144	yes	\(1\)	\(1\)	\(e\left(\frac{47}{144}\right)\)	\(e\left(\frac{125}{144}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{131}{144}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{1}{144}\right)\)
\(\chi_{2368}(23,\cdot)\)	2368.cr	24	no	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{2368}(25,\cdot)\)	2368.dr	72	no	\(1\)	\(1\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{53}{72}\right)\)
\(\chi_{2368}(27,\cdot)\)	2368.di	48	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)
\(\chi_{2368}(29,\cdot)\)	2368.dg	48	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)
\(\chi_{2368}(31,\cdot)\)	2368.j	4	no	\(1\)	\(1\)	\(-1\)	\(i\)	\(-1\)	\(1\)	\(-1\)	\(i\)	\(-i\)	\(-i\)	\(-i\)	\(1\)
\(\chi_{2368}(33,\cdot)\)	2368.ci	18	no	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{2368}(35,\cdot)\)	2368.eb	144	yes	\(1\)	\(1\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{113}{144}\right)\)	\(e\left(\frac{79}{144}\right)\)
\(\chi_{2368}(39,\cdot)\)	2368.do	72	no	\(1\)	\(1\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{17}{72}\right)\)
\(\chi_{2368}(41,\cdot)\)	2368.dr	72	no	\(1\)	\(1\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)
\(\chi_{2368}(43,\cdot)\)	2368.by	16	yes	\(1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{2368}(45,\cdot)\)	2368.dn	48	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)
\(\chi_{2368}(47,\cdot)\)	2368.bq	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{2368}(49,\cdot)\)	2368.dc	36	no	\(1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{2368}(51,\cdot)\)	2368.dm	48	yes	\(1\)	\(1\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)
\(\chi_{2368}(53,\cdot)\)	2368.dw	144	yes	\(1\)	\(1\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{125}{144}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{131}{144}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{73}{144}\right)\)
\(\chi_{2368}(55,\cdot)\)	2368.du	72	no	\(1\)	\(1\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{19}{72}\right)\)
\(\chi_{2368}(57,\cdot)\)	2368.dv	72	no	\(-1\)	\(1\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{29}{72}\right)\)
\(\chi_{2368}(59,\cdot)\)	2368.ea	144	yes	\(1\)	\(1\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{125}{144}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{109}{144}\right)\)
\(\chi_{2368}(61,\cdot)\)	2368.dy	144	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{103}{144}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{23}{144}\right)\)
\(\chi_{2368}(63,\cdot)\)	2368.z	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2368}(65,\cdot)\)	2368.cg	18	no	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)

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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.