LMFDB - Group of Dirichlet characters of modulus 4320

sage:H = DirichletGroup(4320)

pari:g = idealstar(,4320,2)

Character group

sage:G.order() pari:g.no
Order	=	1152
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{72}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{4320}(2431,\cdot)$, $\chi_{4320}(3781,\cdot)$, $\chi_{4320}(2081,\cdot)$, $\chi_{4320}(3457,\cdot)$

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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{4320}(1,\cdot)$	4320.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4320}(7,\cdot)$	4320.fm	36	no	$1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{4320}(11,\cdot)$	4320.fz	72	no	$1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{4320}(13,\cdot)$	4320.gg	72	yes	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{4320}(17,\cdot)$	4320.dc	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{1}{6}\right)$
$\chi_{4320}(19,\cdot)$	4320.et	24	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{24}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{4320}(23,\cdot)$	4320.fl	36	no	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{4320}(29,\cdot)$	4320.gl	72	yes	$-1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{4320}(31,\cdot)$	4320.dx	18	no	$-1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{4320}(37,\cdot)$	4320.ew	24	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{24}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{4320}(41,\cdot)$	4320.ft	36	no	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{4320}(43,\cdot)$	4320.gd	72	yes	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{4320}(47,\cdot)$	4320.fo	36	no	$-1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{4320}(49,\cdot)$	4320.ef	18	no	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{4320}(53,\cdot)$	4320.cr	8	no	$1$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$i$
$\chi_{4320}(59,\cdot)$	4320.gi	72	yes	$1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{4320}(61,\cdot)$	4320.gj	72	no	$1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{4320}(67,\cdot)$	4320.gd	72	yes	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{4320}(71,\cdot)$	4320.cw	12	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{2}{3}\right)$
$\chi_{4320}(73,\cdot)$	4320.di	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{4320}(77,\cdot)$	4320.ga	72	yes	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{4320}(79,\cdot)$	4320.eb	18	no	$-1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{4320}(83,\cdot)$	4320.gf	72	yes	$-1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{4320}(89,\cdot)$	4320.cy	12	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{4320}(91,\cdot)$	4320.eo	24	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{24}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{4320}(97,\cdot)$	4320.fp	36	no	$-1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{4320}(101,\cdot)$	4320.fw	72	no	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{4320}(103,\cdot)$	4320.fg	36	no	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{4320}(107,\cdot)$	4320.cq	8	no	$-1$	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$i$
$\chi_{4320}(109,\cdot)$	4320.co	8	no	$1$	$1$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$i$
$\chi_{4320}(113,\cdot)$	4320.fe	36	no	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{4320}(119,\cdot)$	4320.fa	36	no	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{9}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$4320$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{72}\)
Order	$1152$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{4320}(1,\cdot)\)	4320.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4320}(7,\cdot)\)	4320.fm	36	no	\(1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{4320}(11,\cdot)\)	4320.fz	72	no	\(1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{4320}(13,\cdot)\)	4320.gg	72	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{4320}(17,\cdot)\)	4320.dc	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{4320}(19,\cdot)\)	4320.et	24	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{4320}(23,\cdot)\)	4320.fl	36	no	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{4320}(29,\cdot)\)	4320.gl	72	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{4320}(31,\cdot)\)	4320.dx	18	no	\(-1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{4320}(37,\cdot)\)	4320.ew	24	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{4320}(41,\cdot)\)	4320.ft	36	no	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{4320}(43,\cdot)\)	4320.gd	72	yes	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{4320}(47,\cdot)\)	4320.fo	36	no	\(-1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{4320}(49,\cdot)\)	4320.ef	18	no	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{4320}(53,\cdot)\)	4320.cr	8	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)
\(\chi_{4320}(59,\cdot)\)	4320.gi	72	yes	\(1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{4320}(61,\cdot)\)	4320.gj	72	no	\(1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{4320}(67,\cdot)\)	4320.gd	72	yes	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{4320}(71,\cdot)\)	4320.cw	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{4320}(73,\cdot)\)	4320.di	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{4320}(77,\cdot)\)	4320.ga	72	yes	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{4320}(79,\cdot)\)	4320.eb	18	no	\(-1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{4320}(83,\cdot)\)	4320.gf	72	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{4320}(89,\cdot)\)	4320.cy	12	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{4320}(91,\cdot)\)	4320.eo	24	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{4320}(97,\cdot)\)	4320.fp	36	no	\(-1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{4320}(101,\cdot)\)	4320.fw	72	no	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{4320}(103,\cdot)\)	4320.fg	36	no	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{4320}(107,\cdot)\)	4320.cq	8	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(i\)
\(\chi_{4320}(109,\cdot)\)	4320.co	8	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)
\(\chi_{4320}(113,\cdot)\)	4320.fe	36	no	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{4320}(119,\cdot)\)	4320.fa	36	no	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)

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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.