LMFDB - Group of Dirichlet characters of modulus 5328

sage:H = DirichletGroup(5328)

pari:g = idealstar(,5328,2)

Character group

sage:G.order() pari:g.no
Order	=	1728
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{12}\times C_{36}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{5328}(1999,\cdot)$, $\chi_{5328}(1333,\cdot)$, $\chi_{5328}(2369,\cdot)$, $\chi_{5328}(1297,\cdot)$

First 32 of 1728 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{5328}(1,\cdot)$	5328.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{5328}(5,\cdot)$	5328.lj	36	yes	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{18}\right)$	$i$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{9}\right)$	$i$	$e\left(\frac{2}{9}\right)$	$1$	$e\left(\frac{5}{12}\right)$
$\chi_{5328}(7,\cdot)$	5328.ip	18	no	$-1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{5328}(11,\cdot)$	5328.fj	12	yes	$1$	$1$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{5328}(13,\cdot)$	5328.lg	36	yes	$-1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{18}\right)$	$i$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{17}{18}\right)$	$-i$	$e\left(\frac{8}{9}\right)$	$1$	$e\left(\frac{5}{12}\right)$
$\chi_{5328}(17,\cdot)$	5328.jw	36	no	$1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{12}\right)$	$-i$
$\chi_{5328}(19,\cdot)$	5328.kr	36	no	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$	$i$
$\chi_{5328}(23,\cdot)$	5328.gc	12	no	$-1$	$1$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{5328}(25,\cdot)$	5328.hx	18	no	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{9}\right)$	$-1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$-1$	$e\left(\frac{4}{9}\right)$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{5328}(29,\cdot)$	5328.hu	12	yes	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{5328}(31,\cdot)$	5328.ge	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{5328}(35,\cdot)$	5328.ky	36	no	$-1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$i$
$\chi_{5328}(41,\cdot)$	5328.jl	18	no	$-1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{9}\right)$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$	$1$	$e\left(\frac{8}{9}\right)$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{5328}(43,\cdot)$	5328.hh	12	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{5328}(47,\cdot)$	5328.cv	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{5328}(49,\cdot)$	5328.ea	9	no	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{5328}(53,\cdot)$	5328.kl	36	no	$-1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{12}\right)$	$1$
$\chi_{5328}(55,\cdot)$	5328.ma	36	no	$1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{12}\right)$	$-i$
$\chi_{5328}(59,\cdot)$	5328.ks	36	yes	$-1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{5328}(61,\cdot)$	5328.ld	36	yes	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{5328}(65,\cdot)$	5328.ic	18	no	$-1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$-1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{18}\right)$	$1$	$e\left(\frac{1}{9}\right)$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{5328}(67,\cdot)$	5328.kb	36	yes	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{7}{9}\right)$	$i$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{13}{36}\right)$	$-1$	$e\left(\frac{13}{18}\right)$	$-i$	$e\left(\frac{2}{3}\right)$
$\chi_{5328}(71,\cdot)$	5328.is	18	no	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$	$-1$
$\chi_{5328}(73,\cdot)$	5328.o	2	no	$1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$1$	$-1$
$\chi_{5328}(77,\cdot)$	5328.kd	36	yes	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{17}{18}\right)$	$i$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{19}{36}\right)$	$-1$	$e\left(\frac{1}{18}\right)$	$i$	$e\left(\frac{1}{6}\right)$
$\chi_{5328}(79,\cdot)$	5328.js	36	no	$1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{5328}(83,\cdot)$	5328.kc	36	yes	$1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{8}{9}\right)$	$-i$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{36}\right)$	$-1$	$e\left(\frac{11}{18}\right)$	$-i$	$e\left(\frac{5}{6}\right)$
$\chi_{5328}(85,\cdot)$	5328.ey	12	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{5328}(89,\cdot)$	5328.mb	36	no	$1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{12}\right)$	$i$
$\chi_{5328}(91,\cdot)$	5328.lf	36	no	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{6}\right)$	$i$
$\chi_{5328}(95,\cdot)$	5328.ij	18	no	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{5328}(97,\cdot)$	5328.he	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$5328$
Structure	\(C_{2}\times C_{2}\times C_{12}\times C_{36}\)
Order	$1728$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{5328}(1,\cdot)\)	5328.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{5328}(5,\cdot)\)	5328.lj	36	yes	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(i\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(i\)	\(e\left(\frac{2}{9}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{5328}(7,\cdot)\)	5328.ip	18	no	\(-1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{5328}(11,\cdot)\)	5328.fj	12	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{5328}(13,\cdot)\)	5328.lg	36	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(i\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(-i\)	\(e\left(\frac{8}{9}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{5328}(17,\cdot)\)	5328.jw	36	no	\(1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)
\(\chi_{5328}(19,\cdot)\)	5328.kr	36	no	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)
\(\chi_{5328}(23,\cdot)\)	5328.gc	12	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{5328}(25,\cdot)\)	5328.hx	18	no	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(-1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(-1\)	\(e\left(\frac{4}{9}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{5328}(29,\cdot)\)	5328.hu	12	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{5328}(31,\cdot)\)	5328.ge	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{5328}(35,\cdot)\)	5328.ky	36	no	\(-1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)
\(\chi_{5328}(41,\cdot)\)	5328.jl	18	no	\(-1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{5328}(43,\cdot)\)	5328.hh	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{5328}(47,\cdot)\)	5328.cv	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{5328}(49,\cdot)\)	5328.ea	9	no	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{5328}(53,\cdot)\)	5328.kl	36	no	\(-1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)
\(\chi_{5328}(55,\cdot)\)	5328.ma	36	no	\(1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)
\(\chi_{5328}(59,\cdot)\)	5328.ks	36	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{5328}(61,\cdot)\)	5328.ld	36	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{5328}(65,\cdot)\)	5328.ic	18	no	\(-1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(-1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{5328}(67,\cdot)\)	5328.kb	36	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(i\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(-1\)	\(e\left(\frac{13}{18}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{5328}(71,\cdot)\)	5328.is	18	no	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)
\(\chi_{5328}(73,\cdot)\)	5328.o	2	no	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)
\(\chi_{5328}(77,\cdot)\)	5328.kd	36	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(i\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(-1\)	\(e\left(\frac{1}{18}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{5328}(79,\cdot)\)	5328.js	36	no	\(1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{5328}(83,\cdot)\)	5328.kc	36	yes	\(1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(-i\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(-1\)	\(e\left(\frac{11}{18}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{5328}(85,\cdot)\)	5328.ey	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{5328}(89,\cdot)\)	5328.mb	36	no	\(1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)
\(\chi_{5328}(91,\cdot)\)	5328.lf	36	no	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)
\(\chi_{5328}(95,\cdot)\)	5328.ij	18	no	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{5328}(97,\cdot)\)	5328.he	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)

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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.