LMFDB - Group of Dirichlet characters of modulus 4560

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4560)

pari: g = idealstar(,4560,2)

Character group

sage: G.order() pari: g.no
Order	=	1152
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{36}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4560}(1711,\cdot)$, $\chi_{4560}(1141,\cdot)$, $\chi_{4560}(3041,\cdot)$, $\chi_{4560}(2737,\cdot)$, $\chi_{4560}(1921,\cdot)$

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	$-1$	$1$	$7$	$11$	$13$	$17$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{4560}(1,\cdot)$	4560.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4560}(7,\cdot)$	4560.fq	12	no	$1$	$1$	$-i$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{4560}(11,\cdot)$	4560.gd	12	no	$1$	$1$	$1$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{4560}(13,\cdot)$	4560.ip	36	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{4560}(17,\cdot)$	4560.iq	36	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{4560}(23,\cdot)$	4560.iv	36	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{4560}(29,\cdot)$	4560.hq	36	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{4560}(31,\cdot)$	4560.di	6	no	$1$	$1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{4560}(37,\cdot)$	4560.ch	4	no	$1$	$1$	$-i$	$i$	$1$	$i$	$i$	$-i$	$-1$	$1$	$1$	$1$
$\chi_{4560}(41,\cdot)$	4560.gk	18	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{4560}(43,\cdot)$	4560.in	36	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{4560}(47,\cdot)$	4560.hz	36	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{4560}(49,\cdot)$	4560.ds	6	no	$1$	$1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{4560}(53,\cdot)$	4560.il	36	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{4560}(59,\cdot)$	4560.iy	36	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{4560}(61,\cdot)$	4560.jb	36	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{4560}(67,\cdot)$	4560.ib	36	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{4560}(71,\cdot)$	4560.hf	18	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{4560}(73,\cdot)$	4560.ir	36	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{4560}(77,\cdot)$	4560.cm	4	no	$1$	$1$	$-i$	$i$	$1$	$-i$	$-i$	$i$	$1$	$1$	$1$	$-1$
$\chi_{4560}(79,\cdot)$	4560.go	18	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{4560}(83,\cdot)$	4560.fi	12	yes	$-1$	$1$	$-i$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{4560}(89,\cdot)$	4560.gz	18	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{4560}(91,\cdot)$	4560.hm	36	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{4560}(97,\cdot)$	4560.hx	36	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{4560}(101,\cdot)$	4560.ja	36	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{4560}(103,\cdot)$	4560.fv	12	no	$-1$	$1$	$i$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{4560}(107,\cdot)$	4560.ff	12	yes	$1$	$1$	$i$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{4560}(109,\cdot)$	4560.hr	36	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{4560}(113,\cdot)$	4560.br	4	no	$-1$	$1$	$-i$	$-1$	$-i$	$i$	$-i$	$-1$	$-1$	$i$	$1$	$i$
$\chi_{4560}(119,\cdot)$	4560.gs	18	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{4560}(121,\cdot)$	4560.dx	6	no	$1$	$1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

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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	$4560$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{36}\)
Order	$1152$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{4560}(1,\cdot)\)	4560.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4560}(7,\cdot)\)	4560.fq	12	no	\(1\)	\(1\)	\(-i\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{4560}(11,\cdot)\)	4560.gd	12	no	\(1\)	\(1\)	\(1\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{4560}(13,\cdot)\)	4560.ip	36	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{4560}(17,\cdot)\)	4560.iq	36	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{4560}(23,\cdot)\)	4560.iv	36	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{4560}(29,\cdot)\)	4560.hq	36	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{4560}(31,\cdot)\)	4560.di	6	no	\(1\)	\(1\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{4560}(37,\cdot)\)	4560.ch	4	no	\(1\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(i\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4560}(41,\cdot)\)	4560.gk	18	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{4560}(43,\cdot)\)	4560.in	36	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{4560}(47,\cdot)\)	4560.hz	36	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{4560}(49,\cdot)\)	4560.ds	6	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{4560}(53,\cdot)\)	4560.il	36	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{4560}(59,\cdot)\)	4560.iy	36	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{4560}(61,\cdot)\)	4560.jb	36	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{4560}(67,\cdot)\)	4560.ib	36	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{4560}(71,\cdot)\)	4560.hf	18	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{4560}(73,\cdot)\)	4560.ir	36	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{4560}(77,\cdot)\)	4560.cm	4	no	\(1\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(-i\)	\(-i\)	\(i\)	\(1\)	\(1\)	\(1\)	\(-1\)
\(\chi_{4560}(79,\cdot)\)	4560.go	18	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{4560}(83,\cdot)\)	4560.fi	12	yes	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{4560}(89,\cdot)\)	4560.gz	18	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{4560}(91,\cdot)\)	4560.hm	36	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{4560}(97,\cdot)\)	4560.hx	36	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{4560}(101,\cdot)\)	4560.ja	36	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{4560}(103,\cdot)\)	4560.fv	12	no	\(-1\)	\(1\)	\(i\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{4560}(107,\cdot)\)	4560.ff	12	yes	\(1\)	\(1\)	\(i\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{4560}(109,\cdot)\)	4560.hr	36	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{4560}(113,\cdot)\)	4560.br	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(i\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(1\)	\(i\)
\(\chi_{4560}(119,\cdot)\)	4560.gs	18	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{4560}(121,\cdot)\)	4560.dx	6	no	\(1\)	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)

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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.