LMFDB - Group of Dirichlet characters of modulus 1080

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1080)

pari: g = idealstar(,1080,2)

Character group

sage: G.order() pari: g.no
Order	=	288
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{36}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1080}(271,\cdot)$, $\chi_{1080}(541,\cdot)$, $\chi_{1080}(1001,\cdot)$, $\chi_{1080}(217,\cdot)$

First 32 of 288 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{1080}(1,\cdot)$	1080.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1080}(7,\cdot)$	1080.cp	36	no	$1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{1080}(11,\cdot)$	1080.ch	18	no	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{1080}(13,\cdot)$	1080.cn	36	yes	$-1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1080}(17,\cdot)$	1080.bt	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{1}{6}\right)$
$\chi_{1080}(19,\cdot)$	1080.z	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{1080}(23,\cdot)$	1080.cm	36	no	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{1080}(29,\cdot)$	1080.ca	18	yes	$-1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{1080}(31,\cdot)$	1080.cb	18	no	$-1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{1080}(37,\cdot)$	1080.bv	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{2}{3}\right)$
$\chi_{1080}(41,\cdot)$	1080.ce	18	no	$-1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{1080}(43,\cdot)$	1080.ct	36	yes	$1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{1080}(47,\cdot)$	1080.cm	36	no	$-1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{1080}(49,\cdot)$	1080.cg	18	no	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{1080}(53,\cdot)$	1080.x	4	no	$1$	$1$	$-i$	$1$	$-i$	$i$	$1$	$-i$	$-1$	$1$	$i$	$-1$
$\chi_{1080}(59,\cdot)$	1080.bx	18	yes	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{1080}(61,\cdot)$	1080.cc	18	no	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{1080}(67,\cdot)$	1080.ct	36	yes	$1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1080}(71,\cdot)$	1080.bg	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{1080}(73,\cdot)$	1080.bq	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{1080}(77,\cdot)$	1080.co	36	yes	$1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{1080}(79,\cdot)$	1080.ck	18	no	$-1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{1080}(83,\cdot)$	1080.cq	36	yes	$-1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{1080}(89,\cdot)$	1080.bn	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{1080}(91,\cdot)$	1080.bj	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{1080}(97,\cdot)$	1080.cr	36	no	$-1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{1080}(101,\cdot)$	1080.cl	18	no	$-1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{1080}(103,\cdot)$	1080.cp	36	no	$1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{1080}(107,\cdot)$	1080.r	4	no	$-1$	$1$	$-i$	$-1$	$i$	$-i$	$-1$	$-i$	$-1$	$-1$	$-i$	$-1$
$\chi_{1080}(109,\cdot)$	1080.d	2	no	$1$	$1$	$-1$	$-1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$
$\chi_{1080}(113,\cdot)$	1080.cs	36	no	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{1080}(119,\cdot)$	1080.cd	18	no	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{18}\right)$

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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	$1080$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{36}\)
Order	$288$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{1080}(1,\cdot)\)	1080.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1080}(7,\cdot)\)	1080.cp	36	no	\(1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{1080}(11,\cdot)\)	1080.ch	18	no	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{1080}(13,\cdot)\)	1080.cn	36	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{1080}(17,\cdot)\)	1080.bt	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1080}(19,\cdot)\)	1080.z	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1080}(23,\cdot)\)	1080.cm	36	no	\(-1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{1080}(29,\cdot)\)	1080.ca	18	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{1080}(31,\cdot)\)	1080.cb	18	no	\(-1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{1080}(37,\cdot)\)	1080.bv	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1080}(41,\cdot)\)	1080.ce	18	no	\(-1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{1080}(43,\cdot)\)	1080.ct	36	yes	\(1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{1080}(47,\cdot)\)	1080.cm	36	no	\(-1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{1080}(49,\cdot)\)	1080.cg	18	no	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{1080}(53,\cdot)\)	1080.x	4	no	\(1\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(-1\)
\(\chi_{1080}(59,\cdot)\)	1080.bx	18	yes	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{1080}(61,\cdot)\)	1080.cc	18	no	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{1080}(67,\cdot)\)	1080.ct	36	yes	\(1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{1080}(71,\cdot)\)	1080.bg	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1080}(73,\cdot)\)	1080.bq	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1080}(77,\cdot)\)	1080.co	36	yes	\(1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{1080}(79,\cdot)\)	1080.ck	18	no	\(-1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{1080}(83,\cdot)\)	1080.cq	36	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{1080}(89,\cdot)\)	1080.bn	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1080}(91,\cdot)\)	1080.bj	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1080}(97,\cdot)\)	1080.cr	36	no	\(-1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{1080}(101,\cdot)\)	1080.cl	18	no	\(-1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{1080}(103,\cdot)\)	1080.cp	36	no	\(1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{1080}(107,\cdot)\)	1080.r	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(-i\)	\(-1\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(-1\)
\(\chi_{1080}(109,\cdot)\)	1080.d	2	no	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1080}(113,\cdot)\)	1080.cs	36	no	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{1080}(119,\cdot)\)	1080.cd	18	no	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{18}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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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.