LMFDB - Group of Dirichlet characters of modulus 2220

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2220)

pari: g = idealstar(,2220,2)

Character group

sage: G.order() pari: g.no
Order	=	576
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{36}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2220}(1111,\cdot)$, $\chi_{2220}(1481,\cdot)$, $\chi_{2220}(1777,\cdot)$, $\chi_{2220}(1741,\cdot)$

First 32 of 576 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$41$	$43$
$\chi_{2220}(1,\cdot)$	2220.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2220}(7,\cdot)$	2220.em	36	no	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{7}{9}\right)$	$i$
$\chi_{2220}(11,\cdot)$	2220.cc	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$1$
$\chi_{2220}(13,\cdot)$	2220.eo	36	no	$1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{11}{18}\right)$	$-1$
$\chi_{2220}(17,\cdot)$	2220.ed	36	no	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{8}{9}\right)$	$1$
$\chi_{2220}(19,\cdot)$	2220.dx	36	no	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{17}{18}\right)$	$i$
$\chi_{2220}(23,\cdot)$	2220.cq	12	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$-i$	$i$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{2220}(29,\cdot)$	2220.db	12	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$-i$	$i$	$e\left(\frac{2}{3}\right)$	$i$
$\chi_{2220}(31,\cdot)$	2220.t	4	no	$1$	$1$	$-1$	$1$	$-i$	$-i$	$i$	$i$	$i$	$-i$	$-1$	$i$
$\chi_{2220}(41,\cdot)$	2220.dk	18	no	$-1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{11}{18}\right)$	$-1$
$\chi_{2220}(43,\cdot)$	2220.be	4	no	$-1$	$1$	$i$	$1$	$-1$	$1$	$i$	$1$	$i$	$i$	$-1$	$1$
$\chi_{2220}(47,\cdot)$	2220.cu	12	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$i$
$\chi_{2220}(49,\cdot)$	2220.dg	18	no	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{9}\right)$	$-1$
$\chi_{2220}(53,\cdot)$	2220.eh	36	no	$1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{13}{18}\right)$	$i$
$\chi_{2220}(59,\cdot)$	2220.ek	36	yes	$-1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{2}{9}\right)$	$i$
$\chi_{2220}(61,\cdot)$	2220.ej	36	no	$-1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{11}{18}\right)$	$-i$
$\chi_{2220}(67,\cdot)$	2220.eg	36	no	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{7}{9}\right)$	$-i$
$\chi_{2220}(71,\cdot)$	2220.de	18	no	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{17}{18}\right)$	$-1$
$\chi_{2220}(73,\cdot)$	2220.bi	4	no	$-1$	$1$	$-i$	$1$	$-i$	$i$	$1$	$-i$	$1$	$-1$	$1$	$-i$
$\chi_{2220}(77,\cdot)$	2220.en	36	no	$1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{17}{18}\right)$	$i$
$\chi_{2220}(79,\cdot)$	2220.dx	36	no	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{5}{18}\right)$	$i$
$\chi_{2220}(83,\cdot)$	2220.dv	36	yes	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{7}{18}\right)$	$-i$
$\chi_{2220}(89,\cdot)$	2220.dw	36	no	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{2}{9}\right)$	$i$
$\chi_{2220}(91,\cdot)$	2220.dz	36	no	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{7}{18}\right)$	$-i$
$\chi_{2220}(97,\cdot)$	2220.ck	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$i$	$-i$	$e\left(\frac{5}{6}\right)$	$1$
$\chi_{2220}(101,\cdot)$	2220.br	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$
$\chi_{2220}(103,\cdot)$	2220.cs	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$-i$	$-i$	$e\left(\frac{1}{6}\right)$	$-1$
$\chi_{2220}(107,\cdot)$	2220.dv	36	yes	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{11}{18}\right)$	$i$
$\chi_{2220}(109,\cdot)$	2220.el	36	no	$-1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{1}{18}\right)$	$-i$
$\chi_{2220}(113,\cdot)$	2220.ed	36	no	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{5}{9}\right)$	$1$
$\chi_{2220}(119,\cdot)$	2220.cf	12	yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$i$	$i$	$e\left(\frac{2}{3}\right)$	$i$
$\chi_{2220}(121,\cdot)$	2220.q	3	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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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	$2220$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{36}\)
Order	$576$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(41\)	\(43\)
\(\chi_{2220}(1,\cdot)\)	2220.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2220}(7,\cdot)\)	2220.em	36	no	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{7}{9}\right)\)	\(i\)
\(\chi_{2220}(11,\cdot)\)	2220.cc	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)
\(\chi_{2220}(13,\cdot)\)	2220.eo	36	no	\(1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{11}{18}\right)\)	\(-1\)
\(\chi_{2220}(17,\cdot)\)	2220.ed	36	no	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{8}{9}\right)\)	\(1\)
\(\chi_{2220}(19,\cdot)\)	2220.dx	36	no	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{17}{18}\right)\)	\(i\)
\(\chi_{2220}(23,\cdot)\)	2220.cq	12	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(-i\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{2220}(29,\cdot)\)	2220.db	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(-i\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(i\)
\(\chi_{2220}(31,\cdot)\)	2220.t	4	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(i\)	\(i\)	\(i\)	\(-i\)	\(-1\)	\(i\)
\(\chi_{2220}(41,\cdot)\)	2220.dk	18	no	\(-1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{11}{18}\right)\)	\(-1\)
\(\chi_{2220}(43,\cdot)\)	2220.be	4	no	\(-1\)	\(1\)	\(i\)	\(1\)	\(-1\)	\(1\)	\(i\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(1\)
\(\chi_{2220}(47,\cdot)\)	2220.cu	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(i\)
\(\chi_{2220}(49,\cdot)\)	2220.dg	18	no	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(-1\)
\(\chi_{2220}(53,\cdot)\)	2220.eh	36	no	\(1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(i\)
\(\chi_{2220}(59,\cdot)\)	2220.ek	36	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{2}{9}\right)\)	\(i\)
\(\chi_{2220}(61,\cdot)\)	2220.ej	36	no	\(-1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{11}{18}\right)\)	\(-i\)
\(\chi_{2220}(67,\cdot)\)	2220.eg	36	no	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(-i\)
\(\chi_{2220}(71,\cdot)\)	2220.de	18	no	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{17}{18}\right)\)	\(-1\)
\(\chi_{2220}(73,\cdot)\)	2220.bi	4	no	\(-1\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(-i\)	\(1\)	\(-1\)	\(1\)	\(-i\)
\(\chi_{2220}(77,\cdot)\)	2220.en	36	no	\(1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{17}{18}\right)\)	\(i\)
\(\chi_{2220}(79,\cdot)\)	2220.dx	36	no	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{5}{18}\right)\)	\(i\)
\(\chi_{2220}(83,\cdot)\)	2220.dv	36	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{7}{18}\right)\)	\(-i\)
\(\chi_{2220}(89,\cdot)\)	2220.dw	36	no	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{2}{9}\right)\)	\(i\)
\(\chi_{2220}(91,\cdot)\)	2220.dz	36	no	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{7}{18}\right)\)	\(-i\)
\(\chi_{2220}(97,\cdot)\)	2220.ck	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(i\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(1\)
\(\chi_{2220}(101,\cdot)\)	2220.br	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)
\(\chi_{2220}(103,\cdot)\)	2220.cs	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)
\(\chi_{2220}(107,\cdot)\)	2220.dv	36	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{11}{18}\right)\)	\(i\)
\(\chi_{2220}(109,\cdot)\)	2220.el	36	no	\(-1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{18}\right)\)	\(-i\)
\(\chi_{2220}(113,\cdot)\)	2220.ed	36	no	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{5}{9}\right)\)	\(1\)
\(\chi_{2220}(119,\cdot)\)	2220.cf	12	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(i\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(i\)
\(\chi_{2220}(121,\cdot)\)	2220.q	3	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Character group

First 32 of 576 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.