LMFDB - Group of Dirichlet characters of modulus 441

Show commands: PariGP / SageMath

sage: H = DirichletGroup(441)

pari: g = idealstar(,441,2)

Character group

sage: G.order() pari: g.no
Order	=	252
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{42}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{441}(344,\cdot)$, $\chi_{441}(199,\cdot)$

First 32 of 252 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{441}(1,\cdot)$	441.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{441}(2,\cdot)$	441.bi	42	yes	$-1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{441}(4,\cdot)$	441.z	21	yes	$1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{441}(5,\cdot)$	441.bn	42	yes	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{441}(8,\cdot)$	441.x	14	no	$-1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$1$
$\chi_{441}(10,\cdot)$	441.bj	42	no	$-1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{441}(11,\cdot)$	441.bm	42	yes	$-1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{441}(13,\cdot)$	441.bk	42	yes	$-1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{9}{14}\right)$	$-1$
$\chi_{441}(16,\cdot)$	441.z	21	yes	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{441}(17,\cdot)$	441.bg	42	no	$1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{441}(19,\cdot)$	441.m	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{441}(20,\cdot)$	441.bh	42	yes	$1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{7}\right)$	$-1$
$\chi_{441}(22,\cdot)$	441.ba	21	yes	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{7}\right)$	$1$
$\chi_{441}(23,\cdot)$	441.bm	42	yes	$-1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{441}(25,\cdot)$	441.y	21	yes	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{441}(26,\cdot)$	441.bg	42	no	$1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{441}(29,\cdot)$	441.be	42	yes	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{3}{14}\right)$	$1$
$\chi_{441}(31,\cdot)$	441.k	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{441}(32,\cdot)$	441.bi	42	yes	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{441}(34,\cdot)$	441.bk	42	yes	$-1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{14}\right)$	$-1$
$\chi_{441}(37,\cdot)$	441.bb	21	no	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{441}(38,\cdot)$	441.bn	42	yes	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{441}(40,\cdot)$	441.bc	42	yes	$-1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{441}(41,\cdot)$	441.bh	42	yes	$1$	$1$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{3}{7}\right)$	$-1$
$\chi_{441}(43,\cdot)$	441.ba	21	yes	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{4}{7}\right)$	$1$
$\chi_{441}(44,\cdot)$	441.bf	42	no	$-1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{441}(46,\cdot)$	441.bb	21	no	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{441}(47,\cdot)$	441.bd	42	yes	$1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{441}(50,\cdot)$	441.r	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$
$\chi_{441}(52,\cdot)$	441.bc	42	yes	$-1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{441}(53,\cdot)$	441.bf	42	no	$-1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{441}(55,\cdot)$	441.v	14	no	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$-1$

Click here to search among the remaining 220 characters.

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	$441$
Structure	\(C_{6}\times C_{42}\)
Order	$252$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{441}(1,\cdot)\)	441.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{441}(2,\cdot)\)	441.bi	42	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{441}(4,\cdot)\)	441.z	21	yes	\(1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{441}(5,\cdot)\)	441.bn	42	yes	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{441}(8,\cdot)\)	441.x	14	no	\(-1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(1\)
\(\chi_{441}(10,\cdot)\)	441.bj	42	no	\(-1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{441}(11,\cdot)\)	441.bm	42	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{441}(13,\cdot)\)	441.bk	42	yes	\(-1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-1\)
\(\chi_{441}(16,\cdot)\)	441.z	21	yes	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{441}(17,\cdot)\)	441.bg	42	no	\(1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{441}(19,\cdot)\)	441.m	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{441}(20,\cdot)\)	441.bh	42	yes	\(1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(-1\)
\(\chi_{441}(22,\cdot)\)	441.ba	21	yes	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(1\)
\(\chi_{441}(23,\cdot)\)	441.bm	42	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{441}(25,\cdot)\)	441.y	21	yes	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{441}(26,\cdot)\)	441.bg	42	no	\(1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{441}(29,\cdot)\)	441.be	42	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(1\)
\(\chi_{441}(31,\cdot)\)	441.k	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{441}(32,\cdot)\)	441.bi	42	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{441}(34,\cdot)\)	441.bk	42	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(-1\)
\(\chi_{441}(37,\cdot)\)	441.bb	21	no	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{441}(38,\cdot)\)	441.bn	42	yes	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{441}(40,\cdot)\)	441.bc	42	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{441}(41,\cdot)\)	441.bh	42	yes	\(1\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)
\(\chi_{441}(43,\cdot)\)	441.ba	21	yes	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)
\(\chi_{441}(44,\cdot)\)	441.bf	42	no	\(-1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{441}(46,\cdot)\)	441.bb	21	no	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{441}(47,\cdot)\)	441.bd	42	yes	\(1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{441}(50,\cdot)\)	441.r	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)
\(\chi_{441}(52,\cdot)\)	441.bc	42	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{441}(53,\cdot)\)	441.bf	42	no	\(-1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{441}(55,\cdot)\)	441.v	14	no	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 252 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.