LMFDB - Group of Dirichlet characters of modulus 414

Show commands: PariGP / SageMath

sage: H = DirichletGroup(414)

pari: g = idealstar(,414,2)

Character group

sage: G.order() pari: g.no
Order	=	132
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{66}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{414}(47,\cdot)$, $\chi_{414}(235,\cdot)$

First 32 of 132 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$25$	$29$	$31$	$35$
$\chi_{414}(1,\cdot)$	414.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{414}(5,\cdot)$	414.p	66	no	$1$	$1$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{414}(7,\cdot)$	414.n	66	no	$-1$	$1$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{414}(11,\cdot)$	414.p	66	no	$1$	$1$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{414}(13,\cdot)$	414.m	33	no	$1$	$1$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{414}(17,\cdot)$	414.j	22	no	$1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{414}(19,\cdot)$	414.l	22	no	$-1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{414}(25,\cdot)$	414.m	33	no	$1$	$1$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{414}(29,\cdot)$	414.o	66	no	$-1$	$1$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{414}(31,\cdot)$	414.m	33	no	$1$	$1$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{414}(35,\cdot)$	414.k	22	no	$-1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{414}(37,\cdot)$	414.l	22	no	$-1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{414}(41,\cdot)$	414.o	66	no	$-1$	$1$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{414}(43,\cdot)$	414.n	66	no	$-1$	$1$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{414}(47,\cdot)$	414.g	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{414}(49,\cdot)$	414.m	33	no	$1$	$1$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{414}(53,\cdot)$	414.j	22	no	$1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{414}(55,\cdot)$	414.i	11	no	$1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{414}(59,\cdot)$	414.o	66	no	$-1$	$1$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{414}(61,\cdot)$	414.n	66	no	$-1$	$1$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{414}(65,\cdot)$	414.p	66	no	$1$	$1$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{414}(67,\cdot)$	414.n	66	no	$-1$	$1$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{414}(71,\cdot)$	414.k	22	no	$-1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{414}(73,\cdot)$	414.i	11	no	$1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{414}(77,\cdot)$	414.o	66	no	$-1$	$1$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{414}(79,\cdot)$	414.n	66	no	$-1$	$1$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{414}(83,\cdot)$	414.p	66	no	$1$	$1$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{414}(85,\cdot)$	414.m	33	no	$1$	$1$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{414}(89,\cdot)$	414.j	22	no	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{414}(91,\cdot)$	414.b	2	no	$-1$	$1$	$-1$	$-1$	$-1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$1$
$\chi_{414}(95,\cdot)$	414.o	66	no	$-1$	$1$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{414}(97,\cdot)$	414.n	66	no	$-1$	$1$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{10}{11}\right)$

Click here to search among the remaining 100 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	$414$
Structure	\(C_{2}\times C_{66}\)
Order	$132$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{414}(1,\cdot)\)	414.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{414}(5,\cdot)\)	414.p	66	no	\(1\)	\(1\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{414}(7,\cdot)\)	414.n	66	no	\(-1\)	\(1\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{414}(11,\cdot)\)	414.p	66	no	\(1\)	\(1\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{414}(13,\cdot)\)	414.m	33	no	\(1\)	\(1\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{414}(17,\cdot)\)	414.j	22	no	\(1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{414}(19,\cdot)\)	414.l	22	no	\(-1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{414}(25,\cdot)\)	414.m	33	no	\(1\)	\(1\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{414}(29,\cdot)\)	414.o	66	no	\(-1\)	\(1\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{414}(31,\cdot)\)	414.m	33	no	\(1\)	\(1\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{414}(35,\cdot)\)	414.k	22	no	\(-1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{414}(37,\cdot)\)	414.l	22	no	\(-1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{414}(41,\cdot)\)	414.o	66	no	\(-1\)	\(1\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{414}(43,\cdot)\)	414.n	66	no	\(-1\)	\(1\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{414}(47,\cdot)\)	414.g	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{414}(49,\cdot)\)	414.m	33	no	\(1\)	\(1\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{414}(53,\cdot)\)	414.j	22	no	\(1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{414}(55,\cdot)\)	414.i	11	no	\(1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{414}(59,\cdot)\)	414.o	66	no	\(-1\)	\(1\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{414}(61,\cdot)\)	414.n	66	no	\(-1\)	\(1\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{414}(65,\cdot)\)	414.p	66	no	\(1\)	\(1\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{414}(67,\cdot)\)	414.n	66	no	\(-1\)	\(1\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{414}(71,\cdot)\)	414.k	22	no	\(-1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{414}(73,\cdot)\)	414.i	11	no	\(1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{414}(77,\cdot)\)	414.o	66	no	\(-1\)	\(1\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{414}(79,\cdot)\)	414.n	66	no	\(-1\)	\(1\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{414}(83,\cdot)\)	414.p	66	no	\(1\)	\(1\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{414}(85,\cdot)\)	414.m	33	no	\(1\)	\(1\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{414}(89,\cdot)\)	414.j	22	no	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{414}(91,\cdot)\)	414.b	2	no	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{414}(95,\cdot)\)	414.o	66	no	\(-1\)	\(1\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{414}(97,\cdot)\)	414.n	66	no	\(-1\)	\(1\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 132 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.