LMFDB - Group of Dirichlet characters of modulus 805

sage:H = DirichletGroup(805)

pari:g = idealstar(,805,2)

Character group

sage:G.order() pari:g.no
Order	=	528
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{132}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{805}(162,\cdot)$, $\chi_{805}(346,\cdot)$, $\chi_{805}(281,\cdot)$

First 32 of 528 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	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$11$	$12$	$13$	$16$
$\chi_{805}(1,\cdot)$	805.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{805}(2,\cdot)$	805.bt	132	yes	$-1$	$1$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{13}{33}\right)$
$\chi_{805}(3,\cdot)$	805.bv	132	yes	$1$	$1$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{5}{33}\right)$
$\chi_{805}(4,\cdot)$	805.bm	66	yes	$1$	$1$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{26}{33}\right)$
$\chi_{805}(6,\cdot)$	805.ba	22	no	$-1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{805}(8,\cdot)$	805.bh	44	no	$-1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{805}(9,\cdot)$	805.bm	66	yes	$1$	$1$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{10}{33}\right)$
$\chi_{805}(11,\cdot)$	805.br	66	no	$-1$	$1$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{20}{33}\right)$
$\chi_{805}(12,\cdot)$	805.bv	132	yes	$1$	$1$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{31}{33}\right)$
$\chi_{805}(13,\cdot)$	805.bj	44	yes	$1$	$1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{805}(16,\cdot)$	805.bg	33	no	$1$	$1$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{19}{33}\right)$
$\chi_{805}(17,\cdot)$	805.bu	132	yes	$-1$	$1$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{29}{33}\right)$
$\chi_{805}(18,\cdot)$	805.bt	132	yes	$-1$	$1$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{23}{33}\right)$
$\chi_{805}(19,\cdot)$	805.bn	66	yes	$1$	$1$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{4}{33}\right)$
$\chi_{805}(22,\cdot)$	805.l	4	no	$1$	$1$	$i$	$-i$	$-1$	$1$	$-i$	$-1$	$-1$	$i$	$-i$	$1$
$\chi_{805}(24,\cdot)$	805.q	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{805}(26,\cdot)$	805.bq	66	no	$-1$	$1$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{16}{33}\right)$
$\chi_{805}(27,\cdot)$	805.bj	44	yes	$1$	$1$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{805}(29,\cdot)$	805.be	22	no	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{805}(31,\cdot)$	805.bq	66	no	$-1$	$1$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{17}{33}\right)$
$\chi_{805}(32,\cdot)$	805.bt	132	yes	$-1$	$1$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{32}{33}\right)$
$\chi_{805}(33,\cdot)$	805.bu	132	yes	$-1$	$1$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{25}{33}\right)$
$\chi_{805}(34,\cdot)$	805.bd	22	yes	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{805}(36,\cdot)$	805.u	11	no	$1$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{805}(37,\cdot)$	805.bs	132	yes	$1$	$1$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{10}{33}\right)$
$\chi_{805}(38,\cdot)$	805.bu	132	yes	$-1$	$1$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{17}{33}\right)$
$\chi_{805}(39,\cdot)$	805.bm	66	yes	$1$	$1$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{8}{33}\right)$
$\chi_{805}(41,\cdot)$	805.ba	22	no	$-1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{805}(43,\cdot)$	805.bi	44	no	$1$	$1$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{805}(44,\cdot)$	805.bl	66	yes	$-1$	$1$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{13}{33}\right)$
$\chi_{805}(47,\cdot)$	805.v	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$
$\chi_{805}(48,\cdot)$	805.bj	44	yes	$1$	$1$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{8}{11}\right)$

Click here to search among the remaining 496 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 $\F_{q}$
Belyi maps

Modulus	$805$
Structure	\(C_{2}\times C_{2}\times C_{132}\)
Order	$528$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)	\(16\)
\(\chi_{805}(1,\cdot)\)	805.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{805}(2,\cdot)\)	805.bt	132	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{13}{33}\right)\)
\(\chi_{805}(3,\cdot)\)	805.bv	132	yes	\(1\)	\(1\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{5}{33}\right)\)
\(\chi_{805}(4,\cdot)\)	805.bm	66	yes	\(1\)	\(1\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{26}{33}\right)\)
\(\chi_{805}(6,\cdot)\)	805.ba	22	no	\(-1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{805}(8,\cdot)\)	805.bh	44	no	\(-1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{805}(9,\cdot)\)	805.bm	66	yes	\(1\)	\(1\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{10}{33}\right)\)
\(\chi_{805}(11,\cdot)\)	805.br	66	no	\(-1\)	\(1\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{20}{33}\right)\)
\(\chi_{805}(12,\cdot)\)	805.bv	132	yes	\(1\)	\(1\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{31}{33}\right)\)
\(\chi_{805}(13,\cdot)\)	805.bj	44	yes	\(1\)	\(1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{805}(16,\cdot)\)	805.bg	33	no	\(1\)	\(1\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{19}{33}\right)\)
\(\chi_{805}(17,\cdot)\)	805.bu	132	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{29}{33}\right)\)
\(\chi_{805}(18,\cdot)\)	805.bt	132	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{23}{33}\right)\)
\(\chi_{805}(19,\cdot)\)	805.bn	66	yes	\(1\)	\(1\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{4}{33}\right)\)
\(\chi_{805}(22,\cdot)\)	805.l	4	no	\(1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(-i\)	\(1\)
\(\chi_{805}(24,\cdot)\)	805.q	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{805}(26,\cdot)\)	805.bq	66	no	\(-1\)	\(1\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{16}{33}\right)\)
\(\chi_{805}(27,\cdot)\)	805.bj	44	yes	\(1\)	\(1\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{805}(29,\cdot)\)	805.be	22	no	\(1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{805}(31,\cdot)\)	805.bq	66	no	\(-1\)	\(1\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{17}{33}\right)\)
\(\chi_{805}(32,\cdot)\)	805.bt	132	yes	\(-1\)	\(1\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{32}{33}\right)\)
\(\chi_{805}(33,\cdot)\)	805.bu	132	yes	\(-1\)	\(1\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{25}{33}\right)\)
\(\chi_{805}(34,\cdot)\)	805.bd	22	yes	\(1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{805}(36,\cdot)\)	805.u	11	no	\(1\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{805}(37,\cdot)\)	805.bs	132	yes	\(1\)	\(1\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{47}{132}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{10}{33}\right)\)
\(\chi_{805}(38,\cdot)\)	805.bu	132	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{103}{132}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{17}{33}\right)\)
\(\chi_{805}(39,\cdot)\)	805.bm	66	yes	\(1\)	\(1\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{8}{33}\right)\)
\(\chi_{805}(41,\cdot)\)	805.ba	22	no	\(-1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{805}(43,\cdot)\)	805.bi	44	no	\(1\)	\(1\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{805}(44,\cdot)\)	805.bl	66	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{13}{33}\right)\)
\(\chi_{805}(47,\cdot)\)	805.v	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{805}(48,\cdot)\)	805.bj	44	yes	\(1\)	\(1\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 528 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.