LMFDB - Group of Dirichlet characters of modulus 801

Show commands: PariGP / SageMath

sage: H = DirichletGroup(801)

pari: g = idealstar(,801,2)

Character group

sage: G.order() pari: g.no
Order	=	528
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{264}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{801}(713,\cdot)$, $\chi_{801}(181,\cdot)$

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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{801}(1,\cdot)$	801.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{801}(2,\cdot)$	801.y	66	yes	$-1$	$1$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{10}{33}\right)$
$\chi_{801}(4,\cdot)$	801.u	33	yes	$1$	$1$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{20}{33}\right)$
$\chi_{801}(5,\cdot)$	801.bc	132	yes	$-1$	$1$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{8}{33}\right)$
$\chi_{801}(7,\cdot)$	801.bf	264	yes	$-1$	$1$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{59}{264}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{133}{264}\right)$	$e\left(\frac{163}{264}\right)$	$e\left(\frac{19}{33}\right)$
$\chi_{801}(8,\cdot)$	801.q	22	no	$-1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{801}(10,\cdot)$	801.v	44	no	$1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{801}(11,\cdot)$	801.x	66	yes	$-1$	$1$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{25}{33}\right)$
$\chi_{801}(13,\cdot)$	801.bf	264	yes	$-1$	$1$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{133}{264}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{179}{264}\right)$	$e\left(\frac{5}{264}\right)$	$e\left(\frac{2}{33}\right)$
$\chi_{801}(14,\cdot)$	801.be	264	yes	$1$	$1$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{163}{264}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{5}{264}\right)$	$e\left(\frac{23}{264}\right)$	$e\left(\frac{29}{33}\right)$
$\chi_{801}(16,\cdot)$	801.u	33	yes	$1$	$1$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{7}{33}\right)$
$\chi_{801}(17,\cdot)$	801.w	44	no	$-1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{801}(19,\cdot)$	801.ba	88	no	$-1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{801}(20,\cdot)$	801.bc	132	yes	$-1$	$1$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{28}{33}\right)$
$\chi_{801}(22,\cdot)$	801.z	66	yes	$1$	$1$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{2}{33}\right)$
$\chi_{801}(23,\cdot)$	801.be	264	yes	$1$	$1$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{211}{264}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{149}{264}\right)$	$e\left(\frac{263}{264}\right)$	$e\left(\frac{26}{33}\right)$
$\chi_{801}(25,\cdot)$	801.z	66	yes	$1$	$1$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{16}{33}\right)$
$\chi_{801}(26,\cdot)$	801.bb	88	no	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{801}(28,\cdot)$	801.ba	88	no	$-1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{801}(29,\cdot)$	801.be	264	yes	$1$	$1$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{257}{264}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{199}{264}\right)$	$e\left(\frac{229}{264}\right)$	$e\left(\frac{19}{33}\right)$
$\chi_{801}(31,\cdot)$	801.bf	264	yes	$-1$	$1$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{229}{264}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{203}{264}\right)$	$e\left(\frac{221}{264}\right)$	$e\left(\frac{29}{33}\right)$
$\chi_{801}(32,\cdot)$	801.y	66	yes	$-1$	$1$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{17}{33}\right)$
$\chi_{801}(34,\cdot)$	801.n	12	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{801}(35,\cdot)$	801.bb	88	no	$1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{801}(37,\cdot)$	801.l	8	no	$-1$	$1$	$1$	$1$	$-i$	$e\left(\frac{1}{8}\right)$	$1$	$-i$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$
$\chi_{801}(38,\cdot)$	801.be	264	yes	$1$	$1$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{161}{264}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{175}{264}\right)$	$e\left(\frac{13}{264}\right)$	$e\left(\frac{25}{33}\right)$
$\chi_{801}(40,\cdot)$	801.bd	132	yes	$1$	$1$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{5}{33}\right)$
$\chi_{801}(41,\cdot)$	801.be	264	yes	$1$	$1$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{175}{264}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{41}{264}\right)$	$e\left(\frac{83}{264}\right)$	$e\left(\frac{20}{33}\right)$
$\chi_{801}(43,\cdot)$	801.bf	264	yes	$-1$	$1$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{95}{264}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{241}{264}\right)$	$e\left(\frac{79}{264}\right)$	$e\left(\frac{25}{33}\right)$
$\chi_{801}(44,\cdot)$	801.r	22	no	$-1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{801}(46,\cdot)$	801.ba	88	no	$-1$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{801}(47,\cdot)$	801.bc	132	yes	$-1$	$1$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{31}{33}\right)$

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 $\F_{q}$

Modulus	$801$
Structure	\(C_{2}\times C_{264}\)
Order	$528$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{801}(1,\cdot)\)	801.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{801}(2,\cdot)\)	801.y	66	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)
\(\chi_{801}(4,\cdot)\)	801.u	33	yes	\(1\)	\(1\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)
\(\chi_{801}(5,\cdot)\)	801.bc	132	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{8}{33}\right)\)
\(\chi_{801}(7,\cdot)\)	801.bf	264	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{59}{264}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{133}{264}\right)\)	\(e\left(\frac{163}{264}\right)\)	\(e\left(\frac{19}{33}\right)\)
\(\chi_{801}(8,\cdot)\)	801.q	22	no	\(-1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{801}(10,\cdot)\)	801.v	44	no	\(1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{801}(11,\cdot)\)	801.x	66	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)
\(\chi_{801}(13,\cdot)\)	801.bf	264	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{133}{264}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{179}{264}\right)\)	\(e\left(\frac{5}{264}\right)\)	\(e\left(\frac{2}{33}\right)\)
\(\chi_{801}(14,\cdot)\)	801.be	264	yes	\(1\)	\(1\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{163}{264}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{5}{264}\right)\)	\(e\left(\frac{23}{264}\right)\)	\(e\left(\frac{29}{33}\right)\)
\(\chi_{801}(16,\cdot)\)	801.u	33	yes	\(1\)	\(1\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)
\(\chi_{801}(17,\cdot)\)	801.w	44	no	\(-1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{801}(19,\cdot)\)	801.ba	88	no	\(-1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{801}(20,\cdot)\)	801.bc	132	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{28}{33}\right)\)
\(\chi_{801}(22,\cdot)\)	801.z	66	yes	\(1\)	\(1\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)
\(\chi_{801}(23,\cdot)\)	801.be	264	yes	\(1\)	\(1\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{211}{264}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{149}{264}\right)\)	\(e\left(\frac{263}{264}\right)\)	\(e\left(\frac{26}{33}\right)\)
\(\chi_{801}(25,\cdot)\)	801.z	66	yes	\(1\)	\(1\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)
\(\chi_{801}(26,\cdot)\)	801.bb	88	no	\(1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{801}(28,\cdot)\)	801.ba	88	no	\(-1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{801}(29,\cdot)\)	801.be	264	yes	\(1\)	\(1\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{257}{264}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{199}{264}\right)\)	\(e\left(\frac{229}{264}\right)\)	\(e\left(\frac{19}{33}\right)\)
\(\chi_{801}(31,\cdot)\)	801.bf	264	yes	\(-1\)	\(1\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{229}{264}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{203}{264}\right)\)	\(e\left(\frac{221}{264}\right)\)	\(e\left(\frac{29}{33}\right)\)
\(\chi_{801}(32,\cdot)\)	801.y	66	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{17}{33}\right)\)
\(\chi_{801}(34,\cdot)\)	801.n	12	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{801}(35,\cdot)\)	801.bb	88	no	\(1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{801}(37,\cdot)\)	801.l	8	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(-i\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)
\(\chi_{801}(38,\cdot)\)	801.be	264	yes	\(1\)	\(1\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{161}{264}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{175}{264}\right)\)	\(e\left(\frac{13}{264}\right)\)	\(e\left(\frac{25}{33}\right)\)
\(\chi_{801}(40,\cdot)\)	801.bd	132	yes	\(1\)	\(1\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{5}{33}\right)\)
\(\chi_{801}(41,\cdot)\)	801.be	264	yes	\(1\)	\(1\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{175}{264}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{41}{264}\right)\)	\(e\left(\frac{83}{264}\right)\)	\(e\left(\frac{20}{33}\right)\)
\(\chi_{801}(43,\cdot)\)	801.bf	264	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{95}{264}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{241}{264}\right)\)	\(e\left(\frac{79}{264}\right)\)	\(e\left(\frac{25}{33}\right)\)
\(\chi_{801}(44,\cdot)\)	801.r	22	no	\(-1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{801}(46,\cdot)\)	801.ba	88	no	\(-1\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{801}(47,\cdot)\)	801.bc	132	yes	\(-1\)	\(1\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{47}{132}\right)\)	\(e\left(\frac{31}{33}\right)\)

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.