LMFDB - Group of Dirichlet characters of modulus 837

Show commands: PariGP / SageMath

sage: H = DirichletGroup(837)

pari: g = idealstar(,837,2)

Character group

sage: G.order() pari: g.no
Order	=	540
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{90}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{837}(218,\cdot)$, $\chi_{837}(406,\cdot)$

First 32 of 540 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{837}(1,\cdot)$	837.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{837}(2,\cdot)$	837.cg	90	yes	$-1$	$1$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{837}(4,\cdot)$	837.cc	45	yes	$1$	$1$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{2}{45}\right)$
$\chi_{837}(5,\cdot)$	837.bn	18	yes	$-1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{837}(7,\cdot)$	837.ca	45	yes	$1$	$1$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{837}(8,\cdot)$	837.br	30	no	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{837}(10,\cdot)$	837.be	15	no	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{837}(11,\cdot)$	837.cf	90	yes	$1$	$1$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{837}(13,\cdot)$	837.cj	90	yes	$-1$	$1$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{837}(14,\cdot)$	837.ci	90	yes	$-1$	$1$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{8}{45}\right)$
$\chi_{837}(16,\cdot)$	837.cc	45	yes	$1$	$1$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{4}{45}\right)$
$\chi_{837}(17,\cdot)$	837.bt	30	no	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{837}(19,\cdot)$	837.be	15	no	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{837}(20,\cdot)$	837.ci	90	yes	$-1$	$1$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{837}(22,\cdot)$	837.cj	90	yes	$-1$	$1$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{23}{45}\right)$
$\chi_{837}(23,\cdot)$	837.ch	90	yes	$1$	$1$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{38}{45}\right)$
$\chi_{837}(25,\cdot)$	837.x	9	yes	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{837}(26,\cdot)$	837.j	6	no	$1$	$1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$
$\chi_{837}(28,\cdot)$	837.bb	15	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{837}(29,\cdot)$	837.ch	90	yes	$1$	$1$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{837}(32,\cdot)$	837.bk	18	no	$-1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{837}(34,\cdot)$	837.cj	90	yes	$-1$	$1$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{34}{45}\right)$
$\chi_{837}(35,\cdot)$	837.br	30	no	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{837}(37,\cdot)$	837.l	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{837}(38,\cdot)$	837.cd	90	yes	$-1$	$1$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{837}(40,\cdot)$	837.ca	45	yes	$1$	$1$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{8}{45}\right)$
$\chi_{837}(41,\cdot)$	837.cd	90	yes	$-1$	$1$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{837}(43,\cdot)$	837.cj	90	yes	$-1$	$1$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{31}{45}\right)$
$\chi_{837}(44,\cdot)$	837.bq	30	no	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{15}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{837}(46,\cdot)$	837.bv	30	no	$-1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{837}(47,\cdot)$	837.cg	90	yes	$-1$	$1$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{34}{45}\right)$
$\chi_{837}(49,\cdot)$	837.ca	45	yes	$1$	$1$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{14}{45}\right)$

Click here to search among the remaining 508 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	$837$
Structure	\(C_{6}\times C_{90}\)
Order	$540$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{837}(1,\cdot)\)	837.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{837}(2,\cdot)\)	837.cg	90	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{837}(4,\cdot)\)	837.cc	45	yes	\(1\)	\(1\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)
\(\chi_{837}(5,\cdot)\)	837.bn	18	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{837}(7,\cdot)\)	837.ca	45	yes	\(1\)	\(1\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)
\(\chi_{837}(8,\cdot)\)	837.br	30	no	\(-1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{837}(10,\cdot)\)	837.be	15	no	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{837}(11,\cdot)\)	837.cf	90	yes	\(1\)	\(1\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{837}(13,\cdot)\)	837.cj	90	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)
\(\chi_{837}(14,\cdot)\)	837.ci	90	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)
\(\chi_{837}(16,\cdot)\)	837.cc	45	yes	\(1\)	\(1\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)
\(\chi_{837}(17,\cdot)\)	837.bt	30	no	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{837}(19,\cdot)\)	837.be	15	no	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{837}(20,\cdot)\)	837.ci	90	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)
\(\chi_{837}(22,\cdot)\)	837.cj	90	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)
\(\chi_{837}(23,\cdot)\)	837.ch	90	yes	\(1\)	\(1\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)
\(\chi_{837}(25,\cdot)\)	837.x	9	yes	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{837}(26,\cdot)\)	837.j	6	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)
\(\chi_{837}(28,\cdot)\)	837.bb	15	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{837}(29,\cdot)\)	837.ch	90	yes	\(1\)	\(1\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{837}(32,\cdot)\)	837.bk	18	no	\(-1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{837}(34,\cdot)\)	837.cj	90	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)
\(\chi_{837}(35,\cdot)\)	837.br	30	no	\(-1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{837}(37,\cdot)\)	837.l	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{837}(38,\cdot)\)	837.cd	90	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{837}(40,\cdot)\)	837.ca	45	yes	\(1\)	\(1\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)
\(\chi_{837}(41,\cdot)\)	837.cd	90	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)
\(\chi_{837}(43,\cdot)\)	837.cj	90	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)
\(\chi_{837}(44,\cdot)\)	837.bq	30	no	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{837}(46,\cdot)\)	837.bv	30	no	\(-1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{837}(47,\cdot)\)	837.cg	90	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)
\(\chi_{837}(49,\cdot)\)	837.ca	45	yes	\(1\)	\(1\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 540 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.