# Properties

 Modulus $837$ Structure $$C_{6}\times C_{90}$$ Order $540$

Show commands: Pari/GP / 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 $$1$$ $$1$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{7}{45}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{32}{45}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{45}\right)$$ $$e\left(\frac{34}{45}\right)$$ $$e\left(\frac{13}{45}\right)$$ $$e\left(\frac{14}{45}\right)$$