# Properties

 Modulus $1078$ Structure $$C_{210}\times C_{2}$$ Order $420$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1078)

pari: g = idealstar(,1078,2)

## Character group

 sage: G.order()  pari: g.no Order = 420 sage: H.invariants()  pari: g.cyc Structure = $$C_{210}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1078}(199,\cdot)$, $\chi_{1078}(981,\cdot)$

## First 32 of 420 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$13$$ $$15$$ $$17$$ $$19$$ $$23$$ $$25$$ $$27$$
$$\chi_{1078}(1,\cdot)$$ 1078.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1078}(3,\cdot)$$ 1078.be 210 no $$-1$$ $$1$$ $$e\left(\frac{89}{210}\right)$$ $$e\left(\frac{187}{210}\right)$$ $$e\left(\frac{89}{105}\right)$$ $$e\left(\frac{41}{70}\right)$$ $$e\left(\frac{11}{35}\right)$$ $$e\left(\frac{167}{210}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{82}{105}\right)$$ $$e\left(\frac{19}{70}\right)$$
$$\chi_{1078}(5,\cdot)$$ 1078.be 210 no $$-1$$ $$1$$ $$e\left(\frac{187}{210}\right)$$ $$e\left(\frac{131}{210}\right)$$ $$e\left(\frac{82}{105}\right)$$ $$e\left(\frac{13}{70}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{181}{210}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{26}{105}\right)$$ $$e\left(\frac{47}{70}\right)$$
$$\chi_{1078}(9,\cdot)$$ 1078.bc 105 no $$1$$ $$1$$ $$e\left(\frac{89}{105}\right)$$ $$e\left(\frac{82}{105}\right)$$ $$e\left(\frac{73}{105}\right)$$ $$e\left(\frac{6}{35}\right)$$ $$e\left(\frac{22}{35}\right)$$ $$e\left(\frac{62}{105}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{59}{105}\right)$$ $$e\left(\frac{19}{35}\right)$$
$$\chi_{1078}(13,\cdot)$$ 1078.ba 70 no $$1$$ $$1$$ $$e\left(\frac{41}{70}\right)$$ $$e\left(\frac{13}{70}\right)$$ $$e\left(\frac{6}{35}\right)$$ $$e\left(\frac{1}{35}\right)$$ $$e\left(\frac{27}{35}\right)$$ $$e\left(\frac{19}{35}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{13}{35}\right)$$ $$e\left(\frac{53}{70}\right)$$
$$\chi_{1078}(15,\cdot)$$ 1078.v 35 no $$1$$ $$1$$ $$e\left(\frac{11}{35}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{22}{35}\right)$$ $$e\left(\frac{27}{35}\right)$$ $$e\left(\frac{29}{35}\right)$$ $$e\left(\frac{23}{35}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{1}{35}\right)$$ $$e\left(\frac{33}{35}\right)$$
$$\chi_{1078}(17,\cdot)$$ 1078.bf 210 no $$1$$ $$1$$ $$e\left(\frac{167}{210}\right)$$ $$e\left(\frac{181}{210}\right)$$ $$e\left(\frac{62}{105}\right)$$ $$e\left(\frac{19}{35}\right)$$ $$e\left(\frac{23}{35}\right)$$ $$e\left(\frac{103}{105}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{76}{105}\right)$$ $$e\left(\frac{27}{70}\right)$$
$$\chi_{1078}(19,\cdot)$$ 1078.s 30 no $$1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{1078}(23,\cdot)$$ 1078.r 21 no $$1$$ $$1$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$
$$\chi_{1078}(25,\cdot)$$ 1078.bc 105 no $$1$$ $$1$$ $$e\left(\frac{82}{105}\right)$$ $$e\left(\frac{26}{105}\right)$$ $$e\left(\frac{59}{105}\right)$$ $$e\left(\frac{13}{35}\right)$$ $$e\left(\frac{1}{35}\right)$$ $$e\left(\frac{76}{105}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{52}{105}\right)$$ $$e\left(\frac{12}{35}\right)$$
$$\chi_{1078}(27,\cdot)$$ 1078.z 70 no $$-1$$ $$1$$ $$e\left(\frac{19}{70}\right)$$ $$e\left(\frac{47}{70}\right)$$ $$e\left(\frac{19}{35}\right)$$ $$e\left(\frac{53}{70}\right)$$ $$e\left(\frac{33}{35}\right)$$ $$e\left(\frac{27}{70}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{57}{70}\right)$$
$$\chi_{1078}(29,\cdot)$$ 1078.bb 70 no $$-1$$ $$1$$ $$e\left(\frac{1}{35}\right)$$ $$e\left(\frac{8}{35}\right)$$ $$e\left(\frac{2}{35}\right)$$ $$e\left(\frac{59}{70}\right)$$ $$e\left(\frac{9}{35}\right)$$ $$e\left(\frac{1}{70}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{16}{35}\right)$$ $$e\left(\frac{3}{35}\right)$$
$$\chi_{1078}(31,\cdot)$$ 1078.t 30 no $$-1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{1078}(37,\cdot)$$ 1078.bc 105 no $$1$$ $$1$$ $$e\left(\frac{38}{105}\right)$$ $$e\left(\frac{94}{105}\right)$$ $$e\left(\frac{76}{105}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{9}{35}\right)$$ $$e\left(\frac{89}{105}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{83}{105}\right)$$ $$e\left(\frac{3}{35}\right)$$
$$\chi_{1078}(39,\cdot)$$ 1078.bd 210 no $$-1$$ $$1$$ $$e\left(\frac{1}{105}\right)$$ $$e\left(\frac{8}{105}\right)$$ $$e\left(\frac{2}{105}\right)$$ $$e\left(\frac{43}{70}\right)$$ $$e\left(\frac{3}{35}\right)$$ $$e\left(\frac{71}{210}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{16}{105}\right)$$ $$e\left(\frac{1}{35}\right)$$
$$\chi_{1078}(41,\cdot)$$ 1078.ba 70 no $$1$$ $$1$$ $$e\left(\frac{53}{70}\right)$$ $$e\left(\frac{39}{70}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{3}{35}\right)$$ $$e\left(\frac{11}{35}\right)$$ $$e\left(\frac{22}{35}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{4}{35}\right)$$ $$e\left(\frac{19}{70}\right)$$
$$\chi_{1078}(43,\cdot)$$ 1078.n 14 no $$-1$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$-1$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$
$$\chi_{1078}(45,\cdot)$$ 1078.x 42 no $$-1$$ $$1$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{3}{14}\right)$$
$$\chi_{1078}(47,\cdot)$$ 1078.be 210 no $$-1$$ $$1$$ $$e\left(\frac{109}{210}\right)$$ $$e\left(\frac{137}{210}\right)$$ $$e\left(\frac{4}{105}\right)$$ $$e\left(\frac{51}{70}\right)$$ $$e\left(\frac{6}{35}\right)$$ $$e\left(\frac{37}{210}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{32}{105}\right)$$ $$e\left(\frac{39}{70}\right)$$
$$\chi_{1078}(51,\cdot)$$ 1078.bd 210 no $$-1$$ $$1$$ $$e\left(\frac{23}{105}\right)$$ $$e\left(\frac{79}{105}\right)$$ $$e\left(\frac{46}{105}\right)$$ $$e\left(\frac{9}{70}\right)$$ $$e\left(\frac{34}{35}\right)$$ $$e\left(\frac{163}{210}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{53}{105}\right)$$ $$e\left(\frac{23}{35}\right)$$
$$\chi_{1078}(53,\cdot)$$ 1078.bc 105 no $$1$$ $$1$$ $$e\left(\frac{4}{105}\right)$$ $$e\left(\frac{32}{105}\right)$$ $$e\left(\frac{8}{105}\right)$$ $$e\left(\frac{16}{35}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{37}{105}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{64}{105}\right)$$ $$e\left(\frac{4}{35}\right)$$
$$\chi_{1078}(57,\cdot)$$ 1078.bb 70 no $$-1$$ $$1$$ $$e\left(\frac{23}{35}\right)$$ $$e\left(\frac{9}{35}\right)$$ $$e\left(\frac{11}{35}\right)$$ $$e\left(\frac{27}{70}\right)$$ $$e\left(\frac{32}{35}\right)$$ $$e\left(\frac{23}{70}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{34}{35}\right)$$
$$\chi_{1078}(59,\cdot)$$ 1078.be 210 no $$-1$$ $$1$$ $$e\left(\frac{191}{210}\right)$$ $$e\left(\frac{163}{210}\right)$$ $$e\left(\frac{86}{105}\right)$$ $$e\left(\frac{29}{70}\right)$$ $$e\left(\frac{24}{35}\right)$$ $$e\left(\frac{113}{210}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{58}{105}\right)$$ $$e\left(\frac{51}{70}\right)$$
$$\chi_{1078}(61,\cdot)$$ 1078.bf 210 no $$1$$ $$1$$ $$e\left(\frac{97}{210}\right)$$ $$e\left(\frac{41}{210}\right)$$ $$e\left(\frac{97}{105}\right)$$ $$e\left(\frac{19}{35}\right)$$ $$e\left(\frac{23}{35}\right)$$ $$e\left(\frac{68}{105}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{41}{105}\right)$$ $$e\left(\frac{27}{70}\right)$$
$$\chi_{1078}(65,\cdot)$$ 1078.y 42 no $$-1$$ $$1$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$
$$\chi_{1078}(67,\cdot)$$ 1078.e 3 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$
$$\chi_{1078}(69,\cdot)$$ 1078.z 70 no $$-1$$ $$1$$ $$e\left(\frac{23}{70}\right)$$ $$e\left(\frac{9}{70}\right)$$ $$e\left(\frac{23}{35}\right)$$ $$e\left(\frac{31}{70}\right)$$ $$e\left(\frac{16}{35}\right)$$ $$e\left(\frac{29}{70}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{9}{35}\right)$$ $$e\left(\frac{69}{70}\right)$$
$$\chi_{1078}(71,\cdot)$$ 1078.v 35 no $$1$$ $$1$$ $$e\left(\frac{27}{35}\right)$$ $$e\left(\frac{6}{35}\right)$$ $$e\left(\frac{19}{35}\right)$$ $$e\left(\frac{9}{35}\right)$$ $$e\left(\frac{33}{35}\right)$$ $$e\left(\frac{31}{35}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{11}{35}\right)$$
$$\chi_{1078}(73,\cdot)$$ 1078.bf 210 no $$1$$ $$1$$ $$e\left(\frac{101}{210}\right)$$ $$e\left(\frac{73}{210}\right)$$ $$e\left(\frac{101}{105}\right)$$ $$e\left(\frac{27}{35}\right)$$ $$e\left(\frac{29}{35}\right)$$ $$e\left(\frac{34}{105}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{73}{105}\right)$$ $$e\left(\frac{31}{70}\right)$$
$$\chi_{1078}(75,\cdot)$$ 1078.be 210 no $$-1$$ $$1$$ $$e\left(\frac{43}{210}\right)$$ $$e\left(\frac{29}{210}\right)$$ $$e\left(\frac{43}{105}\right)$$ $$e\left(\frac{67}{70}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{109}{210}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{29}{105}\right)$$ $$e\left(\frac{43}{70}\right)$$
$$\chi_{1078}(79,\cdot)$$ 1078.u 30 no $$-1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{1078}(81,\cdot)$$ 1078.bc 105 no $$1$$ $$1$$ $$e\left(\frac{73}{105}\right)$$ $$e\left(\frac{59}{105}\right)$$ $$e\left(\frac{41}{105}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{9}{35}\right)$$ $$e\left(\frac{19}{105}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{13}{105}\right)$$ $$e\left(\frac{3}{35}\right)$$