# Properties

 Modulus $3234$ Structure $$C_{2}\times C_{2}\times C_{210}$$ Order $840$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3234)

pari: g = idealstar(,3234,2)

## Character group

 sage: G.order()  pari: g.no Order = 840 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{210}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{3234}(1079,\cdot)$, $\chi_{3234}(199,\cdot)$, $\chi_{3234}(2059,\cdot)$

## First 32 of 840 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 $$-1$$ $$1$$ $$5$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{3234}(1,\cdot)$$ 3234.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{3234}(5,\cdot)$$ 3234.cf 210 no $$1$$ $$1$$ $$e\left(\frac{13}{105}\right)$$ $$e\left(\frac{13}{70}\right)$$ $$e\left(\frac{38}{105}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{26}{105}\right)$$ $$e\left(\frac{51}{70}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{94}{105}\right)$$ $$e\left(\frac{2}{35}\right)$$
$$\chi_{3234}(13,\cdot)$$ 3234.ca 70 no $$1$$ $$1$$ $$e\left(\frac{13}{70}\right)$$ $$e\left(\frac{1}{35}\right)$$ $$e\left(\frac{19}{35}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{13}{35}\right)$$ $$e\left(\frac{59}{70}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{3}{35}\right)$$
$$\chi_{3234}(17,\cdot)$$ 3234.ch 210 no $$-1$$ $$1$$ $$e\left(\frac{38}{105}\right)$$ $$e\left(\frac{19}{35}\right)$$ $$e\left(\frac{101}{210}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{76}{105}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{89}{105}\right)$$ $$e\left(\frac{9}{70}\right)$$
$$\chi_{3234}(19,\cdot)$$ 3234.bj 30 no $$1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{3234}(23,\cdot)$$ 3234.bq 42 no $$-1$$ $$1$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{1}{14}\right)$$
$$\chi_{3234}(25,\cdot)$$ 3234.ce 105 no $$1$$ $$1$$ $$e\left(\frac{26}{105}\right)$$ $$e\left(\frac{13}{35}\right)$$ $$e\left(\frac{76}{105}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{52}{105}\right)$$ $$e\left(\frac{16}{35}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{83}{105}\right)$$ $$e\left(\frac{4}{35}\right)$$
$$\chi_{3234}(29,\cdot)$$ 3234.by 70 no $$1$$ $$1$$ $$e\left(\frac{51}{70}\right)$$ $$e\left(\frac{59}{70}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{16}{35}\right)$$ $$e\left(\frac{4}{35}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{35}\right)$$ $$e\left(\frac{1}{35}\right)$$
$$\chi_{3234}(31,\cdot)$$ 3234.bk 30 no $$-1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{3234}(37,\cdot)$$ 3234.ce 105 no $$1$$ $$1$$ $$e\left(\frac{94}{105}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{89}{105}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{83}{105}\right)$$ $$e\left(\frac{4}{35}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{82}{105}\right)$$ $$e\left(\frac{1}{35}\right)$$
$$\chi_{3234}(41,\cdot)$$ 3234.cd 70 no $$-1$$ $$1$$ $$e\left(\frac{2}{35}\right)$$ $$e\left(\frac{3}{35}\right)$$ $$e\left(\frac{9}{70}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{4}{35}\right)$$ $$e\left(\frac{1}{35}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{35}\right)$$ $$e\left(\frac{53}{70}\right)$$
$$\chi_{3234}(43,\cdot)$$ 3234.bb 14 no $$-1$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$-1$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$1$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$
$$\chi_{3234}(47,\cdot)$$ 3234.cf 210 no $$1$$ $$1$$ $$e\left(\frac{16}{105}\right)$$ $$e\left(\frac{51}{70}\right)$$ $$e\left(\frac{71}{105}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{32}{105}\right)$$ $$e\left(\frac{17}{70}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{43}{105}\right)$$ $$e\left(\frac{24}{35}\right)$$
$$\chi_{3234}(53,\cdot)$$ 3234.cl 210 no $$-1$$ $$1$$ $$e\left(\frac{169}{210}\right)$$ $$e\left(\frac{16}{35}\right)$$ $$e\left(\frac{179}{210}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{64}{105}\right)$$ $$e\left(\frac{69}{70}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{86}{105}\right)$$ $$e\left(\frac{61}{70}\right)$$
$$\chi_{3234}(59,\cdot)$$ 3234.cf 210 no $$1$$ $$1$$ $$e\left(\frac{29}{105}\right)$$ $$e\left(\frac{29}{70}\right)$$ $$e\left(\frac{4}{105}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{58}{105}\right)$$ $$e\left(\frac{33}{70}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{32}{105}\right)$$ $$e\left(\frac{26}{35}\right)$$
$$\chi_{3234}(61,\cdot)$$ 3234.ck 210 no $$1$$ $$1$$ $$e\left(\frac{41}{210}\right)$$ $$e\left(\frac{19}{35}\right)$$ $$e\left(\frac{68}{105}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{41}{105}\right)$$ $$e\left(\frac{1}{70}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{19}{105}\right)$$ $$e\left(\frac{22}{35}\right)$$
$$\chi_{3234}(65,\cdot)$$ 3234.bt 42 no $$1$$ $$1$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{1}{7}\right)$$
$$\chi_{3234}(67,\cdot)$$ 3234.i 3 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$
$$\chi_{3234}(71,\cdot)$$ 3234.bz 70 no $$-1$$ $$1$$ $$e\left(\frac{47}{70}\right)$$ $$e\left(\frac{9}{35}\right)$$ $$e\left(\frac{27}{70}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{41}{70}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{35}\right)$$ $$e\left(\frac{19}{70}\right)$$
$$\chi_{3234}(73,\cdot)$$ 3234.ck 210 no $$1$$ $$1$$ $$e\left(\frac{73}{210}\right)$$ $$e\left(\frac{27}{35}\right)$$ $$e\left(\frac{34}{105}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{73}{105}\right)$$ $$e\left(\frac{53}{70}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{62}{105}\right)$$ $$e\left(\frac{11}{35}\right)$$
$$\chi_{3234}(79,\cdot)$$ 3234.bn 30 no $$-1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{3234}(83,\cdot)$$ 3234.cd 70 no $$-1$$ $$1$$ $$e\left(\frac{11}{35}\right)$$ $$e\left(\frac{34}{35}\right)$$ $$e\left(\frac{67}{70}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{22}{35}\right)$$ $$e\left(\frac{23}{35}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{23}{35}\right)$$ $$e\left(\frac{29}{70}\right)$$
$$\chi_{3234}(85,\cdot)$$ 3234.cb 70 no $$-1$$ $$1$$ $$e\left(\frac{17}{35}\right)$$ $$e\left(\frac{51}{70}\right)$$ $$e\left(\frac{59}{70}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{34}{35}\right)$$ $$e\left(\frac{17}{70}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{26}{35}\right)$$ $$e\left(\frac{13}{70}\right)$$
$$\chi_{3234}(89,\cdot)$$ 3234.bw 42 no $$1$$ $$1$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$
$$\chi_{3234}(95,\cdot)$$ 3234.ci 210 no $$1$$ $$1$$ $$e\left(\frac{103}{210}\right)$$ $$e\left(\frac{69}{70}\right)$$ $$e\left(\frac{94}{105}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{103}{105}\right)$$ $$e\left(\frac{29}{35}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{17}{105}\right)$$ $$e\left(\frac{16}{35}\right)$$
$$\chi_{3234}(97,\cdot)$$ 3234.y 10 no $$-1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{3234}(101,\cdot)$$ 3234.ch 210 no $$-1$$ $$1$$ $$e\left(\frac{62}{105}\right)$$ $$e\left(\frac{31}{35}\right)$$ $$e\left(\frac{209}{210}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{19}{105}\right)$$ $$e\left(\frac{22}{35}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{101}{105}\right)$$ $$e\left(\frac{11}{70}\right)$$
$$\chi_{3234}(103,\cdot)$$ 3234.cj 210 no $$-1$$ $$1$$ $$e\left(\frac{173}{210}\right)$$ $$e\left(\frac{69}{70}\right)$$ $$e\left(\frac{13}{210}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{68}{105}\right)$$ $$e\left(\frac{29}{35}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{52}{105}\right)$$ $$e\left(\frac{67}{70}\right)$$
$$\chi_{3234}(107,\cdot)$$ 3234.ci 210 no $$1$$ $$1$$ $$e\left(\frac{17}{210}\right)$$ $$e\left(\frac{61}{70}\right)$$ $$e\left(\frac{41}{105}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{17}{105}\right)$$ $$e\left(\frac{16}{35}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{13}{105}\right)$$ $$e\left(\frac{4}{35}\right)$$
$$\chi_{3234}(109,\cdot)$$ 3234.bv 42 no $$-1$$ $$1$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{11}{14}\right)$$
$$\chi_{3234}(113,\cdot)$$ 3234.bz 70 no $$-1$$ $$1$$ $$e\left(\frac{29}{70}\right)$$ $$e\left(\frac{13}{35}\right)$$ $$e\left(\frac{39}{70}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{29}{35}\right)$$ $$e\left(\frac{67}{70}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{16}{35}\right)$$ $$e\left(\frac{43}{70}\right)$$
$$\chi_{3234}(115,\cdot)$$ 3234.cj 210 no $$-1$$ $$1$$ $$e\left(\frac{181}{210}\right)$$ $$e\left(\frac{3}{70}\right)$$ $$e\left(\frac{101}{210}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{76}{105}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{89}{105}\right)$$ $$e\left(\frac{9}{70}\right)$$