# Properties

 Modulus $1617$ Structure $$C_{2}\times C_{2}\times C_{210}$$ Order $840$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1617)

pari: g = idealstar(,1617,2)

## 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 = $\chi_{1617}(1079,\cdot)$, $\chi_{1617}(199,\cdot)$, $\chi_{1617}(442,\cdot)$

## 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$8$$ $$10$$ $$13$$ $$16$$ $$17$$ $$19$$ $$20$$
$$\chi_{1617}(1,\cdot)$$ 1617.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1617}(2,\cdot)$$ 1617.cg 210 yes $$1$$ $$1$$ $$e\left(\frac{73}{105}\right)$$ $$e\left(\frac{41}{105}\right)$$ $$e\left(\frac{179}{210}\right)$$ $$e\left(\frac{3}{35}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{37}{70}\right)$$ $$e\left(\frac{82}{105}\right)$$ $$e\left(\frac{92}{105}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{17}{70}\right)$$
$$\chi_{1617}(4,\cdot)$$ 1617.ce 105 no $$1$$ $$1$$ $$e\left(\frac{41}{105}\right)$$ $$e\left(\frac{82}{105}\right)$$ $$e\left(\frac{74}{105}\right)$$ $$e\left(\frac{6}{35}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{2}{35}\right)$$ $$e\left(\frac{59}{105}\right)$$ $$e\left(\frac{79}{105}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{17}{35}\right)$$
$$\chi_{1617}(5,\cdot)$$ 1617.ci 210 yes $$1$$ $$1$$ $$e\left(\frac{179}{210}\right)$$ $$e\left(\frac{74}{105}\right)$$ $$e\left(\frac{13}{105}\right)$$ $$e\left(\frac{39}{70}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{13}{70}\right)$$ $$e\left(\frac{43}{105}\right)$$ $$e\left(\frac{38}{105}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{29}{35}\right)$$
$$\chi_{1617}(8,\cdot)$$ 1617.cc 70 yes $$1$$ $$1$$ $$e\left(\frac{3}{35}\right)$$ $$e\left(\frac{6}{35}\right)$$ $$e\left(\frac{39}{70}\right)$$ $$e\left(\frac{9}{35}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{41}{70}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{22}{35}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{51}{70}\right)$$
$$\chi_{1617}(10,\cdot)$$ 1617.br 42 no $$1$$ $$1$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{14}\right)$$
$$\chi_{1617}(13,\cdot)$$ 1617.by 70 no $$1$$ $$1$$ $$e\left(\frac{37}{70}\right)$$ $$e\left(\frac{2}{35}\right)$$ $$e\left(\frac{13}{70}\right)$$ $$e\left(\frac{41}{70}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{35}\right)$$ $$e\left(\frac{4}{35}\right)$$ $$e\left(\frac{19}{35}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{17}{70}\right)$$
$$\chi_{1617}(16,\cdot)$$ 1617.ce 105 no $$1$$ $$1$$ $$e\left(\frac{82}{105}\right)$$ $$e\left(\frac{59}{105}\right)$$ $$e\left(\frac{43}{105}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{4}{35}\right)$$ $$e\left(\frac{13}{105}\right)$$ $$e\left(\frac{53}{105}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{34}{35}\right)$$
$$\chi_{1617}(17,\cdot)$$ 1617.cf 210 yes $$-1$$ $$1$$ $$e\left(\frac{92}{105}\right)$$ $$e\left(\frac{79}{105}\right)$$ $$e\left(\frac{38}{105}\right)$$ $$e\left(\frac{22}{35}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{19}{35}\right)$$ $$e\left(\frac{53}{105}\right)$$ $$e\left(\frac{101}{210}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{4}{35}\right)$$
$$\chi_{1617}(19,\cdot)$$ 1617.bj 30 no $$1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{1617}(20,\cdot)$$ 1617.ca 70 yes $$1$$ $$1$$ $$e\left(\frac{17}{70}\right)$$ $$e\left(\frac{17}{35}\right)$$ $$e\left(\frac{29}{35}\right)$$ $$e\left(\frac{51}{70}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{17}{70}\right)$$ $$e\left(\frac{34}{35}\right)$$ $$e\left(\frac{4}{35}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{35}\right)$$
$$\chi_{1617}(23,\cdot)$$ 1617.bq 42 no $$-1$$ $$1$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{14}\right)$$
$$\chi_{1617}(25,\cdot)$$ 1617.ce 105 no $$1$$ $$1$$ $$e\left(\frac{74}{105}\right)$$ $$e\left(\frac{43}{105}\right)$$ $$e\left(\frac{26}{105}\right)$$ $$e\left(\frac{4}{35}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{13}{35}\right)$$ $$e\left(\frac{86}{105}\right)$$ $$e\left(\frac{76}{105}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{23}{35}\right)$$
$$\chi_{1617}(26,\cdot)$$ 1617.ci 210 yes $$1$$ $$1$$ $$e\left(\frac{47}{210}\right)$$ $$e\left(\frac{47}{105}\right)$$ $$e\left(\frac{4}{105}\right)$$ $$e\left(\frac{47}{70}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{39}{70}\right)$$ $$e\left(\frac{94}{105}\right)$$ $$e\left(\frac{44}{105}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{17}{35}\right)$$
$$\chi_{1617}(29,\cdot)$$ 1617.cc 70 yes $$1$$ $$1$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{24}{35}\right)$$ $$e\left(\frac{51}{70}\right)$$ $$e\left(\frac{1}{35}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{59}{70}\right)$$ $$e\left(\frac{13}{35}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{29}{70}\right)$$
$$\chi_{1617}(31,\cdot)$$ 1617.bm 30 no $$-1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{1617}(32,\cdot)$$ 1617.bv 42 yes $$1$$ $$1$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{3}{14}\right)$$
$$\chi_{1617}(34,\cdot)$$ 1617.bb 14 no $$-1$$ $$1$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$-1$$ $$e\left(\frac{5}{14}\right)$$
$$\chi_{1617}(37,\cdot)$$ 1617.ce 105 no $$1$$ $$1$$ $$e\left(\frac{1}{105}\right)$$ $$e\left(\frac{2}{105}\right)$$ $$e\left(\frac{94}{105}\right)$$ $$e\left(\frac{1}{35}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{4}{105}\right)$$ $$e\left(\frac{89}{105}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{32}{35}\right)$$
$$\chi_{1617}(38,\cdot)$$ 1617.ci 210 yes $$1$$ $$1$$ $$e\left(\frac{139}{210}\right)$$ $$e\left(\frac{34}{105}\right)$$ $$e\left(\frac{23}{105}\right)$$ $$e\left(\frac{69}{70}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{23}{70}\right)$$ $$e\left(\frac{68}{105}\right)$$ $$e\left(\frac{43}{105}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{19}{35}\right)$$
$$\chi_{1617}(40,\cdot)$$ 1617.ck 210 no $$1$$ $$1$$ $$e\left(\frac{197}{210}\right)$$ $$e\left(\frac{92}{105}\right)$$ $$e\left(\frac{143}{210}\right)$$ $$e\left(\frac{57}{70}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{27}{35}\right)$$ $$e\left(\frac{79}{105}\right)$$ $$e\left(\frac{104}{105}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{39}{70}\right)$$
$$\chi_{1617}(41,\cdot)$$ 1617.cd 70 yes $$-1$$ $$1$$ $$e\left(\frac{3}{35}\right)$$ $$e\left(\frac{6}{35}\right)$$ $$e\left(\frac{2}{35}\right)$$ $$e\left(\frac{9}{35}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{35}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{9}{70}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{8}{35}\right)$$
$$\chi_{1617}(43,\cdot)$$ 1617.bd 14 no $$-1$$ $$1$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$-1$$ $$e\left(\frac{4}{7}\right)$$
$$\chi_{1617}(46,\cdot)$$ 1617.cj 210 no $$-1$$ $$1$$ $$e\left(\frac{151}{210}\right)$$ $$e\left(\frac{46}{105}\right)$$ $$e\left(\frac{62}{105}\right)$$ $$e\left(\frac{11}{70}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{27}{70}\right)$$ $$e\left(\frac{92}{105}\right)$$ $$e\left(\frac{209}{210}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{35}\right)$$
$$\chi_{1617}(47,\cdot)$$ 1617.ci 210 yes $$1$$ $$1$$ $$e\left(\frac{83}{210}\right)$$ $$e\left(\frac{83}{105}\right)$$ $$e\left(\frac{16}{105}\right)$$ $$e\left(\frac{13}{70}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{51}{70}\right)$$ $$e\left(\frac{61}{105}\right)$$ $$e\left(\frac{71}{105}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{33}{35}\right)$$
$$\chi_{1617}(50,\cdot)$$ 1617.t 10 no $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$-1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{1617}(52,\cdot)$$ 1617.ck 210 no $$1$$ $$1$$ $$e\left(\frac{193}{210}\right)$$ $$e\left(\frac{88}{105}\right)$$ $$e\left(\frac{187}{210}\right)$$ $$e\left(\frac{53}{70}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{3}{35}\right)$$ $$e\left(\frac{71}{105}\right)$$ $$e\left(\frac{31}{105}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{51}{70}\right)$$
$$\chi_{1617}(53,\cdot)$$ 1617.cl 210 yes $$-1$$ $$1$$ $$e\left(\frac{61}{210}\right)$$ $$e\left(\frac{61}{105}\right)$$ $$e\left(\frac{169}{210}\right)$$ $$e\left(\frac{61}{70}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{16}{35}\right)$$ $$e\left(\frac{17}{105}\right)$$ $$e\left(\frac{179}{210}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{27}{70}\right)$$
$$\chi_{1617}(58,\cdot)$$ 1617.ce 105 no $$1$$ $$1$$ $$e\left(\frac{4}{105}\right)$$ $$e\left(\frac{8}{105}\right)$$ $$e\left(\frac{61}{105}\right)$$ $$e\left(\frac{4}{35}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{13}{35}\right)$$ $$e\left(\frac{16}{105}\right)$$ $$e\left(\frac{41}{105}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{23}{35}\right)$$
$$\chi_{1617}(59,\cdot)$$ 1617.ci 210 yes $$1$$ $$1$$ $$e\left(\frac{157}{210}\right)$$ $$e\left(\frac{52}{105}\right)$$ $$e\left(\frac{29}{105}\right)$$ $$e\left(\frac{17}{70}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{29}{70}\right)$$ $$e\left(\frac{104}{105}\right)$$ $$e\left(\frac{4}{105}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{27}{35}\right)$$
$$\chi_{1617}(61,\cdot)$$ 1617.ck 210 no $$1$$ $$1$$ $$e\left(\frac{149}{210}\right)$$ $$e\left(\frac{44}{105}\right)$$ $$e\left(\frac{41}{210}\right)$$ $$e\left(\frac{9}{70}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{19}{35}\right)$$ $$e\left(\frac{88}{105}\right)$$ $$e\left(\frac{68}{105}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{43}{70}\right)$$
$$\chi_{1617}(62,\cdot)$$ 1617.cd 70 yes $$-1$$ $$1$$ $$e\left(\frac{22}{35}\right)$$ $$e\left(\frac{9}{35}\right)$$ $$e\left(\frac{3}{35}\right)$$ $$e\left(\frac{31}{35}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{22}{35}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{31}{70}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{12}{35}\right)$$