# Properties

 Modulus $1900$ Structure $$C_{2}\times C_{2}\times C_{180}$$ Order $720$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1900)

pari: g = idealstar(,1900,2)

## Character group

 sage: G.order()  pari: g.no Order = 720 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{180}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1900}(951,\cdot)$, $\chi_{1900}(77,\cdot)$, $\chi_{1900}(401,\cdot)$

## First 32 of 720 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 $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$21$$ $$23$$ $$27$$ $$29$$
$$\chi_{1900}(1,\cdot)$$ 1900.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1900}(3,\cdot)$$ 1900.cr 180 yes $$-1$$ $$1$$ $$e\left(\frac{61}{180}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{61}{90}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{47}{180}\right)$$ $$e\left(\frac{139}{180}\right)$$ $$e\left(\frac{83}{90}\right)$$ $$e\left(\frac{143}{180}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{44}{45}\right)$$
$$\chi_{1900}(7,\cdot)$$ 1900.bd 12 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1900}(9,\cdot)$$ 1900.co 90 no $$1$$ $$1$$ $$e\left(\frac{61}{90}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{16}{45}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{47}{90}\right)$$ $$e\left(\frac{49}{90}\right)$$ $$e\left(\frac{38}{45}\right)$$ $$e\left(\frac{53}{90}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{43}{45}\right)$$
$$\chi_{1900}(11,\cdot)$$ 1900.bu 30 yes $$-1$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$-1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{1900}(13,\cdot)$$ 1900.cs 180 no $$1$$ $$1$$ $$e\left(\frac{47}{180}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{47}{90}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{79}{180}\right)$$ $$e\left(\frac{23}{180}\right)$$ $$e\left(\frac{61}{90}\right)$$ $$e\left(\frac{1}{180}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{28}{45}\right)$$
$$\chi_{1900}(17,\cdot)$$ 1900.ct 180 no $$-1$$ $$1$$ $$e\left(\frac{139}{180}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{49}{90}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{23}{180}\right)$$ $$e\left(\frac{1}{180}\right)$$ $$e\left(\frac{16}{45}\right)$$ $$e\left(\frac{47}{180}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{67}{90}\right)$$
$$\chi_{1900}(21,\cdot)$$ 1900.cl 90 no $$-1$$ $$1$$ $$e\left(\frac{83}{90}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{38}{45}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{61}{90}\right)$$ $$e\left(\frac{16}{45}\right)$$ $$e\left(\frac{23}{90}\right)$$ $$e\left(\frac{32}{45}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{13}{90}\right)$$
$$\chi_{1900}(23,\cdot)$$ 1900.cq 180 yes $$1$$ $$1$$ $$e\left(\frac{143}{180}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{53}{90}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{180}\right)$$ $$e\left(\frac{47}{180}\right)$$ $$e\left(\frac{32}{45}\right)$$ $$e\left(\frac{139}{180}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{89}{90}\right)$$
$$\chi_{1900}(27,\cdot)$$ 1900.ch 60 yes $$-1$$ $$1$$ $$e\left(\frac{1}{60}\right)$$ $$-i$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{1900}(29,\cdot)$$ 1900.cp 90 no $$-1$$ $$1$$ $$e\left(\frac{44}{45}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{43}{45}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{28}{45}\right)$$ $$e\left(\frac{67}{90}\right)$$ $$e\left(\frac{13}{90}\right)$$ $$e\left(\frac{89}{90}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{23}{90}\right)$$
$$\chi_{1900}(31,\cdot)$$ 1900.by 30 yes $$1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$-1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{1900}(33,\cdot)$$ 1900.cs 180 no $$1$$ $$1$$ $$e\left(\frac{19}{180}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{19}{90}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{143}{180}\right)$$ $$e\left(\frac{151}{180}\right)$$ $$e\left(\frac{17}{90}\right)$$ $$e\left(\frac{77}{180}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{41}{45}\right)$$
$$\chi_{1900}(37,\cdot)$$ 1900.bq 20 no $$1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{1900}(39,\cdot)$$ 1900.y 10 no $$-1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{1900}(41,\cdot)$$ 1900.cl 90 no $$-1$$ $$1$$ $$e\left(\frac{71}{90}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{37}{90}\right)$$ $$e\left(\frac{37}{45}\right)$$ $$e\left(\frac{11}{90}\right)$$ $$e\left(\frac{29}{45}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{61}{90}\right)$$
$$\chi_{1900}(43,\cdot)$$ 1900.cd 36 no $$1$$ $$1$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{18}\right)$$
$$\chi_{1900}(47,\cdot)$$ 1900.cq 180 yes $$1$$ $$1$$ $$e\left(\frac{41}{180}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{41}{90}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{67}{180}\right)$$ $$e\left(\frac{89}{180}\right)$$ $$e\left(\frac{29}{45}\right)$$ $$e\left(\frac{133}{180}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{23}{90}\right)$$
$$\chi_{1900}(49,\cdot)$$ 1900.s 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1900}(51,\cdot)$$ 1900.bn 18 no $$1$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{18}\right)$$
$$\chi_{1900}(53,\cdot)$$ 1900.cs 180 no $$1$$ $$1$$ $$e\left(\frac{71}{180}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{71}{90}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{127}{180}\right)$$ $$e\left(\frac{119}{180}\right)$$ $$e\left(\frac{73}{90}\right)$$ $$e\left(\frac{13}{180}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{4}{45}\right)$$
$$\chi_{1900}(59,\cdot)$$ 1900.cj 90 yes $$1$$ $$1$$ $$e\left(\frac{11}{90}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{45}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{59}{90}\right)$$ $$e\left(\frac{41}{90}\right)$$ $$e\left(\frac{14}{45}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{31}{90}\right)$$
$$\chi_{1900}(61,\cdot)$$ 1900.ce 45 no $$1$$ $$1$$ $$e\left(\frac{2}{45}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{4}{45}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{34}{45}\right)$$ $$e\left(\frac{23}{45}\right)$$ $$e\left(\frac{32}{45}\right)$$ $$e\left(\frac{1}{45}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{22}{45}\right)$$
$$\chi_{1900}(63,\cdot)$$ 1900.cq 180 yes $$1$$ $$1$$ $$e\left(\frac{47}{180}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{47}{90}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{169}{180}\right)$$ $$e\left(\frac{23}{180}\right)$$ $$e\left(\frac{8}{45}\right)$$ $$e\left(\frac{91}{180}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{11}{90}\right)$$
$$\chi_{1900}(67,\cdot)$$ 1900.cr 180 yes $$-1$$ $$1$$ $$e\left(\frac{59}{180}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{59}{90}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{13}{180}\right)$$ $$e\left(\frac{161}{180}\right)$$ $$e\left(\frac{67}{90}\right)$$ $$e\left(\frac{97}{180}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{16}{45}\right)$$
$$\chi_{1900}(69,\cdot)$$ 1900.bx 30 no $$-1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$-1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{1900}(71,\cdot)$$ 1900.cn 90 yes $$1$$ $$1$$ $$e\left(\frac{34}{45}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{23}{45}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{31}{90}\right)$$ $$e\left(\frac{31}{45}\right)$$ $$e\left(\frac{53}{90}\right)$$ $$e\left(\frac{79}{90}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{73}{90}\right)$$
$$\chi_{1900}(73,\cdot)$$ 1900.ct 180 no $$-1$$ $$1$$ $$e\left(\frac{133}{180}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{43}{90}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{101}{180}\right)$$ $$e\left(\frac{67}{180}\right)$$ $$e\left(\frac{37}{45}\right)$$ $$e\left(\frac{89}{180}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{79}{90}\right)$$
$$\chi_{1900}(77,\cdot)$$ 1900.bp 20 no $$-1$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$i$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{1900}(79,\cdot)$$ 1900.cj 90 yes $$1$$ $$1$$ $$e\left(\frac{53}{90}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{8}{45}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{23}{45}\right)$$ $$e\left(\frac{47}{90}\right)$$ $$e\left(\frac{83}{90}\right)$$ $$e\left(\frac{2}{45}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{43}{90}\right)$$
$$\chi_{1900}(81,\cdot)$$ 1900.ce 45 no $$1$$ $$1$$ $$e\left(\frac{16}{45}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{32}{45}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{45}\right)$$ $$e\left(\frac{4}{45}\right)$$ $$e\left(\frac{31}{45}\right)$$ $$e\left(\frac{8}{45}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{41}{45}\right)$$
$$\chi_{1900}(83,\cdot)$$ 1900.ci 60 yes $$1$$ $$1$$ $$e\left(\frac{53}{60}\right)$$ $$i$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{29}{30}\right)$$