# Properties

 Modulus $2850$ Structure $$C_{180}\times C_{2}\times C_{2}$$ Order $720$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(2850)

pari: g = idealstar(,2850,2)

## Character group

 sage: G.order()  pari: g.no Order = 720 sage: H.invariants()  pari: g.cyc Structure = $$C_{180}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2850}(1901,\cdot)$, $\chi_{2850}(1027,\cdot)$, $\chi_{2850}(1351,\cdot)$

## 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 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$
$$\chi_{2850}(1,\cdot)$$ 2850.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2850}(7,\cdot)$$ 2850.bg 12 no $$-1$$ $$1$$ $$i$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{2850}(11,\cdot)$$ 2850.bz 30 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2850}(13,\cdot)$$ 2850.cs 180 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{79}{180}\right)$$ $$e\left(\frac{23}{180}\right)$$ $$e\left(\frac{1}{180}\right)$$ $$e\left(\frac{28}{45}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{37}{90}\right)$$ $$e\left(\frac{25}{36}\right)$$
$$\chi_{2850}(17,\cdot)$$ 2850.cr 180 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{23}{180}\right)$$ $$e\left(\frac{91}{180}\right)$$ $$e\left(\frac{137}{180}\right)$$ $$e\left(\frac{11}{45}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{29}{90}\right)$$ $$e\left(\frac{23}{36}\right)$$
$$\chi_{2850}(23,\cdot)$$ 2850.cr 180 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{180}\right)$$ $$e\left(\frac{137}{180}\right)$$ $$e\left(\frac{139}{180}\right)$$ $$e\left(\frac{22}{45}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{13}{90}\right)$$ $$e\left(\frac{1}{36}\right)$$
$$\chi_{2850}(29,\cdot)$$ 2850.cm 90 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{28}{45}\right)$$ $$e\left(\frac{11}{45}\right)$$ $$e\left(\frac{22}{45}\right)$$ $$e\left(\frac{34}{45}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{8}{45}\right)$$ $$e\left(\frac{11}{18}\right)$$
$$\chi_{2850}(31,\cdot)$$ 2850.bx 30 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2850}(37,\cdot)$$ 2850.bp 20 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$-i$$
$$\chi_{2850}(41,\cdot)$$ 2850.cj 90 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{37}{90}\right)$$ $$e\left(\frac{29}{90}\right)$$ $$e\left(\frac{13}{90}\right)$$ $$e\left(\frac{8}{45}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{31}{45}\right)$$ $$e\left(\frac{5}{9}\right)$$
$$\chi_{2850}(43,\cdot)$$ 2850.ca 36 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{17}{36}\right)$$
$$\chi_{2850}(47,\cdot)$$ 2850.cr 180 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{67}{180}\right)$$ $$e\left(\frac{179}{180}\right)$$ $$e\left(\frac{133}{180}\right)$$ $$e\left(\frac{34}{45}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{61}{90}\right)$$ $$e\left(\frac{31}{36}\right)$$
$$\chi_{2850}(49,\cdot)$$ 2850.r 6 no $$1$$ $$1$$ $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2850}(53,\cdot)$$ 2850.cq 180 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{127}{180}\right)$$ $$e\left(\frac{29}{180}\right)$$ $$e\left(\frac{103}{180}\right)$$ $$e\left(\frac{53}{90}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{38}{45}\right)$$ $$e\left(\frac{1}{36}\right)$$
$$\chi_{2850}(59,\cdot)$$ 2850.cm 90 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{7}{45}\right)$$ $$e\left(\frac{14}{45}\right)$$ $$e\left(\frac{38}{45}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{45}\right)$$ $$e\left(\frac{7}{18}\right)$$
$$\chi_{2850}(61,\cdot)$$ 2850.ce 45 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{34}{45}\right)$$ $$e\left(\frac{23}{45}\right)$$ $$e\left(\frac{1}{45}\right)$$ $$e\left(\frac{22}{45}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{29}{45}\right)$$ $$e\left(\frac{7}{9}\right)$$
$$\chi_{2850}(67,\cdot)$$ 2850.cs 180 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{13}{180}\right)$$ $$e\left(\frac{161}{180}\right)$$ $$e\left(\frac{7}{180}\right)$$ $$e\left(\frac{16}{45}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{79}{90}\right)$$ $$e\left(\frac{31}{36}\right)$$
$$\chi_{2850}(71,\cdot)$$ 2850.cj 90 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{31}{90}\right)$$ $$e\left(\frac{17}{90}\right)$$ $$e\left(\frac{79}{90}\right)$$ $$e\left(\frac{14}{45}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{43}{45}\right)$$ $$e\left(\frac{2}{9}\right)$$
$$\chi_{2850}(73,\cdot)$$ 2850.ct 180 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{101}{180}\right)$$ $$e\left(\frac{67}{180}\right)$$ $$e\left(\frac{89}{180}\right)$$ $$e\left(\frac{79}{90}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{4}{45}\right)$$ $$e\left(\frac{29}{36}\right)$$
$$\chi_{2850}(77,\cdot)$$ 2850.br 20 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$-i$$
$$\chi_{2850}(79,\cdot)$$ 2850.co 90 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{23}{45}\right)$$ $$e\left(\frac{47}{90}\right)$$ $$e\left(\frac{49}{90}\right)$$ $$e\left(\frac{43}{90}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{71}{90}\right)$$ $$e\left(\frac{1}{18}\right)$$
$$\chi_{2850}(83,\cdot)$$ 2850.ci 60 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{2850}(89,\cdot)$$ 2850.cm 90 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{4}{45}\right)$$ $$e\left(\frac{8}{45}\right)$$ $$e\left(\frac{16}{45}\right)$$ $$e\left(\frac{37}{45}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{14}{45}\right)$$ $$e\left(\frac{17}{18}\right)$$
$$\chi_{2850}(91,\cdot)$$ 2850.cl 90 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{77}{90}\right)$$ $$e\left(\frac{32}{45}\right)$$ $$e\left(\frac{19}{45}\right)$$ $$e\left(\frac{71}{90}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{67}{90}\right)$$ $$e\left(\frac{7}{9}\right)$$
$$\chi_{2850}(97,\cdot)$$ 2850.cs 180 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{77}{180}\right)$$ $$e\left(\frac{109}{180}\right)$$ $$e\left(\frac{83}{180}\right)$$ $$e\left(\frac{29}{45}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{90}\right)$$ $$e\left(\frac{23}{36}\right)$$
$$\chi_{2850}(101,\cdot)$$ 2850.bj 18 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$
$$\chi_{2850}(103,\cdot)$$ 2850.cg 60 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{2850}(107,\cdot)$$ 2850.be 12 no $$-1$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{2850}(109,\cdot)$$ 2850.co 90 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{45}\right)$$ $$e\left(\frac{89}{90}\right)$$ $$e\left(\frac{43}{90}\right)$$ $$e\left(\frac{1}{90}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{77}{90}\right)$$ $$e\left(\frac{13}{18}\right)$$
$$\chi_{2850}(113,\cdot)$$ 2850.bs 20 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$i$$
$$\chi_{2850}(119,\cdot)$$ 2850.cn 90 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{49}{90}\right)$$ $$e\left(\frac{4}{45}\right)$$ $$e\left(\frac{8}{45}\right)$$ $$e\left(\frac{37}{90}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{59}{90}\right)$$ $$e\left(\frac{13}{18}\right)$$
$$\chi_{2850}(121,\cdot)$$ 2850.bh 15 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$