# Properties

 Modulus $1050$ Structure $$C_{2}\times C_{2}\times C_{60}$$ Order $240$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1050)

pari: g = idealstar(,1050,2)

## Character group

 sage: G.order()  pari: g.no Order = 240 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{60}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1050}(701,\cdot)$, $\chi_{1050}(127,\cdot)$, $\chi_{1050}(451,\cdot)$

## First 32 of 240 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 $$-1$$ $$1$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$
$$\chi_{1050}(1,\cdot)$$ 1050.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1050}(11,\cdot)$$ 1050.bm 30 no $$-1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$1$$
$$\chi_{1050}(13,\cdot)$$ 1050.bh 20 no $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$i$$
$$\chi_{1050}(17,\cdot)$$ 1050.bt 60 no $$-1$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-i$$
$$\chi_{1050}(19,\cdot)$$ 1050.bp 30 no $$-1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$-1$$
$$\chi_{1050}(23,\cdot)$$ 1050.bs 60 no $$1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$i$$
$$\chi_{1050}(29,\cdot)$$ 1050.ba 10 no $$-1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-1$$
$$\chi_{1050}(31,\cdot)$$ 1050.bq 30 no $$-1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$1$$
$$\chi_{1050}(37,\cdot)$$ 1050.bu 60 no $$-1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-i$$
$$\chi_{1050}(41,\cdot)$$ 1050.bb 10 no $$1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$1$$
$$\chi_{1050}(43,\cdot)$$ 1050.l 4 no $$-1$$ $$1$$ $$1$$ $$i$$ $$-i$$ $$-1$$ $$i$$ $$-1$$ $$1$$ $$-i$$ $$1$$ $$i$$
$$\chi_{1050}(47,\cdot)$$ 1050.bt 60 no $$-1$$ $$1$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$-i$$
$$\chi_{1050}(53,\cdot)$$ 1050.bs 60 no $$1$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$i$$
$$\chi_{1050}(59,\cdot)$$ 1050.bl 30 no $$1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-1$$
$$\chi_{1050}(61,\cdot)$$ 1050.bq 30 no $$-1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$1$$
$$\chi_{1050}(67,\cdot)$$ 1050.bu 60 no $$-1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-i$$
$$\chi_{1050}(71,\cdot)$$ 1050.y 10 no $$-1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$1$$
$$\chi_{1050}(73,\cdot)$$ 1050.bv 60 no $$1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$i$$
$$\chi_{1050}(79,\cdot)$$ 1050.br 30 no $$1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$-1$$
$$\chi_{1050}(83,\cdot)$$ 1050.bj 20 no $$-1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$i$$
$$\chi_{1050}(89,\cdot)$$ 1050.bl 30 no $$1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$-1$$
$$\chi_{1050}(97,\cdot)$$ 1050.bh 20 no $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-i$$
$$\chi_{1050}(101,\cdot)$$ 1050.s 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$
$$\chi_{1050}(103,\cdot)$$ 1050.bv 60 no $$1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$i$$
$$\chi_{1050}(107,\cdot)$$ 1050.bf 12 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$-i$$
$$\chi_{1050}(109,\cdot)$$ 1050.br 30 no $$1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-1$$
$$\chi_{1050}(113,\cdot)$$ 1050.bk 20 no $$1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$i$$
$$\chi_{1050}(121,\cdot)$$ 1050.bg 15 no $$1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$1$$
$$\chi_{1050}(127,\cdot)$$ 1050.bi 20 no $$-1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$-i$$
$$\chi_{1050}(131,\cdot)$$ 1050.bn 30 no $$1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$1$$
$$\chi_{1050}(137,\cdot)$$ 1050.bs 60 no $$1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$-i$$
$$\chi_{1050}(139,\cdot)$$ 1050.v 10 no $$-1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$-1$$