# Properties

 Modulus $1575$ Structure $$C_{2}\times C_{6}\times C_{60}$$ Order $720$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1575)

pari: g = idealstar(,1575,2)

## Character group

 sage: G.order()  pari: g.no Order = 720 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{6}\times C_{60}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1575}(1226,\cdot)$, $\chi_{1575}(127,\cdot)$, $\chi_{1575}(451,\cdot)$

## 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$8$$ $$11$$ $$13$$ $$16$$ $$17$$ $$19$$ $$22$$ $$23$$
$$\chi_{1575}(1,\cdot)$$ 1575.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1575}(2,\cdot)$$ 1575.ek 60 yes $$1$$ $$1$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{1575}(4,\cdot)$$ 1575.db 30 yes $$1$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{1575}(8,\cdot)$$ 1575.cx 20 no $$1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{1575}(11,\cdot)$$ 1575.dx 30 yes $$-1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{1575}(13,\cdot)$$ 1575.eg 60 yes $$1$$ $$1$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$
$$\chi_{1575}(16,\cdot)$$ 1575.cr 15 yes $$1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{1575}(17,\cdot)$$ 1575.ee 60 no $$-1$$ $$1$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{59}{60}\right)$$
$$\chi_{1575}(19,\cdot)$$ 1575.dh 30 no $$-1$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$
$$\chi_{1575}(22,\cdot)$$ 1575.ej 60 no $$-1$$ $$1$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{1}{60}\right)$$
$$\chi_{1575}(23,\cdot)$$ 1575.em 60 yes $$1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{53}{60}\right)$$
$$\chi_{1575}(26,\cdot)$$ 1575.bk 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1575}(29,\cdot)$$ 1575.dp 30 no $$-1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{1575}(31,\cdot)$$ 1575.dn 30 yes $$-1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{1575}(32,\cdot)$$ 1575.cf 12 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$i$$
$$\chi_{1575}(34,\cdot)$$ 1575.dj 30 yes $$-1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{1575}(37,\cdot)$$ 1575.eh 60 no $$-1$$ $$1$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{37}{60}\right)$$
$$\chi_{1575}(38,\cdot)$$ 1575.en 60 yes $$-1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{37}{60}\right)$$
$$\chi_{1575}(41,\cdot)$$ 1575.de 30 yes $$1$$ $$1$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{1575}(43,\cdot)$$ 1575.cg 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-i$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{1575}(44,\cdot)$$ 1575.dr 30 no $$-1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{1575}(46,\cdot)$$ 1575.cs 15 no $$1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{1575}(47,\cdot)$$ 1575.el 60 yes $$-1$$ $$1$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{1575}(52,\cdot)$$ 1575.ep 60 yes $$1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$
$$\chi_{1575}(53,\cdot)$$ 1575.ed 60 no $$1$$ $$1$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{41}{60}\right)$$
$$\chi_{1575}(58,\cdot)$$ 1575.eo 60 yes $$-1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{59}{60}\right)$$
$$\chi_{1575}(59,\cdot)$$ 1575.dv 30 yes $$1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{1575}(61,\cdot)$$ 1575.dn 30 yes $$-1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{1575}(62,\cdot)$$ 1575.cw 20 no $$-1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{1575}(64,\cdot)$$ 1575.bx 10 no $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{1575}(67,\cdot)$$ 1575.ea 60 yes $$-1$$ $$1$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{1575}(68,\cdot)$$ 1575.cc 12 no $$-1$$ $$1$$ $$i$$ $$-1$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$