# Properties

 Modulus $2475$ Structure $$C_{2}\times C_{10}\times C_{60}$$ Order $1200$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2475)

pari: g = idealstar(,2475,2)

## Character group

 sage: G.order()  pari: g.no Order = 1200 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{10}\times C_{60}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2475}(551,\cdot)$, $\chi_{2475}(2377,\cdot)$, $\chi_{2475}(2026,\cdot)$

## First 32 of 1200 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$7$$ $$8$$ $$13$$ $$14$$ $$16$$ $$17$$ $$19$$ $$23$$
$$\chi_{2475}(1,\cdot)$$ 2475.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2475}(2,\cdot)$$ 2475.fz 60 yes $$-1$$ $$1$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{23}{60}\right)$$
$$\chi_{2475}(4,\cdot)$$ 2475.ef 30 yes $$1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$
$$\chi_{2475}(7,\cdot)$$ 2475.fs 60 no $$1$$ $$1$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{2475}(8,\cdot)$$ 2475.dj 20 no $$-1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{2475}(13,\cdot)$$ 2475.gg 60 yes $$1$$ $$1$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$i$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{60}\right)$$
$$\chi_{2475}(14,\cdot)$$ 2475.fc 30 yes $$-1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{2475}(16,\cdot)$$ 2475.cz 15 yes $$1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{2475}(17,\cdot)$$ 2475.di 20 no $$-1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$i$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$
$$\chi_{2475}(19,\cdot)$$ 2475.bh 10 no $$-1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{2475}(23,\cdot)$$ 2475.gc 60 no $$1$$ $$1$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{13}{60}\right)$$
$$\chi_{2475}(26,\cdot)$$ 2475.bx 10 no $$-1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-1$$
$$\chi_{2475}(28,\cdot)$$ 2475.dd 20 no $$1$$ $$1$$ $$i$$ $$-1$$ $$e\left(\frac{1}{20}\right)$$ $$-i$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$1$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{2475}(29,\cdot)$$ 2475.eq 30 yes $$1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{2475}(31,\cdot)$$ 2475.cu 15 yes $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$1$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{2475}(32,\cdot)$$ 2475.cr 12 no $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$1$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{2475}(34,\cdot)$$ 2475.et 30 no $$1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{2475}(37,\cdot)$$ 2475.dt 20 no $$-1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$-i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{2475}(38,\cdot)$$ 2475.gd 60 yes $$1$$ $$1$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{60}\right)$$
$$\chi_{2475}(41,\cdot)$$ 2475.dy 30 yes $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-1$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{2475}(43,\cdot)$$ 2475.ct 12 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$1$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{2475}(46,\cdot)$$ 2475.ce 10 no $$-1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$-1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{2475}(47,\cdot)$$ 2475.fp 60 yes $$1$$ $$1$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$-i$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{11}{60}\right)$$
$$\chi_{2475}(49,\cdot)$$ 2475.eg 30 no $$1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2475}(52,\cdot)$$ 2475.fr 60 yes $$1$$ $$1$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{53}{60}\right)$$
$$\chi_{2475}(53,\cdot)$$ 2475.dm 20 no $$1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$i$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$
$$\chi_{2475}(56,\cdot)$$ 2475.eb 30 no $$-1$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{2475}(58,\cdot)$$ 2475.fu 60 yes $$-1$$ $$1$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{60}\right)$$
$$\chi_{2475}(59,\cdot)$$ 2475.fc 30 yes $$-1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{2475}(61,\cdot)$$ 2475.ee 30 yes $$-1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$-1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{2475}(62,\cdot)$$ 2475.di 20 no $$-1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$i$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{2475}(64,\cdot)$$ 2475.cg 10 no $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$
Click here to search among the remaining 1168 characters.