# Properties

 Modulus $2925$ Structure $$C_{2}\times C_{12}\times C_{60}$$ Order $1440$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2925)

pari: g = idealstar(,2925,2)

## Character group

 sage: G.order()  pari: g.no Order = 1440 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{12}\times C_{60}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2925}(326,\cdot)$, $\chi_{2925}(352,\cdot)$, $\chi_{2925}(2251,\cdot)$

## First 32 of 1440 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$7$$ $$8$$ $$11$$ $$14$$ $$16$$ $$17$$ $$19$$ $$22$$
$$\chi_{2925}(1,\cdot)$$ 2925.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2925}(2,\cdot)$$ 2925.hr 60 yes $$-1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{2925}(4,\cdot)$$ 2925.eu 30 yes $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{2925}(7,\cdot)$$ 2925.eb 12 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{2925}(8,\cdot)$$ 2925.es 20 no $$-1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{2925}(11,\cdot)$$ 2925.hf 60 yes $$1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{2925}(14,\cdot)$$ 2925.fn 30 no $$-1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$
$$\chi_{2925}(16,\cdot)$$ 2925.ee 15 yes $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{2925}(17,\cdot)$$ 2925.gw 60 no $$1$$ $$1$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{23}{60}\right)$$
$$\chi_{2925}(19,\cdot)$$ 2925.gl 60 no $$-1$$ $$1$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{2925}(22,\cdot)$$ 2925.hc 60 yes $$-1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{2925}(23,\cdot)$$ 2925.ha 60 yes $$1$$ $$1$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$i$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{41}{60}\right)$$
$$\chi_{2925}(28,\cdot)$$ 2925.ga 60 no $$1$$ $$1$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{37}{60}\right)$$
$$\chi_{2925}(29,\cdot)$$ 2925.ew 30 yes $$-1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{2925}(31,\cdot)$$ 2925.gt 60 yes $$-1$$ $$1$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{2925}(32,\cdot)$$ 2925.cj 12 no $$-1$$ $$1$$ $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$
$$\chi_{2925}(34,\cdot)$$ 2925.gq 60 yes $$-1$$ $$1$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{2925}(37,\cdot)$$ 2925.ga 60 no $$1$$ $$1$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{19}{60}\right)$$
$$\chi_{2925}(38,\cdot)$$ 2925.gz 60 yes $$1$$ $$1$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{29}{60}\right)$$
$$\chi_{2925}(41,\cdot)$$ 2925.go 60 yes $$1$$ $$1$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$i$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{2925}(43,\cdot)$$ 2925.dt 12 no $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{2925}(44,\cdot)$$ 2925.ep 20 no $$1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$-i$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{2925}(46,\cdot)$$ 2925.gk 60 no $$-1$$ $$1$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{2925}(47,\cdot)$$ 2925.hm 60 yes $$-1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{47}{60}\right)$$
$$\chi_{2925}(49,\cdot)$$ 2925.bl 6 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2925}(53,\cdot)$$ 2925.eq 20 no $$1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$-i$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{2925}(56,\cdot)$$ 2925.fk 30 yes $$-1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$-1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{2925}(58,\cdot)$$ 2925.hq 60 yes $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{2925}(59,\cdot)$$ 2925.he 60 yes $$1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{2925}(61,\cdot)$$ 2925.eh 15 yes $$1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{2925}(62,\cdot)$$ 2925.gw 60 no $$1$$ $$1$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$
$$\chi_{2925}(64,\cdot)$$ 2925.cd 10 no $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$