Properties

 Modulus $6825$ Structure $$C_{2}\times C_{2}\times C_{12}\times C_{60}$$ Order $2880$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6825)

pari: g = idealstar(,6825,2)

Character group

 sage: G.order()  pari: g.no Order = 2880 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{12}\times C_{60}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{6825}(2276,\cdot)$, $\chi_{6825}(3277,\cdot)$, $\chi_{6825}(976,\cdot)$, $\chi_{6825}(4201,\cdot)$

First 32 of 2880 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$8$$ $$11$$ $$16$$ $$17$$ $$19$$ $$22$$ $$23$$ $$29$$
$$\chi_{6825}(1,\cdot)$$ 6825.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{6825}(2,\cdot)$$ 6825.pj 60 yes $$-1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{6825}(4,\cdot)$$ 6825.jn 30 no $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{6825}(8,\cdot)$$ 6825.jg 20 no $$-1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{6825}(11,\cdot)$$ 6825.np 60 yes $$1$$ $$1$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$
$$\chi_{6825}(16,\cdot)$$ 6825.ii 15 no $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{6825}(17,\cdot)$$ 6825.or 60 yes $$-1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{6825}(19,\cdot)$$ 6825.my 60 no $$1$$ $$1$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{6825}(22,\cdot)$$ 6825.nt 60 no $$-1$$ $$1$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{6825}(23,\cdot)$$ 6825.ot 60 yes $$1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{6825}(29,\cdot)$$ 6825.kx 30 no $$-1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{6825}(31,\cdot)$$ 6825.ng 60 no $$1$$ $$1$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{6825}(32,\cdot)$$ 6825.eq 12 no $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{6825}(34,\cdot)$$ 6825.ja 20 no $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{6825}(37,\cdot)$$ 6825.ph 60 no $$1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{6825}(38,\cdot)$$ 6825.ns 60 yes $$-1$$ $$1$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{6825}(41,\cdot)$$ 6825.nd 60 yes $$-1$$ $$1$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{6825}(43,\cdot)$$ 6825.hi 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{6825}(44,\cdot)$$ 6825.ne 60 yes $$1$$ $$1$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{6825}(46,\cdot)$$ 6825.op 60 no $$-1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{6825}(47,\cdot)$$ 6825.ov 60 yes $$1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{6825}(53,\cdot)$$ 6825.mm 60 no $$1$$ $$1$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{6825}(58,\cdot)$$ 6825.ma 60 no $$1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{6825}(59,\cdot)$$ 6825.oj 60 yes $$-1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$
$$\chi_{6825}(61,\cdot)$$ 6825.kq 30 no $$-1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{6825}(62,\cdot)$$ 6825.nu 60 yes $$-1$$ $$1$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{6825}(64,\cdot)$$ 6825.eh 10 no $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{6825}(67,\cdot)$$ 6825.ox 60 no $$1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{6825}(68,\cdot)$$ 6825.fs 12 no $$-1$$ $$1$$ $$i$$ $$-1$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{6825}(71,\cdot)$$ 6825.no 60 no $$1$$ $$1$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{6825}(73,\cdot)$$ 6825.pf 60 no $$-1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{6825}(74,\cdot)$$ 6825.ea 6 no $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$