Properties

 Modulus $483$ Structure $$C_{2}\times C_{2}\times C_{66}$$ Order $264$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(483)

pari: g = idealstar(,483,2)

Character group

 sage: G.order()  pari: g.no Order = 264 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{66}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{483}(323,\cdot)$, $\chi_{483}(346,\cdot)$, $\chi_{483}(442,\cdot)$

First 32 of 264 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$8$$ $$10$$ $$11$$ $$13$$ $$16$$ $$17$$ $$19$$
$$\chi_{483}(1,\cdot)$$ 483.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{483}(2,\cdot)$$ 483.z 66 yes $$-1$$ $$1$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$
$$\chi_{483}(4,\cdot)$$ 483.y 33 no $$1$$ $$1$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$
$$\chi_{483}(5,\cdot)$$ 483.ba 66 yes $$-1$$ $$1$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$
$$\chi_{483}(8,\cdot)$$ 483.x 22 no $$-1$$ $$1$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{483}(10,\cdot)$$ 483.bf 66 no $$1$$ $$1$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$
$$\chi_{483}(11,\cdot)$$ 483.bc 66 yes $$1$$ $$1$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$
$$\chi_{483}(13,\cdot)$$ 483.s 22 no $$-1$$ $$1$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{483}(16,\cdot)$$ 483.y 33 no $$1$$ $$1$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$
$$\chi_{483}(17,\cdot)$$ 483.ba 66 yes $$-1$$ $$1$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{20}{33}\right)$$
$$\chi_{483}(19,\cdot)$$ 483.bf 66 no $$1$$ $$1$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$
$$\chi_{483}(20,\cdot)$$ 483.w 22 yes $$-1$$ $$1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{483}(22,\cdot)$$ 483.f 2 no $$-1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$
$$\chi_{483}(25,\cdot)$$ 483.y 33 no $$1$$ $$1$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$
$$\chi_{483}(26,\cdot)$$ 483.bb 66 yes $$1$$ $$1$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{5}{66}\right)$$
$$\chi_{483}(29,\cdot)$$ 483.x 22 no $$-1$$ $$1$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{483}(31,\cdot)$$ 483.be 66 no $$-1$$ $$1$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{61}{66}\right)$$
$$\chi_{483}(32,\cdot)$$ 483.z 66 yes $$-1$$ $$1$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{5}{33}\right)$$
$$\chi_{483}(34,\cdot)$$ 483.r 22 no $$1$$ $$1$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{483}(37,\cdot)$$ 483.bd 66 no $$-1$$ $$1$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{65}{66}\right)$$
$$\chi_{483}(38,\cdot)$$ 483.ba 66 yes $$-1$$ $$1$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{14}{33}\right)$$
$$\chi_{483}(40,\cdot)$$ 483.bf 66 no $$1$$ $$1$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$
$$\chi_{483}(41,\cdot)$$ 483.v 22 yes $$1$$ $$1$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{483}(43,\cdot)$$ 483.t 22 no $$-1$$ $$1$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$
$$\chi_{483}(44,\cdot)$$ 483.bc 66 yes $$1$$ $$1$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{35}{66}\right)$$
$$\chi_{483}(47,\cdot)$$ 483.n 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{483}(50,\cdot)$$ 483.x 22 no $$-1$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{483}(52,\cdot)$$ 483.be 66 no $$-1$$ $$1$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{7}{66}\right)$$
$$\chi_{483}(53,\cdot)$$ 483.bc 66 yes $$1$$ $$1$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{19}{66}\right)$$
$$\chi_{483}(55,\cdot)$$ 483.s 22 no $$-1$$ $$1$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$
$$\chi_{483}(58,\cdot)$$ 483.y 33 no $$1$$ $$1$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$
$$\chi_{483}(59,\cdot)$$ 483.bb 66 yes $$1$$ $$1$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{25}{66}\right)$$