sage: H = DirichletGroup(199)
pari: g = idealstar(,199,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 198 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{198}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{199}(3,\cdot)$ |
First 32 of 198 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{199}(1,\cdot)\) | 199.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{199}(2,\cdot)\) | 199.k | 99 | yes | \(1\) | \(1\) | \(e\left(\frac{74}{99}\right)\) | \(e\left(\frac{53}{99}\right)\) | \(e\left(\frac{49}{99}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{28}{99}\right)\) | \(e\left(\frac{2}{99}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{7}{99}\right)\) | \(e\left(\frac{62}{99}\right)\) | \(e\left(\frac{2}{11}\right)\) |
\(\chi_{199}(3,\cdot)\) | 199.l | 198 | yes | \(-1\) | \(1\) | \(e\left(\frac{53}{99}\right)\) | \(e\left(\frac{1}{198}\right)\) | \(e\left(\frac{7}{99}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{107}{198}\right)\) | \(e\left(\frac{71}{99}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{1}{99}\right)\) | \(e\left(\frac{23}{99}\right)\) | \(e\left(\frac{21}{22}\right)\) |
\(\chi_{199}(4,\cdot)\) | 199.k | 99 | yes | \(1\) | \(1\) | \(e\left(\frac{49}{99}\right)\) | \(e\left(\frac{7}{99}\right)\) | \(e\left(\frac{98}{99}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{56}{99}\right)\) | \(e\left(\frac{4}{99}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{14}{99}\right)\) | \(e\left(\frac{25}{99}\right)\) | \(e\left(\frac{4}{11}\right)\) |
\(\chi_{199}(5,\cdot)\) | 199.i | 33 | yes | \(1\) | \(1\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{8}{11}\right)\) |
\(\chi_{199}(6,\cdot)\) | 199.l | 198 | yes | \(-1\) | \(1\) | \(e\left(\frac{28}{99}\right)\) | \(e\left(\frac{107}{198}\right)\) | \(e\left(\frac{56}{99}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{163}{198}\right)\) | \(e\left(\frac{73}{99}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{8}{99}\right)\) | \(e\left(\frac{85}{99}\right)\) | \(e\left(\frac{3}{22}\right)\) |
\(\chi_{199}(7,\cdot)\) | 199.k | 99 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{99}\right)\) | \(e\left(\frac{71}{99}\right)\) | \(e\left(\frac{4}{99}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{73}{99}\right)\) | \(e\left(\frac{83}{99}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{43}{99}\right)\) | \(e\left(\frac{98}{99}\right)\) | \(e\left(\frac{6}{11}\right)\) |
\(\chi_{199}(8,\cdot)\) | 199.i | 33 | yes | \(1\) | \(1\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{6}{11}\right)\) |
\(\chi_{199}(9,\cdot)\) | 199.k | 99 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{99}\right)\) | \(e\left(\frac{1}{99}\right)\) | \(e\left(\frac{14}{99}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{8}{99}\right)\) | \(e\left(\frac{43}{99}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{2}{99}\right)\) | \(e\left(\frac{46}{99}\right)\) | \(e\left(\frac{10}{11}\right)\) |
\(\chi_{199}(10,\cdot)\) | 199.k | 99 | yes | \(1\) | \(1\) | \(e\left(\frac{62}{99}\right)\) | \(e\left(\frac{23}{99}\right)\) | \(e\left(\frac{25}{99}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{85}{99}\right)\) | \(e\left(\frac{98}{99}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{46}{99}\right)\) | \(e\left(\frac{68}{99}\right)\) | \(e\left(\frac{10}{11}\right)\) |
\(\chi_{199}(11,\cdot)\) | 199.h | 22 | yes | \(-1\) | \(1\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) |
\(\chi_{199}(12,\cdot)\) | 199.j | 66 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{5}{66}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{7}{22}\right)\) |
\(\chi_{199}(13,\cdot)\) | 199.k | 99 | yes | \(1\) | \(1\) | \(e\left(\frac{8}{99}\right)\) | \(e\left(\frac{86}{99}\right)\) | \(e\left(\frac{16}{99}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{94}{99}\right)\) | \(e\left(\frac{35}{99}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{73}{99}\right)\) | \(e\left(\frac{95}{99}\right)\) | \(e\left(\frac{2}{11}\right)\) |
\(\chi_{199}(14,\cdot)\) | 199.k | 99 | yes | \(1\) | \(1\) | \(e\left(\frac{76}{99}\right)\) | \(e\left(\frac{25}{99}\right)\) | \(e\left(\frac{53}{99}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{2}{99}\right)\) | \(e\left(\frac{85}{99}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{50}{99}\right)\) | \(e\left(\frac{61}{99}\right)\) | \(e\left(\frac{8}{11}\right)\) |
\(\chi_{199}(15,\cdot)\) | 199.l | 198 | yes | \(-1\) | \(1\) | \(e\left(\frac{41}{99}\right)\) | \(e\left(\frac{139}{198}\right)\) | \(e\left(\frac{82}{99}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{23}{198}\right)\) | \(e\left(\frac{68}{99}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{40}{99}\right)\) | \(e\left(\frac{29}{99}\right)\) | \(e\left(\frac{15}{22}\right)\) |
\(\chi_{199}(16,\cdot)\) | 199.k | 99 | yes | \(1\) | \(1\) | \(e\left(\frac{98}{99}\right)\) | \(e\left(\frac{14}{99}\right)\) | \(e\left(\frac{97}{99}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{13}{99}\right)\) | \(e\left(\frac{8}{99}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{28}{99}\right)\) | \(e\left(\frac{50}{99}\right)\) | \(e\left(\frac{8}{11}\right)\) |
\(\chi_{199}(17,\cdot)\) | 199.j | 66 | yes | \(-1\) | \(1\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{9}{22}\right)\) |
\(\chi_{199}(18,\cdot)\) | 199.f | 11 | yes | \(1\) | \(1\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) |
\(\chi_{199}(19,\cdot)\) | 199.g | 18 | yes | \(-1\) | \(1\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(-1\) |
\(\chi_{199}(20,\cdot)\) | 199.k | 99 | yes | \(1\) | \(1\) | \(e\left(\frac{37}{99}\right)\) | \(e\left(\frac{76}{99}\right)\) | \(e\left(\frac{74}{99}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{14}{99}\right)\) | \(e\left(\frac{1}{99}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{53}{99}\right)\) | \(e\left(\frac{31}{99}\right)\) | \(e\left(\frac{1}{11}\right)\) |
\(\chi_{199}(21,\cdot)\) | 199.g | 18 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(-1\) |
\(\chi_{199}(22,\cdot)\) | 199.l | 198 | yes | \(-1\) | \(1\) | \(e\left(\frac{92}{99}\right)\) | \(e\left(\frac{97}{198}\right)\) | \(e\left(\frac{85}{99}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{83}{198}\right)\) | \(e\left(\frac{56}{99}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{97}{99}\right)\) | \(e\left(\frac{53}{99}\right)\) | \(e\left(\frac{13}{22}\right)\) |
\(\chi_{199}(23,\cdot)\) | 199.k | 99 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{99}\right)\) | \(e\left(\frac{59}{99}\right)\) | \(e\left(\frac{34}{99}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{76}{99}\right)\) | \(e\left(\frac{62}{99}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{19}{99}\right)\) | \(e\left(\frac{41}{99}\right)\) | \(e\left(\frac{7}{11}\right)\) |
\(\chi_{199}(24,\cdot)\) | 199.g | 18 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(-1\) |
\(\chi_{199}(25,\cdot)\) | 199.i | 33 | yes | \(1\) | \(1\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{5}{11}\right)\) |
\(\chi_{199}(26,\cdot)\) | 199.k | 99 | yes | \(1\) | \(1\) | \(e\left(\frac{82}{99}\right)\) | \(e\left(\frac{40}{99}\right)\) | \(e\left(\frac{65}{99}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{23}{99}\right)\) | \(e\left(\frac{37}{99}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{80}{99}\right)\) | \(e\left(\frac{58}{99}\right)\) | \(e\left(\frac{4}{11}\right)\) |
\(\chi_{199}(27,\cdot)\) | 199.j | 66 | yes | \(-1\) | \(1\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{19}{22}\right)\) |
\(\chi_{199}(28,\cdot)\) | 199.i | 33 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{10}{11}\right)\) |
\(\chi_{199}(29,\cdot)\) | 199.k | 99 | yes | \(1\) | \(1\) | \(e\left(\frac{47}{99}\right)\) | \(e\left(\frac{35}{99}\right)\) | \(e\left(\frac{94}{99}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{82}{99}\right)\) | \(e\left(\frac{20}{99}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{70}{99}\right)\) | \(e\left(\frac{26}{99}\right)\) | \(e\left(\frac{9}{11}\right)\) |
\(\chi_{199}(30,\cdot)\) | 199.l | 198 | yes | \(-1\) | \(1\) | \(e\left(\frac{16}{99}\right)\) | \(e\left(\frac{47}{198}\right)\) | \(e\left(\frac{32}{99}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{79}{198}\right)\) | \(e\left(\frac{70}{99}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{47}{99}\right)\) | \(e\left(\frac{91}{99}\right)\) | \(e\left(\frac{19}{22}\right)\) |
\(\chi_{199}(31,\cdot)\) | 199.k | 99 | yes | \(1\) | \(1\) | \(e\left(\frac{79}{99}\right)\) | \(e\left(\frac{82}{99}\right)\) | \(e\left(\frac{59}{99}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{62}{99}\right)\) | \(e\left(\frac{61}{99}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{65}{99}\right)\) | \(e\left(\frac{10}{99}\right)\) | \(e\left(\frac{6}{11}\right)\) |
\(\chi_{199}(32,\cdot)\) | 199.k | 99 | yes | \(1\) | \(1\) | \(e\left(\frac{73}{99}\right)\) | \(e\left(\frac{67}{99}\right)\) | \(e\left(\frac{47}{99}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{41}{99}\right)\) | \(e\left(\frac{10}{99}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{35}{99}\right)\) | \(e\left(\frac{13}{99}\right)\) | \(e\left(\frac{10}{11}\right)\) |