sage: H = DirichletGroup(3969)
pari: g = idealstar(,3969,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 2268 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{6}\times C_{378}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{3969}(2108,\cdot)$, $\chi_{3969}(3727,\cdot)$ |
First 32 of 2268 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{3969}(1,\cdot)\) | 3969.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{3969}(2,\cdot)\) | 3969.dd | 378 | yes | \(-1\) | \(1\) | \(e\left(\frac{43}{378}\right)\) | \(e\left(\frac{43}{189}\right)\) | \(e\left(\frac{143}{378}\right)\) | \(e\left(\frac{43}{126}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{1}{378}\right)\) | \(e\left(\frac{109}{189}\right)\) | \(e\left(\frac{86}{189}\right)\) | \(e\left(\frac{11}{126}\right)\) | \(e\left(\frac{5}{9}\right)\) |
\(\chi_{3969}(4,\cdot)\) | 3969.cz | 189 | yes | \(1\) | \(1\) | \(e\left(\frac{43}{189}\right)\) | \(e\left(\frac{86}{189}\right)\) | \(e\left(\frac{143}{189}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{1}{189}\right)\) | \(e\left(\frac{29}{189}\right)\) | \(e\left(\frac{172}{189}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{1}{9}\right)\) |
\(\chi_{3969}(5,\cdot)\) | 3969.db | 378 | yes | \(1\) | \(1\) | \(e\left(\frac{143}{378}\right)\) | \(e\left(\frac{143}{189}\right)\) | \(e\left(\frac{155}{189}\right)\) | \(e\left(\frac{17}{126}\right)\) | \(e\left(\frac{25}{126}\right)\) | \(e\left(\frac{59}{378}\right)\) | \(e\left(\frac{73}{378}\right)\) | \(e\left(\frac{97}{189}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{11}{18}\right)\) |
\(\chi_{3969}(8,\cdot)\) | 3969.ct | 126 | no | \(-1\) | \(1\) | \(e\left(\frac{43}{126}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{17}{126}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{1}{126}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{3969}(10,\cdot)\) | 3969.cv | 126 | no | \(-1\) | \(1\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{25}{126}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{97}{126}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{3969}(11,\cdot)\) | 3969.dj | 378 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{378}\right)\) | \(e\left(\frac{1}{189}\right)\) | \(e\left(\frac{59}{378}\right)\) | \(e\left(\frac{1}{126}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{85}{378}\right)\) | \(e\left(\frac{67}{189}\right)\) | \(e\left(\frac{2}{189}\right)\) | \(e\left(\frac{95}{126}\right)\) | \(e\left(\frac{8}{9}\right)\) |
\(\chi_{3969}(13,\cdot)\) | 3969.de | 378 | yes | \(-1\) | \(1\) | \(e\left(\frac{109}{189}\right)\) | \(e\left(\frac{29}{189}\right)\) | \(e\left(\frac{73}{378}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{97}{126}\right)\) | \(e\left(\frac{67}{189}\right)\) | \(e\left(\frac{43}{378}\right)\) | \(e\left(\frac{58}{189}\right)\) | \(e\left(\frac{67}{126}\right)\) | \(e\left(\frac{11}{18}\right)\) |
\(\chi_{3969}(16,\cdot)\) | 3969.cz | 189 | yes | \(1\) | \(1\) | \(e\left(\frac{86}{189}\right)\) | \(e\left(\frac{172}{189}\right)\) | \(e\left(\frac{97}{189}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{2}{189}\right)\) | \(e\left(\frac{58}{189}\right)\) | \(e\left(\frac{155}{189}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{2}{9}\right)\) |
\(\chi_{3969}(17,\cdot)\) | 3969.cr | 126 | no | \(1\) | \(1\) | \(e\left(\frac{11}{126}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{95}{126}\right)\) | \(e\left(\frac{67}{126}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{3969}(19,\cdot)\) | 3969.bd | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{3969}(20,\cdot)\) | 3969.dh | 378 | yes | \(1\) | \(1\) | \(e\left(\frac{229}{378}\right)\) | \(e\left(\frac{40}{189}\right)\) | \(e\left(\frac{109}{189}\right)\) | \(e\left(\frac{103}{126}\right)\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{61}{378}\right)\) | \(e\left(\frac{131}{378}\right)\) | \(e\left(\frac{80}{189}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{13}{18}\right)\) |
\(\chi_{3969}(22,\cdot)\) | 3969.da | 189 | yes | \(1\) | \(1\) | \(e\left(\frac{22}{189}\right)\) | \(e\left(\frac{44}{189}\right)\) | \(e\left(\frac{101}{189}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{43}{189}\right)\) | \(e\left(\frac{176}{189}\right)\) | \(e\left(\frac{88}{189}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{4}{9}\right)\) |
\(\chi_{3969}(23,\cdot)\) | 3969.dj | 378 | yes | \(-1\) | \(1\) | \(e\left(\frac{275}{378}\right)\) | \(e\left(\frac{86}{189}\right)\) | \(e\left(\frac{349}{378}\right)\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{317}{378}\right)\) | \(e\left(\frac{92}{189}\right)\) | \(e\left(\frac{172}{189}\right)\) | \(e\left(\frac{43}{126}\right)\) | \(e\left(\frac{4}{9}\right)\) |
\(\chi_{3969}(25,\cdot)\) | 3969.cy | 189 | yes | \(1\) | \(1\) | \(e\left(\frac{143}{189}\right)\) | \(e\left(\frac{97}{189}\right)\) | \(e\left(\frac{121}{189}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{59}{189}\right)\) | \(e\left(\frac{73}{189}\right)\) | \(e\left(\frac{5}{189}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{2}{9}\right)\) |
\(\chi_{3969}(26,\cdot)\) | 3969.bs | 42 | no | \(1\) | \(1\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{3969}(29,\cdot)\) | 3969.dc | 378 | yes | \(-1\) | \(1\) | \(e\left(\frac{313}{378}\right)\) | \(e\left(\frac{124}{189}\right)\) | \(e\left(\frac{71}{378}\right)\) | \(e\left(\frac{61}{126}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{19}{378}\right)\) | \(e\left(\frac{118}{189}\right)\) | \(e\left(\frac{59}{189}\right)\) | \(e\left(\frac{41}{126}\right)\) | \(e\left(\frac{8}{9}\right)\) |
\(\chi_{3969}(31,\cdot)\) | 3969.ci | 54 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) |
\(\chi_{3969}(32,\cdot)\) | 3969.dd | 378 | yes | \(-1\) | \(1\) | \(e\left(\frac{215}{378}\right)\) | \(e\left(\frac{26}{189}\right)\) | \(e\left(\frac{337}{378}\right)\) | \(e\left(\frac{89}{126}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{5}{378}\right)\) | \(e\left(\frac{167}{189}\right)\) | \(e\left(\frac{52}{189}\right)\) | \(e\left(\frac{55}{126}\right)\) | \(e\left(\frac{7}{9}\right)\) |
\(\chi_{3969}(34,\cdot)\) | 3969.de | 378 | yes | \(-1\) | \(1\) | \(e\left(\frac{38}{189}\right)\) | \(e\left(\frac{76}{189}\right)\) | \(e\left(\frac{263}{378}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{113}{126}\right)\) | \(e\left(\frac{143}{189}\right)\) | \(e\left(\frac{41}{378}\right)\) | \(e\left(\frac{152}{189}\right)\) | \(e\left(\frac{17}{126}\right)\) | \(e\left(\frac{13}{18}\right)\) |
\(\chi_{3969}(37,\cdot)\) | 3969.cm | 63 | no | \(1\) | \(1\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(1\) |
\(\chi_{3969}(38,\cdot)\) | 3969.db | 378 | yes | \(1\) | \(1\) | \(e\left(\frac{253}{378}\right)\) | \(e\left(\frac{64}{189}\right)\) | \(e\left(\frac{187}{189}\right)\) | \(e\left(\frac{1}{126}\right)\) | \(e\left(\frac{83}{126}\right)\) | \(e\left(\frac{337}{378}\right)\) | \(e\left(\frac{71}{378}\right)\) | \(e\left(\frac{128}{189}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{7}{18}\right)\) |
\(\chi_{3969}(40,\cdot)\) | 3969.di | 378 | yes | \(-1\) | \(1\) | \(e\left(\frac{136}{189}\right)\) | \(e\left(\frac{83}{189}\right)\) | \(e\left(\frac{361}{378}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{85}{126}\right)\) | \(e\left(\frac{31}{189}\right)\) | \(e\left(\frac{349}{378}\right)\) | \(e\left(\frac{166}{189}\right)\) | \(e\left(\frac{73}{126}\right)\) | \(e\left(\frac{5}{18}\right)\) |
\(\chi_{3969}(41,\cdot)\) | 3969.dh | 378 | yes | \(1\) | \(1\) | \(e\left(\frac{101}{378}\right)\) | \(e\left(\frac{101}{189}\right)\) | \(e\left(\frac{176}{189}\right)\) | \(e\left(\frac{101}{126}\right)\) | \(e\left(\frac{25}{126}\right)\) | \(e\left(\frac{17}{378}\right)\) | \(e\left(\frac{241}{378}\right)\) | \(e\left(\frac{13}{189}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{11}{18}\right)\) |
\(\chi_{3969}(43,\cdot)\) | 3969.da | 189 | yes | \(1\) | \(1\) | \(e\left(\frac{23}{189}\right)\) | \(e\left(\frac{46}{189}\right)\) | \(e\left(\frac{97}{189}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{2}{189}\right)\) | \(e\left(\frac{184}{189}\right)\) | \(e\left(\frac{92}{189}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{5}{9}\right)\) |
\(\chi_{3969}(44,\cdot)\) | 3969.cp | 126 | no | \(-1\) | \(1\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{115}{126}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(1\) |
\(\chi_{3969}(46,\cdot)\) | 3969.cm | 63 | no | \(1\) | \(1\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(1\) |
\(\chi_{3969}(47,\cdot)\) | 3969.dg | 378 | yes | \(1\) | \(1\) | \(e\left(\frac{85}{378}\right)\) | \(e\left(\frac{85}{189}\right)\) | \(e\left(\frac{82}{189}\right)\) | \(e\left(\frac{85}{126}\right)\) | \(e\left(\frac{83}{126}\right)\) | \(e\left(\frac{169}{378}\right)\) | \(e\left(\frac{365}{378}\right)\) | \(e\left(\frac{170}{189}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{7}{18}\right)\) |
\(\chi_{3969}(50,\cdot)\) | 3969.cj | 54 | no | \(-1\) | \(1\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{1}{54}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{17}{54}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) |
\(\chi_{3969}(52,\cdot)\) | 3969.di | 378 | yes | \(-1\) | \(1\) | \(e\left(\frac{152}{189}\right)\) | \(e\left(\frac{115}{189}\right)\) | \(e\left(\frac{359}{378}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{95}{126}\right)\) | \(e\left(\frac{68}{189}\right)\) | \(e\left(\frac{101}{378}\right)\) | \(e\left(\frac{41}{189}\right)\) | \(e\left(\frac{89}{126}\right)\) | \(e\left(\frac{13}{18}\right)\) |
\(\chi_{3969}(53,\cdot)\) | 3969.bx | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{3969}(55,\cdot)\) | 3969.bz | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(-1\) |