sage: H = DirichletGroup(889)
pari: g = idealstar(,889,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 756 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{6}\times C_{126}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{889}(255,\cdot)$, $\chi_{889}(638,\cdot)$ |
First 32 of 756 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{889}(1,\cdot)\) | 889.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{889}(2,\cdot)\) | 889.bm | 21 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) |
\(\chi_{889}(3,\cdot)\) | 889.cj | 126 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) |
\(\chi_{889}(4,\cdot)\) | 889.bm | 21 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) |
\(\chi_{889}(5,\cdot)\) | 889.bx | 42 | yes | \(1\) | \(1\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) |
\(\chi_{889}(6,\cdot)\) | 889.cf | 126 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{32}{63}\right)\) |
\(\chi_{889}(8,\cdot)\) | 889.u | 7 | no | \(1\) | \(1\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) |
\(\chi_{889}(9,\cdot)\) | 889.cc | 63 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{61}{63}\right)\) |
\(\chi_{889}(10,\cdot)\) | 889.br | 42 | yes | \(1\) | \(1\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) |
\(\chi_{889}(11,\cdot)\) | 889.cb | 63 | yes | \(1\) | \(1\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{37}{63}\right)\) |
\(\chi_{889}(12,\cdot)\) | 889.cg | 126 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{2}{63}\right)\) |
\(\chi_{889}(13,\cdot)\) | 889.ce | 126 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{31}{126}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{121}{126}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{85}{126}\right)\) |
\(\chi_{889}(15,\cdot)\) | 889.ca | 63 | no | \(1\) | \(1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{17}{63}\right)\) |
\(\chi_{889}(16,\cdot)\) | 889.bm | 21 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) |
\(\chi_{889}(17,\cdot)\) | 889.cl | 126 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{59}{126}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{65}{126}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{71}{126}\right)\) |
\(\chi_{889}(18,\cdot)\) | 889.cb | 63 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) |
\(\chi_{889}(19,\cdot)\) | 889.j | 6 | yes | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{889}(20,\cdot)\) | 889.r | 6 | yes | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{889}(22,\cdot)\) | 889.x | 9 | no | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(1\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) |
\(\chi_{889}(23,\cdot)\) | 889.ck | 126 | yes | \(-1\) | \(1\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{37}{126}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{13}{126}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{115}{126}\right)\) |
\(\chi_{889}(24,\cdot)\) | 889.bd | 18 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(1\) | \(e\left(\frac{7}{9}\right)\) | \(1\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) |
\(\chi_{889}(25,\cdot)\) | 889.bn | 21 | yes | \(1\) | \(1\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) |
\(\chi_{889}(26,\cdot)\) | 889.cl | 126 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{85}{126}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{25}{126}\right)\) |
\(\chi_{889}(27,\cdot)\) | 889.bq | 42 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) |
\(\chi_{889}(29,\cdot)\) | 889.cd | 126 | no | \(-1\) | \(1\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{113}{126}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{59}{126}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{5}{126}\right)\) |
\(\chi_{889}(30,\cdot)\) | 889.cb | 63 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{50}{63}\right)\) |
\(\chi_{889}(31,\cdot)\) | 889.ch | 126 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{67}{126}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{97}{126}\right)\) |
\(\chi_{889}(32,\cdot)\) | 889.bm | 21 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) |
\(\chi_{889}(33,\cdot)\) | 889.bx | 42 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) |
\(\chi_{889}(34,\cdot)\) | 889.ce | 126 | yes | \(-1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{47}{126}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{11}{126}\right)\) |
\(\chi_{889}(36,\cdot)\) | 889.ca | 63 | no | \(1\) | \(1\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{1}{63}\right)\) |
\(\chi_{889}(37,\cdot)\) | 889.v | 9 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(1\) | \(e\left(\frac{2}{9}\right)\) | \(1\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) |