sage: H = DirichletGroup(1323)
pari: g = idealstar(,1323,2)
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 | = | $\chi_{1323}(785,\cdot)$, $\chi_{1323}(1081,\cdot)$ |
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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1323}(1,\cdot)\) | 1323.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{1323}(2,\cdot)\) | 1323.cg | 126 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{61}{126}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{1323}(4,\cdot)\) | 1323.cc | 63 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{1323}(5,\cdot)\) | 1323.ci | 126 | yes | \(1\) | \(1\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{1}{126}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(-1\) |
\(\chi_{1323}(8,\cdot)\) | 1323.bq | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(1\) |
\(\chi_{1323}(10,\cdot)\) | 1323.bx | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{1323}(11,\cdot)\) | 1323.cd | 126 | yes | \(-1\) | \(1\) | \(e\left(\frac{61}{126}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{61}{126}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(1\) |
\(\chi_{1323}(13,\cdot)\) | 1323.ck | 126 | yes | \(-1\) | \(1\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{1}{126}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{61}{126}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{1323}(16,\cdot)\) | 1323.cc | 63 | yes | \(1\) | \(1\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{1323}(17,\cdot)\) | 1323.bp | 42 | no | \(1\) | \(1\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{1323}(19,\cdot)\) | 1323.k | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{1323}(20,\cdot)\) | 1323.ce | 126 | yes | \(1\) | \(1\) | \(e\left(\frac{67}{126}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{25}{126}\right)\) | \(e\left(\frac{95}{126}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{1323}(22,\cdot)\) | 1323.cb | 63 | yes | \(1\) | \(1\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{1323}(23,\cdot)\) | 1323.cd | 126 | yes | \(-1\) | \(1\) | \(e\left(\frac{17}{126}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{37}{126}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{17}{126}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(1\) |
\(\chi_{1323}(25,\cdot)\) | 1323.ca | 63 | yes | \(1\) | \(1\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(1\) |
\(\chi_{1323}(26,\cdot)\) | 1323.bs | 42 | no | \(1\) | \(1\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{1323}(29,\cdot)\) | 1323.ch | 126 | yes | \(-1\) | \(1\) | \(e\left(\frac{25}{126}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{89}{126}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{109}{126}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{1323}(31,\cdot)\) | 1323.bd | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{1323}(32,\cdot)\) | 1323.cg | 126 | yes | \(-1\) | \(1\) | \(e\left(\frac{95}{126}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{53}{126}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{1323}(34,\cdot)\) | 1323.ck | 126 | yes | \(-1\) | \(1\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{83}{126}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{53}{63}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{1323}(37,\cdot)\) | 1323.bk | 21 | no | \(1\) | \(1\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{1323}(38,\cdot)\) | 1323.ci | 126 | yes | \(1\) | \(1\) | \(e\left(\frac{61}{126}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{61}{126}\right)\) | \(e\left(\frac{89}{126}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(-1\) |
\(\chi_{1323}(40,\cdot)\) | 1323.cl | 126 | yes | \(-1\) | \(1\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{13}{126}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{79}{126}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(-1\) |
\(\chi_{1323}(41,\cdot)\) | 1323.ce | 126 | yes | \(1\) | \(1\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{43}{126}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{1323}(43,\cdot)\) | 1323.cb | 63 | yes | \(1\) | \(1\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{1323}(44,\cdot)\) | 1323.by | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{1323}(46,\cdot)\) | 1323.bk | 21 | no | \(1\) | \(1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{1323}(47,\cdot)\) | 1323.cf | 126 | yes | \(1\) | \(1\) | \(e\left(\frac{61}{126}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{103}{126}\right)\) | \(e\left(\frac{5}{126}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{1323}(50,\cdot)\) | 1323.bf | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{1323}(52,\cdot)\) | 1323.cl | 126 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{59}{126}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(-1\) |
\(\chi_{1323}(53,\cdot)\) | 1323.br | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{1323}(55,\cdot)\) | 1323.y | 14 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(-1\) |