sage: H = DirichletGroup(1134)
pari: g = idealstar(,1134,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 324 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{6}\times C_{54}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{1134}(407,\cdot)$, $\chi_{1134}(325,\cdot)$ |
First 32 of 324 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 | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1134}(1,\cdot)\) | 1134.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{1134}(5,\cdot)\) | 1134.bk | 54 | no | \(1\) | \(1\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{49}{54}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{41}{54}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{5}{9}\right)\) |
\(\chi_{1134}(11,\cdot)\) | 1134.bj | 54 | no | \(-1\) | \(1\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{49}{54}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{4}{9}\right)\) |
\(\chi_{1134}(13,\cdot)\) | 1134.bm | 54 | no | \(-1\) | \(1\) | \(e\left(\frac{49}{54}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{37}{54}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{2}{9}\right)\) |
\(\chi_{1134}(17,\cdot)\) | 1134.ba | 18 | no | \(1\) | \(1\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(1\) |
\(\chi_{1134}(19,\cdot)\) | 1134.be | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(1\) |
\(\chi_{1134}(23,\cdot)\) | 1134.bj | 54 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{49}{54}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{29}{54}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{2}{9}\right)\) |
\(\chi_{1134}(25,\cdot)\) | 1134.bi | 27 | no | \(1\) | \(1\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{1}{9}\right)\) |
\(\chi_{1134}(29,\cdot)\) | 1134.bo | 54 | no | \(-1\) | \(1\) | \(e\left(\frac{41}{54}\right)\) | \(e\left(\frac{49}{54}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{29}{54}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{7}{9}\right)\) |
\(\chi_{1134}(31,\cdot)\) | 1134.bl | 54 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{8}{9}\right)\) |
\(\chi_{1134}(37,\cdot)\) | 1134.w | 9 | no | \(1\) | \(1\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{1134}(41,\cdot)\) | 1134.bq | 54 | no | \(1\) | \(1\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{41}{54}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{17}{54}\right)\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{2}{9}\right)\) |
\(\chi_{1134}(43,\cdot)\) | 1134.bh | 27 | no | \(1\) | \(1\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{1}{9}\right)\) |
\(\chi_{1134}(47,\cdot)\) | 1134.bp | 54 | no | \(1\) | \(1\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{1}{54}\right)\) | \(e\left(\frac{29}{54}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{1}{9}\right)\) |
\(\chi_{1134}(53,\cdot)\) | 1134.i | 6 | no | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{1134}(55,\cdot)\) | 1134.o | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
\(\chi_{1134}(59,\cdot)\) | 1134.bp | 54 | no | \(1\) | \(1\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{29}{54}\right)\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{37}{54}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{2}{9}\right)\) |
\(\chi_{1134}(61,\cdot)\) | 1134.bl | 54 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{54}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{1}{9}\right)\) |
\(\chi_{1134}(65,\cdot)\) | 1134.bn | 54 | no | \(-1\) | \(1\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{13}{54}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{7}{9}\right)\) |
\(\chi_{1134}(67,\cdot)\) | 1134.bg | 27 | no | \(1\) | \(1\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{5}{9}\right)\) |
\(\chi_{1134}(71,\cdot)\) | 1134.bb | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{1134}(73,\cdot)\) | 1134.x | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(-1\) | \(-1\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{1134}(79,\cdot)\) | 1134.bg | 27 | no | \(1\) | \(1\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{4}{9}\right)\) |
\(\chi_{1134}(83,\cdot)\) | 1134.bq | 54 | no | \(1\) | \(1\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{13}{54}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{37}{54}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{7}{9}\right)\) |
\(\chi_{1134}(85,\cdot)\) | 1134.bh | 27 | no | \(1\) | \(1\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{5}{9}\right)\) |
\(\chi_{1134}(89,\cdot)\) | 1134.ba | 18 | no | \(1\) | \(1\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(1\) |
\(\chi_{1134}(95,\cdot)\) | 1134.bn | 54 | no | \(-1\) | \(1\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{41}{54}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{5}{9}\right)\) |
\(\chi_{1134}(97,\cdot)\) | 1134.bm | 54 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{1}{9}\right)\) |
\(\chi_{1134}(101,\cdot)\) | 1134.bk | 54 | no | \(1\) | \(1\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{37}{54}\right)\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{7}{9}\right)\) |
\(\chi_{1134}(103,\cdot)\) | 1134.br | 54 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{1}{54}\right)\) | \(e\left(\frac{5}{9}\right)\) |
\(\chi_{1134}(107,\cdot)\) | 1134.i | 6 | no | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{1134}(109,\cdot)\) | 1134.h | 3 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |