sage: H = DirichletGroup(4536)
pari: g = idealstar(,4536,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 1296 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{6}\times C_{54}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{4536}(1135,\cdot)$, $\chi_{4536}(2269,\cdot)$, $\chi_{4536}(3809,\cdot)$, $\chi_{4536}(2593,\cdot)$ |
First 32 of 1296 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 | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{4536}(1,\cdot)\) | 4536.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{4536}(5,\cdot)\) | 4536.gs | 54 | yes | \(1\) | \(1\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{1}{18}\right)\) |
\(\chi_{4536}(11,\cdot)\) | 4536.gq | 54 | yes | \(1\) | \(1\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{17}{18}\right)\) |
\(\chi_{4536}(13,\cdot)\) | 4536.gl | 54 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{13}{18}\right)\) |
\(\chi_{4536}(17,\cdot)\) | 4536.ea | 18 | no | \(1\) | \(1\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(1\) |
\(\chi_{4536}(19,\cdot)\) | 4536.ek | 18 | no | \(1\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(-1\) |
\(\chi_{4536}(23,\cdot)\) | 4536.fi | 54 | no | \(1\) | \(1\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{29}{54}\right)\) | \(e\left(\frac{49}{54}\right)\) | \(e\left(\frac{2}{9}\right)\) |
\(\chi_{4536}(25,\cdot)\) | 4536.fa | 27 | no | \(1\) | \(1\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{1}{9}\right)\) |
\(\chi_{4536}(29,\cdot)\) | 4536.fj | 54 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{29}{54}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{5}{18}\right)\) |
\(\chi_{4536}(31,\cdot)\) | 4536.fm | 54 | no | \(1\) | \(1\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{49}{54}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{8}{9}\right)\) |
\(\chi_{4536}(37,\cdot)\) | 4536.eu | 18 | no | \(1\) | \(1\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{4536}(41,\cdot)\) | 4536.gk | 54 | no | \(1\) | \(1\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{41}{54}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{17}{54}\right)\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{2}{9}\right)\) |
\(\chi_{4536}(43,\cdot)\) | 4536.gi | 54 | no | \(-1\) | \(1\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{41}{54}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{11}{18}\right)\) |
\(\chi_{4536}(47,\cdot)\) | 4536.fy | 54 | no | \(-1\) | \(1\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{29}{54}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{1}{9}\right)\) |
\(\chi_{4536}(53,\cdot)\) | 4536.db | 6 | no | \(-1\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{4536}(55,\cdot)\) | 4536.cp | 6 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
\(\chi_{4536}(59,\cdot)\) | 4536.fn | 54 | yes | \(-1\) | \(1\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{29}{54}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{13}{18}\right)\) |
\(\chi_{4536}(61,\cdot)\) | 4536.gm | 54 | yes | \(-1\) | \(1\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{11}{18}\right)\) |
\(\chi_{4536}(65,\cdot)\) | 4536.gb | 54 | no | \(-1\) | \(1\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{13}{54}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{7}{9}\right)\) |
\(\chi_{4536}(67,\cdot)\) | 4536.gh | 54 | yes | \(-1\) | \(1\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{1}{54}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{1}{18}\right)\) |
\(\chi_{4536}(71,\cdot)\) | 4536.el | 18 | no | \(1\) | \(1\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{4536}(73,\cdot)\) | 4536.df | 18 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(-1\) | \(-1\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{4536}(79,\cdot)\) | 4536.fu | 54 | no | \(-1\) | \(1\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{4}{9}\right)\) |
\(\chi_{4536}(83,\cdot)\) | 4536.fo | 54 | yes | \(-1\) | \(1\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{13}{54}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{5}{18}\right)\) |
\(\chi_{4536}(85,\cdot)\) | 4536.gd | 54 | no | \(1\) | \(1\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{1}{18}\right)\) |
\(\chi_{4536}(89,\cdot)\) | 4536.ea | 18 | no | \(1\) | \(1\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(1\) |
\(\chi_{4536}(95,\cdot)\) | 4536.gg | 54 | no | \(1\) | \(1\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{5}{9}\right)\) |
\(\chi_{4536}(97,\cdot)\) | 4536.fq | 54 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{1}{9}\right)\) |
\(\chi_{4536}(101,\cdot)\) | 4536.gs | 54 | yes | \(1\) | \(1\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{5}{18}\right)\) |
\(\chi_{4536}(103,\cdot)\) | 4536.go | 54 | no | \(1\) | \(1\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{1}{54}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{5}{9}\right)\) |
\(\chi_{4536}(107,\cdot)\) | 4536.cy | 6 | no | \(1\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{4536}(109,\cdot)\) | 4536.w | 6 | no | \(1\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) |