sage: H = DirichletGroup(1547)
pari: g = idealstar(,1547,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 1152 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{12}\times C_{48}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{1547}(885,\cdot)$, $\chi_{1547}(834,\cdot)$, $\chi_{1547}(547,\cdot)$ |
First 32 of 1152 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1547}(1,\cdot)\) | 1547.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{1547}(2,\cdot)\) | 1547.fq | 24 | yes | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{13}{24}\right)\) | \(1\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{13}{24}\right)\) |
\(\chi_{1547}(3,\cdot)\) | 1547.gf | 48 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{31}{48}\right)\) |
\(\chi_{1547}(4,\cdot)\) | 1547.ec | 12 | yes | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{1547}(5,\cdot)\) | 1547.gl | 48 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{35}{48}\right)\) |
\(\chi_{1547}(6,\cdot)\) | 1547.gg | 48 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{3}{16}\right)\) |
\(\chi_{1547}(8,\cdot)\) | 1547.ch | 8 | no | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(1\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{1547}(9,\cdot)\) | 1547.fb | 24 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(i\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{24}\right)\) |
\(\chi_{1547}(10,\cdot)\) | 1547.gs | 48 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{13}{48}\right)\) |
\(\chi_{1547}(11,\cdot)\) | 1547.go | 48 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{25}{48}\right)\) |
\(\chi_{1547}(12,\cdot)\) | 1547.gu | 48 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{35}{48}\right)\) |
\(\chi_{1547}(15,\cdot)\) | 1547.ep | 24 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{1547}(16,\cdot)\) | 1547.bz | 6 | yes | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{1547}(18,\cdot)\) | 1547.cx | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(-i\) | \(i\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{1547}(19,\cdot)\) | 1547.eo | 24 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(1\) | \(-i\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{24}\right)\) |
\(\chi_{1547}(20,\cdot)\) | 1547.gg | 48 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{1}{48}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{13}{16}\right)\) |
\(\chi_{1547}(22,\cdot)\) | 1547.gx | 48 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{1}{48}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{1}{16}\right)\) |
\(\chi_{1547}(23,\cdot)\) | 1547.fy | 48 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(i\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{41}{48}\right)\) |
\(\chi_{1547}(24,\cdot)\) | 1547.gj | 48 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{13}{48}\right)\) |
\(\chi_{1547}(25,\cdot)\) | 1547.fh | 24 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(-i\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{11}{24}\right)\) |
\(\chi_{1547}(27,\cdot)\) | 1547.el | 16 | no | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(i\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) |
\(\chi_{1547}(29,\cdot)\) | 1547.gx | 48 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{1}{48}\right)\) | \(e\left(\frac{9}{16}\right)\) |
\(\chi_{1547}(30,\cdot)\) | 1547.cl | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(i\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(1\) | \(-1\) | \(-i\) | \(i\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{1547}(31,\cdot)\) | 1547.gl | 48 | yes | \(-1\) | \(1\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{31}{48}\right)\) |
\(\chi_{1547}(32,\cdot)\) | 1547.fq | 24 | yes | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{17}{24}\right)\) | \(1\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{17}{24}\right)\) |
\(\chi_{1547}(33,\cdot)\) | 1547.dv | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(-i\) | \(1\) | \(-1\) | \(i\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{1547}(36,\cdot)\) | 1547.ez | 24 | no | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(i\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{1547}(37,\cdot)\) | 1547.fv | 48 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(i\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{47}{48}\right)\) |
\(\chi_{1547}(38,\cdot)\) | 1547.cp | 12 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(i\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{1547}(40,\cdot)\) | 1547.gd | 48 | no | \(1\) | \(1\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{43}{48}\right)\) | \(e\left(\frac{17}{48}\right)\) |
\(\chi_{1547}(41,\cdot)\) | 1547.gg | 48 | yes | \(-1\) | \(1\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{15}{16}\right)\) |
\(\chi_{1547}(43,\cdot)\) | 1547.ez | 24 | no | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(-i\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{5}{8}\right)\) |