sage: H = DirichletGroup(1152)
pari: g = idealstar(,1152,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 384 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{96}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{1152}(127,\cdot)$, $\chi_{1152}(901,\cdot)$, $\chi_{1152}(641,\cdot)$ |
First 32 of 384 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 | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1152}(1,\cdot)\) | 1152.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{1152}(5,\cdot)\) | 1152.bt | 96 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{96}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{47}{96}\right)\) | \(e\left(\frac{13}{96}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{65}{96}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{1152}(7,\cdot)\) | 1152.bo | 48 | no | \(-1\) | \(1\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{1}{48}\right)\) | \(-i\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{1152}(11,\cdot)\) | 1152.bs | 96 | yes | \(1\) | \(1\) | \(e\left(\frac{47}{96}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{43}{96}\right)\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{85}{96}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{1152}(13,\cdot)\) | 1152.bv | 96 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{96}\right)\) | \(e\left(\frac{1}{48}\right)\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{67}{96}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{95}{96}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{1152}(17,\cdot)\) | 1152.x | 8 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(-i\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
\(\chi_{1152}(19,\cdot)\) | 1152.bk | 32 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(i\) |
\(\chi_{1152}(23,\cdot)\) | 1152.bp | 48 | no | \(1\) | \(1\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(-i\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{1152}(25,\cdot)\) | 1152.bq | 48 | no | \(1\) | \(1\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(-i\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{1152}(29,\cdot)\) | 1152.bt | 96 | yes | \(-1\) | \(1\) | \(e\left(\frac{65}{96}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{85}{96}\right)\) | \(e\left(\frac{95}{96}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{91}{96}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{1152}(31,\cdot)\) | 1152.z | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(1\) | \(i\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{1152}(35,\cdot)\) | 1152.bm | 32 | no | \(1\) | \(1\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(i\) |
\(\chi_{1152}(37,\cdot)\) | 1152.bl | 32 | no | \(1\) | \(1\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(i\) |
\(\chi_{1152}(41,\cdot)\) | 1152.br | 48 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(-i\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{1152}(43,\cdot)\) | 1152.bu | 96 | yes | \(-1\) | \(1\) | \(e\left(\frac{23}{96}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{19}{96}\right)\) | \(e\left(\frac{89}{96}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{13}{96}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{1152}(47,\cdot)\) | 1152.bj | 24 | no | \(1\) | \(1\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{1152}(49,\cdot)\) | 1152.bg | 24 | no | \(1\) | \(1\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{1152}(53,\cdot)\) | 1152.bn | 32 | no | \(-1\) | \(1\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(i\) |
\(\chi_{1152}(55,\cdot)\) | 1152.bf | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(i\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(1\) |
\(\chi_{1152}(59,\cdot)\) | 1152.bs | 96 | yes | \(1\) | \(1\) | \(e\left(\frac{67}{96}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{47}{96}\right)\) | \(e\left(\frac{61}{96}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{1152}(61,\cdot)\) | 1152.bv | 96 | yes | \(1\) | \(1\) | \(e\left(\frac{89}{96}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{13}{96}\right)\) | \(e\left(\frac{23}{96}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{67}{96}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{1152}(65,\cdot)\) | 1152.n | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{1152}(67,\cdot)\) | 1152.bu | 96 | yes | \(-1\) | \(1\) | \(e\left(\frac{25}{96}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{29}{96}\right)\) | \(e\left(\frac{55}{96}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{35}{96}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{1152}(71,\cdot)\) | 1152.be | 16 | no | \(1\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(i\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(1\) |
\(\chi_{1152}(73,\cdot)\) | 1152.bd | 16 | no | \(1\) | \(1\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(i\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(-1\) |
\(\chi_{1152}(77,\cdot)\) | 1152.bt | 96 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{96}\right)\) | \(e\left(\frac{1}{48}\right)\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{19}{96}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{95}{96}\right)\) | \(e\left(\frac{5}{12}\right)\) |
\(\chi_{1152}(79,\cdot)\) | 1152.bh | 24 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(-1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{1152}(83,\cdot)\) | 1152.bs | 96 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{96}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{25}{96}\right)\) | \(e\left(\frac{59}{96}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{7}{96}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{1152}(85,\cdot)\) | 1152.bv | 96 | yes | \(1\) | \(1\) | \(e\left(\frac{55}{96}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{35}{96}\right)\) | \(e\left(\frac{25}{96}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{77}{96}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{1152}(89,\cdot)\) | 1152.bc | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(i\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(-1\) |
\(\chi_{1152}(91,\cdot)\) | 1152.bk | 32 | no | \(-1\) | \(1\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(-i\) |
\(\chi_{1152}(95,\cdot)\) | 1152.y | 12 | no | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(-1\) | \(-i\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) |