sage: H = DirichletGroup(640)
pari: g = idealstar(,640,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 256 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{4}\times C_{32}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{640}(511,\cdot)$, $\chi_{640}(261,\cdot)$, $\chi_{640}(257,\cdot)$ |
First 32 of 256 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 | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{640}(1,\cdot)\) | 640.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{640}(3,\cdot)\) | 640.bl | 32 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{3}{32}\right)\) |
\(\chi_{640}(7,\cdot)\) | 640.bj | 16 | no | \(1\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) |
\(\chi_{640}(9,\cdot)\) | 640.bf | 16 | no | \(1\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(-i\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) |
\(\chi_{640}(11,\cdot)\) | 640.bp | 32 | no | \(-1\) | \(1\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{13}{32}\right)\) |
\(\chi_{640}(13,\cdot)\) | 640.bk | 32 | yes | \(-1\) | \(1\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{31}{32}\right)\) |
\(\chi_{640}(17,\cdot)\) | 640.bb | 8 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(1\) | \(-i\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(-i\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{640}(19,\cdot)\) | 640.bn | 32 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{15}{32}\right)\) |
\(\chi_{640}(21,\cdot)\) | 640.bm | 32 | no | \(1\) | \(1\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{21}{32}\right)\) |
\(\chi_{640}(23,\cdot)\) | 640.bj | 16 | no | \(1\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) |
\(\chi_{640}(27,\cdot)\) | 640.bl | 32 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{9}{32}\right)\) |
\(\chi_{640}(29,\cdot)\) | 640.bo | 32 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{3}{32}\right)\) |
\(\chi_{640}(31,\cdot)\) | 640.r | 4 | no | \(-1\) | \(1\) | \(i\) | \(1\) | \(-1\) | \(-i\) | \(-i\) | \(1\) | \(i\) | \(i\) | \(1\) | \(-i\) |
\(\chi_{640}(33,\cdot)\) | 640.i | 4 | no | \(-1\) | \(1\) | \(-1\) | \(i\) | \(1\) | \(-i\) | \(-1\) | \(-i\) | \(-i\) | \(-i\) | \(-i\) | \(-1\) |
\(\chi_{640}(37,\cdot)\) | 640.bk | 32 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{9}{32}\right)\) |
\(\chi_{640}(39,\cdot)\) | 640.bh | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(i\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) |
\(\chi_{640}(41,\cdot)\) | 640.be | 16 | no | \(1\) | \(1\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(i\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{16}\right)\) |
\(\chi_{640}(43,\cdot)\) | 640.br | 32 | yes | \(1\) | \(1\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{13}{32}\right)\) |
\(\chi_{640}(47,\cdot)\) | 640.u | 8 | no | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) | \(-i\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{640}(49,\cdot)\) | 640.z | 8 | no | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(i\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{640}(51,\cdot)\) | 640.bp | 32 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{7}{32}\right)\) |
\(\chi_{640}(53,\cdot)\) | 640.bq | 32 | yes | \(-1\) | \(1\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{32}\right)\) |
\(\chi_{640}(57,\cdot)\) | 640.bi | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) |
\(\chi_{640}(59,\cdot)\) | 640.bn | 32 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{25}{32}\right)\) |
\(\chi_{640}(61,\cdot)\) | 640.bm | 32 | no | \(1\) | \(1\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{11}{32}\right)\) |
\(\chi_{640}(63,\cdot)\) | 640.o | 4 | no | \(1\) | \(1\) | \(i\) | \(i\) | \(-1\) | \(1\) | \(-i\) | \(-i\) | \(-1\) | \(-1\) | \(-i\) | \(-i\) |
\(\chi_{640}(67,\cdot)\) | 640.br | 32 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{32}\right)\) |
\(\chi_{640}(69,\cdot)\) | 640.bo | 32 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{9}{32}\right)\) |
\(\chi_{640}(71,\cdot)\) | 640.bg | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(-i\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) |
\(\chi_{640}(73,\cdot)\) | 640.bi | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) |
\(\chi_{640}(77,\cdot)\) | 640.bq | 32 | yes | \(-1\) | \(1\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{31}{32}\right)\) |
\(\chi_{640}(79,\cdot)\) | 640.y | 8 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(i\) | \(-i\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(-i\) | \(e\left(\frac{5}{8}\right)\) |