sage: H = DirichletGroup(1360)
pari: g = idealstar(,1360,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 512 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{4}\times C_{4}\times C_{16}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{1360}(511,\cdot)$, $\chi_{1360}(341,\cdot)$, $\chi_{1360}(817,\cdot)$, $\chi_{1360}(241,\cdot)$ |
First 32 of 512 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 | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1360}(1,\cdot)\) | 1360.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{1360}(3,\cdot)\) | 1360.ei | 16 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(-1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) |
\(\chi_{1360}(7,\cdot)\) | 1360.fb | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(-i\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) |
\(\chi_{1360}(9,\cdot)\) | 1360.cz | 8 | no | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) | \(i\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{1360}(11,\cdot)\) | 1360.eb | 16 | no | \(1\) | \(1\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) |
\(\chi_{1360}(13,\cdot)\) | 1360.cb | 4 | yes | \(-1\) | \(1\) | \(-i\) | \(1\) | \(-1\) | \(-1\) | \(-1\) | \(i\) | \(-i\) | \(-1\) | \(i\) | \(1\) |
\(\chi_{1360}(19,\cdot)\) | 1360.do | 8 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(i\) | \(1\) | \(i\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{1360}(21,\cdot)\) | 1360.s | 4 | no | \(1\) | \(1\) | \(-1\) | \(-i\) | \(1\) | \(-1\) | \(-i\) | \(i\) | \(i\) | \(-i\) | \(-1\) | \(-1\) |
\(\chi_{1360}(23,\cdot)\) | 1360.ef | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(-1\) | \(e\left(\frac{5}{8}\right)\) | \(-i\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) |
\(\chi_{1360}(27,\cdot)\) | 1360.ei | 16 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) |
\(\chi_{1360}(29,\cdot)\) | 1360.ez | 16 | yes | \(-1\) | \(1\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(-1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) |
\(\chi_{1360}(31,\cdot)\) | 1360.ep | 16 | no | \(1\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) |
\(\chi_{1360}(33,\cdot)\) | 1360.bl | 4 | no | \(-1\) | \(1\) | \(-i\) | \(i\) | \(-1\) | \(-1\) | \(i\) | \(-1\) | \(1\) | \(-i\) | \(i\) | \(1\) |
\(\chi_{1360}(37,\cdot)\) | 1360.ev | 16 | yes | \(1\) | \(1\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) |
\(\chi_{1360}(39,\cdot)\) | 1360.es | 16 | no | \(1\) | \(1\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(i\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) |
\(\chi_{1360}(41,\cdot)\) | 1360.eo | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(i\) | \(e\left(\frac{1}{8}\right)\) | \(-i\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) |
\(\chi_{1360}(43,\cdot)\) | 1360.cv | 8 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(i\) | \(e\left(\frac{5}{8}\right)\) | \(-1\) | \(-1\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{1360}(47,\cdot)\) | 1360.q | 4 | no | \(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(i\) | \(-i\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(-i\) |
\(\chi_{1360}(49,\cdot)\) | 1360.dv | 8 | no | \(1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(-i\) | \(e\left(\frac{5}{8}\right)\) | \(1\) | \(i\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{1360}(53,\cdot)\) | 1360.cu | 8 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(-i\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) | \(-1\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{1360}(57,\cdot)\) | 1360.fd | 16 | no | \(1\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(-i\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) |
\(\chi_{1360}(59,\cdot)\) | 1360.do | 8 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(-i\) | \(1\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{1360}(61,\cdot)\) | 1360.fe | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) |
\(\chi_{1360}(63,\cdot)\) | 1360.ec | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) |
\(\chi_{1360}(67,\cdot)\) | 1360.co | 4 | yes | \(1\) | \(1\) | \(1\) | \(-i\) | \(1\) | \(-i\) | \(1\) | \(i\) | \(-i\) | \(i\) | \(1\) | \(i\) |
\(\chi_{1360}(69,\cdot)\) | 1360.ce | 4 | no | \(1\) | \(1\) | \(i\) | \(1\) | \(-1\) | \(i\) | \(i\) | \(-i\) | \(i\) | \(1\) | \(-i\) | \(-i\) |
\(\chi_{1360}(71,\cdot)\) | 1360.em | 16 | no | \(1\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(i\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) |
\(\chi_{1360}(73,\cdot)\) | 1360.fd | 16 | no | \(1\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(i\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) |
\(\chi_{1360}(77,\cdot)\) | 1360.cu | 8 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(i\) | \(e\left(\frac{5}{8}\right)\) | \(-1\) | \(-1\) | \(i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{1360}(79,\cdot)\) | 1360.er | 16 | no | \(1\) | \(1\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(i\) | \(e\left(\frac{5}{8}\right)\) | \(i\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) |
\(\chi_{1360}(81,\cdot)\) | 1360.bt | 4 | no | \(1\) | \(1\) | \(i\) | \(-i\) | \(-1\) | \(-i\) | \(1\) | \(-1\) | \(1\) | \(-i\) | \(-i\) | \(i\) |
\(\chi_{1360}(83,\cdot)\) | 1360.ds | 8 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(1\) | \(-1\) | \(i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) |