sage: H = DirichletGroup(680)
pari: g = idealstar(,680,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 256 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{4}\times C_{16}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{680}(511,\cdot)$, $\chi_{680}(341,\cdot)$, $\chi_{680}(137,\cdot)$, $\chi_{680}(241,\cdot)$ |
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 | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{680}(1,\cdot)\) | 680.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{680}(3,\cdot)\) | 680.cr | 16 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(i\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) |
\(\chi_{680}(7,\cdot)\) | 680.ce | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(-1\) | \(e\left(\frac{5}{8}\right)\) | \(i\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) |
\(\chi_{680}(9,\cdot)\) | 680.cb | 8 | no | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(i\) | \(e\left(\frac{7}{8}\right)\) | \(1\) | \(-i\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{680}(11,\cdot)\) | 680.ci | 16 | no | \(1\) | \(1\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(i\) | \(e\left(\frac{1}{8}\right)\) | \(-i\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) |
\(\chi_{680}(13,\cdot)\) | 680.bk | 4 | yes | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(i\) | \(-i\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(i\) |
\(\chi_{680}(19,\cdot)\) | 680.bq | 8 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(-1\) | \(i\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{680}(21,\cdot)\) | 680.ba | 4 | no | \(1\) | \(1\) | \(i\) | \(i\) | \(-1\) | \(-i\) | \(-1\) | \(1\) | \(-1\) | \(i\) | \(-i\) | \(i\) |
\(\chi_{680}(23,\cdot)\) | 680.cs | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(i\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) |
\(\chi_{680}(27,\cdot)\) | 680.cr | 16 | yes | \(-1\) | \(1\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(-i\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) |
\(\chi_{680}(29,\cdot)\) | 680.cm | 16 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(i\) | \(e\left(\frac{7}{8}\right)\) | \(i\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) |
\(\chi_{680}(31,\cdot)\) | 680.cl | 16 | no | \(1\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) |
\(\chi_{680}(33,\cdot)\) | 680.v | 4 | no | \(-1\) | \(1\) | \(-i\) | \(i\) | \(-1\) | \(-1\) | \(i\) | \(-1\) | \(1\) | \(-i\) | \(i\) | \(1\) |
\(\chi_{680}(37,\cdot)\) | 680.cf | 16 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(-1\) | \(e\left(\frac{7}{8}\right)\) | \(i\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) |
\(\chi_{680}(39,\cdot)\) | 680.cn | 16 | no | \(1\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(-i\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) |
\(\chi_{680}(41,\cdot)\) | 680.cj | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(-i\) | \(e\left(\frac{5}{8}\right)\) | \(i\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) |
\(\chi_{680}(43,\cdot)\) | 680.bw | 8 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(i\) | \(i\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{680}(47,\cdot)\) | 680.q | 4 | no | \(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(i\) | \(-i\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(-i\) |
\(\chi_{680}(49,\cdot)\) | 680.cb | 8 | no | \(1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(-i\) | \(e\left(\frac{5}{8}\right)\) | \(1\) | \(i\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{680}(53,\cdot)\) | 680.bx | 8 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(i\) | \(e\left(\frac{5}{8}\right)\) | \(i\) | \(i\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{680}(57,\cdot)\) | 680.cg | 16 | no | \(1\) | \(1\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(-1\) | \(e\left(\frac{5}{8}\right)\) | \(i\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) |
\(\chi_{680}(59,\cdot)\) | 680.bq | 8 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) | \(-i\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{680}(61,\cdot)\) | 680.ck | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(i\) | \(e\left(\frac{1}{8}\right)\) | \(-i\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) |
\(\chi_{680}(63,\cdot)\) | 680.ce | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) |
\(\chi_{680}(67,\cdot)\) | 680.u | 4 | yes | \(1\) | \(1\) | \(i\) | \(i\) | \(-1\) | \(-1\) | \(i\) | \(-1\) | \(-1\) | \(-i\) | \(-i\) | \(-1\) |
\(\chi_{680}(69,\cdot)\) | 680.j | 2 | no | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
\(\chi_{680}(71,\cdot)\) | 680.cl | 16 | no | \(1\) | \(1\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) |
\(\chi_{680}(73,\cdot)\) | 680.cg | 16 | no | \(1\) | \(1\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(-1\) | \(e\left(\frac{7}{8}\right)\) | \(-i\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) |
\(\chi_{680}(77,\cdot)\) | 680.bx | 8 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(-i\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(-i\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{680}(79,\cdot)\) | 680.cn | 16 | no | \(1\) | \(1\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(i\) | \(e\left(\frac{5}{8}\right)\) | \(i\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) |
\(\chi_{680}(81,\cdot)\) | 680.bd | 4 | no | \(1\) | \(1\) | \(i\) | \(-i\) | \(-1\) | \(-i\) | \(1\) | \(-1\) | \(1\) | \(-i\) | \(-i\) | \(i\) |
\(\chi_{680}(83,\cdot)\) | 680.bz | 8 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(i\) | \(e\left(\frac{5}{8}\right)\) | \(i\) | \(-i\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) |