sage: H = DirichletGroup(320)
pari: g = idealstar(,320,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 128 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{4}\times C_{16}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{320}(191,\cdot)$, $\chi_{320}(261,\cdot)$, $\chi_{320}(257,\cdot)$ |
First 32 of 128 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 | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{320}(1,\cdot)\) | 320.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{320}(3,\cdot)\) | 320.bj | 16 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) |
\(\chi_{320}(7,\cdot)\) | 320.ba | 8 | no | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(1\) | \(i\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(-i\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{320}(9,\cdot)\) | 320.z | 8 | no | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(i\) | \(i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{320}(11,\cdot)\) | 320.bg | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(-i\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{16}\right)\) |
\(\chi_{320}(13,\cdot)\) | 320.bi | 16 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) |
\(\chi_{320}(17,\cdot)\) | 320.t | 4 | no | \(-1\) | \(1\) | \(1\) | \(-i\) | \(1\) | \(-i\) | \(1\) | \(i\) | \(-i\) | \(-i\) | \(i\) | \(1\) |
\(\chi_{320}(19,\cdot)\) | 320.bh | 16 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(-i\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) |
\(\chi_{320}(21,\cdot)\) | 320.be | 16 | no | \(1\) | \(1\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(-i\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{16}\right)\) |
\(\chi_{320}(23,\cdot)\) | 320.ba | 8 | no | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(1\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{320}(27,\cdot)\) | 320.bj | 16 | yes | \(1\) | \(1\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(1\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) |
\(\chi_{320}(29,\cdot)\) | 320.bf | 16 | yes | \(1\) | \(1\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(-i\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) |
\(\chi_{320}(31,\cdot)\) | 320.g | 2 | no | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
\(\chi_{320}(33,\cdot)\) | 320.m | 4 | no | \(-1\) | \(1\) | \(-i\) | \(-i\) | \(-1\) | \(-1\) | \(-i\) | \(-i\) | \(1\) | \(-1\) | \(i\) | \(i\) |
\(\chi_{320}(37,\cdot)\) | 320.bi | 16 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(1\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{5}{16}\right)\) |
\(\chi_{320}(39,\cdot)\) | 320.y | 8 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(i\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{320}(41,\cdot)\) | 320.x | 8 | no | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(-i\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(i\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{320}(43,\cdot)\) | 320.bd | 16 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(-1\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) |
\(\chi_{320}(47,\cdot)\) | 320.j | 4 | no | \(1\) | \(1\) | \(-1\) | \(i\) | \(1\) | \(i\) | \(1\) | \(i\) | \(i\) | \(-i\) | \(-i\) | \(-1\) |
\(\chi_{320}(49,\cdot)\) | 320.q | 4 | no | \(1\) | \(1\) | \(i\) | \(1\) | \(-1\) | \(i\) | \(i\) | \(-1\) | \(-i\) | \(i\) | \(1\) | \(-i\) |
\(\chi_{320}(51,\cdot)\) | 320.bg | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(i\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) |
\(\chi_{320}(53,\cdot)\) | 320.bc | 16 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(-1\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) |
\(\chi_{320}(57,\cdot)\) | 320.v | 8 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(-1\) | \(i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(-1\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{320}(59,\cdot)\) | 320.bh | 16 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(i\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) |
\(\chi_{320}(61,\cdot)\) | 320.be | 16 | no | \(1\) | \(1\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(i\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) |
\(\chi_{320}(63,\cdot)\) | 320.n | 4 | no | \(1\) | \(1\) | \(-i\) | \(i\) | \(-1\) | \(-1\) | \(i\) | \(-i\) | \(1\) | \(1\) | \(-i\) | \(i\) |
\(\chi_{320}(67,\cdot)\) | 320.bd | 16 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(-1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{16}\right)\) |
\(\chi_{320}(69,\cdot)\) | 320.bf | 16 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(i\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) |
\(\chi_{320}(71,\cdot)\) | 320.w | 8 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(-i\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(i\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{320}(73,\cdot)\) | 320.v | 8 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{320}(77,\cdot)\) | 320.bc | 16 | yes | \(-1\) | \(1\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(-1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) |
\(\chi_{320}(79,\cdot)\) | 320.k | 4 | no | \(-1\) | \(1\) | \(-i\) | \(-1\) | \(-1\) | \(-i\) | \(i\) | \(-1\) | \(i\) | \(i\) | \(-1\) | \(i\) |