sage: H = DirichletGroup(192)
pari: g = idealstar(,192,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 64 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{16}\times C_{2}\times C_{2}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{192}(127,\cdot)$, $\chi_{192}(133,\cdot)$, $\chi_{192}(65,\cdot)$ |
First 32 of 64 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 | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{192}(1,\cdot)\) | 192.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{192}(5,\cdot)\) | 192.q | 16 | yes | \(-1\) | \(1\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(i\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(-1\) |
\(\chi_{192}(7,\cdot)\) | 192.m | 8 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(-i\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) | \(e\left(\frac{7}{8}\right)\) | \(i\) | \(i\) | \(e\left(\frac{7}{8}\right)\) | \(-1\) |
\(\chi_{192}(11,\cdot)\) | 192.s | 16 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(i\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(1\) |
\(\chi_{192}(13,\cdot)\) | 192.r | 16 | no | \(1\) | \(1\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(i\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(-1\) |
\(\chi_{192}(17,\cdot)\) | 192.i | 4 | no | \(-1\) | \(1\) | \(i\) | \(-1\) | \(i\) | \(i\) | \(-1\) | \(i\) | \(1\) | \(-1\) | \(-i\) | \(1\) |
\(\chi_{192}(19,\cdot)\) | 192.t | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(i\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(1\) |
\(\chi_{192}(23,\cdot)\) | 192.o | 8 | no | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(i\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(-1\) |
\(\chi_{192}(25,\cdot)\) | 192.n | 8 | no | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(i\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(-1\) | \(e\left(\frac{7}{8}\right)\) | \(-i\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(1\) |
\(\chi_{192}(29,\cdot)\) | 192.q | 16 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(-i\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(-1\) |
\(\chi_{192}(31,\cdot)\) | 192.b | 2 | no | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
\(\chi_{192}(35,\cdot)\) | 192.s | 16 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(-i\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(1\) |
\(\chi_{192}(37,\cdot)\) | 192.r | 16 | no | \(1\) | \(1\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(-i\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(-1\) |
\(\chi_{192}(41,\cdot)\) | 192.p | 8 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(-i\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
\(\chi_{192}(43,\cdot)\) | 192.t | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(-i\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(1\) |
\(\chi_{192}(47,\cdot)\) | 192.k | 4 | no | \(1\) | \(1\) | \(i\) | \(1\) | \(-i\) | \(i\) | \(-1\) | \(-i\) | \(-1\) | \(-1\) | \(-i\) | \(-1\) |
\(\chi_{192}(49,\cdot)\) | 192.j | 4 | no | \(1\) | \(1\) | \(i\) | \(-1\) | \(i\) | \(-i\) | \(1\) | \(-i\) | \(-1\) | \(-1\) | \(-i\) | \(1\) |
\(\chi_{192}(53,\cdot)\) | 192.q | 16 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(i\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(-1\) |
\(\chi_{192}(55,\cdot)\) | 192.m | 8 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) | \(-i\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(-1\) |
\(\chi_{192}(59,\cdot)\) | 192.s | 16 | yes | \(1\) | \(1\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(i\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(1\) |
\(\chi_{192}(61,\cdot)\) | 192.r | 16 | no | \(1\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(i\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(-1\) |
\(\chi_{192}(65,\cdot)\) | 192.e | 2 | no | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
\(\chi_{192}(67,\cdot)\) | 192.t | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(i\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(1\) |
\(\chi_{192}(71,\cdot)\) | 192.o | 8 | no | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(-i\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) |
\(\chi_{192}(73,\cdot)\) | 192.n | 8 | no | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(-1\) | \(e\left(\frac{5}{8}\right)\) | \(i\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
\(\chi_{192}(77,\cdot)\) | 192.q | 16 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(-i\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(-1\) |
\(\chi_{192}(79,\cdot)\) | 192.l | 4 | no | \(-1\) | \(1\) | \(i\) | \(1\) | \(-i\) | \(-i\) | \(1\) | \(i\) | \(1\) | \(-1\) | \(-i\) | \(-1\) |
\(\chi_{192}(83,\cdot)\) | 192.s | 16 | yes | \(1\) | \(1\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(-i\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(1\) |
\(\chi_{192}(85,\cdot)\) | 192.r | 16 | no | \(1\) | \(1\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(-i\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(-1\) |
\(\chi_{192}(89,\cdot)\) | 192.p | 8 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(i\) | \(i\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |
\(\chi_{192}(91,\cdot)\) | 192.t | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(-i\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(1\) |
\(\chi_{192}(95,\cdot)\) | 192.f | 2 | no | \(1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(-1\) |