sage: H = DirichletGroup(150)
pari: g = idealstar(,150,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 40 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{20}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{150}(101,\cdot)$, $\chi_{150}(127,\cdot)$ |
First 32 of 40 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 | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{150}(1,\cdot)\) | 150.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{150}(7,\cdot)\) | 150.f | 4 | no | \(-1\) | \(1\) | \(i\) | \(1\) | \(-i\) | \(i\) | \(-1\) | \(-i\) | \(-1\) | \(1\) | \(i\) | \(1\) |
\(\chi_{150}(11,\cdot)\) | 150.j | 10 | no | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{150}(13,\cdot)\) | 150.k | 20 | no | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{150}(17,\cdot)\) | 150.l | 20 | no | \(1\) | \(1\) | \(i\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{150}(19,\cdot)\) | 150.h | 10 | no | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{150}(23,\cdot)\) | 150.l | 20 | no | \(1\) | \(1\) | \(-i\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{150}(29,\cdot)\) | 150.i | 10 | no | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) |
\(\chi_{150}(31,\cdot)\) | 150.g | 5 | no | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{150}(37,\cdot)\) | 150.k | 20 | no | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{150}(41,\cdot)\) | 150.j | 10 | no | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{150}(43,\cdot)\) | 150.f | 4 | no | \(-1\) | \(1\) | \(-i\) | \(1\) | \(i\) | \(-i\) | \(-1\) | \(i\) | \(-1\) | \(1\) | \(-i\) | \(1\) |
\(\chi_{150}(47,\cdot)\) | 150.l | 20 | no | \(1\) | \(1\) | \(i\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) |
\(\chi_{150}(49,\cdot)\) | 150.c | 2 | no | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
\(\chi_{150}(53,\cdot)\) | 150.l | 20 | no | \(1\) | \(1\) | \(-i\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) |
\(\chi_{150}(59,\cdot)\) | 150.i | 10 | no | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{150}(61,\cdot)\) | 150.g | 5 | no | \(1\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{150}(67,\cdot)\) | 150.k | 20 | no | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{150}(71,\cdot)\) | 150.j | 10 | no | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) |
\(\chi_{150}(73,\cdot)\) | 150.k | 20 | no | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{150}(77,\cdot)\) | 150.l | 20 | no | \(1\) | \(1\) | \(i\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{150}(79,\cdot)\) | 150.h | 10 | no | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{150}(83,\cdot)\) | 150.l | 20 | no | \(1\) | \(1\) | \(-i\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{150}(89,\cdot)\) | 150.i | 10 | no | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{150}(91,\cdot)\) | 150.g | 5 | no | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{150}(97,\cdot)\) | 150.k | 20 | no | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{150}(101,\cdot)\) | 150.d | 2 | no | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
\(\chi_{150}(103,\cdot)\) | 150.k | 20 | no | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{150}(107,\cdot)\) | 150.e | 4 | no | \(1\) | \(1\) | \(i\) | \(-1\) | \(-i\) | \(-i\) | \(-1\) | \(i\) | \(1\) | \(1\) | \(i\) | \(-1\) |
\(\chi_{150}(109,\cdot)\) | 150.h | 10 | no | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{150}(113,\cdot)\) | 150.l | 20 | no | \(1\) | \(1\) | \(-i\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{150}(119,\cdot)\) | 150.i | 10 | no | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) |