sage: H = DirichletGroup(124)
pari: g = idealstar(,124,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 60 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{30}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{124}(63,\cdot)$, $\chi_{124}(65,\cdot)$ |
First 32 of 60 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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{124}(1,\cdot)\) | 124.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{124}(3,\cdot)\) | 124.p | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) |
\(\chi_{124}(5,\cdot)\) | 124.e | 3 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{124}(7,\cdot)\) | 124.n | 30 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) |
\(\chi_{124}(9,\cdot)\) | 124.m | 15 | no | \(1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) |
\(\chi_{124}(11,\cdot)\) | 124.p | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) |
\(\chi_{124}(13,\cdot)\) | 124.o | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) |
\(\chi_{124}(15,\cdot)\) | 124.j | 10 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{124}(17,\cdot)\) | 124.o | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) |
\(\chi_{124}(19,\cdot)\) | 124.n | 30 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) |
\(\chi_{124}(21,\cdot)\) | 124.o | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) |
\(\chi_{124}(23,\cdot)\) | 124.j | 10 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{124}(25,\cdot)\) | 124.e | 3 | no | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{124}(27,\cdot)\) | 124.j | 10 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) |
\(\chi_{124}(29,\cdot)\) | 124.k | 10 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{124}(33,\cdot)\) | 124.f | 5 | no | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{124}(35,\cdot)\) | 124.l | 10 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{124}(37,\cdot)\) | 124.h | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{124}(39,\cdot)\) | 124.l | 10 | yes | \(-1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{124}(41,\cdot)\) | 124.m | 15 | no | \(1\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) |
\(\chi_{124}(43,\cdot)\) | 124.p | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) |
\(\chi_{124}(45,\cdot)\) | 124.m | 15 | no | \(1\) | \(1\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) |
\(\chi_{124}(47,\cdot)\) | 124.l | 10 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{124}(49,\cdot)\) | 124.m | 15 | no | \(1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) |
\(\chi_{124}(51,\cdot)\) | 124.n | 30 | yes | \(-1\) | \(1\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) |
\(\chi_{124}(53,\cdot)\) | 124.o | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) |
\(\chi_{124}(55,\cdot)\) | 124.p | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{17}{30}\right)\) |
\(\chi_{124}(57,\cdot)\) | 124.h | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{124}(59,\cdot)\) | 124.n | 30 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) |
\(\chi_{124}(61,\cdot)\) | 124.c | 2 | no | \(-1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
\(\chi_{124}(63,\cdot)\) | 124.b | 2 | no | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
\(\chi_{124}(65,\cdot)\) | 124.o | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) |