sage: H = DirichletGroup(15600)
pari: g = idealstar(,15600,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 3840 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{4}\times C_{4}\times C_{60}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{15600}(1951,\cdot)$, $\chi_{15600}(11701,\cdot)$, $\chi_{15600}(5201,\cdot)$, $\chi_{15600}(14977,\cdot)$, $\chi_{15600}(12001,\cdot)$ |
First 32 of 3840 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 | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{15600}(1,\cdot)\) | 15600.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{15600}(7,\cdot)\) | 15600.lu | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-i\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{15600}(11,\cdot)\) | 15600.vd | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{15600}(17,\cdot)\) | 15600.vb | 60 | no | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{15600}(19,\cdot)\) | 15600.th | 60 | no | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{15600}(23,\cdot)\) | 15600.uz | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{15600}(29,\cdot)\) | 15600.sm | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{15600}(31,\cdot)\) | 15600.ov | 20 | no | \(1\) | \(1\) | \(-i\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(1\) |
\(\chi_{15600}(37,\cdot)\) | 15600.wb | 60 | no | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{15600}(41,\cdot)\) | 15600.uo | 60 | no | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{15600}(43,\cdot)\) | 15600.kj | 12 | no | \(1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{15600}(47,\cdot)\) | 15600.mr | 20 | no | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(-i\) |
\(\chi_{15600}(49,\cdot)\) | 15600.ge | 6 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{15600}(53,\cdot)\) | 15600.og | 20 | no | \(1\) | \(1\) | \(i\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(-1\) |
\(\chi_{15600}(59,\cdot)\) | 15600.uq | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{15600}(61,\cdot)\) | 15600.vw | 60 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{15600}(67,\cdot)\) | 15600.vj | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{15600}(71,\cdot)\) | 15600.uk | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{15600}(73,\cdot)\) | 15600.ms | 20 | no | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(i\) |
\(\chi_{15600}(77,\cdot)\) | 15600.ot | 20 | yes | \(1\) | \(1\) | \(i\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(-1\) |
\(\chi_{15600}(79,\cdot)\) | 15600.hy | 10 | no | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) |
\(\chi_{15600}(83,\cdot)\) | 15600.pu | 20 | yes | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(1\) |
\(\chi_{15600}(89,\cdot)\) | 15600.tn | 60 | no | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{15600}(97,\cdot)\) | 15600.vp | 60 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{15600}(101,\cdot)\) | 15600.iq | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(-1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{15600}(103,\cdot)\) | 15600.pi | 20 | no | \(1\) | \(1\) | \(-i\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(i\) |
\(\chi_{15600}(107,\cdot)\) | 15600.kb | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{15600}(109,\cdot)\) | 15600.ni | 20 | no | \(-1\) | \(1\) | \(i\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(-i\) |
\(\chi_{15600}(113,\cdot)\) | 15600.ta | 60 | no | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{15600}(119,\cdot)\) | 15600.tr | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{15600}(121,\cdot)\) | 15600.rv | 30 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{15600}(127,\cdot)\) | 15600.uu | 60 | no | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{11}{12}\right)\) |