sage: H = DirichletGroup(715)
pari: g = idealstar(,715,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 480 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{4}\times C_{60}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{715}(287,\cdot)$, $\chi_{715}(651,\cdot)$, $\chi_{715}(496,\cdot)$ |
First 32 of 480 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(14\) | \(16\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{715}(1,\cdot)\) | 715.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{715}(2,\cdot)\) | 715.cr | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(-i\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{11}{15}\right)\) |
\(\chi_{715}(3,\cdot)\) | 715.cw | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(-i\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{8}{15}\right)\) |
\(\chi_{715}(4,\cdot)\) | 715.cn | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(-1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{15}\right)\) |
\(\chi_{715}(6,\cdot)\) | 715.cz | 60 | no | \(1\) | \(1\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(-1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{15}\right)\) |
\(\chi_{715}(7,\cdot)\) | 715.db | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(-i\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{15}\right)\) |
\(\chi_{715}(8,\cdot)\) | 715.ch | 20 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(i\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{715}(9,\cdot)\) | 715.cj | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{15}\right)\) |
\(\chi_{715}(12,\cdot)\) | 715.n | 4 | no | \(-1\) | \(1\) | \(-i\) | \(-i\) | \(-1\) | \(-1\) | \(-i\) | \(i\) | \(-1\) | \(i\) | \(-1\) | \(1\) |
\(\chi_{715}(14,\cdot)\) | 715.bj | 10 | no | \(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(-1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{715}(16,\cdot)\) | 715.bw | 15 | no | \(1\) | \(1\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{14}{15}\right)\) |
\(\chi_{715}(17,\cdot)\) | 715.cx | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(i\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{15}\right)\) |
\(\chi_{715}(18,\cdot)\) | 715.bx | 20 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(i\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{715}(19,\cdot)\) | 715.cs | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{13}{15}\right)\) |
\(\chi_{715}(21,\cdot)\) | 715.s | 4 | no | \(1\) | \(1\) | \(-i\) | \(1\) | \(-1\) | \(-i\) | \(i\) | \(i\) | \(1\) | \(-1\) | \(1\) | \(1\) |
\(\chi_{715}(23,\cdot)\) | 715.br | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(-i\) | \(e\left(\frac{1}{6}\right)\) | \(-i\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{715}(24,\cdot)\) | 715.cs | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{15}\right)\) |
\(\chi_{715}(27,\cdot)\) | 715.cc | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(i\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{715}(28,\cdot)\) | 715.db | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(i\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{14}{15}\right)\) |
\(\chi_{715}(29,\cdot)\) | 715.co | 30 | yes | \(-1\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(-1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{15}\right)\) |
\(\chi_{715}(31,\cdot)\) | 715.ca | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{715}(32,\cdot)\) | 715.bu | 12 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-i\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{715}(34,\cdot)\) | 715.m | 4 | no | \(-1\) | \(1\) | \(-i\) | \(-1\) | \(-1\) | \(i\) | \(i\) | \(i\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{715}(36,\cdot)\) | 715.cm | 30 | no | \(1\) | \(1\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{8}{15}\right)\) |
\(\chi_{715}(37,\cdot)\) | 715.cq | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(-i\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{15}\right)\) |
\(\chi_{715}(38,\cdot)\) | 715.ce | 20 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(-i\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{715}(41,\cdot)\) | 715.cz | 60 | no | \(1\) | \(1\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(-1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{8}{15}\right)\) |
\(\chi_{715}(42,\cdot)\) | 715.cw | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(i\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{11}{15}\right)\) |
\(\chi_{715}(43,\cdot)\) | 715.bo | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(i\) | \(e\left(\frac{5}{6}\right)\) | \(-i\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{715}(46,\cdot)\) | 715.cz | 60 | no | \(1\) | \(1\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{15}\right)\) |
\(\chi_{715}(47,\cdot)\) | 715.ci | 20 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(-i\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{715}(48,\cdot)\) | 715.cw | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(-i\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{15}\right)\) |