sage: H = DirichletGroup(633)
pari: g = idealstar(,633,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 420 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{210}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{633}(212,\cdot)$, $\chi_{633}(424,\cdot)$ |
First 32 of 420 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{633}(1,\cdot)\) | 633.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{633}(2,\cdot)\) | 633.bd | 210 | yes | \(1\) | \(1\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{139}{210}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{105}\right)\) |
\(\chi_{633}(4,\cdot)\) | 633.bc | 105 | no | \(1\) | \(1\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{105}\right)\) |
\(\chi_{633}(5,\cdot)\) | 633.z | 70 | yes | \(-1\) | \(1\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(-1\) | \(e\left(\frac{18}{35}\right)\) |
\(\chi_{633}(7,\cdot)\) | 633.bf | 210 | no | \(-1\) | \(1\) | \(e\left(\frac{139}{210}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{1}{210}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{68}{105}\right)\) |
\(\chi_{633}(8,\cdot)\) | 633.bb | 70 | yes | \(1\) | \(1\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(-1\) | \(e\left(\frac{2}{35}\right)\) |
\(\chi_{633}(10,\cdot)\) | 633.s | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{8}{15}\right)\) |
\(\chi_{633}(11,\cdot)\) | 633.z | 70 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(-1\) | \(e\left(\frac{3}{35}\right)\) |
\(\chi_{633}(13,\cdot)\) | 633.v | 35 | no | \(1\) | \(1\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(1\) | \(e\left(\frac{26}{35}\right)\) |
\(\chi_{633}(14,\cdot)\) | 633.h | 6 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{633}(16,\cdot)\) | 633.bc | 105 | no | \(1\) | \(1\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{8}{105}\right)\) |
\(\chi_{633}(17,\cdot)\) | 633.bd | 210 | yes | \(1\) | \(1\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{151}{210}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{83}{105}\right)\) |
\(\chi_{633}(19,\cdot)\) | 633.q | 15 | no | \(1\) | \(1\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{14}{15}\right)\) |
\(\chi_{633}(20,\cdot)\) | 633.be | 210 | yes | \(-1\) | \(1\) | \(e\left(\frac{29}{210}\right)\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{58}{105}\right)\) |
\(\chi_{633}(22,\cdot)\) | 633.bf | 210 | no | \(-1\) | \(1\) | \(e\left(\frac{163}{210}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{187}{210}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{105}\right)\) |
\(\chi_{633}(23,\cdot)\) | 633.k | 10 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(-1\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{633}(25,\cdot)\) | 633.v | 35 | no | \(1\) | \(1\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(1\) | \(e\left(\frac{1}{35}\right)\) |
\(\chi_{633}(26,\cdot)\) | 633.y | 42 | yes | \(1\) | \(1\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{16}{21}\right)\) |
\(\chi_{633}(28,\cdot)\) | 633.ba | 70 | no | \(-1\) | \(1\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(1\) | \(e\left(\frac{24}{35}\right)\) |
\(\chi_{633}(29,\cdot)\) | 633.bd | 210 | yes | \(1\) | \(1\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{101}{210}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{43}{105}\right)\) |
\(\chi_{633}(31,\cdot)\) | 633.w | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{4}{21}\right)\) |
\(\chi_{633}(32,\cdot)\) | 633.y | 42 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{21}\right)\) |
\(\chi_{633}(34,\cdot)\) | 633.r | 21 | no | \(1\) | \(1\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{17}{21}\right)\) |
\(\chi_{633}(35,\cdot)\) | 633.bd | 210 | yes | \(1\) | \(1\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{79}{210}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{17}{105}\right)\) |
\(\chi_{633}(37,\cdot)\) | 633.bc | 105 | no | \(1\) | \(1\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{26}{105}\right)\) |
\(\chi_{633}(38,\cdot)\) | 633.y | 42 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{20}{21}\right)\) |
\(\chi_{633}(40,\cdot)\) | 633.o | 14 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(-1\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(1\) | \(e\left(\frac{4}{7}\right)\) |
\(\chi_{633}(41,\cdot)\) | 633.bd | 210 | yes | \(1\) | \(1\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{53}{210}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{34}{105}\right)\) |
\(\chi_{633}(43,\cdot)\) | 633.r | 21 | no | \(1\) | \(1\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{21}\right)\) |
\(\chi_{633}(44,\cdot)\) | 633.be | 210 | yes | \(-1\) | \(1\) | \(e\left(\frac{59}{210}\right)\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{105}\right)\) |
\(\chi_{633}(46,\cdot)\) | 633.bc | 105 | no | \(1\) | \(1\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{44}{105}\right)\) |
\(\chi_{633}(47,\cdot)\) | 633.be | 210 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{210}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{8}{105}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{38}{105}\right)\) |