sage: H = DirichletGroup(4725)
pari: g = idealstar(,4725,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 2160 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{6}\times C_{180}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{4725}(4376,\cdot)$, $\chi_{4725}(1702,\cdot)$, $\chi_{4725}(2026,\cdot)$ |
First 32 of 2160 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(23\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{4725}(1,\cdot)\) | 4725.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{4725}(2,\cdot)\) | 4725.hc | 180 | yes | \(1\) | \(1\) | \(e\left(\frac{139}{180}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{71}{180}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{113}{180}\right)\) | \(e\left(\frac{149}{180}\right)\) |
\(\chi_{4725}(4,\cdot)\) | 4725.gg | 90 | yes | \(1\) | \(1\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{59}{90}\right)\) |
\(\chi_{4725}(8,\cdot)\) | 4725.fs | 60 | no | \(1\) | \(1\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{29}{60}\right)\) |
\(\chi_{4725}(11,\cdot)\) | 4725.go | 90 | yes | \(-1\) | \(1\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{7}{90}\right)\) |
\(\chi_{4725}(13,\cdot)\) | 4725.he | 180 | yes | \(1\) | \(1\) | \(e\left(\frac{71}{180}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{19}{180}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{67}{180}\right)\) | \(e\left(\frac{61}{180}\right)\) |
\(\chi_{4725}(16,\cdot)\) | 4725.fl | 45 | yes | \(1\) | \(1\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{14}{45}\right)\) |
\(\chi_{4725}(17,\cdot)\) | 4725.fy | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{13}{20}\right)\) |
\(\chi_{4725}(19,\cdot)\) | 4725.ea | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) |
\(\chi_{4725}(22,\cdot)\) | 4725.hd | 180 | no | \(-1\) | \(1\) | \(e\left(\frac{113}{180}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{67}{180}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{61}{180}\right)\) | \(e\left(\frac{163}{180}\right)\) |
\(\chi_{4725}(23,\cdot)\) | 4725.hj | 180 | yes | \(1\) | \(1\) | \(e\left(\frac{149}{180}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{61}{180}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{163}{180}\right)\) | \(e\left(\frac{79}{180}\right)\) |
\(\chi_{4725}(26,\cdot)\) | 4725.bk | 6 | no | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{4725}(29,\cdot)\) | 4725.gu | 90 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{32}{45}\right)\) |
\(\chi_{4725}(31,\cdot)\) | 4725.gs | 90 | yes | \(-1\) | \(1\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{43}{45}\right)\) |
\(\chi_{4725}(32,\cdot)\) | 4725.fg | 36 | no | \(1\) | \(1\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{5}{36}\right)\) |
\(\chi_{4725}(34,\cdot)\) | 4725.gj | 90 | yes | \(-1\) | \(1\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{43}{90}\right)\) |
\(\chi_{4725}(37,\cdot)\) | 4725.gb | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{17}{60}\right)\) |
\(\chi_{4725}(38,\cdot)\) | 4725.gy | 180 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{180}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{59}{180}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{47}{180}\right)\) | \(e\left(\frac{131}{180}\right)\) |
\(\chi_{4725}(41,\cdot)\) | 4725.gm | 90 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{53}{90}\right)\) |
\(\chi_{4725}(43,\cdot)\) | 4725.fh | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{25}{36}\right)\) |
\(\chi_{4725}(44,\cdot)\) | 4725.dw | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) |
\(\chi_{4725}(46,\cdot)\) | 4725.ct | 15 | no | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) |
\(\chi_{4725}(47,\cdot)\) | 4725.hf | 180 | yes | \(-1\) | \(1\) | \(e\left(\frac{163}{180}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{137}{180}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{161}{180}\right)\) | \(e\left(\frac{53}{180}\right)\) |
\(\chi_{4725}(52,\cdot)\) | 4725.gz | 180 | yes | \(1\) | \(1\) | \(e\left(\frac{169}{180}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{161}{180}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{113}{180}\right)\) | \(e\left(\frac{179}{180}\right)\) |
\(\chi_{4725}(53,\cdot)\) | 4725.fq | 60 | no | \(1\) | \(1\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{41}{60}\right)\) |
\(\chi_{4725}(58,\cdot)\) | 4725.hi | 180 | yes | \(-1\) | \(1\) | \(e\left(\frac{167}{180}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{133}{180}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{19}{180}\right)\) | \(e\left(\frac{97}{180}\right)\) |
\(\chi_{4725}(59,\cdot)\) | 4725.gr | 90 | yes | \(1\) | \(1\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{4}{45}\right)\) |
\(\chi_{4725}(61,\cdot)\) | 4725.gs | 90 | yes | \(-1\) | \(1\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{11}{45}\right)\) |
\(\chi_{4725}(62,\cdot)\) | 4725.fp | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{47}{60}\right)\) |
\(\chi_{4725}(64,\cdot)\) | 4725.eg | 30 | no | \(1\) | \(1\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) |
\(\chi_{4725}(67,\cdot)\) | 4725.hb | 180 | yes | \(-1\) | \(1\) | \(e\left(\frac{77}{180}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{163}{180}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{49}{180}\right)\) | \(e\left(\frac{67}{180}\right)\) |
\(\chi_{4725}(68,\cdot)\) | 4725.fi | 36 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{36}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(-i\) | \(1\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{11}{36}\right)\) |