sage: H = DirichletGroup(3724)
pari: g = idealstar(,3724,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 1512 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{6}\times C_{126}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{3724}(1863,\cdot)$, $\chi_{3724}(3041,\cdot)$, $\chi_{3724}(3137,\cdot)$ |
First 32 of 1512 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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{3724}(1,\cdot)\) | 3724.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{3724}(3,\cdot)\) | 3724.eg | 126 | yes | \(-1\) | \(1\) | \(e\left(\frac{115}{126}\right)\) | \(e\left(\frac{31}{126}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{103}{126}\right)\) | \(e\left(\frac{107}{126}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{31}{42}\right)\) |
\(\chi_{3724}(5,\cdot)\) | 3724.ee | 126 | no | \(-1\) | \(1\) | \(e\left(\frac{31}{126}\right)\) | \(e\left(\frac{31}{126}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{31}{42}\right)\) |
\(\chi_{3724}(9,\cdot)\) | 3724.ec | 63 | no | \(1\) | \(1\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{10}{21}\right)\) |
\(\chi_{3724}(11,\cdot)\) | 3724.db | 42 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{5}{14}\right)\) |
\(\chi_{3724}(13,\cdot)\) | 3724.es | 126 | no | \(1\) | \(1\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{79}{126}\right)\) | \(e\left(\frac{53}{126}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{4}{21}\right)\) |
\(\chi_{3724}(15,\cdot)\) | 3724.el | 126 | yes | \(1\) | \(1\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{79}{126}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{109}{126}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{10}{21}\right)\) |
\(\chi_{3724}(17,\cdot)\) | 3724.ep | 126 | no | \(-1\) | \(1\) | \(e\left(\frac{103}{126}\right)\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{40}{63}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{53}{126}\right)\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{55}{126}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{19}{42}\right)\) |
\(\chi_{3724}(23,\cdot)\) | 3724.eh | 126 | yes | \(-1\) | \(1\) | \(e\left(\frac{107}{126}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{109}{126}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{13}{126}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{23}{42}\right)\) |
\(\chi_{3724}(25,\cdot)\) | 3724.ea | 63 | no | \(1\) | \(1\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{62}{63}\right)\) | \(e\left(\frac{10}{21}\right)\) |
\(\chi_{3724}(27,\cdot)\) | 3724.dg | 42 | yes | \(-1\) | \(1\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{3}{14}\right)\) |
\(\chi_{3724}(29,\cdot)\) | 3724.er | 126 | no | \(-1\) | \(1\) | \(e\left(\frac{89}{126}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{109}{126}\right)\) | \(e\left(\frac{31}{126}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{5}{42}\right)\) |
\(\chi_{3724}(31,\cdot)\) | 3724.p | 6 | no | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
\(\chi_{3724}(33,\cdot)\) | 3724.ef | 126 | no | \(1\) | \(1\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{67}{126}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{37}{126}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{2}{21}\right)\) |
\(\chi_{3724}(37,\cdot)\) | 3724.dj | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{11}{14}\right)\) |
\(\chi_{3724}(39,\cdot)\) | 3724.di | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{13}{14}\right)\) |
\(\chi_{3724}(41,\cdot)\) | 3724.es | 126 | no | \(1\) | \(1\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{115}{126}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{83}{126}\right)\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{5}{21}\right)\) |
\(\chi_{3724}(43,\cdot)\) | 3724.ei | 126 | yes | \(-1\) | \(1\) | \(e\left(\frac{25}{126}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{89}{126}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{25}{42}\right)\) |
\(\chi_{3724}(45,\cdot)\) | 3724.dx | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{3}{14}\right)\) |
\(\chi_{3724}(47,\cdot)\) | 3724.en | 126 | yes | \(1\) | \(1\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{121}{126}\right)\) | \(e\left(\frac{53}{126}\right)\) | \(e\left(\frac{115}{126}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{4}{21}\right)\) |
\(\chi_{3724}(51,\cdot)\) | 3724.em | 126 | yes | \(1\) | \(1\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{103}{126}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{73}{126}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{4}{21}\right)\) |
\(\chi_{3724}(53,\cdot)\) | 3724.ed | 126 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{115}{126}\right)\) | \(e\left(\frac{109}{126}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{23}{42}\right)\) |
\(\chi_{3724}(55,\cdot)\) | 3724.ek | 126 | yes | \(1\) | \(1\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{67}{126}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{125}{126}\right)\) | \(e\left(\frac{113}{126}\right)\) | \(e\left(\frac{79}{126}\right)\) | \(e\left(\frac{5}{126}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{2}{21}\right)\) |
\(\chi_{3724}(59,\cdot)\) | 3724.eg | 126 | yes | \(-1\) | \(1\) | \(e\left(\frac{67}{126}\right)\) | \(e\left(\frac{109}{126}\right)\) | \(e\left(\frac{4}{63}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{25}{63}\right)\) | \(e\left(\frac{37}{126}\right)\) | \(e\left(\frac{47}{126}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{25}{42}\right)\) |
\(\chi_{3724}(61,\cdot)\) | 3724.ep | 126 | no | \(-1\) | \(1\) | \(e\left(\frac{89}{126}\right)\) | \(e\left(\frac{47}{126}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{25}{126}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{83}{126}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{5}{42}\right)\) |
\(\chi_{3724}(65,\cdot)\) | 3724.dz | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{13}{14}\right)\) |
\(\chi_{3724}(67,\cdot)\) | 3724.ca | 18 | no | \(1\) | \(1\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(-1\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{3724}(69,\cdot)\) | 3724.do | 42 | no | \(1\) | \(1\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) |
\(\chi_{3724}(71,\cdot)\) | 3724.el | 126 | yes | \(1\) | \(1\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{101}{126}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{125}{126}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{8}{21}\right)\) |
\(\chi_{3724}(73,\cdot)\) | 3724.ep | 126 | no | \(-1\) | \(1\) | \(e\left(\frac{97}{126}\right)\) | \(e\left(\frac{13}{126}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{31}{126}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{13}{42}\right)\) |
\(\chi_{3724}(75,\cdot)\) | 3724.de | 42 | yes | \(-1\) | \(1\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{3}{14}\right)\) |
\(\chi_{3724}(79,\cdot)\) | 3724.ca | 18 | no | \(1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(-1\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) |