sage: H = DirichletGroup(7098)
pari: g = idealstar(,7098,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 1872 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{6}\times C_{156}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{7098}(4733,\cdot)$, $\chi_{7098}(5071,\cdot)$, $\chi_{7098}(6931,\cdot)$ |
First 32 of 1872 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 | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{7098}(1,\cdot)\) | 7098.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{7098}(5,\cdot)\) | 7098.ed | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{29}{156}\right)\) | \(e\left(\frac{121}{156}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{47}{52}\right)\) |
\(\chi_{7098}(11,\cdot)\) | 7098.ei | 156 | no | \(1\) | \(1\) | \(e\left(\frac{121}{156}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(i\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{83}{156}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{97}{156}\right)\) |
\(\chi_{7098}(17,\cdot)\) | 7098.dh | 78 | no | \(1\) | \(1\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{43}{78}\right)\) |
\(\chi_{7098}(19,\cdot)\) | 7098.by | 12 | no | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(i\) | \(e\left(\frac{2}{3}\right)\) | \(i\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{7098}(23,\cdot)\) | 7098.w | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{7098}(25,\cdot)\) | 7098.df | 78 | no | \(1\) | \(1\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{21}{26}\right)\) |
\(\chi_{7098}(29,\cdot)\) | 7098.dw | 78 | no | \(-1\) | \(1\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{23}{78}\right)\) |
\(\chi_{7098}(31,\cdot)\) | 7098.el | 156 | no | \(1\) | \(1\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{83}{156}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{155}{156}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{49}{52}\right)\) |
\(\chi_{7098}(37,\cdot)\) | 7098.eo | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(-1\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{43}{156}\right)\) |
\(\chi_{7098}(41,\cdot)\) | 7098.ee | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{43}{156}\right)\) | \(e\left(\frac{49}{156}\right)\) |
\(\chi_{7098}(43,\cdot)\) | 7098.dx | 78 | no | \(1\) | \(1\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{37}{78}\right)\) |
\(\chi_{7098}(47,\cdot)\) | 7098.ed | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{67}{156}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{49}{156}\right)\) | \(e\left(\frac{101}{156}\right)\) | \(e\left(\frac{17}{52}\right)\) |
\(\chi_{7098}(53,\cdot)\) | 7098.de | 78 | no | \(-1\) | \(1\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{23}{26}\right)\) |
\(\chi_{7098}(55,\cdot)\) | 7098.dy | 78 | no | \(-1\) | \(1\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{41}{78}\right)\) |
\(\chi_{7098}(59,\cdot)\) | 7098.ep | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{55}{156}\right)\) | \(e\left(\frac{43}{156}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(1\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{137}{156}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{11}{156}\right)\) |
\(\chi_{7098}(61,\cdot)\) | 7098.db | 78 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{61}{78}\right)\) |
\(\chi_{7098}(67,\cdot)\) | 7098.eg | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{73}{156}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(-i\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{101}{156}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{25}{156}\right)\) |
\(\chi_{7098}(71,\cdot)\) | 7098.ek | 156 | no | \(1\) | \(1\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{149}{156}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{95}{156}\right)\) | \(e\left(\frac{23}{156}\right)\) |
\(\chi_{7098}(73,\cdot)\) | 7098.el | 156 | no | \(1\) | \(1\) | \(e\left(\frac{121}{156}\right)\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{43}{78}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{109}{156}\right)\) | \(e\left(\frac{15}{52}\right)\) |
\(\chi_{7098}(79,\cdot)\) | 7098.ct | 39 | no | \(1\) | \(1\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{1}{13}\right)\) |
\(\chi_{7098}(83,\cdot)\) | 7098.cx | 52 | no | \(-1\) | \(1\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(i\) | \(1\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{27}{52}\right)\) |
\(\chi_{7098}(85,\cdot)\) | 7098.eh | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{71}{156}\right)\) |
\(\chi_{7098}(89,\cdot)\) | 7098.bt | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(-1\) | \(e\left(\frac{1}{12}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(-i\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{7098}(95,\cdot)\) | 7098.dt | 78 | no | \(-1\) | \(1\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{32}{39}\right)\) |
\(\chi_{7098}(97,\cdot)\) | 7098.en | 156 | no | \(1\) | \(1\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{35}{156}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{71}{156}\right)\) | \(e\left(\frac{119}{156}\right)\) |
\(\chi_{7098}(101,\cdot)\) | 7098.dc | 78 | no | \(1\) | \(1\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{11}{78}\right)\) |
\(\chi_{7098}(103,\cdot)\) | 7098.dp | 78 | no | \(-1\) | \(1\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{3}{13}\right)\) |
\(\chi_{7098}(107,\cdot)\) | 7098.dg | 78 | no | \(-1\) | \(1\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{77}{78}\right)\) |
\(\chi_{7098}(109,\cdot)\) | 7098.ef | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{3}{52}\right)\) |
\(\chi_{7098}(113,\cdot)\) | 7098.dw | 78 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{73}{78}\right)\) |
\(\chi_{7098}(115,\cdot)\) | 7098.em | 156 | no | \(1\) | \(1\) | \(e\left(\frac{133}{156}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(-i\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{137}{156}\right)\) | \(e\left(\frac{137}{156}\right)\) | \(e\left(\frac{37}{156}\right)\) |