sage: H = DirichletGroup(1007)
pari: g = idealstar(,1007,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 936 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{468}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{1007}(743,\cdot)$, $\chi_{1007}(267,\cdot)$ |
First 32 of 936 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{1007}(1,\cdot)\) | 1007.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{1007}(2,\cdot)\) | 1007.bi | 468 | yes | \(1\) | \(1\) | \(e\left(\frac{35}{468}\right)\) | \(e\left(\frac{23}{468}\right)\) | \(e\left(\frac{35}{234}\right)\) | \(e\left(\frac{371}{468}\right)\) | \(e\left(\frac{29}{234}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{35}{156}\right)\) | \(e\left(\frac{23}{234}\right)\) | \(e\left(\frac{203}{234}\right)\) | \(e\left(\frac{61}{78}\right)\) |
| \(\chi_{1007}(3,\cdot)\) | 1007.bi | 468 | yes | \(1\) | \(1\) | \(e\left(\frac{23}{468}\right)\) | \(e\left(\frac{443}{468}\right)\) | \(e\left(\frac{23}{234}\right)\) | \(e\left(\frac{431}{468}\right)\) | \(e\left(\frac{233}{234}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{209}{234}\right)\) | \(e\left(\frac{227}{234}\right)\) | \(e\left(\frac{49}{78}\right)\) |
| \(\chi_{1007}(4,\cdot)\) | 1007.bg | 234 | yes | \(1\) | \(1\) | \(e\left(\frac{35}{234}\right)\) | \(e\left(\frac{23}{234}\right)\) | \(e\left(\frac{35}{117}\right)\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{29}{117}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{23}{117}\right)\) | \(e\left(\frac{86}{117}\right)\) | \(e\left(\frac{22}{39}\right)\) |
| \(\chi_{1007}(5,\cdot)\) | 1007.bj | 468 | yes | \(-1\) | \(1\) | \(e\left(\frac{371}{468}\right)\) | \(e\left(\frac{431}{468}\right)\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{329}{468}\right)\) | \(e\left(\frac{167}{234}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{197}{234}\right)\) | \(e\left(\frac{58}{117}\right)\) | \(e\left(\frac{7}{78}\right)\) |
| \(\chi_{1007}(6,\cdot)\) | 1007.bg | 234 | yes | \(1\) | \(1\) | \(e\left(\frac{29}{234}\right)\) | \(e\left(\frac{233}{234}\right)\) | \(e\left(\frac{29}{117}\right)\) | \(e\left(\frac{167}{234}\right)\) | \(e\left(\frac{14}{117}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{116}{117}\right)\) | \(e\left(\frac{98}{117}\right)\) | \(e\left(\frac{16}{39}\right)\) |
| \(\chi_{1007}(7,\cdot)\) | 1007.z | 78 | yes | \(1\) | \(1\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) |
| \(\chi_{1007}(8,\cdot)\) | 1007.bd | 156 | yes | \(1\) | \(1\) | \(e\left(\frac{35}{156}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{9}{26}\right)\) |
| \(\chi_{1007}(9,\cdot)\) | 1007.bg | 234 | yes | \(1\) | \(1\) | \(e\left(\frac{23}{234}\right)\) | \(e\left(\frac{209}{234}\right)\) | \(e\left(\frac{23}{117}\right)\) | \(e\left(\frac{197}{234}\right)\) | \(e\left(\frac{116}{117}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{92}{117}\right)\) | \(e\left(\frac{110}{117}\right)\) | \(e\left(\frac{10}{39}\right)\) |
| \(\chi_{1007}(10,\cdot)\) | 1007.bf | 234 | yes | \(-1\) | \(1\) | \(e\left(\frac{203}{234}\right)\) | \(e\left(\frac{227}{234}\right)\) | \(e\left(\frac{86}{117}\right)\) | \(e\left(\frac{58}{117}\right)\) | \(e\left(\frac{98}{117}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{110}{117}\right)\) | \(e\left(\frac{85}{234}\right)\) | \(e\left(\frac{34}{39}\right)\) |
| \(\chi_{1007}(11,\cdot)\) | 1007.z | 78 | yes | \(1\) | \(1\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) |
| \(\chi_{1007}(12,\cdot)\) | 1007.bd | 156 | yes | \(1\) | \(1\) | \(e\left(\frac{31}{156}\right)\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{5}{26}\right)\) |
| \(\chi_{1007}(13,\cdot)\) | 1007.bf | 234 | yes | \(-1\) | \(1\) | \(e\left(\frac{173}{234}\right)\) | \(e\left(\frac{107}{234}\right)\) | \(e\left(\frac{56}{117}\right)\) | \(e\left(\frac{16}{117}\right)\) | \(e\left(\frac{23}{117}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{107}{117}\right)\) | \(e\left(\frac{205}{234}\right)\) | \(e\left(\frac{4}{39}\right)\) |
| \(\chi_{1007}(14,\cdot)\) | 1007.bi | 468 | yes | \(1\) | \(1\) | \(e\left(\frac{317}{468}\right)\) | \(e\left(\frac{449}{468}\right)\) | \(e\left(\frac{83}{234}\right)\) | \(e\left(\frac{365}{468}\right)\) | \(e\left(\frac{149}{234}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{215}{234}\right)\) | \(e\left(\frac{107}{234}\right)\) | \(e\left(\frac{31}{78}\right)\) |
| \(\chi_{1007}(15,\cdot)\) | 1007.bf | 234 | yes | \(-1\) | \(1\) | \(e\left(\frac{197}{234}\right)\) | \(e\left(\frac{203}{234}\right)\) | \(e\left(\frac{80}{117}\right)\) | \(e\left(\frac{73}{117}\right)\) | \(e\left(\frac{83}{117}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{86}{117}\right)\) | \(e\left(\frac{109}{234}\right)\) | \(e\left(\frac{28}{39}\right)\) |
| \(\chi_{1007}(16,\cdot)\) | 1007.bc | 117 | yes | \(1\) | \(1\) | \(e\left(\frac{35}{117}\right)\) | \(e\left(\frac{23}{117}\right)\) | \(e\left(\frac{70}{117}\right)\) | \(e\left(\frac{20}{117}\right)\) | \(e\left(\frac{58}{117}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{46}{117}\right)\) | \(e\left(\frac{55}{117}\right)\) | \(e\left(\frac{5}{39}\right)\) |
| \(\chi_{1007}(17,\cdot)\) | 1007.bg | 234 | yes | \(1\) | \(1\) | \(e\left(\frac{175}{234}\right)\) | \(e\left(\frac{115}{234}\right)\) | \(e\left(\frac{58}{117}\right)\) | \(e\left(\frac{217}{234}\right)\) | \(e\left(\frac{28}{117}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{115}{117}\right)\) | \(e\left(\frac{79}{117}\right)\) | \(e\left(\frac{32}{39}\right)\) |
| \(\chi_{1007}(18,\cdot)\) | 1007.y | 52 | yes | \(1\) | \(1\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{1}{26}\right)\) |
| \(\chi_{1007}(20,\cdot)\) | 1007.x | 52 | no | \(-1\) | \(1\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{17}{26}\right)\) |
| \(\chi_{1007}(21,\cdot)\) | 1007.bi | 468 | yes | \(1\) | \(1\) | \(e\left(\frac{305}{468}\right)\) | \(e\left(\frac{401}{468}\right)\) | \(e\left(\frac{71}{234}\right)\) | \(e\left(\frac{425}{468}\right)\) | \(e\left(\frac{119}{234}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{149}{156}\right)\) | \(e\left(\frac{167}{234}\right)\) | \(e\left(\frac{131}{234}\right)\) | \(e\left(\frac{19}{78}\right)\) |
| \(\chi_{1007}(22,\cdot)\) | 1007.bi | 468 | yes | \(1\) | \(1\) | \(e\left(\frac{401}{468}\right)\) | \(e\left(\frac{317}{468}\right)\) | \(e\left(\frac{167}{234}\right)\) | \(e\left(\frac{413}{468}\right)\) | \(e\left(\frac{125}{234}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{83}{234}\right)\) | \(e\left(\frac{173}{234}\right)\) | \(e\left(\frac{37}{78}\right)\) |
| \(\chi_{1007}(23,\cdot)\) | 1007.u | 36 | yes | \(-1\) | \(1\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) |
| \(\chi_{1007}(24,\cdot)\) | 1007.bc | 117 | yes | \(1\) | \(1\) | \(e\left(\frac{32}{117}\right)\) | \(e\left(\frac{11}{117}\right)\) | \(e\left(\frac{64}{117}\right)\) | \(e\left(\frac{35}{117}\right)\) | \(e\left(\frac{43}{117}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{22}{117}\right)\) | \(e\left(\frac{67}{117}\right)\) | \(e\left(\frac{38}{39}\right)\) |
| \(\chi_{1007}(25,\cdot)\) | 1007.bg | 234 | yes | \(1\) | \(1\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{197}{234}\right)\) | \(e\left(\frac{20}{117}\right)\) | \(e\left(\frac{95}{234}\right)\) | \(e\left(\frac{50}{117}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{80}{117}\right)\) | \(e\left(\frac{116}{117}\right)\) | \(e\left(\frac{7}{39}\right)\) |
| \(\chi_{1007}(26,\cdot)\) | 1007.be | 156 | yes | \(-1\) | \(1\) | \(e\left(\frac{127}{156}\right)\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{23}{26}\right)\) |
| \(\chi_{1007}(27,\cdot)\) | 1007.bd | 156 | yes | \(1\) | \(1\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{131}{156}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{119}{156}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{23}{26}\right)\) |
| \(\chi_{1007}(28,\cdot)\) | 1007.bc | 117 | yes | \(1\) | \(1\) | \(e\left(\frac{88}{117}\right)\) | \(e\left(\frac{1}{117}\right)\) | \(e\left(\frac{59}{117}\right)\) | \(e\left(\frac{67}{117}\right)\) | \(e\left(\frac{89}{117}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{2}{117}\right)\) | \(e\left(\frac{38}{117}\right)\) | \(e\left(\frac{7}{39}\right)\) |
| \(\chi_{1007}(29,\cdot)\) | 1007.bh | 234 | yes | \(-1\) | \(1\) | \(e\left(\frac{97}{117}\right)\) | \(e\left(\frac{37}{117}\right)\) | \(e\left(\frac{77}{117}\right)\) | \(e\left(\frac{161}{234}\right)\) | \(e\left(\frac{17}{117}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{74}{117}\right)\) | \(e\left(\frac{121}{234}\right)\) | \(e\left(\frac{25}{39}\right)\) |
| \(\chi_{1007}(30,\cdot)\) | 1007.l | 12 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(-i\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
| \(\chi_{1007}(31,\cdot)\) | 1007.bd | 156 | yes | \(1\) | \(1\) | \(e\left(\frac{73}{156}\right)\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{25}{156}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{49}{78}\right)\) | \(e\left(\frac{21}{26}\right)\) |
| \(\chi_{1007}(32,\cdot)\) | 1007.bi | 468 | yes | \(1\) | \(1\) | \(e\left(\frac{175}{468}\right)\) | \(e\left(\frac{115}{468}\right)\) | \(e\left(\frac{175}{234}\right)\) | \(e\left(\frac{451}{468}\right)\) | \(e\left(\frac{145}{234}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{19}{156}\right)\) | \(e\left(\frac{115}{234}\right)\) | \(e\left(\frac{79}{234}\right)\) | \(e\left(\frac{71}{78}\right)\) |
| \(\chi_{1007}(33,\cdot)\) | 1007.bi | 468 | yes | \(1\) | \(1\) | \(e\left(\frac{389}{468}\right)\) | \(e\left(\frac{269}{468}\right)\) | \(e\left(\frac{155}{234}\right)\) | \(e\left(\frac{5}{468}\right)\) | \(e\left(\frac{95}{234}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{77}{156}\right)\) | \(e\left(\frac{35}{234}\right)\) | \(e\left(\frac{197}{234}\right)\) | \(e\left(\frac{25}{78}\right)\) |