from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3267, base_ring=CyclotomicField(198))
M = H._module
chi = DirichletCharacter(H, M([176,90]))
chi.galois_orbit()
[g,chi] = znchar(Mod(34,3267))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(3267\) | |
| Conductor: | \(3267\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(99\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{99})$ |
| Fixed field: | Number field defined by a degree 99 polynomial |
First 31 of 60 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{3267}(34,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{34}{99}\right)\) | \(e\left(\frac{68}{99}\right)\) | \(e\left(\frac{8}{99}\right)\) | \(e\left(\frac{40}{99}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{2}{99}\right)\) | \(e\left(\frac{74}{99}\right)\) | \(e\left(\frac{37}{99}\right)\) | \(e\left(\frac{20}{33}\right)\) |
| \(\chi_{3267}(67,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{35}{99}\right)\) | \(e\left(\frac{70}{99}\right)\) | \(e\left(\frac{49}{99}\right)\) | \(e\left(\frac{47}{99}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{37}{99}\right)\) | \(e\left(\frac{82}{99}\right)\) | \(e\left(\frac{41}{99}\right)\) | \(e\left(\frac{7}{33}\right)\) |
| \(\chi_{3267}(133,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{99}\right)\) | \(e\left(\frac{74}{99}\right)\) | \(e\left(\frac{32}{99}\right)\) | \(e\left(\frac{61}{99}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{8}{99}\right)\) | \(e\left(\frac{98}{99}\right)\) | \(e\left(\frac{49}{99}\right)\) | \(e\left(\frac{14}{33}\right)\) |
| \(\chi_{3267}(166,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{38}{99}\right)\) | \(e\left(\frac{76}{99}\right)\) | \(e\left(\frac{73}{99}\right)\) | \(e\left(\frac{68}{99}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{43}{99}\right)\) | \(e\left(\frac{7}{99}\right)\) | \(e\left(\frac{53}{99}\right)\) | \(e\left(\frac{1}{33}\right)\) |
| \(\chi_{3267}(232,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{40}{99}\right)\) | \(e\left(\frac{80}{99}\right)\) | \(e\left(\frac{56}{99}\right)\) | \(e\left(\frac{82}{99}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{14}{99}\right)\) | \(e\left(\frac{23}{99}\right)\) | \(e\left(\frac{61}{99}\right)\) | \(e\left(\frac{8}{33}\right)\) |
| \(\chi_{3267}(265,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{99}\right)\) | \(e\left(\frac{82}{99}\right)\) | \(e\left(\frac{97}{99}\right)\) | \(e\left(\frac{89}{99}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{49}{99}\right)\) | \(e\left(\frac{31}{99}\right)\) | \(e\left(\frac{65}{99}\right)\) | \(e\left(\frac{28}{33}\right)\) |
| \(\chi_{3267}(331,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{99}\right)\) | \(e\left(\frac{86}{99}\right)\) | \(e\left(\frac{80}{99}\right)\) | \(e\left(\frac{4}{99}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{20}{99}\right)\) | \(e\left(\frac{47}{99}\right)\) | \(e\left(\frac{73}{99}\right)\) | \(e\left(\frac{2}{33}\right)\) |
| \(\chi_{3267}(430,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{46}{99}\right)\) | \(e\left(\frac{92}{99}\right)\) | \(e\left(\frac{5}{99}\right)\) | \(e\left(\frac{25}{99}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{26}{99}\right)\) | \(e\left(\frac{71}{99}\right)\) | \(e\left(\frac{85}{99}\right)\) | \(e\left(\frac{29}{33}\right)\) |
| \(\chi_{3267}(463,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{99}\right)\) | \(e\left(\frac{94}{99}\right)\) | \(e\left(\frac{46}{99}\right)\) | \(e\left(\frac{32}{99}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{61}{99}\right)\) | \(e\left(\frac{79}{99}\right)\) | \(e\left(\frac{89}{99}\right)\) | \(e\left(\frac{16}{33}\right)\) |
| \(\chi_{3267}(529,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{99}\right)\) | \(e\left(\frac{98}{99}\right)\) | \(e\left(\frac{29}{99}\right)\) | \(e\left(\frac{46}{99}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{32}{99}\right)\) | \(e\left(\frac{95}{99}\right)\) | \(e\left(\frac{97}{99}\right)\) | \(e\left(\frac{23}{33}\right)\) |
| \(\chi_{3267}(562,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{50}{99}\right)\) | \(e\left(\frac{1}{99}\right)\) | \(e\left(\frac{70}{99}\right)\) | \(e\left(\frac{53}{99}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{67}{99}\right)\) | \(e\left(\frac{4}{99}\right)\) | \(e\left(\frac{2}{99}\right)\) | \(e\left(\frac{10}{33}\right)\) |
| \(\chi_{3267}(628,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{52}{99}\right)\) | \(e\left(\frac{5}{99}\right)\) | \(e\left(\frac{53}{99}\right)\) | \(e\left(\frac{67}{99}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{38}{99}\right)\) | \(e\left(\frac{20}{99}\right)\) | \(e\left(\frac{10}{99}\right)\) | \(e\left(\frac{17}{33}\right)\) |
| \(\chi_{3267}(661,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{99}\right)\) | \(e\left(\frac{7}{99}\right)\) | \(e\left(\frac{94}{99}\right)\) | \(e\left(\frac{74}{99}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{73}{99}\right)\) | \(e\left(\frac{28}{99}\right)\) | \(e\left(\frac{14}{99}\right)\) | \(e\left(\frac{4}{33}\right)\) |
| \(\chi_{3267}(760,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{56}{99}\right)\) | \(e\left(\frac{13}{99}\right)\) | \(e\left(\frac{19}{99}\right)\) | \(e\left(\frac{95}{99}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{79}{99}\right)\) | \(e\left(\frac{52}{99}\right)\) | \(e\left(\frac{26}{99}\right)\) | \(e\left(\frac{31}{33}\right)\) |
| \(\chi_{3267}(826,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{58}{99}\right)\) | \(e\left(\frac{17}{99}\right)\) | \(e\left(\frac{2}{99}\right)\) | \(e\left(\frac{10}{99}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{50}{99}\right)\) | \(e\left(\frac{68}{99}\right)\) | \(e\left(\frac{34}{99}\right)\) | \(e\left(\frac{5}{33}\right)\) |
| \(\chi_{3267}(859,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{99}\right)\) | \(e\left(\frac{19}{99}\right)\) | \(e\left(\frac{43}{99}\right)\) | \(e\left(\frac{17}{99}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{85}{99}\right)\) | \(e\left(\frac{76}{99}\right)\) | \(e\left(\frac{38}{99}\right)\) | \(e\left(\frac{25}{33}\right)\) |
| \(\chi_{3267}(925,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{99}\right)\) | \(e\left(\frac{23}{99}\right)\) | \(e\left(\frac{26}{99}\right)\) | \(e\left(\frac{31}{99}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{56}{99}\right)\) | \(e\left(\frac{92}{99}\right)\) | \(e\left(\frac{46}{99}\right)\) | \(e\left(\frac{32}{33}\right)\) |
| \(\chi_{3267}(958,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{62}{99}\right)\) | \(e\left(\frac{25}{99}\right)\) | \(e\left(\frac{67}{99}\right)\) | \(e\left(\frac{38}{99}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{91}{99}\right)\) | \(e\left(\frac{1}{99}\right)\) | \(e\left(\frac{50}{99}\right)\) | \(e\left(\frac{19}{33}\right)\) |
| \(\chi_{3267}(1024,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{64}{99}\right)\) | \(e\left(\frac{29}{99}\right)\) | \(e\left(\frac{50}{99}\right)\) | \(e\left(\frac{52}{99}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{62}{99}\right)\) | \(e\left(\frac{17}{99}\right)\) | \(e\left(\frac{58}{99}\right)\) | \(e\left(\frac{26}{33}\right)\) |
| \(\chi_{3267}(1057,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{65}{99}\right)\) | \(e\left(\frac{31}{99}\right)\) | \(e\left(\frac{91}{99}\right)\) | \(e\left(\frac{59}{99}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{97}{99}\right)\) | \(e\left(\frac{25}{99}\right)\) | \(e\left(\frac{62}{99}\right)\) | \(e\left(\frac{13}{33}\right)\) |
| \(\chi_{3267}(1123,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{99}\right)\) | \(e\left(\frac{35}{99}\right)\) | \(e\left(\frac{74}{99}\right)\) | \(e\left(\frac{73}{99}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{68}{99}\right)\) | \(e\left(\frac{41}{99}\right)\) | \(e\left(\frac{70}{99}\right)\) | \(e\left(\frac{20}{33}\right)\) |
| \(\chi_{3267}(1156,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{68}{99}\right)\) | \(e\left(\frac{37}{99}\right)\) | \(e\left(\frac{16}{99}\right)\) | \(e\left(\frac{80}{99}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{28}{33}\right)\) | \(e\left(\frac{4}{99}\right)\) | \(e\left(\frac{49}{99}\right)\) | \(e\left(\frac{74}{99}\right)\) | \(e\left(\frac{7}{33}\right)\) |
| \(\chi_{3267}(1222,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{70}{99}\right)\) | \(e\left(\frac{41}{99}\right)\) | \(e\left(\frac{98}{99}\right)\) | \(e\left(\frac{94}{99}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{74}{99}\right)\) | \(e\left(\frac{65}{99}\right)\) | \(e\left(\frac{82}{99}\right)\) | \(e\left(\frac{14}{33}\right)\) |
| \(\chi_{3267}(1255,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{99}\right)\) | \(e\left(\frac{43}{99}\right)\) | \(e\left(\frac{40}{99}\right)\) | \(e\left(\frac{2}{99}\right)\) | \(e\left(\frac{5}{33}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{10}{99}\right)\) | \(e\left(\frac{73}{99}\right)\) | \(e\left(\frac{86}{99}\right)\) | \(e\left(\frac{1}{33}\right)\) |
| \(\chi_{3267}(1321,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{99}\right)\) | \(e\left(\frac{47}{99}\right)\) | \(e\left(\frac{23}{99}\right)\) | \(e\left(\frac{16}{99}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{80}{99}\right)\) | \(e\left(\frac{89}{99}\right)\) | \(e\left(\frac{94}{99}\right)\) | \(e\left(\frac{8}{33}\right)\) |
| \(\chi_{3267}(1354,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{74}{99}\right)\) | \(e\left(\frac{49}{99}\right)\) | \(e\left(\frac{64}{99}\right)\) | \(e\left(\frac{23}{99}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{16}{99}\right)\) | \(e\left(\frac{97}{99}\right)\) | \(e\left(\frac{98}{99}\right)\) | \(e\left(\frac{28}{33}\right)\) |
| \(\chi_{3267}(1420,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{76}{99}\right)\) | \(e\left(\frac{53}{99}\right)\) | \(e\left(\frac{47}{99}\right)\) | \(e\left(\frac{37}{99}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{8}{33}\right)\) | \(e\left(\frac{86}{99}\right)\) | \(e\left(\frac{14}{99}\right)\) | \(e\left(\frac{7}{99}\right)\) | \(e\left(\frac{2}{33}\right)\) |
| \(\chi_{3267}(1519,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{99}\right)\) | \(e\left(\frac{59}{99}\right)\) | \(e\left(\frac{71}{99}\right)\) | \(e\left(\frac{58}{99}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{92}{99}\right)\) | \(e\left(\frac{38}{99}\right)\) | \(e\left(\frac{19}{99}\right)\) | \(e\left(\frac{29}{33}\right)\) |
| \(\chi_{3267}(1552,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{80}{99}\right)\) | \(e\left(\frac{61}{99}\right)\) | \(e\left(\frac{13}{99}\right)\) | \(e\left(\frac{65}{99}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{28}{99}\right)\) | \(e\left(\frac{46}{99}\right)\) | \(e\left(\frac{23}{99}\right)\) | \(e\left(\frac{16}{33}\right)\) |
| \(\chi_{3267}(1618,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{82}{99}\right)\) | \(e\left(\frac{65}{99}\right)\) | \(e\left(\frac{95}{99}\right)\) | \(e\left(\frac{79}{99}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{26}{33}\right)\) | \(e\left(\frac{98}{99}\right)\) | \(e\left(\frac{62}{99}\right)\) | \(e\left(\frac{31}{99}\right)\) | \(e\left(\frac{23}{33}\right)\) |
| \(\chi_{3267}(1651,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{99}\right)\) | \(e\left(\frac{67}{99}\right)\) | \(e\left(\frac{37}{99}\right)\) | \(e\left(\frac{86}{99}\right)\) | \(e\left(\frac{17}{33}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{34}{99}\right)\) | \(e\left(\frac{70}{99}\right)\) | \(e\left(\frac{35}{99}\right)\) | \(e\left(\frac{10}{33}\right)\) |