from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, base_ring=CyclotomicField(468))
M = H._module
chi = DirichletCharacter(H, M([399,286]))
chi.galois_orbit()
[g,chi] = znchar(Mod(15,6422))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(6422\) | |
| Conductor: | \(3211\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(468\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 3211.dr | 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: | $\Q(\zeta_{468})$ |
| Fixed field: | Number field defined by a degree 468 polynomial (not computed) |
First 31 of 144 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{6422}(15,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{155}{234}\right)\) | \(e\left(\frac{211}{468}\right)\) | \(e\left(\frac{139}{156}\right)\) | \(e\left(\frac{38}{117}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{53}{468}\right)\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{259}{468}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{211}{234}\right)\) |
| \(\chi_{6422}(33,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{115}{234}\right)\) | \(e\left(\frac{149}{468}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{115}{117}\right)\) | \(e\left(\frac{85}{156}\right)\) | \(e\left(\frac{379}{468}\right)\) | \(e\left(\frac{79}{234}\right)\) | \(e\left(\frac{245}{468}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{149}{234}\right)\) |
| \(\chi_{6422}(59,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{127}{234}\right)\) | \(e\left(\frac{425}{468}\right)\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{10}{117}\right)\) | \(e\left(\frac{121}{156}\right)\) | \(e\left(\frac{211}{468}\right)\) | \(e\left(\frac{73}{234}\right)\) | \(e\left(\frac{413}{468}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{191}{234}\right)\) |
| \(\chi_{6422}(67,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{161}{234}\right)\) | \(e\left(\frac{115}{468}\right)\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{44}{117}\right)\) | \(e\left(\frac{119}{156}\right)\) | \(e\left(\frac{437}{468}\right)\) | \(e\left(\frac{17}{234}\right)\) | \(e\left(\frac{343}{468}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{115}{234}\right)\) |
| \(\chi_{6422}(71,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{223}{234}\right)\) | \(e\left(\frac{59}{468}\right)\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{106}{117}\right)\) | \(e\left(\frac{19}{156}\right)\) | \(e\left(\frac{37}{468}\right)\) | \(e\left(\frac{25}{234}\right)\) | \(e\left(\frac{119}{468}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{59}{234}\right)\) |
| \(\chi_{6422}(97,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{55}{234}\right)\) | \(e\left(\frac{407}{468}\right)\) | \(e\left(\frac{155}{156}\right)\) | \(e\left(\frac{55}{117}\right)\) | \(e\left(\frac{139}{156}\right)\) | \(e\left(\frac{49}{468}\right)\) | \(e\left(\frac{109}{234}\right)\) | \(e\left(\frac{107}{468}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{173}{234}\right)\) |
| \(\chi_{6422}(167,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{173}{234}\right)\) | \(e\left(\frac{157}{468}\right)\) | \(e\left(\frac{133}{156}\right)\) | \(e\left(\frac{56}{117}\right)\) | \(e\left(\frac{77}{156}\right)\) | \(e\left(\frac{35}{468}\right)\) | \(e\left(\frac{11}{234}\right)\) | \(e\left(\frac{277}{468}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{157}{234}\right)\) |
| \(\chi_{6422}(219,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{234}\right)\) | \(e\left(\frac{97}{468}\right)\) | \(e\left(\frac{109}{156}\right)\) | \(e\left(\frac{89}{117}\right)\) | \(e\left(\frac{137}{156}\right)\) | \(e\left(\frac{275}{468}\right)\) | \(e\left(\frac{53}{234}\right)\) | \(e\left(\frac{37}{468}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{97}{234}\right)\) |
| \(\chi_{6422}(345,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{234}\right)\) | \(e\left(\frac{341}{468}\right)\) | \(e\left(\frac{113}{156}\right)\) | \(e\left(\frac{103}{117}\right)\) | \(e\left(\frac{49}{156}\right)\) | \(e\left(\frac{79}{468}\right)\) | \(e\left(\frac{85}{234}\right)\) | \(e\left(\frac{77}{468}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{107}{234}\right)\) |
| \(\chi_{6422}(383,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{157}{234}\right)\) | \(e\left(\frac{179}{468}\right)\) | \(e\left(\frac{95}{156}\right)\) | \(e\left(\frac{40}{117}\right)\) | \(e\left(\frac{55}{156}\right)\) | \(e\left(\frac{25}{468}\right)\) | \(e\left(\frac{175}{234}\right)\) | \(e\left(\frac{131}{468}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{179}{234}\right)\) |
| \(\chi_{6422}(431,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{203}{234}\right)\) | \(e\left(\frac{379}{468}\right)\) | \(e\left(\frac{19}{156}\right)\) | \(e\left(\frac{86}{117}\right)\) | \(e\left(\frac{11}{156}\right)\) | \(e\left(\frac{317}{468}\right)\) | \(e\left(\frac{113}{234}\right)\) | \(e\left(\frac{463}{468}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{145}{234}\right)\) |
| \(\chi_{6422}(509,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{173}{234}\right)\) | \(e\left(\frac{391}{468}\right)\) | \(e\left(\frac{55}{156}\right)\) | \(e\left(\frac{56}{117}\right)\) | \(e\left(\frac{155}{156}\right)\) | \(e\left(\frac{269}{468}\right)\) | \(e\left(\frac{11}{234}\right)\) | \(e\left(\frac{43}{468}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{157}{234}\right)\) |
| \(\chi_{6422}(527,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{187}{234}\right)\) | \(e\left(\frac{401}{468}\right)\) | \(e\left(\frac{137}{156}\right)\) | \(e\left(\frac{70}{117}\right)\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{307}{468}\right)\) | \(e\left(\frac{43}{234}\right)\) | \(e\left(\frac{317}{468}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{167}{234}\right)\) |
| \(\chi_{6422}(553,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{199}{234}\right)\) | \(e\left(\frac{209}{468}\right)\) | \(e\left(\frac{29}{156}\right)\) | \(e\left(\frac{82}{117}\right)\) | \(e\left(\frac{25}{156}\right)\) | \(e\left(\frac{139}{468}\right)\) | \(e\left(\frac{37}{234}\right)\) | \(e\left(\frac{17}{468}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{209}{234}\right)\) |
| \(\chi_{6422}(561,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{179}{234}\right)\) | \(e\left(\frac{295}{468}\right)\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{62}{117}\right)\) | \(e\left(\frac{95}{156}\right)\) | \(e\left(\frac{185}{468}\right)\) | \(e\left(\frac{125}{234}\right)\) | \(e\left(\frac{127}{468}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{61}{234}\right)\) |
| \(\chi_{6422}(565,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{151}{234}\right)\) | \(e\left(\frac{275}{468}\right)\) | \(e\left(\frac{71}{156}\right)\) | \(e\left(\frac{34}{117}\right)\) | \(e\left(\frac{115}{156}\right)\) | \(e\left(\frac{109}{468}\right)\) | \(e\left(\frac{61}{234}\right)\) | \(e\left(\frac{47}{468}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{41}{234}\right)\) |
| \(\chi_{6422}(583,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{203}{234}\right)\) | \(e\left(\frac{145}{468}\right)\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{86}{117}\right)\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{83}{468}\right)\) | \(e\left(\frac{113}{234}\right)\) | \(e\left(\frac{229}{468}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{145}{234}\right)\) |
| \(\chi_{6422}(591,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{217}{234}\right)\) | \(e\left(\frac{155}{468}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{100}{117}\right)\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{121}{468}\right)\) | \(e\left(\frac{145}{234}\right)\) | \(e\left(\frac{35}{468}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{155}{234}\right)\) |
| \(\chi_{6422}(661,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{155}{234}\right)\) | \(e\left(\frac{445}{468}\right)\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{38}{117}\right)\) | \(e\left(\frac{101}{156}\right)\) | \(e\left(\frac{287}{468}\right)\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{25}{468}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{211}{234}\right)\) |
| \(\chi_{6422}(713,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{234}\right)\) | \(e\left(\frac{385}{468}\right)\) | \(e\left(\frac{37}{156}\right)\) | \(e\left(\frac{71}{117}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{59}{468}\right)\) | \(e\left(\frac{179}{234}\right)\) | \(e\left(\frac{253}{468}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{151}{234}\right)\) |
| \(\chi_{6422}(839,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{175}{234}\right)\) | \(e\left(\frac{125}{468}\right)\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{58}{117}\right)\) | \(e\left(\frac{109}{156}\right)\) | \(e\left(\frac{7}{468}\right)\) | \(e\left(\frac{49}{234}\right)\) | \(e\left(\frac{149}{468}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{125}{234}\right)\) |
| \(\chi_{6422}(877,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{85}{234}\right)\) | \(e\left(\frac{395}{468}\right)\) | \(e\left(\frac{119}{156}\right)\) | \(e\left(\frac{85}{117}\right)\) | \(e\left(\frac{151}{156}\right)\) | \(e\left(\frac{97}{468}\right)\) | \(e\left(\frac{211}{234}\right)\) | \(e\left(\frac{59}{468}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{161}{234}\right)\) |
| \(\chi_{6422}(1003,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{191}{234}\right)\) | \(e\left(\frac{103}{468}\right)\) | \(e\left(\frac{127}{156}\right)\) | \(e\left(\frac{74}{117}\right)\) | \(e\left(\frac{131}{156}\right)\) | \(e\left(\frac{17}{468}\right)\) | \(e\left(\frac{119}{234}\right)\) | \(e\left(\frac{295}{468}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{103}{234}\right)\) |
| \(\chi_{6422}(1021,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{234}\right)\) | \(e\left(\frac{185}{468}\right)\) | \(e\left(\frac{113}{156}\right)\) | \(e\left(\frac{25}{117}\right)\) | \(e\left(\frac{49}{156}\right)\) | \(e\left(\frac{235}{468}\right)\) | \(e\left(\frac{7}{234}\right)\) | \(e\left(\frac{389}{468}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{185}{234}\right)\) |
| \(\chi_{6422}(1047,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{234}\right)\) | \(e\left(\frac{461}{468}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{37}{117}\right)\) | \(e\left(\frac{85}{156}\right)\) | \(e\left(\frac{67}{468}\right)\) | \(e\left(\frac{1}{234}\right)\) | \(e\left(\frac{89}{468}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{227}{234}\right)\) |
| \(\chi_{6422}(1055,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{197}{234}\right)\) | \(e\left(\frac{7}{468}\right)\) | \(e\left(\frac{151}{156}\right)\) | \(e\left(\frac{80}{117}\right)\) | \(e\left(\frac{71}{156}\right)\) | \(e\left(\frac{401}{468}\right)\) | \(e\left(\frac{233}{234}\right)\) | \(e\left(\frac{379}{468}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{7}{234}\right)\) |
| \(\chi_{6422}(1059,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{234}\right)\) | \(e\left(\frac{23}{468}\right)\) | \(e\left(\frac{95}{156}\right)\) | \(e\left(\frac{79}{117}\right)\) | \(e\left(\frac{55}{156}\right)\) | \(e\left(\frac{181}{468}\right)\) | \(e\left(\frac{97}{234}\right)\) | \(e\left(\frac{443}{468}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{23}{234}\right)\) |
| \(\chi_{6422}(1077,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{185}{234}\right)\) | \(e\left(\frac{433}{468}\right)\) | \(e\left(\frac{25}{156}\right)\) | \(e\left(\frac{68}{117}\right)\) | \(e\left(\frac{113}{156}\right)\) | \(e\left(\frac{335}{468}\right)\) | \(e\left(\frac{5}{234}\right)\) | \(e\left(\frac{445}{468}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{199}{234}\right)\) |
| \(\chi_{6422}(1085,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{145}{234}\right)\) | \(e\left(\frac{371}{468}\right)\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{28}{117}\right)\) | \(e\left(\frac{19}{156}\right)\) | \(e\left(\frac{193}{468}\right)\) | \(e\left(\frac{181}{234}\right)\) | \(e\left(\frac{431}{468}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{137}{234}\right)\) |
| \(\chi_{6422}(1155,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{265}{468}\right)\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{20}{117}\right)\) | \(e\left(\frac{125}{156}\right)\) | \(e\left(\frac{71}{468}\right)\) | \(e\left(\frac{29}{234}\right)\) | \(e\left(\frac{241}{468}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{31}{234}\right)\) |
| \(\chi_{6422}(1207,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{234}\right)\) | \(e\left(\frac{205}{468}\right)\) | \(e\left(\frac{121}{156}\right)\) | \(e\left(\frac{53}{117}\right)\) | \(e\left(\frac{29}{156}\right)\) | \(e\left(\frac{311}{468}\right)\) | \(e\left(\frac{71}{234}\right)\) | \(e\left(\frac{1}{468}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{205}{234}\right)\) |