from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, base_ring=CyclotomicField(468))
M = H._module
chi = DirichletCharacter(H, M([255,338]))
chi.galois_orbit()
[g,chi] = znchar(Mod(41,6422))
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.dq | 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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{6422}(41,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{223}{234}\right)\) | \(e\left(\frac{215}{468}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{106}{117}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{193}{468}\right)\) | \(e\left(\frac{181}{234}\right)\) | \(e\left(\frac{275}{468}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{215}{234}\right)\) |
| \(\chi_{6422}(193,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{234}\right)\) | \(e\left(\frac{413}{468}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{79}{117}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{103}{468}\right)\) | \(e\left(\frac{19}{234}\right)\) | \(e\left(\frac{365}{468}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{179}{234}\right)\) |
| \(\chi_{6422}(223,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{127}{234}\right)\) | \(e\left(\frac{347}{468}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{10}{117}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{133}{468}\right)\) | \(e\left(\frac{229}{234}\right)\) | \(e\left(\frac{335}{468}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{113}{234}\right)\) |
| \(\chi_{6422}(241,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{234}\right)\) | \(e\left(\frac{433}{468}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{29}{117}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{23}{468}\right)\) | \(e\left(\frac{161}{234}\right)\) | \(e\left(\frac{445}{468}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{199}{234}\right)\) |
| \(\chi_{6422}(279,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{234}\right)\) | \(e\left(\frac{451}{468}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{101}{117}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{185}{468}\right)\) | \(e\left(\frac{125}{234}\right)\) | \(e\left(\frac{283}{468}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{217}{234}\right)\) |
| \(\chi_{6422}(371,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{167}{234}\right)\) | \(e\left(\frac{97}{468}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{50}{117}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{431}{468}\right)\) | \(e\left(\frac{209}{234}\right)\) | \(e\left(\frac{37}{468}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{97}{234}\right)\) |
| \(\chi_{6422}(375,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{234}\right)\) | \(e\left(\frac{437}{468}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{19}{117}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{7}{468}\right)\) | \(e\left(\frac{49}{234}\right)\) | \(e\left(\frac{461}{468}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{203}{234}\right)\) |
| \(\chi_{6422}(401,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{211}{234}\right)\) | \(e\left(\frac{173}{468}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{94}{117}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{127}{468}\right)\) | \(e\left(\frac{187}{234}\right)\) | \(e\left(\frac{341}{468}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{173}{234}\right)\) |
| \(\chi_{6422}(409,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{234}\right)\) | \(e\left(\frac{7}{468}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{41}{117}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{89}{468}\right)\) | \(e\left(\frac{155}{234}\right)\) | \(e\left(\frac{379}{468}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{7}{234}\right)\) |
| \(\chi_{6422}(535,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{234}\right)\) | \(e\left(\frac{395}{468}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{7}{117}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{409}{468}\right)\) | \(e\left(\frac{55}{234}\right)\) | \(e\left(\frac{59}{468}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{161}{234}\right)\) |
| \(\chi_{6422}(687,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{234}\right)\) | \(e\left(\frac{233}{468}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{61}{117}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{355}{468}\right)\) | \(e\left(\frac{145}{234}\right)\) | \(e\left(\frac{113}{468}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{233}{234}\right)\) |
| \(\chi_{6422}(717,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{145}{234}\right)\) | \(e\left(\frac{59}{468}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{28}{117}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{349}{468}\right)\) | \(e\left(\frac{103}{234}\right)\) | \(e\left(\frac{119}{468}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{59}{234}\right)\) |
| \(\chi_{6422}(735,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{234}\right)\) | \(e\left(\frac{217}{468}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{101}{117}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{419}{468}\right)\) | \(e\left(\frac{125}{234}\right)\) | \(e\left(\frac{49}{468}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{217}{234}\right)\) |
| \(\chi_{6422}(743,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{234}\right)\) | \(e\left(\frac{11}{468}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{31}{117}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{73}{468}\right)\) | \(e\left(\frac{43}{234}\right)\) | \(e\left(\frac{395}{468}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{11}{234}\right)\) |
| \(\chi_{6422}(773,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{234}\right)\) | \(e\left(\frac{199}{468}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{29}{117}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{257}{468}\right)\) | \(e\left(\frac{161}{234}\right)\) | \(e\left(\frac{211}{468}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{199}{234}\right)\) |
| \(\chi_{6422}(813,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{215}{234}\right)\) | \(e\left(\frac{265}{468}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{98}{117}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(e\left(\frac{227}{468}\right)\) | \(e\left(\frac{185}{234}\right)\) | \(e\left(\frac{241}{468}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{31}{234}\right)\) |
| \(\chi_{6422}(851,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{234}\right)\) | \(e\left(\frac{463}{468}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{71}{117}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{137}{468}\right)\) | \(e\left(\frac{23}{234}\right)\) | \(e\left(\frac{331}{468}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{229}{234}\right)\) |
| \(\chi_{6422}(865,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{234}\right)\) | \(e\left(\frac{349}{468}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{5}{117}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{359}{468}\right)\) | \(e\left(\frac{173}{234}\right)\) | \(e\left(\frac{109}{468}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{115}{234}\right)\) |
| \(\chi_{6422}(869,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{234}\right)\) | \(e\left(\frac{257}{468}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{1}{117}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{259}{468}\right)\) | \(e\left(\frac{175}{234}\right)\) | \(e\left(\frac{209}{468}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{23}{234}\right)\) |
| \(\chi_{6422}(895,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{234}\right)\) | \(e\left(\frac{461}{468}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{76}{117}\right)\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{379}{468}\right)\) | \(e\left(\frac{79}{234}\right)\) | \(e\left(\frac{89}{468}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{227}{234}\right)\) |
| \(\chi_{6422}(903,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{203}{234}\right)\) | \(e\left(\frac{223}{468}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{86}{117}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{161}{468}\right)\) | \(e\left(\frac{191}{234}\right)\) | \(e\left(\frac{307}{468}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{223}{234}\right)\) |
| \(\chi_{6422}(1029,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{234}\right)\) | \(e\left(\frac{107}{468}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{25}{117}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{157}{468}\right)\) | \(e\left(\frac{163}{234}\right)\) | \(e\left(\frac{311}{468}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{107}{234}\right)\) |
| \(\chi_{6422}(1181,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{234}\right)\) | \(e\left(\frac{53}{468}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{43}{117}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{139}{468}\right)\) | \(e\left(\frac{37}{234}\right)\) | \(e\left(\frac{329}{468}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{53}{234}\right)\) |
| \(\chi_{6422}(1211,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{163}{234}\right)\) | \(e\left(\frac{239}{468}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{46}{117}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{97}{468}\right)\) | \(e\left(\frac{211}{234}\right)\) | \(e\left(\frac{371}{468}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{5}{234}\right)\) |
| \(\chi_{6422}(1229,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{173}{234}\right)\) | \(e\left(\frac{1}{468}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{56}{117}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{347}{468}\right)\) | \(e\left(\frac{89}{234}\right)\) | \(e\left(\frac{121}{468}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{234}\right)\) |
| \(\chi_{6422}(1237,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{49}{234}\right)\) | \(e\left(\frac{191}{468}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{49}{117}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{289}{468}\right)\) | \(e\left(\frac{151}{234}\right)\) | \(e\left(\frac{179}{468}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{191}{234}\right)\) |
| \(\chi_{6422}(1267,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{191}{234}\right)\) | \(e\left(\frac{415}{468}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{74}{117}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{329}{468}\right)\) | \(e\left(\frac{197}{234}\right)\) | \(e\left(\frac{139}{468}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{181}{234}\right)\) |
| \(\chi_{6422}(1307,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{234}\right)\) | \(e\left(\frac{49}{468}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{53}{117}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{155}{468}\right)\) | \(e\left(\frac{149}{234}\right)\) | \(e\left(\frac{313}{468}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{49}{234}\right)\) |
| \(\chi_{6422}(1345,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{233}{234}\right)\) | \(e\left(\frac{211}{468}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{116}{117}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{209}{468}\right)\) | \(e\left(\frac{59}{234}\right)\) | \(e\left(\frac{259}{468}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{211}{234}\right)\) |
| \(\chi_{6422}(1359,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{77}{234}\right)\) | \(e\left(\frac{133}{468}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{77}{117}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{287}{468}\right)\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{181}{468}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{133}{234}\right)\) |
| \(\chi_{6422}(1363,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{217}{234}\right)\) | \(e\left(\frac{77}{468}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{100}{117}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{43}{468}\right)\) | \(e\left(\frac{67}{234}\right)\) | \(e\left(\frac{425}{468}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{77}{234}\right)\) |