from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, base_ring=CyclotomicField(468))
M = H._module
chi = DirichletCharacter(H, M([225,26]))
chi.galois_orbit()
[g,chi] = znchar(Mod(21,6422))
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.dp | 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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{6422}(21,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{234}\right)\) | \(e\left(\frac{101}{468}\right)\) | \(e\left(\frac{121}{156}\right)\) | \(e\left(\frac{79}{117}\right)\) | \(e\left(\frac{29}{156}\right)\) | \(e\left(\frac{259}{468}\right)\) | \(e\left(\frac{175}{234}\right)\) | \(e\left(\frac{53}{468}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{101}{234}\right)\) |
| \(\chi_{6422}(109,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{85}{234}\right)\) | \(e\left(\frac{239}{468}\right)\) | \(e\left(\frac{67}{156}\right)\) | \(e\left(\frac{85}{117}\right)\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{409}{468}\right)\) | \(e\left(\frac{55}{234}\right)\) | \(e\left(\frac{371}{468}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{5}{234}\right)\) |
| \(\chi_{6422}(135,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{133}{234}\right)\) | \(e\left(\frac{407}{468}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{16}{117}\right)\) | \(e\left(\frac{35}{156}\right)\) | \(e\left(\frac{205}{468}\right)\) | \(e\left(\frac{31}{234}\right)\) | \(e\left(\frac{107}{468}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{173}{234}\right)\) |
| \(\chi_{6422}(203,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{107}{234}\right)\) | \(e\left(\frac{433}{468}\right)\) | \(e\left(\frac{77}{156}\right)\) | \(e\left(\frac{107}{117}\right)\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{179}{468}\right)\) | \(e\left(\frac{83}{234}\right)\) | \(e\left(\frac{445}{468}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{199}{234}\right)\) |
| \(\chi_{6422}(281,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{234}\right)\) | \(e\left(\frac{85}{468}\right)\) | \(e\left(\frac{125}{156}\right)\) | \(e\left(\frac{41}{117}\right)\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{167}{468}\right)\) | \(e\left(\frac{233}{234}\right)\) | \(e\left(\frac{457}{468}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{85}{234}\right)\) |
| \(\chi_{6422}(307,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{234}\right)\) | \(e\left(\frac{125}{468}\right)\) | \(e\left(\frac{37}{156}\right)\) | \(e\left(\frac{19}{117}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{163}{468}\right)\) | \(e\left(\frac{205}{234}\right)\) | \(e\left(\frac{149}{468}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{125}{234}\right)\) |
| \(\chi_{6422}(317,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{234}\right)\) | \(e\left(\frac{127}{468}\right)\) | \(e\left(\frac{95}{156}\right)\) | \(e\left(\frac{53}{117}\right)\) | \(e\left(\frac{55}{156}\right)\) | \(e\left(\frac{233}{468}\right)\) | \(e\left(\frac{227}{234}\right)\) | \(e\left(\frac{391}{468}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{127}{234}\right)\) |
| \(\chi_{6422}(333,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{101}{234}\right)\) | \(e\left(\frac{61}{468}\right)\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{101}{117}\right)\) | \(e\left(\frac{121}{156}\right)\) | \(e\left(\frac{263}{468}\right)\) | \(e\left(\frac{203}{234}\right)\) | \(e\left(\frac{361}{468}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{61}{234}\right)\) |
| \(\chi_{6422}(395,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{234}\right)\) | \(e\left(\frac{319}{468}\right)\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{41}{117}\right)\) | \(e\left(\frac{19}{156}\right)\) | \(e\left(\frac{401}{468}\right)\) | \(e\left(\frac{233}{234}\right)\) | \(e\left(\frac{223}{468}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{85}{234}\right)\) |
| \(\chi_{6422}(421,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{234}\right)\) | \(e\left(\frac{71}{468}\right)\) | \(e\left(\frac{31}{156}\right)\) | \(e\left(\frac{37}{117}\right)\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{145}{468}\right)\) | \(e\left(\frac{79}{234}\right)\) | \(e\left(\frac{167}{468}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{71}{234}\right)\) |
| \(\chi_{6422}(447,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{187}{468}\right)\) | \(e\left(\frac{119}{156}\right)\) | \(e\left(\frac{20}{117}\right)\) | \(e\left(\frac{151}{156}\right)\) | \(e\left(\frac{461}{468}\right)\) | \(e\left(\frac{185}{234}\right)\) | \(e\left(\frac{163}{468}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{187}{234}\right)\) |
| \(\chi_{6422}(489,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{229}{234}\right)\) | \(e\left(\frac{41}{468}\right)\) | \(e\left(\frac{97}{156}\right)\) | \(e\left(\frac{112}{117}\right)\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{31}{468}\right)\) | \(e\left(\frac{217}{234}\right)\) | \(e\left(\frac{281}{468}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{41}{234}\right)\) |
| \(\chi_{6422}(515,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{234}\right)\) | \(e\left(\frac{29}{468}\right)\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{25}{117}\right)\) | \(e\left(\frac{101}{156}\right)\) | \(e\left(\frac{79}{468}\right)\) | \(e\left(\frac{85}{234}\right)\) | \(e\left(\frac{233}{468}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{29}{234}\right)\) |
| \(\chi_{6422}(603,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{139}{234}\right)\) | \(e\left(\frac{311}{468}\right)\) | \(e\left(\frac{127}{156}\right)\) | \(e\left(\frac{22}{117}\right)\) | \(e\left(\frac{131}{156}\right)\) | \(e\left(\frac{121}{468}\right)\) | \(e\left(\frac{145}{234}\right)\) | \(e\left(\frac{191}{468}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{77}{234}\right)\) |
| \(\chi_{6422}(629,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{187}{234}\right)\) | \(e\left(\frac{11}{468}\right)\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{70}{117}\right)\) | \(e\left(\frac{119}{156}\right)\) | \(e\left(\frac{385}{468}\right)\) | \(e\left(\frac{121}{234}\right)\) | \(e\left(\frac{395}{468}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{11}{234}\right)\) |
| \(\chi_{6422}(697,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{234}\right)\) | \(e\left(\frac{361}{468}\right)\) | \(e\left(\frac{17}{156}\right)\) | \(e\left(\frac{53}{117}\right)\) | \(e\left(\frac{133}{156}\right)\) | \(e\left(\frac{467}{468}\right)\) | \(e\left(\frac{227}{234}\right)\) | \(e\left(\frac{157}{468}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{127}{234}\right)\) |
| \(\chi_{6422}(801,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{199}{234}\right)\) | \(e\left(\frac{53}{468}\right)\) | \(e\left(\frac{133}{156}\right)\) | \(e\left(\frac{82}{117}\right)\) | \(e\left(\frac{77}{156}\right)\) | \(e\left(\frac{451}{468}\right)\) | \(e\left(\frac{115}{234}\right)\) | \(e\left(\frac{329}{468}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{53}{234}\right)\) |
| \(\chi_{6422}(811,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{107}{234}\right)\) | \(e\left(\frac{199}{468}\right)\) | \(e\left(\frac{155}{156}\right)\) | \(e\left(\frac{107}{117}\right)\) | \(e\left(\frac{139}{156}\right)\) | \(e\left(\frac{413}{468}\right)\) | \(e\left(\frac{83}{234}\right)\) | \(e\left(\frac{211}{468}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{199}{234}\right)\) |
| \(\chi_{6422}(827,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{234}\right)\) | \(e\left(\frac{457}{468}\right)\) | \(e\left(\frac{149}{156}\right)\) | \(e\left(\frac{47}{117}\right)\) | \(e\left(\frac{37}{156}\right)\) | \(e\left(\frac{83}{468}\right)\) | \(e\left(\frac{113}{234}\right)\) | \(e\left(\frac{73}{468}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{223}{234}\right)\) |
| \(\chi_{6422}(889,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{95}{234}\right)\) | \(e\left(\frac{391}{468}\right)\) | \(e\left(\frac{107}{156}\right)\) | \(e\left(\frac{95}{117}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{113}{468}\right)\) | \(e\left(\frac{89}{234}\right)\) | \(e\left(\frac{43}{468}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{157}{234}\right)\) |
| \(\chi_{6422}(941,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{191}{234}\right)\) | \(e\left(\frac{259}{468}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{74}{117}\right)\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{173}{468}\right)\) | \(e\left(\frac{41}{234}\right)\) | \(e\left(\frac{451}{468}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{25}{234}\right)\) |
| \(\chi_{6422}(983,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{175}{234}\right)\) | \(e\left(\frac{437}{468}\right)\) | \(e\left(\frac{37}{156}\right)\) | \(e\left(\frac{58}{117}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{319}{468}\right)\) | \(e\left(\frac{127}{234}\right)\) | \(e\left(\frac{461}{468}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{203}{234}\right)\) |
| \(\chi_{6422}(1009,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{205}{234}\right)\) | \(e\left(\frac{425}{468}\right)\) | \(e\left(\frac{1}{156}\right)\) | \(e\left(\frac{88}{117}\right)\) | \(e\left(\frac{17}{156}\right)\) | \(e\left(\frac{367}{468}\right)\) | \(e\left(\frac{229}{234}\right)\) | \(e\left(\frac{413}{468}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{191}{234}\right)\) |
| \(\chi_{6422}(1097,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{234}\right)\) | \(e\left(\frac{383}{468}\right)\) | \(e\left(\frac{31}{156}\right)\) | \(e\left(\frac{76}{117}\right)\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{301}{468}\right)\) | \(e\left(\frac{1}{234}\right)\) | \(e\left(\frac{11}{468}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{149}{234}\right)\) |
| \(\chi_{6422}(1123,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{234}\right)\) | \(e\left(\frac{83}{468}\right)\) | \(e\left(\frac{67}{156}\right)\) | \(e\left(\frac{7}{117}\right)\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{97}{468}\right)\) | \(e\left(\frac{211}{234}\right)\) | \(e\left(\frac{215}{468}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{83}{234}\right)\) |
| \(\chi_{6422}(1191,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{233}{234}\right)\) | \(e\left(\frac{289}{468}\right)\) | \(e\left(\frac{113}{156}\right)\) | \(e\left(\frac{116}{117}\right)\) | \(e\left(\frac{49}{156}\right)\) | \(e\left(\frac{287}{468}\right)\) | \(e\left(\frac{137}{234}\right)\) | \(e\left(\frac{337}{468}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{55}{234}\right)\) |
| \(\chi_{6422}(1269,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{167}{234}\right)\) | \(e\left(\frac{409}{468}\right)\) | \(e\left(\frac{5}{156}\right)\) | \(e\left(\frac{50}{117}\right)\) | \(e\left(\frac{85}{156}\right)\) | \(e\left(\frac{275}{468}\right)\) | \(e\left(\frac{53}{234}\right)\) | \(e\left(\frac{349}{468}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{175}{234}\right)\) |
| \(\chi_{6422}(1295,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{145}{234}\right)\) | \(e\left(\frac{449}{468}\right)\) | \(e\left(\frac{73}{156}\right)\) | \(e\left(\frac{28}{117}\right)\) | \(e\left(\frac{149}{156}\right)\) | \(e\left(\frac{271}{468}\right)\) | \(e\left(\frac{25}{234}\right)\) | \(e\left(\frac{41}{468}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{215}{234}\right)\) |
| \(\chi_{6422}(1305,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{161}{234}\right)\) | \(e\left(\frac{271}{468}\right)\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{44}{117}\right)\) | \(e\left(\frac{67}{156}\right)\) | \(e\left(\frac{125}{468}\right)\) | \(e\left(\frac{173}{234}\right)\) | \(e\left(\frac{31}{468}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{37}{234}\right)\) |
| \(\chi_{6422}(1321,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{227}{234}\right)\) | \(e\left(\frac{385}{468}\right)\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{110}{117}\right)\) | \(e\left(\frac{109}{156}\right)\) | \(e\left(\frac{371}{468}\right)\) | \(e\left(\frac{23}{234}\right)\) | \(e\left(\frac{253}{468}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{151}{234}\right)\) |
| \(\chi_{6422}(1383,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{149}{234}\right)\) | \(e\left(\frac{463}{468}\right)\) | \(e\left(\frac{11}{156}\right)\) | \(e\left(\frac{32}{117}\right)\) | \(e\left(\frac{31}{156}\right)\) | \(e\left(\frac{293}{468}\right)\) | \(e\left(\frac{179}{234}\right)\) | \(e\left(\frac{331}{468}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{229}{234}\right)\) |