from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3283, base_ring=CyclotomicField(462))
M = H._module
chi = DirichletCharacter(H, M([121,287]))
chi.galois_orbit()
[g,chi] = znchar(Mod(12,3283))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(3283\) | |
| Conductor: | \(3283\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(462\) | 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: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
First 31 of 120 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{3283}(12,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{199}{462}\right)\) | \(e\left(\frac{113}{231}\right)\) | \(e\left(\frac{199}{231}\right)\) | \(e\left(\frac{211}{231}\right)\) | \(e\left(\frac{425}{462}\right)\) | \(e\left(\frac{45}{154}\right)\) | \(e\left(\frac{226}{231}\right)\) | \(e\left(\frac{53}{154}\right)\) | \(e\left(\frac{59}{462}\right)\) | \(e\left(\frac{27}{77}\right)\) |
| \(\chi_{3283}(115,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{462}\right)\) | \(e\left(\frac{1}{231}\right)\) | \(e\left(\frac{59}{231}\right)\) | \(e\left(\frac{8}{231}\right)\) | \(e\left(\frac{61}{462}\right)\) | \(e\left(\frac{59}{154}\right)\) | \(e\left(\frac{2}{231}\right)\) | \(e\left(\frac{25}{154}\right)\) | \(e\left(\frac{115}{462}\right)\) | \(e\left(\frac{20}{77}\right)\) |
| \(\chi_{3283}(136,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{359}{462}\right)\) | \(e\left(\frac{10}{231}\right)\) | \(e\left(\frac{128}{231}\right)\) | \(e\left(\frac{80}{231}\right)\) | \(e\left(\frac{379}{462}\right)\) | \(e\left(\frac{51}{154}\right)\) | \(e\left(\frac{20}{231}\right)\) | \(e\left(\frac{19}{154}\right)\) | \(e\left(\frac{457}{462}\right)\) | \(e\left(\frac{46}{77}\right)\) |
| \(\chi_{3283}(145,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{457}{462}\right)\) | \(e\left(\frac{227}{231}\right)\) | \(e\left(\frac{226}{231}\right)\) | \(e\left(\frac{199}{231}\right)\) | \(e\left(\frac{449}{462}\right)\) | \(e\left(\frac{149}{154}\right)\) | \(e\left(\frac{223}{231}\right)\) | \(e\left(\frac{131}{154}\right)\) | \(e\left(\frac{233}{462}\right)\) | \(e\left(\frac{74}{77}\right)\) |
| \(\chi_{3283}(180,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{379}{462}\right)\) | \(e\left(\frac{26}{231}\right)\) | \(e\left(\frac{148}{231}\right)\) | \(e\left(\frac{208}{231}\right)\) | \(e\left(\frac{431}{462}\right)\) | \(e\left(\frac{71}{154}\right)\) | \(e\left(\frac{52}{231}\right)\) | \(e\left(\frac{111}{154}\right)\) | \(e\left(\frac{449}{462}\right)\) | \(e\left(\frac{58}{77}\right)\) |
| \(\chi_{3283}(185,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{149}{462}\right)\) | \(e\left(\frac{73}{231}\right)\) | \(e\left(\frac{149}{231}\right)\) | \(e\left(\frac{122}{231}\right)\) | \(e\left(\frac{295}{462}\right)\) | \(e\left(\frac{149}{154}\right)\) | \(e\left(\frac{146}{231}\right)\) | \(e\left(\frac{131}{154}\right)\) | \(e\left(\frac{79}{462}\right)\) | \(e\left(\frac{74}{77}\right)\) |
| \(\chi_{3283}(208,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{462}\right)\) | \(e\left(\frac{197}{231}\right)\) | \(e\left(\frac{73}{231}\right)\) | \(e\left(\frac{190}{231}\right)\) | \(e\left(\frac{5}{462}\right)\) | \(e\left(\frac{73}{154}\right)\) | \(e\left(\frac{163}{231}\right)\) | \(e\left(\frac{151}{154}\right)\) | \(e\left(\frac{17}{462}\right)\) | \(e\left(\frac{13}{77}\right)\) |
| \(\chi_{3283}(262,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{269}{462}\right)\) | \(e\left(\frac{169}{231}\right)\) | \(e\left(\frac{38}{231}\right)\) | \(e\left(\frac{197}{231}\right)\) | \(e\left(\frac{145}{462}\right)\) | \(e\left(\frac{115}{154}\right)\) | \(e\left(\frac{107}{231}\right)\) | \(e\left(\frac{67}{154}\right)\) | \(e\left(\frac{31}{462}\right)\) | \(e\left(\frac{69}{77}\right)\) |
| \(\chi_{3283}(299,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{307}{462}\right)\) | \(e\left(\frac{107}{231}\right)\) | \(e\left(\frac{76}{231}\right)\) | \(e\left(\frac{163}{231}\right)\) | \(e\left(\frac{59}{462}\right)\) | \(e\left(\frac{153}{154}\right)\) | \(e\left(\frac{214}{231}\right)\) | \(e\left(\frac{57}{154}\right)\) | \(e\left(\frac{293}{462}\right)\) | \(e\left(\frac{61}{77}\right)\) |
| \(\chi_{3283}(318,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{173}{462}\right)\) | \(e\left(\frac{46}{231}\right)\) | \(e\left(\frac{173}{231}\right)\) | \(e\left(\frac{137}{231}\right)\) | \(e\left(\frac{265}{462}\right)\) | \(e\left(\frac{19}{154}\right)\) | \(e\left(\frac{92}{231}\right)\) | \(e\left(\frac{149}{154}\right)\) | \(e\left(\frac{439}{462}\right)\) | \(e\left(\frac{73}{77}\right)\) |
| \(\chi_{3283}(353,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{113}{462}\right)\) | \(e\left(\frac{229}{231}\right)\) | \(e\left(\frac{113}{231}\right)\) | \(e\left(\frac{215}{231}\right)\) | \(e\left(\frac{109}{462}\right)\) | \(e\left(\frac{113}{154}\right)\) | \(e\left(\frac{227}{231}\right)\) | \(e\left(\frac{27}{154}\right)\) | \(e\left(\frac{1}{462}\right)\) | \(e\left(\frac{37}{77}\right)\) |
| \(\chi_{3283}(355,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{462}\right)\) | \(e\left(\frac{71}{231}\right)\) | \(e\left(\frac{31}{231}\right)\) | \(e\left(\frac{106}{231}\right)\) | \(e\left(\frac{173}{462}\right)\) | \(e\left(\frac{31}{154}\right)\) | \(e\left(\frac{142}{231}\right)\) | \(e\left(\frac{81}{154}\right)\) | \(e\left(\frac{311}{462}\right)\) | \(e\left(\frac{34}{77}\right)\) |
| \(\chi_{3283}(369,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{235}{462}\right)\) | \(e\left(\frac{188}{231}\right)\) | \(e\left(\frac{4}{231}\right)\) | \(e\left(\frac{118}{231}\right)\) | \(e\left(\frac{149}{462}\right)\) | \(e\left(\frac{81}{154}\right)\) | \(e\left(\frac{145}{231}\right)\) | \(e\left(\frac{3}{154}\right)\) | \(e\left(\frac{137}{462}\right)\) | \(e\left(\frac{64}{77}\right)\) |
| \(\chi_{3283}(376,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{85}{462}\right)\) | \(e\left(\frac{68}{231}\right)\) | \(e\left(\frac{85}{231}\right)\) | \(e\left(\frac{82}{231}\right)\) | \(e\left(\frac{221}{462}\right)\) | \(e\left(\frac{85}{154}\right)\) | \(e\left(\frac{136}{231}\right)\) | \(e\left(\frac{83}{154}\right)\) | \(e\left(\frac{197}{462}\right)\) | \(e\left(\frac{51}{77}\right)\) |
| \(\chi_{3283}(430,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{65}{462}\right)\) | \(e\left(\frac{52}{231}\right)\) | \(e\left(\frac{65}{231}\right)\) | \(e\left(\frac{185}{231}\right)\) | \(e\left(\frac{169}{462}\right)\) | \(e\left(\frac{65}{154}\right)\) | \(e\left(\frac{104}{231}\right)\) | \(e\left(\frac{145}{154}\right)\) | \(e\left(\frac{205}{462}\right)\) | \(e\left(\frac{39}{77}\right)\) |
| \(\chi_{3283}(481,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{397}{462}\right)\) | \(e\left(\frac{179}{231}\right)\) | \(e\left(\frac{166}{231}\right)\) | \(e\left(\frac{46}{231}\right)\) | \(e\left(\frac{293}{462}\right)\) | \(e\left(\frac{89}{154}\right)\) | \(e\left(\frac{127}{231}\right)\) | \(e\left(\frac{9}{154}\right)\) | \(e\left(\frac{257}{462}\right)\) | \(e\left(\frac{38}{77}\right)\) |
| \(\chi_{3283}(549,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{155}{462}\right)\) | \(e\left(\frac{124}{231}\right)\) | \(e\left(\frac{155}{231}\right)\) | \(e\left(\frac{68}{231}\right)\) | \(e\left(\frac{403}{462}\right)\) | \(e\left(\frac{1}{154}\right)\) | \(e\left(\frac{17}{231}\right)\) | \(e\left(\frac{97}{154}\right)\) | \(e\left(\frac{169}{462}\right)\) | \(e\left(\frac{16}{77}\right)\) |
| \(\chi_{3283}(584,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{389}{462}\right)\) | \(e\left(\frac{34}{231}\right)\) | \(e\left(\frac{158}{231}\right)\) | \(e\left(\frac{41}{231}\right)\) | \(e\left(\frac{457}{462}\right)\) | \(e\left(\frac{81}{154}\right)\) | \(e\left(\frac{68}{231}\right)\) | \(e\left(\frac{3}{154}\right)\) | \(e\left(\frac{445}{462}\right)\) | \(e\left(\frac{64}{77}\right)\) |
| \(\chi_{3283}(605,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{227}{462}\right)\) | \(e\left(\frac{43}{231}\right)\) | \(e\left(\frac{227}{231}\right)\) | \(e\left(\frac{113}{231}\right)\) | \(e\left(\frac{313}{462}\right)\) | \(e\left(\frac{73}{154}\right)\) | \(e\left(\frac{86}{231}\right)\) | \(e\left(\frac{151}{154}\right)\) | \(e\left(\frac{325}{462}\right)\) | \(e\left(\frac{13}{77}\right)\) |
| \(\chi_{3283}(614,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{462}\right)\) | \(e\left(\frac{62}{231}\right)\) | \(e\left(\frac{193}{231}\right)\) | \(e\left(\frac{34}{231}\right)\) | \(e\left(\frac{317}{462}\right)\) | \(e\left(\frac{39}{154}\right)\) | \(e\left(\frac{124}{231}\right)\) | \(e\left(\frac{87}{154}\right)\) | \(e\left(\frac{431}{462}\right)\) | \(e\left(\frac{8}{77}\right)\) |
| \(\chi_{3283}(635,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{462}\right)\) | \(e\left(\frac{17}{231}\right)\) | \(e\left(\frac{79}{231}\right)\) | \(e\left(\frac{136}{231}\right)\) | \(e\left(\frac{113}{462}\right)\) | \(e\left(\frac{79}{154}\right)\) | \(e\left(\frac{34}{231}\right)\) | \(e\left(\frac{117}{154}\right)\) | \(e\left(\frac{107}{462}\right)\) | \(e\left(\frac{32}{77}\right)\) |
| \(\chi_{3283}(647,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{449}{462}\right)\) | \(e\left(\frac{82}{231}\right)\) | \(e\left(\frac{218}{231}\right)\) | \(e\left(\frac{194}{231}\right)\) | \(e\left(\frac{151}{462}\right)\) | \(e\left(\frac{141}{154}\right)\) | \(e\left(\frac{164}{231}\right)\) | \(e\left(\frac{125}{154}\right)\) | \(e\left(\frac{421}{462}\right)\) | \(e\left(\frac{23}{77}\right)\) |
| \(\chi_{3283}(649,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{115}{462}\right)\) | \(e\left(\frac{92}{231}\right)\) | \(e\left(\frac{115}{231}\right)\) | \(e\left(\frac{43}{231}\right)\) | \(e\left(\frac{299}{462}\right)\) | \(e\left(\frac{115}{154}\right)\) | \(e\left(\frac{184}{231}\right)\) | \(e\left(\frac{67}{154}\right)\) | \(e\left(\frac{185}{462}\right)\) | \(e\left(\frac{69}{77}\right)\) |
| \(\chi_{3283}(654,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17}{462}\right)\) | \(e\left(\frac{106}{231}\right)\) | \(e\left(\frac{17}{231}\right)\) | \(e\left(\frac{155}{231}\right)\) | \(e\left(\frac{229}{462}\right)\) | \(e\left(\frac{17}{154}\right)\) | \(e\left(\frac{212}{231}\right)\) | \(e\left(\frac{109}{154}\right)\) | \(e\left(\frac{409}{462}\right)\) | \(e\left(\frac{41}{77}\right)\) |
| \(\chi_{3283}(677,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{271}{462}\right)\) | \(e\left(\frac{32}{231}\right)\) | \(e\left(\frac{40}{231}\right)\) | \(e\left(\frac{25}{231}\right)\) | \(e\left(\frac{335}{462}\right)\) | \(e\left(\frac{117}{154}\right)\) | \(e\left(\frac{64}{231}\right)\) | \(e\left(\frac{107}{154}\right)\) | \(e\left(\frac{215}{462}\right)\) | \(e\left(\frac{24}{77}\right)\) |
| \(\chi_{3283}(731,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{137}{462}\right)\) | \(e\left(\frac{202}{231}\right)\) | \(e\left(\frac{137}{231}\right)\) | \(e\left(\frac{230}{231}\right)\) | \(e\left(\frac{79}{462}\right)\) | \(e\left(\frac{137}{154}\right)\) | \(e\left(\frac{173}{231}\right)\) | \(e\left(\frac{45}{154}\right)\) | \(e\left(\frac{361}{462}\right)\) | \(e\left(\frac{36}{77}\right)\) |
| \(\chi_{3283}(733,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{289}{462}\right)\) | \(e\left(\frac{185}{231}\right)\) | \(e\left(\frac{58}{231}\right)\) | \(e\left(\frac{94}{231}\right)\) | \(e\left(\frac{197}{462}\right)\) | \(e\left(\frac{135}{154}\right)\) | \(e\left(\frac{139}{231}\right)\) | \(e\left(\frac{5}{154}\right)\) | \(e\left(\frac{23}{462}\right)\) | \(e\left(\frac{4}{77}\right)\) |
| \(\chi_{3283}(768,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{462}\right)\) | \(e\left(\frac{173}{231}\right)\) | \(e\left(\frac{43}{231}\right)\) | \(e\left(\frac{229}{231}\right)\) | \(e\left(\frac{389}{462}\right)\) | \(e\left(\frac{43}{154}\right)\) | \(e\left(\frac{115}{231}\right)\) | \(e\left(\frac{13}{154}\right)\) | \(e\left(\frac{29}{462}\right)\) | \(e\left(\frac{72}{77}\right)\) |
| \(\chi_{3283}(787,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{462}\right)\) | \(e\left(\frac{79}{231}\right)\) | \(e\left(\frac{41}{231}\right)\) | \(e\left(\frac{170}{231}\right)\) | \(e\left(\frac{199}{462}\right)\) | \(e\left(\frac{41}{154}\right)\) | \(e\left(\frac{158}{231}\right)\) | \(e\left(\frac{127}{154}\right)\) | \(e\left(\frac{307}{462}\right)\) | \(e\left(\frac{40}{77}\right)\) |
| \(\chi_{3283}(794,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{365}{462}\right)\) | \(e\left(\frac{61}{231}\right)\) | \(e\left(\frac{134}{231}\right)\) | \(e\left(\frac{26}{231}\right)\) | \(e\left(\frac{25}{462}\right)\) | \(e\left(\frac{57}{154}\right)\) | \(e\left(\frac{122}{231}\right)\) | \(e\left(\frac{139}{154}\right)\) | \(e\left(\frac{85}{462}\right)\) | \(e\left(\frac{65}{77}\right)\) |
| \(\chi_{3283}(822,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{443}{462}\right)\) | \(e\left(\frac{31}{231}\right)\) | \(e\left(\frac{212}{231}\right)\) | \(e\left(\frac{17}{231}\right)\) | \(e\left(\frac{43}{462}\right)\) | \(e\left(\frac{135}{154}\right)\) | \(e\left(\frac{62}{231}\right)\) | \(e\left(\frac{5}{154}\right)\) | \(e\left(\frac{331}{462}\right)\) | \(e\left(\frac{4}{77}\right)\) |