from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3381, base_ring=CyclotomicField(462))
M = H._module
chi = DirichletCharacter(H, M([0,143,63]))
chi.galois_orbit()
[g,chi] = znchar(Mod(10,3381))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(3381\) | |
| Conductor: | \(1127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(462\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 1127.be | 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{3381}(10,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{74}{231}\right)\) | \(e\left(\frac{148}{231}\right)\) | \(e\left(\frac{26}{231}\right)\) | \(e\left(\frac{74}{77}\right)\) | \(e\left(\frac{100}{231}\right)\) | \(e\left(\frac{281}{462}\right)\) | \(e\left(\frac{19}{154}\right)\) | \(e\left(\frac{65}{231}\right)\) | \(e\left(\frac{160}{231}\right)\) | \(e\left(\frac{29}{33}\right)\) |
| \(\chi_{3381}(40,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{202}{231}\right)\) | \(e\left(\frac{173}{231}\right)\) | \(e\left(\frac{46}{231}\right)\) | \(e\left(\frac{48}{77}\right)\) | \(e\left(\frac{17}{231}\right)\) | \(e\left(\frac{355}{462}\right)\) | \(e\left(\frac{81}{154}\right)\) | \(e\left(\frac{115}{231}\right)\) | \(e\left(\frac{212}{231}\right)\) | \(e\left(\frac{31}{33}\right)\) |
| \(\chi_{3381}(61,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{82}{231}\right)\) | \(e\left(\frac{164}{231}\right)\) | \(e\left(\frac{85}{231}\right)\) | \(e\left(\frac{5}{77}\right)\) | \(e\left(\frac{167}{231}\right)\) | \(e\left(\frac{199}{462}\right)\) | \(e\left(\frac{71}{154}\right)\) | \(e\left(\frac{97}{231}\right)\) | \(e\left(\frac{221}{231}\right)\) | \(e\left(\frac{25}{33}\right)\) |
| \(\chi_{3381}(103,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{178}{231}\right)\) | \(e\left(\frac{125}{231}\right)\) | \(e\left(\frac{100}{231}\right)\) | \(e\left(\frac{24}{77}\right)\) | \(e\left(\frac{47}{231}\right)\) | \(e\left(\frac{139}{462}\right)\) | \(e\left(\frac{79}{154}\right)\) | \(e\left(\frac{19}{231}\right)\) | \(e\left(\frac{29}{231}\right)\) | \(e\left(\frac{10}{33}\right)\) |
| \(\chi_{3381}(136,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{218}{231}\right)\) | \(e\left(\frac{205}{231}\right)\) | \(e\left(\frac{164}{231}\right)\) | \(e\left(\frac{64}{77}\right)\) | \(e\left(\frac{151}{231}\right)\) | \(e\left(\frac{191}{462}\right)\) | \(e\left(\frac{31}{154}\right)\) | \(e\left(\frac{179}{231}\right)\) | \(e\left(\frac{103}{231}\right)\) | \(e\left(\frac{23}{33}\right)\) |
| \(\chi_{3381}(145,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{190}{231}\right)\) | \(e\left(\frac{149}{231}\right)\) | \(e\left(\frac{73}{231}\right)\) | \(e\left(\frac{36}{77}\right)\) | \(e\left(\frac{32}{231}\right)\) | \(e\left(\frac{247}{462}\right)\) | \(e\left(\frac{3}{154}\right)\) | \(e\left(\frac{67}{231}\right)\) | \(e\left(\frac{5}{231}\right)\) | \(e\left(\frac{4}{33}\right)\) |
| \(\chi_{3381}(157,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{95}{231}\right)\) | \(e\left(\frac{190}{231}\right)\) | \(e\left(\frac{152}{231}\right)\) | \(e\left(\frac{18}{77}\right)\) | \(e\left(\frac{16}{231}\right)\) | \(e\left(\frac{239}{462}\right)\) | \(e\left(\frac{117}{154}\right)\) | \(e\left(\frac{149}{231}\right)\) | \(e\left(\frac{118}{231}\right)\) | \(e\left(\frac{2}{33}\right)\) |
| \(\chi_{3381}(199,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{38}{231}\right)\) | \(e\left(\frac{76}{231}\right)\) | \(e\left(\frac{107}{231}\right)\) | \(e\left(\frac{38}{77}\right)\) | \(e\left(\frac{145}{231}\right)\) | \(e\left(\frac{419}{462}\right)\) | \(e\left(\frac{93}{154}\right)\) | \(e\left(\frac{152}{231}\right)\) | \(e\left(\frac{1}{231}\right)\) | \(e\left(\frac{14}{33}\right)\) |
| \(\chi_{3381}(241,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2}{231}\right)\) | \(e\left(\frac{4}{231}\right)\) | \(e\left(\frac{188}{231}\right)\) | \(e\left(\frac{2}{77}\right)\) | \(e\left(\frac{190}{231}\right)\) | \(e\left(\frac{95}{462}\right)\) | \(e\left(\frac{13}{154}\right)\) | \(e\left(\frac{8}{231}\right)\) | \(e\left(\frac{73}{231}\right)\) | \(e\left(\frac{32}{33}\right)\) |
| \(\chi_{3381}(250,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{94}{231}\right)\) | \(e\left(\frac{188}{231}\right)\) | \(e\left(\frac{58}{231}\right)\) | \(e\left(\frac{17}{77}\right)\) | \(e\left(\frac{152}{231}\right)\) | \(e\left(\frac{307}{462}\right)\) | \(e\left(\frac{149}{154}\right)\) | \(e\left(\frac{145}{231}\right)\) | \(e\left(\frac{197}{231}\right)\) | \(e\left(\frac{19}{33}\right)\) |
| \(\chi_{3381}(283,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{113}{231}\right)\) | \(e\left(\frac{226}{231}\right)\) | \(e\left(\frac{227}{231}\right)\) | \(e\left(\frac{36}{77}\right)\) | \(e\left(\frac{109}{231}\right)\) | \(e\left(\frac{401}{462}\right)\) | \(e\left(\frac{3}{154}\right)\) | \(e\left(\frac{221}{231}\right)\) | \(e\left(\frac{82}{231}\right)\) | \(e\left(\frac{26}{33}\right)\) |
| \(\chi_{3381}(304,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{32}{231}\right)\) | \(e\left(\frac{64}{231}\right)\) | \(e\left(\frac{5}{231}\right)\) | \(e\left(\frac{32}{77}\right)\) | \(e\left(\frac{37}{231}\right)\) | \(e\left(\frac{365}{462}\right)\) | \(e\left(\frac{131}{154}\right)\) | \(e\left(\frac{128}{231}\right)\) | \(e\left(\frac{13}{231}\right)\) | \(e\left(\frac{17}{33}\right)\) |
| \(\chi_{3381}(355,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19}{231}\right)\) | \(e\left(\frac{38}{231}\right)\) | \(e\left(\frac{169}{231}\right)\) | \(e\left(\frac{19}{77}\right)\) | \(e\left(\frac{188}{231}\right)\) | \(e\left(\frac{325}{462}\right)\) | \(e\left(\frac{85}{154}\right)\) | \(e\left(\frac{76}{231}\right)\) | \(e\left(\frac{116}{231}\right)\) | \(e\left(\frac{7}{33}\right)\) |
| \(\chi_{3381}(388,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{149}{231}\right)\) | \(e\left(\frac{67}{231}\right)\) | \(e\left(\frac{146}{231}\right)\) | \(e\left(\frac{72}{77}\right)\) | \(e\left(\frac{64}{231}\right)\) | \(e\left(\frac{263}{462}\right)\) | \(e\left(\frac{83}{154}\right)\) | \(e\left(\frac{134}{231}\right)\) | \(e\left(\frac{10}{231}\right)\) | \(e\left(\frac{8}{33}\right)\) |
| \(\chi_{3381}(451,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{221}{231}\right)\) | \(e\left(\frac{211}{231}\right)\) | \(e\left(\frac{215}{231}\right)\) | \(e\left(\frac{67}{77}\right)\) | \(e\left(\frac{205}{231}\right)\) | \(e\left(\frac{449}{462}\right)\) | \(e\left(\frac{89}{154}\right)\) | \(e\left(\frac{191}{231}\right)\) | \(e\left(\frac{97}{231}\right)\) | \(e\left(\frac{5}{33}\right)\) |
| \(\chi_{3381}(481,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{231}\right)\) | \(e\left(\frac{194}{231}\right)\) | \(e\left(\frac{109}{231}\right)\) | \(e\left(\frac{20}{77}\right)\) | \(e\left(\frac{206}{231}\right)\) | \(e\left(\frac{103}{462}\right)\) | \(e\left(\frac{53}{154}\right)\) | \(e\left(\frac{157}{231}\right)\) | \(e\left(\frac{191}{231}\right)\) | \(e\left(\frac{1}{33}\right)\) |
| \(\chi_{3381}(493,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{206}{231}\right)\) | \(e\left(\frac{181}{231}\right)\) | \(e\left(\frac{191}{231}\right)\) | \(e\left(\frac{52}{77}\right)\) | \(e\left(\frac{166}{231}\right)\) | \(e\left(\frac{83}{462}\right)\) | \(e\left(\frac{107}{154}\right)\) | \(e\left(\frac{131}{231}\right)\) | \(e\left(\frac{127}{231}\right)\) | \(e\left(\frac{29}{33}\right)\) |
| \(\chi_{3381}(502,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{40}{231}\right)\) | \(e\left(\frac{80}{231}\right)\) | \(e\left(\frac{64}{231}\right)\) | \(e\left(\frac{40}{77}\right)\) | \(e\left(\frac{104}{231}\right)\) | \(e\left(\frac{283}{462}\right)\) | \(e\left(\frac{29}{154}\right)\) | \(e\left(\frac{160}{231}\right)\) | \(e\left(\frac{74}{231}\right)\) | \(e\left(\frac{13}{33}\right)\) |
| \(\chi_{3381}(523,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{231}\right)\) | \(e\left(\frac{8}{231}\right)\) | \(e\left(\frac{145}{231}\right)\) | \(e\left(\frac{4}{77}\right)\) | \(e\left(\frac{149}{231}\right)\) | \(e\left(\frac{421}{462}\right)\) | \(e\left(\frac{103}{154}\right)\) | \(e\left(\frac{16}{231}\right)\) | \(e\left(\frac{146}{231}\right)\) | \(e\left(\frac{31}{33}\right)\) |
| \(\chi_{3381}(544,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{115}{231}\right)\) | \(e\left(\frac{230}{231}\right)\) | \(e\left(\frac{184}{231}\right)\) | \(e\left(\frac{38}{77}\right)\) | \(e\left(\frac{68}{231}\right)\) | \(e\left(\frac{265}{462}\right)\) | \(e\left(\frac{93}{154}\right)\) | \(e\left(\frac{229}{231}\right)\) | \(e\left(\frac{155}{231}\right)\) | \(e\left(\frac{25}{33}\right)\) |
| \(\chi_{3381}(586,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{211}{231}\right)\) | \(e\left(\frac{191}{231}\right)\) | \(e\left(\frac{199}{231}\right)\) | \(e\left(\frac{57}{77}\right)\) | \(e\left(\frac{179}{231}\right)\) | \(e\left(\frac{205}{462}\right)\) | \(e\left(\frac{101}{154}\right)\) | \(e\left(\frac{151}{231}\right)\) | \(e\left(\frac{194}{231}\right)\) | \(e\left(\frac{10}{33}\right)\) |
| \(\chi_{3381}(628,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{223}{231}\right)\) | \(e\left(\frac{215}{231}\right)\) | \(e\left(\frac{172}{231}\right)\) | \(e\left(\frac{69}{77}\right)\) | \(e\left(\frac{164}{231}\right)\) | \(e\left(\frac{313}{462}\right)\) | \(e\left(\frac{25}{154}\right)\) | \(e\left(\frac{199}{231}\right)\) | \(e\left(\frac{170}{231}\right)\) | \(e\left(\frac{4}{33}\right)\) |
| \(\chi_{3381}(640,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{227}{231}\right)\) | \(e\left(\frac{223}{231}\right)\) | \(e\left(\frac{86}{231}\right)\) | \(e\left(\frac{73}{77}\right)\) | \(e\left(\frac{82}{231}\right)\) | \(e\left(\frac{41}{462}\right)\) | \(e\left(\frac{51}{154}\right)\) | \(e\left(\frac{215}{231}\right)\) | \(e\left(\frac{85}{231}\right)\) | \(e\left(\frac{2}{33}\right)\) |
| \(\chi_{3381}(649,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{208}{231}\right)\) | \(e\left(\frac{185}{231}\right)\) | \(e\left(\frac{148}{231}\right)\) | \(e\left(\frac{54}{77}\right)\) | \(e\left(\frac{125}{231}\right)\) | \(e\left(\frac{409}{462}\right)\) | \(e\left(\frac{43}{154}\right)\) | \(e\left(\frac{139}{231}\right)\) | \(e\left(\frac{200}{231}\right)\) | \(e\left(\frac{28}{33}\right)\) |
| \(\chi_{3381}(661,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{125}{231}\right)\) | \(e\left(\frac{19}{231}\right)\) | \(e\left(\frac{200}{231}\right)\) | \(e\left(\frac{48}{77}\right)\) | \(e\left(\frac{94}{231}\right)\) | \(e\left(\frac{47}{462}\right)\) | \(e\left(\frac{81}{154}\right)\) | \(e\left(\frac{38}{231}\right)\) | \(e\left(\frac{58}{231}\right)\) | \(e\left(\frac{20}{33}\right)\) |
| \(\chi_{3381}(682,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{170}{231}\right)\) | \(e\left(\frac{109}{231}\right)\) | \(e\left(\frac{41}{231}\right)\) | \(e\left(\frac{16}{77}\right)\) | \(e\left(\frac{211}{231}\right)\) | \(e\left(\frac{221}{462}\right)\) | \(e\left(\frac{27}{154}\right)\) | \(e\left(\frac{218}{231}\right)\) | \(e\left(\frac{199}{231}\right)\) | \(e\left(\frac{14}{33}\right)\) |
| \(\chi_{3381}(724,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{134}{231}\right)\) | \(e\left(\frac{37}{231}\right)\) | \(e\left(\frac{122}{231}\right)\) | \(e\left(\frac{57}{77}\right)\) | \(e\left(\frac{25}{231}\right)\) | \(e\left(\frac{359}{462}\right)\) | \(e\left(\frac{101}{154}\right)\) | \(e\left(\frac{74}{231}\right)\) | \(e\left(\frac{40}{231}\right)\) | \(e\left(\frac{32}{33}\right)\) |
| \(\chi_{3381}(733,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{127}{231}\right)\) | \(e\left(\frac{23}{231}\right)\) | \(e\left(\frac{157}{231}\right)\) | \(e\left(\frac{50}{77}\right)\) | \(e\left(\frac{53}{231}\right)\) | \(e\left(\frac{373}{462}\right)\) | \(e\left(\frac{17}{154}\right)\) | \(e\left(\frac{46}{231}\right)\) | \(e\left(\frac{131}{231}\right)\) | \(e\left(\frac{19}{33}\right)\) |
| \(\chi_{3381}(787,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{164}{231}\right)\) | \(e\left(\frac{97}{231}\right)\) | \(e\left(\frac{170}{231}\right)\) | \(e\left(\frac{10}{77}\right)\) | \(e\left(\frac{103}{231}\right)\) | \(e\left(\frac{167}{462}\right)\) | \(e\left(\frac{65}{154}\right)\) | \(e\left(\frac{194}{231}\right)\) | \(e\left(\frac{211}{231}\right)\) | \(e\left(\frac{17}{33}\right)\) |
| \(\chi_{3381}(796,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{166}{231}\right)\) | \(e\left(\frac{101}{231}\right)\) | \(e\left(\frac{127}{231}\right)\) | \(e\left(\frac{12}{77}\right)\) | \(e\left(\frac{62}{231}\right)\) | \(e\left(\frac{31}{462}\right)\) | \(e\left(\frac{1}{154}\right)\) | \(e\left(\frac{202}{231}\right)\) | \(e\left(\frac{53}{231}\right)\) | \(e\left(\frac{16}{33}\right)\) |
| \(\chi_{3381}(838,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{52}{231}\right)\) | \(e\left(\frac{104}{231}\right)\) | \(e\left(\frac{37}{231}\right)\) | \(e\left(\frac{52}{77}\right)\) | \(e\left(\frac{89}{231}\right)\) | \(e\left(\frac{391}{462}\right)\) | \(e\left(\frac{107}{154}\right)\) | \(e\left(\frac{208}{231}\right)\) | \(e\left(\frac{50}{231}\right)\) | \(e\left(\frac{7}{33}\right)\) |