from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3381, base_ring=CyclotomicField(462))
M = H._module
chi = DirichletCharacter(H, M([231,187,336]))
chi.galois_orbit()
[g,chi] = znchar(Mod(26,3381))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(3381\) | |
| Conductor: | \(3381\) | 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{3381}(26,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{221}{462}\right)\) | \(e\left(\frac{221}{231}\right)\) | \(e\left(\frac{223}{231}\right)\) | \(e\left(\frac{67}{154}\right)\) | \(e\left(\frac{205}{462}\right)\) | \(e\left(\frac{109}{462}\right)\) | \(e\left(\frac{83}{154}\right)\) | \(e\left(\frac{211}{231}\right)\) | \(e\left(\frac{164}{231}\right)\) | \(e\left(\frac{5}{66}\right)\) |
| \(\chi_{3381}(59,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{379}{462}\right)\) | \(e\left(\frac{148}{231}\right)\) | \(e\left(\frac{26}{231}\right)\) | \(e\left(\frac{71}{154}\right)\) | \(e\left(\frac{431}{462}\right)\) | \(e\left(\frac{281}{462}\right)\) | \(e\left(\frac{19}{154}\right)\) | \(e\left(\frac{65}{231}\right)\) | \(e\left(\frac{160}{231}\right)\) | \(e\left(\frac{25}{66}\right)\) |
| \(\chi_{3381}(101,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13}{462}\right)\) | \(e\left(\frac{13}{231}\right)\) | \(e\left(\frac{149}{231}\right)\) | \(e\left(\frac{13}{154}\right)\) | \(e\left(\frac{311}{462}\right)\) | \(e\left(\frac{251}{462}\right)\) | \(e\left(\frac{23}{154}\right)\) | \(e\left(\frac{26}{231}\right)\) | \(e\left(\frac{64}{231}\right)\) | \(e\left(\frac{43}{66}\right)\) |
| \(\chi_{3381}(110,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{185}{462}\right)\) | \(e\left(\frac{185}{231}\right)\) | \(e\left(\frac{148}{231}\right)\) | \(e\left(\frac{31}{154}\right)\) | \(e\left(\frac{19}{462}\right)\) | \(e\left(\frac{409}{462}\right)\) | \(e\left(\frac{43}{154}\right)\) | \(e\left(\frac{139}{231}\right)\) | \(e\left(\frac{200}{231}\right)\) | \(e\left(\frac{23}{66}\right)\) |
| \(\chi_{3381}(131,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{281}{462}\right)\) | \(e\left(\frac{50}{231}\right)\) | \(e\left(\frac{40}{231}\right)\) | \(e\left(\frac{127}{154}\right)\) | \(e\left(\frac{361}{462}\right)\) | \(e\left(\frac{379}{462}\right)\) | \(e\left(\frac{47}{154}\right)\) | \(e\left(\frac{100}{231}\right)\) | \(e\left(\frac{104}{231}\right)\) | \(e\left(\frac{41}{66}\right)\) |
| \(\chi_{3381}(164,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{199}{462}\right)\) | \(e\left(\frac{199}{231}\right)\) | \(e\left(\frac{113}{231}\right)\) | \(e\left(\frac{45}{154}\right)\) | \(e\left(\frac{425}{462}\right)\) | \(e\left(\frac{395}{462}\right)\) | \(e\left(\frac{127}{154}\right)\) | \(e\left(\frac{167}{231}\right)\) | \(e\left(\frac{109}{231}\right)\) | \(e\left(\frac{49}{66}\right)\) |
| \(\chi_{3381}(173,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{389}{462}\right)\) | \(e\left(\frac{158}{231}\right)\) | \(e\left(\frac{34}{231}\right)\) | \(e\left(\frac{81}{154}\right)\) | \(e\left(\frac{457}{462}\right)\) | \(e\left(\frac{403}{462}\right)\) | \(e\left(\frac{13}{154}\right)\) | \(e\left(\frac{85}{231}\right)\) | \(e\left(\frac{227}{231}\right)\) | \(e\left(\frac{53}{66}\right)\) |
| \(\chi_{3381}(236,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{173}{462}\right)\) | \(e\left(\frac{173}{231}\right)\) | \(e\left(\frac{46}{231}\right)\) | \(e\left(\frac{19}{154}\right)\) | \(e\left(\frac{265}{462}\right)\) | \(e\left(\frac{355}{462}\right)\) | \(e\left(\frac{81}{154}\right)\) | \(e\left(\frac{115}{231}\right)\) | \(e\left(\frac{212}{231}\right)\) | \(e\left(\frac{29}{66}\right)\) |
| \(\chi_{3381}(248,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{462}\right)\) | \(e\left(\frac{97}{231}\right)\) | \(e\left(\frac{170}{231}\right)\) | \(e\left(\frac{97}{154}\right)\) | \(e\left(\frac{437}{462}\right)\) | \(e\left(\frac{167}{462}\right)\) | \(e\left(\frac{65}{154}\right)\) | \(e\left(\frac{194}{231}\right)\) | \(e\left(\frac{211}{231}\right)\) | \(e\left(\frac{1}{66}\right)\) |
| \(\chi_{3381}(257,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{311}{462}\right)\) | \(e\left(\frac{80}{231}\right)\) | \(e\left(\frac{64}{231}\right)\) | \(e\left(\frac{3}{154}\right)\) | \(e\left(\frac{439}{462}\right)\) | \(e\left(\frac{283}{462}\right)\) | \(e\left(\frac{29}{154}\right)\) | \(e\left(\frac{160}{231}\right)\) | \(e\left(\frac{74}{231}\right)\) | \(e\left(\frac{59}{66}\right)\) |
| \(\chi_{3381}(269,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{462}\right)\) | \(e\left(\frac{61}{231}\right)\) | \(e\left(\frac{95}{231}\right)\) | \(e\left(\frac{61}{154}\right)\) | \(e\left(\frac{251}{462}\right)\) | \(e\left(\frac{5}{462}\right)\) | \(e\left(\frac{25}{154}\right)\) | \(e\left(\frac{122}{231}\right)\) | \(e\left(\frac{16}{231}\right)\) | \(e\left(\frac{19}{66}\right)\) |
| \(\chi_{3381}(278,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{29}{462}\right)\) | \(e\left(\frac{29}{231}\right)\) | \(e\left(\frac{208}{231}\right)\) | \(e\left(\frac{29}{154}\right)\) | \(e\left(\frac{445}{462}\right)\) | \(e\left(\frac{169}{462}\right)\) | \(e\left(\frac{75}{154}\right)\) | \(e\left(\frac{58}{231}\right)\) | \(e\left(\frac{125}{231}\right)\) | \(e\left(\frac{35}{66}\right)\) |
| \(\chi_{3381}(311,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{367}{462}\right)\) | \(e\left(\frac{136}{231}\right)\) | \(e\left(\frac{155}{231}\right)\) | \(e\left(\frac{59}{154}\right)\) | \(e\left(\frac{215}{462}\right)\) | \(e\left(\frac{227}{462}\right)\) | \(e\left(\frac{57}{154}\right)\) | \(e\left(\frac{41}{231}\right)\) | \(e\left(\frac{172}{231}\right)\) | \(e\left(\frac{31}{66}\right)\) |
| \(\chi_{3381}(353,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{462}\right)\) | \(e\left(\frac{43}{231}\right)\) | \(e\left(\frac{173}{231}\right)\) | \(e\left(\frac{43}{154}\right)\) | \(e\left(\frac{389}{462}\right)\) | \(e\left(\frac{155}{462}\right)\) | \(e\left(\frac{5}{154}\right)\) | \(e\left(\frac{86}{231}\right)\) | \(e\left(\frac{34}{231}\right)\) | \(e\left(\frac{61}{66}\right)\) |
| \(\chi_{3381}(395,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{223}{462}\right)\) | \(e\left(\frac{223}{231}\right)\) | \(e\left(\frac{86}{231}\right)\) | \(e\left(\frac{69}{154}\right)\) | \(e\left(\frac{395}{462}\right)\) | \(e\left(\frac{41}{462}\right)\) | \(e\left(\frac{51}{154}\right)\) | \(e\left(\frac{215}{231}\right)\) | \(e\left(\frac{85}{231}\right)\) | \(e\left(\frac{37}{66}\right)\) |
| \(\chi_{3381}(404,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{269}{462}\right)\) | \(e\left(\frac{38}{231}\right)\) | \(e\left(\frac{169}{231}\right)\) | \(e\left(\frac{115}{154}\right)\) | \(e\left(\frac{145}{462}\right)\) | \(e\left(\frac{325}{462}\right)\) | \(e\left(\frac{85}{154}\right)\) | \(e\left(\frac{76}{231}\right)\) | \(e\left(\frac{116}{231}\right)\) | \(e\left(\frac{47}{66}\right)\) |
| \(\chi_{3381}(416,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{271}{462}\right)\) | \(e\left(\frac{40}{231}\right)\) | \(e\left(\frac{32}{231}\right)\) | \(e\left(\frac{117}{154}\right)\) | \(e\left(\frac{335}{462}\right)\) | \(e\left(\frac{257}{462}\right)\) | \(e\left(\frac{53}{154}\right)\) | \(e\left(\frac{80}{231}\right)\) | \(e\left(\frac{37}{231}\right)\) | \(e\left(\frac{13}{66}\right)\) |
| \(\chi_{3381}(446,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{167}{462}\right)\) | \(e\left(\frac{167}{231}\right)\) | \(e\left(\frac{226}{231}\right)\) | \(e\left(\frac{13}{154}\right)\) | \(e\left(\frac{157}{462}\right)\) | \(e\left(\frac{97}{462}\right)\) | \(e\left(\frac{23}{154}\right)\) | \(e\left(\frac{103}{231}\right)\) | \(e\left(\frac{218}{231}\right)\) | \(e\left(\frac{65}{66}\right)\) |
| \(\chi_{3381}(542,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{181}{462}\right)\) | \(e\left(\frac{181}{231}\right)\) | \(e\left(\frac{191}{231}\right)\) | \(e\left(\frac{27}{154}\right)\) | \(e\left(\frac{101}{462}\right)\) | \(e\left(\frac{83}{462}\right)\) | \(e\left(\frac{107}{154}\right)\) | \(e\left(\frac{131}{231}\right)\) | \(e\left(\frac{127}{231}\right)\) | \(e\left(\frac{25}{66}\right)\) |
| \(\chi_{3381}(584,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{277}{462}\right)\) | \(e\left(\frac{46}{231}\right)\) | \(e\left(\frac{83}{231}\right)\) | \(e\left(\frac{123}{154}\right)\) | \(e\left(\frac{443}{462}\right)\) | \(e\left(\frac{53}{462}\right)\) | \(e\left(\frac{111}{154}\right)\) | \(e\left(\frac{92}{231}\right)\) | \(e\left(\frac{31}{231}\right)\) | \(e\left(\frac{43}{66}\right)\) |
| \(\chi_{3381}(593,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{251}{462}\right)\) | \(e\left(\frac{20}{231}\right)\) | \(e\left(\frac{16}{231}\right)\) | \(e\left(\frac{97}{154}\right)\) | \(e\left(\frac{283}{462}\right)\) | \(e\left(\frac{13}{462}\right)\) | \(e\left(\frac{65}{154}\right)\) | \(e\left(\frac{40}{231}\right)\) | \(e\left(\frac{134}{231}\right)\) | \(e\left(\frac{23}{66}\right)\) |
| \(\chi_{3381}(614,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{347}{462}\right)\) | \(e\left(\frac{116}{231}\right)\) | \(e\left(\frac{139}{231}\right)\) | \(e\left(\frac{39}{154}\right)\) | \(e\left(\frac{163}{462}\right)\) | \(e\left(\frac{445}{462}\right)\) | \(e\left(\frac{69}{154}\right)\) | \(e\left(\frac{1}{231}\right)\) | \(e\left(\frac{38}{231}\right)\) | \(e\left(\frac{41}{66}\right)\) |
| \(\chi_{3381}(647,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{462}\right)\) | \(e\left(\frac{1}{231}\right)\) | \(e\left(\frac{47}{231}\right)\) | \(e\left(\frac{1}{154}\right)\) | \(e\left(\frac{95}{462}\right)\) | \(e\left(\frac{197}{462}\right)\) | \(e\left(\frac{61}{154}\right)\) | \(e\left(\frac{2}{231}\right)\) | \(e\left(\frac{76}{231}\right)\) | \(e\left(\frac{49}{66}\right)\) |
| \(\chi_{3381}(698,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{395}{462}\right)\) | \(e\left(\frac{164}{231}\right)\) | \(e\left(\frac{85}{231}\right)\) | \(e\left(\frac{87}{154}\right)\) | \(e\left(\frac{103}{462}\right)\) | \(e\left(\frac{199}{462}\right)\) | \(e\left(\frac{71}{154}\right)\) | \(e\left(\frac{97}{231}\right)\) | \(e\left(\frac{221}{231}\right)\) | \(e\left(\frac{17}{66}\right)\) |
| \(\chi_{3381}(719,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{239}{462}\right)\) | \(e\left(\frac{8}{231}\right)\) | \(e\left(\frac{145}{231}\right)\) | \(e\left(\frac{85}{154}\right)\) | \(e\left(\frac{67}{462}\right)\) | \(e\left(\frac{421}{462}\right)\) | \(e\left(\frac{103}{154}\right)\) | \(e\left(\frac{16}{231}\right)\) | \(e\left(\frac{146}{231}\right)\) | \(e\left(\frac{29}{66}\right)\) |
| \(\chi_{3381}(731,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{361}{462}\right)\) | \(e\left(\frac{130}{231}\right)\) | \(e\left(\frac{104}{231}\right)\) | \(e\left(\frac{53}{154}\right)\) | \(e\left(\frac{107}{462}\right)\) | \(e\left(\frac{431}{462}\right)\) | \(e\left(\frac{153}{154}\right)\) | \(e\left(\frac{29}{231}\right)\) | \(e\left(\frac{178}{231}\right)\) | \(e\left(\frac{1}{66}\right)\) |
| \(\chi_{3381}(740,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{377}{462}\right)\) | \(e\left(\frac{146}{231}\right)\) | \(e\left(\frac{163}{231}\right)\) | \(e\left(\frac{69}{154}\right)\) | \(e\left(\frac{241}{462}\right)\) | \(e\left(\frac{349}{462}\right)\) | \(e\left(\frac{51}{154}\right)\) | \(e\left(\frac{61}{231}\right)\) | \(e\left(\frac{8}{231}\right)\) | \(e\left(\frac{59}{66}\right)\) |
| \(\chi_{3381}(752,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{325}{462}\right)\) | \(e\left(\frac{94}{231}\right)\) | \(e\left(\frac{29}{231}\right)\) | \(e\left(\frac{17}{154}\right)\) | \(e\left(\frac{383}{462}\right)\) | \(e\left(\frac{269}{462}\right)\) | \(e\left(\frac{113}{154}\right)\) | \(e\left(\frac{188}{231}\right)\) | \(e\left(\frac{214}{231}\right)\) | \(e\left(\frac{19}{66}\right)\) |
| \(\chi_{3381}(761,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{95}{462}\right)\) | \(e\left(\frac{95}{231}\right)\) | \(e\left(\frac{76}{231}\right)\) | \(e\left(\frac{95}{154}\right)\) | \(e\left(\frac{247}{462}\right)\) | \(e\left(\frac{235}{462}\right)\) | \(e\left(\frac{97}{154}\right)\) | \(e\left(\frac{190}{231}\right)\) | \(e\left(\frac{59}{231}\right)\) | \(e\left(\frac{35}{66}\right)\) |
| \(\chi_{3381}(794,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{169}{462}\right)\) | \(e\left(\frac{169}{231}\right)\) | \(e\left(\frac{89}{231}\right)\) | \(e\left(\frac{15}{154}\right)\) | \(e\left(\frac{347}{462}\right)\) | \(e\left(\frac{29}{462}\right)\) | \(e\left(\frac{145}{154}\right)\) | \(e\left(\frac{107}{231}\right)\) | \(e\left(\frac{139}{231}\right)\) | \(e\left(\frac{31}{66}\right)\) |
| \(\chi_{3381}(836,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{307}{462}\right)\) | \(e\left(\frac{76}{231}\right)\) | \(e\left(\frac{107}{231}\right)\) | \(e\left(\frac{153}{154}\right)\) | \(e\left(\frac{59}{462}\right)\) | \(e\left(\frac{419}{462}\right)\) | \(e\left(\frac{93}{154}\right)\) | \(e\left(\frac{152}{231}\right)\) | \(e\left(\frac{1}{231}\right)\) | \(e\left(\frac{61}{66}\right)\) |