from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(30148, base_ring=CyclotomicField(1884))
M = H._module
chi = DirichletCharacter(H, M([942,371]))
chi.galois_orbit()
[g,chi] = znchar(Mod(3,30148))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(30148\) | |
| Conductor: | \(30148\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1884\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{1884})$ |
| Fixed field: | Number field defined by a degree 1884 polynomial (not computed) |
First 26 of 624 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{30148}(3,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{689}{942}\right)\) | \(e\left(\frac{67}{628}\right)\) | \(e\left(\frac{1313}{1884}\right)\) | \(e\left(\frac{218}{471}\right)\) | \(e\left(\frac{1235}{1884}\right)\) | \(e\left(\frac{595}{942}\right)\) | \(e\left(\frac{1579}{1884}\right)\) | \(e\left(\frac{251}{628}\right)\) | \(e\left(\frac{151}{1884}\right)\) | \(e\left(\frac{269}{628}\right)\) |
| \(\chi_{30148}(35,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{757}{942}\right)\) | \(e\left(\frac{327}{628}\right)\) | \(e\left(\frac{625}{1884}\right)\) | \(e\left(\frac{286}{471}\right)\) | \(e\left(\frac{1819}{1884}\right)\) | \(e\left(\frac{167}{942}\right)\) | \(e\left(\frac{611}{1884}\right)\) | \(e\left(\frac{119}{628}\right)\) | \(e\left(\frac{587}{1884}\right)\) | \(e\left(\frac{85}{628}\right)\) |
| \(\chi_{30148}(103,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{187}{942}\right)\) | \(e\left(\frac{401}{628}\right)\) | \(e\left(\frac{463}{1884}\right)\) | \(e\left(\frac{187}{471}\right)\) | \(e\left(\frac{193}{1884}\right)\) | \(e\left(\frac{707}{942}\right)\) | \(e\left(\frac{1577}{1884}\right)\) | \(e\left(\frac{265}{628}\right)\) | \(e\left(\frac{257}{1884}\right)\) | \(e\left(\frac{279}{628}\right)\) |
| \(\chi_{30148}(119,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{91}{942}\right)\) | \(e\left(\frac{625}{628}\right)\) | \(e\left(\frac{991}{1884}\right)\) | \(e\left(\frac{91}{471}\right)\) | \(e\left(\frac{1585}{1884}\right)\) | \(e\left(\frac{203}{942}\right)\) | \(e\left(\frac{173}{1884}\right)\) | \(e\left(\frac{45}{628}\right)\) | \(e\left(\frac{1193}{1884}\right)\) | \(e\left(\frac{391}{628}\right)\) |
| \(\chi_{30148}(215,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{811}{942}\right)\) | \(e\left(\frac{201}{628}\right)\) | \(e\left(\frac{799}{1884}\right)\) | \(e\left(\frac{340}{471}\right)\) | \(e\left(\frac{565}{1884}\right)\) | \(e\left(\frac{215}{942}\right)\) | \(e\left(\frac{341}{1884}\right)\) | \(e\left(\frac{125}{628}\right)\) | \(e\left(\frac{1709}{1884}\right)\) | \(e\left(\frac{179}{628}\right)\) |
| \(\chi_{30148}(231,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{79}{942}\right)\) | \(e\left(\frac{25}{628}\right)\) | \(e\left(\frac{115}{1884}\right)\) | \(e\left(\frac{79}{471}\right)\) | \(e\left(\frac{817}{1884}\right)\) | \(e\left(\frac{611}{942}\right)\) | \(e\left(\frac{233}{1884}\right)\) | \(e\left(\frac{253}{628}\right)\) | \(e\left(\frac{1781}{1884}\right)\) | \(e\left(\frac{91}{628}\right)\) |
| \(\chi_{30148}(243,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{619}{942}\right)\) | \(e\left(\frac{335}{628}\right)\) | \(e\left(\frac{913}{1884}\right)\) | \(e\left(\frac{148}{471}\right)\) | \(e\left(\frac{523}{1884}\right)\) | \(e\left(\frac{149}{942}\right)\) | \(e\left(\frac{359}{1884}\right)\) | \(e\left(\frac{627}{628}\right)\) | \(e\left(\frac{755}{1884}\right)\) | \(e\left(\frac{89}{628}\right)\) |
| \(\chi_{30148}(251,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{605}{942}\right)\) | \(e\left(\frac{577}{628}\right)\) | \(e\left(\frac{1775}{1884}\right)\) | \(e\left(\frac{134}{471}\right)\) | \(e\left(\frac{569}{1884}\right)\) | \(e\left(\frac{625}{942}\right)\) | \(e\left(\frac{1057}{1884}\right)\) | \(e\left(\frac{137}{628}\right)\) | \(e\left(\frac{1441}{1884}\right)\) | \(e\left(\frac{367}{628}\right)\) |
| \(\chi_{30148}(283,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{553}{942}\right)\) | \(e\left(\frac{489}{628}\right)\) | \(e\left(\frac{1747}{1884}\right)\) | \(e\left(\frac{82}{471}\right)\) | \(e\left(\frac{1009}{1884}\right)\) | \(e\left(\frac{509}{942}\right)\) | \(e\left(\frac{689}{1884}\right)\) | \(e\left(\frac{201}{628}\right)\) | \(e\left(\frac{221}{1884}\right)\) | \(e\left(\frac{323}{628}\right)\) |
| \(\chi_{30148}(311,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{565}{942}\right)\) | \(e\left(\frac{147}{628}\right)\) | \(e\left(\frac{1681}{1884}\right)\) | \(e\left(\frac{94}{471}\right)\) | \(e\left(\frac{835}{1884}\right)\) | \(e\left(\frac{101}{942}\right)\) | \(e\left(\frac{1571}{1884}\right)\) | \(e\left(\frac{307}{628}\right)\) | \(e\left(\frac{575}{1884}\right)\) | \(e\left(\frac{309}{628}\right)\) |
| \(\chi_{30148}(315,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{251}{942}\right)\) | \(e\left(\frac{461}{628}\right)\) | \(e\left(\frac{1367}{1884}\right)\) | \(e\left(\frac{251}{471}\right)\) | \(e\left(\frac{521}{1884}\right)\) | \(e\left(\frac{415}{942}\right)\) | \(e\left(\frac{1}{1884}\right)\) | \(e\left(\frac{621}{628}\right)\) | \(e\left(\frac{889}{1884}\right)\) | \(e\left(\frac{623}{628}\right)\) |
| \(\chi_{30148}(415,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{607}{942}\right)\) | \(e\left(\frac{49}{628}\right)\) | \(e\left(\frac{979}{1884}\right)\) | \(e\left(\frac{136}{471}\right)\) | \(e\left(\frac{697}{1884}\right)\) | \(e\left(\frac{557}{942}\right)\) | \(e\left(\frac{1361}{1884}\right)\) | \(e\left(\frac{521}{628}\right)\) | \(e\left(\frac{401}{1884}\right)\) | \(e\left(\frac{103}{628}\right)\) |
| \(\chi_{30148}(451,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{523}{942}\right)\) | \(e\left(\frac{245}{628}\right)\) | \(e\left(\frac{499}{1884}\right)\) | \(e\left(\frac{52}{471}\right)\) | \(e\left(\frac{973}{1884}\right)\) | \(e\left(\frac{587}{942}\right)\) | \(e\left(\frac{1781}{1884}\right)\) | \(e\left(\frac{93}{628}\right)\) | \(e\left(\frac{749}{1884}\right)\) | \(e\left(\frac{515}{628}\right)\) |
| \(\chi_{30148}(615,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{695}{942}\right)\) | \(e\left(\frac{53}{628}\right)\) | \(e\left(\frac{1751}{1884}\right)\) | \(e\left(\frac{224}{471}\right)\) | \(e\left(\frac{677}{1884}\right)\) | \(e\left(\frac{391}{942}\right)\) | \(e\left(\frac{1549}{1884}\right)\) | \(e\left(\frac{461}{628}\right)\) | \(e\left(\frac{1741}{1884}\right)\) | \(e\left(\frac{419}{628}\right)\) |
| \(\chi_{30148}(631,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{131}{942}\right)\) | \(e\left(\frac{113}{628}\right)\) | \(e\left(\frac{143}{1884}\right)\) | \(e\left(\frac{131}{471}\right)\) | \(e\left(\frac{377}{1884}\right)\) | \(e\left(\frac{727}{942}\right)\) | \(e\left(\frac{601}{1884}\right)\) | \(e\left(\frac{189}{628}\right)\) | \(e\left(\frac{1117}{1884}\right)\) | \(e\left(\frac{135}{628}\right)\) |
| \(\chi_{30148}(731,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{145}{942}\right)\) | \(e\left(\frac{499}{628}\right)\) | \(e\left(\frac{1165}{1884}\right)\) | \(e\left(\frac{145}{471}\right)\) | \(e\left(\frac{331}{1884}\right)\) | \(e\left(\frac{251}{942}\right)\) | \(e\left(\frac{1787}{1884}\right)\) | \(e\left(\frac{51}{628}\right)\) | \(e\left(\frac{431}{1884}\right)\) | \(e\left(\frac{485}{628}\right)\) |
| \(\chi_{30148}(843,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{911}{942}\right)\) | \(e\left(\frac{491}{628}\right)\) | \(e\left(\frac{1505}{1884}\right)\) | \(e\left(\frac{440}{471}\right)\) | \(e\left(\frac{371}{1884}\right)\) | \(e\left(\frac{583}{942}\right)\) | \(e\left(\frac{1411}{1884}\right)\) | \(e\left(\frac{171}{628}\right)\) | \(e\left(\frac{1519}{1884}\right)\) | \(e\left(\frac{481}{628}\right)\) |
| \(\chi_{30148}(927,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{623}{942}\right)\) | \(e\left(\frac{535}{628}\right)\) | \(e\left(\frac{1205}{1884}\right)\) | \(e\left(\frac{152}{471}\right)\) | \(e\left(\frac{779}{1884}\right)\) | \(e\left(\frac{13}{942}\right)\) | \(e\left(\frac{967}{1884}\right)\) | \(e\left(\frac{139}{628}\right)\) | \(e\left(\frac{559}{1884}\right)\) | \(e\left(\frac{189}{628}\right)\) |
| \(\chi_{30148}(983,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{65}{942}\right)\) | \(e\left(\frac{267}{628}\right)\) | \(e\left(\frac{977}{1884}\right)\) | \(e\left(\frac{65}{471}\right)\) | \(e\left(\frac{863}{1884}\right)\) | \(e\left(\frac{145}{942}\right)\) | \(e\left(\frac{931}{1884}\right)\) | \(e\left(\frac{391}{628}\right)\) | \(e\left(\frac{583}{1884}\right)\) | \(e\left(\frac{369}{628}\right)\) |
| \(\chi_{30148}(1039,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{791}{942}\right)\) | \(e\left(\frac{457}{628}\right)\) | \(e\left(\frac{1223}{1884}\right)\) | \(e\left(\frac{320}{471}\right)\) | \(e\left(\frac{1169}{1884}\right)\) | \(e\left(\frac{895}{942}\right)\) | \(e\left(\frac{1069}{1884}\right)\) | \(e\left(\frac{53}{628}\right)\) | \(e\left(\frac{805}{1884}\right)\) | \(e\left(\frac{307}{628}\right)\) |
| \(\chi_{30148}(1055,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{942}\right)\) | \(e\left(\frac{451}{628}\right)\) | \(e\left(\frac{1321}{1884}\right)\) | \(e\left(\frac{31}{471}\right)\) | \(e\left(\frac{571}{1884}\right)\) | \(e\left(\frac{359}{942}\right)\) | \(e\left(\frac{1415}{1884}\right)\) | \(e\left(\frac{143}{628}\right)\) | \(e\left(\frac{1307}{1884}\right)\) | \(e\left(\frac{461}{628}\right)\) |
| \(\chi_{30148}(1071,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{527}{942}\right)\) | \(e\left(\frac{131}{628}\right)\) | \(e\left(\frac{1733}{1884}\right)\) | \(e\left(\frac{56}{471}\right)\) | \(e\left(\frac{287}{1884}\right)\) | \(e\left(\frac{451}{942}\right)\) | \(e\left(\frac{1447}{1884}\right)\) | \(e\left(\frac{547}{628}\right)\) | \(e\left(\frac{1495}{1884}\right)\) | \(e\left(\frac{301}{628}\right)\) |
| \(\chi_{30148}(1147,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{817}{942}\right)\) | \(e\left(\frac{501}{628}\right)\) | \(e\left(\frac{295}{1884}\right)\) | \(e\left(\frac{346}{471}\right)\) | \(e\left(\frac{949}{1884}\right)\) | \(e\left(\frac{11}{942}\right)\) | \(e\left(\frac{1253}{1884}\right)\) | \(e\left(\frac{21}{628}\right)\) | \(e\left(\frac{473}{1884}\right)\) | \(e\left(\frac{15}{628}\right)\) |
| \(\chi_{30148}(1411,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{883}{942}\right)\) | \(e\left(\frac{347}{628}\right)\) | \(e\left(\frac{1345}{1884}\right)\) | \(e\left(\frac{412}{471}\right)\) | \(e\left(\frac{463}{1884}\right)\) | \(e\left(\frac{593}{942}\right)\) | \(e\left(\frac{923}{1884}\right)\) | \(e\left(\frac{447}{628}\right)\) | \(e\left(\frac{1007}{1884}\right)\) | \(e\left(\frac{409}{628}\right)\) |
| \(\chi_{30148}(1419,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{133}{942}\right)\) | \(e\left(\frac{527}{628}\right)\) | \(e\left(\frac{289}{1884}\right)\) | \(e\left(\frac{133}{471}\right)\) | \(e\left(\frac{1447}{1884}\right)\) | \(e\left(\frac{659}{942}\right)\) | \(e\left(\frac{1847}{1884}\right)\) | \(e\left(\frac{259}{628}\right)\) | \(e\left(\frac{1019}{1884}\right)\) | \(e\left(\frac{185}{628}\right)\) |
| \(\chi_{30148}(1423,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{505}{942}\right)\) | \(e\left(\frac{287}{628}\right)\) | \(e\left(\frac{1069}{1884}\right)\) | \(e\left(\frac{34}{471}\right)\) | \(e\left(\frac{763}{1884}\right)\) | \(e\left(\frac{257}{942}\right)\) | \(e\left(\frac{1871}{1884}\right)\) | \(e\left(\frac{91}{628}\right)\) | \(e\left(\frac{1631}{1884}\right)\) | \(e\left(\frac{65}{628}\right)\) |