from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(40310, base_ring=CyclotomicField(1932))
M = H._module
chi = DirichletCharacter(H, M([966,621,854]))
chi.galois_orbit()
[g,chi] = znchar(Mod(19,40310))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(40310\) | |
| Conductor: | \(20155\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1932\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 20155.fx | 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: | $\Q(\zeta_{1932})$ |
| Fixed field: | Number field defined by a degree 1932 polynomial (not computed) |
First 19 of 528 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{40310}(19,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{445}{1932}\right)\) | \(e\left(\frac{443}{966}\right)\) | \(e\left(\frac{445}{966}\right)\) | \(e\left(\frac{1217}{1932}\right)\) | \(e\left(\frac{278}{483}\right)\) | \(e\left(\frac{151}{276}\right)\) | \(e\left(\frac{1655}{1932}\right)\) | \(e\left(\frac{1331}{1932}\right)\) | \(e\left(\frac{139}{161}\right)\) | \(e\left(\frac{445}{644}\right)\) |
| \(\chi_{40310}(119,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{73}{1932}\right)\) | \(e\left(\frac{509}{966}\right)\) | \(e\left(\frac{73}{966}\right)\) | \(e\left(\frac{1793}{1932}\right)\) | \(e\left(\frac{254}{483}\right)\) | \(e\left(\frac{271}{276}\right)\) | \(e\left(\frac{11}{1932}\right)\) | \(e\left(\frac{1091}{1932}\right)\) | \(e\left(\frac{127}{161}\right)\) | \(e\left(\frac{73}{644}\right)\) |
| \(\chi_{40310}(189,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1391}{1932}\right)\) | \(e\left(\frac{727}{966}\right)\) | \(e\left(\frac{425}{966}\right)\) | \(e\left(\frac{739}{1932}\right)\) | \(e\left(\frac{43}{483}\right)\) | \(e\left(\frac{245}{276}\right)\) | \(e\left(\frac{289}{1932}\right)\) | \(e\left(\frac{913}{1932}\right)\) | \(e\left(\frac{102}{161}\right)\) | \(e\left(\frac{103}{644}\right)\) |
| \(\chi_{40310}(229,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{199}{1932}\right)\) | \(e\left(\frac{845}{966}\right)\) | \(e\left(\frac{199}{966}\right)\) | \(e\left(\frac{71}{1932}\right)\) | \(e\left(\frac{44}{483}\right)\) | \(e\left(\frac{217}{276}\right)\) | \(e\left(\frac{1565}{1932}\right)\) | \(e\left(\frac{1889}{1932}\right)\) | \(e\left(\frac{22}{161}\right)\) | \(e\left(\frac{199}{644}\right)\) |
| \(\chi_{40310}(269,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1735}{1932}\right)\) | \(e\left(\frac{479}{966}\right)\) | \(e\left(\frac{769}{966}\right)\) | \(e\left(\frac{1619}{1932}\right)\) | \(e\left(\frac{221}{483}\right)\) | \(e\left(\frac{229}{276}\right)\) | \(e\left(\frac{1373}{1932}\right)\) | \(e\left(\frac{761}{1932}\right)\) | \(e\left(\frac{30}{161}\right)\) | \(e\left(\frac{447}{644}\right)\) |
| \(\chi_{40310}(379,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1157}{1932}\right)\) | \(e\left(\frac{379}{966}\right)\) | \(e\left(\frac{191}{966}\right)\) | \(e\left(\frac{73}{1932}\right)\) | \(e\left(\frac{433}{483}\right)\) | \(e\left(\frac{227}{276}\right)\) | \(e\left(\frac{439}{1932}\right)\) | \(e\left(\frac{1915}{1932}\right)\) | \(e\left(\frac{136}{161}\right)\) | \(e\left(\frac{513}{644}\right)\) |
| \(\chi_{40310}(449,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{593}{1932}\right)\) | \(e\left(\frac{853}{966}\right)\) | \(e\left(\frac{593}{966}\right)\) | \(e\left(\frac{697}{1932}\right)\) | \(e\left(\frac{85}{483}\right)\) | \(e\left(\frac{35}{276}\right)\) | \(e\left(\frac{751}{1932}\right)\) | \(e\left(\frac{367}{1932}\right)\) | \(e\left(\frac{123}{161}\right)\) | \(e\left(\frac{593}{644}\right)\) |
| \(\chi_{40310}(519,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{311}{1932}\right)\) | \(e\left(\frac{607}{966}\right)\) | \(e\left(\frac{311}{966}\right)\) | \(e\left(\frac{43}{1932}\right)\) | \(e\left(\frac{394}{483}\right)\) | \(e\left(\frac{77}{276}\right)\) | \(e\left(\frac{1873}{1932}\right)\) | \(e\left(\frac{1525}{1932}\right)\) | \(e\left(\frac{36}{161}\right)\) | \(e\left(\frac{311}{644}\right)\) |
| \(\chi_{40310}(549,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1031}{1932}\right)\) | \(e\left(\frac{43}{966}\right)\) | \(e\left(\frac{65}{966}\right)\) | \(e\left(\frac{1795}{1932}\right)\) | \(e\left(\frac{160}{483}\right)\) | \(e\left(\frac{5}{276}\right)\) | \(e\left(\frac{817}{1932}\right)\) | \(e\left(\frac{1117}{1932}\right)\) | \(e\left(\frac{80}{161}\right)\) | \(e\left(\frac{387}{644}\right)\) |
| \(\chi_{40310}(559,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{419}{1932}\right)\) | \(e\left(\frac{619}{966}\right)\) | \(e\left(\frac{419}{966}\right)\) | \(e\left(\frac{499}{1932}\right)\) | \(e\left(\frac{214}{483}\right)\) | \(e\left(\frac{149}{276}\right)\) | \(e\left(\frac{169}{1932}\right)\) | \(e\left(\frac{1657}{1932}\right)\) | \(e\left(\frac{107}{161}\right)\) | \(e\left(\frac{419}{644}\right)\) |
| \(\chi_{40310}(649,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1513}{1932}\right)\) | \(e\left(\frac{347}{966}\right)\) | \(e\left(\frac{547}{966}\right)\) | \(e\left(\frac{1433}{1932}\right)\) | \(e\left(\frac{269}{483}\right)\) | \(e\left(\frac{127}{276}\right)\) | \(e\left(\frac{1763}{1932}\right)\) | \(e\left(\frac{275}{1932}\right)\) | \(e\left(\frac{54}{161}\right)\) | \(e\left(\frac{225}{644}\right)\) |
| \(\chi_{40310}(809,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{955}{1932}\right)\) | \(e\left(\frac{929}{966}\right)\) | \(e\left(\frac{955}{966}\right)\) | \(e\left(\frac{1331}{1932}\right)\) | \(e\left(\frac{233}{483}\right)\) | \(e\left(\frac{169}{276}\right)\) | \(e\left(\frac{1229}{1932}\right)\) | \(e\left(\frac{881}{1932}\right)\) | \(e\left(\frac{36}{161}\right)\) | \(e\left(\frac{311}{644}\right)\) |
| \(\chi_{40310}(849,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1483}{1932}\right)\) | \(e\left(\frac{773}{966}\right)\) | \(e\left(\frac{517}{966}\right)\) | \(e\left(\frac{1199}{1932}\right)\) | \(e\left(\frac{158}{483}\right)\) | \(e\left(\frac{61}{276}\right)\) | \(e\left(\frac{197}{1932}\right)\) | \(e\left(\frac{1097}{1932}\right)\) | \(e\left(\frac{79}{161}\right)\) | \(e\left(\frac{195}{644}\right)\) |
| \(\chi_{40310}(949,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{209}{1932}\right)\) | \(e\left(\frac{703}{966}\right)\) | \(e\left(\frac{209}{966}\right)\) | \(e\left(\frac{793}{1932}\right)\) | \(e\left(\frac{403}{483}\right)\) | \(e\left(\frac{239}{276}\right)\) | \(e\left(\frac{799}{1932}\right)\) | \(e\left(\frac{1615}{1932}\right)\) | \(e\left(\frac{121}{161}\right)\) | \(e\left(\frac{209}{644}\right)\) |
| \(\chi_{40310}(1029,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1097}{1932}\right)\) | \(e\left(\frac{265}{966}\right)\) | \(e\left(\frac{131}{966}\right)\) | \(e\left(\frac{1537}{1932}\right)\) | \(e\left(\frac{211}{483}\right)\) | \(e\left(\frac{95}{276}\right)\) | \(e\left(\frac{1171}{1932}\right)\) | \(e\left(\frac{1627}{1932}\right)\) | \(e\left(\frac{25}{161}\right)\) | \(e\left(\frac{453}{644}\right)\) |
| \(\chi_{40310}(1099,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{787}{1932}\right)\) | \(e\left(\frac{803}{966}\right)\) | \(e\left(\frac{787}{966}\right)\) | \(e\left(\frac{407}{1932}\right)\) | \(e\left(\frac{191}{483}\right)\) | \(e\left(\frac{241}{276}\right)\) | \(e\left(\frac{1733}{1932}\right)\) | \(e\left(\frac{461}{1932}\right)\) | \(e\left(\frac{15}{161}\right)\) | \(e\left(\frac{143}{644}\right)\) |
| \(\chi_{40310}(1129,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1871}{1932}\right)\) | \(e\left(\frac{673}{966}\right)\) | \(e\left(\frac{905}{966}\right)\) | \(e\left(\frac{619}{1932}\right)\) | \(e\left(\frac{370}{483}\right)\) | \(e\left(\frac{197}{276}\right)\) | \(e\left(\frac{229}{1932}\right)\) | \(e\left(\frac{1285}{1932}\right)\) | \(e\left(\frac{24}{161}\right)\) | \(e\left(\frac{583}{644}\right)\) |
| \(\chi_{40310}(1319,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{397}{1932}\right)\) | \(e\left(\frac{545}{966}\right)\) | \(e\left(\frac{397}{966}\right)\) | \(e\left(\frac{1229}{1932}\right)\) | \(e\left(\frac{197}{483}\right)\) | \(e\left(\frac{211}{276}\right)\) | \(e\left(\frac{695}{1932}\right)\) | \(e\left(\frac{1487}{1932}\right)\) | \(e\left(\frac{18}{161}\right)\) | \(e\left(\frac{397}{644}\right)\) |
| \(\chi_{40310}(1349,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{635}{1932}\right)\) | \(e\left(\frac{643}{966}\right)\) | \(e\left(\frac{635}{966}\right)\) | \(e\left(\frac{1411}{1932}\right)\) | \(e\left(\frac{337}{483}\right)\) | \(e\left(\frac{17}{276}\right)\) | \(e\left(\frac{625}{1932}\right)\) | \(e\left(\frac{1921}{1932}\right)\) | \(e\left(\frac{88}{161}\right)\) | \(e\left(\frac{635}{644}\right)\) |