from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(40310, base_ring=CyclotomicField(1932))
M = H._module
chi = DirichletCharacter(H, M([966,1725,952]))
chi.galois_orbit()
[g,chi] = znchar(Mod(69,40310))
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.fw | 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: | $\Q(\zeta_{1932})$ |
| Fixed field: | Number field defined by a degree 1932 polynomial (not computed) |
First 23 of 528 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{40310}(69,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{323}{1932}\right)\) | \(e\left(\frac{823}{966}\right)\) | \(e\left(\frac{323}{966}\right)\) | \(e\left(\frac{1489}{1932}\right)\) | \(e\left(\frac{52}{483}\right)\) | \(e\left(\frac{269}{276}\right)\) | \(e\left(\frac{181}{1932}\right)\) | \(e\left(\frac{37}{1932}\right)\) | \(e\left(\frac{213}{322}\right)\) | \(e\left(\frac{323}{644}\right)\) |
| \(\chi_{40310}(89,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1115}{1932}\right)\) | \(e\left(\frac{589}{966}\right)\) | \(e\left(\frac{149}{966}\right)\) | \(e\left(\frac{325}{1932}\right)\) | \(e\left(\frac{181}{483}\right)\) | \(e\left(\frac{245}{276}\right)\) | \(e\left(\frac{565}{1932}\right)\) | \(e\left(\frac{361}{1932}\right)\) | \(e\left(\frac{181}{322}\right)\) | \(e\left(\frac{471}{644}\right)\) |
| \(\chi_{40310}(159,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1867}{1932}\right)\) | \(e\left(\frac{923}{966}\right)\) | \(e\left(\frac{901}{966}\right)\) | \(e\left(\frac{137}{1932}\right)\) | \(e\left(\frac{323}{483}\right)\) | \(e\left(\frac{133}{276}\right)\) | \(e\left(\frac{149}{1932}\right)\) | \(e\left(\frac{1781}{1932}\right)\) | \(e\left(\frac{1}{322}\right)\) | \(e\left(\frac{579}{644}\right)\) |
| \(\chi_{40310}(259,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1549}{1932}\right)\) | \(e\left(\frac{29}{966}\right)\) | \(e\left(\frac{583}{966}\right)\) | \(e\left(\frac{1907}{1932}\right)\) | \(e\left(\frac{209}{483}\right)\) | \(e\left(\frac{151}{276}\right)\) | \(e\left(\frac{551}{1932}\right)\) | \(e\left(\frac{1607}{1932}\right)\) | \(e\left(\frac{209}{322}\right)\) | \(e\left(\frac{261}{644}\right)\) |
| \(\chi_{40310}(309,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1439}{1932}\right)\) | \(e\left(\frac{625}{966}\right)\) | \(e\left(\frac{473}{966}\right)\) | \(e\left(\frac{1693}{1932}\right)\) | \(e\left(\frac{124}{483}\right)\) | \(e\left(\frac{185}{276}\right)\) | \(e\left(\frac{1249}{1932}\right)\) | \(e\left(\frac{757}{1932}\right)\) | \(e\left(\frac{285}{322}\right)\) | \(e\left(\frac{151}{644}\right)\) |
| \(\chi_{40310}(329,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1117}{1932}\right)\) | \(e\left(\frac{947}{966}\right)\) | \(e\left(\frac{151}{966}\right)\) | \(e\left(\frac{83}{1932}\right)\) | \(e\left(\frac{446}{483}\right)\) | \(e\left(\frac{139}{276}\right)\) | \(e\left(\frac{1571}{1932}\right)\) | \(e\left(\frac{1079}{1932}\right)\) | \(e\left(\frac{285}{322}\right)\) | \(e\left(\frac{473}{644}\right)\) |
| \(\chi_{40310}(359,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1331}{1932}\right)\) | \(e\left(\frac{613}{966}\right)\) | \(e\left(\frac{365}{966}\right)\) | \(e\left(\frac{1237}{1932}\right)\) | \(e\left(\frac{304}{483}\right)\) | \(e\left(\frac{113}{276}\right)\) | \(e\left(\frac{1021}{1932}\right)\) | \(e\left(\frac{625}{1932}\right)\) | \(e\left(\frac{143}{322}\right)\) | \(e\left(\frac{43}{644}\right)\) |
| \(\chi_{40310}(569,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{925}{1932}\right)\) | \(e\left(\frac{389}{966}\right)\) | \(e\left(\frac{925}{966}\right)\) | \(e\left(\frac{131}{1932}\right)\) | \(e\left(\frac{122}{483}\right)\) | \(e\left(\frac{103}{276}\right)\) | \(e\left(\frac{1595}{1932}\right)\) | \(e\left(\frac{1703}{1932}\right)\) | \(e\left(\frac{283}{322}\right)\) | \(e\left(\frac{281}{644}\right)\) |
| \(\chi_{40310}(669,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{947}{1932}\right)\) | \(e\left(\frac{463}{966}\right)\) | \(e\left(\frac{947}{966}\right)\) | \(e\left(\frac{1333}{1932}\right)\) | \(e\left(\frac{139}{483}\right)\) | \(e\left(\frac{41}{276}\right)\) | \(e\left(\frac{1069}{1932}\right)\) | \(e\left(\frac{1873}{1932}\right)\) | \(e\left(\frac{139}{322}\right)\) | \(e\left(\frac{303}{644}\right)\) |
| \(\chi_{40310}(699,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1907}{1932}\right)\) | \(e\left(\frac{355}{966}\right)\) | \(e\left(\frac{941}{966}\right)\) | \(e\left(\frac{1093}{1932}\right)\) | \(e\left(\frac{310}{483}\right)\) | \(e\left(\frac{221}{276}\right)\) | \(e\left(\frac{949}{1932}\right)\) | \(e\left(\frac{685}{1932}\right)\) | \(e\left(\frac{149}{322}\right)\) | \(e\left(\frac{619}{644}\right)\) |
| \(\chi_{40310}(839,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1409}{1932}\right)\) | \(e\left(\frac{85}{966}\right)\) | \(e\left(\frac{443}{966}\right)\) | \(e\left(\frac{1459}{1932}\right)\) | \(e\left(\frac{13}{483}\right)\) | \(e\left(\frac{119}{276}\right)\) | \(e\left(\frac{1615}{1932}\right)\) | \(e\left(\frac{1579}{1932}\right)\) | \(e\left(\frac{13}{322}\right)\) | \(e\left(\frac{121}{644}\right)\) |
| \(\chi_{40310}(859,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1093}{1932}\right)\) | \(e\left(\frac{515}{966}\right)\) | \(e\left(\frac{127}{966}\right)\) | \(e\left(\frac{1055}{1932}\right)\) | \(e\left(\frac{164}{483}\right)\) | \(e\left(\frac{31}{276}\right)\) | \(e\left(\frac{1091}{1932}\right)\) | \(e\left(\frac{191}{1932}\right)\) | \(e\left(\frac{3}{322}\right)\) | \(e\left(\frac{449}{644}\right)\) |
| \(\chi_{40310}(989,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1123}{1932}\right)\) | \(e\left(\frac{89}{966}\right)\) | \(e\left(\frac{157}{966}\right)\) | \(e\left(\frac{1289}{1932}\right)\) | \(e\left(\frac{275}{483}\right)\) | \(e\left(\frac{97}{276}\right)\) | \(e\left(\frac{725}{1932}\right)\) | \(e\left(\frac{1301}{1932}\right)\) | \(e\left(\frac{275}{322}\right)\) | \(e\left(\frac{479}{644}\right)\) |
| \(\chi_{40310}(1059,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1517}{1932}\right)\) | \(e\left(\frac{97}{966}\right)\) | \(e\left(\frac{551}{966}\right)\) | \(e\left(\frac{1915}{1932}\right)\) | \(e\left(\frac{316}{483}\right)\) | \(e\left(\frac{191}{276}\right)\) | \(e\left(\frac{1843}{1932}\right)\) | \(e\left(\frac{1711}{1932}\right)\) | \(e\left(\frac{155}{322}\right)\) | \(e\left(\frac{229}{644}\right)\) |
| \(\chi_{40310}(1149,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{449}{1932}\right)\) | \(e\left(\frac{193}{966}\right)\) | \(e\left(\frac{449}{966}\right)\) | \(e\left(\frac{1699}{1932}\right)\) | \(e\left(\frac{325}{483}\right)\) | \(e\left(\frac{215}{276}\right)\) | \(e\left(\frac{1735}{1932}\right)\) | \(e\left(\frac{835}{1932}\right)\) | \(e\left(\frac{3}{322}\right)\) | \(e\left(\frac{449}{644}\right)\) |
| \(\chi_{40310}(1179,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1663}{1932}\right)\) | \(e\left(\frac{149}{966}\right)\) | \(e\left(\frac{697}{966}\right)\) | \(e\left(\frac{1637}{1932}\right)\) | \(e\left(\frac{341}{483}\right)\) | \(e\left(\frac{181}{276}\right)\) | \(e\left(\frac{1865}{1932}\right)\) | \(e\left(\frac{29}{1932}\right)\) | \(e\left(\frac{19}{322}\right)\) | \(e\left(\frac{375}{644}\right)\) |
| \(\chi_{40310}(1229,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{659}{1932}\right)\) | \(e\left(\frac{109}{966}\right)\) | \(e\left(\frac{659}{966}\right)\) | \(e\left(\frac{1405}{1932}\right)\) | \(e\left(\frac{136}{483}\right)\) | \(e\left(\frac{125}{276}\right)\) | \(e\left(\frac{1105}{1932}\right)\) | \(e\left(\frac{877}{1932}\right)\) | \(e\left(\frac{297}{322}\right)\) | \(e\left(\frac{15}{644}\right)\) |
| \(\chi_{40310}(1239,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1567}{1932}\right)\) | \(e\left(\frac{353}{966}\right)\) | \(e\left(\frac{601}{966}\right)\) | \(e\left(\frac{1661}{1932}\right)\) | \(e\left(\frac{179}{483}\right)\) | \(e\left(\frac{25}{276}\right)\) | \(e\left(\frac{1877}{1932}\right)\) | \(e\left(\frac{341}{1932}\right)\) | \(e\left(\frac{179}{322}\right)\) | \(e\left(\frac{279}{644}\right)\) |
| \(\chi_{40310}(1249,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{919}{1932}\right)\) | \(e\left(\frac{281}{966}\right)\) | \(e\left(\frac{919}{966}\right)\) | \(e\left(\frac{857}{1932}\right)\) | \(e\left(\frac{293}{483}\right)\) | \(e\left(\frac{145}{276}\right)\) | \(e\left(\frac{509}{1932}\right)\) | \(e\left(\frac{1481}{1932}\right)\) | \(e\left(\frac{293}{322}\right)\) | \(e\left(\frac{275}{644}\right)\) |
| \(\chi_{40310}(1279,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1627}{1932}\right)\) | \(e\left(\frac{467}{966}\right)\) | \(e\left(\frac{661}{966}\right)\) | \(e\left(\frac{197}{1932}\right)\) | \(e\left(\frac{401}{483}\right)\) | \(e\left(\frac{157}{276}\right)\) | \(e\left(\frac{1145}{1932}\right)\) | \(e\left(\frac{629}{1932}\right)\) | \(e\left(\frac{79}{322}\right)\) | \(e\left(\frac{339}{644}\right)\) |
| \(\chi_{40310}(1419,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{205}{1932}\right)\) | \(e\left(\frac{953}{966}\right)\) | \(e\left(\frac{205}{966}\right)\) | \(e\left(\frac{311}{1932}\right)\) | \(e\left(\frac{356}{483}\right)\) | \(e\left(\frac{175}{276}\right)\) | \(e\left(\frac{719}{1932}\right)\) | \(e\left(\frac{179}{1932}\right)\) | \(e\left(\frac{195}{322}\right)\) | \(e\left(\frac{205}{644}\right)\) |
| \(\chi_{40310}(1439,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{337}{1932}\right)\) | \(e\left(\frac{431}{966}\right)\) | \(e\left(\frac{337}{966}\right)\) | \(e\left(\frac{1727}{1932}\right)\) | \(e\left(\frac{458}{483}\right)\) | \(e\left(\frac{79}{276}\right)\) | \(e\left(\frac{1427}{1932}\right)\) | \(e\left(\frac{1199}{1932}\right)\) | \(e\left(\frac{297}{322}\right)\) | \(e\left(\frac{337}{644}\right)\) |
| \(\chi_{40310}(1489,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1061}{1932}\right)\) | \(e\left(\frac{583}{966}\right)\) | \(e\left(\frac{95}{966}\right)\) | \(e\left(\frac{1063}{1932}\right)\) | \(e\left(\frac{271}{483}\right)\) | \(e\left(\frac{71}{276}\right)\) | \(e\left(\frac{451}{1932}\right)\) | \(e\left(\frac{295}{1932}\right)\) | \(e\left(\frac{271}{322}\right)\) | \(e\left(\frac{417}{644}\right)\) |