from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35937, base_ring=CyclotomicField(3630))
M = H._module
chi = DirichletCharacter(H, M([2420,3219]))
chi.galois_orbit()
[g,chi] = znchar(Mod(19,35937))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(35937\) | |
| Conductor: | \(11979\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(3630\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 11979.bv | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{1815})$ |
| Fixed field: | Number field defined by a degree 3630 polynomial (not computed) |
First 31 of 880 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{35937}(19,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2009}{3630}\right)\) | \(e\left(\frac{194}{1815}\right)\) | \(e\left(\frac{908}{1815}\right)\) | \(e\left(\frac{2183}{3630}\right)\) | \(e\left(\frac{799}{1210}\right)\) | \(e\left(\frac{13}{242}\right)\) | \(e\left(\frac{1279}{3630}\right)\) | \(e\left(\frac{281}{1815}\right)\) | \(e\left(\frac{388}{1815}\right)\) | \(e\left(\frac{1207}{1210}\right)\) |
| \(\chi_{35937}(46,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3293}{3630}\right)\) | \(e\left(\frac{1478}{1815}\right)\) | \(e\left(\frac{1061}{1815}\right)\) | \(e\left(\frac{2261}{3630}\right)\) | \(e\left(\frac{873}{1210}\right)\) | \(e\left(\frac{119}{242}\right)\) | \(e\left(\frac{613}{3630}\right)\) | \(e\left(\frac{962}{1815}\right)\) | \(e\left(\frac{1141}{1815}\right)\) | \(e\left(\frac{289}{1210}\right)\) |
| \(\chi_{35937}(73,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{881}{3630}\right)\) | \(e\left(\frac{881}{1815}\right)\) | \(e\left(\frac{587}{1815}\right)\) | \(e\left(\frac{1877}{3630}\right)\) | \(e\left(\frac{881}{1210}\right)\) | \(e\left(\frac{137}{242}\right)\) | \(e\left(\frac{541}{3630}\right)\) | \(e\left(\frac{1379}{1815}\right)\) | \(e\left(\frac{1762}{1815}\right)\) | \(e\left(\frac{713}{1210}\right)\) |
| \(\chi_{35937}(127,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{3017}{3630}\right)\) | \(e\left(\frac{1202}{1815}\right)\) | \(e\left(\frac{1079}{1815}\right)\) | \(e\left(\frac{989}{3630}\right)\) | \(e\left(\frac{597}{1210}\right)\) | \(e\left(\frac{103}{242}\right)\) | \(e\left(\frac{3097}{3630}\right)\) | \(e\left(\frac{188}{1815}\right)\) | \(e\left(\frac{589}{1815}\right)\) | \(e\left(\frac{181}{1210}\right)\) |
| \(\chi_{35937}(145,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2803}{3630}\right)\) | \(e\left(\frac{988}{1815}\right)\) | \(e\left(\frac{751}{1815}\right)\) | \(e\left(\frac{2791}{3630}\right)\) | \(e\left(\frac{383}{1210}\right)\) | \(e\left(\frac{45}{242}\right)\) | \(e\left(\frac{2603}{3630}\right)\) | \(e\left(\frac{982}{1815}\right)\) | \(e\left(\frac{161}{1815}\right)\) | \(e\left(\frac{939}{1210}\right)\) |
| \(\chi_{35937}(172,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1951}{3630}\right)\) | \(e\left(\frac{136}{1815}\right)\) | \(e\left(\frac{412}{1815}\right)\) | \(e\left(\frac{127}{3630}\right)\) | \(e\left(\frac{741}{1210}\right)\) | \(e\left(\frac{185}{242}\right)\) | \(e\left(\frac{3011}{3630}\right)\) | \(e\left(\frac{1039}{1815}\right)\) | \(e\left(\frac{272}{1815}\right)\) | \(e\left(\frac{553}{1210}\right)\) |
| \(\chi_{35937}(226,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{397}{3630}\right)\) | \(e\left(\frac{397}{1815}\right)\) | \(e\left(\frac{829}{1815}\right)\) | \(e\left(\frac{2119}{3630}\right)\) | \(e\left(\frac{397}{1210}\right)\) | \(e\left(\frac{137}{242}\right)\) | \(e\left(\frac{2477}{3630}\right)\) | \(e\left(\frac{1258}{1815}\right)\) | \(e\left(\frac{794}{1815}\right)\) | \(e\left(\frac{471}{1210}\right)\) |
| \(\chi_{35937}(316,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{239}{3630}\right)\) | \(e\left(\frac{239}{1815}\right)\) | \(e\left(\frac{1418}{1815}\right)\) | \(e\left(\frac{23}{3630}\right)\) | \(e\left(\frac{239}{1210}\right)\) | \(e\left(\frac{205}{242}\right)\) | \(e\left(\frac{2689}{3630}\right)\) | \(e\left(\frac{131}{1815}\right)\) | \(e\left(\frac{478}{1815}\right)\) | \(e\left(\frac{567}{1210}\right)\) |
| \(\chi_{35937}(343,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{173}{3630}\right)\) | \(e\left(\frac{173}{1815}\right)\) | \(e\left(\frac{791}{1815}\right)\) | \(e\left(\frac{3191}{3630}\right)\) | \(e\left(\frac{173}{1210}\right)\) | \(e\left(\frac{117}{242}\right)\) | \(e\left(\frac{3283}{3630}\right)\) | \(e\left(\frac{1682}{1815}\right)\) | \(e\left(\frac{346}{1815}\right)\) | \(e\left(\frac{699}{1210}\right)\) |
| \(\chi_{35937}(370,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2771}{3630}\right)\) | \(e\left(\frac{956}{1815}\right)\) | \(e\left(\frac{227}{1815}\right)\) | \(e\left(\frac{1907}{3630}\right)\) | \(e\left(\frac{351}{1210}\right)\) | \(e\left(\frac{215}{242}\right)\) | \(e\left(\frac{1681}{3630}\right)\) | \(e\left(\frac{524}{1815}\right)\) | \(e\left(\frac{97}{1815}\right)\) | \(e\left(\frac{453}{1210}\right)\) |
| \(\chi_{35937}(415,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1849}{3630}\right)\) | \(e\left(\frac{34}{1815}\right)\) | \(e\left(\frac{103}{1815}\right)\) | \(e\left(\frac{1393}{3630}\right)\) | \(e\left(\frac{639}{1210}\right)\) | \(e\left(\frac{137}{242}\right)\) | \(e\left(\frac{299}{3630}\right)\) | \(e\left(\frac{1621}{1815}\right)\) | \(e\left(\frac{68}{1815}\right)\) | \(e\left(\frac{1197}{1210}\right)\) |
| \(\chi_{35937}(424,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1427}{3630}\right)\) | \(e\left(\frac{1427}{1815}\right)\) | \(e\left(\frac{1814}{1815}\right)\) | \(e\left(\frac{1079}{3630}\right)\) | \(e\left(\frac{217}{1210}\right)\) | \(e\left(\frac{95}{242}\right)\) | \(e\left(\frac{2887}{3630}\right)\) | \(e\left(\frac{1253}{1815}\right)\) | \(e\left(\frac{1039}{1815}\right)\) | \(e\left(\frac{611}{1210}\right)\) |
| \(\chi_{35937}(442,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1663}{3630}\right)\) | \(e\left(\frac{1663}{1815}\right)\) | \(e\left(\frac{1141}{1815}\right)\) | \(e\left(\frac{3061}{3630}\right)\) | \(e\left(\frac{453}{1210}\right)\) | \(e\left(\frac{21}{242}\right)\) | \(e\left(\frac{1973}{3630}\right)\) | \(e\left(\frac{547}{1815}\right)\) | \(e\left(\frac{1511}{1815}\right)\) | \(e\left(\frac{1019}{1210}\right)\) |
| \(\chi_{35937}(469,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2521}{3630}\right)\) | \(e\left(\frac{706}{1815}\right)\) | \(e\left(\frac{217}{1815}\right)\) | \(e\left(\frac{1807}{3630}\right)\) | \(e\left(\frac{101}{1210}\right)\) | \(e\left(\frac{197}{242}\right)\) | \(e\left(\frac{1511}{3630}\right)\) | \(e\left(\frac{349}{1815}\right)\) | \(e\left(\frac{1412}{1815}\right)\) | \(e\left(\frac{513}{1210}\right)\) |
| \(\chi_{35937}(523,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1447}{3630}\right)\) | \(e\left(\frac{1447}{1815}\right)\) | \(e\left(\frac{1234}{1815}\right)\) | \(e\left(\frac{2539}{3630}\right)\) | \(e\left(\frac{237}{1210}\right)\) | \(e\left(\frac{19}{242}\right)\) | \(e\left(\frac{287}{3630}\right)\) | \(e\left(\frac{178}{1815}\right)\) | \(e\left(\frac{1079}{1815}\right)\) | \(e\left(\frac{461}{1210}\right)\) |
| \(\chi_{35937}(613,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1109}{3630}\right)\) | \(e\left(\frac{1109}{1815}\right)\) | \(e\left(\frac{1598}{1815}\right)\) | \(e\left(\frac{1823}{3630}\right)\) | \(e\left(\frac{1109}{1210}\right)\) | \(e\left(\frac{45}{242}\right)\) | \(e\left(\frac{2119}{3630}\right)\) | \(e\left(\frac{1466}{1815}\right)\) | \(e\left(\frac{403}{1815}\right)\) | \(e\left(\frac{697}{1210}\right)\) |
| \(\chi_{35937}(640,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2993}{3630}\right)\) | \(e\left(\frac{1178}{1815}\right)\) | \(e\left(\frac{686}{1815}\right)\) | \(e\left(\frac{2141}{3630}\right)\) | \(e\left(\frac{573}{1210}\right)\) | \(e\left(\frac{49}{242}\right)\) | \(e\left(\frac{3313}{3630}\right)\) | \(e\left(\frac{752}{1815}\right)\) | \(e\left(\frac{541}{1815}\right)\) | \(e\left(\frac{119}{1210}\right)\) |
| \(\chi_{35937}(667,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{701}{3630}\right)\) | \(e\left(\frac{701}{1815}\right)\) | \(e\left(\frac{362}{1815}\right)\) | \(e\left(\frac{3257}{3630}\right)\) | \(e\left(\frac{701}{1210}\right)\) | \(e\left(\frac{95}{242}\right)\) | \(e\left(\frac{2161}{3630}\right)\) | \(e\left(\frac{164}{1815}\right)\) | \(e\left(\frac{1402}{1815}\right)\) | \(e\left(\frac{853}{1210}\right)\) |
| \(\chi_{35937}(712,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2389}{3630}\right)\) | \(e\left(\frac{574}{1815}\right)\) | \(e\left(\frac{778}{1815}\right)\) | \(e\left(\frac{883}{3630}\right)\) | \(e\left(\frac{1179}{1210}\right)\) | \(e\left(\frac{21}{242}\right)\) | \(e\left(\frac{2699}{3630}\right)\) | \(e\left(\frac{1636}{1815}\right)\) | \(e\left(\frac{1148}{1815}\right)\) | \(e\left(\frac{777}{1210}\right)\) |
| \(\chi_{35937}(721,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{497}{3630}\right)\) | \(e\left(\frac{497}{1815}\right)\) | \(e\left(\frac{1559}{1815}\right)\) | \(e\left(\frac{2159}{3630}\right)\) | \(e\left(\frac{497}{1210}\right)\) | \(e\left(\frac{241}{242}\right)\) | \(e\left(\frac{367}{3630}\right)\) | \(e\left(\frac{1328}{1815}\right)\) | \(e\left(\frac{994}{1815}\right)\) | \(e\left(\frac{931}{1210}\right)\) |
| \(\chi_{35937}(739,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2833}{3630}\right)\) | \(e\left(\frac{1018}{1815}\right)\) | \(e\left(\frac{1696}{1815}\right)\) | \(e\left(\frac{1351}{3630}\right)\) | \(e\left(\frac{413}{1210}\right)\) | \(e\left(\frac{173}{242}\right)\) | \(e\left(\frac{2333}{3630}\right)\) | \(e\left(\frac{277}{1815}\right)\) | \(e\left(\frac{221}{1815}\right)\) | \(e\left(\frac{109}{1210}\right)\) |
| \(\chi_{35937}(910,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{989}{3630}\right)\) | \(e\left(\frac{989}{1815}\right)\) | \(e\left(\frac{1448}{1815}\right)\) | \(e\left(\frac{323}{3630}\right)\) | \(e\left(\frac{989}{1210}\right)\) | \(e\left(\frac{17}{242}\right)\) | \(e\left(\frac{3199}{3630}\right)\) | \(e\left(\frac{656}{1815}\right)\) | \(e\left(\frac{163}{1815}\right)\) | \(e\left(\frac{387}{1210}\right)\) |
| \(\chi_{35937}(937,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{863}{3630}\right)\) | \(e\left(\frac{863}{1815}\right)\) | \(e\left(\frac{746}{1815}\right)\) | \(e\left(\frac{2741}{3630}\right)\) | \(e\left(\frac{863}{1210}\right)\) | \(e\left(\frac{157}{242}\right)\) | \(e\left(\frac{703}{3630}\right)\) | \(e\left(\frac{1802}{1815}\right)\) | \(e\left(\frac{1726}{1815}\right)\) | \(e\left(\frac{969}{1210}\right)\) |
| \(\chi_{35937}(964,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1931}{3630}\right)\) | \(e\left(\frac{116}{1815}\right)\) | \(e\left(\frac{992}{1815}\right)\) | \(e\left(\frac{2297}{3630}\right)\) | \(e\left(\frac{721}{1210}\right)\) | \(e\left(\frac{19}{242}\right)\) | \(e\left(\frac{1981}{3630}\right)\) | \(e\left(\frac{299}{1815}\right)\) | \(e\left(\frac{232}{1815}\right)\) | \(e\left(\frac{703}{1210}\right)\) |
| \(\chi_{35937}(1009,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1939}{3630}\right)\) | \(e\left(\frac{124}{1815}\right)\) | \(e\left(\frac{1123}{1815}\right)\) | \(e\left(\frac{703}{3630}\right)\) | \(e\left(\frac{729}{1210}\right)\) | \(e\left(\frac{37}{242}\right)\) | \(e\left(\frac{3119}{3630}\right)\) | \(e\left(\frac{1321}{1815}\right)\) | \(e\left(\frac{248}{1815}\right)\) | \(e\left(\frac{1127}{1210}\right)\) |
| \(\chi_{35937}(1018,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{227}{3630}\right)\) | \(e\left(\frac{227}{1815}\right)\) | \(e\left(\frac{314}{1815}\right)\) | \(e\left(\frac{599}{3630}\right)\) | \(e\left(\frac{227}{1210}\right)\) | \(e\left(\frac{57}{242}\right)\) | \(e\left(\frac{2797}{3630}\right)\) | \(e\left(\frac{413}{1815}\right)\) | \(e\left(\frac{454}{1815}\right)\) | \(e\left(\frac{1141}{1210}\right)\) |
| \(\chi_{35937}(1036,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2683}{3630}\right)\) | \(e\left(\frac{868}{1815}\right)\) | \(e\left(\frac{601}{1815}\right)\) | \(e\left(\frac{1291}{3630}\right)\) | \(e\left(\frac{263}{1210}\right)\) | \(e\left(\frac{17}{242}\right)\) | \(e\left(\frac{53}{3630}\right)\) | \(e\left(\frac{172}{1815}\right)\) | \(e\left(\frac{1736}{1815}\right)\) | \(e\left(\frac{629}{1210}\right)\) |
| \(\chi_{35937}(1063,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2671}{3630}\right)\) | \(e\left(\frac{856}{1815}\right)\) | \(e\left(\frac{1312}{1815}\right)\) | \(e\left(\frac{1867}{3630}\right)\) | \(e\left(\frac{251}{1210}\right)\) | \(e\left(\frac{111}{242}\right)\) | \(e\left(\frac{161}{3630}\right)\) | \(e\left(\frac{454}{1815}\right)\) | \(e\left(\frac{1712}{1815}\right)\) | \(e\left(\frac{1203}{1210}\right)\) |
| \(\chi_{35937}(1117,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1897}{3630}\right)\) | \(e\left(\frac{82}{1815}\right)\) | \(e\left(\frac{889}{1815}\right)\) | \(e\left(\frac{2719}{3630}\right)\) | \(e\left(\frac{687}{1210}\right)\) | \(e\left(\frac{3}{242}\right)\) | \(e\left(\frac{3497}{3630}\right)\) | \(e\left(\frac{493}{1815}\right)\) | \(e\left(\frac{164}{1815}\right)\) | \(e\left(\frac{111}{1210}\right)\) |
| \(\chi_{35937}(1234,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1043}{3630}\right)\) | \(e\left(\frac{1043}{1815}\right)\) | \(e\left(\frac{971}{1815}\right)\) | \(e\left(\frac{1361}{3630}\right)\) | \(e\left(\frac{1043}{1210}\right)\) | \(e\left(\frac{199}{242}\right)\) | \(e\left(\frac{2713}{3630}\right)\) | \(e\left(\frac{1202}{1815}\right)\) | \(e\left(\frac{271}{1815}\right)\) | \(e\left(\frac{829}{1210}\right)\) |
| \(\chi_{35937}(1261,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{2831}{3630}\right)\) | \(e\left(\frac{1016}{1815}\right)\) | \(e\left(\frac{302}{1815}\right)\) | \(e\left(\frac{2657}{3630}\right)\) | \(e\left(\frac{411}{1210}\right)\) | \(e\left(\frac{229}{242}\right)\) | \(e\left(\frac{1141}{3630}\right)\) | \(e\left(\frac{929}{1815}\right)\) | \(e\left(\frac{217}{1815}\right)\) | \(e\left(\frac{3}{1210}\right)\) |