from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(85600, base_ring=CyclotomicField(2120))
M = H._module
chi = DirichletCharacter(H, M([1060,265,1484,420]))
chi.galois_orbit()
[g,chi] = znchar(Mod(59,85600))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(85600\) | |
| Conductor: | \(85600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2120\) | 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: | $\Q(\zeta_{2120})$ |
| Fixed field: | Number field defined by a degree 2120 polynomial (not computed) |
First 20 of 832 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{85600}(59,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1363}{2120}\right)\) | \(e\left(\frac{163}{212}\right)\) | \(e\left(\frac{303}{1060}\right)\) | \(e\left(\frac{1449}{2120}\right)\) | \(e\left(\frac{2011}{2120}\right)\) | \(e\left(\frac{183}{530}\right)\) | \(e\left(\frac{907}{2120}\right)\) | \(e\left(\frac{873}{2120}\right)\) | \(e\left(\frac{247}{1060}\right)\) | \(e\left(\frac{1969}{2120}\right)\) |
| \(\chi_{85600}(139,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1647}{2120}\right)\) | \(e\left(\frac{59}{212}\right)\) | \(e\left(\frac{587}{1060}\right)\) | \(e\left(\frac{981}{2120}\right)\) | \(e\left(\frac{1559}{2120}\right)\) | \(e\left(\frac{407}{530}\right)\) | \(e\left(\frac{2023}{2120}\right)\) | \(e\left(\frac{117}{2120}\right)\) | \(e\left(\frac{503}{1060}\right)\) | \(e\left(\frac{701}{2120}\right)\) |
| \(\chi_{85600}(179,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{549}{2120}\right)\) | \(e\left(\frac{161}{212}\right)\) | \(e\left(\frac{549}{1060}\right)\) | \(e\left(\frac{327}{2120}\right)\) | \(e\left(\frac{1933}{2120}\right)\) | \(e\left(\frac{489}{530}\right)\) | \(e\left(\frac{1381}{2120}\right)\) | \(e\left(\frac{39}{2120}\right)\) | \(e\left(\frac{521}{1060}\right)\) | \(e\left(\frac{1647}{2120}\right)\) |
| \(\chi_{85600}(219,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{451}{2120}\right)\) | \(e\left(\frac{67}{212}\right)\) | \(e\left(\frac{451}{1060}\right)\) | \(e\left(\frac{593}{2120}\right)\) | \(e\left(\frac{387}{2120}\right)\) | \(e\left(\frac{31}{530}\right)\) | \(e\left(\frac{339}{2120}\right)\) | \(e\left(\frac{1121}{2120}\right)\) | \(e\left(\frac{679}{1060}\right)\) | \(e\left(\frac{1353}{2120}\right)\) |
| \(\chi_{85600}(259,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{33}{2120}\right)\) | \(e\left(\frac{129}{212}\right)\) | \(e\left(\frac{33}{1060}\right)\) | \(e\left(\frac{819}{2120}\right)\) | \(e\left(\frac{1321}{2120}\right)\) | \(e\left(\frac{403}{530}\right)\) | \(e\left(\frac{697}{2120}\right)\) | \(e\left(\frac{1323}{2120}\right)\) | \(e\left(\frac{877}{1060}\right)\) | \(e\left(\frac{99}{2120}\right)\) |
| \(\chi_{85600}(339,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{717}{2120}\right)\) | \(e\left(\frac{201}{212}\right)\) | \(e\left(\frac{717}{1060}\right)\) | \(e\left(\frac{1991}{2120}\right)\) | \(e\left(\frac{949}{2120}\right)\) | \(e\left(\frac{517}{530}\right)\) | \(e\left(\frac{1653}{2120}\right)\) | \(e\left(\frac{607}{2120}\right)\) | \(e\left(\frac{553}{1060}\right)\) | \(e\left(\frac{31}{2120}\right)\) |
| \(\chi_{85600}(379,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{779}{2120}\right)\) | \(e\left(\frac{135}{212}\right)\) | \(e\left(\frac{779}{1060}\right)\) | \(e\left(\frac{1217}{2120}\right)\) | \(e\left(\frac{283}{2120}\right)\) | \(e\left(\frac{439}{530}\right)\) | \(e\left(\frac{971}{2120}\right)\) | \(e\left(\frac{9}{2120}\right)\) | \(e\left(\frac{691}{1060}\right)\) | \(e\left(\frac{217}{2120}\right)\) |
| \(\chi_{85600}(419,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{801}{2120}\right)\) | \(e\left(\frac{9}{212}\right)\) | \(e\left(\frac{801}{1060}\right)\) | \(e\left(\frac{1763}{2120}\right)\) | \(e\left(\frac{457}{2120}\right)\) | \(e\left(\frac{1}{530}\right)\) | \(e\left(\frac{729}{2120}\right)\) | \(e\left(\frac{891}{2120}\right)\) | \(e\left(\frac{569}{1060}\right)\) | \(e\left(\frac{283}{2120}\right)\) |
| \(\chi_{85600}(459,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{223}{2120}\right)\) | \(e\left(\frac{43}{212}\right)\) | \(e\left(\frac{223}{1060}\right)\) | \(e\left(\frac{909}{2120}\right)\) | \(e\left(\frac{511}{2120}\right)\) | \(e\left(\frac{523}{530}\right)\) | \(e\left(\frac{727}{2120}\right)\) | \(e\left(\frac{653}{2120}\right)\) | \(e\left(\frac{787}{1060}\right)\) | \(e\left(\frac{669}{2120}\right)\) |
| \(\chi_{85600}(619,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1311}{2120}\right)\) | \(e\left(\frac{191}{212}\right)\) | \(e\left(\frac{251}{1060}\right)\) | \(e\left(\frac{1893}{2120}\right)\) | \(e\left(\frac{1407}{2120}\right)\) | \(e\left(\frac{351}{530}\right)\) | \(e\left(\frac{1479}{2120}\right)\) | \(e\left(\frac{1101}{2120}\right)\) | \(e\left(\frac{439}{1060}\right)\) | \(e\left(\frac{1813}{2120}\right)\) |
| \(\chi_{85600}(659,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{373}{2120}\right)\) | \(e\left(\frac{109}{212}\right)\) | \(e\left(\frac{373}{1060}\right)\) | \(e\left(\frac{199}{2120}\right)\) | \(e\left(\frac{541}{2120}\right)\) | \(e\left(\frac{283}{530}\right)\) | \(e\left(\frac{1197}{2120}\right)\) | \(e\left(\frac{1463}{2120}\right)\) | \(e\left(\frac{437}{1060}\right)\) | \(e\left(\frac{1119}{2120}\right)\) |
| \(\chi_{85600}(739,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{897}{2120}\right)\) | \(e\left(\frac{153}{212}\right)\) | \(e\left(\frac{897}{1060}\right)\) | \(e\left(\frac{291}{2120}\right)\) | \(e\left(\frac{1409}{2120}\right)\) | \(e\left(\frac{17}{530}\right)\) | \(e\left(\frac{1793}{2120}\right)\) | \(e\left(\frac{307}{2120}\right)\) | \(e\left(\frac{133}{1060}\right)\) | \(e\left(\frac{571}{2120}\right)\) |
| \(\chi_{85600}(819,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1101}{2120}\right)\) | \(e\left(\frac{141}{212}\right)\) | \(e\left(\frac{41}{1060}\right)\) | \(e\left(\frac{343}{2120}\right)\) | \(e\left(\frac{517}{2120}\right)\) | \(e\left(\frac{51}{530}\right)\) | \(e\left(\frac{1669}{2120}\right)\) | \(e\left(\frac{391}{2120}\right)\) | \(e\left(\frac{929}{1060}\right)\) | \(e\left(\frac{1183}{2120}\right)\) |
| \(\chi_{85600}(1059,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{113}{2120}\right)\) | \(e\left(\frac{37}{212}\right)\) | \(e\left(\frac{113}{1060}\right)\) | \(e\left(\frac{299}{2120}\right)\) | \(e\left(\frac{1761}{2120}\right)\) | \(e\left(\frac{63}{530}\right)\) | \(e\left(\frac{1937}{2120}\right)\) | \(e\left(\frac{483}{2120}\right)\) | \(e\left(\frac{337}{1060}\right)\) | \(e\left(\frac{339}{2120}\right)\) |
| \(\chi_{85600}(1179,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{499}{2120}\right)\) | \(e\left(\frac{139}{212}\right)\) | \(e\left(\frac{499}{1060}\right)\) | \(e\left(\frac{1977}{2120}\right)\) | \(e\left(\frac{1923}{2120}\right)\) | \(e\left(\frac{39}{530}\right)\) | \(e\left(\frac{1931}{2120}\right)\) | \(e\left(\frac{1889}{2120}\right)\) | \(e\left(\frac{991}{1060}\right)\) | \(e\left(\frac{1497}{2120}\right)\) |
| \(\chi_{85600}(1259,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{743}{2120}\right)\) | \(e\left(\frac{187}{212}\right)\) | \(e\left(\frac{743}{1060}\right)\) | \(e\left(\frac{709}{2120}\right)\) | \(e\left(\frac{191}{2120}\right)\) | \(e\left(\frac{433}{530}\right)\) | \(e\left(\frac{1367}{2120}\right)\) | \(e\left(\frac{493}{2120}\right)\) | \(e\left(\frac{987}{1060}\right)\) | \(e\left(\frac{109}{2120}\right)\) |
| \(\chi_{85600}(1339,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1147}{2120}\right)\) | \(e\left(\frac{51}{212}\right)\) | \(e\left(\frac{87}{1060}\right)\) | \(e\left(\frac{521}{2120}\right)\) | \(e\left(\frac{1459}{2120}\right)\) | \(e\left(\frac{147}{530}\right)\) | \(e\left(\frac{1163}{2120}\right)\) | \(e\left(\frac{1657}{2120}\right)\) | \(e\left(\frac{963}{1060}\right)\) | \(e\left(\frac{1321}{2120}\right)\) |
| \(\chi_{85600}(1379,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1849}{2120}\right)\) | \(e\left(\frac{97}{212}\right)\) | \(e\left(\frac{789}{1060}\right)\) | \(e\left(\frac{1947}{2120}\right)\) | \(e\left(\frac{73}{2120}\right)\) | \(e\left(\frac{529}{530}\right)\) | \(e\left(\frac{1921}{2120}\right)\) | \(e\left(\frac{699}{2120}\right)\) | \(e\left(\frac{1021}{1060}\right)\) | \(e\left(\frac{1307}{2120}\right)\) |
| \(\chi_{85600}(1419,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{831}{2120}\right)\) | \(e\left(\frac{107}{212}\right)\) | \(e\left(\frac{831}{1060}\right)\) | \(e\left(\frac{773}{2120}\right)\) | \(e\left(\frac{887}{2120}\right)\) | \(e\left(\frac{271}{530}\right)\) | \(e\left(\frac{399}{2120}\right)\) | \(e\left(\frac{1901}{2120}\right)\) | \(e\left(\frac{499}{1060}\right)\) | \(e\left(\frac{373}{2120}\right)\) |
| \(\chi_{85600}(1459,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1053}{2120}\right)\) | \(e\left(\frac{69}{212}\right)\) | \(e\left(\frac{1053}{1060}\right)\) | \(e\left(\frac{1079}{2120}\right)\) | \(e\left(\frac{1101}{2120}\right)\) | \(e\left(\frac{43}{530}\right)\) | \(e\left(\frac{77}{2120}\right)\) | \(e\left(\frac{1743}{2120}\right)\) | \(e\left(\frac{617}{1060}\right)\) | \(e\left(\frac{1039}{2120}\right)\) |