from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(586971, base_ring=CyclotomicField(2310))
M = H._module
chi = DirichletCharacter(H, M([770,1265,357]))
chi.galois_orbit()
[g,chi] = znchar(Mod(40,586971))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(586971\) | |
| Conductor: | \(53361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2310\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 53361.mf | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{1155})$ |
| Fixed field: | Number field defined by a degree 2310 polynomial (not computed) |
First 31 of 480 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{586971}(40,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{559}{770}\right)\) | \(e\left(\frac{174}{385}\right)\) | \(e\left(\frac{2273}{2310}\right)\) | \(e\left(\frac{137}{770}\right)\) | \(e\left(\frac{164}{231}\right)\) | \(e\left(\frac{401}{1155}\right)\) | \(e\left(\frac{348}{385}\right)\) | \(e\left(\frac{304}{1155}\right)\) | \(e\left(\frac{164}{165}\right)\) | \(e\left(\frac{1007}{2310}\right)\) |
| \(\chi_{586971}(481,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{391}{770}\right)\) | \(e\left(\frac{6}{385}\right)\) | \(e\left(\frac{1937}{2310}\right)\) | \(e\left(\frac{403}{770}\right)\) | \(e\left(\frac{80}{231}\right)\) | \(e\left(\frac{359}{1155}\right)\) | \(e\left(\frac{12}{385}\right)\) | \(e\left(\frac{661}{1155}\right)\) | \(e\left(\frac{146}{165}\right)\) | \(e\left(\frac{1973}{2310}\right)\) |
| \(\chi_{586971}(1564,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{177}{770}\right)\) | \(e\left(\frac{177}{385}\right)\) | \(e\left(\frac{739}{2310}\right)\) | \(e\left(\frac{531}{770}\right)\) | \(e\left(\frac{127}{231}\right)\) | \(e\left(\frac{388}{1155}\right)\) | \(e\left(\frac{354}{385}\right)\) | \(e\left(\frac{827}{1155}\right)\) | \(e\left(\frac{127}{165}\right)\) | \(e\left(\frac{1801}{2310}\right)\) |
| \(\chi_{586971}(2635,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{393}{770}\right)\) | \(e\left(\frac{8}{385}\right)\) | \(e\left(\frac{1171}{2310}\right)\) | \(e\left(\frac{409}{770}\right)\) | \(e\left(\frac{4}{231}\right)\) | \(e\left(\frac{607}{1155}\right)\) | \(e\left(\frac{16}{385}\right)\) | \(e\left(\frac{368}{1155}\right)\) | \(e\left(\frac{103}{165}\right)\) | \(e\left(\frac{1219}{2310}\right)\) |
| \(\chi_{586971}(3379,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{337}{770}\right)\) | \(e\left(\frac{337}{385}\right)\) | \(e\left(\frac{1829}{2310}\right)\) | \(e\left(\frac{241}{770}\right)\) | \(e\left(\frac{53}{231}\right)\) | \(e\left(\frac{593}{1155}\right)\) | \(e\left(\frac{289}{385}\right)\) | \(e\left(\frac{487}{1155}\right)\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{1541}{2310}\right)\) |
| \(\chi_{586971}(4450,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{153}{770}\right)\) | \(e\left(\frac{153}{385}\right)\) | \(e\left(\frac{2231}{2310}\right)\) | \(e\left(\frac{459}{770}\right)\) | \(e\left(\frac{38}{231}\right)\) | \(e\left(\frac{107}{1155}\right)\) | \(e\left(\frac{306}{385}\right)\) | \(e\left(\frac{493}{1155}\right)\) | \(e\left(\frac{38}{165}\right)\) | \(e\left(\frac{839}{2310}\right)\) |
| \(\chi_{586971}(5848,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{369}{770}\right)\) | \(e\left(\frac{369}{385}\right)\) | \(e\left(\frac{1123}{2310}\right)\) | \(e\left(\frac{337}{770}\right)\) | \(e\left(\frac{223}{231}\right)\) | \(e\left(\frac{1096}{1155}\right)\) | \(e\left(\frac{353}{385}\right)\) | \(e\left(\frac{419}{1155}\right)\) | \(e\left(\frac{124}{165}\right)\) | \(e\left(\frac{1027}{2310}\right)\) |
| \(\chi_{586971}(6289,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{761}{770}\right)\) | \(e\left(\frac{376}{385}\right)\) | \(e\left(\frac{367}{2310}\right)\) | \(e\left(\frac{743}{770}\right)\) | \(e\left(\frac{34}{231}\right)\) | \(e\left(\frac{424}{1155}\right)\) | \(e\left(\frac{367}{385}\right)\) | \(e\left(\frac{356}{1155}\right)\) | \(e\left(\frac{1}{165}\right)\) | \(e\left(\frac{313}{2310}\right)\) |
| \(\chi_{586971}(9187,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{167}{770}\right)\) | \(e\left(\frac{167}{385}\right)\) | \(e\left(\frac{1489}{2310}\right)\) | \(e\left(\frac{501}{770}\right)\) | \(e\left(\frac{199}{231}\right)\) | \(e\left(\frac{688}{1155}\right)\) | \(e\left(\frac{334}{385}\right)\) | \(e\left(\frac{752}{1155}\right)\) | \(e\left(\frac{67}{165}\right)\) | \(e\left(\frac{181}{2310}\right)\) |
| \(\chi_{586971}(10258,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{243}{770}\right)\) | \(e\left(\frac{243}{385}\right)\) | \(e\left(\frac{871}{2310}\right)\) | \(e\left(\frac{729}{770}\right)\) | \(e\left(\frac{160}{231}\right)\) | \(e\left(\frac{487}{1155}\right)\) | \(e\left(\frac{101}{385}\right)\) | \(e\left(\frac{398}{1155}\right)\) | \(e\left(\frac{28}{165}\right)\) | \(e\left(\frac{19}{2310}\right)\) |
| \(\chi_{586971}(11002,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{107}{770}\right)\) | \(e\left(\frac{107}{385}\right)\) | \(e\left(\frac{599}{2310}\right)\) | \(e\left(\frac{321}{770}\right)\) | \(e\left(\frac{92}{231}\right)\) | \(e\left(\frac{563}{1155}\right)\) | \(e\left(\frac{214}{385}\right)\) | \(e\left(\frac{1072}{1155}\right)\) | \(e\left(\frac{92}{165}\right)\) | \(e\left(\frac{1241}{2310}\right)\) |
| \(\chi_{586971}(13912,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{401}{770}\right)\) | \(e\left(\frac{16}{385}\right)\) | \(e\left(\frac{1957}{2310}\right)\) | \(e\left(\frac{433}{770}\right)\) | \(e\left(\frac{85}{231}\right)\) | \(e\left(\frac{829}{1155}\right)\) | \(e\left(\frac{32}{385}\right)\) | \(e\left(\frac{1121}{1155}\right)\) | \(e\left(\frac{151}{165}\right)\) | \(e\left(\frac{2053}{2310}\right)\) |
| \(\chi_{586971}(15286,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{239}{770}\right)\) | \(e\left(\frac{239}{385}\right)\) | \(e\left(\frac{863}{2310}\right)\) | \(e\left(\frac{717}{770}\right)\) | \(e\left(\frac{158}{231}\right)\) | \(e\left(\frac{761}{1155}\right)\) | \(e\left(\frac{93}{385}\right)\) | \(e\left(\frac{214}{1155}\right)\) | \(e\left(\frac{59}{165}\right)\) | \(e\left(\frac{2297}{2310}\right)\) |
| \(\chi_{586971}(15727,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{770}\right)\) | \(e\left(\frac{1}{385}\right)\) | \(e\left(\frac{1157}{2310}\right)\) | \(e\left(\frac{3}{770}\right)\) | \(e\left(\frac{116}{231}\right)\) | \(e\left(\frac{509}{1155}\right)\) | \(e\left(\frac{2}{385}\right)\) | \(e\left(\frac{46}{1155}\right)\) | \(e\left(\frac{116}{165}\right)\) | \(e\left(\frac{1163}{2310}\right)\) |
| \(\chi_{586971}(16810,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{157}{770}\right)\) | \(e\left(\frac{157}{385}\right)\) | \(e\left(\frac{2239}{2310}\right)\) | \(e\left(\frac{471}{770}\right)\) | \(e\left(\frac{40}{231}\right)\) | \(e\left(\frac{988}{1155}\right)\) | \(e\left(\frac{314}{385}\right)\) | \(e\left(\frac{677}{1155}\right)\) | \(e\left(\frac{7}{165}\right)\) | \(e\left(\frac{871}{2310}\right)\) |
| \(\chi_{586971}(17881,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{93}{770}\right)\) | \(e\left(\frac{93}{385}\right)\) | \(e\left(\frac{571}{2310}\right)\) | \(e\left(\frac{279}{770}\right)\) | \(e\left(\frac{85}{231}\right)\) | \(e\left(\frac{367}{1155}\right)\) | \(e\left(\frac{186}{385}\right)\) | \(e\left(\frac{428}{1155}\right)\) | \(e\left(\frac{118}{165}\right)\) | \(e\left(\frac{1129}{2310}\right)\) |
| \(\chi_{586971}(18625,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{647}{770}\right)\) | \(e\left(\frac{262}{385}\right)\) | \(e\left(\frac{1679}{2310}\right)\) | \(e\left(\frac{401}{770}\right)\) | \(e\left(\frac{131}{231}\right)\) | \(e\left(\frac{533}{1155}\right)\) | \(e\left(\frac{139}{385}\right)\) | \(e\left(\frac{502}{1155}\right)\) | \(e\left(\frac{32}{165}\right)\) | \(e\left(\frac{941}{2310}\right)\) |
| \(\chi_{586971}(19696,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{183}{770}\right)\) | \(e\left(\frac{183}{385}\right)\) | \(e\left(\frac{2291}{2310}\right)\) | \(e\left(\frac{549}{770}\right)\) | \(e\left(\frac{53}{231}\right)\) | \(e\left(\frac{362}{1155}\right)\) | \(e\left(\frac{366}{385}\right)\) | \(e\left(\frac{718}{1155}\right)\) | \(e\left(\frac{53}{165}\right)\) | \(e\left(\frac{1079}{2310}\right)\) |
| \(\chi_{586971}(21094,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{489}{770}\right)\) | \(e\left(\frac{104}{385}\right)\) | \(e\left(\frac{1363}{2310}\right)\) | \(e\left(\frac{697}{770}\right)\) | \(e\left(\frac{52}{231}\right)\) | \(e\left(\frac{961}{1155}\right)\) | \(e\left(\frac{208}{385}\right)\) | \(e\left(\frac{164}{1155}\right)\) | \(e\left(\frac{19}{165}\right)\) | \(e\left(\frac{1987}{2310}\right)\) |
| \(\chi_{586971}(21535,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{770}\right)\) | \(e\left(\frac{41}{385}\right)\) | \(e\left(\frac{1237}{2310}\right)\) | \(e\left(\frac{123}{770}\right)\) | \(e\left(\frac{136}{231}\right)\) | \(e\left(\frac{79}{1155}\right)\) | \(e\left(\frac{82}{385}\right)\) | \(e\left(\frac{731}{1155}\right)\) | \(e\left(\frac{136}{165}\right)\) | \(e\left(\frac{1483}{2310}\right)\) |
| \(\chi_{586971}(22909,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{770}\right)\) | \(e\left(\frac{79}{385}\right)\) | \(e\left(\frac{1313}{2310}\right)\) | \(e\left(\frac{237}{770}\right)\) | \(e\left(\frac{155}{231}\right)\) | \(e\left(\frac{941}{1155}\right)\) | \(e\left(\frac{158}{385}\right)\) | \(e\left(\frac{169}{1155}\right)\) | \(e\left(\frac{89}{165}\right)\) | \(e\left(\frac{1787}{2310}\right)\) |
| \(\chi_{586971}(23350,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{191}{770}\right)\) | \(e\left(\frac{191}{385}\right)\) | \(e\left(\frac{767}{2310}\right)\) | \(e\left(\frac{573}{770}\right)\) | \(e\left(\frac{134}{231}\right)\) | \(e\left(\frac{584}{1155}\right)\) | \(e\left(\frac{382}{385}\right)\) | \(e\left(\frac{316}{1155}\right)\) | \(e\left(\frac{101}{165}\right)\) | \(e\left(\frac{1913}{2310}\right)\) |
| \(\chi_{586971}(25504,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{713}{770}\right)\) | \(e\left(\frac{328}{385}\right)\) | \(e\left(\frac{271}{2310}\right)\) | \(e\left(\frac{599}{770}\right)\) | \(e\left(\frac{10}{231}\right)\) | \(e\left(\frac{247}{1155}\right)\) | \(e\left(\frac{271}{385}\right)\) | \(e\left(\frac{458}{1155}\right)\) | \(e\left(\frac{43}{165}\right)\) | \(e\left(\frac{2239}{2310}\right)\) |
| \(\chi_{586971}(26248,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{417}{770}\right)\) | \(e\left(\frac{32}{385}\right)\) | \(e\left(\frac{449}{2310}\right)\) | \(e\left(\frac{481}{770}\right)\) | \(e\left(\frac{170}{231}\right)\) | \(e\left(\frac{503}{1155}\right)\) | \(e\left(\frac{64}{385}\right)\) | \(e\left(\frac{1087}{1155}\right)\) | \(e\left(\frac{137}{165}\right)\) | \(e\left(\frac{641}{2310}\right)\) |
| \(\chi_{586971}(28717,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{549}{770}\right)\) | \(e\left(\frac{164}{385}\right)\) | \(e\left(\frac{1483}{2310}\right)\) | \(e\left(\frac{107}{770}\right)\) | \(e\left(\frac{82}{231}\right)\) | \(e\left(\frac{316}{1155}\right)\) | \(e\left(\frac{328}{385}\right)\) | \(e\left(\frac{614}{1155}\right)\) | \(e\left(\frac{49}{165}\right)\) | \(e\left(\frac{157}{2310}\right)\) |
| \(\chi_{586971}(30532,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{689}{770}\right)\) | \(e\left(\frac{304}{385}\right)\) | \(e\left(\frac{1763}{2310}\right)\) | \(e\left(\frac{527}{770}\right)\) | \(e\left(\frac{152}{231}\right)\) | \(e\left(\frac{1121}{1155}\right)\) | \(e\left(\frac{223}{385}\right)\) | \(e\left(\frac{124}{1155}\right)\) | \(e\left(\frac{119}{165}\right)\) | \(e\left(\frac{1277}{2310}\right)\) |
| \(\chi_{586971}(30973,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{381}{770}\right)\) | \(e\left(\frac{381}{385}\right)\) | \(e\left(\frac{377}{2310}\right)\) | \(e\left(\frac{373}{770}\right)\) | \(e\left(\frac{152}{231}\right)\) | \(e\left(\frac{659}{1155}\right)\) | \(e\left(\frac{377}{385}\right)\) | \(e\left(\frac{586}{1155}\right)\) | \(e\left(\frac{86}{165}\right)\) | \(e\left(\frac{353}{2310}\right)\) |
| \(\chi_{586971}(32056,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{137}{770}\right)\) | \(e\left(\frac{137}{385}\right)\) | \(e\left(\frac{1429}{2310}\right)\) | \(e\left(\frac{411}{770}\right)\) | \(e\left(\frac{184}{231}\right)\) | \(e\left(\frac{433}{1155}\right)\) | \(e\left(\frac{274}{385}\right)\) | \(e\left(\frac{527}{1155}\right)\) | \(e\left(\frac{52}{165}\right)\) | \(e\left(\frac{2251}{2310}\right)\) |
| \(\chi_{586971}(33127,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{563}{770}\right)\) | \(e\left(\frac{178}{385}\right)\) | \(e\left(\frac{2281}{2310}\right)\) | \(e\left(\frac{149}{770}\right)\) | \(e\left(\frac{166}{231}\right)\) | \(e\left(\frac{127}{1155}\right)\) | \(e\left(\frac{356}{385}\right)\) | \(e\left(\frac{488}{1155}\right)\) | \(e\left(\frac{133}{165}\right)\) | \(e\left(\frac{1039}{2310}\right)\) |
| \(\chi_{586971}(34942,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{213}{770}\right)\) | \(e\left(\frac{213}{385}\right)\) | \(e\left(\frac{41}{2310}\right)\) | \(e\left(\frac{639}{770}\right)\) | \(e\left(\frac{68}{231}\right)\) | \(e\left(\frac{617}{1155}\right)\) | \(e\left(\frac{41}{385}\right)\) | \(e\left(\frac{943}{1155}\right)\) | \(e\left(\frac{68}{165}\right)\) | \(e\left(\frac{1319}{2310}\right)\) |
| \(\chi_{586971}(38155,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{529}{770}\right)\) | \(e\left(\frac{144}{385}\right)\) | \(e\left(\frac{2213}{2310}\right)\) | \(e\left(\frac{47}{770}\right)\) | \(e\left(\frac{149}{231}\right)\) | \(e\left(\frac{146}{1155}\right)\) | \(e\left(\frac{288}{385}\right)\) | \(e\left(\frac{79}{1155}\right)\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{767}{2310}\right)\) |