from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4889, base_ring=CyclotomicField(1222))
M = H._module
chi = DirichletCharacter(H, M([617]))
chi.galois_orbit()
[g,chi] = znchar(Mod(4,4889))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(4889\) | |
| Conductor: | \(4889\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1222\) | 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: | $\Q(\zeta_{611})$ |
| Fixed field: | Number field defined by a degree 1222 polynomial (not computed) |
First 31 of 552 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{4889}(4,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{36}{611}\right)\) | \(e\left(\frac{617}{1222}\right)\) | \(e\left(\frac{72}{611}\right)\) | \(e\left(\frac{227}{611}\right)\) | \(e\left(\frac{53}{94}\right)\) | \(e\left(\frac{1057}{1222}\right)\) | \(e\left(\frac{108}{611}\right)\) | \(e\left(\frac{6}{611}\right)\) | \(e\left(\frac{263}{611}\right)\) | \(e\left(\frac{361}{611}\right)\) |
| \(\chi_{4889}(5,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{419}{611}\right)\) | \(e\left(\frac{579}{1222}\right)\) | \(e\left(\frac{227}{611}\right)\) | \(e\left(\frac{215}{611}\right)\) | \(e\left(\frac{15}{94}\right)\) | \(e\left(\frac{269}{1222}\right)\) | \(e\left(\frac{35}{611}\right)\) | \(e\left(\frac{579}{611}\right)\) | \(e\left(\frac{23}{611}\right)\) | \(e\left(\frac{315}{611}\right)\) |
| \(\chi_{4889}(18,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{21}{611}\right)\) | \(e\left(\frac{309}{1222}\right)\) | \(e\left(\frac{42}{611}\right)\) | \(e\left(\frac{387}{611}\right)\) | \(e\left(\frac{27}{94}\right)\) | \(e\left(\frac{973}{1222}\right)\) | \(e\left(\frac{63}{611}\right)\) | \(e\left(\frac{309}{611}\right)\) | \(e\left(\frac{408}{611}\right)\) | \(e\left(\frac{567}{611}\right)\) |
| \(\chi_{4889}(19,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{611}\right)\) | \(e\left(\frac{523}{1222}\right)\) | \(e\left(\frac{166}{611}\right)\) | \(e\left(\frac{133}{611}\right)\) | \(e\left(\frac{53}{94}\right)\) | \(e\left(\frac{587}{1222}\right)\) | \(e\left(\frac{249}{611}\right)\) | \(e\left(\frac{523}{611}\right)\) | \(e\left(\frac{216}{611}\right)\) | \(e\left(\frac{408}{611}\right)\) |
| \(\chi_{4889}(26,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{111}{611}\right)\) | \(e\left(\frac{935}{1222}\right)\) | \(e\left(\frac{222}{611}\right)\) | \(e\left(\frac{38}{611}\right)\) | \(e\left(\frac{89}{94}\right)\) | \(e\left(\frac{255}{1222}\right)\) | \(e\left(\frac{333}{611}\right)\) | \(e\left(\frac{324}{611}\right)\) | \(e\left(\frac{149}{611}\right)\) | \(e\left(\frac{553}{611}\right)\) |
| \(\chi_{4889}(41,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{307}{611}\right)\) | \(e\left(\frac{153}{1222}\right)\) | \(e\left(\frac{3}{611}\right)\) | \(e\left(\frac{595}{611}\right)\) | \(e\left(\frac{59}{94}\right)\) | \(e\left(\frac{375}{1222}\right)\) | \(e\left(\frac{310}{611}\right)\) | \(e\left(\frac{153}{611}\right)\) | \(e\left(\frac{291}{611}\right)\) | \(e\left(\frac{346}{611}\right)\) |
| \(\chi_{4889}(42,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{131}{611}\right)\) | \(e\left(\frac{531}{1222}\right)\) | \(e\left(\frac{262}{611}\right)\) | \(e\left(\frac{232}{611}\right)\) | \(e\left(\frac{61}{94}\right)\) | \(e\left(\frac{367}{1222}\right)\) | \(e\left(\frac{393}{611}\right)\) | \(e\left(\frac{531}{611}\right)\) | \(e\left(\frac{363}{611}\right)\) | \(e\left(\frac{482}{611}\right)\) |
| \(\chi_{4889}(47,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{464}{611}\right)\) | \(e\left(\frac{281}{1222}\right)\) | \(e\left(\frac{317}{611}\right)\) | \(e\left(\frac{346}{611}\right)\) | \(e\left(\frac{93}{94}\right)\) | \(e\left(\frac{521}{1222}\right)\) | \(e\left(\frac{170}{611}\right)\) | \(e\left(\frac{281}{611}\right)\) | \(e\left(\frac{199}{611}\right)\) | \(e\left(\frac{308}{611}\right)\) |
| \(\chi_{4889}(59,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{306}{611}\right)\) | \(e\left(\frac{51}{1222}\right)\) | \(e\left(\frac{1}{611}\right)\) | \(e\left(\frac{402}{611}\right)\) | \(e\left(\frac{51}{94}\right)\) | \(e\left(\frac{125}{1222}\right)\) | \(e\left(\frac{307}{611}\right)\) | \(e\left(\frac{51}{611}\right)\) | \(e\left(\frac{97}{611}\right)\) | \(e\left(\frac{319}{611}\right)\) |
| \(\chi_{4889}(64,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{108}{611}\right)\) | \(e\left(\frac{629}{1222}\right)\) | \(e\left(\frac{216}{611}\right)\) | \(e\left(\frac{70}{611}\right)\) | \(e\left(\frac{65}{94}\right)\) | \(e\left(\frac{727}{1222}\right)\) | \(e\left(\frac{324}{611}\right)\) | \(e\left(\frac{18}{611}\right)\) | \(e\left(\frac{178}{611}\right)\) | \(e\left(\frac{472}{611}\right)\) |
| \(\chi_{4889}(80,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{491}{611}\right)\) | \(e\left(\frac{591}{1222}\right)\) | \(e\left(\frac{371}{611}\right)\) | \(e\left(\frac{58}{611}\right)\) | \(e\left(\frac{27}{94}\right)\) | \(e\left(\frac{1161}{1222}\right)\) | \(e\left(\frac{251}{611}\right)\) | \(e\left(\frac{591}{611}\right)\) | \(e\left(\frac{549}{611}\right)\) | \(e\left(\frac{426}{611}\right)\) |
| \(\chi_{4889}(81,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6}{611}\right)\) | \(e\left(\frac{1}{1222}\right)\) | \(e\left(\frac{12}{611}\right)\) | \(e\left(\frac{547}{611}\right)\) | \(e\left(\frac{1}{94}\right)\) | \(e\left(\frac{889}{1222}\right)\) | \(e\left(\frac{18}{611}\right)\) | \(e\left(\frac{1}{611}\right)\) | \(e\left(\frac{553}{611}\right)\) | \(e\left(\frac{162}{611}\right)\) |
| \(\chi_{4889}(88,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{540}{611}\right)\) | \(e\left(\frac{701}{1222}\right)\) | \(e\left(\frac{469}{611}\right)\) | \(e\left(\frac{350}{611}\right)\) | \(e\left(\frac{43}{94}\right)\) | \(e\left(\frac{1191}{1222}\right)\) | \(e\left(\frac{398}{611}\right)\) | \(e\left(\frac{90}{611}\right)\) | \(e\left(\frac{279}{611}\right)\) | \(e\left(\frac{527}{611}\right)\) |
| \(\chi_{4889}(98,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{241}{611}\right)\) | \(e\left(\frac{753}{1222}\right)\) | \(e\left(\frac{482}{611}\right)\) | \(e\left(\frac{77}{611}\right)\) | \(e\left(\frac{1}{94}\right)\) | \(e\left(\frac{983}{1222}\right)\) | \(e\left(\frac{112}{611}\right)\) | \(e\left(\frac{142}{611}\right)\) | \(e\left(\frac{318}{611}\right)\) | \(e\left(\frac{397}{611}\right)\) |
| \(\chi_{4889}(100,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{263}{611}\right)\) | \(e\left(\frac{553}{1222}\right)\) | \(e\left(\frac{526}{611}\right)\) | \(e\left(\frac{46}{611}\right)\) | \(e\left(\frac{83}{94}\right)\) | \(e\left(\frac{373}{1222}\right)\) | \(e\left(\frac{178}{611}\right)\) | \(e\left(\frac{553}{611}\right)\) | \(e\left(\frac{309}{611}\right)\) | \(e\left(\frac{380}{611}\right)\) |
| \(\chi_{4889}(106,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{319}{611}\right)\) | \(e\left(\frac{155}{1222}\right)\) | \(e\left(\frac{27}{611}\right)\) | \(e\left(\frac{467}{611}\right)\) | \(e\left(\frac{61}{94}\right)\) | \(e\left(\frac{931}{1222}\right)\) | \(e\left(\frac{346}{611}\right)\) | \(e\left(\frac{155}{611}\right)\) | \(e\left(\frac{175}{611}\right)\) | \(e\left(\frac{59}{611}\right)\) |
| \(\chi_{4889}(115,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{175}{611}\right)\) | \(e\left(\frac{131}{1222}\right)\) | \(e\left(\frac{350}{611}\right)\) | \(e\left(\frac{170}{611}\right)\) | \(e\left(\frac{37}{94}\right)\) | \(e\left(\frac{369}{1222}\right)\) | \(e\left(\frac{525}{611}\right)\) | \(e\left(\frac{131}{611}\right)\) | \(e\left(\frac{345}{611}\right)\) | \(e\left(\frac{448}{611}\right)\) |
| \(\chi_{4889}(117,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{96}{611}\right)\) | \(e\left(\frac{627}{1222}\right)\) | \(e\left(\frac{192}{611}\right)\) | \(e\left(\frac{198}{611}\right)\) | \(e\left(\frac{63}{94}\right)\) | \(e\left(\frac{171}{1222}\right)\) | \(e\left(\frac{288}{611}\right)\) | \(e\left(\frac{16}{611}\right)\) | \(e\left(\frac{294}{611}\right)\) | \(e\left(\frac{148}{611}\right)\) |
| \(\chi_{4889}(121,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{361}{611}\right)\) | \(e\left(\frac{773}{1222}\right)\) | \(e\left(\frac{111}{611}\right)\) | \(e\left(\frac{19}{611}\right)\) | \(e\left(\frac{21}{94}\right)\) | \(e\left(\frac{433}{1222}\right)\) | \(e\left(\frac{472}{611}\right)\) | \(e\left(\frac{162}{611}\right)\) | \(e\left(\frac{380}{611}\right)\) | \(e\left(\frac{582}{611}\right)\) |
| \(\chi_{4889}(125,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{35}{611}\right)\) | \(e\left(\frac{515}{1222}\right)\) | \(e\left(\frac{70}{611}\right)\) | \(e\left(\frac{34}{611}\right)\) | \(e\left(\frac{45}{94}\right)\) | \(e\left(\frac{807}{1222}\right)\) | \(e\left(\frac{105}{611}\right)\) | \(e\left(\frac{515}{611}\right)\) | \(e\left(\frac{69}{611}\right)\) | \(e\left(\frac{334}{611}\right)\) |
| \(\chi_{4889}(129,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{603}{611}\right)\) | \(e\left(\frac{1017}{1222}\right)\) | \(e\left(\frac{595}{611}\right)\) | \(e\left(\frac{289}{611}\right)\) | \(e\left(\frac{77}{94}\right)\) | \(e\left(\frac{1055}{1222}\right)\) | \(e\left(\frac{587}{611}\right)\) | \(e\left(\frac{406}{611}\right)\) | \(e\left(\frac{281}{611}\right)\) | \(e\left(\frac{395}{611}\right)\) |
| \(\chi_{4889}(134,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{473}{611}\right)\) | \(e\left(\frac{1199}{1222}\right)\) | \(e\left(\frac{335}{611}\right)\) | \(e\left(\frac{250}{611}\right)\) | \(e\left(\frac{71}{94}\right)\) | \(e\left(\frac{327}{1222}\right)\) | \(e\left(\frac{197}{611}\right)\) | \(e\left(\frac{588}{611}\right)\) | \(e\left(\frac{112}{611}\right)\) | \(e\left(\frac{551}{611}\right)\) |
| \(\chi_{4889}(169,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{186}{611}\right)\) | \(e\left(\frac{31}{1222}\right)\) | \(e\left(\frac{372}{611}\right)\) | \(e\left(\frac{460}{611}\right)\) | \(e\left(\frac{31}{94}\right)\) | \(e\left(\frac{675}{1222}\right)\) | \(e\left(\frac{558}{611}\right)\) | \(e\left(\frac{31}{611}\right)\) | \(e\left(\frac{35}{611}\right)\) | \(e\left(\frac{134}{611}\right)\) |
| \(\chi_{4889}(174,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{482}{611}\right)\) | \(e\left(\frac{895}{1222}\right)\) | \(e\left(\frac{353}{611}\right)\) | \(e\left(\frac{154}{611}\right)\) | \(e\left(\frac{49}{94}\right)\) | \(e\left(\frac{133}{1222}\right)\) | \(e\left(\frac{224}{611}\right)\) | \(e\left(\frac{284}{611}\right)\) | \(e\left(\frac{25}{611}\right)\) | \(e\left(\frac{183}{611}\right)\) |
| \(\chi_{4889}(189,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{116}{611}\right)\) | \(e\left(\frac{223}{1222}\right)\) | \(e\left(\frac{232}{611}\right)\) | \(e\left(\frac{392}{611}\right)\) | \(e\left(\frac{35}{94}\right)\) | \(e\left(\frac{283}{1222}\right)\) | \(e\left(\frac{348}{611}\right)\) | \(e\left(\frac{223}{611}\right)\) | \(e\left(\frac{508}{611}\right)\) | \(e\left(\frac{77}{611}\right)\) |
| \(\chi_{4889}(218,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{279}{611}\right)\) | \(e\left(\frac{963}{1222}\right)\) | \(e\left(\frac{558}{611}\right)\) | \(e\left(\frac{79}{611}\right)\) | \(e\left(\frac{23}{94}\right)\) | \(e\left(\frac{707}{1222}\right)\) | \(e\left(\frac{226}{611}\right)\) | \(e\left(\frac{352}{611}\right)\) | \(e\left(\frac{358}{611}\right)\) | \(e\left(\frac{201}{611}\right)\) |
| \(\chi_{4889}(269,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{443}{611}\right)\) | \(e\left(\frac{583}{1222}\right)\) | \(e\left(\frac{275}{611}\right)\) | \(e\left(\frac{570}{611}\right)\) | \(e\left(\frac{19}{94}\right)\) | \(e\left(\frac{159}{1222}\right)\) | \(e\left(\frac{107}{611}\right)\) | \(e\left(\frac{583}{611}\right)\) | \(e\left(\frac{402}{611}\right)\) | \(e\left(\frac{352}{611}\right)\) |
| \(\chi_{4889}(273,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{206}{611}\right)\) | \(e\left(\frac{849}{1222}\right)\) | \(e\left(\frac{412}{611}\right)\) | \(e\left(\frac{43}{611}\right)\) | \(e\left(\frac{3}{94}\right)\) | \(e\left(\frac{787}{1222}\right)\) | \(e\left(\frac{7}{611}\right)\) | \(e\left(\frac{238}{611}\right)\) | \(e\left(\frac{249}{611}\right)\) | \(e\left(\frac{63}{611}\right)\) |
| \(\chi_{4889}(288,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{93}{611}\right)\) | \(e\left(\frac{321}{1222}\right)\) | \(e\left(\frac{186}{611}\right)\) | \(e\left(\frac{230}{611}\right)\) | \(e\left(\frac{39}{94}\right)\) | \(e\left(\frac{643}{1222}\right)\) | \(e\left(\frac{279}{611}\right)\) | \(e\left(\frac{321}{611}\right)\) | \(e\left(\frac{323}{611}\right)\) | \(e\left(\frac{67}{611}\right)\) |
| \(\chi_{4889}(292,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{210}{611}\right)\) | \(e\left(\frac{35}{1222}\right)\) | \(e\left(\frac{420}{611}\right)\) | \(e\left(\frac{204}{611}\right)\) | \(e\left(\frac{35}{94}\right)\) | \(e\left(\frac{565}{1222}\right)\) | \(e\left(\frac{19}{611}\right)\) | \(e\left(\frac{35}{611}\right)\) | \(e\left(\frac{414}{611}\right)\) | \(e\left(\frac{171}{611}\right)\) |
| \(\chi_{4889}(301,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{102}{611}\right)\) | \(e\left(\frac{17}{1222}\right)\) | \(e\left(\frac{204}{611}\right)\) | \(e\left(\frac{134}{611}\right)\) | \(e\left(\frac{17}{94}\right)\) | \(e\left(\frac{449}{1222}\right)\) | \(e\left(\frac{306}{611}\right)\) | \(e\left(\frac{17}{611}\right)\) | \(e\left(\frac{236}{611}\right)\) | \(e\left(\frac{310}{611}\right)\) |