from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2183, base_ring=CyclotomicField(1044))
M = H._module
chi = DirichletCharacter(H, M([667,108]))
chi.galois_orbit()
[g,chi] = znchar(Mod(5,2183))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(2183\) | |
| Conductor: | \(2183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1044\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | 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: | $\Q(\zeta_{1044})$ |
| Fixed field: | Number field defined by a degree 1044 polynomial (not computed) |
First 31 of 336 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{2183}(5,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{775}{1044}\right)\) | \(e\left(\frac{409}{522}\right)\) | \(e\left(\frac{253}{522}\right)\) | \(e\left(\frac{329}{1044}\right)\) | \(e\left(\frac{61}{116}\right)\) | \(e\left(\frac{80}{261}\right)\) | \(e\left(\frac{79}{348}\right)\) | \(e\left(\frac{148}{261}\right)\) | \(e\left(\frac{5}{87}\right)\) | \(e\left(\frac{131}{174}\right)\) |
| \(\chi_{2183}(15,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{341}{1044}\right)\) | \(e\left(\frac{347}{522}\right)\) | \(e\left(\frac{341}{522}\right)\) | \(e\left(\frac{103}{1044}\right)\) | \(e\left(\frac{115}{116}\right)\) | \(e\left(\frac{244}{261}\right)\) | \(e\left(\frac{341}{348}\right)\) | \(e\left(\frac{86}{261}\right)\) | \(e\left(\frac{37}{87}\right)\) | \(e\left(\frac{169}{174}\right)\) |
| \(\chi_{2183}(17,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{923}{1044}\right)\) | \(e\left(\frac{281}{522}\right)\) | \(e\left(\frac{401}{522}\right)\) | \(e\left(\frac{637}{1044}\right)\) | \(e\left(\frac{49}{116}\right)\) | \(e\left(\frac{166}{261}\right)\) | \(e\left(\frac{227}{348}\right)\) | \(e\left(\frac{20}{261}\right)\) | \(e\left(\frac{43}{87}\right)\) | \(e\left(\frac{13}{174}\right)\) |
| \(\chi_{2183}(19,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{655}{1044}\right)\) | \(e\left(\frac{19}{522}\right)\) | \(e\left(\frac{133}{522}\right)\) | \(e\left(\frac{305}{1044}\right)\) | \(e\left(\frac{77}{116}\right)\) | \(e\left(\frac{236}{261}\right)\) | \(e\left(\frac{307}{348}\right)\) | \(e\left(\frac{19}{261}\right)\) | \(e\left(\frac{80}{87}\right)\) | \(e\left(\frac{95}{174}\right)\) |
| \(\chi_{2183}(20,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{869}{1044}\right)\) | \(e\left(\frac{497}{522}\right)\) | \(e\left(\frac{347}{522}\right)\) | \(e\left(\frac{835}{1044}\right)\) | \(e\left(\frac{91}{116}\right)\) | \(e\left(\frac{184}{261}\right)\) | \(e\left(\frac{173}{348}\right)\) | \(e\left(\frac{236}{261}\right)\) | \(e\left(\frac{55}{87}\right)\) | \(e\left(\frac{49}{174}\right)\) |
| \(\chi_{2183}(22,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{323}{1044}\right)\) | \(e\left(\frac{419}{522}\right)\) | \(e\left(\frac{323}{522}\right)\) | \(e\left(\frac{517}{1044}\right)\) | \(e\left(\frac{13}{116}\right)\) | \(e\left(\frac{163}{261}\right)\) | \(e\left(\frac{323}{348}\right)\) | \(e\left(\frac{158}{261}\right)\) | \(e\left(\frac{70}{87}\right)\) | \(e\left(\frac{7}{174}\right)\) |
| \(\chi_{2183}(35,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{983}{1044}\right)\) | \(e\left(\frac{215}{522}\right)\) | \(e\left(\frac{461}{522}\right)\) | \(e\left(\frac{649}{1044}\right)\) | \(e\left(\frac{41}{116}\right)\) | \(e\left(\frac{88}{261}\right)\) | \(e\left(\frac{287}{348}\right)\) | \(e\left(\frac{215}{261}\right)\) | \(e\left(\frac{49}{87}\right)\) | \(e\left(\frac{31}{174}\right)\) |
| \(\chi_{2183}(57,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{221}{1044}\right)\) | \(e\left(\frac{479}{522}\right)\) | \(e\left(\frac{221}{522}\right)\) | \(e\left(\frac{79}{1044}\right)\) | \(e\left(\frac{15}{116}\right)\) | \(e\left(\frac{139}{261}\right)\) | \(e\left(\frac{221}{348}\right)\) | \(e\left(\frac{218}{261}\right)\) | \(e\left(\frac{25}{87}\right)\) | \(e\left(\frac{133}{174}\right)\) |
| \(\chi_{2183}(76,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{749}{1044}\right)\) | \(e\left(\frac{107}{522}\right)\) | \(e\left(\frac{227}{522}\right)\) | \(e\left(\frac{811}{1044}\right)\) | \(e\left(\frac{107}{116}\right)\) | \(e\left(\frac{79}{261}\right)\) | \(e\left(\frac{53}{348}\right)\) | \(e\left(\frac{107}{261}\right)\) | \(e\left(\frac{43}{87}\right)\) | \(e\left(\frac{13}{174}\right)\) |
| \(\chi_{2183}(79,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{811}{1044}\right)\) | \(e\left(\frac{265}{522}\right)\) | \(e\left(\frac{289}{522}\right)\) | \(e\left(\frac{545}{1044}\right)\) | \(e\left(\frac{33}{116}\right)\) | \(e\left(\frac{242}{261}\right)\) | \(e\left(\frac{115}{348}\right)\) | \(e\left(\frac{4}{261}\right)\) | \(e\left(\frac{26}{87}\right)\) | \(e\left(\frac{107}{174}\right)\) |
| \(\chi_{2183}(87,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{679}{1044}\right)\) | \(e\left(\frac{97}{522}\right)\) | \(e\left(\frac{157}{522}\right)\) | \(e\left(\frac{101}{1044}\right)\) | \(e\left(\frac{97}{116}\right)\) | \(e\left(\frac{257}{261}\right)\) | \(e\left(\frac{331}{348}\right)\) | \(e\left(\frac{97}{261}\right)\) | \(e\left(\frac{65}{87}\right)\) | \(e\left(\frac{137}{174}\right)\) |
| \(\chi_{2183}(94,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{113}{1044}\right)\) | \(e\left(\frac{389}{522}\right)\) | \(e\left(\frac{113}{522}\right)\) | \(e\left(\frac{475}{1044}\right)\) | \(e\left(\frac{99}{116}\right)\) | \(e\left(\frac{175}{261}\right)\) | \(e\left(\frac{113}{348}\right)\) | \(e\left(\frac{128}{261}\right)\) | \(e\left(\frac{49}{87}\right)\) | \(e\left(\frac{31}{174}\right)\) |
| \(\chi_{2183}(116,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{163}{1044}\right)\) | \(e\left(\frac{247}{522}\right)\) | \(e\left(\frac{163}{522}\right)\) | \(e\left(\frac{833}{1044}\right)\) | \(e\left(\frac{73}{116}\right)\) | \(e\left(\frac{197}{261}\right)\) | \(e\left(\frac{163}{348}\right)\) | \(e\left(\frac{247}{261}\right)\) | \(e\left(\frac{83}{87}\right)\) | \(e\left(\frac{17}{174}\right)\) |
| \(\chi_{2183}(130,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{907}{1044}\right)\) | \(e\left(\frac{55}{522}\right)\) | \(e\left(\frac{385}{522}\right)\) | \(e\left(\frac{773}{1044}\right)\) | \(e\left(\frac{113}{116}\right)\) | \(e\left(\frac{65}{261}\right)\) | \(e\left(\frac{211}{348}\right)\) | \(e\left(\frac{55}{261}\right)\) | \(e\left(\frac{53}{87}\right)\) | \(e\left(\frac{101}{174}\right)\) |
| \(\chi_{2183}(133,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{863}{1044}\right)\) | \(e\left(\frac{347}{522}\right)\) | \(e\left(\frac{341}{522}\right)\) | \(e\left(\frac{625}{1044}\right)\) | \(e\left(\frac{57}{116}\right)\) | \(e\left(\frac{244}{261}\right)\) | \(e\left(\frac{167}{348}\right)\) | \(e\left(\frac{86}{261}\right)\) | \(e\left(\frac{37}{87}\right)\) | \(e\left(\frac{169}{174}\right)\) |
| \(\chi_{2183}(135,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{517}{1044}\right)\) | \(e\left(\frac{223}{522}\right)\) | \(e\left(\frac{517}{522}\right)\) | \(e\left(\frac{695}{1044}\right)\) | \(e\left(\frac{107}{116}\right)\) | \(e\left(\frac{50}{261}\right)\) | \(e\left(\frac{169}{348}\right)\) | \(e\left(\frac{223}{261}\right)\) | \(e\left(\frac{14}{87}\right)\) | \(e\left(\frac{71}{174}\right)\) |
| \(\chi_{2183}(143,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{361}{1044}\right)\) | \(e\left(\frac{499}{522}\right)\) | \(e\left(\frac{361}{522}\right)\) | \(e\left(\frac{455}{1044}\right)\) | \(e\left(\frac{35}{116}\right)\) | \(e\left(\frac{44}{261}\right)\) | \(e\left(\frac{13}{348}\right)\) | \(e\left(\frac{238}{261}\right)\) | \(e\left(\frac{68}{87}\right)\) | \(e\left(\frac{59}{174}\right)\) |
| \(\chi_{2183}(146,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{911}{1044}\right)\) | \(e\left(\frac{503}{522}\right)\) | \(e\left(\frac{389}{522}\right)\) | \(e\left(\frac{217}{1044}\right)\) | \(e\left(\frac{97}{116}\right)\) | \(e\left(\frac{25}{261}\right)\) | \(e\left(\frac{215}{348}\right)\) | \(e\left(\frac{242}{261}\right)\) | \(e\left(\frac{7}{87}\right)\) | \(e\left(\frac{79}{174}\right)\) |
| \(\chi_{2183}(153,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{55}{1044}\right)\) | \(e\left(\frac{157}{522}\right)\) | \(e\left(\frac{55}{522}\right)\) | \(e\left(\frac{185}{1044}\right)\) | \(e\left(\frac{41}{116}\right)\) | \(e\left(\frac{233}{261}\right)\) | \(e\left(\frac{55}{348}\right)\) | \(e\left(\frac{157}{261}\right)\) | \(e\left(\frac{20}{87}\right)\) | \(e\left(\frac{89}{174}\right)\) |
| \(\chi_{2183}(163,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{197}{1044}\right)\) | \(e\left(\frac{401}{522}\right)\) | \(e\left(\frac{197}{522}\right)\) | \(e\left(\frac{283}{1044}\right)\) | \(e\left(\frac{111}{116}\right)\) | \(e\left(\frac{118}{261}\right)\) | \(e\left(\frac{197}{348}\right)\) | \(e\left(\frac{140}{261}\right)\) | \(e\left(\frac{40}{87}\right)\) | \(e\left(\frac{91}{174}\right)\) |
| \(\chi_{2183}(166,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{421}{1044}\right)\) | \(e\left(\frac{433}{522}\right)\) | \(e\left(\frac{421}{522}\right)\) | \(e\left(\frac{467}{1044}\right)\) | \(e\left(\frac{27}{116}\right)\) | \(e\left(\frac{227}{261}\right)\) | \(e\left(\frac{73}{348}\right)\) | \(e\left(\frac{172}{261}\right)\) | \(e\left(\frac{74}{87}\right)\) | \(e\left(\frac{77}{174}\right)\) |
| \(\chi_{2183}(167,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{619}{1044}\right)\) | \(e\left(\frac{163}{522}\right)\) | \(e\left(\frac{97}{522}\right)\) | \(e\left(\frac{89}{1044}\right)\) | \(e\left(\frac{105}{116}\right)\) | \(e\left(\frac{74}{261}\right)\) | \(e\left(\frac{271}{348}\right)\) | \(e\left(\frac{163}{261}\right)\) | \(e\left(\frac{59}{87}\right)\) | \(e\left(\frac{119}{174}\right)\) |
| \(\chi_{2183}(180,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{1044}\right)\) | \(e\left(\frac{373}{522}\right)\) | \(e\left(\frac{1}{522}\right)\) | \(e\left(\frac{383}{1044}\right)\) | \(e\left(\frac{83}{116}\right)\) | \(e\left(\frac{251}{261}\right)\) | \(e\left(\frac{1}{348}\right)\) | \(e\left(\frac{112}{261}\right)\) | \(e\left(\frac{32}{87}\right)\) | \(e\left(\frac{125}{174}\right)\) |
| \(\chi_{2183}(198,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{499}{1044}\right)\) | \(e\left(\frac{295}{522}\right)\) | \(e\left(\frac{499}{522}\right)\) | \(e\left(\frac{65}{1044}\right)\) | \(e\left(\frac{5}{116}\right)\) | \(e\left(\frac{230}{261}\right)\) | \(e\left(\frac{151}{348}\right)\) | \(e\left(\frac{34}{261}\right)\) | \(e\left(\frac{47}{87}\right)\) | \(e\left(\frac{83}{174}\right)\) |
| \(\chi_{2183}(202,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{419}{1044}\right)\) | \(e\left(\frac{209}{522}\right)\) | \(e\left(\frac{419}{522}\right)\) | \(e\left(\frac{745}{1044}\right)\) | \(e\left(\frac{93}{116}\right)\) | \(e\left(\frac{247}{261}\right)\) | \(e\left(\frac{71}{348}\right)\) | \(e\left(\frac{209}{261}\right)\) | \(e\left(\frac{10}{87}\right)\) | \(e\left(\frac{1}{174}\right)\) |
| \(\chi_{2183}(203,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{277}{1044}\right)\) | \(e\left(\frac{487}{522}\right)\) | \(e\left(\frac{277}{522}\right)\) | \(e\left(\frac{647}{1044}\right)\) | \(e\left(\frac{23}{116}\right)\) | \(e\left(\frac{101}{261}\right)\) | \(e\left(\frac{277}{348}\right)\) | \(e\left(\frac{226}{261}\right)\) | \(e\left(\frac{77}{87}\right)\) | \(e\left(\frac{173}{174}\right)\) |
| \(\chi_{2183}(204,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{583}{1044}\right)\) | \(e\left(\frac{307}{522}\right)\) | \(e\left(\frac{61}{522}\right)\) | \(e\left(\frac{917}{1044}\right)\) | \(e\left(\frac{17}{116}\right)\) | \(e\left(\frac{173}{261}\right)\) | \(e\left(\frac{235}{348}\right)\) | \(e\left(\frac{46}{261}\right)\) | \(e\left(\frac{38}{87}\right)\) | \(e\left(\frac{143}{174}\right)\) |
| \(\chi_{2183}(205,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{41}{1044}\right)\) | \(e\left(\frac{155}{522}\right)\) | \(e\left(\frac{41}{522}\right)\) | \(e\left(\frac{43}{1044}\right)\) | \(e\left(\frac{39}{116}\right)\) | \(e\left(\frac{112}{261}\right)\) | \(e\left(\frac{41}{348}\right)\) | \(e\left(\frac{155}{261}\right)\) | \(e\left(\frac{7}{87}\right)\) | \(e\left(\frac{79}{174}\right)\) |
| \(\chi_{2183}(239,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{59}{1044}\right)\) | \(e\left(\frac{83}{522}\right)\) | \(e\left(\frac{59}{522}\right)\) | \(e\left(\frac{673}{1044}\right)\) | \(e\left(\frac{25}{116}\right)\) | \(e\left(\frac{193}{261}\right)\) | \(e\left(\frac{59}{348}\right)\) | \(e\left(\frac{83}{261}\right)\) | \(e\left(\frac{61}{87}\right)\) | \(e\left(\frac{67}{174}\right)\) |
| \(\chi_{2183}(240,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{529}{1044}\right)\) | \(e\left(\frac{1}{522}\right)\) | \(e\left(\frac{7}{522}\right)\) | \(e\left(\frac{71}{1044}\right)\) | \(e\left(\frac{59}{116}\right)\) | \(e\left(\frac{191}{261}\right)\) | \(e\left(\frac{181}{348}\right)\) | \(e\left(\frac{1}{261}\right)\) | \(e\left(\frac{50}{87}\right)\) | \(e\left(\frac{5}{174}\right)\) |
| \(\chi_{2183}(241,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{79}{1044}\right)\) | \(e\left(\frac{235}{522}\right)\) | \(e\left(\frac{79}{522}\right)\) | \(e\left(\frac{1025}{1044}\right)\) | \(e\left(\frac{61}{116}\right)\) | \(e\left(\frac{254}{261}\right)\) | \(e\left(\frac{79}{348}\right)\) | \(e\left(\frac{235}{261}\right)\) | \(e\left(\frac{5}{87}\right)\) | \(e\left(\frac{131}{174}\right)\) |