from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2183, base_ring=CyclotomicField(1044))
M = H._module
chi = DirichletCharacter(H, M([29,18]))
chi.galois_orbit()
[g,chi] = znchar(Mod(2,2183))
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: | even | 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{2183}(2,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{47}{1044}\right)\) | \(e\left(\frac{305}{522}\right)\) | \(e\left(\frac{47}{522}\right)\) | \(e\left(\frac{775}{1044}\right)\) | \(e\left(\frac{73}{116}\right)\) | \(e\left(\frac{52}{261}\right)\) | \(e\left(\frac{47}{348}\right)\) | \(e\left(\frac{44}{261}\right)\) | \(e\left(\frac{137}{174}\right)\) | \(e\left(\frac{23}{87}\right)\) |
| \(\chi_{2183}(13,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{85}{1044}\right)\) | \(e\left(\frac{385}{522}\right)\) | \(e\left(\frac{85}{522}\right)\) | \(e\left(\frac{713}{1044}\right)\) | \(e\left(\frac{95}{116}\right)\) | \(e\left(\frac{194}{261}\right)\) | \(e\left(\frac{85}{348}\right)\) | \(e\left(\frac{124}{261}\right)\) | \(e\left(\frac{133}{174}\right)\) | \(e\left(\frac{49}{87}\right)\) |
| \(\chi_{2183}(18,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{223}{1044}\right)\) | \(e\left(\frac{181}{522}\right)\) | \(e\left(\frac{223}{522}\right)\) | \(e\left(\frac{323}{1044}\right)\) | \(e\left(\frac{65}{116}\right)\) | \(e\left(\frac{119}{261}\right)\) | \(e\left(\frac{223}{348}\right)\) | \(e\left(\frac{181}{261}\right)\) | \(e\left(\frac{91}{174}\right)\) | \(e\left(\frac{61}{87}\right)\) |
| \(\chi_{2183}(24,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{751}{1044}\right)\) | \(e\left(\frac{331}{522}\right)\) | \(e\left(\frac{229}{522}\right)\) | \(e\left(\frac{11}{1044}\right)\) | \(e\left(\frac{41}{116}\right)\) | \(e\left(\frac{59}{261}\right)\) | \(e\left(\frac{55}{348}\right)\) | \(e\left(\frac{70}{261}\right)\) | \(e\left(\frac{127}{174}\right)\) | \(e\left(\frac{1}{87}\right)\) |
| \(\chi_{2183}(32,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{235}{1044}\right)\) | \(e\left(\frac{481}{522}\right)\) | \(e\left(\frac{235}{522}\right)\) | \(e\left(\frac{743}{1044}\right)\) | \(e\left(\frac{17}{116}\right)\) | \(e\left(\frac{260}{261}\right)\) | \(e\left(\frac{235}{348}\right)\) | \(e\left(\frac{220}{261}\right)\) | \(e\left(\frac{163}{174}\right)\) | \(e\left(\frac{28}{87}\right)\) |
| \(\chi_{2183}(39,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{695}{1044}\right)\) | \(e\left(\frac{323}{522}\right)\) | \(e\left(\frac{173}{522}\right)\) | \(e\left(\frac{487}{1044}\right)\) | \(e\left(\frac{33}{116}\right)\) | \(e\left(\frac{97}{261}\right)\) | \(e\left(\frac{347}{348}\right)\) | \(e\left(\frac{62}{261}\right)\) | \(e\left(\frac{23}{174}\right)\) | \(e\left(\frac{68}{87}\right)\) |
| \(\chi_{2183}(42,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{865}{1044}\right)\) | \(e\left(\frac{49}{522}\right)\) | \(e\left(\frac{343}{522}\right)\) | \(e\left(\frac{869}{1044}\right)\) | \(e\left(\frac{107}{116}\right)\) | \(e\left(\frac{224}{261}\right)\) | \(e\left(\frac{169}{348}\right)\) | \(e\left(\frac{49}{261}\right)\) | \(e\left(\frac{115}{174}\right)\) | \(e\left(\frac{79}{87}\right)\) |
| \(\chi_{2183}(50,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{553}{1044}\right)\) | \(e\left(\frac{79}{522}\right)\) | \(e\left(\frac{31}{522}\right)\) | \(e\left(\frac{389}{1044}\right)\) | \(e\left(\frac{79}{116}\right)\) | \(e\left(\frac{212}{261}\right)\) | \(e\left(\frac{205}{348}\right)\) | \(e\left(\frac{79}{261}\right)\) | \(e\left(\frac{157}{174}\right)\) | \(e\left(\frac{67}{87}\right)\) |
| \(\chi_{2183}(52,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{179}{1044}\right)\) | \(e\left(\frac{473}{522}\right)\) | \(e\left(\frac{179}{522}\right)\) | \(e\left(\frac{175}{1044}\right)\) | \(e\left(\frac{9}{116}\right)\) | \(e\left(\frac{37}{261}\right)\) | \(e\left(\frac{179}{348}\right)\) | \(e\left(\frac{212}{261}\right)\) | \(e\left(\frac{59}{174}\right)\) | \(e\left(\frac{8}{87}\right)\) |
| \(\chi_{2183}(54,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{833}{1044}\right)\) | \(e\left(\frac{119}{522}\right)\) | \(e\left(\frac{311}{522}\right)\) | \(e\left(\frac{97}{1044}\right)\) | \(e\left(\frac{3}{116}\right)\) | \(e\left(\frac{22}{261}\right)\) | \(e\left(\frac{137}{348}\right)\) | \(e\left(\frac{119}{261}\right)\) | \(e\left(\frac{155}{174}\right)\) | \(e\left(\frac{80}{87}\right)\) |
| \(\chi_{2183}(55,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7}{1044}\right)\) | \(e\left(\frac{1}{522}\right)\) | \(e\left(\frac{7}{522}\right)\) | \(e\left(\frac{71}{1044}\right)\) | \(e\left(\frac{1}{116}\right)\) | \(e\left(\frac{191}{261}\right)\) | \(e\left(\frac{7}{348}\right)\) | \(e\left(\frac{1}{261}\right)\) | \(e\left(\frac{13}{174}\right)\) | \(e\left(\frac{46}{87}\right)\) |
| \(\chi_{2183}(56,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{349}{1044}\right)\) | \(e\left(\frac{199}{522}\right)\) | \(e\left(\frac{349}{522}\right)\) | \(e\left(\frac{557}{1044}\right)\) | \(e\left(\frac{83}{116}\right)\) | \(e\left(\frac{164}{261}\right)\) | \(e\left(\frac{1}{348}\right)\) | \(e\left(\frac{199}{261}\right)\) | \(e\left(\frac{151}{174}\right)\) | \(e\left(\frac{19}{87}\right)\) |
| \(\chi_{2183}(61,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{859}{1044}\right)\) | \(e\left(\frac{421}{522}\right)\) | \(e\left(\frac{337}{522}\right)\) | \(e\left(\frac{659}{1044}\right)\) | \(e\left(\frac{73}{116}\right)\) | \(e\left(\frac{23}{261}\right)\) | \(e\left(\frac{163}{348}\right)\) | \(e\left(\frac{160}{261}\right)\) | \(e\left(\frac{79}{174}\right)\) | \(e\left(\frac{52}{87}\right)\) |
| \(\chi_{2183}(69,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{271}{1044}\right)\) | \(e\left(\frac{337}{522}\right)\) | \(e\left(\frac{271}{522}\right)\) | \(e\left(\frac{959}{1044}\right)\) | \(e\left(\frac{105}{116}\right)\) | \(e\left(\frac{161}{261}\right)\) | \(e\left(\frac{271}{348}\right)\) | \(e\left(\frac{76}{261}\right)\) | \(e\left(\frac{31}{174}\right)\) | \(e\left(\frac{16}{87}\right)\) |
| \(\chi_{2183}(72,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{317}{1044}\right)\) | \(e\left(\frac{269}{522}\right)\) | \(e\left(\frac{317}{522}\right)\) | \(e\left(\frac{829}{1044}\right)\) | \(e\left(\frac{95}{116}\right)\) | \(e\left(\frac{223}{261}\right)\) | \(e\left(\frac{317}{348}\right)\) | \(e\left(\frac{8}{261}\right)\) | \(e\left(\frac{17}{174}\right)\) | \(e\left(\frac{20}{87}\right)\) |
| \(\chi_{2183}(89,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{359}{1044}\right)\) | \(e\left(\frac{275}{522}\right)\) | \(e\left(\frac{359}{522}\right)\) | \(e\left(\frac{211}{1044}\right)\) | \(e\left(\frac{101}{116}\right)\) | \(e\left(\frac{64}{261}\right)\) | \(e\left(\frac{11}{348}\right)\) | \(e\left(\frac{14}{261}\right)\) | \(e\left(\frac{95}{174}\right)\) | \(e\left(\frac{35}{87}\right)\) |
| \(\chi_{2183}(91,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{293}{1044}\right)\) | \(e\left(\frac{191}{522}\right)\) | \(e\left(\frac{293}{522}\right)\) | \(e\left(\frac{1033}{1044}\right)\) | \(e\left(\frac{75}{116}\right)\) | \(e\left(\frac{202}{261}\right)\) | \(e\left(\frac{293}{348}\right)\) | \(e\left(\frac{191}{261}\right)\) | \(e\left(\frac{47}{174}\right)\) | \(e\left(\frac{86}{87}\right)\) |
| \(\chi_{2183}(92,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{799}{1044}\right)\) | \(e\left(\frac{487}{522}\right)\) | \(e\left(\frac{277}{522}\right)\) | \(e\left(\frac{647}{1044}\right)\) | \(e\left(\frac{81}{116}\right)\) | \(e\left(\frac{101}{261}\right)\) | \(e\left(\frac{103}{348}\right)\) | \(e\left(\frac{226}{261}\right)\) | \(e\left(\frac{67}{174}\right)\) | \(e\left(\frac{43}{87}\right)\) |
| \(\chi_{2183}(93,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{709}{1044}\right)\) | \(e\left(\frac{325}{522}\right)\) | \(e\left(\frac{187}{522}\right)\) | \(e\left(\frac{629}{1044}\right)\) | \(e\left(\frac{35}{116}\right)\) | \(e\left(\frac{218}{261}\right)\) | \(e\left(\frac{13}{348}\right)\) | \(e\left(\frac{64}{261}\right)\) | \(e\left(\frac{49}{174}\right)\) | \(e\left(\frac{73}{87}\right)\) |
| \(\chi_{2183}(96,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{845}{1044}\right)\) | \(e\left(\frac{419}{522}\right)\) | \(e\left(\frac{323}{522}\right)\) | \(e\left(\frac{517}{1044}\right)\) | \(e\left(\frac{71}{116}\right)\) | \(e\left(\frac{163}{261}\right)\) | \(e\left(\frac{149}{348}\right)\) | \(e\left(\frac{158}{261}\right)\) | \(e\left(\frac{53}{174}\right)\) | \(e\left(\frac{47}{87}\right)\) |
| \(\chi_{2183}(98,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{463}{1044}\right)\) | \(e\left(\frac{439}{522}\right)\) | \(e\left(\frac{463}{522}\right)\) | \(e\left(\frac{371}{1044}\right)\) | \(e\left(\frac{33}{116}\right)\) | \(e\left(\frac{68}{261}\right)\) | \(e\left(\frac{115}{348}\right)\) | \(e\left(\frac{178}{261}\right)\) | \(e\left(\frac{139}{174}\right)\) | \(e\left(\frac{10}{87}\right)\) |
| \(\chi_{2183}(106,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{559}{1044}\right)\) | \(e\left(\frac{229}{522}\right)\) | \(e\left(\frac{37}{522}\right)\) | \(e\left(\frac{599}{1044}\right)\) | \(e\left(\frac{113}{116}\right)\) | \(e\left(\frac{152}{261}\right)\) | \(e\left(\frac{211}{348}\right)\) | \(e\left(\frac{229}{261}\right)\) | \(e\left(\frac{19}{174}\right)\) | \(e\left(\frac{7}{87}\right)\) |
| \(\chi_{2183}(109,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{785}{1044}\right)\) | \(e\left(\frac{485}{522}\right)\) | \(e\left(\frac{263}{522}\right)\) | \(e\left(\frac{505}{1044}\right)\) | \(e\left(\frac{79}{116}\right)\) | \(e\left(\frac{241}{261}\right)\) | \(e\left(\frac{89}{348}\right)\) | \(e\left(\frac{224}{261}\right)\) | \(e\left(\frac{41}{174}\right)\) | \(e\left(\frac{38}{87}\right)\) |
| \(\chi_{2183}(113,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{659}{1044}\right)\) | \(e\left(\frac{467}{522}\right)\) | \(e\left(\frac{137}{522}\right)\) | \(e\left(\frac{271}{1044}\right)\) | \(e\left(\frac{61}{116}\right)\) | \(e\left(\frac{196}{261}\right)\) | \(e\left(\frac{311}{348}\right)\) | \(e\left(\frac{206}{261}\right)\) | \(e\left(\frac{155}{174}\right)\) | \(e\left(\frac{80}{87}\right)\) |
| \(\chi_{2183}(124,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{193}{1044}\right)\) | \(e\left(\frac{475}{522}\right)\) | \(e\left(\frac{193}{522}\right)\) | \(e\left(\frac{317}{1044}\right)\) | \(e\left(\frac{11}{116}\right)\) | \(e\left(\frac{158}{261}\right)\) | \(e\left(\frac{193}{348}\right)\) | \(e\left(\frac{214}{261}\right)\) | \(e\left(\frac{85}{174}\right)\) | \(e\left(\frac{13}{87}\right)\) |
| \(\chi_{2183}(126,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{431}{1044}\right)\) | \(e\left(\frac{509}{522}\right)\) | \(e\left(\frac{431}{522}\right)\) | \(e\left(\frac{643}{1044}\right)\) | \(e\left(\frac{45}{116}\right)\) | \(e\left(\frac{127}{261}\right)\) | \(e\left(\frac{83}{348}\right)\) | \(e\left(\frac{248}{261}\right)\) | \(e\left(\frac{5}{174}\right)\) | \(e\left(\frac{11}{87}\right)\) |
| \(\chi_{2183}(128,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{329}{1044}\right)\) | \(e\left(\frac{47}{522}\right)\) | \(e\left(\frac{329}{522}\right)\) | \(e\left(\frac{205}{1044}\right)\) | \(e\left(\frac{47}{116}\right)\) | \(e\left(\frac{103}{261}\right)\) | \(e\left(\frac{329}{348}\right)\) | \(e\left(\frac{47}{261}\right)\) | \(e\left(\frac{89}{174}\right)\) | \(e\left(\frac{74}{87}\right)\) |
| \(\chi_{2183}(129,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{943}{1044}\right)\) | \(e\left(\frac{433}{522}\right)\) | \(e\left(\frac{421}{522}\right)\) | \(e\left(\frac{467}{1044}\right)\) | \(e\left(\frac{85}{116}\right)\) | \(e\left(\frac{227}{261}\right)\) | \(e\left(\frac{247}{348}\right)\) | \(e\left(\frac{172}{261}\right)\) | \(e\left(\frac{61}{174}\right)\) | \(e\left(\frac{82}{87}\right)\) |
| \(\chi_{2183}(131,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{491}{1044}\right)\) | \(e\left(\frac{443}{522}\right)\) | \(e\left(\frac{491}{522}\right)\) | \(e\left(\frac{655}{1044}\right)\) | \(e\left(\frac{37}{116}\right)\) | \(e\left(\frac{49}{261}\right)\) | \(e\left(\frac{143}{348}\right)\) | \(e\left(\frac{182}{261}\right)\) | \(e\left(\frac{17}{174}\right)\) | \(e\left(\frac{20}{87}\right)\) |
| \(\chi_{2183}(150,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{119}{1044}\right)\) | \(e\left(\frac{17}{522}\right)\) | \(e\left(\frac{119}{522}\right)\) | \(e\left(\frac{163}{1044}\right)\) | \(e\left(\frac{17}{116}\right)\) | \(e\left(\frac{115}{261}\right)\) | \(e\left(\frac{119}{348}\right)\) | \(e\left(\frac{17}{261}\right)\) | \(e\left(\frac{47}{174}\right)\) | \(e\left(\frac{86}{87}\right)\) |
| \(\chi_{2183}(161,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{913}{1044}\right)\) | \(e\left(\frac{205}{522}\right)\) | \(e\left(\frac{391}{522}\right)\) | \(e\left(\frac{461}{1044}\right)\) | \(e\left(\frac{31}{116}\right)\) | \(e\left(\frac{5}{261}\right)\) | \(e\left(\frac{217}{348}\right)\) | \(e\left(\frac{205}{261}\right)\) | \(e\left(\frac{55}{174}\right)\) | \(e\left(\frac{34}{87}\right)\) |