Properties

Modulus 1849
Conductor 1849
Order 129
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 1849.k

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1849)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([110]))
 
pari: [g,chi] = znchar(Mod(6,1849))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 1849
Conductor = 1849
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 129
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 1849.k
Orbit index = 11

Galois orbit

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{1849}(6,\cdot)\) \(\chi_{1849}(36,\cdot)\) \(\chi_{1849}(49,\cdot)\) \(\chi_{1849}(79,\cdot)\) \(\chi_{1849}(92,\cdot)\) \(\chi_{1849}(122,\cdot)\) \(\chi_{1849}(135,\cdot)\) \(\chi_{1849}(165,\cdot)\) \(\chi_{1849}(178,\cdot)\) \(\chi_{1849}(208,\cdot)\) \(\chi_{1849}(221,\cdot)\) \(\chi_{1849}(251,\cdot)\) \(\chi_{1849}(264,\cdot)\) \(\chi_{1849}(294,\cdot)\) \(\chi_{1849}(307,\cdot)\) \(\chi_{1849}(337,\cdot)\) \(\chi_{1849}(350,\cdot)\) \(\chi_{1849}(380,\cdot)\) \(\chi_{1849}(393,\cdot)\) \(\chi_{1849}(436,\cdot)\) \(\chi_{1849}(466,\cdot)\) \(\chi_{1849}(479,\cdot)\) \(\chi_{1849}(509,\cdot)\) \(\chi_{1849}(522,\cdot)\) \(\chi_{1849}(552,\cdot)\) \(\chi_{1849}(565,\cdot)\) \(\chi_{1849}(595,\cdot)\) \(\chi_{1849}(608,\cdot)\) \(\chi_{1849}(638,\cdot)\) \(\chi_{1849}(651,\cdot)\) ...

Values on generators

\(3\) → \(e\left(\frac{110}{129}\right)\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{14}{43}\right)\)\(e\left(\frac{110}{129}\right)\)\(e\left(\frac{28}{43}\right)\)\(e\left(\frac{74}{129}\right)\)\(e\left(\frac{23}{129}\right)\)\(e\left(\frac{118}{129}\right)\)\(e\left(\frac{42}{43}\right)\)\(e\left(\frac{91}{129}\right)\)\(e\left(\frac{116}{129}\right)\)\(e\left(\frac{11}{43}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{129})\)