Properties

Modulus 4032
Conductor 144
Order 12
Real no
Primitive no
Minimal no
Parity even
Orbit label 4032.du

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4032)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([6,3,10,0]))
 
pari: [g,chi] = znchar(Mod(2255,4032))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4032
Conductor = 144
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 12
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = no
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4032.du
Orbit index = 99

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 ]
 

\(\chi_{4032}(239,\cdot)\) \(\chi_{4032}(911,\cdot)\) \(\chi_{4032}(2255,\cdot)\) \(\chi_{4032}(2927,\cdot)\)

Values on generators

\((127,3781,1793,577)\) → \((-1,i,e\left(\frac{5}{6}\right),1)\)

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{5}{12}\right)\)\(-1\)\(i\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{1}{6}\right)\)\(i\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{12})\)