Properties

Modulus 6048
Conductor 3024
Order 36
Real no
Primitive no
Minimal no
Parity even
Orbit label 6048.iw

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(6048)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,9,10,30]))
 
pari: [g,chi] = znchar(Mod(761,6048))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 6048
Conductor = 3024
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 36
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 = 6048.iw
Orbit index = 231

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 ]
 

\(\chi_{6048}(761,\cdot)\) \(\chi_{6048}(857,\cdot)\) \(\chi_{6048}(1769,\cdot)\) \(\chi_{6048}(1865,\cdot)\) \(\chi_{6048}(2777,\cdot)\) \(\chi_{6048}(2873,\cdot)\) \(\chi_{6048}(3785,\cdot)\) \(\chi_{6048}(3881,\cdot)\) \(\chi_{6048}(4793,\cdot)\) \(\chi_{6048}(4889,\cdot)\) \(\chi_{6048}(5801,\cdot)\) \(\chi_{6048}(5897,\cdot)\)

Values on generators

\((4159,3781,3809,2593)\) → \((1,i,e\left(\frac{5}{18}\right),e\left(\frac{5}{6}\right))\)

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{29}{36}\right)\)\(e\left(\frac{7}{36}\right)\)\(e\left(\frac{17}{36}\right)\)\(1\)\(i\)\(e\left(\frac{2}{9}\right)\)\(e\left(\frac{11}{18}\right)\)\(e\left(\frac{1}{36}\right)\)\(e\left(\frac{7}{18}\right)\)\(e\left(\frac{7}{12}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{36})\)