Properties

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

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([18,27,10,24]))
 
pari: [g,chi] = znchar(Mod(599,6048))
 

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.iq
Orbit index = 225

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 ]
 

\(\chi_{6048}(599,\cdot)\) \(\chi_{6048}(695,\cdot)\) \(\chi_{6048}(1607,\cdot)\) \(\chi_{6048}(1703,\cdot)\) \(\chi_{6048}(2615,\cdot)\) \(\chi_{6048}(2711,\cdot)\) \(\chi_{6048}(3623,\cdot)\) \(\chi_{6048}(3719,\cdot)\) \(\chi_{6048}(4631,\cdot)\) \(\chi_{6048}(4727,\cdot)\) \(\chi_{6048}(5639,\cdot)\) \(\chi_{6048}(5735,\cdot)\)

Values on generators

\((4159,3781,3809,2593)\) → \((-1,-i,e\left(\frac{5}{18}\right),e\left(\frac{2}{3}\right))\)

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{17}{36}\right)\)\(e\left(\frac{19}{36}\right)\)\(e\left(\frac{17}{36}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{7}{18}\right)\)\(e\left(\frac{17}{18}\right)\)\(e\left(\frac{19}{36}\right)\)\(e\left(\frac{13}{18}\right)\)\(-i\)
value at  e.g. 2

Related number fields

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