Conductor 1008
Order 12
Real no
Primitive no
Minimal no
Parity even
Orbit label 6048.ex

Related objects

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Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(6048)
sage: chi = H[4409]
pari: [g,chi] = znchar(Mod(4409,6048))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1008
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 = 6048.ex
Orbit index = 128

Galois orbit

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

\(\chi_{6048}(1385,\cdot)\) \(\chi_{6048}(2393,\cdot)\) \(\chi_{6048}(4409,\cdot)\) \(\chi_{6048}(5417,\cdot)\)

Values on generators

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


value at  e.g. 2

Related number fields

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