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Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(164836)
sage: chi = H[1]
pari: [g,chi] = znchar(Mod(1,164836))

Basic properties

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

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 ]


Related number fields

Field of values \(\Q\)