Related objects

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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(27200)
sage: chi = H[1]
pari: [g,chi] = znchar(Mod(1,27200))

Basic properties

Modulus: \(27200\)
Conductor: \(1\)
sage: chi.conductor()
pari: znconreyconductor(g,chi)
Order: \(1\)
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Real: yes
Primitive: no, induced from \(\chi_{1}(1,\cdot)\)
sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
Parity: even
sage: chi.is_odd()
pari: zncharisodd(g,chi)

Galois orbit 27200.None


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

Values on generators

sage: chi(k) for k in H.gens()
pari: [ chareval(g,chi,x) | x <- g.gen ] \\ value in Q/Z

\((20877,1601,19857,5951)\) → \((1,1,1,1)\)

First values

value at e.g. 2

Related number fields

Field of values: \(\Q\)