Properties

Conductor 176684
Order 2
Real Yes
Primitive Yes
Parity Even

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(176684)
sage: chi = H[176683]
pari: [g,chi] = znchar(Mod(176683,176684))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 176684
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 2
Real = Yes
sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
Primitive = Yes
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 ]

\(\chi_{176684}(176683,\cdot)\)

Related number fields

Field of values \(\Q\)