Conductor 448
Order 16
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4032.fb

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(4032)
sage: chi = H[307]
pari: [g,chi] = znchar(Mod(307,4032))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 448
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 16
Real = no
sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
Primitive = no
Minimal = yes
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = even
Orbit label = 4032.fb
Orbit index = 132

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 ]

\(\chi_{4032}(307,\cdot)\) \(\chi_{4032}(811,\cdot)\) \(\chi_{4032}(1315,\cdot)\) \(\chi_{4032}(1819,\cdot)\) \(\chi_{4032}(2323,\cdot)\) \(\chi_{4032}(2827,\cdot)\) \(\chi_{4032}(3331,\cdot)\) \(\chi_{4032}(3835,\cdot)\)

Values on generators

\((127,3781,1793,577)\) → \((-1,e\left(\frac{15}{16}\right),1,-1)\)


value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{16})\)