Conductor 51
Order 16
Real No
Primitive No
Parity Even
Orbit Label 6018.q

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(6018)
sage: chi = H[473]
pari: [g,chi] = znchar(Mod(473,6018))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 51
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
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Even
Orbit label = 6018.q
Orbit index = 17

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 ]

\(\chi_{6018}(473,\cdot)\) \(\chi_{6018}(827,\cdot)\) \(\chi_{6018}(1535,\cdot)\) \(\chi_{6018}(2951,\cdot)\) \(\chi_{6018}(3305,\cdot)\) \(\chi_{6018}(4721,\cdot)\) \(\chi_{6018}(5429,\cdot)\) \(\chi_{6018}(5783,\cdot)\)

Inducing primitive character


Values on generators

\((4013,1771,1123)\) → \((-1,e\left(\frac{9}{16}\right),1)\)


value at  e.g. 2

Related number fields

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