Conductor 6008
Order 10
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 6008.x

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(6008)
sage: chi = H[291]
pari: [g,chi] = znchar(Mod(291,6008))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 6008
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 10
Real = no
sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
Primitive = yes
Minimal = yes
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = even
Orbit label = 6008.x
Orbit index = 24

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 ]

\(\chi_{6008}(291,\cdot)\) \(\chi_{6008}(2435,\cdot)\) \(\chi_{6008}(3363,\cdot)\) \(\chi_{6008}(3675,\cdot)\)

Values on generators

\((1503,3005,1505)\) → \((-1,-1,e\left(\frac{3}{10}\right))\)


value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{5})\)