Conductor 4029
Order 12
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4029.y

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(4029)
sage: chi = H[293]
pari: [g,chi] = znchar(Mod(293,4029))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4029
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 12
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 = 4029.y
Orbit index = 25

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 ]

\(\chi_{4029}(293,\cdot)\) \(\chi_{4029}(2078,\cdot)\) \(\chi_{4029}(2189,\cdot)\) \(\chi_{4029}(3974,\cdot)\)

Values on generators

\((2687,3556,3163)\) → \((-1,-i,e\left(\frac{5}{6}\right))\)


value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{12})\)