Conductor 215
Order 14
Real no
Primitive no
Minimal yes
Parity even
Orbit label

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(4730)
sage: chi = H[3389]
pari: [g,chi] = znchar(Mod(3389,4730))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 215
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 14
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 =
Orbit index = 38

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 ]

\(\chi_{4730}(1079,\cdot)\) \(\chi_{4730}(3279,\cdot)\) \(\chi_{4730}(3389,\cdot)\) \(\chi_{4730}(3499,\cdot)\) \(\chi_{4730}(3719,\cdot)\) \(\chi_{4730}(4599,\cdot)\)

Values on generators

\((947,431,1981)\) → \((-1,1,e\left(\frac{3}{7}\right))\)


value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{7})\)