Conductor 547
Order 7
Real no
Primitive no
Minimal yes
Parity even
Orbit label 6017.j

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(6017)
sage: chi = H[628]
pari: [g,chi] = znchar(Mod(628,6017))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 547
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 7
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 = 6017.j
Orbit index = 10

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 ]

\(\chi_{6017}(628,\cdot)\) \(\chi_{6017}(1398,\cdot)\) \(\chi_{6017}(3279,\cdot)\) \(\chi_{6017}(4896,\cdot)\) \(\chi_{6017}(5105,\cdot)\) \(\chi_{6017}(5479,\cdot)\)

Values on generators

\((3830,2190)\) → \((1,e\left(\frac{1}{7}\right))\)


value at  e.g. 2

Related number fields

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