Conductor 6017
Order 30
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 6017.y

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[41]
pari: [g,chi] = znchar(Mod(41,6017))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 6017
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 30
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 = 6017.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 ]

\(\chi_{6017}(41,\cdot)\) \(\chi_{6017}(1135,\cdot)\) \(\chi_{6017}(1601,\cdot)\) \(\chi_{6017}(2229,\cdot)\) \(\chi_{6017}(3242,\cdot)\) \(\chi_{6017}(4336,\cdot)\) \(\chi_{6017}(4417,\cdot)\) \(\chi_{6017}(5430,\cdot)\)

Values on generators

\((3830,2190)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{1}{6}\right))\)


value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{15})\)