Conductor 45
Order 12
Real No
Primitive No
Parity Odd
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(3600)
sage: chi = H[193]
pari: [g,chi] = znchar(Mod(193,3600))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 45
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 = No
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Odd
Orbit label =
Orbit index = 78

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 ]

\(\chi_{3600}(193,\cdot)\) \(\chi_{3600}(1057,\cdot)\) \(\chi_{3600}(1393,\cdot)\) \(\chi_{3600}(2257,\cdot)\)

Inducing primitive character


Values on generators

\((3151,901,2801,577)\) → \((1,1,e\left(\frac{1}{3}\right),-i)\)


value at  e.g. 2

Related number fields

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