Conductor 4033
Order 9
Real no
Primitive yes
Minimal yes
Parity even
Orbit label

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(4033)
sage: chi = H[1274]
pari: [g,chi] = znchar(Mod(1274,4033))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4033
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 9
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 =
Orbit index = 34

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 ]

\(\chi_{4033}(1274,\cdot)\) \(\chi_{4033}(1304,\cdot)\) \(\chi_{4033}(1455,\cdot)\) \(\chi_{4033}(1810,\cdot)\) \(\chi_{4033}(2523,\cdot)\) \(\chi_{4033}(3733,\cdot)\)

Values on generators

\((1963,2295)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{8}{9}\right))\)


value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{9})\)