Conductor 3300
Order 10
Real No
Primitive No
Parity Even
Orbit Label 9900.dx

Related objects

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Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(9900)
sage: chi = H[71]
pari: [g,chi] = znchar(Mod(71,9900))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 3300
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 10
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 = Even
Orbit label = 9900.dx
Orbit index = 102

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 ]

\(\chi_{9900}(71,\cdot)\) \(\chi_{9900}(1511,\cdot)\) \(\chi_{9900}(2231,\cdot)\) \(\chi_{9900}(8891,\cdot)\)

Inducing primitive character


Values on generators

\((4951,5501,2377,4501)\) → \((-1,-1,e\left(\frac{3}{5}\right),e\left(\frac{2}{5}\right))\)


value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{5})\)