Conductor 1100
Order 10
Real No
Primitive Yes
Parity Odd
Orbit Label

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(1100)
sage: chi = H[411]
pari: [g,chi] = znchar(Mod(411,1100))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1100
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 = Yes
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Odd
Orbit label =
Orbit index = 48

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 ]

\(\chi_{1100}(31,\cdot)\) \(\chi_{1100}(71,\cdot)\) \(\chi_{1100}(91,\cdot)\) \(\chi_{1100}(411,\cdot)\)

Values on generators

\((551,177,101)\) → \((-1,e\left(\frac{4}{5}\right),e\left(\frac{1}{5}\right))\)


value at  e.g. 2

Related number fields

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