Properties

Conductor 4033
Order 4
Real No
Primitive Yes
Parity Even
Orbit Label 4033.n

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(4033)
sage: chi = H[512]
pari: [g,chi] = znchar(Mod(512,4033))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4033
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 4
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 = Even
Orbit label = 4033.n
Orbit index = 14

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 ]

\(\chi_{4033}(512,\cdot)\) \(\chi_{4033}(3521,\cdot)\)

Values on generators

\((1963,2295)\) → \((i,-i)\)

Values

-11234567891011
\(1\)\(1\)\(1\)\(-1\)\(1\)\(-i\)\(-1\)\(1\)\(1\)\(1\)\(-i\)\(-i\)
value at  e.g. 2

Related number fields

Field of values \(\Q(i)\)