Properties

Conductor 1045
Order 2
Real Yes
Primitive Yes
Parity Even
Orbit Label 1045.e

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(1045)
sage: chi = H[1044]
pari: [g,chi] = znchar(Mod(1044,1045))

Kronecker symbol representation

sage: kronecker_character(1045)
pari: znchartokronecker(g,chi)

\(\displaystyle\left(\frac{1045}{\bullet}\right)\)

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1045
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 2
Real = Yes
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 = 1045.e
Orbit index = 5

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 ]

\(\chi_{1045}(1044,\cdot)\)

Values on generators

\((837,761,496)\) → \((-1,-1,-1)\)

Values

-112346789121314
\(1\)\(1\)\(-1\)\(1\)\(1\)\(-1\)\(1\)\(-1\)\(1\)\(1\)\(-1\)\(-1\)
value at  e.g. 2

Related number fields

Field of values \(\Q\)