Properties

Conductor 1
Order 1
Real Yes
Primitive No
Parity Even
Orbit Label 8036.a

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(8036)
sage: chi = H[1]
pari: [g,chi] = znchar(Mod(1,8036))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 1
Real = Yes
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 = 8036.a
Orbit index = 1

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 ]

\(\chi_{8036}(1,\cdot)\)

Inducing primitive character

\(\chi_{1}(1,\cdot)\)

Values on generators

\((4019,493,785)\) → \((1,1,1)\)

Values

-1135911131517192325
\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
value at  e.g. 2

Related number fields

Field of values \(\Q\)