Properties

Conductor 4008
Order 2
Real Yes
Primitive Yes
Parity Even
Orbit Label 4008.i

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(4008)
sage: chi = H[3005]
pari: [g,chi] = znchar(Mod(3005,4008))

Kronecker symbol representation

sage: kronecker_character(4008)
pari: znchartokronecker(g,chi)

\(\displaystyle\left(\frac{4008}{\bullet}\right)\)

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4008
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 = 4008.i
Orbit index = 9

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 ]

\(\chi_{4008}(3005,\cdot)\)

Values on generators

\((3007,2005,1337,673)\) → \((1,-1,-1,-1)\)

Values

-11571113171923252931
\(1\)\(1\)\(-1\)\(1\)\(1\)\(1\)\(1\)\(-1\)\(1\)\(1\)\(1\)\(1\)
value at  e.g. 2

Related number fields

Field of values \(\Q\)