Properties

Conductor 7031
Order 2
Real Yes
Primitive Yes
Parity Odd
Orbit Label 7031.d

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(7031)
sage: chi = H[7030]
pari: [g,chi] = znchar(Mod(7030,7031))

Kronecker symbol representation

sage: kronecker_character(-7031)
pari: znchartokronecker(g,chi)

\(\displaystyle\left(\frac{-7031}{\bullet}\right)\)

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 7031
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 = Odd
Orbit label = 7031.d
Orbit index = 4

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 ]

\(\chi_{7031}(7030,\cdot)\)

Values on generators

\((1425,5610)\) → \((-1,-1)\)

Values

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

Related number fields

Field of values \(\Q\)