Properties

Conductor 1057
Order 2
Real yes
Primitive yes
Minimal yes
Parity even
Orbit label 1057.d

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(1057)
 
sage: chi = H[1056]
 
pari: [g,chi] = znchar(Mod(1056,1057))
 

Kronecker symbol representation

sage: kronecker_character(1057)
 
pari: znchartokronecker(g,chi)
 

\(\displaystyle\left(\frac{1057}{\bullet}\right)\)

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1057
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
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 1057.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 ]
 

\(\chi_{1057}(1056,\cdot)\)

Values on generators

\((605,610)\) → \((-1,-1)\)

Values

-112345689101112
\(1\)\(1\)\(1\)\(1\)\(1\)\(-1\)\(1\)\(1\)\(1\)\(-1\)\(1\)\(1\)
value at  e.g. 2

Related number fields

Field of values \(\Q\)