Properties

Modulus 1137
Conductor 1137
Order 2
Real yes
Primitive yes
Minimal yes
Parity even
Orbit label 1137.d

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1137)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([1,1]))
 
pari: [g,chi] = znchar(Mod(1136,1137))
 

Kronecker symbol representation

sage: kronecker_character(1137)
 
pari: znchartokronecker(g,chi)
 

\(\displaystyle\left(\frac{1137}{\bullet}\right)\)

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 1137
Conductor = 1137
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 = 1137.d
Orbit index = 4

Galois orbit

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{1137}(1136,\cdot)\)

Values on generators

\((380,760)\) → \((-1,-1)\)

Values

-11245781011131416
\(1\)\(1\)\(1\)\(1\)\(-1\)\(-1\)\(1\)\(-1\)\(1\)\(-1\)\(-1\)\(1\)
value at  e.g. 2

Related number fields

Field of values \(\Q\)