Properties

Label 7948.7947
Modulus $7948$
Conductor $7948$
Order $2$
Real yes
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(7948, base_ring=CyclotomicField(2))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([1,1]))
 
pari: [g,chi] = znchar(Mod(7947,7948))
 

Kronecker symbol representation

sage: kronecker_character(7948)
 
pari: znchartokronecker(g,chi)
 

\(\displaystyle\left(\frac{7948}{\bullet}\right)\)

Basic properties

Modulus: \(7948\)
Conductor: \(7948\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(2\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: yes
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 7948.d

\(\chi_{7948}(7947,\cdot)\)

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

Related number fields

Field of values: \(\Q\)
Fixed field: \(\Q(\sqrt{1987}) \)

Values on generators

\((3975,1989)\) → \((-1,-1)\)

Values

\(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(21\)
\(1\)\(1\)\(1\)\(-1\)\(-1\)\(1\)\(-1\)\(-1\)\(-1\)\(1\)\(1\)\(-1\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 7948 }(7947,a) \;\) at \(\;a = \) e.g. 2