Properties

Label 4008.3005
Modulus $4008$
Conductor $4008$
Order $2$
Real yes
Primitive yes
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4008)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,1,1,1]))
 
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

Modulus: \(4008\)
Conductor: \(4008\)
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 4008.i

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

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

Values on generators

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

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)
\(1\)\(1\)\(-1\)\(1\)\(1\)\(1\)\(1\)\(-1\)\(1\)\(1\)\(1\)\(1\)
value at e.g. 2

Related number fields

Field of values: \(\Q\)
Fixed field: \(\Q(\sqrt{1002}) \)