Properties

Label 1600.49
Modulus $1600$
Conductor $80$
Order $4$
Real no
Primitive no
Minimal no
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1600, base_ring=CyclotomicField(4))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,1,2]))
 
pari: [g,chi] = znchar(Mod(49,1600))
 

Basic properties

Modulus: \(1600\)
Conductor: \(80\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(4\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{80}(69,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1600.q

\(\chi_{1600}(49,\cdot)\) \(\chi_{1600}(849,\cdot)\)

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: \(\Q(\sqrt{-1}) \)
Fixed field: 4.4.51200.1

Values on generators

\((1151,901,577)\) → \((1,i,-1)\)

Values

\(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)
\(1\)\(1\)\(i\)\(1\)\(-1\)\(i\)\(i\)\(-1\)\(-i\)\(i\)\(1\)\(-i\)
value at e.g. 2