Properties

Label 1600.207
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([2,1,1]))
 
pari: [g,chi] = znchar(Mod(207,1600))
 

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 \(\chi_{80}(27,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1600.s

\(\chi_{1600}(207,\cdot)\) \(\chi_{1600}(943,\cdot)\)

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: 4.4.256000.1

Values on generators

\((1151,901,577)\) → \((-1,i,i)\)

Values

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