Properties

Label 104.k
Modulus $104$
Conductor $52$
Order $4$
Real no
Primitive no
Minimal no
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(104, base_ring=CyclotomicField(4))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([2,0,3]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(31,104))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(104\)
Conductor: \(52\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(4\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 52.f
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\sqrt{-1}) \)
Fixed field: 4.4.35152.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(15\) \(17\) \(19\) \(21\) \(23\)
\(\chi_{104}(31,\cdot)\) \(1\) \(1\) \(-1\) \(-i\) \(-i\) \(1\) \(-i\) \(i\) \(-1\) \(i\) \(i\) \(1\)
\(\chi_{104}(47,\cdot)\) \(1\) \(1\) \(-1\) \(i\) \(i\) \(1\) \(i\) \(-i\) \(-1\) \(-i\) \(-i\) \(1\)