Properties

Label 240.bb
Modulus $240$
Conductor $240$
Order $4$
Real no
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(240, base_ring=CyclotomicField(4))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,3,2,3]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(173,240))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(240\)
Conductor: \(240\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(4\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\sqrt{-1}) \)
Fixed field: 4.4.2304000.1

Characters in Galois orbit

Character \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{240}(173,\cdot)\) \(1\) \(1\) \(i\) \(i\) \(-1\) \(i\) \(-i\) \(i\) \(i\) \(1\) \(-1\) \(1\)
\(\chi_{240}(197,\cdot)\) \(1\) \(1\) \(-i\) \(-i\) \(-1\) \(-i\) \(i\) \(-i\) \(-i\) \(1\) \(-1\) \(1\)