Properties

Label 4560.ca
Modulus $4560$
Conductor $1520$
Order $4$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4560, base_ring=CyclotomicField(4))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,3,0,1,2]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(2317,4560))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(4560\)
Conductor: \(1520\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(4\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 1520.r
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: 4.4.92416000.2

Characters in Galois orbit

Character \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{4560}(2317,\cdot)\) \(1\) \(1\) \(-i\) \(-i\) \(-1\) \(i\) \(i\) \(i\) \(-1\) \(-1\) \(1\) \(-1\)
\(\chi_{4560}(2773,\cdot)\) \(1\) \(1\) \(i\) \(i\) \(-1\) \(-i\) \(-i\) \(-i\) \(-1\) \(-1\) \(1\) \(-1\)