Properties

Label 5520.2621
Modulus $5520$
Conductor $1104$
Order $4$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(5520, base_ring=CyclotomicField(4))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,3,2,0,2]))
 
pari: [g,chi] = znchar(Mod(2621,5520))
 

Basic properties

Modulus: \(5520\)
Conductor: \(1104\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(4\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1104}(413,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5520.da

\(\chi_{5520}(2621,\cdot)\) \(\chi_{5520}(5381,\cdot)\)

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: 4.4.9750528.2

Values on generators

\((4831,1381,1841,4417,1201)\) → \((1,-i,-1,1,-1)\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(1\)\(-i\)\(i\)\(1\)\(-i\)\(-i\)\(1\)\(i\)\(1\)\(i\)
value at e.g. 2