Properties

Label 5520.967
Modulus $5520$
Conductor $40$
Order $4$
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5520, base_ring=CyclotomicField(4))
 
M = H._module
 
chi = DirichletCharacter(H, M([2,2,0,1,0]))
 
pari: [g,chi] = znchar(Mod(967,5520))
 

Basic properties

Modulus: \(5520\)
Conductor: \(40\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(4\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{40}(27,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5520.co

\(\chi_{5520}(967,\cdot)\) \(\chi_{5520}(5383,\cdot)\)

sage: chi.galois_orbit()
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q(\sqrt{-1}) \)
Fixed field: 4.4.8000.1

Values on generators

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

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 5520 }(967, a) \) \(1\)\(1\)\(-i\)\(1\)\(i\)\(i\)\(-1\)\(1\)\(-1\)\(-i\)\(1\)\(-i\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 5520 }(967,a) \;\) at \(\;a = \) e.g. 2