Properties

Label 1045.k
Modulus 10451045
Conductor 10451045
Order 44
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1045, base_ring=CyclotomicField(4))
 
M = H._module
 
chi = DirichletCharacter(H, M([3,2,2]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(208,1045))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 10451045
Conductor: 10451045
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 44
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(i)\mathbb{Q}(i)
Fixed field: 4.0.5460125.4

Characters in Galois orbit

Character 1-1 11 22 33 44 66 77 88 99 1212 1313 1414
χ1045(208,)\chi_{1045}(208,\cdot) 1-1 11 i-i i-i 1-1 1-1 ii ii 1-1 ii ii 11
χ1045(417,)\chi_{1045}(417,\cdot) 1-1 11 ii ii 1-1 1-1 i-i i-i 1-1 i-i i-i 11