Properties

Label 2600.p
Modulus 26002600
Conductor 520520
Order 22
Real yes
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2600, base_ring=CyclotomicField(2))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,1,1,1]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(1949,2600))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 26002600
Conductor: 520520
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 22
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: yes
Primitive: no, induced from 520.p
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q\Q
Fixed field: Q(130)\Q(\sqrt{130})

Characters in Galois orbit

Character 1-1 11 33 77 99 1111 1717 1919 2121 2323 2727 2929
χ2600(1949,)\chi_{2600}(1949,\cdot) 11 11 11 11 11 11 1-1 11 11 1-1 11 1-1