Properties

Label 104.h
Modulus 104104
Conductor 104104
Order 22
Real yes
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(104, base_ring=CyclotomicField(2))
 
M = H._module
 
chi = DirichletCharacter(H, M([1,1,1]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(51,104))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Kronecker symbol representation

sage: kronecker_character(-104)
 
pari: znchartokronecker(g,chi)
 

(104)\displaystyle\left(\frac{-104}{\bullet}\right)

Basic properties

Modulus: 104104
Conductor: 104104
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 22
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: yes
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\Q
Fixed field: Q(26)\Q(\sqrt{-26})

Characters in Galois orbit

Character 1-1 11 33 55 77 99 1111 1515 1717 1919 2121 2323
χ104(51,)\chi_{104}(51,\cdot) 1-1 11 11 11 11 11 1-1 11 11 1-1 11 1-1