Properties

Label 105.g
Modulus 105105
Conductor 105105
Order 22
Real yes
Primitive yes
Minimal yes
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(2))
 
M = H._module
 
chi = DirichletCharacter(H, M([1,1,1]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(104,105))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Kronecker symbol representation

sage: kronecker_character(105)
 
pari: znchartokronecker(g,chi)
 

(105)\displaystyle\left(\frac{105}{\bullet}\right)

Basic properties

Modulus: 105105
Conductor: 105105
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: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q\Q
Fixed field: Q(105)\Q(\sqrt{105})

Characters in Galois orbit

Character 1-1 11 22 44 88 1111 1313 1616 1717 1919 2222 2323
χ105(104,)\chi_{105}(104,\cdot) 11 11 11 11 11 1-1 11 11 1-1 1-1 1-1 11