Properties

Label 2023.2022
Modulus 20232023
Conductor 119119
Order 22
Real yes
Primitive no
Minimal no
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2023, base_ring=CyclotomicField(2))
 
M = H._module
 
chi = DirichletCharacter(H, M([1,1]))
 
pari: [g,chi] = znchar(Mod(2022,2023))
 

Basic properties

Modulus: 20232023
Conductor: 119119
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 22
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: yes
Primitive: no, induced from χ119(118,)\chi_{119}(118,\cdot)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2023.d

χ2023(2022,)\chi_{2023}(2022,\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\Q
Fixed field: Q(119)\Q(\sqrt{-119})

Values on generators

(290,1737)(290,1737)(1,1)(-1,-1)

First values

aa 1-11122334455668899101011111212
χ2023(2022,a) \chi_{ 2023 }(2022, a) 1-11111111111111111111-111
sage: chi.jacobi_sum(n)
 
χ2023(2022,a)   \chi_{ 2023 }(2022,a) \; at   a=\;a = e.g. 2