Properties

Label 3762.2089
Modulus 37623762
Conductor 209209
Order 22
Real yes
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3762, base_ring=CyclotomicField(2))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,1,1]))
 
pari: [g,chi] = znchar(Mod(2089,3762))
 

Basic properties

Modulus: 37623762
Conductor: 209209
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 22
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: yes
Primitive: no, induced from χ209(208,)\chi_{209}(208,\cdot)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3762.g

χ3762(2089,)\chi_{3762}(2089,\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(209)\Q(\sqrt{209})

Values on generators

(2927,343,2377)(2927,343,2377)(1,1,1)(1,-1,-1)

First values

aa 1-111557713131717232325252929313135353737
χ3762(2089,a) \chi_{ 3762 }(2089, a) 1111111-1111-11111111-11-11-1
sage: chi.jacobi_sum(n)
 
χ3762(2089,a)   \chi_{ 3762 }(2089,a) \; at   a=\;a = e.g. 2