Properties

Label 1323.1
Modulus 13231323
Conductor 11
Order 11
Real yes
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1323, base_ring=CyclotomicField(2))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0]))
 
pari: [g,chi] = znchar(Mod(1,1323))
 

Basic properties

Modulus: 13231323
Conductor: 11
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 11
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: yes
Primitive: no, induced from χ1(0,)\chi_{1}(0,\cdot)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1323.a

χ1323(1,)\chi_{1323}(1,\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\Q

Values on generators

(785,1081)(785,1081)(1,1)(1,1)

First values

aa 1-11122445588101011111313161617171919
χ1323(1,a) \chi_{ 1323 }(1, a) 111111111111111111111111
sage: chi.jacobi_sum(n)
 
χ1323(1,a)   \chi_{ 1323 }(1,a) \; at   a=\;a = e.g. 2