Properties

Label 1805.1
Modulus 18051805
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(1805, base_ring=CyclotomicField(2))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0]))
 
pari: [g,chi] = znchar(Mod(1,1805))
 

Basic properties

Modulus: 18051805
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 1805.a

χ1805(1,)\chi_{1805}(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

(362,1446)(362,1446)(1,1)(1,1)

First values

aa 1-11122334466778899111112121313
χ1805(1,a) \chi_{ 1805 }(1, a) 111111111111111111111111
sage: chi.jacobi_sum(n)
 
χ1805(1,a)   \chi_{ 1805 }(1,a) \; at   a=\;a = e.g. 2