Properties

Label 46208.28159
Modulus 4620846208
Conductor 44
Order 22
Real yes
Primitive no
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(46208, base_ring=CyclotomicField(2))
 
M = H._module
 
chi = DirichletCharacter(H, M([1,0,0]))
 
pari: [g,chi] = znchar(Mod(28159,46208))
 

Basic properties

Modulus: 4620846208
Conductor: 44
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 22
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: yes
Primitive: no, induced from χ4(3,)\chi_{4}(3,\cdot)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 46208.d

χ46208(28159,)\chi_{46208}(28159,\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(1)\Q(\sqrt{-1})

Values on generators

(28159,36101,14081)(28159,36101,14081)(1,1,1)(-1,1,1)

First values

aa 1-11133557799111113131515171721212323
χ46208(28159,a) \chi_{ 46208 }(28159, a) 1-1111-1111-1111-1111-111111-1
sage: chi.jacobi_sum(n)
 
χ46208(28159,a)   \chi_{ 46208 }(28159,a) \; at   a=\;a = e.g. 2