Properties

Label 176.j
Modulus $176$
Conductor $16$
Order $4$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(176, base_ring=CyclotomicField(4))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,3,0]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(45,176))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(176\)
Conductor: \(16\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(4\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 16.e
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\sqrt{-1}) \)
Fixed field: \(\Q(\zeta_{16})^+\)

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(13\) \(15\) \(17\) \(19\) \(21\) \(23\)
\(\chi_{176}(45,\cdot)\) \(1\) \(1\) \(i\) \(-i\) \(-1\) \(-1\) \(i\) \(1\) \(1\) \(i\) \(-i\) \(-1\)
\(\chi_{176}(133,\cdot)\) \(1\) \(1\) \(-i\) \(i\) \(-1\) \(-1\) \(-i\) \(1\) \(1\) \(-i\) \(i\) \(-1\)