Properties

Label 1088.y
Modulus $1088$
Conductor $544$
Order $8$
Real no
Primitive no
Minimal no
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1088, base_ring=CyclotomicField(8))
 
M = H._module
 
chi = DirichletCharacter(H, M([4,3,6]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(55,1088))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1088\)
Conductor: \(544\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(8\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 544.y
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{8})\)
Fixed field: 8.0.51835034729971712.50

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(19\) \(21\) \(23\)
\(\chi_{1088}(55,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\)
\(\chi_{1088}(455,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\)
\(\chi_{1088}(599,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\)
\(\chi_{1088}(999,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(1\)