Properties

Label 4256.bj
Modulus $4256$
Conductor $1064$
Order $6$
Real no
Primitive no
Minimal no
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4256, base_ring=CyclotomicField(6))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,3,4,2]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(2097,4256))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(4256\)
Conductor: \(1064\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(6\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 1064.bb
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\mathbb{Q}(\zeta_3)\)
Fixed field: 6.6.160205169152.2

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(9\) \(11\) \(13\) \(15\) \(17\) \(23\) \(25\) \(27\)
\(\chi_{4256}(2097,\cdot)\) \(1\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)
\(\chi_{4256}(3089,\cdot)\) \(1\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)