Properties

Conductor 16
Order 4
Real no
Primitive no
Minimal no
Parity even
Orbit label 6048.z

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(6048)
 
sage: chi = H[4537]
 
pari: [g,chi] = znchar(Mod(4537,6048))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 16
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 4
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = no
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 6048.z
Orbit index = 26

Galois orbit

sage: chi.sage_character().galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{6048}(1513,\cdot)\) \(\chi_{6048}(4537,\cdot)\)

Values on generators

\((4159,3781,3809,2593)\) → \((1,i,1,1)\)

Values

-115111317192325293137
\(1\)\(1\)\(i\)\(i\)\(-i\)\(1\)\(-i\)\(-1\)\(-1\)\(-i\)\(1\)\(i\)
value at  e.g. 2

Related number fields

Field of values \(\Q(i)\)