Properties

Conductor 1015
Order 4
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 1015.l

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(1015)
 
sage: chi = H[608]
 
pari: [g,chi] = znchar(Mod(608,1015))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1015
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 = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 1015.l
Orbit index = 12

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 ]
 

\(\chi_{1015}(202,\cdot)\) \(\chi_{1015}(608,\cdot)\)

Values on generators

\((407,871,176)\) → \((-i,-1,-1)\)

Values

-1123468911121316
\(1\)\(1\)\(i\)\(i\)\(-1\)\(-1\)\(-i\)\(-1\)\(-1\)\(-i\)\(-i\)\(1\)
value at  e.g. 2

Related number fields

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