Properties

Conductor 8
Order 2
Real Yes
Primitive No
Parity Even
Orbit Label 6008.c

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(6008)
 
sage: chi = H[3005]
 
pari: [g,chi] = znchar(Mod(3005,6008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 2
Real = Yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 6008.c
Orbit index = 3

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 ]
 

\(\chi_{6008}(3005,\cdot)\)

Inducing primitive character

\(\chi_{8}(5,\cdot)\) = \(\displaystyle\left(\frac{8}{\bullet}\right)\)

Values on generators

\((1503,3005,1505)\) → \((1,-1,1)\)

Values

-113579111315171921
\(1\)\(1\)\(-1\)\(-1\)\(1\)\(1\)\(-1\)\(-1\)\(1\)\(1\)\(-1\)\(-1\)
value at  e.g. 2

Related number fields

Field of values \(\Q\)