# Properties

 Modulus 8016 Conductor 4008 Order 2 Real yes Primitive no Minimal no Parity even Orbit label 8016.i

# Related objects

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter

sage: H = DirichletGroup(8016)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,1,1,1]))

pari: [g,chi] = znchar(Mod(1001,8016))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 8016 Conductor = 4008 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 Minimal = no sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 8016.i Orbit index = 9

## Galois orbit

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

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

## Values on generators

$$(3007,2005,5345,673)$$ → $$(1,-1,-1,-1)$$

## Values

 -1 1 5 7 11 13 17 19 23 25 29 31 $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q$$