# Properties

 Conductor 1004 Order 2 Real Yes Primitive Yes Parity Even Orbit Label 1004.c

# Related objects

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(1004)
sage: chi = H[1003]
pari: [g,chi] = znchar(Mod(1003,1004))

## Kronecker symbol representation

sage: kronecker_character(1004)
pari: znchartokronecker(g,chi)

$$\displaystyle\left(\frac{1004}{\bullet}\right)$$

## Basic properties

 sage: chi.conductor() pari: znconreyconductor(g,chi) Conductor = 1004 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 = Yes sage: chi.is_odd() pari: zncharisodd(g,chi) Parity = Even Orbit label = 1004.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 ]

## Values on generators

$$(503,257)$$ → $$(-1,-1)$$

## Values

 -1 1 3 5 7 9 11 13 15 17 19 21 $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q$$