# Properties

 Conductor 1020 Order 4 Real no Primitive yes Minimal yes Parity odd Orbit label 1020.x

# 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(1020)

sage: chi = H[407]

pari: [g,chi] = znchar(Mod(407,1020))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 1020 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 = odd Orbit label = 1020.x Orbit index = 24

## 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

$$(511,341,817,241)$$ → $$(-1,-1,i,-1)$$

## Values

 -1 1 7 11 13 19 23 29 31 37 41 43 $$-1$$ $$1$$ $$i$$ $$-1$$ $$-i$$ $$1$$ $$i$$ $$-1$$ $$1$$ $$-i$$ $$1$$ $$i$$
value at  e.g. 2

## Related number fields

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