# Properties

 Conductor 80 Order 4 Real no Primitive no Minimal no Parity odd Orbit label 4000.i

# 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(4000)

sage: chi = H[57]

pari: [g,chi] = znchar(Mod(57,4000))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 80 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 = no Minimal = no sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = odd Orbit label = 4000.i Orbit index = 9

## 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

$$(2751,2501,1377)$$ → $$(1,i,i)$$

## Values

 -1 1 3 7 9 11 13 17 19 21 23 27 $$-1$$ $$1$$ $$-1$$ $$-i$$ $$1$$ $$i$$ $$-1$$ $$i$$ $$i$$ $$i$$ $$i$$ $$-1$$
value at  e.g. 2

## Related number fields

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