# Properties

 Modulus 1224 Conductor 51 Order 2 Real yes Primitive no Minimal yes Parity odd Orbit label 1224.m

# Related objects

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

sage: H = DirichletGroup(1224)

sage: M = H._module

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

pari: [g,chi] = znchar(Mod(305,1224))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 1224 Conductor = 51 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 = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = odd Orbit label = 1224.m Orbit index = 13

## 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

$$(919,613,137,649)$$ → $$(1,1,-1,-1)$$

## Values

 -1 1 5 7 11 13 19 23 25 29 31 35 $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q$$