# Properties

 Label 1224.523 Modulus $1224$ Conductor $136$ Order $4$ Real no Primitive no Minimal yes Parity odd

# 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([2,2,0,1]))

pari: [g,chi] = znchar(Mod(523,1224))

## Basic properties

 Modulus: $$1224$$ Conductor: $$136$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{136}(115,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1224.s

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

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

## Values

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

## Related number fields

 Field of values: $$\Q(\sqrt{-1})$$ Fixed field: 4.0.314432.2