# Properties

 Label 6003.737 Modulus $6003$ Conductor $87$ Order $4$ Real no Primitive no Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(6003)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([2,0,1]))

pari: [g,chi] = znchar(Mod(737,6003))

## Basic properties

 Modulus: $$6003$$ Conductor: $$87$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{87}(41,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 6003.m

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

$$(668,3133,4555)$$ → $$(-1,1,i)$$

## Values

 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$7$$ $$8$$ $$10$$ $$11$$ $$13$$ $$14$$ $$16$$ $$1$$ $$1$$ $$-i$$ $$-1$$ $$1$$ $$1$$ $$i$$ $$-i$$ $$-i$$ $$-1$$ $$-i$$ $$1$$
 value at e.g. 2

## Related number fields

 Field of values: $$\Q(\sqrt{-1})$$ Fixed field: 4.4.219501.1