# Properties

 Label 3366.1 Modulus $3366$ Conductor $1$ Order $1$ Real yes Primitive no Minimal yes Parity even

# Learn more

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

sage: H = DirichletGroup(3366, base_ring=CyclotomicField(2))

sage: M = H._module

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

pari: [g,chi] = znchar(Mod(1,3366))

## Basic properties

 Modulus: $$3366$$ Conductor: $$1$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$1$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: yes Primitive: no, induced from $$\chi_{1}(1,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 3366.a

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Related number fields

 Field of values: $$\Q$$ Fixed field: $$\Q$$

## Values on generators

$$(749,1531,2179)$$ → $$(1,1,1)$$

## Values

 $$-1$$ $$1$$ $$5$$ $$7$$ $$13$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$35$$ $$37$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
 value at e.g. 2