# Properties

 Label 3360.2897 Modulus $3360$ Conductor $840$ Order $4$ Real no Primitive no Minimal no Parity odd

# Related objects

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

sage: H = DirichletGroup(3360, base_ring=CyclotomicField(4))

sage: M = H._module

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

pari: [g,chi] = znchar(Mod(2897,3360))

## Basic properties

 Modulus: $$3360$$ Conductor: $$840$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{840}(797,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 3360.cv

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: $$\Q(\sqrt{-1})$$ Fixed field: 4.0.3528000.1

## Values on generators

$$(1471,421,1121,2017,1921)$$ → $$(1,-1,-1,i,-1)$$

## Values

 $$a$$ $$-1$$ $$1$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$\chi_{ 3360 }(2897, a)$$ $$-1$$ $$1$$ $$1$$ $$-i$$ $$i$$ $$-1$$ $$i$$ $$-1$$ $$-1$$ $$-i$$ $$1$$ $$i$$
sage: chi.jacobi_sum(n)

$$\chi_{ 3360 }(2897,a) \;$$ at $$\;a =$$ e.g. 2