# Properties

 Label 1089.485 Modulus $1089$ Conductor $3$ Order $2$ Real yes Primitive no Minimal yes Parity odd

# Related objects

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

sage: H = DirichletGroup(1089, base_ring=CyclotomicField(2))

sage: M = H._module

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

pari: [g,chi] = znchar(Mod(485,1089))

## Basic properties

 Modulus: $$1089$$ Conductor: $$3$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$2$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: yes Primitive: no, induced from $$\chi_{3}(2,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1089.b

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: $$\Q(\sqrt{-3})$$

## Values on generators

$$(848,244)$$ → $$(-1,1)$$

## Values

 $$a$$ $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$7$$ $$8$$ $$10$$ $$13$$ $$14$$ $$16$$ $$17$$ $$\chi_{ 1089 }(485, a)$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$
sage: chi.jacobi_sum(n)

$$\chi_{ 1089 }(485,a) \;$$ at $$\;a =$$ e.g. 2