# Properties

 Label 2665.2664 Modulus $2665$ Conductor $2665$ Order $2$ Real yes Primitive yes Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(2665, base_ring=CyclotomicField(2))

sage: M = H._module

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

pari: [g,chi] = znchar(Mod(2664,2665))

## Kronecker symbol representation

sage: kronecker_character(2665)

pari: znchartokronecker(g,chi)

$$\displaystyle\left(\frac{2665}{\bullet}\right)$$

## Basic properties

 Modulus: $$2665$$ Conductor: $$2665$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$2$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: yes Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 2665.h

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: $$\Q(\sqrt{2665})$$

## Values on generators

$$(1067,821,1236)$$ → $$(-1,-1,-1)$$

## Values

 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$11$$ $$12$$ $$14$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$
sage: chi.jacobi_sum(n)

$$\chi_{ 2665 }(2664,a) \;$$ at $$\;a =$$ e.g. 2