# Properties

 Label 1596.1595 Modulus $1596$ Conductor $1596$ Order $2$ Real yes Primitive yes Minimal yes Parity even

# Related objects

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

H = DirichletGroup(1596, base_ring=CyclotomicField(2))

M = H._module

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

pari: [g,chi] = znchar(Mod(1595,1596))

## Kronecker symbol representation

sage: kronecker_character(1596)

pari: znchartokronecker(g,chi)

$$\displaystyle\left(\frac{1596}{\bullet}\right)$$

## Basic properties

 Modulus: $$1596$$ Conductor: $$1596$$ 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 1596.p

sage: chi.galois_orbit()

order = charorder(g,chi)

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

## Related number fields

 Field of values: $$\Q$$ Fixed field: $$\Q(\sqrt{399})$$

## Values on generators

$$(799,533,913,1009)$$ → $$(-1,-1,-1,-1)$$

## First values

 $$a$$ $$-1$$ $$1$$ $$5$$ $$11$$ $$13$$ $$17$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$ $$\chi_{ 1596 }(1595, a)$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$
sage: chi.jacobi_sum(n)

$$\chi_{ 1596 }(1595,a) \;$$ at $$\;a =$$ e.g. 2