# Properties

 Label 1469.1468 Modulus $1469$ Conductor $1469$ Order $2$ Real yes Primitive yes Minimal yes Parity even

# Related objects

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

H = DirichletGroup(1469, base_ring=CyclotomicField(2))

M = H._module

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

pari: [g,chi] = znchar(Mod(1468,1469))

## Kronecker symbol representation

sage: kronecker_character(1469)

pari: znchartokronecker(g,chi)

$$\displaystyle\left(\frac{1469}{\bullet}\right)$$

## Basic properties

 Modulus: $$1469$$ Conductor: $$1469$$ 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 1469.b

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: $$\Q(\sqrt{1469})$$

## Values on generators

$$(340,794)$$ → $$(-1,-1)$$

## First values

 $$a$$ $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$ $$\chi_{ 1469 }(1468, a)$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$
sage: chi.jacobi_sum(n)

$$\chi_{ 1469 }(1468,a) \;$$ at $$\;a =$$ e.g. 2