# Properties

 Label 1560.389 Modulus $1560$ Conductor $1560$ Order $2$ Real yes Primitive yes Minimal yes Parity odd

# Related objects

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

sage: H = DirichletGroup(1560, base_ring=CyclotomicField(2))

sage: M = H._module

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

pari: [g,chi] = znchar(Mod(389,1560))

## Kronecker symbol representation

sage: kronecker_character(-1560)

pari: znchartokronecker(g,chi)

$$\displaystyle\left(\frac{-1560}{\bullet}\right)$$

## Basic properties

 Modulus: $$1560$$ Conductor: $$1560$$ 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: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1560.y

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: $$\Q(\sqrt{-390})$$

## Values on generators

$$(391,781,521,937,1081)$$ → $$(1,-1,-1,-1,-1)$$

## Values

 $$a$$ $$-1$$ $$1$$ $$7$$ $$11$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$\chi_{ 1560 }(389, a)$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$
sage: chi.jacobi_sum(n)

$$\chi_{ 1560 }(389,a) \;$$ at $$\;a =$$ e.g. 2