# Properties

 Conductor 2019 Order 2 Real yes Primitive yes Minimal yes Parity odd Orbit label 2019.c

# Related objects

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(2019)

sage: chi = H[2018]

pari: [g,chi] = znchar(Mod(2018,2019))

## Kronecker symbol representation

sage: kronecker_character(-2019)

pari: znchartokronecker(g,chi)

$$\displaystyle\left(\frac{-2019}{\bullet}\right)$$

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 2019 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 2 Real = yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = yes Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = odd Orbit label = 2019.c Orbit index = 3

## Galois orbit

sage: chi.sage_character().galois_orbit()

pari: order = charorder(g,chi)

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

## Values on generators

$$(674,1351)$$ → $$(-1,-1)$$

## Values

 -1 1 2 4 5 7 8 10 11 13 14 16 $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q$$