# Properties

 Modulus 3215 Conductor 3215 Order 2 Real yes Primitive yes Minimal yes Parity odd Orbit label 3215.d

# Related objects

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

sage: H = DirichletGroup(3215)

sage: M = H._module

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

pari: [g,chi] = znchar(Mod(3214,3215))

## Kronecker symbol representation

sage: kronecker_character(-3215)

pari: znchartokronecker(g,chi)

$$\displaystyle\left(\frac{-3215}{\bullet}\right)$$

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 3215 Conductor = 3215 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 = 3215.d Orbit index = 4

## Galois orbit

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

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

## Values on generators

$$(1287,11)$$ → $$(-1,-1)$$

## Values

 -1 1 2 3 4 6 7 8 9 11 12 13 $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q$$