# Properties

 Modulus 3234 Conductor 539 Order 42 Real no Primitive no Minimal yes Parity even Orbit label 3234.br

# Related objects

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

sage: H = DirichletGroup(3234)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,11,21]))

pari: [g,chi] = znchar(Mod(1825,3234))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 3234 Conductor = 539 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 42 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = no Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 3234.br Orbit index = 44

## 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

$$(1079,199,2059)$$ → $$(1,e\left(\frac{11}{42}\right),-1)$$

## Values

 -1 1 5 13 17 19 23 25 29 31 37 41 $$1$$ $$1$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{21})$$