# Properties

 Modulus 2100 Conductor 25 Order 5 Real no Primitive no Minimal yes Parity even Orbit label 2100.z

# Learn more about

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

sage: H = DirichletGroup(2100)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,0,3,0]))

pari: [g,chi] = znchar(Mod(421,2100))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 2100 Conductor = 25 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 5 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 = 2100.z Orbit index = 26

## 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

$$(1051,701,1177,1501)$$ → $$(1,1,e\left(\frac{3}{5}\right),1)$$

## Values

 -1 1 11 13 17 19 23 29 31 37 41 43 $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$1$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{5})$$