# Properties

 Modulus 3600 Conductor 3600 Order 60 Real no Primitive yes Minimal yes Parity odd Orbit label 3600.fh

# Related objects

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

sage: H = DirichletGroup(3600)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([30,45,20,48]))

pari: [g,chi] = znchar(Mod(211,3600))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 3600 Conductor = 3600 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 60 Real = no 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 = 3600.fh Orbit index = 138

## 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

$$(3151,901,2801,577)$$ → $$(-1,-i,e\left(\frac{1}{3}\right),e\left(\frac{4}{5}\right))$$

## Values

 -1 1 7 11 13 17 19 23 29 31 37 41 $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{30}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{60})$$