Properties

 Modulus 6048 Conductor 189 Order 9 Real no Primitive no Minimal yes Parity even Orbit label 6048.du

Related objects

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

sage: H = DirichletGroup(6048)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,0,5,6]))

pari: [g,chi] = znchar(Mod(1537,6048))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 6048 Conductor = 189 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 9 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 = 6048.du Orbit index = 99

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

$$(4159,3781,3809,2593)$$ → $$(1,1,e\left(\frac{5}{9}\right),e\left(\frac{2}{3}\right))$$

Values

 -1 1 5 11 13 17 19 23 25 29 31 37 $$1$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$1$$ $$1$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$
value at  e.g. 2

Related number fields

 Field of values $$\Q(\zeta_{9})$$