Properties

 Modulus 4000 Conductor 100 Order 10 Real no Primitive no Minimal no Parity odd Orbit label 4000.bh

Related objects

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

sage: H = DirichletGroup(4000)

sage: M = H._module

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

pari: [g,chi] = znchar(Mod(351,4000))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 4000 Conductor = 100 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 10 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = no Minimal = no sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = odd Orbit label = 4000.bh Orbit index = 34

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

$$(2751,2501,1377)$$ → $$(-1,1,e\left(\frac{3}{5}\right))$$

Values

 -1 1 3 7 9 11 13 17 19 21 23 27 $$-1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$-1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$
value at  e.g. 2

Related number fields

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