Properties

 Modulus 4033 Conductor 4033 Order 108 Real no Primitive yes Minimal yes Parity odd Orbit label 4033.il

Related objects

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

sage: H = DirichletGroup(4033)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([81,2]))

pari: [g,chi] = znchar(Mod(1671,4033))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 4033 Conductor = 4033 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 108 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 = 4033.il Orbit index = 220

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

$$(1963,2295)$$ → $$(-i,e\left(\frac{1}{54}\right))$$

Values

 -1 1 2 3 4 5 6 7 8 9 10 11 $$-1$$ $$1$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{25}{54}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{71}{108}\right)$$ $$e\left(\frac{29}{108}\right)$$ $$e\left(\frac{20}{27}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{25}{27}\right)$$ $$e\left(\frac{25}{54}\right)$$ $$e\left(\frac{1}{27}\right)$$
value at  e.g. 2

Related number fields

 Field of values $$\Q(\zeta_{108})$$