# Properties

 Modulus 9128 Conductor 9128 Order 54 Real no Primitive yes Minimal yes Parity odd Orbit label 9128.fg

# Related objects

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

sage: H = DirichletGroup(9128)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([27,27,18,38]))

pari: [g,chi] = znchar(Mod(2571,9128))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 9128 Conductor = 9128 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 54 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 = 9128.fg Orbit index = 137

## 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

$$(6847,4565,1305,7337)$$ → $$(-1,-1,e\left(\frac{1}{3}\right),e\left(\frac{19}{27}\right))$$

## Values

 -1 1 3 5 9 11 13 15 17 19 23 25 $$-1$$ $$1$$ $$e\left(\frac{11}{27}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{22}{27}\right)$$ $$e\left(\frac{11}{27}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{7}{54}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{17}{27}\right)$$ $$-1$$ $$e\left(\frac{4}{9}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{27})$$