# Properties

 Label 5184.3671 Modulus $5184$ Conductor $288$ Order $24$ Real no Primitive no Minimal no Parity even

# Related objects

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

sage: H = DirichletGroup(5184, base_ring=CyclotomicField(24))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([12,21,4]))

pari: [g,chi] = znchar(Mod(3671,5184))

## Basic properties

 Modulus: $$5184$$ Conductor: $$288$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$24$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{288}(83,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 5184.br

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Related number fields

 Field of values: $$\Q(\zeta_{24})$$ Fixed field: 24.24.1486465269728735333725176976133731985582456832.1

## Values on generators

$$(2431,325,1217)$$ → $$(-1,e\left(\frac{7}{8}\right),e\left(\frac{1}{6}\right))$$

## Values

 $$a$$ $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$\chi_{ 5184 }(3671, a)$$ $$1$$ $$1$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{5}{6}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 5184 }(3671,a) \;$$ at $$\;a =$$ e.g. 2