# Properties

 Label 1792.87 Modulus $1792$ Conductor $896$ Order $96$ 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(1792, base_ring=CyclotomicField(96))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([48,45,16]))

pari: [g,chi] = znchar(Mod(87,1792))

## Basic properties

 Modulus: $$1792$$ Conductor: $$896$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$96$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{896}(115,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1792.bx

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: $\Q(\zeta_{96})$ Fixed field: Number field defined by a degree 96 polynomial

## Values on generators

$$(1023,1541,1025)$$ → $$(-1,e\left(\frac{15}{32}\right),e\left(\frac{1}{6}\right))$$

## Values

 $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$23$$ $$25$$ $$1$$ $$1$$ $$e\left(\frac{7}{96}\right)$$ $$e\left(\frac{29}{96}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{1}{96}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{11}{96}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{29}{48}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 1792 }(87,a) \;$$ at $$\;a =$$ e.g. 2