# Properties

 Label 1792.1075 Modulus $1792$ Conductor $1792$ Order $192$ Real no Primitive yes Minimal yes Parity odd

# Related objects

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

sage: H = DirichletGroup(1792, base_ring=CyclotomicField(192))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([96,189,128]))

pari: [g,chi] = znchar(Mod(1075,1792))

## Basic properties

 Modulus: $$1792$$ Conductor: $$1792$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$192$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1792.cd

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: $\Q(\zeta_{192})$ Fixed field: Number field defined by a degree 192 polynomial (not computed)

## Values on generators

$$(1023,1541,1025)$$ → $$(-1,e\left(\frac{63}{64}\right),e\left(\frac{2}{3}\right))$$

## Values

 $$a$$ $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$23$$ $$25$$ $$\chi_{ 1792 }(1075, a)$$ $$-1$$ $$1$$ $$e\left(\frac{119}{192}\right)$$ $$e\left(\frac{61}{192}\right)$$ $$e\left(\frac{23}{96}\right)$$ $$e\left(\frac{161}{192}\right)$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{91}{192}\right)$$ $$e\left(\frac{59}{96}\right)$$ $$e\left(\frac{61}{96}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 1792 }(1075,a) \;$$ at $$\;a =$$ e.g. 2