# Properties

 Label 4235.734 Modulus $4235$ Conductor $4235$ Order $110$ Real no Primitive yes Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(4235, base_ring=CyclotomicField(110))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([55,55,3]))

pari: [g,chi] = znchar(Mod(734,4235))

## Basic properties

 Modulus: $$4235$$ Conductor: $$4235$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$110$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 4235.cv

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: $\Q(\zeta_{55})$ Fixed field: Number field defined by a degree 110 polynomial (not computed)

## Values on generators

$$(2542,1816,2906)$$ → $$(-1,-1,e\left(\frac{3}{110}\right))$$

## Values

 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$8$$ $$9$$ $$12$$ $$13$$ $$16$$ $$17$$ $$1$$ $$1$$ $$e\left(\frac{29}{55}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{55}\right)$$ $$e\left(\frac{51}{55}\right)$$ $$e\left(\frac{32}{55}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{83}{110}\right)$$ $$e\left(\frac{6}{55}\right)$$ $$e\left(\frac{37}{110}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 4235 }(734,a) \;$$ at $$\;a =$$ e.g. 2