# Properties

 Label 2240.1111 Modulus $2240$ Conductor $224$ 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(2240, base_ring=CyclotomicField(24))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([12,21,0,20]))

pari: [g,chi] = znchar(Mod(1111,2240))

## Basic properties

 Modulus: $$2240$$ Conductor: $$224$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$24$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{224}(19,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 2240.ej

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: 24.24.790224330201082600125157415256880139617697792.1

## Values on generators

$$(1471,1541,897,1921)$$ → $$(-1,e\left(\frac{7}{8}\right),1,e\left(\frac{5}{6}\right))$$

## Values

 $$-1$$ $$1$$ $$3$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$27$$ $$29$$ $$31$$ $$1$$ $$1$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 2240 }(1111,a) \;$$ at $$\;a =$$ e.g. 2