# Properties

 Label 2888.69 Modulus $2888$ Conductor $152$ Order $6$ Real no Primitive no Minimal no Parity odd

# Learn more

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

sage: H = DirichletGroup(2888, base_ring=CyclotomicField(6))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,3,5]))

pari: [g,chi] = znchar(Mod(69,2888))

## Basic properties

 Modulus: $$2888$$ Conductor: $$152$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$6$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{152}(69,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 2888.l

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: $$\Q(\sqrt{-3})$$ Fixed field: 6.0.1267762688.1

## Values on generators

$$(2167,1445,2529)$$ → $$(1,-1,e\left(\frac{5}{6}\right))$$

## Values

 $$a$$ $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$21$$ $$23$$ $$\chi_{ 2888 }(69, a)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 2888 }(69,a) \;$$ at $$\;a =$$ e.g. 2