Properties

 Label 3381.779 Modulus $3381$ Conductor $3381$ Order $462$ Real no Primitive yes Minimal yes Parity even

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

sage: H = DirichletGroup(3381, base_ring=CyclotomicField(462))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([231,88,105]))

pari: [g,chi] = znchar(Mod(779,3381))

Basic properties

 Modulus: $$3381$$ Conductor: $$3381$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$462$$ 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 3381.ci

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: $\Q(\zeta_{231})$ Fixed field: Number field defined by a degree 462 polynomial (not computed)

Values on generators

$$(2255,346,442)$$ → $$(-1,e\left(\frac{4}{21}\right),e\left(\frac{5}{22}\right))$$

Values

 $$a$$ $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$8$$ $$10$$ $$11$$ $$13$$ $$16$$ $$17$$ $$19$$ $$\chi_{ 3381 }(779, a)$$ $$1$$ $$1$$ $$e\left(\frac{419}{462}\right)$$ $$e\left(\frac{188}{231}\right)$$ $$e\left(\frac{58}{231}\right)$$ $$e\left(\frac{111}{154}\right)$$ $$e\left(\frac{73}{462}\right)$$ $$e\left(\frac{38}{231}\right)$$ $$e\left(\frac{36}{77}\right)$$ $$e\left(\frac{145}{231}\right)$$ $$e\left(\frac{197}{231}\right)$$ $$e\left(\frac{5}{66}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 3381 }(779,a) \;$$ at $$\;a =$$ e.g. 2