Properties

 Label 3969.3347 Modulus $3969$ Conductor $441$ Order $42$ Real no Primitive no Minimal no Parity odd

Related objects

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

sage: H = DirichletGroup(3969, base_ring=CyclotomicField(42))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([7,30]))

pari: [g,chi] = znchar(Mod(3347,3969))

Basic properties

 Modulus: $$3969$$ Conductor: $$441$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$42$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{441}(407,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 3969.bt

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Values on generators

$$(2108,3727)$$ → $$(e\left(\frac{1}{6}\right),e\left(\frac{5}{7}\right))$$

Values

 $$a$$ $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$8$$ $$10$$ $$11$$ $$13$$ $$16$$ $$17$$ $$19$$ $$\chi_{ 3969 }(3347, a)$$ $$-1$$ $$1$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$1$$
sage: chi.jacobi_sum(n)

$$\chi_{ 3969 }(3347,a) \;$$ at $$\;a =$$ e.g. 2