Properties

 Label 3381.134 Modulus $3381$ Conductor $3381$ Order $154$ 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(3381, base_ring=CyclotomicField(154))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([77,44,105]))

pari: [g,chi] = znchar(Mod(134,3381))

Basic properties

 Modulus: $$3381$$ Conductor: $$3381$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$154$$ 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.ca

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: $\Q(\zeta_{77})$ Fixed field: Number field defined by a degree 154 polynomial (not computed)

Values on generators

$$(2255,346,442)$$ → $$(-1,e\left(\frac{2}{7}\right),e\left(\frac{15}{22}\right))$$

Values

 $$a$$ $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$8$$ $$10$$ $$11$$ $$13$$ $$16$$ $$17$$ $$19$$ $$\chi_{ 3381 }(134, a)$$ $$1$$ $$1$$ $$e\left(\frac{45}{154}\right)$$ $$e\left(\frac{45}{77}\right)$$ $$e\left(\frac{36}{77}\right)$$ $$e\left(\frac{135}{154}\right)$$ $$e\left(\frac{117}{154}\right)$$ $$e\left(\frac{5}{77}\right)$$ $$e\left(\frac{75}{77}\right)$$ $$e\left(\frac{13}{77}\right)$$ $$e\left(\frac{32}{77}\right)$$ $$e\left(\frac{5}{22}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 3381 }(134,a) \;$$ at $$\;a =$$ e.g. 2