Properties

 Label 2960.737 Modulus $2960$ Conductor $185$ Order $36$ 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(2960, base_ring=CyclotomicField(36))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,0,9,8]))

pari: [g,chi] = znchar(Mod(737,2960))

Basic properties

 Modulus: $$2960$$ Conductor: $$185$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$36$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{185}(182,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 2960.gk

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

$$(2591,741,1777,2481)$$ → $$(1,1,i,e\left(\frac{2}{9}\right))$$

Values

 $$a$$ $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$21$$ $$23$$ $$27$$ $$\chi_{ 2960 }(737, a)$$ $$-1$$ $$1$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 2960 }(737,a) \;$$ at $$\;a =$$ e.g. 2