Properties

 Label 1200.1199 Modulus $1200$ Conductor $60$ Order $2$ Real yes Primitive no Minimal no Parity even

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

sage: H = DirichletGroup(1200, base_ring=CyclotomicField(2))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([1,0,1,1]))

pari: [g,chi] = znchar(Mod(1199,1200))

Basic properties

 Modulus: $$1200$$ Conductor: $$60$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$2$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: yes Primitive: no, induced from $$\chi_{60}(59,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 1200.o

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: $$\Q$$ Fixed field: $$\Q(\sqrt{15})$$

Values on generators

$$(751,901,401,577)$$ → $$(-1,1,-1,-1)$$

Values

 $$a$$ $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$\chi_{ 1200 }(1199, a)$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$
sage: chi.jacobi_sum(n)

$$\chi_{ 1200 }(1199,a) \;$$ at $$\;a =$$ e.g. 2