Properties

 Label 5520.1471 Modulus $5520$ Conductor $92$ Order $2$ Real yes Primitive no Minimal yes Parity even

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

sage: H = DirichletGroup(5520, base_ring=CyclotomicField(2))

sage: M = H._module

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

pari: [g,chi] = znchar(Mod(1471,5520))

Basic properties

 Modulus: $$5520$$ Conductor: $$92$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$2$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: yes Primitive: no, induced from $$\chi_{92}(91,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 5520.be

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: $$\Q(\sqrt{23})$$

Values on generators

$$(4831,1381,1841,4417,1201)$$ → $$(-1,1,1,1,-1)$$

Values

 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$
 value at e.g. 2