Properties

 Label 8004.1 Modulus $8004$ Conductor $1$ Order $1$ 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(8004)

sage: M = H._module

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

pari: [g,chi] = znchar(Mod(1,8004))

Basic properties

 Modulus: $$8004$$ Conductor: $$1$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$1$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: yes Primitive: no, induced from $$\chi_{1}(1,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 8004.a

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

$$(4003,2669,3133,553)$$ → $$(1,1,1,1)$$

Values

 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$25$$ $$31$$ $$35$$ $$37$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
 value at e.g. 2

Related number fields

 Field of values: $$\Q$$ Fixed field: $$\Q$$