Properties

 Conductor 1008 Order 12 Real no Primitive no Minimal no Parity even Orbit label 6048.ej

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Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(6048)

sage: chi = H[89]

pari: [g,chi] = znchar(Mod(89,6048))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 1008 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 12 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = no Minimal = no sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 6048.ej Orbit index = 114

Galois orbit

sage: chi.sage_character().galois_orbit()

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Values on generators

$$(4159,3781,3809,2593)$$ → $$(1,i,e\left(\frac{1}{6}\right),e\left(\frac{5}{6}\right))$$

Values

 -1 1 5 11 13 17 19 23 25 29 31 37 $$1$$ $$1$$ $$i$$ $$-i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$
value at  e.g. 2

Related number fields

 Field of values $$\Q(\zeta_{12})$$