Properties

 Conductor 9 Order 6 Real No Primitive No Parity Odd Orbit Label 3600.bt

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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(3600)
sage: chi = H[401]
pari: [g,chi] = znchar(Mod(401,3600))

Basic properties

 sage: chi.conductor() pari: znconreyconductor(g,chi) Conductor = 9 sage: chi.multiplicative_order() pari: charorder(g,chi) Order = 6 Real = No sage: chi.is_primitive() pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = No sage: chi.is_odd() pari: zncharisodd(g,chi) Parity = Odd Orbit label = 3600.bt Orbit index = 46

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

$$(3151,901,2801,577)$$ → $$(1,1,e\left(\frac{5}{6}\right),1)$$

Values

 -1 1 7 11 13 17 19 23 29 31 37 41 $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$
value at  e.g. 2

Related number fields

 Field of values $$\Q(\zeta_{3})$$