Properties

 Conductor 4033 Order 54 Real No Primitive Yes Parity Even Orbit Label 4033.he

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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(4033)
sage: chi = H[138]
pari: [g,chi] = znchar(Mod(138,4033))

Basic properties

 sage: chi.conductor() pari: znconreyconductor(g,chi) Conductor = 4033 sage: chi.multiplicative_order() pari: charorder(g,chi) Order = 54 Real = No sage: chi.is_primitive() pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = Yes sage: chi.is_odd() pari: zncharisodd(g,chi) Parity = Even Orbit label = 4033.he Orbit index = 187

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

$$(1963,2295)$$ → $$(e\left(\frac{1}{6}\right),e\left(\frac{17}{54}\right))$$

Values

 -1 1 2 3 4 5 6 7 8 9 10 11 $$1$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{19}{27}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{41}{54}\right)$$ $$e\left(\frac{22}{27}\right)$$ $$e\left(\frac{25}{27}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{27}\right)$$ $$e\left(\frac{47}{54}\right)$$ $$e\left(\frac{7}{54}\right)$$
value at  e.g. 2

Related number fields

 Field of values $$\Q(\zeta_{27})$$