Properties

 Conductor 2015 Order 60 Real No Primitive Yes Parity Even Orbit Label 2015.gu

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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(2015)

sage: chi = H[393]

pari: [g,chi] = znchar(Mod(393,2015))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 2015 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 60 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 = 2015.gu Orbit index = 177

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

$$(807,1861,716)$$ → $$(-i,e\left(\frac{1}{3}\right),e\left(\frac{29}{30}\right))$$

Values

 -1 1 2 3 4 6 7 8 9 11 12 14 $$1$$ $$1$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$
value at  e.g. 2

Related number fields

 Field of values $$\Q(\zeta_{60})$$