Properties

 Modulus 2015 Conductor 403 Order 60 Real no Primitive no Minimal yes Parity odd Orbit label 2015.hd

Related objects

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter

sage: H = DirichletGroup(2015)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,25,4]))

pari: [g,chi] = znchar(Mod(71,2015))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 2015 Conductor = 403 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 = no Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = odd Orbit label = 2015.hd Orbit index = 186

Galois orbit

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

$$(807,1861,716)$$ → $$(1,e\left(\frac{5}{12}\right),e\left(\frac{1}{15}\right))$$

Values

 -1 1 2 3 4 6 7 8 9 11 12 14 $$-1$$ $$1$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$-i$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$
value at  e.g. 2

Related number fields

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