Properties

 Conductor 525 Order 10 Real no Primitive no Minimal yes Parity even Orbit label 3150.bx

Related objects

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

sage: H = DirichletGroup_conrey(3150)

sage: chi = H[1889]

pari: [g,chi] = znchar(Mod(1889,3150))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 525 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 10 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 = even Orbit label = 3150.bx Orbit index = 50

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

$$(2801,127,451)$$ → $$(-1,e\left(\frac{3}{10}\right),-1)$$

Values

 -1 1 11 13 17 19 23 29 31 37 41 43 $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$-1$$
value at  e.g. 2

Related number fields

 Field of values $$\Q(\zeta_{5})$$