Properties

 Conductor 6027 Order 210 Real no Primitive yes Minimal yes Parity even Orbit label 6027.ej

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(6027)

sage: chi = H[857]

pari: [g,chi] = znchar(Mod(857,6027))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 6027 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 210 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = yes Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 6027.ej Orbit index = 114

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

$$(4019,493,2794)$$ → $$(-1,e\left(\frac{37}{42}\right),e\left(\frac{4}{5}\right))$$

Values

 -1 1 2 4 5 8 10 11 13 16 17 19 $$1$$ $$1$$ $$e\left(\frac{43}{210}\right)$$ $$e\left(\frac{43}{105}\right)$$ $$e\left(\frac{68}{105}\right)$$ $$e\left(\frac{43}{70}\right)$$ $$e\left(\frac{179}{210}\right)$$ $$e\left(\frac{29}{210}\right)$$ $$e\left(\frac{61}{70}\right)$$ $$e\left(\frac{86}{105}\right)$$ $$e\left(\frac{97}{105}\right)$$ $$e\left(\frac{1}{30}\right)$$
value at  e.g. 2

Related number fields

 Field of values $$\Q(\zeta_{105})$$