Properties

 Conductor 315 Order 12 Real no Primitive no Minimal no Parity even Orbit label 9450.ch

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(9450)

sage: chi = H[6193]

pari: [g,chi] = znchar(Mod(6193,9450))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 315 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 12 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = no Minimal = no sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 9450.ch Orbit index = 60

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

$$(9101,6427,6751)$$ → $$(e\left(\frac{1}{3}\right),-i,e\left(\frac{5}{6}\right))$$

Values

 -1 1 11 13 17 19 23 29 31 37 41 43 $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$
value at  e.g. 2

Related number fields

 Field of values $$\Q(\zeta_{12})$$