Properties

 Conductor 675 Order 45 Real no Primitive no Minimal yes Parity even Orbit label 9450.fm

Related objects

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

sage: H = DirichletGroup_conrey(9450)

sage: chi = H[1471]

pari: [g,chi] = znchar(Mod(1471,9450))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 675 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 45 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 = 9450.fm Orbit index = 143

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

$$(9101,6427,6751)$$ → $$(e\left(\frac{4}{9}\right),e\left(\frac{3}{5}\right),1)$$

Values

 -1 1 11 13 17 19 23 29 31 37 41 43 $$1$$ $$1$$ $$e\left(\frac{17}{45}\right)$$ $$e\left(\frac{43}{45}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{22}{45}\right)$$ $$e\left(\frac{29}{45}\right)$$ $$e\left(\frac{31}{45}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{43}{45}\right)$$ $$e\left(\frac{7}{9}\right)$$
value at  e.g. 2

Related number fields

 Field of values $$\Q(\zeta_{45})$$