Properties

 Conductor 8 Order 2 Real yes Primitive no Minimal yes Parity even Orbit label 4032.c

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(4032)

sage: chi = H[2017]

pari: [g,chi] = znchar(Mod(2017,4032))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 8 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 2 Real = yes 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 = 4032.c Orbit index = 3

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

$$(127,3781,1793,577)$$ → $$(1,-1,1,1)$$

Values

 -1 1 5 11 13 17 19 23 25 29 31 37 $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$
value at  e.g. 2

Related number fields

 Field of values $$\Q$$