Properties

 Conductor 8 Order 2 Real Yes Primitive No Parity Odd Orbit Label 3600.g

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(3600)
sage: chi = H[1351]
pari: [g,chi] = znchar(Mod(1351,3600))

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 sage: chi.is_odd() pari: zncharisodd(g,chi) Parity = Odd Orbit label = 3600.g Orbit index = 7

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 ]

Inducingprimitive character

$$\chi_{8}(3,\cdot)$$ = $$\displaystyle\left(\frac{-8}{\bullet}\right)$$

Values on generators

$$(3151,901,2801,577)$$ → $$(-1,-1,1,1)$$

Values

 -1 1 7 11 13 17 19 23 29 31 37 41 $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$
value at  e.g. 2

Related number fields

 Field of values $$\Q$$