Properties

 Conductor 24 Order 2 Real Yes Primitive No Parity Even Orbit Label 4008.j

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(4008)
sage: chi = H[2339]
pari: [g,chi] = znchar(Mod(2339,4008))

Basic properties

 sage: chi.conductor() pari: znconreyconductor(g,chi) Conductor = 24 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 = Even Orbit label = 4008.j Orbit index = 10

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

$$\chi_{24}(11,\cdot)$$ = $$\displaystyle\left(\frac{24}{\bullet}\right)$$

Values on generators

$$(3007,2005,1337,673)$$ → $$(-1,-1,-1,1)$$

Values

 -1 1 5 7 11 13 17 19 23 25 29 31 $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$
value at  e.g. 2

Related number fields

 Field of values $$\Q$$