Properties

 Conductor 360 Order 12 Real No Primitive No Parity Odd Orbit Label 3600.dl

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[407]
pari: [g,chi] = znchar(Mod(407,3600))

Basic properties

 sage: chi.conductor() pari: znconreyconductor(g,chi) Conductor = 360 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 sage: chi.is_odd() pari: zncharisodd(g,chi) Parity = Odd Orbit label = 3600.dl Orbit index = 90

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

$$(3151,901,2801,577)$$ → $$(-1,-1,e\left(\frac{1}{6}\right),i)$$

Values

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

Related number fields

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