# Properties

 Conductor 2432 Order 32 Real No Primitive Yes Parity Even Orbit Label 2432.bv

# 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(2432)

sage: chi = H[1443]

pari: [g,chi] = znchar(Mod(1443,2432))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 2432 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 32 Real = No sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = Yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = Even Orbit label = 2432.bv Orbit index = 48

## 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

$$(1407,2053,1921)$$ → $$(-1,e\left(\frac{11}{32}\right),-1)$$

## Values

 -1 1 3 5 7 9 11 13 15 17 21 23 $$1$$ $$1$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{5}{16}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{32})$$