# Properties

 Conductor 4032 Order 48 Real no Primitive yes Minimal yes Parity even Orbit label 4032.hd

# 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[139]

pari: [g,chi] = znchar(Mod(139,4032))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 4032 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 48 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = yes Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 4032.hd Orbit index = 186

## 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

$$(127,3781,1793,577)$$ → $$(-1,e\left(\frac{5}{16}\right),e\left(\frac{1}{3}\right),-1)$$

## Values

 -1 1 5 11 13 17 19 23 25 29 31 37 $$1$$ $$1$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$i$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{16}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{48})$$