# Properties

 Conductor 448 Order 48 Real no Primitive no Minimal yes Parity even Orbit label 4032.hf

# 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[37]

pari: [g,chi] = znchar(Mod(37,4032))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 448 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 = no Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 4032.hf Orbit index = 188

## 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

$$(127,3781,1793,577)$$ → $$(1,e\left(\frac{9}{16}\right),1,e\left(\frac{1}{3}\right))$$

## Values

 -1 1 5 11 13 17 19 23 25 29 31 37 $$1$$ $$1$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{35}{48}\right)$$
value at  e.g. 2

## Related number fields

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