# Properties

 Conductor 6048 Order 72 Real no Primitive yes Minimal yes Parity even Orbit label 6048.jl

# 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(6048)

sage: chi = H[437]

pari: [g,chi] = znchar(Mod(437,6048))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 6048 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 72 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 = 6048.jl Orbit index = 246

## 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

$$(4159,3781,3809,2593)$$ → $$(1,e\left(\frac{5}{8}\right),e\left(\frac{5}{18}\right),e\left(\frac{1}{6}\right))$$

## Values

 -1 1 5 11 13 17 19 23 25 29 31 37 $$1$$ $$1$$ $$e\left(\frac{61}{72}\right)$$ $$e\left(\frac{29}{72}\right)$$ $$e\left(\frac{7}{72}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{11}{72}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{8}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{72})$$