# Properties

 Conductor 4033 Order 36 Real no Primitive yes Minimal yes Parity even Orbit label 4033.ef

# 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(4033)

sage: chi = H[3020]

pari: [g,chi] = znchar(Mod(3020,4033))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 4033 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 36 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 = 4033.ef Orbit index = 110

## 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

$$(1963,2295)$$ → $$(e\left(\frac{5}{12}\right),e\left(\frac{5}{36}\right))$$

## Values

 -1 1 2 3 4 5 6 7 8 9 10 11 $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{36})$$