# Properties

 Conductor 4033 Order 108 Real No Primitive Yes Parity Odd Orbit Label 4033.ic

# Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(4033)
sage: chi = H[22]
pari: [g,chi] = znchar(Mod(22,4033))

## Basic properties

 sage: chi.conductor() pari: znconreyconductor(g,chi) Conductor = 4033 sage: chi.multiplicative_order() pari: charorder(g,chi) Order = 108 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 = Odd Orbit label = 4033.ic Orbit index = 211

## 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

$$(1963,2295)$$ → $$(e\left(\frac{31}{36}\right),e\left(\frac{8}{27}\right))$$

## Values

 -1 1 2 3 4 5 6 7 8 9 10 11 $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{43}{54}\right)$$ $$-1$$ $$e\left(\frac{35}{108}\right)$$ $$e\left(\frac{59}{108}\right)$$ $$e\left(\frac{11}{27}\right)$$ $$i$$ $$e\left(\frac{16}{27}\right)$$ $$e\left(\frac{2}{27}\right)$$ $$e\left(\frac{23}{54}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{108})$$