# Properties

 Modulus 4033 Conductor 4033 Order 108 Real no Primitive yes Minimal yes Parity odd Orbit label 4033.ic

# Related objects

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter

sage: H = DirichletGroup(4033)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([69,40]))

pari: [g,chi] = znchar(Mod(116,4033))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 4033 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 Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = odd Orbit label = 4033.ic Orbit index = 211

## Galois orbit

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Values on generators

$$(1963,2295)$$ → $$(e\left(\frac{23}{36}\right),e\left(\frac{10}{27}\right))$$

## Values

 -1 1 2 3 4 5 6 7 8 9 10 11 $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{47}{54}\right)$$ $$-1$$ $$e\left(\frac{91}{108}\right)$$ $$e\left(\frac{67}{108}\right)$$ $$e\left(\frac{7}{27}\right)$$ $$i$$ $$e\left(\frac{20}{27}\right)$$ $$e\left(\frac{16}{27}\right)$$ $$e\left(\frac{49}{54}\right)$$
value at  e.g. 2

## Related number fields

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