# Properties

 Label 4033.1661 Modulus $4033$ Conductor $4033$ Order $27$ Real no Primitive yes Minimal yes Parity even

# Learn more about

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([15,4]))

pari: [g,chi] = znchar(Mod(1661,4033))

## Basic properties

 Modulus: $$4033$$ Conductor: $$4033$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$27$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 4033.ec

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

$$(1963,2295)$$ → $$(e\left(\frac{5}{9}\right),e\left(\frac{4}{27}\right))$$

## Values

 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{4}{27}\right)$$ $$1$$ $$e\left(\frac{1}{27}\right)$$ $$e\left(\frac{4}{27}\right)$$ $$e\left(\frac{19}{27}\right)$$ $$1$$ $$e\left(\frac{8}{27}\right)$$ $$e\left(\frac{1}{27}\right)$$ $$e\left(\frac{26}{27}\right)$$
 value at e.g. 2

## Related number fields

 Field of values: $$\Q(\zeta_{27})$$ Fixed field: Number field defined by a degree %d polynomial (not computed)