# Properties

 Label 4033.812 Modulus $4033$ Conductor $4033$ Order $108$ Real no Primitive yes Minimal yes Parity odd

# 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([57,80]))

pari: [g,chi] = znchar(Mod(812,4033))

## Basic properties

 Modulus: $$4033$$ Conductor: $$4033$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$108$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 4033.ic

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

$$(1963,2295)$$ → $$(e\left(\frac{19}{36}\right),e\left(\frac{20}{27}\right))$$

## Values

 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$ $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{13}{54}\right)$$ $$-1$$ $$e\left(\frac{47}{108}\right)$$ $$e\left(\frac{107}{108}\right)$$ $$e\left(\frac{14}{27}\right)$$ $$i$$ $$e\left(\frac{13}{27}\right)$$ $$e\left(\frac{5}{27}\right)$$ $$e\left(\frac{17}{54}\right)$$
 value at e.g. 2

## Related number fields

 Field of values: $\Q(\zeta_{108})$ Fixed field: Number field defined by a degree 108 polynomial