# Properties

 Label 8033.17 Modulus $8033$ Conductor $8033$ Order $276$ Real no Primitive yes Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(8033)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([207,103]))

pari: [g,chi] = znchar(Mod(17,8033))

## Basic properties

 Modulus: $$8033$$ Conductor: $$8033$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$276$$ 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 8033.cd

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

$$(5541,1944)$$ → $$(-i,e\left(\frac{103}{276}\right))$$

## Values

 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$ $$1$$ $$1$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{251}{276}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{241}{276}\right)$$ $$e\left(\frac{143}{276}\right)$$ $$e\left(\frac{29}{138}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{113}{138}\right)$$ $$e\left(\frac{133}{276}\right)$$ $$e\left(\frac{25}{69}\right)$$
 value at e.g. 2

## Related number fields

 Field of values: $\Q(\zeta_{276})$ Fixed field: Number field defined by a degree %d polynomial (not computed)