Properties

 Label 8033.933 Modulus $8033$ Conductor $8033$ Order $322$ 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([253,189]))

pari: [g,chi] = znchar(Mod(933,8033))

Basic properties

 Modulus: $$8033$$ Conductor: $$8033$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$322$$ 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.cl

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

$$(5541,1944)$$ → $$(e\left(\frac{11}{14}\right),e\left(\frac{27}{46}\right))$$

Values

 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$ $$1$$ $$1$$ $$e\left(\frac{11}{161}\right)$$ $$e\left(\frac{89}{322}\right)$$ $$e\left(\frac{22}{161}\right)$$ $$e\left(\frac{281}{322}\right)$$ $$e\left(\frac{111}{322}\right)$$ $$e\left(\frac{55}{161}\right)$$ $$e\left(\frac{33}{161}\right)$$ $$e\left(\frac{89}{161}\right)$$ $$e\left(\frac{303}{322}\right)$$ $$e\left(\frac{121}{161}\right)$$
 value at e.g. 2

Related number fields

 Field of values: $\Q(\zeta_{161})$ Fixed field: Number field defined by a degree 322 polynomial