Properties

 Label 8033.2 Modulus $8033$ Conductor $8033$ Order $644$ Real no Primitive yes Minimal yes Parity even

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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([23,343]))

pari: [g,chi] = znchar(Mod(2,8033))

Basic properties

 Modulus: $$8033$$ Conductor: $$8033$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$644$$ 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.cs

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

$$(5541,1944)$$ → $$(e\left(\frac{1}{28}\right),e\left(\frac{49}{92}\right))$$

Values

 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$ $$1$$ $$1$$ $$e\left(\frac{53}{161}\right)$$ $$e\left(\frac{199}{644}\right)$$ $$e\left(\frac{106}{161}\right)$$ $$e\left(\frac{205}{644}\right)$$ $$e\left(\frac{411}{644}\right)$$ $$e\left(\frac{47}{322}\right)$$ $$e\left(\frac{159}{161}\right)$$ $$e\left(\frac{199}{322}\right)$$ $$e\left(\frac{417}{644}\right)$$ $$e\left(\frac{100}{161}\right)$$
 value at e.g. 2

Related number fields

 Field of values: $\Q(\zeta_{644})$ Fixed field: Number field defined by a degree 644 polynomial