Properties

 Conductor 2003 Order 2002 Real No Primitive Yes Parity Odd Orbit Label 2003.p

Related objects

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(2003)

sage: chi = H[5]

pari: [g,chi] = znchar(Mod(5,2003))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 2003 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 2002 Real = No sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = Yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = Odd Orbit label = 2003.p Orbit index = 16

Galois orbit

sage: chi.sage_character().galois_orbit()

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Values on generators

$$5$$ → $$e\left(\frac{1}{2002}\right)$$

Values

 -1 1 2 3 4 5 6 7 8 9 10 11 $$-1$$ $$1$$ $$e\left(\frac{191}{286}\right)$$ $$e\left(\frac{173}{1001}\right)$$ $$e\left(\frac{48}{143}\right)$$ $$e\left(\frac{1}{2002}\right)$$ $$e\left(\frac{153}{182}\right)$$ $$e\left(\frac{123}{2002}\right)$$ $$e\left(\frac{1}{286}\right)$$ $$e\left(\frac{346}{1001}\right)$$ $$e\left(\frac{669}{1001}\right)$$ $$e\left(\frac{7}{286}\right)$$
value at  e.g. 2

Related number fields

 Field of values $$\Q(\zeta_{1001})$$