Properties

 Conductor 4024 Order 502 Real no Primitive yes Minimal yes Parity even Orbit label 4024.o

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(4024)

sage: chi = H[13]

pari: [g,chi] = znchar(Mod(13,4024))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 4024 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 502 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = yes Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 4024.o Orbit index = 15

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

$$(1007,2013,2017)$$ → $$(1,-1,e\left(\frac{62}{251}\right))$$

Values

 -1 1 3 5 7 9 11 13 15 17 19 21 $$1$$ $$1$$ $$e\left(\frac{17}{502}\right)$$ $$e\left(\frac{375}{502}\right)$$ $$e\left(\frac{61}{251}\right)$$ $$e\left(\frac{17}{251}\right)$$ $$e\left(\frac{439}{502}\right)$$ $$e\left(\frac{65}{502}\right)$$ $$e\left(\frac{196}{251}\right)$$ $$e\left(\frac{142}{251}\right)$$ $$e\left(\frac{21}{502}\right)$$ $$e\left(\frac{139}{502}\right)$$
value at  e.g. 2

Related number fields

 Field of values $$\Q(\zeta_{251})$$