Properties

 Conductor 6008 Order 30 Real No Primitive Yes Parity Even Orbit Label 6008.ba

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(6008)

sage: chi = H[675]

pari: [g,chi] = znchar(Mod(675,6008))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 6008 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 30 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 = Even Orbit label = 6008.ba Orbit index = 27

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

$$(1503,3005,1505)$$ → $$(-1,-1,e\left(\frac{29}{30}\right))$$

Values

 -1 1 3 5 7 9 11 13 15 17 19 21 $$1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$
value at  e.g. 2

Related number fields

 Field of values $$\Q(\zeta_{15})$$