Properties

 Conductor 17 Order 8 Real No Primitive No Parity Even Orbit Label 5610.bq

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(5610)

sage: chi = H[331]

pari: [g,chi] = znchar(Mod(331,5610))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 17 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 8 Real = No sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = No sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = Even Orbit label = 5610.bq Orbit index = 43

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

$$(1871,3367,1531,3301)$$ → $$(1,1,1,e\left(\frac{5}{8}\right))$$

Values

 -1 1 7 13 19 23 29 31 37 41 43 47 $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$-1$$
value at  e.g. 2

Related number fields

 Field of values $$\Q(\zeta_{8})$$