Properties

 Conductor 9900 Order 30 Real no Primitive yes Minimal yes Parity odd Orbit label 9900.hq

Related objects

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

sage: H = DirichletGroup_conrey(9900)

sage: chi = H[131]

pari: [g,chi] = znchar(Mod(131,9900))

Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 9900 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 Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = odd Orbit label = 9900.hq Orbit index = 199

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

$$(4951,5501,2377,4501)$$ → $$(-1,e\left(\frac{5}{6}\right),e\left(\frac{2}{5}\right),-1)$$

Values

 -1 1 7 13 17 19 23 29 31 37 41 43 $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$
value at  e.g. 2

Related number fields

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