# Properties

 Conductor 9900 Order 30 Real No Primitive Yes Parity Odd Orbit Label 9900.it

# 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(9900)
sage: chi = H[31]
pari: [g,chi] = znchar(Mod(31,9900))

## 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 sage: chi.is_odd() pari: zncharisodd(g,chi) Parity = Odd Orbit label = 9900.it Orbit index = 228

## 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

$$(4951,5501,2377,4501)$$ → $$(-1,e\left(\frac{1}{3}\right),e\left(\frac{2}{5}\right),e\left(\frac{3}{5}\right))$$

## Values

 -1 1 7 13 17 19 23 29 31 37 41 43 $$-1$$ $$1$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$
value at  e.g. 2

## Related number fields

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