# Properties

 Conductor 473 Order 30 Real No Primitive No Parity Even Orbit Label 8041.cl

# Learn more about

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

sage: H = DirichletGroup_conrey(8041)

sage: chi = H[222]

pari: [g,chi] = znchar(Mod(222,8041))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 473 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 = No sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = Even Orbit label = 8041.cl Orbit index = 64

## 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

$$(6580,2366,562)$$ → $$(e\left(\frac{1}{10}\right),1,e\left(\frac{5}{6}\right))$$

## Values

 -1 1 2 3 4 5 6 7 8 9 10 12 $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
value at  e.g. 2

## Related number fields

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