# Properties

 Conductor 41 Order 5 Real No Primitive No Parity Even Orbit Label 6027.n

# 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(6027)

sage: chi = H[2353]

pari: [g,chi] = znchar(Mod(2353,6027))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 41 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 5 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 = 6027.n Orbit index = 14

## 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

$$(4019,493,2794)$$ → $$(1,1,e\left(\frac{3}{5}\right))$$

## Values

 -1 1 2 4 5 8 10 11 13 16 17 19 $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{5})$$