# Properties

 Conductor 187 Order 10 Real No Primitive No Parity Even Orbit Label 5610.cm

# 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[1291]

pari: [g,chi] = znchar(Mod(1291,5610))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 187 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 10 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.cm Orbit index = 65

## 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

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

## Values

 -1 1 7 13 19 23 29 31 37 41 43 47 $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$1$$ $$e\left(\frac{3}{5}\right)$$
value at  e.g. 2

## Related number fields

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