# Properties

 Conductor 2000 Order 100 Real no Primitive no Minimal no Parity odd Orbit label 4000.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(4000)

sage: chi = H[71]

pari: [g,chi] = znchar(Mod(71,4000))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 2000 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 100 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = no Minimal = no sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = odd Orbit label = 4000.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

$$(2751,2501,1377)$$ → $$(-1,i,e\left(\frac{18}{25}\right))$$

## Values

 -1 1 3 7 9 11 13 17 19 21 23 27 $$-1$$ $$1$$ $$e\left(\frac{29}{100}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{29}{50}\right)$$ $$e\left(\frac{47}{100}\right)$$ $$e\left(\frac{83}{100}\right)$$ $$e\left(\frac{14}{25}\right)$$ $$e\left(\frac{21}{100}\right)$$ $$e\left(\frac{49}{100}\right)$$ $$e\left(\frac{8}{25}\right)$$ $$e\left(\frac{87}{100}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{100})$$