# Properties

 Conductor 825 Order 20 Real no Primitive no Minimal yes Parity even Orbit label 9900.gv

# Related objects

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

sage: H = DirichletGroup_conrey(9900)

sage: chi = H[53]

pari: [g,chi] = znchar(Mod(53,9900))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 825 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 20 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = no Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 9900.gv Orbit index = 178

## 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

$$(4951,5501,2377,4501)$$ → $$(1,-1,e\left(\frac{7}{20}\right),e\left(\frac{3}{5}\right))$$

## Values

 -1 1 7 13 17 19 23 29 31 37 41 43 $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$i$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$i$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{20})$$