# Properties

 Conductor 1200 Order 20 Real No Primitive Yes Parity Odd Orbit Label 1200.cs

# 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(1200)

sage: chi = H[1067]

pari: [g,chi] = znchar(Mod(1067,1200))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 1200 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 = Yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = Odd Orbit label = 1200.cs Orbit index = 71

## 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

$$(751,901,401,577)$$ → $$(-1,i,-1,e\left(\frac{13}{20}\right))$$

## Values

 -1 1 7 11 13 17 19 23 29 31 37 41 $$-1$$ $$1$$ $$i$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$
value at  e.g. 2

## Related number fields

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