# Properties

 Conductor 2015 Order 12 Real No Primitive Yes Parity Even Orbit Label 2015.cy

# 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(2015)

sage: chi = H[987]

pari: [g,chi] = znchar(Mod(987,2015))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 2015 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 12 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 = Even Orbit label = 2015.cy Orbit index = 77

## 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

$$(807,1861,716)$$ → $$(i,-1,e\left(\frac{1}{6}\right))$$

## Values

 -1 1 2 3 4 6 7 8 9 11 12 14 $$1$$ $$1$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{12})$$