# Properties

 Modulus 2015 Conductor 2015 Order 60 Real no Primitive yes Minimal yes Parity odd Orbit label 2015.gm

# Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter

sage: H = DirichletGroup(2015)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([15,10,16]))

pari: [g,chi] = znchar(Mod(82,2015))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 2015 Conductor = 2015 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 60 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = yes Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = odd Orbit label = 2015.gm Orbit index = 169

## Galois orbit

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Values on generators

$$(807,1861,716)$$ → $$(i,e\left(\frac{1}{6}\right),e\left(\frac{4}{15}\right))$$

## Values

 -1 1 2 3 4 6 7 8 9 11 12 14 $$-1$$ $$1$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$-1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{60})$$