# Properties

 Conductor 751 Order 125 Real No Primitive No Parity Even Orbit Label 6008.bp

# 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(6008)

sage: chi = H[305]

pari: [g,chi] = znchar(Mod(305,6008))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 751 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 125 Real = No sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = No sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = Even Orbit label = 6008.bp Orbit index = 42

## 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

$$(1503,3005,1505)$$ → $$(1,1,e\left(\frac{91}{125}\right))$$

## Values

 -1 1 3 5 7 9 11 13 15 17 19 21 $$1$$ $$1$$ $$e\left(\frac{91}{125}\right)$$ $$e\left(\frac{101}{125}\right)$$ $$e\left(\frac{116}{125}\right)$$ $$e\left(\frac{57}{125}\right)$$ $$e\left(\frac{13}{25}\right)$$ $$e\left(\frac{103}{125}\right)$$ $$e\left(\frac{67}{125}\right)$$ $$e\left(\frac{64}{125}\right)$$ $$e\left(\frac{13}{125}\right)$$ $$e\left(\frac{82}{125}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{125})$$