# Properties

 Conductor 6008 Order 750 Real No Primitive Yes Parity Even Orbit Label 6008.ch

# 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(6008)

sage: chi = H[461]

pari: [g,chi] = znchar(Mod(461,6008))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 6008 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 750 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 = 6008.ch Orbit index = 60

## 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

$$(1503,3005,1505)$$ → $$(1,-1,e\left(\frac{302}{375}\right))$$

## Values

 -1 1 3 5 7 9 11 13 15 17 19 21 $$1$$ $$1$$ $$e\left(\frac{229}{750}\right)$$ $$e\left(\frac{169}{750}\right)$$ $$e\left(\frac{34}{125}\right)$$ $$e\left(\frac{229}{375}\right)$$ $$e\left(\frac{47}{150}\right)$$ $$e\left(\frac{457}{750}\right)$$ $$e\left(\frac{199}{375}\right)$$ $$e\left(\frac{358}{375}\right)$$ $$e\left(\frac{247}{750}\right)$$ $$e\left(\frac{433}{750}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{375})$$