# Properties

 Conductor 3021 Order 468 Real No Primitive No Parity Odd Orbit Label 6042.cs

# 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(6042)

sage: chi = H[41]

pari: [g,chi] = znchar(Mod(41,6042))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 3021 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 468 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 = Odd Orbit label = 6042.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

$$(2015,4771,2281)$$ → $$(-1,e\left(\frac{13}{18}\right),e\left(\frac{45}{52}\right))$$

## Values

 -1 1 5 7 11 13 17 23 25 29 31 35 $$-1$$ $$1$$ $$e\left(\frac{341}{468}\right)$$ $$e\left(\frac{35}{78}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{89}{234}\right)$$ $$e\left(\frac{44}{117}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{107}{234}\right)$$ $$e\left(\frac{137}{234}\right)$$ $$e\left(\frac{61}{156}\right)$$ $$e\left(\frac{83}{468}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{468})$$