# Properties

 Conductor 3009 Order 464 Real No Primitive No Parity Even Orbit Label 6018.bn

# 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(6018)

sage: chi = H[449]

pari: [g,chi] = znchar(Mod(449,6018))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 3009 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 464 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 = 6018.bn Orbit index = 40

## 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

$$(4013,1771,1123)$$ → $$(-1,e\left(\frac{11}{16}\right),e\left(\frac{22}{29}\right))$$

## Values

 -1 1 5 7 11 13 19 23 25 29 31 35 $$1$$ $$1$$ $$e\left(\frac{227}{464}\right)$$ $$e\left(\frac{101}{464}\right)$$ $$e\left(\frac{129}{464}\right)$$ $$e\left(\frac{103}{116}\right)$$ $$e\left(\frac{105}{232}\right)$$ $$e\left(\frac{89}{464}\right)$$ $$e\left(\frac{227}{232}\right)$$ $$e\left(\frac{315}{464}\right)$$ $$e\left(\frac{167}{464}\right)$$ $$e\left(\frac{41}{58}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{464})$$