# Properties

 Conductor 1337 Order 570 Real No Primitive Yes Parity Odd Orbit Label 1337.bf

# 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(1337)

sage: chi = H[40]

pari: [g,chi] = znchar(Mod(40,1337))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 1337 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 570 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 = Odd Orbit label = 1337.bf Orbit index = 32

## 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

$$(192,974)$$ → $$(e\left(\frac{5}{6}\right),e\left(\frac{91}{95}\right))$$

## Values

 -1 1 2 3 4 5 6 8 9 10 11 12 $$-1$$ $$1$$ $$e\left(\frac{232}{285}\right)$$ $$e\left(\frac{541}{570}\right)$$ $$e\left(\frac{179}{285}\right)$$ $$e\left(\frac{7}{114}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{42}{95}\right)$$ $$e\left(\frac{256}{285}\right)$$ $$e\left(\frac{499}{570}\right)$$ $$e\left(\frac{43}{57}\right)$$ $$e\left(\frac{329}{570}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{285})$$