# Properties

 Conductor 1337 Order 114 Real No Primitive No Parity Odd Orbit Label 4011.bw

# 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(4011)

sage: chi = H[37]

pari: [g,chi] = znchar(Mod(37,4011))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 1337 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 114 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 = 4011.bw Orbit index = 49

## 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

$$(2675,2866,2311)$$ → $$(1,e\left(\frac{1}{3}\right),e\left(\frac{3}{38}\right))$$

## Values

 -1 1 2 4 5 8 10 11 13 16 17 19 $$-1$$ $$1$$ $$e\left(\frac{8}{57}\right)$$ $$e\left(\frac{16}{57}\right)$$ $$e\left(\frac{35}{57}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{43}{57}\right)$$ $$e\left(\frac{5}{114}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{32}{57}\right)$$ $$e\left(\frac{4}{57}\right)$$ $$e\left(\frac{85}{114}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{57})$$