# Properties

 Conductor 4011 Order 38 Real No Primitive Yes Parity Odd Orbit Label 4011.bk

# 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[2267]

pari: [g,chi] = znchar(Mod(2267,4011))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 4011 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 38 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 = 4011.bk Orbit index = 37

## 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

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

## Values

 -1 1 2 4 5 8 10 11 13 16 17 19 $$-1$$ $$1$$ $$e\left(\frac{25}{38}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{37}{38}\right)$$ $$e\left(\frac{37}{38}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{17}{38}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{19})$$