# Properties

 Conductor 847 Order 22 Real no Primitive no Minimal yes Parity even Orbit label 2541.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(2541)

sage: chi = H[76]

pari: [g,chi] = znchar(Mod(76,2541))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 847 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 22 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = no Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 2541.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

$$(848,1816,2059)$$ → $$(1,-1,e\left(\frac{17}{22}\right))$$

## Values

 -1 1 2 4 5 8 10 13 16 17 19 20 $$1$$ $$1$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{11})$$