# Properties

 Conductor 1157 Order 132 Real No Primitive Yes Parity Odd Orbit Label 1157.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(1157)
sage: chi = H[20]
pari: [g,chi] = znchar(Mod(20,1157))

## Basic properties

 sage: chi.conductor() pari: znconreyconductor(g,chi) Conductor = 1157 sage: chi.multiplicative_order() pari: charorder(g,chi) Order = 132 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 = 1157.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

$$(535,92)$$ → $$(e\left(\frac{11}{12}\right),e\left(\frac{7}{44}\right))$$

## Values

 -1 1 2 3 4 5 6 7 8 9 10 11 $$-1$$ $$1$$ $$e\left(\frac{61}{132}\right)$$ $$e\left(\frac{109}{132}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{103}{132}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{132})$$