# Properties

 Modulus 1157 Conductor 1157 Order 8 Real no Primitive yes Minimal yes Parity odd Orbit label 1157.o

# Related objects

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter

sage: H = DirichletGroup(1157)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([4,1]))

pari: [g,chi] = znchar(Mod(571,1157))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 1157 Conductor = 1157 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 8 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = yes Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = odd Orbit label = 1157.o Orbit index = 15

## Galois orbit

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Values on generators

$$(535,92)$$ → $$(-1,e\left(\frac{1}{8}\right))$$

## Values

 -1 1 2 3 4 5 6 7 8 9 10 11 $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$ $$i$$ $$-i$$ $$1$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{8})$$