# Properties

 Conductor 1157 Order 264 Real no Primitive yes Minimal yes Parity odd Orbit label 1157.ca

# Related objects

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(1157)

sage: chi = H[23]

pari: [g,chi] = znchar(Mod(23,1157))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 1157 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 264 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.ca Orbit index = 53

## 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

$$(535,92)$$ → $$(e\left(\frac{5}{6}\right),e\left(\frac{57}{88}\right))$$

## Values

 -1 1 2 3 4 5 6 7 8 9 10 11 $$-1$$ $$1$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{259}{264}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{47}{264}\right)$$ $$e\left(\frac{167}{264}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{127}{132}\right)$$ $$e\left(\frac{5}{132}\right)$$ $$e\left(\frac{8}{33}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{264})$$