# Properties

 Conductor 7623 Order 165 Real no Primitive yes Minimal yes Parity even Orbit label 7623.fa

# Learn more about

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

sage: H = DirichletGroup_conrey(7623)

sage: chi = H[2347]

pari: [g,chi] = znchar(Mod(2347,7623))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 7623 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 165 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 = even Orbit label = 7623.fa Orbit index = 131

## 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

$$(848,4357,4600)$$ → $$(e\left(\frac{2}{3}\right),e\left(\frac{1}{3}\right),e\left(\frac{46}{55}\right))$$

## Values

 -1 1 2 4 5 8 10 13 16 17 19 20 $$1$$ $$1$$ $$e\left(\frac{28}{165}\right)$$ $$e\left(\frac{56}{165}\right)$$ $$e\left(\frac{49}{55}\right)$$ $$e\left(\frac{28}{55}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{133}{165}\right)$$ $$e\left(\frac{112}{165}\right)$$ $$e\left(\frac{52}{165}\right)$$ $$e\left(\frac{14}{165}\right)$$ $$e\left(\frac{38}{165}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{165})$$