# Properties

 Conductor 121 Order 55 Real no Primitive no Minimal yes Parity even Orbit label 7623.do

# 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[757]

pari: [g,chi] = znchar(Mod(757,7623))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 121 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 55 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 = 7623.do Orbit index = 93

## 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

$$(848,4357,4600)$$ → $$(1,1,e\left(\frac{43}{55}\right))$$

## Values

 -1 1 2 4 5 8 10 13 16 17 19 20 $$1$$ $$1$$ $$e\left(\frac{43}{55}\right)$$ $$e\left(\frac{31}{55}\right)$$ $$e\left(\frac{47}{55}\right)$$ $$e\left(\frac{19}{55}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{53}{55}\right)$$ $$e\left(\frac{7}{55}\right)$$ $$e\left(\frac{17}{55}\right)$$ $$e\left(\frac{49}{55}\right)$$ $$e\left(\frac{23}{55}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{55})$$