# Properties

 Conductor 77 Order 30 Real no Primitive no Minimal no Parity even Orbit label 7623.co

# 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[766]

pari: [g,chi] = znchar(Mod(766,7623))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 77 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 30 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = no Minimal = no sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 7623.co Orbit index = 67

## 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

$$(848,4357,4600)$$ → $$(1,e\left(\frac{1}{6}\right),e\left(\frac{7}{10}\right))$$

## Values

 -1 1 2 4 5 8 10 13 16 17 19 20 $$1$$ $$1$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{15})$$