# Properties

 Conductor 473 Order 30 Real no Primitive no Minimal yes Parity even Orbit label 4730.ca

# 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(4730)

sage: chi = H[2961]

pari: [g,chi] = znchar(Mod(2961,4730))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 473 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 = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 4730.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

$$(947,431,1981)$$ → $$(1,e\left(\frac{1}{10}\right),e\left(\frac{1}{6}\right))$$

## Values

 -1 1 3 7 9 13 17 19 21 23 27 29 $$1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$
value at  e.g. 2

## Related number fields

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