# Properties

 Conductor 2365 Order 420 Real no Primitive no Minimal yes Parity even Orbit label 4730.dp

# Related objects

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[13]

pari: [g,chi] = znchar(Mod(13,4730))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 2365 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 420 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.dp Orbit index = 94

## 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

$$(947,431,1981)$$ → $$(-i,e\left(\frac{1}{10}\right),e\left(\frac{16}{21}\right))$$

## Values

 -1 1 3 7 9 13 17 19 21 23 27 29 $$1$$ $$1$$ $$e\left(\frac{341}{420}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{131}{210}\right)$$ $$e\left(\frac{307}{420}\right)$$ $$e\left(\frac{253}{420}\right)$$ $$e\left(\frac{29}{105}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{61}{140}\right)$$ $$e\left(\frac{46}{105}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{420})$$