# Properties

 Conductor 1021 Order 85 Real no Primitive yes Minimal yes Parity even Orbit label 1021.q

# Related objects

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

sage: H = DirichletGroup_conrey(1021)

sage: chi = H[310]

pari: [g,chi] = znchar(Mod(310,1021))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 1021 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 85 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 = 1021.q Orbit index = 17

## 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

$$10$$ → $$e\left(\frac{4}{85}\right)$$

## Values

 -1 1 2 3 4 5 6 7 8 9 10 11 $$1$$ $$1$$ $$e\left(\frac{57}{85}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{29}{85}\right)$$ $$e\left(\frac{32}{85}\right)$$ $$e\left(\frac{32}{85}\right)$$ $$e\left(\frac{37}{85}\right)$$ $$e\left(\frac{1}{85}\right)$$ $$e\left(\frac{7}{17}\right)$$ $$e\left(\frac{4}{85}\right)$$ $$e\left(\frac{64}{85}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{85})$$