# Properties

 Conductor 79 Order 13 Real no Primitive no Minimal yes Parity even Orbit label 4029.bc

# 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(4029)

sage: chi = H[52]

pari: [g,chi] = znchar(Mod(52,4029))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 79 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 13 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 = 4029.bc Orbit index = 29

## 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

$$(2687,3556,3163)$$ → $$(1,1,e\left(\frac{7}{13}\right))$$

## Values

 -1 1 2 4 5 7 8 10 11 13 14 16 $$1$$ $$1$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{8}{13}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{13})$$