# Properties

 Conductor 5025 Order 330 Real No Primitive Yes Parity Odd

# 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(5025)
sage: chi = H[4871]
pari: [g,chi] = znchar(Mod(4871,5025))

## Values on generators

sage: chi(k) for k in H.gens()
pari: [ chareval(g,chi,x) | x <- g.gen ] \\ value in Q/Z

$(538,3751,1676)$ → $(e\left(\frac{26}{165}\right),1,-1)$

## First values

 1 2 4 7 8 11 13 14 16 17 19 22 23 26 28 29 31 32 34 37 38 41 43 44 46 47 49 52 53 56 1 $e\left(\frac{283}{330}\right)$ $e\left(\frac{118}{165}\right)$ $e\left(\frac{14}{33}\right)$ $e\left(\frac{63}{110}\right)$ $e\left(\frac{263}{330}\right)$ $e\left(\frac{131}{165}\right)$ $e\left(\frac{31}{110}\right)$ $e\left(\frac{71}{165}\right)$ $e\left(\frac{259}{330}\right)$ $e\left(\frac{62}{165}\right)$ $e\left(\frac{36}{55}\right)$ $e\left(\frac{103}{330}\right)$ $e\left(\frac{43}{66}\right)$ $e\left(\frac{23}{165}\right)$ $e\left(\frac{1}{30}\right)$ $e\left(\frac{67}{165}\right)$ $e\left(\frac{19}{66}\right)$ $e\left(\frac{106}{165}\right)$ $e\left(\frac{1}{15}\right)$ $e\left(\frac{7}{30}\right)$ $e\left(\frac{17}{330}\right)$ $e\left(\frac{9}{11}\right)$ $e\left(\frac{169}{330}\right)$ $e\left(\frac{28}{165}\right)$ $e\left(\frac{191}{330}\right)$ $e\left(\frac{28}{33}\right)$ $e\left(\frac{28}{55}\right)$ $e\left(\frac{97}{110}\right)$ $e\left(\frac{329}{330}\right)$
value at  e.g. 2

## Basic properties

 sage: chi.conductor() pari: znconreyconductor(g,chi) Conductor = 5025 sage: chi.multiplicative_order() pari: charorder(g,chi) Order = 330 sage: chi.is_odd() pari: zncharisodd(g,chi) Parity = Odd Real = No sage: chi.is_primitive() pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = Yes

## 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 ]

## Related number fields

 Field of values $\Q(\zeta_{165})$