# Properties

 Conductor 4025 Order 330 Real No Primitive Yes Parity Odd Orbit Label 4025.dn

# 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(4025)

sage: chi = H[44]

pari: [g,chi] = znchar(Mod(44,4025))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 4025 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 330 Real = No sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = Yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = Odd Orbit label = 4025.dn Orbit index = 92

## 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

$$(2577,1151,3501)$$ → $$(e\left(\frac{9}{10}\right),e\left(\frac{1}{3}\right),e\left(\frac{13}{22}\right))$$

## Values

 -1 1 2 3 4 6 8 9 11 12 13 16 $$-1$$ $$1$$ $$e\left(\frac{247}{330}\right)$$ $$e\left(\frac{29}{330}\right)$$ $$e\left(\frac{82}{165}\right)$$ $$e\left(\frac{46}{55}\right)$$ $$e\left(\frac{27}{110}\right)$$ $$e\left(\frac{29}{165}\right)$$ $$e\left(\frac{17}{330}\right)$$ $$e\left(\frac{193}{330}\right)$$ $$e\left(\frac{41}{110}\right)$$ $$e\left(\frac{164}{165}\right)$$
value at  e.g. 2

## Related number fields

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