# Properties

 Conductor 575 Order 220 Real No Primitive No Parity Odd Orbit Label 4025.dg

# 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[8]

pari: [g,chi] = znchar(Mod(8,4025))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 575 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 220 Real = No sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = No sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = Odd Orbit label = 4025.dg Orbit index = 85

## 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

$$(2577,1151,3501)$$ → $$(e\left(\frac{3}{20}\right),1,e\left(\frac{3}{11}\right))$$

## Values

 -1 1 2 3 4 6 8 9 11 12 13 16 $$-1$$ $$1$$ $$e\left(\frac{153}{220}\right)$$ $$e\left(\frac{91}{220}\right)$$ $$e\left(\frac{43}{110}\right)$$ $$e\left(\frac{6}{55}\right)$$ $$e\left(\frac{19}{220}\right)$$ $$e\left(\frac{91}{110}\right)$$ $$e\left(\frac{47}{55}\right)$$ $$e\left(\frac{177}{220}\right)$$ $$e\left(\frac{147}{220}\right)$$ $$e\left(\frac{43}{55}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{220})$$