# Properties

 Conductor 335 Order 132 Real No Primitive No Parity Odd Orbit Label 4020.dp

# 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(4020)

sage: chi = H[73]

pari: [g,chi] = znchar(Mod(73,4020))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 335 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 132 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 = 4020.dp Orbit index = 94

## 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

$$(2011,2681,3217,1141)$$ → $$(1,1,-i,e\left(\frac{20}{33}\right))$$

## Values

 -1 1 7 11 13 17 19 23 29 31 37 41 $$-1$$ $$1$$ $$e\left(\frac{91}{132}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{101}{132}\right)$$ $$e\left(\frac{71}{132}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{29}{132}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{4}{33}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{132})$$