# Properties

 Conductor 1005 Order 132 Real No Primitive No Parity Odd Orbit Label 4020.do

# 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[113]

pari: [g,chi] = znchar(Mod(113,4020))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 1005 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.do Orbit index = 93

## 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

$$(2011,2681,3217,1141)$$ → $$(1,-1,-i,e\left(\frac{29}{66}\right))$$

## Values

 -1 1 7 11 13 17 19 23 29 31 37 41 $$-1$$ $$1$$ $$e\left(\frac{113}{132}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{79}{132}\right)$$ $$e\left(\frac{49}{132}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{7}{132}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{26}{33}\right)$$
value at  e.g. 2

## Related number fields

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