# Properties

 Conductor 4033 Order 108 Real No Primitive Yes Parity Odd Orbit Label 4033.il

# 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(4033)

sage: chi = H[31]

pari: [g,chi] = znchar(Mod(31,4033))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 4033 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 108 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 = 4033.il Orbit index = 220

## 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

$$(1963,2295)$$ → $$(i,e\left(\frac{7}{54}\right))$$

## Values

 -1 1 2 3 4 5 6 7 8 9 10 11 $$-1$$ $$1$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{13}{54}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{65}{108}\right)$$ $$e\left(\frac{95}{108}\right)$$ $$e\left(\frac{5}{27}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{13}{27}\right)$$ $$e\left(\frac{13}{54}\right)$$ $$e\left(\frac{7}{27}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{108})$$