# Properties

 Conductor 4725 Order 90 Real no Primitive no Minimal yes Parity even Orbit label 9450.gf

# 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(9450)

sage: chi = H[131]

pari: [g,chi] = znchar(Mod(131,9450))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 4725 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 90 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = no Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 9450.gf Orbit index = 162

## 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

$$(9101,6427,6751)$$ → $$(e\left(\frac{11}{18}\right),e\left(\frac{2}{5}\right),e\left(\frac{5}{6}\right))$$

## Values

 -1 1 11 13 17 19 23 29 31 37 41 43 $$1$$ $$1$$ $$e\left(\frac{61}{90}\right)$$ $$e\left(\frac{89}{90}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{71}{90}\right)$$ $$e\left(\frac{37}{90}\right)$$ $$e\left(\frac{23}{90}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{22}{45}\right)$$ $$e\left(\frac{4}{9}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{45})$$