# Properties

 Conductor 4725 Order 180 Real no Primitive no Minimal yes Parity even Orbit label 9450.gz

# 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[103]

pari: [g,chi] = znchar(Mod(103,9450))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 4725 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 180 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.gz Orbit index = 182

## 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

$$(9101,6427,6751)$$ → $$(e\left(\frac{7}{9}\right),e\left(\frac{7}{20}\right),e\left(\frac{5}{6}\right))$$

## Values

 -1 1 11 13 17 19 23 29 31 37 41 43 $$1$$ $$1$$ $$e\left(\frac{2}{45}\right)$$ $$e\left(\frac{67}{180}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{180}\right)$$ $$e\left(\frac{43}{90}\right)$$ $$e\left(\frac{17}{90}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{11}{90}\right)$$ $$e\left(\frac{13}{36}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{180})$$