# Properties

 Conductor 4725 Order 180 Real No Primitive No Parity Even Orbit Label 9450.ha

# 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[317]
pari: [g,chi] = znchar(Mod(317,9450))

## 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 sage: chi.is_odd() pari: zncharisodd(g,chi) Parity = Even Orbit label = 9450.ha Orbit index = 183

## 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

$$(9101,6427,6751)$$ → $$(e\left(\frac{7}{18}\right),e\left(\frac{13}{20}\right),e\left(\frac{1}{3}\right))$$

## Values

 -1 1 11 13 17 19 23 29 31 37 41 43 $$1$$ $$1$$ $$e\left(\frac{71}{90}\right)$$ $$e\left(\frac{83}{180}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{17}{180}\right)$$ $$e\left(\frac{31}{45}\right)$$ $$e\left(\frac{14}{45}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{19}{90}\right)$$ $$e\left(\frac{11}{36}\right)$$
value at  e.g. 2

## Related number fields

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