Properties

 Conductor 1575 Order 60 Real No Primitive No Parity Even Orbit Label 9450.fo

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[397]
pari: [g,chi] = znchar(Mod(397,9450))

Basic properties

 sage: chi.conductor() pari: znconreyconductor(g,chi) Conductor = 1575 sage: chi.multiplicative_order() pari: charorder(g,chi) Order = 60 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.fo Orbit index = 145

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

$$(9101,6427,6751)$$ → $$(e\left(\frac{2}{3}\right),e\left(\frac{17}{20}\right),e\left(\frac{5}{6}\right))$$

Values

 -1 1 11 13 17 19 23 29 31 37 41 43 $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{5}{12}\right)$$
value at  e.g. 2

Related number fields

 Field of values $$\Q(\zeta_{60})$$