Properties

Conductor 1027
Order 3
Real No
Primitive Yes
Parity Even
Orbit Label 1027.e

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(1027)
sage: chi = H[497]
pari: [g,chi] = znchar(Mod(497,1027))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1027
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 3
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 = Even
Orbit label = 1027.e
Orbit index = 5

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 ]

\(\chi_{1027}(497,\cdot)\) \(\chi_{1027}(529,\cdot)\)

Values on generators

\((80,872)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{3}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{1}{3}\right)\)\(1\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{1}{3}\right)\)\(1\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{3})\)