Conductor 2003
Order 14
Real No
Primitive Yes
Parity Odd
Orbit Label 2003.f

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(2003)
sage: chi = H[318]
pari: [g,chi] = znchar(Mod(318,2003))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 2003
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 14
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 = Odd
Orbit label = 2003.f
Orbit index = 6

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 ]

\(\chi_{2003}(318,\cdot)\) \(\chi_{2003}(746,\cdot)\) \(\chi_{2003}(1029,\cdot)\) \(\chi_{2003}(1129,\cdot)\) \(\chi_{2003}(1270,\cdot)\) \(\chi_{2003}(1518,\cdot)\)

Values on generators

\(5\) → \(e\left(\frac{13}{14}\right)\)


value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{7})\)