Conductor 8041
Order 24
Real No
Primitive Yes
Parity Even
Orbit Label

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(8041)
sage: chi = H[824]
pari: [g,chi] = znchar(Mod(824,8041))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 8041
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 24
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 =
Orbit index = 55

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 ]

\(\chi_{8041}(824,\cdot)\) \(\chi_{8041}(1198,\cdot)\) \(\chi_{8041}(1770,\cdot)\) \(\chi_{8041}(2144,\cdot)\) \(\chi_{8041}(5081,\cdot)\) \(\chi_{8041}(5455,\cdot)\) \(\chi_{8041}(6027,\cdot)\) \(\chi_{8041}(6401,\cdot)\)

Values on generators

\((6580,2366,562)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{5}{6}\right))\)


value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{24})\)