Properties

Conductor 8041
Order 336
Real No
Primitive Yes
Parity Even
Orbit Label 8041.fl

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[10]
 
pari: [g,chi] = znchar(Mod(10,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8041
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 336
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 = 8041.fl
Orbit index = 142

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 ]
 

\(\chi_{8041}(10,\cdot)\) \(\chi_{8041}(109,\cdot)\) \(\chi_{8041}(142,\cdot)\) \(\chi_{8041}(197,\cdot)\) \(\chi_{8041}(296,\cdot)\) \(\chi_{8041}(318,\cdot)\) \(\chi_{8041}(384,\cdot)\) \(\chi_{8041}(439,\cdot)\) \(\chi_{8041}(483,\cdot)\) \(\chi_{8041}(615,\cdot)\) \(\chi_{8041}(626,\cdot)\) \(\chi_{8041}(670,\cdot)\) \(\chi_{8041}(703,\cdot)\) \(\chi_{8041}(857,\cdot)\) \(\chi_{8041}(912,\cdot)\) \(\chi_{8041}(1099,\cdot)\) \(\chi_{8041}(1132,\cdot)\) \(\chi_{8041}(1176,\cdot)\) \(\chi_{8041}(1264,\cdot)\) \(\chi_{8041}(1561,\cdot)\) \(\chi_{8041}(1605,\cdot)\) \(\chi_{8041}(1737,\cdot)\) \(\chi_{8041}(1858,\cdot)\) \(\chi_{8041}(1880,\cdot)\) \(\chi_{8041}(2001,\cdot)\) \(\chi_{8041}(2034,\cdot)\) \(\chi_{8041}(2045,\cdot)\) \(\chi_{8041}(2122,\cdot)\) \(\chi_{8041}(2188,\cdot)\) \(\chi_{8041}(2353,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((-1,e\left(\frac{3}{16}\right),e\left(\frac{5}{21}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{31}{56}\right)\)\(e\left(\frac{143}{336}\right)\)\(e\left(\frac{3}{28}\right)\)\(e\left(\frac{299}{336}\right)\)\(e\left(\frac{47}{48}\right)\)\(e\left(\frac{43}{48}\right)\)\(e\left(\frac{37}{56}\right)\)\(e\left(\frac{143}{168}\right)\)\(e\left(\frac{149}{336}\right)\)\(e\left(\frac{179}{336}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{336})\)