Properties

Conductor 8041
Order 168
Real No
Primitive Yes
Parity Even
Orbit Label 8041.eu

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[76]
 
pari: [g,chi] = znchar(Mod(76,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8041
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 168
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.eu
Orbit index = 125

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 ]
 

\(\chi_{8041}(76,\cdot)\) \(\chi_{8041}(263,\cdot)\) \(\chi_{8041}(406,\cdot)\) \(\chi_{8041}(417,\cdot)\) \(\chi_{8041}(450,\cdot)\) \(\chi_{8041}(593,\cdot)\) \(\chi_{8041}(648,\cdot)\) \(\chi_{8041}(835,\cdot)\) \(\chi_{8041}(1022,\cdot)\) \(\chi_{8041}(1209,\cdot)\) \(\chi_{8041}(1352,\cdot)\) \(\chi_{8041}(1396,\cdot)\) \(\chi_{8041}(1539,\cdot)\) \(\chi_{8041}(2133,\cdot)\) \(\chi_{8041}(2463,\cdot)\) \(\chi_{8041}(2694,\cdot)\) \(\chi_{8041}(3079,\cdot)\) \(\chi_{8041}(3211,\cdot)\) \(\chi_{8041}(3255,\cdot)\) \(\chi_{8041}(3409,\cdot)\) \(\chi_{8041}(3640,\cdot)\) \(\chi_{8041}(3959,\cdot)\) \(\chi_{8041}(4146,\cdot)\) \(\chi_{8041}(4157,\cdot)\) \(\chi_{8041}(4190,\cdot)\) \(\chi_{8041}(4201,\cdot)\) \(\chi_{8041}(4333,\cdot)\) \(\chi_{8041}(4377,\cdot)\) \(\chi_{8041}(4520,\cdot)\) \(\chi_{8041}(4707,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{31}{42}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{5}{28}\right)\)\(e\left(\frac{61}{168}\right)\)\(e\left(\frac{5}{14}\right)\)\(e\left(\frac{97}{168}\right)\)\(e\left(\frac{13}{24}\right)\)\(e\left(\frac{5}{24}\right)\)\(e\left(\frac{15}{28}\right)\)\(e\left(\frac{61}{84}\right)\)\(e\left(\frac{127}{168}\right)\)\(e\left(\frac{121}{168}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{168})\)