Properties

Conductor 8041
Order 840
Real No
Primitive Yes
Parity Even
Orbit Label 8041.fy

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[9]
 
pari: [g,chi] = znchar(Mod(9,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8041
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 840
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.fy
Orbit index = 155

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 ]
 

\(\chi_{8041}(9,\cdot)\) \(\chi_{8041}(15,\cdot)\) \(\chi_{8041}(25,\cdot)\) \(\chi_{8041}(53,\cdot)\) \(\chi_{8041}(60,\cdot)\) \(\chi_{8041}(185,\cdot)\) \(\chi_{8041}(196,\cdot)\) \(\chi_{8041}(212,\cdot)\) \(\chi_{8041}(229,\cdot)\) \(\chi_{8041}(240,\cdot)\) \(\chi_{8041}(246,\cdot)\) \(\chi_{8041}(400,\cdot)\) \(\chi_{8041}(410,\cdot)\) \(\chi_{8041}(427,\cdot)\) \(\chi_{8041}(444,\cdot)\) \(\chi_{8041}(576,\cdot)\) \(\chi_{8041}(597,\cdot)\) \(\chi_{8041}(654,\cdot)\) \(\chi_{8041}(740,\cdot)\) \(\chi_{8041}(746,\cdot)\) \(\chi_{8041}(784,\cdot)\) \(\chi_{8041}(797,\cdot)\) \(\chi_{8041}(841,\cdot)\) \(\chi_{8041}(916,\cdot)\) \(\chi_{8041}(927,\cdot)\) \(\chi_{8041}(960,\cdot)\) \(\chi_{8041}(961,\cdot)\) \(\chi_{8041}(971,\cdot)\) \(\chi_{8041}(977,\cdot)\) \(\chi_{8041}(984,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{1}{8}\right),e\left(\frac{1}{21}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{89}{140}\right)\)\(e\left(\frac{817}{840}\right)\)\(e\left(\frac{19}{70}\right)\)\(e\left(\frac{181}{840}\right)\)\(e\left(\frac{73}{120}\right)\)\(e\left(\frac{29}{120}\right)\)\(e\left(\frac{127}{140}\right)\)\(e\left(\frac{397}{420}\right)\)\(e\left(\frac{143}{168}\right)\)\(e\left(\frac{41}{168}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{840})\)