Properties

Conductor 8041
Order 84
Real No
Primitive Yes
Parity Even
Orbit Label 8041.ec

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[98]
 
pari: [g,chi] = znchar(Mod(98,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8041
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 84
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.ec
Orbit index = 107

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 ]
 

\(\chi_{8041}(98,\cdot)\) \(\chi_{8041}(846,\cdot)\) \(\chi_{8041}(1517,\cdot)\) \(\chi_{8041}(1594,\cdot)\) \(\chi_{8041}(1781,\cdot)\) \(\chi_{8041}(1968,\cdot)\) \(\chi_{8041}(2155,\cdot)\) \(\chi_{8041}(2265,\cdot)\) \(\chi_{8041}(2342,\cdot)\) \(\chi_{8041}(3013,\cdot)\) \(\chi_{8041}(3200,\cdot)\) \(\chi_{8041}(3387,\cdot)\) \(\chi_{8041}(3574,\cdot)\) \(\chi_{8041}(3761,\cdot)\) \(\chi_{8041}(4025,\cdot)\) \(\chi_{8041}(4586,\cdot)\) \(\chi_{8041}(5147,\cdot)\) \(\chi_{8041}(5444,\cdot)\) \(\chi_{8041}(6005,\cdot)\) \(\chi_{8041}(6082,\cdot)\) \(\chi_{8041}(6269,\cdot)\) \(\chi_{8041}(6566,\cdot)\) \(\chi_{8041}(7501,\cdot)\) \(\chi_{8041}(7688,\cdot)\)

Values on generators

\((6580,2366,562)\) → \((-1,i,e\left(\frac{13}{42}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{5}{14}\right)\)\(e\left(\frac{47}{84}\right)\)\(e\left(\frac{5}{7}\right)\)\(e\left(\frac{83}{84}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{1}{14}\right)\)\(e\left(\frac{5}{42}\right)\)\(e\left(\frac{29}{84}\right)\)\(e\left(\frac{23}{84}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{84})\)