Properties

Conductor 731
Order 84
Real no
Primitive no
Minimal yes
Parity even
Orbit label 8041.ed

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[5028]
 
pari: [g,chi] = znchar(Mod(5028,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 731
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 = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 8041.ed
Orbit index = 108

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 ]
 

\(\chi_{8041}(353,\cdot)\) \(\chi_{8041}(540,\cdot)\) \(\chi_{8041}(1475,\cdot)\) \(\chi_{8041}(1772,\cdot)\) \(\chi_{8041}(1959,\cdot)\) \(\chi_{8041}(2036,\cdot)\) \(\chi_{8041}(2597,\cdot)\) \(\chi_{8041}(2894,\cdot)\) \(\chi_{8041}(3455,\cdot)\) \(\chi_{8041}(4016,\cdot)\) \(\chi_{8041}(4280,\cdot)\) \(\chi_{8041}(4467,\cdot)\) \(\chi_{8041}(4654,\cdot)\) \(\chi_{8041}(4841,\cdot)\) \(\chi_{8041}(5028,\cdot)\) \(\chi_{8041}(5699,\cdot)\) \(\chi_{8041}(5776,\cdot)\) \(\chi_{8041}(5886,\cdot)\) \(\chi_{8041}(6073,\cdot)\) \(\chi_{8041}(6260,\cdot)\) \(\chi_{8041}(6447,\cdot)\) \(\chi_{8041}(6524,\cdot)\) \(\chi_{8041}(7195,\cdot)\) \(\chi_{8041}(7943,\cdot)\)

Values on generators

\((6580,2366,562)\) → \((1,i,e\left(\frac{11}{21}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{9}{14}\right)\)\(e\left(\frac{65}{84}\right)\)\(e\left(\frac{2}{7}\right)\)\(e\left(\frac{29}{84}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{13}{14}\right)\)\(e\left(\frac{23}{42}\right)\)\(e\left(\frac{83}{84}\right)\)\(e\left(\frac{5}{84}\right)\)
value at  e.g. 2

Related number fields

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