Properties

Conductor 8041
Order 60
Real No
Primitive Yes
Parity Even
Orbit Label 8041.do

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[251]
 
pari: [g,chi] = znchar(Mod(251,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8041
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 60
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.do
Orbit index = 93

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 ]
 

\(\chi_{8041}(251,\cdot)\) \(\chi_{8041}(565,\cdot)\) \(\chi_{8041}(608,\cdot)\) \(\chi_{8041}(939,\cdot)\) \(\chi_{8041}(982,\cdot)\) \(\chi_{8041}(1296,\cdot)\) \(\chi_{8041}(1670,\cdot)\) \(\chi_{8041}(2027,\cdot)\) \(\chi_{8041}(2401,\cdot)\) \(\chi_{8041}(5725,\cdot)\) \(\chi_{8041}(6099,\cdot)\) \(\chi_{8041}(7144,\cdot)\) \(\chi_{8041}(7187,\cdot)\) \(\chi_{8041}(7518,\cdot)\) \(\chi_{8041}(7561,\cdot)\) \(\chi_{8041}(7918,\cdot)\)

Values on generators

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

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{23}{60}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{59}{60}\right)\)\(e\left(\frac{29}{60}\right)\)\(e\left(\frac{37}{60}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{23}{30}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{7}{12}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{60})\)