Properties

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

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[123]
 
pari: [g,chi] = znchar(Mod(123,8041))
 

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.dn
Orbit index = 92

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 ]
 

\(\chi_{8041}(123,\cdot)\) \(\chi_{8041}(480,\cdot)\) \(\chi_{8041}(523,\cdot)\) \(\chi_{8041}(854,\cdot)\) \(\chi_{8041}(897,\cdot)\) \(\chi_{8041}(1942,\cdot)\) \(\chi_{8041}(2316,\cdot)\) \(\chi_{8041}(5640,\cdot)\) \(\chi_{8041}(6014,\cdot)\) \(\chi_{8041}(6371,\cdot)\) \(\chi_{8041}(6745,\cdot)\) \(\chi_{8041}(7059,\cdot)\) \(\chi_{8041}(7102,\cdot)\) \(\chi_{8041}(7433,\cdot)\) \(\chi_{8041}(7476,\cdot)\) \(\chi_{8041}(7790,\cdot)\)

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{1}{10}\right),-i,e\left(\frac{1}{6}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{43}{60}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{49}{60}\right)\)\(e\left(\frac{47}{60}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{11}{12}\right)\)
value at  e.g. 2

Related number fields

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