Properties

Conductor 8041
Order 280
Real No
Primitive Yes
Parity Even
Orbit Label 8041.fh

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[59]
 
pari: [g,chi] = znchar(Mod(59,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8041
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 280
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.fh
Orbit index = 138

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 ]
 

\(\chi_{8041}(59,\cdot)\) \(\chi_{8041}(213,\cdot)\) \(\chi_{8041}(236,\cdot)\) \(\chi_{8041}(355,\cdot)\) \(\chi_{8041}(434,\cdot)\) \(\chi_{8041}(570,\cdot)\) \(\chi_{8041}(729,\cdot)\) \(\chi_{8041}(790,\cdot)\) \(\chi_{8041}(852,\cdot)\) \(\chi_{8041}(944,\cdot)\) \(\chi_{8041}(950,\cdot)\) \(\chi_{8041}(1005,\cdot)\) \(\chi_{8041}(1182,\cdot)\) \(\chi_{8041}(1215,\cdot)\) \(\chi_{8041}(1301,\cdot)\) \(\chi_{8041}(1368,\cdot)\) \(\chi_{8041}(1521,\cdot)\) \(\chi_{8041}(1589,\cdot)\) \(\chi_{8041}(1675,\cdot)\) \(\chi_{8041}(1681,\cdot)\) \(\chi_{8041}(1698,\cdot)\) \(\chi_{8041}(1736,\cdot)\) \(\chi_{8041}(1896,\cdot)\) \(\chi_{8041}(2099,\cdot)\) \(\chi_{8041}(2161,\cdot)\) \(\chi_{8041}(2314,\cdot)\) \(\chi_{8041}(2412,\cdot)\) \(\chi_{8041}(2429,\cdot)\) \(\chi_{8041}(2467,\cdot)\) \(\chi_{8041}(2535,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{5}{8}\right),e\left(\frac{4}{7}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{53}{140}\right)\)\(e\left(\frac{223}{280}\right)\)\(e\left(\frac{53}{70}\right)\)\(e\left(\frac{59}{280}\right)\)\(e\left(\frac{7}{40}\right)\)\(e\left(\frac{11}{40}\right)\)\(e\left(\frac{19}{140}\right)\)\(e\left(\frac{83}{140}\right)\)\(e\left(\frac{33}{56}\right)\)\(e\left(\frac{31}{56}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{280})\)