Properties

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

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[2]
 
pari: [g,chi] = znchar(Mod(2,8041))
 

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.fj
Orbit index = 140

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 ]
 

\(\chi_{8041}(2,\cdot)\) \(\chi_{8041}(8,\cdot)\) \(\chi_{8041}(94,\cdot)\) \(\chi_{8041}(151,\cdot)\) \(\chi_{8041}(161,\cdot)\) \(\chi_{8041}(376,\cdot)\) \(\chi_{8041}(457,\cdot)\) \(\chi_{8041}(512,\cdot)\) \(\chi_{8041}(733,\cdot)\) \(\chi_{8041}(739,\cdot)\) \(\chi_{8041}(882,\cdot)\) \(\chi_{8041}(899,\cdot)\) \(\chi_{8041}(954,\cdot)\) \(\chi_{8041}(1097,\cdot)\) \(\chi_{8041}(1107,\cdot)\) \(\chi_{8041}(1249,\cdot)\) \(\chi_{8041}(1317,\cdot)\) \(\chi_{8041}(1403,\cdot)\) \(\chi_{8041}(1470,\cdot)\) \(\chi_{8041}(1613,\cdot)\) \(\chi_{8041}(1623,\cdot)\) \(\chi_{8041}(1630,\cdot)\) \(\chi_{8041}(1685,\cdot)\) \(\chi_{8041}(1828,\cdot)\) \(\chi_{8041}(1845,\cdot)\) \(\chi_{8041}(2048,\cdot)\) \(\chi_{8041}(2195,\cdot)\) \(\chi_{8041}(2263,\cdot)\) \(\chi_{8041}(2361,\cdot)\) \(\chi_{8041}(2416,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{7}{8}\right),e\left(\frac{9}{14}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{99}{140}\right)\)\(e\left(\frac{89}{280}\right)\)\(e\left(\frac{29}{70}\right)\)\(e\left(\frac{237}{280}\right)\)\(e\left(\frac{1}{40}\right)\)\(e\left(\frac{33}{40}\right)\)\(e\left(\frac{17}{140}\right)\)\(e\left(\frac{89}{140}\right)\)\(e\left(\frac{31}{56}\right)\)\(e\left(\frac{41}{56}\right)\)
value at  e.g. 2

Related number fields

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