Properties

Conductor 8041
Order 140
Real No
Primitive Yes
Parity Even
Orbit Label 8041.en

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[217]
 
pari: [g,chi] = znchar(Mod(217,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8041
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 140
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.en
Orbit index = 118

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 ]
 

\(\chi_{8041}(217,\cdot)\) \(\chi_{8041}(591,\cdot)\) \(\chi_{8041}(667,\cdot)\) \(\chi_{8041}(684,\cdot)\) \(\chi_{8041}(710,\cdot)\) \(\chi_{8041}(948,\cdot)\) \(\chi_{8041}(1322,\cdot)\) \(\chi_{8041}(1415,\cdot)\) \(\chi_{8041}(1458,\cdot)\) \(\chi_{8041}(1636,\cdot)\) \(\chi_{8041}(1679,\cdot)\) \(\chi_{8041}(1900,\cdot)\) \(\chi_{8041}(2010,\cdot)\) \(\chi_{8041}(2053,\cdot)\) \(\chi_{8041}(2129,\cdot)\) \(\chi_{8041}(2367,\cdot)\) \(\chi_{8041}(2631,\cdot)\) \(\chi_{8041}(2741,\cdot)\) \(\chi_{8041}(2877,\cdot)\) \(\chi_{8041}(3098,\cdot)\) \(\chi_{8041}(3141,\cdot)\) \(\chi_{8041}(3209,\cdot)\) \(\chi_{8041}(3319,\cdot)\) \(\chi_{8041}(3362,\cdot)\) \(\chi_{8041}(3472,\cdot)\) \(\chi_{8041}(3515,\cdot)\) \(\chi_{8041}(3940,\cdot)\) \(\chi_{8041}(4050,\cdot)\) \(\chi_{8041}(4560,\cdot)\) \(\chi_{8041}(4628,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{3}{10}\right),i,e\left(\frac{9}{14}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{11}{70}\right)\)\(e\left(\frac{41}{140}\right)\)\(e\left(\frac{11}{35}\right)\)\(e\left(\frac{73}{140}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{33}{70}\right)\)\(e\left(\frac{41}{70}\right)\)\(e\left(\frac{19}{28}\right)\)\(e\left(\frac{17}{28}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{140})\)