Properties

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

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[4]
 
pari: [g,chi] = znchar(Mod(4,8041))
 

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.eo
Orbit index = 119

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 ]
 

\(\chi_{8041}(4,\cdot)\) \(\chi_{8041}(47,\cdot)\) \(\chi_{8041}(64,\cdot)\) \(\chi_{8041}(489,\cdot)\) \(\chi_{8041}(735,\cdot)\) \(\chi_{8041}(752,\cdot)\) \(\chi_{8041}(795,\cdot)\) \(\chi_{8041}(1466,\cdot)\) \(\chi_{8041}(1483,\cdot)\) \(\chi_{8041}(1798,\cdot)\) \(\chi_{8041}(1908,\cdot)\) \(\chi_{8041}(1951,\cdot)\) \(\chi_{8041}(2214,\cdot)\) \(\chi_{8041}(2682,\cdot)\) \(\chi_{8041}(3107,\cdot)\) \(\chi_{8041}(3217,\cdot)\) \(\chi_{8041}(3260,\cdot)\) \(\chi_{8041}(3370,\cdot)\) \(\chi_{8041}(3413,\cdot)\) \(\chi_{8041}(3481,\cdot)\) \(\chi_{8041}(3991,\cdot)\) \(\chi_{8041}(4101,\cdot)\) \(\chi_{8041}(4526,\cdot)\) \(\chi_{8041}(4569,\cdot)\) \(\chi_{8041}(4679,\cdot)\) \(\chi_{8041}(4722,\cdot)\) \(\chi_{8041}(4832,\cdot)\) \(\chi_{8041}(4900,\cdot)\) \(\chi_{8041}(4943,\cdot)\) \(\chi_{8041}(5164,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{1}{5}\right),-i,e\left(\frac{2}{7}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{29}{70}\right)\)\(e\left(\frac{89}{140}\right)\)\(e\left(\frac{29}{35}\right)\)\(e\left(\frac{97}{140}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{17}{70}\right)\)\(e\left(\frac{19}{70}\right)\)\(e\left(\frac{3}{28}\right)\)\(e\left(\frac{13}{28}\right)\)
value at  e.g. 2

Related number fields

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