Properties

Conductor 8041
Order 420
Real No
Primitive Yes
Parity Even
Orbit Label 8041.fo

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[38]
 
pari: [g,chi] = znchar(Mod(38,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8041
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 420
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.fo
Orbit index = 145

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 ]
 

\(\chi_{8041}(38,\cdot)\) \(\chi_{8041}(81,\cdot)\) \(\chi_{8041}(225,\cdot)\) \(\chi_{8041}(268,\cdot)\) \(\chi_{8041}(361,\cdot)\) \(\chi_{8041}(412,\cdot)\) \(\chi_{8041}(455,\cdot)\) \(\chi_{8041}(531,\cdot)\) \(\chi_{8041}(599,\cdot)\) \(\chi_{8041}(625,\cdot)\) \(\chi_{8041}(642,\cdot)\) \(\chi_{8041}(676,\cdot)\) \(\chi_{8041}(812,\cdot)\) \(\chi_{8041}(999,\cdot)\) \(\chi_{8041}(1092,\cdot)\) \(\chi_{8041}(1186,\cdot)\) \(\chi_{8041}(1313,\cdot)\) \(\chi_{8041}(1347,\cdot)\) \(\chi_{8041}(1356,\cdot)\) \(\chi_{8041}(1373,\cdot)\) \(\chi_{8041}(1390,\cdot)\) \(\chi_{8041}(1500,\cdot)\) \(\chi_{8041}(1543,\cdot)\) \(\chi_{8041}(1687,\cdot)\) \(\chi_{8041}(1730,\cdot)\) \(\chi_{8041}(1874,\cdot)\) \(\chi_{8041}(1917,\cdot)\) \(\chi_{8041}(2044,\cdot)\) \(\chi_{8041}(2061,\cdot)\) \(\chi_{8041}(2095,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{2}{5}\right),-i,e\left(\frac{2}{21}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{33}{70}\right)\)\(e\left(\frac{19}{420}\right)\)\(e\left(\frac{33}{35}\right)\)\(e\left(\frac{307}{420}\right)\)\(e\left(\frac{31}{60}\right)\)\(e\left(\frac{23}{60}\right)\)\(e\left(\frac{29}{70}\right)\)\(e\left(\frac{19}{210}\right)\)\(e\left(\frac{17}{84}\right)\)\(e\left(\frac{83}{84}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{420})\)