Properties

Conductor 8041
Order 80
Real No
Primitive Yes
Parity Even
Orbit Label 8041.dy

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[214]
 
pari: [g,chi] = znchar(Mod(214,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8041
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 80
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.dy
Orbit index = 103

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 ]
 

\(\chi_{8041}(214,\cdot)\) \(\chi_{8041}(300,\cdot)\) \(\chi_{8041}(515,\cdot)\) \(\chi_{8041}(687,\cdot)\) \(\chi_{8041}(1246,\cdot)\) \(\chi_{8041}(1676,\cdot)\) \(\chi_{8041}(2149,\cdot)\) \(\chi_{8041}(2407,\cdot)\) \(\chi_{8041}(2579,\cdot)\) \(\chi_{8041}(2880,\cdot)\) \(\chi_{8041}(3138,\cdot)\) \(\chi_{8041}(3525,\cdot)\) \(\chi_{8041}(3611,\cdot)\) \(\chi_{8041}(3998,\cdot)\) \(\chi_{8041}(4041,\cdot)\) \(\chi_{8041}(4772,\cdot)\) \(\chi_{8041}(4944,\cdot)\) \(\chi_{8041}(4987,\cdot)\) \(\chi_{8041}(5417,\cdot)\) \(\chi_{8041}(5460,\cdot)\) \(\chi_{8041}(5503,\cdot)\) \(\chi_{8041}(5718,\cdot)\) \(\chi_{8041}(6191,\cdot)\) \(\chi_{8041}(6363,\cdot)\) \(\chi_{8041}(6406,\cdot)\) \(\chi_{8041}(6449,\cdot)\) \(\chi_{8041}(6879,\cdot)\) \(\chi_{8041}(6922,\cdot)\) \(\chi_{8041}(7137,\cdot)\) \(\chi_{8041}(7610,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{3}{16}\right),-1)\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{21}{40}\right)\)\(e\left(\frac{71}{80}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{3}{80}\right)\)\(e\left(\frac{33}{80}\right)\)\(e\left(\frac{29}{80}\right)\)\(e\left(\frac{23}{40}\right)\)\(e\left(\frac{31}{40}\right)\)\(e\left(\frac{9}{16}\right)\)\(e\left(\frac{15}{16}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{80})\)