Properties

Conductor 8041
Order 112
Real No
Primitive Yes
Parity Even
Orbit Label 8041.ei

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[54]
 
pari: [g,chi] = znchar(Mod(54,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8041
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 112
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.ei
Orbit index = 113

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 ]
 

\(\chi_{8041}(54,\cdot)\) \(\chi_{8041}(164,\cdot)\) \(\chi_{8041}(428,\cdot)\) \(\chi_{8041}(692,\cdot)\) \(\chi_{8041}(1000,\cdot)\) \(\chi_{8041}(1110,\cdot)\) \(\chi_{8041}(1374,\cdot)\) \(\chi_{8041}(1440,\cdot)\) \(\chi_{8041}(1473,\cdot)\) \(\chi_{8041}(1638,\cdot)\) \(\chi_{8041}(1693,\cdot)\) \(\chi_{8041}(1847,\cdot)\) \(\chi_{8041}(2111,\cdot)\) \(\chi_{8041}(2166,\cdot)\) \(\chi_{8041}(2386,\cdot)\) \(\chi_{8041}(2419,\cdot)\) \(\chi_{8041}(2793,\cdot)\) \(\chi_{8041}(2859,\cdot)\) \(\chi_{8041}(3002,\cdot)\) \(\chi_{8041}(3057,\cdot)\) \(\chi_{8041}(3475,\cdot)\) \(\chi_{8041}(3530,\cdot)\) \(\chi_{8041}(3805,\cdot)\) \(\chi_{8041}(4058,\cdot)\) \(\chi_{8041}(4278,\cdot)\) \(\chi_{8041}(4311,\cdot)\) \(\chi_{8041}(4476,\cdot)\) \(\chi_{8041}(4685,\cdot)\) \(\chi_{8041}(4784,\cdot)\) \(\chi_{8041}(5004,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((-1,e\left(\frac{1}{16}\right),e\left(\frac{5}{7}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{37}{56}\right)\)\(e\left(\frac{87}{112}\right)\)\(e\left(\frac{9}{28}\right)\)\(e\left(\frac{19}{112}\right)\)\(e\left(\frac{7}{16}\right)\)\(e\left(\frac{3}{16}\right)\)\(e\left(\frac{55}{56}\right)\)\(e\left(\frac{31}{56}\right)\)\(e\left(\frac{93}{112}\right)\)\(e\left(\frac{11}{112}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{112})\)