Properties

Conductor 8041
Order 840
Real No
Primitive Yes
Parity Even
Orbit Label 8041.fw

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[19]
 
pari: [g,chi] = znchar(Mod(19,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8041
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 840
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.fw
Orbit index = 153

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 ]
 

\(\chi_{8041}(19,\cdot)\) \(\chi_{8041}(134,\cdot)\) \(\chi_{8041}(162,\cdot)\) \(\chi_{8041}(206,\cdot)\) \(\chi_{8041}(270,\cdot)\) \(\chi_{8041}(304,\cdot)\) \(\chi_{8041}(321,\cdot)\) \(\chi_{8041}(349,\cdot)\) \(\chi_{8041}(491,\cdot)\) \(\chi_{8041}(501,\cdot)\) \(\chi_{8041}(502,\cdot)\) \(\chi_{8041}(519,\cdot)\) \(\chi_{8041}(535,\cdot)\) \(\chi_{8041}(536,\cdot)\) \(\chi_{8041}(546,\cdot)\) \(\chi_{8041}(678,\cdot)\) \(\chi_{8041}(706,\cdot)\) \(\chi_{8041}(722,\cdot)\) \(\chi_{8041}(750,\cdot)\) \(\chi_{8041}(865,\cdot)\) \(\chi_{8041}(886,\cdot)\) \(\chi_{8041}(893,\cdot)\) \(\chi_{8041}(937,\cdot)\) \(\chi_{8041}(1018,\cdot)\) \(\chi_{8041}(1052,\cdot)\) \(\chi_{8041}(1062,\cdot)\) \(\chi_{8041}(1080,\cdot)\) \(\chi_{8041}(1130,\cdot)\) \(\chi_{8041}(1216,\cdot)\) \(\chi_{8041}(1250,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{7}{8}\right),e\left(\frac{19}{42}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{107}{140}\right)\)\(e\left(\frac{611}{840}\right)\)\(e\left(\frac{37}{70}\right)\)\(e\left(\frac{743}{840}\right)\)\(e\left(\frac{59}{120}\right)\)\(e\left(\frac{67}{120}\right)\)\(e\left(\frac{41}{140}\right)\)\(e\left(\frac{191}{420}\right)\)\(e\left(\frac{109}{168}\right)\)\(e\left(\frac{43}{168}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{840})\)