Properties

Conductor 8041
Order 1680
Real No
Primitive Yes
Parity Even
Orbit Label 8041.gd

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[3]
 
pari: [g,chi] = znchar(Mod(3,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8041
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 1680
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.gd
Orbit index = 160

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 ]
 

\(\chi_{8041}(3,\cdot)\) \(\chi_{8041}(5,\cdot)\) \(\chi_{8041}(20,\cdot)\) \(\chi_{8041}(48,\cdot)\) \(\chi_{8041}(71,\cdot)\) \(\chi_{8041}(91,\cdot)\) \(\chi_{8041}(114,\cdot)\) \(\chi_{8041}(141,\cdot)\) \(\chi_{8041}(147,\cdot)\) \(\chi_{8041}(148,\cdot)\) \(\chi_{8041}(158,\cdot)\) \(\chi_{8041}(159,\cdot)\) \(\chi_{8041}(163,\cdot)\) \(\chi_{8041}(190,\cdot)\) \(\chi_{8041}(192,\cdot)\) \(\chi_{8041}(201,\cdot)\) \(\chi_{8041}(218,\cdot)\) \(\chi_{8041}(235,\cdot)\) \(\chi_{8041}(245,\cdot)\) \(\chi_{8041}(278,\cdot)\) \(\chi_{8041}(284,\cdot)\) \(\chi_{8041}(313,\cdot)\) \(\chi_{8041}(334,\cdot)\) \(\chi_{8041}(335,\cdot)\) \(\chi_{8041}(377,\cdot)\) \(\chi_{8041}(405,\cdot)\) \(\chi_{8041}(449,\cdot)\) \(\chi_{8041}(456,\cdot)\) \(\chi_{8041}(499,\cdot)\) \(\chi_{8041}(521,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{1}{16}\right),e\left(\frac{1}{42}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{89}{280}\right)\)\(e\left(\frac{817}{1680}\right)\)\(e\left(\frac{89}{140}\right)\)\(e\left(\frac{181}{1680}\right)\)\(e\left(\frac{193}{240}\right)\)\(e\left(\frac{29}{240}\right)\)\(e\left(\frac{267}{280}\right)\)\(e\left(\frac{817}{840}\right)\)\(e\left(\frac{143}{336}\right)\)\(e\left(\frac{41}{336}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{1680})\)