Properties

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

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[24]
 
pari: [g,chi] = znchar(Mod(24,8041))
 

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.gc
Orbit index = 159

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 ]
 

\(\chi_{8041}(24,\cdot)\) \(\chi_{8041}(40,\cdot)\) \(\chi_{8041}(57,\cdot)\) \(\chi_{8041}(74,\cdot)\) \(\chi_{8041}(95,\cdot)\) \(\chi_{8041}(96,\cdot)\) \(\chi_{8041}(139,\cdot)\) \(\chi_{8041}(160,\cdot)\) \(\chi_{8041}(167,\cdot)\) \(\chi_{8041}(182,\cdot)\) \(\chi_{8041}(228,\cdot)\) \(\chi_{8041}(282,\cdot)\) \(\chi_{8041}(283,\cdot)\) \(\chi_{8041}(316,\cdot)\) \(\chi_{8041}(326,\cdot)\) \(\chi_{8041}(354,\cdot)\) \(\chi_{8041}(369,\cdot)\) \(\chi_{8041}(402,\cdot)\) \(\chi_{8041}(447,\cdot)\) \(\chi_{8041}(453,\cdot)\) \(\chi_{8041}(470,\cdot)\) \(\chi_{8041}(486,\cdot)\) \(\chi_{8041}(490,\cdot)\) \(\chi_{8041}(513,\cdot)\) \(\chi_{8041}(530,\cdot)\) \(\chi_{8041}(541,\cdot)\) \(\chi_{8041}(547,\cdot)\) \(\chi_{8041}(556,\cdot)\) \(\chi_{8041}(568,\cdot)\) \(\chi_{8041}(590,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{11}{16}\right),e\left(\frac{20}{21}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{123}{280}\right)\)\(e\left(\frac{739}{1680}\right)\)\(e\left(\frac{123}{140}\right)\)\(e\left(\frac{1087}{1680}\right)\)\(e\left(\frac{211}{240}\right)\)\(e\left(\frac{143}{240}\right)\)\(e\left(\frac{89}{280}\right)\)\(e\left(\frac{739}{840}\right)\)\(e\left(\frac{29}{336}\right)\)\(e\left(\frac{107}{336}\right)\)
value at  e.g. 2

Related number fields

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