Properties

Conductor 8041
Order 560
Real No
Primitive Yes
Parity Even
Orbit Label 8041.ft

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[27]
 
pari: [g,chi] = znchar(Mod(27,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8041
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 560
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.ft
Orbit index = 150

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 ]
 

\(\chi_{8041}(27,\cdot)\) \(\chi_{8041}(75,\cdot)\) \(\chi_{8041}(82,\cdot)\) \(\chi_{8041}(108,\cdot)\) \(\chi_{8041}(113,\cdot)\) \(\chi_{8041}(125,\cdot)\) \(\chi_{8041}(180,\cdot)\) \(\chi_{8041}(328,\cdot)\) \(\chi_{8041}(333,\cdot)\) \(\chi_{8041}(346,\cdot)\) \(\chi_{8041}(432,\cdot)\) \(\chi_{8041}(500,\cdot)\) \(\chi_{8041}(555,\cdot)\) \(\chi_{8041}(581,\cdot)\) \(\chi_{8041}(598,\cdot)\) \(\chi_{8041}(641,\cdot)\) \(\chi_{8041}(653,\cdot)\) \(\chi_{8041}(720,\cdot)\) \(\chi_{8041}(753,\cdot)\) \(\chi_{8041}(796,\cdot)\) \(\chi_{8041}(806,\cdot)\) \(\chi_{8041}(819,\cdot)\) \(\chi_{8041}(839,\cdot)\) \(\chi_{8041}(856,\cdot)\) \(\chi_{8041}(862,\cdot)\) \(\chi_{8041}(911,\cdot)\) \(\chi_{8041}(1059,\cdot)\) \(\chi_{8041}(1083,\cdot)\) \(\chi_{8041}(1193,\cdot)\) \(\chi_{8041}(1236,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{3}{16}\right),e\left(\frac{1}{14}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{267}{280}\right)\)\(e\left(\frac{257}{560}\right)\)\(e\left(\frac{127}{140}\right)\)\(e\left(\frac{181}{560}\right)\)\(e\left(\frac{33}{80}\right)\)\(e\left(\frac{29}{80}\right)\)\(e\left(\frac{241}{280}\right)\)\(e\left(\frac{257}{280}\right)\)\(e\left(\frac{31}{112}\right)\)\(e\left(\frac{41}{112}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{560})\)