Properties

Conductor 8027
Order 348
Real No
Primitive Yes
Parity Even
Orbit Label 8027.bk

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(8027)
 
sage: chi = H[114]
 
pari: [g,chi] = znchar(Mod(114,8027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8027
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 348
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 = 8027.bk
Orbit index = 37

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 ]
 

\(\chi_{8027}(114,\cdot)\) \(\chi_{8027}(137,\cdot)\) \(\chi_{8027}(183,\cdot)\) \(\chi_{8027}(229,\cdot)\) \(\chi_{8027}(252,\cdot)\) \(\chi_{8027}(275,\cdot)\) \(\chi_{8027}(367,\cdot)\) \(\chi_{8027}(505,\cdot)\) \(\chi_{8027}(643,\cdot)\) \(\chi_{8027}(666,\cdot)\) \(\chi_{8027}(827,\cdot)\) \(\chi_{8027}(850,\cdot)\) \(\chi_{8027}(873,\cdot)\) \(\chi_{8027}(919,\cdot)\) \(\chi_{8027}(942,\cdot)\) \(\chi_{8027}(965,\cdot)\) \(\chi_{8027}(988,\cdot)\) \(\chi_{8027}(1034,\cdot)\) \(\chi_{8027}(1080,\cdot)\) \(\chi_{8027}(1264,\cdot)\) \(\chi_{8027}(1333,\cdot)\) \(\chi_{8027}(1356,\cdot)\) \(\chi_{8027}(1586,\cdot)\) \(\chi_{8027}(1632,\cdot)\) \(\chi_{8027}(1655,\cdot)\) \(\chi_{8027}(1701,\cdot)\) \(\chi_{8027}(1747,\cdot)\) \(\chi_{8027}(1816,\cdot)\) \(\chi_{8027}(1862,\cdot)\) \(\chi_{8027}(1885,\cdot)\) ...

Values on generators

\((350,5935)\) → \((-1,e\left(\frac{215}{348}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{215}{348}\right)\)\(e\left(\frac{11}{174}\right)\)\(e\left(\frac{41}{174}\right)\)\(e\left(\frac{43}{87}\right)\)\(e\left(\frac{79}{116}\right)\)\(e\left(\frac{311}{348}\right)\)\(e\left(\frac{99}{116}\right)\)\(e\left(\frac{11}{87}\right)\)\(e\left(\frac{13}{116}\right)\)\(e\left(\frac{55}{116}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{348})\)