Properties

Conductor 8027
Order 1914
Real No
Primitive Yes
Parity Even
Orbit Label 8027.bs

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[3]
 
pari: [g,chi] = znchar(Mod(3,8027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8027
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 1914
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.bs
Orbit index = 45

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 ]
 

\(\chi_{8027}(3,\cdot)\) \(\chi_{8027}(4,\cdot)\) \(\chi_{8027}(29,\cdot)\) \(\chi_{8027}(49,\cdot)\) \(\chi_{8027}(73,\cdot)\) \(\chi_{8027}(78,\cdot)\) \(\chi_{8027}(95,\cdot)\) \(\chi_{8027}(104,\cdot)\) \(\chi_{8027}(124,\cdot)\) \(\chi_{8027}(142,\cdot)\) \(\chi_{8027}(164,\cdot)\) \(\chi_{8027}(169,\cdot)\) \(\chi_{8027}(202,\cdot)\) \(\chi_{8027}(233,\cdot)\) \(\chi_{8027}(238,\cdot)\) \(\chi_{8027}(243,\cdot)\) \(\chi_{8027}(255,\cdot)\) \(\chi_{8027}(262,\cdot)\) \(\chi_{8027}(324,\cdot)\) \(\chi_{8027}(326,\cdot)\) \(\chi_{8027}(330,\cdot)\) \(\chi_{8027}(334,\cdot)\) \(\chi_{8027}(335,\cdot)\) \(\chi_{8027}(340,\cdot)\) \(\chi_{8027}(353,\cdot)\) \(\chi_{8027}(354,\cdot)\) \(\chi_{8027}(371,\cdot)\) \(\chi_{8027}(422,\cdot)\) \(\chi_{8027}(427,\cdot)\) \(\chi_{8027}(432,\cdot)\) ...

Values on generators

\((350,5935)\) → \((e\left(\frac{8}{11}\right),e\left(\frac{13}{174}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{1013}{1914}\right)\)\(e\left(\frac{554}{957}\right)\)\(e\left(\frac{56}{957}\right)\)\(e\left(\frac{179}{957}\right)\)\(e\left(\frac{69}{638}\right)\)\(e\left(\frac{1577}{1914}\right)\)\(e\left(\frac{375}{638}\right)\)\(e\left(\frac{151}{957}\right)\)\(e\left(\frac{457}{638}\right)\)\(e\left(\frac{73}{638}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{957})\)