Properties

Conductor 6047
Order 3023
Real No
Primitive Yes
Parity Even
Orbit Label 6047.c

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(6047)
 
sage: chi = H[2]
 
pari: [g,chi] = znchar(Mod(2,6047))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6047
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 3023
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 = 6047.c
Orbit index = 3

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 ]
 

\(\chi_{6047}(2,\cdot)\) \(\chi_{6047}(3,\cdot)\) \(\chi_{6047}(4,\cdot)\) \(\chi_{6047}(6,\cdot)\) \(\chi_{6047}(7,\cdot)\) \(\chi_{6047}(8,\cdot)\) \(\chi_{6047}(9,\cdot)\) \(\chi_{6047}(11,\cdot)\) \(\chi_{6047}(12,\cdot)\) \(\chi_{6047}(14,\cdot)\) \(\chi_{6047}(16,\cdot)\) \(\chi_{6047}(18,\cdot)\) \(\chi_{6047}(21,\cdot)\) \(\chi_{6047}(22,\cdot)\) \(\chi_{6047}(23,\cdot)\) \(\chi_{6047}(24,\cdot)\) \(\chi_{6047}(25,\cdot)\) \(\chi_{6047}(27,\cdot)\) \(\chi_{6047}(28,\cdot)\) \(\chi_{6047}(32,\cdot)\) \(\chi_{6047}(33,\cdot)\) \(\chi_{6047}(36,\cdot)\) \(\chi_{6047}(37,\cdot)\) \(\chi_{6047}(41,\cdot)\) \(\chi_{6047}(42,\cdot)\) \(\chi_{6047}(43,\cdot)\) \(\chi_{6047}(44,\cdot)\) \(\chi_{6047}(46,\cdot)\) \(\chi_{6047}(47,\cdot)\) \(\chi_{6047}(48,\cdot)\) ...

Values on generators

\(5\) → \(e\left(\frac{859}{3023}\right)\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{538}{3023}\right)\)\(e\left(\frac{1095}{3023}\right)\)\(e\left(\frac{1076}{3023}\right)\)\(e\left(\frac{859}{3023}\right)\)\(e\left(\frac{1633}{3023}\right)\)\(e\left(\frac{71}{3023}\right)\)\(e\left(\frac{1614}{3023}\right)\)\(e\left(\frac{2190}{3023}\right)\)\(e\left(\frac{1397}{3023}\right)\)\(e\left(\frac{931}{3023}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{3023})\)