Properties

Conductor 6017
Order 1365
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 6017.ci

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(6017)
 
sage: chi = H[4]
 
pari: [g,chi] = znchar(Mod(4,6017))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6017
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 1365
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 6017.ci
Orbit index = 61

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 ]
 

\(\chi_{6017}(4,\cdot)\) \(\chi_{6017}(15,\cdot)\) \(\chi_{6017}(16,\cdot)\) \(\chi_{6017}(25,\cdot)\) \(\chi_{6017}(36,\cdot)\) \(\chi_{6017}(49,\cdot)\) \(\chi_{6017}(53,\cdot)\) \(\chi_{6017}(60,\cdot)\) \(\chi_{6017}(69,\cdot)\) \(\chi_{6017}(82,\cdot)\) \(\chi_{6017}(86,\cdot)\) \(\chi_{6017}(97,\cdot)\) \(\chi_{6017}(113,\cdot)\) \(\chi_{6017}(115,\cdot)\) \(\chi_{6017}(119,\cdot)\) \(\chi_{6017}(130,\cdot)\) \(\chi_{6017}(135,\cdot)\) \(\chi_{6017}(137,\cdot)\) \(\chi_{6017}(157,\cdot)\) \(\chi_{6017}(158,\cdot)\) \(\chi_{6017}(174,\cdot)\) \(\chi_{6017}(190,\cdot)\) \(\chi_{6017}(191,\cdot)\) \(\chi_{6017}(202,\cdot)\) \(\chi_{6017}(213,\cdot)\) \(\chi_{6017}(214,\cdot)\) \(\chi_{6017}(225,\cdot)\) \(\chi_{6017}(256,\cdot)\) \(\chi_{6017}(269,\cdot)\) \(\chi_{6017}(273,\cdot)\) ...

Values on generators

\((3830,2190)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{1}{273}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{278}{1365}\right)\)\(e\left(\frac{6}{35}\right)\)\(e\left(\frac{556}{1365}\right)\)\(e\left(\frac{622}{1365}\right)\)\(e\left(\frac{512}{1365}\right)\)\(e\left(\frac{1061}{1365}\right)\)\(e\left(\frac{278}{455}\right)\)\(e\left(\frac{12}{35}\right)\)\(e\left(\frac{60}{91}\right)\)\(e\left(\frac{158}{273}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{1365})\)