Properties

Conductor 6017
Order 2730
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 6017.cl

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[2]
 
pari: [g,chi] = znchar(Mod(2,6017))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6017
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 2730
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.cl
Orbit index = 64

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 ]
 

\(\chi_{6017}(2,\cdot)\) \(\chi_{6017}(7,\cdot)\) \(\chi_{6017}(17,\cdot)\) \(\chi_{6017}(18,\cdot)\) \(\chi_{6017}(50,\cdot)\) \(\chi_{6017}(57,\cdot)\) \(\chi_{6017}(61,\cdot)\) \(\chi_{6017}(63,\cdot)\) \(\chi_{6017}(95,\cdot)\) \(\chi_{6017}(112,\cdot)\) \(\chi_{6017}(134,\cdot)\) \(\chi_{6017}(162,\cdot)\) \(\chi_{6017}(200,\cdot)\) \(\chi_{6017}(211,\cdot)\) \(\chi_{6017}(228,\cdot)\) \(\chi_{6017}(260,\cdot)\) \(\chi_{6017}(271,\cdot)\) \(\chi_{6017}(272,\cdot)\) \(\chi_{6017}(281,\cdot)\) \(\chi_{6017}(283,\cdot)\) \(\chi_{6017}(288,\cdot)\) \(\chi_{6017}(337,\cdot)\) \(\chi_{6017}(354,\cdot)\) \(\chi_{6017}(358,\cdot)\) \(\chi_{6017}(359,\cdot)\) \(\chi_{6017}(370,\cdot)\) \(\chi_{6017}(371,\cdot)\) \(\chi_{6017}(376,\cdot)\) \(\chi_{6017}(381,\cdot)\) \(\chi_{6017}(387,\cdot)\) ...

Values on generators

\((3830,2190)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{1}{546}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{139}{1365}\right)\)\(e\left(\frac{41}{70}\right)\)\(e\left(\frac{278}{1365}\right)\)\(e\left(\frac{1987}{2730}\right)\)\(e\left(\frac{1877}{2730}\right)\)\(e\left(\frac{1213}{1365}\right)\)\(e\left(\frac{139}{455}\right)\)\(e\left(\frac{6}{35}\right)\)\(e\left(\frac{151}{182}\right)\)\(e\left(\frac{431}{546}\right)\)
value at  e.g. 2

Related number fields

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