Properties

Conductor 6008
Order 750
Real No
Primitive Yes
Parity Even
Orbit Label 6008.cj

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(6008)
 
sage: chi = H[3]
 
pari: [g,chi] = znchar(Mod(3,6008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6008
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 750
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 = 6008.cj
Orbit index = 62

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 ]
 

\(\chi_{6008}(3,\cdot)\) \(\chi_{6008}(35,\cdot)\) \(\chi_{6008}(67,\cdot)\) \(\chi_{6008}(91,\cdot)\) \(\chi_{6008}(147,\cdot)\) \(\chi_{6008}(227,\cdot)\) \(\chi_{6008}(259,\cdot)\) \(\chi_{6008}(283,\cdot)\) \(\chi_{6008}(427,\cdot)\) \(\chi_{6008}(443,\cdot)\) \(\chi_{6008}(515,\cdot)\) \(\chi_{6008}(539,\cdot)\) \(\chi_{6008}(547,\cdot)\) \(\chi_{6008}(555,\cdot)\) \(\chi_{6008}(563,\cdot)\) \(\chi_{6008}(579,\cdot)\) \(\chi_{6008}(659,\cdot)\) \(\chi_{6008}(667,\cdot)\) \(\chi_{6008}(731,\cdot)\) \(\chi_{6008}(747,\cdot)\) \(\chi_{6008}(763,\cdot)\) \(\chi_{6008}(779,\cdot)\) \(\chi_{6008}(795,\cdot)\) \(\chi_{6008}(867,\cdot)\) \(\chi_{6008}(891,\cdot)\) \(\chi_{6008}(915,\cdot)\) \(\chi_{6008}(1019,\cdot)\) \(\chi_{6008}(1043,\cdot)\) \(\chi_{6008}(1091,\cdot)\) \(\chi_{6008}(1115,\cdot)\) ...

Values on generators

\((1503,3005,1505)\) → \((-1,-1,e\left(\frac{1}{750}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{1}{750}\right)\)\(e\left(\frac{361}{750}\right)\)\(e\left(\frac{46}{125}\right)\)\(e\left(\frac{1}{375}\right)\)\(e\left(\frac{143}{150}\right)\)\(e\left(\frac{133}{750}\right)\)\(e\left(\frac{181}{375}\right)\)\(e\left(\frac{329}{750}\right)\)\(e\left(\frac{134}{375}\right)\)\(e\left(\frac{277}{750}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{375})\)