Properties

Conductor 6008
Order 150
Real No
Primitive Yes
Parity Even
Orbit Label 6008.bt

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[11]
 
pari: [g,chi] = znchar(Mod(11,6008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6008
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 150
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.bt
Orbit index = 46

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 ]
 

\(\chi_{6008}(11,\cdot)\) \(\chi_{6008}(83,\cdot)\) \(\chi_{6008}(243,\cdot)\) \(\chi_{6008}(251,\cdot)\) \(\chi_{6008}(379,\cdot)\) \(\chi_{6008}(467,\cdot)\) \(\chi_{6008}(571,\cdot)\) \(\chi_{6008}(699,\cdot)\) \(\chi_{6008}(859,\cdot)\) \(\chi_{6008}(1051,\cdot)\) \(\chi_{6008}(1195,\cdot)\) \(\chi_{6008}(1203,\cdot)\) \(\chi_{6008}(1339,\cdot)\) \(\chi_{6008}(1371,\cdot)\) \(\chi_{6008}(1395,\cdot)\) \(\chi_{6008}(1875,\cdot)\) \(\chi_{6008}(2059,\cdot)\) \(\chi_{6008}(2123,\cdot)\) \(\chi_{6008}(2731,\cdot)\) \(\chi_{6008}(2883,\cdot)\) \(\chi_{6008}(3227,\cdot)\) \(\chi_{6008}(3459,\cdot)\) \(\chi_{6008}(3555,\cdot)\) \(\chi_{6008}(3571,\cdot)\) \(\chi_{6008}(3723,\cdot)\) \(\chi_{6008}(3867,\cdot)\) \(\chi_{6008}(3875,\cdot)\) \(\chi_{6008}(4035,\cdot)\) \(\chi_{6008}(4107,\cdot)\) \(\chi_{6008}(4387,\cdot)\) ...

Values on generators

\((1503,3005,1505)\) → \((-1,-1,e\left(\frac{143}{150}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{143}{150}\right)\)\(e\left(\frac{23}{150}\right)\)\(e\left(\frac{3}{25}\right)\)\(e\left(\frac{68}{75}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{119}{150}\right)\)\(e\left(\frac{8}{75}\right)\)\(e\left(\frac{97}{150}\right)\)\(e\left(\frac{37}{75}\right)\)\(e\left(\frac{11}{150}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{75})\)