Properties

Conductor 6008
Order 250
Real No
Primitive Yes
Parity Even
Orbit Label 6008.ca

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[27]
 
pari: [g,chi] = znchar(Mod(27,6008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6008
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 250
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.ca
Orbit index = 53

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 ]
 

\(\chi_{6008}(27,\cdot)\) \(\chi_{6008}(75,\cdot)\) \(\chi_{6008}(99,\cdot)\) \(\chi_{6008}(155,\cdot)\) \(\chi_{6008}(267,\cdot)\) \(\chi_{6008}(275,\cdot)\) \(\chi_{6008}(315,\cdot)\) \(\chi_{6008}(323,\cdot)\) \(\chi_{6008}(363,\cdot)\) \(\chi_{6008}(371,\cdot)\) \(\chi_{6008}(395,\cdot)\) \(\chi_{6008}(491,\cdot)\) \(\chi_{6008}(507,\cdot)\) \(\chi_{6008}(603,\cdot)\) \(\chi_{6008}(619,\cdot)\) \(\chi_{6008}(651,\cdot)\) \(\chi_{6008}(715,\cdot)\) \(\chi_{6008}(811,\cdot)\) \(\chi_{6008}(819,\cdot)\) \(\chi_{6008}(875,\cdot)\) \(\chi_{6008}(907,\cdot)\) \(\chi_{6008}(971,\cdot)\) \(\chi_{6008}(979,\cdot)\) \(\chi_{6008}(1067,\cdot)\) \(\chi_{6008}(1083,\cdot)\) \(\chi_{6008}(1155,\cdot)\) \(\chi_{6008}(1315,\cdot)\) \(\chi_{6008}(1459,\cdot)\) \(\chi_{6008}(1659,\cdot)\) \(\chi_{6008}(1675,\cdot)\) ...

Values on generators

\((1503,3005,1505)\) → \((-1,-1,e\left(\frac{1}{250}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{1}{250}\right)\)\(e\left(\frac{111}{250}\right)\)\(e\left(\frac{13}{125}\right)\)\(e\left(\frac{1}{125}\right)\)\(e\left(\frac{43}{50}\right)\)\(e\left(\frac{133}{250}\right)\)\(e\left(\frac{56}{125}\right)\)\(e\left(\frac{79}{250}\right)\)\(e\left(\frac{9}{125}\right)\)\(e\left(\frac{27}{250}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{125})\)