Properties

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

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[45]
 
pari: [g,chi] = znchar(Mod(45,6008))
 

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.cb
Orbit index = 54

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 ]
 

\(\chi_{6008}(45,\cdot)\) \(\chi_{6008}(93,\cdot)\) \(\chi_{6008}(125,\cdot)\) \(\chi_{6008}(165,\cdot)\) \(\chi_{6008}(189,\cdot)\) \(\chi_{6008}(237,\cdot)\) \(\chi_{6008}(341,\cdot)\) \(\chi_{6008}(429,\cdot)\) \(\chi_{6008}(445,\cdot)\) \(\chi_{6008}(493,\cdot)\) \(\chi_{6008}(525,\cdot)\) \(\chi_{6008}(605,\cdot)\) \(\chi_{6008}(693,\cdot)\) \(\chi_{6008}(789,\cdot)\) \(\chi_{6008}(797,\cdot)\) \(\chi_{6008}(845,\cdot)\) \(\chi_{6008}(869,\cdot)\) \(\chi_{6008}(997,\cdot)\) \(\chi_{6008}(1005,\cdot)\) \(\chi_{6008}(1013,\cdot)\) \(\chi_{6008}(1085,\cdot)\) \(\chi_{6008}(1157,\cdot)\) \(\chi_{6008}(1181,\cdot)\) \(\chi_{6008}(1261,\cdot)\) \(\chi_{6008}(1365,\cdot)\) \(\chi_{6008}(1573,\cdot)\) \(\chi_{6008}(1653,\cdot)\) \(\chi_{6008}(1693,\cdot)\) \(\chi_{6008}(1709,\cdot)\) \(\chi_{6008}(1773,\cdot)\) ...

Values on generators

\((1503,3005,1505)\) → \((1,-1,e\left(\frac{123}{125}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{121}{250}\right)\)\(e\left(\frac{181}{250}\right)\)\(e\left(\frac{73}{125}\right)\)\(e\left(\frac{121}{125}\right)\)\(e\left(\frac{3}{50}\right)\)\(e\left(\frac{93}{250}\right)\)\(e\left(\frac{26}{125}\right)\)\(e\left(\frac{92}{125}\right)\)\(e\left(\frac{53}{250}\right)\)\(e\left(\frac{17}{250}\right)\)
value at  e.g. 2

Related number fields

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