Properties

Conductor 6008
Order 50
Real No
Primitive Yes
Parity Even
Orbit Label 6008.bl

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[53]
 
pari: [g,chi] = znchar(Mod(53,6008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6008
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 50
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.bl
Orbit index = 38

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 ]
 

\(\chi_{6008}(53,\cdot)\) \(\chi_{6008}(117,\cdot)\) \(\chi_{6008}(325,\cdot)\) \(\chi_{6008}(485,\cdot)\) \(\chi_{6008}(1461,\cdot)\) \(\chi_{6008}(2205,\cdot)\) \(\chi_{6008}(3197,\cdot)\) \(\chi_{6008}(3485,\cdot)\) \(\chi_{6008}(3917,\cdot)\) \(\chi_{6008}(4205,\cdot)\) \(\chi_{6008}(4221,\cdot)\) \(\chi_{6008}(4421,\cdot)\) \(\chi_{6008}(4557,\cdot)\) \(\chi_{6008}(4677,\cdot)\) \(\chi_{6008}(4685,\cdot)\) \(\chi_{6008}(4981,\cdot)\) \(\chi_{6008}(5005,\cdot)\) \(\chi_{6008}(5605,\cdot)\) \(\chi_{6008}(5677,\cdot)\) \(\chi_{6008}(5813,\cdot)\)

Values on generators

\((1503,3005,1505)\) → \((1,-1,e\left(\frac{2}{25}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{29}{50}\right)\)\(e\left(\frac{19}{50}\right)\)\(e\left(\frac{2}{25}\right)\)\(e\left(\frac{4}{25}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{7}{50}\right)\)\(e\left(\frac{24}{25}\right)\)\(e\left(\frac{8}{25}\right)\)\(e\left(\frac{47}{50}\right)\)\(e\left(\frac{33}{50}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{25})\)