Properties

Conductor 3004
Order 50
Real No
Primitive No
Parity Even
Orbit Label 6008.bi

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[799]
 
pari: [g,chi] = znchar(Mod(799,6008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 3004
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 = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 6008.bi
Orbit index = 35

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 ]
 

\(\chi_{6008}(799,\cdot)\) \(\chi_{6008}(1543,\cdot)\) \(\chi_{6008}(2519,\cdot)\) \(\chi_{6008}(2679,\cdot)\) \(\chi_{6008}(2887,\cdot)\) \(\chi_{6008}(2951,\cdot)\) \(\chi_{6008}(3199,\cdot)\) \(\chi_{6008}(3335,\cdot)\) \(\chi_{6008}(3407,\cdot)\) \(\chi_{6008}(4007,\cdot)\) \(\chi_{6008}(4031,\cdot)\) \(\chi_{6008}(4327,\cdot)\) \(\chi_{6008}(4335,\cdot)\) \(\chi_{6008}(4455,\cdot)\) \(\chi_{6008}(4591,\cdot)\) \(\chi_{6008}(4791,\cdot)\) \(\chi_{6008}(4807,\cdot)\) \(\chi_{6008}(5095,\cdot)\) \(\chi_{6008}(5527,\cdot)\) \(\chi_{6008}(5815,\cdot)\)

Inducing primitive character

\(\chi_{3004}(799,\cdot)\)

Values on generators

\((1503,3005,1505)\) → \((-1,1,e\left(\frac{11}{50}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{18}{25}\right)\)\(e\left(\frac{23}{25}\right)\)\(e\left(\frac{18}{25}\right)\)\(e\left(\frac{11}{25}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{19}{25}\right)\)\(e\left(\frac{16}{25}\right)\)\(e\left(\frac{19}{50}\right)\)\(e\left(\frac{23}{50}\right)\)\(e\left(\frac{11}{25}\right)\)
value at  e.g. 2

Related number fields

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