Properties

Conductor 6048
Order 72
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 6048.ji

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(6048)
 
sage: chi = H[5683]
 
pari: [g,chi] = znchar(Mod(5683,6048))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6048
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 72
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 6048.ji
Orbit index = 243

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 ]
 

\(\chi_{6048}(139,\cdot)\) \(\chi_{6048}(475,\cdot)\) \(\chi_{6048}(643,\cdot)\) \(\chi_{6048}(979,\cdot)\) \(\chi_{6048}(1147,\cdot)\) \(\chi_{6048}(1483,\cdot)\) \(\chi_{6048}(1651,\cdot)\) \(\chi_{6048}(1987,\cdot)\) \(\chi_{6048}(2155,\cdot)\) \(\chi_{6048}(2491,\cdot)\) \(\chi_{6048}(2659,\cdot)\) \(\chi_{6048}(2995,\cdot)\) \(\chi_{6048}(3163,\cdot)\) \(\chi_{6048}(3499,\cdot)\) \(\chi_{6048}(3667,\cdot)\) \(\chi_{6048}(4003,\cdot)\) \(\chi_{6048}(4171,\cdot)\) \(\chi_{6048}(4507,\cdot)\) \(\chi_{6048}(4675,\cdot)\) \(\chi_{6048}(5011,\cdot)\) \(\chi_{6048}(5179,\cdot)\) \(\chi_{6048}(5515,\cdot)\) \(\chi_{6048}(5683,\cdot)\) \(\chi_{6048}(6019,\cdot)\)

Values on generators

\((4159,3781,3809,2593)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{4}{9}\right),-1)\)

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{43}{72}\right)\)\(e\left(\frac{47}{72}\right)\)\(e\left(\frac{13}{72}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{11}{24}\right)\)\(e\left(\frac{23}{36}\right)\)\(e\left(\frac{7}{36}\right)\)\(e\left(\frac{5}{72}\right)\)\(e\left(\frac{8}{9}\right)\)\(e\left(\frac{13}{24}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{72})\)