Properties

Conductor 4032
Order 48
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4032.gp

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(4032)
 
sage: chi = H[115]
 
pari: [g,chi] = znchar(Mod(115,4032))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4032
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 48
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 = 4032.gp
Orbit index = 172

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 ]
 

\(\chi_{4032}(115,\cdot)\) \(\chi_{4032}(355,\cdot)\) \(\chi_{4032}(619,\cdot)\) \(\chi_{4032}(859,\cdot)\) \(\chi_{4032}(1123,\cdot)\) \(\chi_{4032}(1363,\cdot)\) \(\chi_{4032}(1627,\cdot)\) \(\chi_{4032}(1867,\cdot)\) \(\chi_{4032}(2131,\cdot)\) \(\chi_{4032}(2371,\cdot)\) \(\chi_{4032}(2635,\cdot)\) \(\chi_{4032}(2875,\cdot)\) \(\chi_{4032}(3139,\cdot)\) \(\chi_{4032}(3379,\cdot)\) \(\chi_{4032}(3643,\cdot)\) \(\chi_{4032}(3883,\cdot)\)

Values on generators

\((127,3781,1793,577)\) → \((-1,e\left(\frac{15}{16}\right),e\left(\frac{2}{3}\right),e\left(\frac{1}{6}\right))\)

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{5}{48}\right)\)\(e\left(\frac{25}{48}\right)\)\(e\left(\frac{43}{48}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{43}{48}\right)\)\(e\left(\frac{7}{24}\right)\)\(e\left(\frac{5}{24}\right)\)\(e\left(\frac{47}{48}\right)\)\(-1\)\(e\left(\frac{37}{48}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{48})\)