Properties

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

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[347]
 
pari: [g,chi] = znchar(Mod(347,4032))
 

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.ha
Orbit index = 183

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 ]
 

\(\chi_{4032}(347,\cdot)\) \(\chi_{4032}(443,\cdot)\) \(\chi_{4032}(851,\cdot)\) \(\chi_{4032}(947,\cdot)\) \(\chi_{4032}(1355,\cdot)\) \(\chi_{4032}(1451,\cdot)\) \(\chi_{4032}(1859,\cdot)\) \(\chi_{4032}(1955,\cdot)\) \(\chi_{4032}(2363,\cdot)\) \(\chi_{4032}(2459,\cdot)\) \(\chi_{4032}(2867,\cdot)\) \(\chi_{4032}(2963,\cdot)\) \(\chi_{4032}(3371,\cdot)\) \(\chi_{4032}(3467,\cdot)\) \(\chi_{4032}(3875,\cdot)\) \(\chi_{4032}(3971,\cdot)\)

Values on generators

\((127,3781,1793,577)\) → \((-1,e\left(\frac{9}{16}\right),e\left(\frac{5}{6}\right),e\left(\frac{2}{3}\right))\)

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{1}{16}\right)\)\(e\left(\frac{13}{16}\right)\)\(e\left(\frac{5}{48}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{37}{48}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{1}{48}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{19}{48}\right)\)
value at  e.g. 2

Related number fields

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