Properties

Conductor 448
Order 48
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4032.he

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[19]
 
pari: [g,chi] = znchar(Mod(19,4032))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 448
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 = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4032.he
Orbit index = 187

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 ]
 

\(\chi_{4032}(19,\cdot)\) \(\chi_{4032}(451,\cdot)\) \(\chi_{4032}(523,\cdot)\) \(\chi_{4032}(955,\cdot)\) \(\chi_{4032}(1027,\cdot)\) \(\chi_{4032}(1459,\cdot)\) \(\chi_{4032}(1531,\cdot)\) \(\chi_{4032}(1963,\cdot)\) \(\chi_{4032}(2035,\cdot)\) \(\chi_{4032}(2467,\cdot)\) \(\chi_{4032}(2539,\cdot)\) \(\chi_{4032}(2971,\cdot)\) \(\chi_{4032}(3043,\cdot)\) \(\chi_{4032}(3475,\cdot)\) \(\chi_{4032}(3547,\cdot)\) \(\chi_{4032}(3979,\cdot)\)

Values on generators

\((127,3781,1793,577)\) → \((-1,e\left(\frac{7}{16}\right),1,e\left(\frac{5}{6}\right))\)

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{29}{48}\right)\)\(e\left(\frac{1}{48}\right)\)\(e\left(\frac{1}{16}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{35}{48}\right)\)\(e\left(\frac{7}{24}\right)\)\(e\left(\frac{5}{24}\right)\)\(e\left(\frac{13}{16}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{29}{48}\right)\)
value at  e.g. 2

Related number fields

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