Properties

Conductor 576
Order 48
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4032.hb

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[155]
 
pari: [g,chi] = znchar(Mod(155,4032))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 576
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.hb
Orbit index = 184

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 ]
 

\(\chi_{4032}(155,\cdot)\) \(\chi_{4032}(491,\cdot)\) \(\chi_{4032}(659,\cdot)\) \(\chi_{4032}(995,\cdot)\) \(\chi_{4032}(1163,\cdot)\) \(\chi_{4032}(1499,\cdot)\) \(\chi_{4032}(1667,\cdot)\) \(\chi_{4032}(2003,\cdot)\) \(\chi_{4032}(2171,\cdot)\) \(\chi_{4032}(2507,\cdot)\) \(\chi_{4032}(2675,\cdot)\) \(\chi_{4032}(3011,\cdot)\) \(\chi_{4032}(3179,\cdot)\) \(\chi_{4032}(3515,\cdot)\) \(\chi_{4032}(3683,\cdot)\) \(\chi_{4032}(4019,\cdot)\)

Values on generators

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

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{19}{48}\right)\)\(e\left(\frac{23}{48}\right)\)\(e\left(\frac{37}{48}\right)\)\(i\)\(e\left(\frac{7}{16}\right)\)\(e\left(\frac{5}{24}\right)\)\(e\left(\frac{19}{24}\right)\)\(e\left(\frac{17}{48}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{1}{16}\right)\)
value at  e.g. 2

Related number fields

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