Properties

Conductor 1344
Order 48
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4032.gz

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[107]
 
pari: [g,chi] = znchar(Mod(107,4032))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1344
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.gz
Orbit index = 182

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 ]
 

\(\chi_{4032}(107,\cdot)\) \(\chi_{4032}(179,\cdot)\) \(\chi_{4032}(611,\cdot)\) \(\chi_{4032}(683,\cdot)\) \(\chi_{4032}(1115,\cdot)\) \(\chi_{4032}(1187,\cdot)\) \(\chi_{4032}(1619,\cdot)\) \(\chi_{4032}(1691,\cdot)\) \(\chi_{4032}(2123,\cdot)\) \(\chi_{4032}(2195,\cdot)\) \(\chi_{4032}(2627,\cdot)\) \(\chi_{4032}(2699,\cdot)\) \(\chi_{4032}(3131,\cdot)\) \(\chi_{4032}(3203,\cdot)\) \(\chi_{4032}(3635,\cdot)\) \(\chi_{4032}(3707,\cdot)\)

Values on generators

\((127,3781,1793,577)\) → \((-1,e\left(\frac{13}{16}\right),-1,e\left(\frac{1}{3}\right))\)

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{47}{48}\right)\)\(e\left(\frac{19}{48}\right)\)\(e\left(\frac{3}{16}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{41}{48}\right)\)\(e\left(\frac{1}{24}\right)\)\(e\left(\frac{23}{24}\right)\)\(e\left(\frac{7}{16}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{47}{48}\right)\)
value at  e.g. 2

Related number fields

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