Properties

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

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[269]
 
pari: [g,chi] = znchar(Mod(269,4032))
 

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.gy
Orbit index = 181

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 ]
 

\(\chi_{4032}(269,\cdot)\) \(\chi_{4032}(341,\cdot)\) \(\chi_{4032}(773,\cdot)\) \(\chi_{4032}(845,\cdot)\) \(\chi_{4032}(1277,\cdot)\) \(\chi_{4032}(1349,\cdot)\) \(\chi_{4032}(1781,\cdot)\) \(\chi_{4032}(1853,\cdot)\) \(\chi_{4032}(2285,\cdot)\) \(\chi_{4032}(2357,\cdot)\) \(\chi_{4032}(2789,\cdot)\) \(\chi_{4032}(2861,\cdot)\) \(\chi_{4032}(3293,\cdot)\) \(\chi_{4032}(3365,\cdot)\) \(\chi_{4032}(3797,\cdot)\) \(\chi_{4032}(3869,\cdot)\)

Values on generators

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

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{13}{48}\right)\)\(e\left(\frac{41}{48}\right)\)\(e\left(\frac{9}{16}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{19}{48}\right)\)\(e\left(\frac{23}{24}\right)\)\(e\left(\frac{13}{24}\right)\)\(e\left(\frac{13}{16}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{37}{48}\right)\)
value at  e.g. 2

Related number fields

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