Properties

Label 1792.807
Modulus $1792$
Conductor $896$
Order $96$
Real no
Primitive no
Minimal no
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1792, base_ring=CyclotomicField(96))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([48,27,32]))
 
pari: [g,chi] = znchar(Mod(807,1792))
 

Basic properties

Modulus: \(1792\)
Conductor: \(896\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(96\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{896}(667,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1792.bw

\(\chi_{1792}(23,\cdot)\) \(\chi_{1792}(39,\cdot)\) \(\chi_{1792}(135,\cdot)\) \(\chi_{1792}(151,\cdot)\) \(\chi_{1792}(247,\cdot)\) \(\chi_{1792}(263,\cdot)\) \(\chi_{1792}(359,\cdot)\) \(\chi_{1792}(375,\cdot)\) \(\chi_{1792}(471,\cdot)\) \(\chi_{1792}(487,\cdot)\) \(\chi_{1792}(583,\cdot)\) \(\chi_{1792}(599,\cdot)\) \(\chi_{1792}(695,\cdot)\) \(\chi_{1792}(711,\cdot)\) \(\chi_{1792}(807,\cdot)\) \(\chi_{1792}(823,\cdot)\) \(\chi_{1792}(919,\cdot)\) \(\chi_{1792}(935,\cdot)\) \(\chi_{1792}(1031,\cdot)\) \(\chi_{1792}(1047,\cdot)\) \(\chi_{1792}(1143,\cdot)\) \(\chi_{1792}(1159,\cdot)\) \(\chi_{1792}(1255,\cdot)\) \(\chi_{1792}(1271,\cdot)\) \(\chi_{1792}(1367,\cdot)\) \(\chi_{1792}(1383,\cdot)\) \(\chi_{1792}(1479,\cdot)\) \(\chi_{1792}(1495,\cdot)\) \(\chi_{1792}(1591,\cdot)\) \(\chi_{1792}(1607,\cdot)\) ...

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: $\Q(\zeta_{96})$
Fixed field: Number field defined by a degree 96 polynomial

Values on generators

\((1023,1541,1025)\) → \((-1,e\left(\frac{9}{32}\right),e\left(\frac{1}{3}\right))\)

Values

\(-1\)\(1\)\(3\)\(5\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(23\)\(25\)
\(-1\)\(1\)\(e\left(\frac{65}{96}\right)\)\(e\left(\frac{91}{96}\right)\)\(e\left(\frac{17}{48}\right)\)\(e\left(\frac{71}{96}\right)\)\(e\left(\frac{7}{32}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{5}{24}\right)\)\(e\left(\frac{61}{96}\right)\)\(e\left(\frac{5}{48}\right)\)\(e\left(\frac{43}{48}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 1792 }(807,a) \;\) at \(\;a = \) e.g. 2