Properties

Label 1792.87
Modulus $1792$
Conductor $896$
Order $96$
Real no
Primitive no
Minimal no
Parity even

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([48,45,16]))
 
pari: [g,chi] = znchar(Mod(87,1792))
 

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 \(\chi_{896}(115,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1792.bx

\(\chi_{1792}(87,\cdot)\) \(\chi_{1792}(103,\cdot)\) \(\chi_{1792}(199,\cdot)\) \(\chi_{1792}(215,\cdot)\) \(\chi_{1792}(311,\cdot)\) \(\chi_{1792}(327,\cdot)\) \(\chi_{1792}(423,\cdot)\) \(\chi_{1792}(439,\cdot)\) \(\chi_{1792}(535,\cdot)\) \(\chi_{1792}(551,\cdot)\) \(\chi_{1792}(647,\cdot)\) \(\chi_{1792}(663,\cdot)\) \(\chi_{1792}(759,\cdot)\) \(\chi_{1792}(775,\cdot)\) \(\chi_{1792}(871,\cdot)\) \(\chi_{1792}(887,\cdot)\) \(\chi_{1792}(983,\cdot)\) \(\chi_{1792}(999,\cdot)\) \(\chi_{1792}(1095,\cdot)\) \(\chi_{1792}(1111,\cdot)\) \(\chi_{1792}(1207,\cdot)\) \(\chi_{1792}(1223,\cdot)\) \(\chi_{1792}(1319,\cdot)\) \(\chi_{1792}(1335,\cdot)\) \(\chi_{1792}(1431,\cdot)\) \(\chi_{1792}(1447,\cdot)\) \(\chi_{1792}(1543,\cdot)\) \(\chi_{1792}(1559,\cdot)\) \(\chi_{1792}(1655,\cdot)\) \(\chi_{1792}(1671,\cdot)\) ...

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

\((1023,1541,1025)\) → \((-1,e\left(\frac{15}{32}\right),e\left(\frac{1}{6}\right))\)

Values

\(-1\)\(1\)\(3\)\(5\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(23\)\(25\)
\(1\)\(1\)\(e\left(\frac{7}{96}\right)\)\(e\left(\frac{29}{96}\right)\)\(e\left(\frac{7}{48}\right)\)\(e\left(\frac{1}{96}\right)\)\(e\left(\frac{17}{32}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{7}{24}\right)\)\(e\left(\frac{11}{96}\right)\)\(e\left(\frac{19}{48}\right)\)\(e\left(\frac{29}{48}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 1792 }(87,a) \;\) at \(\;a = \) e.g. 2