Properties

Label 1792.1143
Modulus $1792$
Conductor $896$
Order $96$
Real no
Primitive no
Minimal no
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1792, base_ring=CyclotomicField(96))
 
M = H._module
 
chi = DirichletCharacter(H, M([48,57,32]))
 
pari: [g,chi] = znchar(Mod(1143,1792))
 

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 \(\chi_{896}(835,\cdot)\)
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()
 
order = charorder(g,chi)
 
[ 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

\((1023,1541,1025)\) → \((-1,e\left(\frac{19}{32}\right),e\left(\frac{1}{3}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(23\)\(25\)
\( \chi_{ 1792 }(1143, a) \) \(-1\)\(1\)\(e\left(\frac{59}{96}\right)\)\(e\left(\frac{25}{96}\right)\)\(e\left(\frac{11}{48}\right)\)\(e\left(\frac{29}{96}\right)\)\(e\left(\frac{29}{32}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{23}{24}\right)\)\(e\left(\frac{79}{96}\right)\)\(e\left(\frac{23}{48}\right)\)\(e\left(\frac{25}{48}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 1792 }(1143,a) \;\) at \(\;a = \) e.g. 2