Properties

Label 1152.43
Modulus $1152$
Conductor $1152$
Order $96$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1152, base_ring=CyclotomicField(96))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([48,87,64]))
 
pari: [g,chi] = znchar(Mod(43,1152))
 

Basic properties

Modulus: \(1152\)
Conductor: \(1152\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(96\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1152.bu

\(\chi_{1152}(43,\cdot)\) \(\chi_{1152}(67,\cdot)\) \(\chi_{1152}(115,\cdot)\) \(\chi_{1152}(139,\cdot)\) \(\chi_{1152}(187,\cdot)\) \(\chi_{1152}(211,\cdot)\) \(\chi_{1152}(259,\cdot)\) \(\chi_{1152}(283,\cdot)\) \(\chi_{1152}(331,\cdot)\) \(\chi_{1152}(355,\cdot)\) \(\chi_{1152}(403,\cdot)\) \(\chi_{1152}(427,\cdot)\) \(\chi_{1152}(475,\cdot)\) \(\chi_{1152}(499,\cdot)\) \(\chi_{1152}(547,\cdot)\) \(\chi_{1152}(571,\cdot)\) \(\chi_{1152}(619,\cdot)\) \(\chi_{1152}(643,\cdot)\) \(\chi_{1152}(691,\cdot)\) \(\chi_{1152}(715,\cdot)\) \(\chi_{1152}(763,\cdot)\) \(\chi_{1152}(787,\cdot)\) \(\chi_{1152}(835,\cdot)\) \(\chi_{1152}(859,\cdot)\) \(\chi_{1152}(907,\cdot)\) \(\chi_{1152}(931,\cdot)\) \(\chi_{1152}(979,\cdot)\) \(\chi_{1152}(1003,\cdot)\) \(\chi_{1152}(1051,\cdot)\) \(\chi_{1152}(1075,\cdot)\) ...

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

\((127,901,641)\) → \((-1,e\left(\frac{29}{32}\right),e\left(\frac{2}{3}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)
\(-1\)\(1\)\(e\left(\frac{23}{96}\right)\)\(e\left(\frac{11}{48}\right)\)\(e\left(\frac{19}{96}\right)\)\(e\left(\frac{89}{96}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{11}{32}\right)\)\(e\left(\frac{25}{48}\right)\)\(e\left(\frac{23}{48}\right)\)\(e\left(\frac{13}{96}\right)\)\(e\left(\frac{1}{12}\right)\)
value at e.g. 2