Properties

Label 1183.902
Modulus $1183$
Conductor $1183$
Order $52$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1183, base_ring=CyclotomicField(52))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([26,11]))
 
pari: [g,chi] = znchar(Mod(902,1183))
 

Basic properties

Modulus: \(1183\)
Conductor: \(1183\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(52\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1183.bn

\(\chi_{1183}(34,\cdot)\) \(\chi_{1183}(83,\cdot)\) \(\chi_{1183}(125,\cdot)\) \(\chi_{1183}(174,\cdot)\) \(\chi_{1183}(216,\cdot)\) \(\chi_{1183}(265,\cdot)\) \(\chi_{1183}(307,\cdot)\) \(\chi_{1183}(356,\cdot)\) \(\chi_{1183}(398,\cdot)\) \(\chi_{1183}(447,\cdot)\) \(\chi_{1183}(489,\cdot)\) \(\chi_{1183}(538,\cdot)\) \(\chi_{1183}(580,\cdot)\) \(\chi_{1183}(629,\cdot)\) \(\chi_{1183}(671,\cdot)\) \(\chi_{1183}(720,\cdot)\) \(\chi_{1183}(762,\cdot)\) \(\chi_{1183}(811,\cdot)\) \(\chi_{1183}(853,\cdot)\) \(\chi_{1183}(902,\cdot)\) \(\chi_{1183}(993,\cdot)\) \(\chi_{1183}(1035,\cdot)\) \(\chi_{1183}(1126,\cdot)\) \(\chi_{1183}(1175,\cdot)\)

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: $\Q(\zeta_{52})$
Fixed field: Number field defined by a degree 52 polynomial

Values on generators

\((339,1016)\) → \((-1,e\left(\frac{11}{52}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(8\)\(9\)\(10\)\(11\)\(12\)
\(1\)\(1\)\(e\left(\frac{11}{52}\right)\)\(e\left(\frac{19}{26}\right)\)\(e\left(\frac{11}{26}\right)\)\(e\left(\frac{21}{52}\right)\)\(e\left(\frac{49}{52}\right)\)\(e\left(\frac{33}{52}\right)\)\(e\left(\frac{6}{13}\right)\)\(e\left(\frac{8}{13}\right)\)\(e\left(\frac{41}{52}\right)\)\(e\left(\frac{2}{13}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 1183 }(902,a) \;\) at \(\;a = \) e.g. 2