Properties

Label 1287.1
Modulus $1287$
Conductor $1$
Order $1$
Real yes
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1287, base_ring=CyclotomicField(2))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,0,0]))
 
pari: [g,chi] = znchar(Mod(1,1287))
 

Basic properties

Modulus: \(1287\)
Conductor: \(1\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(1\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: yes
Primitive: no, induced from \(\chi_{1}(1,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1287.a

\(\chi_{1287}(1,\cdot)\)

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: \(\Q\)
Fixed field: \(\Q\)

Values on generators

\((1145,937,496)\) → \((1,1,1)\)

Values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(7\)\(8\)\(10\)\(14\)\(16\)\(17\)\(19\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 1287 }(1,a) \;\) at \(\;a = \) e.g. 2