↑

Properties

Label 1.1
Modulus 11
Conductor 11
Order 11
Real yes
Primitive yes
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath

Basic properties

Modulus: 11
Conductor: 11
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 11
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: yes
Primitive: yes
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 1.a

χ1(1,⋅)\chi_{1}(1,\cdot)

Copy content sage:chi.galois_orbit()
 
Copy content pari:order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: Q\Q
Fixed field: Q\Q

Values

aa 11
χ1(1,a) \chi_{ 1 }(1, a) 11
Copy content sage:chi.jacobi_sum(n)
 
χ1(1,a)   \chi_{ 1 }(1,a) \; at   a=\;a = e.g. 2

Gauss sum

Copy content sage:chi.gauss_sum(a)
 
Copy content pari:znchargauss(g,chi,a)
 
τa(χ1(1,⋅))   \tau_{ a }( \chi_{ 1 }(1,·) )\; at   a=\;a = e.g. 2

Jacobi sum

Copy content sage:chi.jacobi_sum(n)
 
J(χ1(1,⋅),χ1(n,⋅))   J(\chi_{ 1 }(1,·),\chi_{ 1 }(n,·)) \; for   n= \; n = e.g. 1

Kloosterman sum

Copy content sage:chi.kloosterman_sum(a,b)
 
K(a,b,χ1(1,⋅))  K(a,b,\chi_{ 1 }(1,·)) \; at   a,b=\; a,b = e.g. 1,2