Properties

Label 1120.449
Modulus 11201120
Conductor 55
Order 22
Real yes
Primitive no
Minimal yes
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1120, base_ring=CyclotomicField(2)) M = H._module chi = DirichletCharacter(H, M([0,0,1,0]))
 
Copy content pari:[g,chi] = znchar(Mod(449,1120))
 

Basic properties

Modulus: 11201120
Conductor: 55
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 22
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: yes
Primitive: no, induced from χ5(4,)\chi_{5}(4,\cdot)
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 1120.g

χ1120(449,)\chi_{1120}(449,\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(5)\Q(\sqrt{5})

Values on generators

(351,421,897,801)(351,421,897,801)(1,1,1,1)(1,1,-1,1)

First values

aa 1-111339911111313171719192323272729293131
χ1120(449,a) \chi_{ 1120 }(449, a) 11111-111111-11-1111-11-11111
Copy content sage:chi.jacobi_sum(n)
 
χ1120(449,a)   \chi_{ 1120 }(449,a) \; at   a=\;a = e.g. 2