Properties

Label 3600.3493
Modulus $3600$
Conductor $80$
Order $4$
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3600, base_ring=CyclotomicField(4))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,1,0,3]))
 
pari: [g,chi] = znchar(Mod(3493,3600))
 

Basic properties

Modulus: \(3600\)
Conductor: \(80\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(4\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{80}(53,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3600.bf

\(\chi_{3600}(2557,\cdot)\) \(\chi_{3600}(3493,\cdot)\)

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

Related number fields

Field of values: \(\mathbb{Q}(i)\)
Fixed field: 4.0.256000.2

Values on generators

\((3151,901,2801,577)\) → \((1,i,1,-i)\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\( \chi_{ 3600 }(3493, a) \) \(-1\)\(1\)\(i\)\(i\)\(1\)\(-i\)\(i\)\(-i\)\(i\)\(1\)\(1\)\(-1\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 3600 }(3493,a) \;\) at \(\;a = \) e.g. 2