Properties

Label 4680.1529
Modulus $4680$
Conductor $195$
Order $4$
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4680, base_ring=CyclotomicField(4))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,2,2,1]))
 
pari: [g,chi] = znchar(Mod(1529,4680))
 

Basic properties

Modulus: \(4680\)
Conductor: \(195\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(4\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{195}(164,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4680.cb

\(\chi_{4680}(1529,\cdot)\) \(\chi_{4680}(2969,\cdot)\)

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: \(\Q(\sqrt{-1}) \)
Fixed field: 4.4.494325.1

Values on generators

\((3511,2341,2081,937,1081)\) → \((1,1,-1,-1,i)\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 4680 }(1529, a) \) \(1\)\(1\)\(i\)\(i\)\(-1\)\(i\)\(-1\)\(-1\)\(i\)\(i\)\(-i\)\(1\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4680 }(1529,a) \;\) at \(\;a = \) e.g. 2