Properties

Label 6025.5136
Modulus $6025$
Conductor $6025$
Order $120$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6025, base_ring=CyclotomicField(120))
 
M = H._module
 
chi = DirichletCharacter(H, M([96,109]))
 
pari: [g,chi] = znchar(Mod(5136,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(6025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(120\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6025.il

\(\chi_{6025}(161,\cdot)\) \(\chi_{6025}(261,\cdot)\) \(\chi_{6025}(646,\cdot)\) \(\chi_{6025}(1396,\cdot)\) \(\chi_{6025}(1491,\cdot)\) \(\chi_{6025}(1496,\cdot)\) \(\chi_{6025}(1856,\cdot)\) \(\chi_{6025}(1916,\cdot)\) \(\chi_{6025}(1981,\cdot)\) \(\chi_{6025}(2166,\cdot)\) \(\chi_{6025}(2246,\cdot)\) \(\chi_{6025}(2381,\cdot)\) \(\chi_{6025}(2941,\cdot)\) \(\chi_{6025}(3356,\cdot)\) \(\chi_{6025}(3566,\cdot)\) \(\chi_{6025}(3836,\cdot)\) \(\chi_{6025}(3936,\cdot)\) \(\chi_{6025}(4271,\cdot)\) \(\chi_{6025}(4341,\cdot)\) \(\chi_{6025}(4356,\cdot)\) \(\chi_{6025}(4446,\cdot)\) \(\chi_{6025}(4471,\cdot)\) \(\chi_{6025}(4591,\cdot)\) \(\chi_{6025}(4646,\cdot)\) \(\chi_{6025}(4761,\cdot)\) \(\chi_{6025}(4986,\cdot)\) \(\chi_{6025}(5016,\cdot)\) \(\chi_{6025}(5136,\cdot)\) \(\chi_{6025}(5331,\cdot)\) \(\chi_{6025}(5361,\cdot)\) ...

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: $\Q(\zeta_{120})$
Fixed field: Number field defined by a degree 120 polynomial (not computed)

Values on generators

\((2652,2176)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{109}{120}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\( \chi_{ 6025 }(5136, a) \) \(1\)\(1\)\(e\left(\frac{23}{60}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{23}{30}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{109}{120}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{61}{120}\right)\)\(e\left(\frac{41}{60}\right)\)\(e\left(\frac{107}{120}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6025 }(5136,a) \;\) at \(\;a = \) e.g. 2