Properties

Label 6025.2
Modulus $6025$
Conductor $6025$
Order $120$
Real no
Primitive yes
Minimal yes
Parity odd

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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([6,95]))
 
pari: [g,chi] = znchar(Mod(2,6025))
 

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: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6025.ip

\(\chi_{6025}(2,\cdot)\) \(\chi_{6025}(113,\cdot)\) \(\chi_{6025}(128,\cdot)\) \(\chi_{6025}(603,\cdot)\) \(\chi_{6025}(962,\cdot)\) \(\chi_{6025}(1237,\cdot)\) \(\chi_{6025}(1333,\cdot)\) \(\chi_{6025}(1808,\cdot)\) \(\chi_{6025}(2048,\cdot)\) \(\chi_{6025}(2137,\cdot)\) \(\chi_{6025}(2167,\cdot)\) \(\chi_{6025}(2412,\cdot)\) \(\chi_{6025}(2442,\cdot)\) \(\chi_{6025}(2523,\cdot)\) \(\chi_{6025}(2538,\cdot)\) \(\chi_{6025}(3013,\cdot)\) \(\chi_{6025}(3253,\cdot)\) \(\chi_{6025}(3342,\cdot)\) \(\chi_{6025}(3372,\cdot)\) \(\chi_{6025}(3617,\cdot)\) \(\chi_{6025}(3647,\cdot)\) \(\chi_{6025}(3728,\cdot)\) \(\chi_{6025}(4458,\cdot)\) \(\chi_{6025}(4547,\cdot)\) \(\chi_{6025}(4577,\cdot)\) \(\chi_{6025}(4822,\cdot)\) \(\chi_{6025}(4852,\cdot)\) \(\chi_{6025}(4933,\cdot)\) \(\chi_{6025}(4948,\cdot)\) \(\chi_{6025}(5423,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{1}{20}\right),e\left(\frac{19}{24}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\( \chi_{ 6025 }(2, a) \) \(-1\)\(1\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{1}{24}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{71}{120}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{19}{120}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6025 }(2,a) \;\) at \(\;a = \) e.g. 2