Properties

Label 6025.2628
Modulus $6025$
Conductor $6025$
Order $80$
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(80))
 
M = H._module
 
chi = DirichletCharacter(H, M([28,59]))
 
pari: [g,chi] = znchar(Mod(2628,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(6025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(80\)
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.hp

\(\chi_{6025}(138,\cdot)\) \(\chi_{6025}(638,\cdot)\) \(\chi_{6025}(997,\cdot)\) \(\chi_{6025}(1162,\cdot)\) \(\chi_{6025}(1172,\cdot)\) \(\chi_{6025}(1228,\cdot)\) \(\chi_{6025}(1467,\cdot)\) \(\chi_{6025}(1823,\cdot)\) \(\chi_{6025}(2013,\cdot)\) \(\chi_{6025}(2052,\cdot)\) \(\chi_{6025}(2067,\cdot)\) \(\chi_{6025}(2152,\cdot)\) \(\chi_{6025}(2212,\cdot)\) \(\chi_{6025}(2427,\cdot)\) \(\chi_{6025}(2483,\cdot)\) \(\chi_{6025}(2513,\cdot)\) \(\chi_{6025}(2527,\cdot)\) \(\chi_{6025}(2558,\cdot)\) \(\chi_{6025}(2623,\cdot)\) \(\chi_{6025}(2628,\cdot)\) \(\chi_{6025}(3672,\cdot)\) \(\chi_{6025}(3708,\cdot)\) \(\chi_{6025}(3717,\cdot)\) \(\chi_{6025}(3783,\cdot)\) \(\chi_{6025}(4237,\cdot)\) \(\chi_{6025}(4317,\cdot)\) \(\chi_{6025}(4522,\cdot)\) \(\chi_{6025}(4553,\cdot)\) \(\chi_{6025}(4848,\cdot)\) \(\chi_{6025}(5162,\cdot)\) ...

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: $\Q(\zeta_{80})$
Fixed field: Number field defined by a degree 80 polynomial

Values on generators

\((2652,2176)\) → \((e\left(\frac{7}{20}\right),e\left(\frac{59}{80}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\( \chi_{ 6025 }(2628, a) \) \(1\)\(1\)\(e\left(\frac{19}{40}\right)\)\(e\left(\frac{27}{40}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{39}{80}\right)\)\(e\left(\frac{17}{40}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{3}{80}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{5}{16}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6025 }(2628,a) \;\) at \(\;a = \) e.g. 2