Properties

Label 6025.3136
Modulus $6025$
Conductor $6025$
Order $120$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6025, base_ring=CyclotomicField(120))
 
M = H._module
 
chi = DirichletCharacter(H, M([96,91]))
 
pari: [g,chi] = znchar(Mod(3136,6025))
 

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.id

\(\chi_{6025}(166,\cdot)\) \(\chi_{6025}(286,\cdot)\) \(\chi_{6025}(316,\cdot)\) \(\chi_{6025}(541,\cdot)\) \(\chi_{6025}(656,\cdot)\) \(\chi_{6025}(711,\cdot)\) \(\chi_{6025}(831,\cdot)\) \(\chi_{6025}(856,\cdot)\) \(\chi_{6025}(946,\cdot)\) \(\chi_{6025}(961,\cdot)\) \(\chi_{6025}(1031,\cdot)\) \(\chi_{6025}(1366,\cdot)\) \(\chi_{6025}(1466,\cdot)\) \(\chi_{6025}(1736,\cdot)\) \(\chi_{6025}(1946,\cdot)\) \(\chi_{6025}(2361,\cdot)\) \(\chi_{6025}(2921,\cdot)\) \(\chi_{6025}(3056,\cdot)\) \(\chi_{6025}(3136,\cdot)\) \(\chi_{6025}(3321,\cdot)\) \(\chi_{6025}(3386,\cdot)\) \(\chi_{6025}(3446,\cdot)\) \(\chi_{6025}(3806,\cdot)\) \(\chi_{6025}(3811,\cdot)\) \(\chi_{6025}(3906,\cdot)\) \(\chi_{6025}(4656,\cdot)\) \(\chi_{6025}(5041,\cdot)\) \(\chi_{6025}(5141,\cdot)\) \(\chi_{6025}(5471,\cdot)\) \(\chi_{6025}(5596,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{91}{120}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\( \chi_{ 6025 }(3136, a) \) \(1\)\(1\)\(e\left(\frac{53}{60}\right)\)\(e\left(\frac{37}{60}\right)\)\(e\left(\frac{23}{30}\right)\)\(-1\)\(e\left(\frac{91}{120}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{7}{30}\right)\)\(e\left(\frac{91}{120}\right)\)\(e\left(\frac{23}{60}\right)\)\(e\left(\frac{101}{120}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6025 }(3136,a) \;\) at \(\;a = \) e.g. 2