Properties

Label 6025.327
Modulus $6025$
Conductor $6025$
Order $240$
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(240))
 
M = H._module
 
chi = DirichletCharacter(H, M([12,169]))
 
pari: [g,chi] = znchar(Mod(327,6025))
 

Basic properties

Modulus: \(6025\)
Conductor: \(6025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(240\)
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.iz

\(\chi_{6025}(62,\cdot)\) \(\chi_{6025}(92,\cdot)\) \(\chi_{6025}(112,\cdot)\) \(\chi_{6025}(202,\cdot)\) \(\chi_{6025}(327,\cdot)\) \(\chi_{6025}(372,\cdot)\) \(\chi_{6025}(513,\cdot)\) \(\chi_{6025}(538,\cdot)\) \(\chi_{6025}(552,\cdot)\) \(\chi_{6025}(628,\cdot)\) \(\chi_{6025}(672,\cdot)\) \(\chi_{6025}(778,\cdot)\) \(\chi_{6025}(922,\cdot)\) \(\chi_{6025}(1212,\cdot)\) \(\chi_{6025}(1247,\cdot)\) \(\chi_{6025}(1342,\cdot)\) \(\chi_{6025}(1412,\cdot)\) \(\chi_{6025}(1433,\cdot)\) \(\chi_{6025}(1497,\cdot)\) \(\chi_{6025}(1603,\cdot)\) \(\chi_{6025}(1733,\cdot)\) \(\chi_{6025}(1797,\cdot)\) \(\chi_{6025}(1962,\cdot)\) \(\chi_{6025}(2027,\cdot)\) \(\chi_{6025}(2042,\cdot)\) \(\chi_{6025}(2098,\cdot)\) \(\chi_{6025}(2113,\cdot)\) \(\chi_{6025}(2138,\cdot)\) \(\chi_{6025}(2162,\cdot)\) \(\chi_{6025}(2253,\cdot)\) ...

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: $\Q(\zeta_{240})$
Fixed field: Number field defined by a degree 240 polynomial (not computed)

Values on generators

\((2652,2176)\) → \((e\left(\frac{1}{20}\right),e\left(\frac{169}{240}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\( \chi_{ 6025 }(327, a) \) \(1\)\(1\)\(e\left(\frac{101}{120}\right)\)\(e\left(\frac{61}{120}\right)\)\(e\left(\frac{41}{60}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{229}{240}\right)\)\(e\left(\frac{21}{40}\right)\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{97}{240}\right)\)\(e\left(\frac{23}{120}\right)\)\(e\left(\frac{11}{240}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6025 }(327,a) \;\) at \(\;a = \) e.g. 2