Properties

Label 6025.1492
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([156,7]))
 
pari: [g,chi] = znchar(Mod(1492,6025))
 

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.iy

\(\chi_{6025}(278,\cdot)\) \(\chi_{6025}(333,\cdot)\) \(\chi_{6025}(652,\cdot)\) \(\chi_{6025}(737,\cdot)\) \(\chi_{6025}(797,\cdot)\) \(\chi_{6025}(1127,\cdot)\) \(\chi_{6025}(1137,\cdot)\) \(\chi_{6025}(1192,\cdot)\) \(\chi_{6025}(1372,\cdot)\) \(\chi_{6025}(1377,\cdot)\) \(\chi_{6025}(1492,\cdot)\) \(\chi_{6025}(1583,\cdot)\) \(\chi_{6025}(1648,\cdot)\) \(\chi_{6025}(1652,\cdot)\) \(\chi_{6025}(1773,\cdot)\) \(\chi_{6025}(1998,\cdot)\) \(\chi_{6025}(2117,\cdot)\) \(\chi_{6025}(2237,\cdot)\) \(\chi_{6025}(2283,\cdot)\) \(\chi_{6025}(2542,\cdot)\) \(\chi_{6025}(2637,\cdot)\) \(\chi_{6025}(2713,\cdot)\) \(\chi_{6025}(2763,\cdot)\) \(\chi_{6025}(2797,\cdot)\) \(\chi_{6025}(2927,\cdot)\) \(\chi_{6025}(2947,\cdot)\) \(\chi_{6025}(2958,\cdot)\) \(\chi_{6025}(3202,\cdot)\) \(\chi_{6025}(3242,\cdot)\) \(\chi_{6025}(3308,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{13}{20}\right),e\left(\frac{7}{240}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\( \chi_{ 6025 }(1492, a) \) \(1\)\(1\)\(e\left(\frac{23}{120}\right)\)\(e\left(\frac{103}{120}\right)\)\(e\left(\frac{23}{60}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{67}{240}\right)\)\(e\left(\frac{23}{40}\right)\)\(e\left(\frac{43}{60}\right)\)\(e\left(\frac{31}{240}\right)\)\(e\left(\frac{29}{120}\right)\)\(e\left(\frac{173}{240}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6025 }(1492,a) \;\) at \(\;a = \) e.g. 2