Properties

Label 6025.4837
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([36,37]))
 
pari: [g,chi] = znchar(Mod(4837,6025))
 

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.ht

\(\chi_{6025}(213,\cdot)\) \(\chi_{6025}(508,\cdot)\) \(\chi_{6025}(1278,\cdot)\) \(\chi_{6025}(1353,\cdot)\) \(\chi_{6025}(1827,\cdot)\) \(\chi_{6025}(2433,\cdot)\) \(\chi_{6025}(2438,\cdot)\) \(\chi_{6025}(2467,\cdot)\) \(\chi_{6025}(2503,\cdot)\) \(\chi_{6025}(2548,\cdot)\) \(\chi_{6025}(2578,\cdot)\) \(\chi_{6025}(2672,\cdot)\) \(\chi_{6025}(2752,\cdot)\) \(\chi_{6025}(3048,\cdot)\) \(\chi_{6025}(3238,\cdot)\) \(\chi_{6025}(3272,\cdot)\) \(\chi_{6025}(3317,\cdot)\) \(\chi_{6025}(3833,\cdot)\) \(\chi_{6025}(4423,\cdot)\) \(\chi_{6025}(4462,\cdot)\) \(\chi_{6025}(4562,\cdot)\) \(\chi_{6025}(4777,\cdot)\) \(\chi_{6025}(4837,\cdot)\) \(\chi_{6025}(4922,\cdot)\) \(\chi_{6025}(4923,\cdot)\) \(\chi_{6025}(4937,\cdot)\) \(\chi_{6025}(5438,\cdot)\) \(\chi_{6025}(5522,\cdot)\) \(\chi_{6025}(5758,\cdot)\) \(\chi_{6025}(5817,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{9}{20}\right),e\left(\frac{37}{80}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\( \chi_{ 6025 }(4837, a) \) \(1\)\(1\)\(e\left(\frac{13}{40}\right)\)\(e\left(\frac{13}{40}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{57}{80}\right)\)\(e\left(\frac{39}{40}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{61}{80}\right)\)\(e\left(\frac{39}{40}\right)\)\(e\left(\frac{23}{80}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6025 }(4837,a) \;\) at \(\;a = \) e.g. 2