Properties

Label 6025.2417
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([156,1]))
 
pari: [g,chi] = znchar(Mod(2417,6025))
 

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.ix

\(\chi_{6025}(37,\cdot)\) \(\chi_{6025}(78,\cdot)\) \(\chi_{6025}(127,\cdot)\) \(\chi_{6025}(373,\cdot)\) \(\chi_{6025}(553,\cdot)\) \(\chi_{6025}(822,\cdot)\) \(\chi_{6025}(827,\cdot)\) \(\chi_{6025}(908,\cdot)\) \(\chi_{6025}(933,\cdot)\) \(\chi_{6025}(1038,\cdot)\) \(\chi_{6025}(1073,\cdot)\) \(\chi_{6025}(1267,\cdot)\) \(\chi_{6025}(1317,\cdot)\) \(\chi_{6025}(1347,\cdot)\) \(\chi_{6025}(1498,\cdot)\) \(\chi_{6025}(1613,\cdot)\) \(\chi_{6025}(2077,\cdot)\) \(\chi_{6025}(2123,\cdot)\) \(\chi_{6025}(2183,\cdot)\) \(\chi_{6025}(2417,\cdot)\) \(\chi_{6025}(2423,\cdot)\) \(\chi_{6025}(2502,\cdot)\) \(\chi_{6025}(2583,\cdot)\) \(\chi_{6025}(2617,\cdot)\) \(\chi_{6025}(2822,\cdot)\) \(\chi_{6025}(3038,\cdot)\) \(\chi_{6025}(3047,\cdot)\) \(\chi_{6025}(3167,\cdot)\) \(\chi_{6025}(3172,\cdot)\) \(\chi_{6025}(3188,\cdot)\) ...

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

\((2652,2176)\) → \((e\left(\frac{13}{20}\right),e\left(\frac{1}{240}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\( \chi_{ 6025 }(2417, a) \) \(1\)\(1\)\(e\left(\frac{53}{120}\right)\)\(e\left(\frac{37}{120}\right)\)\(e\left(\frac{53}{60}\right)\)\(-i\)\(e\left(\frac{61}{240}\right)\)\(e\left(\frac{13}{40}\right)\)\(e\left(\frac{37}{60}\right)\)\(e\left(\frac{121}{240}\right)\)\(e\left(\frac{23}{120}\right)\)\(e\left(\frac{131}{240}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6025 }(2417,a) \;\) at \(\;a = \) e.g. 2