Properties

Label 8027.15
Modulus $8027$
Conductor $8027$
Order $1914$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8027, base_ring=CyclotomicField(1914))
 
M = H._module
 
chi = DirichletCharacter(H, M([1479,1870]))
 
pari: [g,chi] = znchar(Mod(15,8027))
 

Basic properties

Modulus: \(8027\)
Conductor: \(8027\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(1914\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8027.br

\(\chi_{8027}(14,\cdot)\) \(\chi_{8027}(15,\cdot)\) \(\chi_{8027}(19,\cdot)\) \(\chi_{8027}(20,\cdot)\) \(\chi_{8027}(51,\cdot)\) \(\chi_{8027}(106,\cdot)\) \(\chi_{8027}(111,\cdot)\) \(\chi_{8027}(135,\cdot)\) \(\chi_{8027}(143,\cdot)\) \(\chi_{8027}(145,\cdot)\) \(\chi_{8027}(148,\cdot)\) \(\chi_{8027}(158,\cdot)\) \(\chi_{8027}(180,\cdot)\) \(\chi_{8027}(194,\cdot)\) \(\chi_{8027}(240,\cdot)\) \(\chi_{8027}(245,\cdot)\) \(\chi_{8027}(258,\cdot)\) \(\chi_{8027}(273,\cdot)\) \(\chi_{8027}(293,\cdot)\) \(\chi_{8027}(320,\cdot)\) \(\chi_{8027}(327,\cdot)\) \(\chi_{8027}(364,\cdot)\) \(\chi_{8027}(365,\cdot)\) \(\chi_{8027}(375,\cdot)\) \(\chi_{8027}(434,\cdot)\) \(\chi_{8027}(457,\cdot)\) \(\chi_{8027}(465,\cdot)\) \(\chi_{8027}(493,\cdot)\) \(\chi_{8027}(494,\cdot)\) \(\chi_{8027}(497,\cdot)\) ...

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: $\Q(\zeta_{957})$
Fixed field: Number field defined by a degree 1914 polynomial (not computed)

Values on generators

\((350,5935)\) → \((e\left(\frac{17}{22}\right),e\left(\frac{85}{87}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\( \chi_{ 8027 }(15, a) \) \(-1\)\(1\)\(e\left(\frac{500}{957}\right)\)\(e\left(\frac{733}{957}\right)\)\(e\left(\frac{43}{957}\right)\)\(e\left(\frac{1061}{1914}\right)\)\(e\left(\frac{92}{319}\right)\)\(e\left(\frac{271}{1914}\right)\)\(e\left(\frac{181}{319}\right)\)\(e\left(\frac{509}{957}\right)\)\(e\left(\frac{49}{638}\right)\)\(e\left(\frac{301}{638}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 8027 }(15,a) \;\) at \(\;a = \) e.g. 2