Properties

Label 8027.87
Modulus $8027$
Conductor $8027$
Order $957$
Real no
Primitive yes
Minimal yes
Parity even

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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([1044,946]))
 
pari: [g,chi] = znchar(Mod(87,8027))
 

Basic properties

Modulus: \(8027\)
Conductor: \(8027\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(957\)
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 8027.bo

\(\chi_{8027}(9,\cdot)\) \(\chi_{8027}(12,\cdot)\) \(\chi_{8027}(16,\cdot)\) \(\chi_{8027}(25,\cdot)\) \(\chi_{8027}(26,\cdot)\) \(\chi_{8027}(77,\cdot)\) \(\chi_{8027}(81,\cdot)\) \(\chi_{8027}(85,\cdot)\) \(\chi_{8027}(87,\cdot)\) \(\chi_{8027}(94,\cdot)\) \(\chi_{8027}(108,\cdot)\) \(\chi_{8027}(144,\cdot)\) \(\chi_{8027}(147,\cdot)\) \(\chi_{8027}(151,\cdot)\) \(\chi_{8027}(192,\cdot)\) \(\chi_{8027}(196,\cdot)\) \(\chi_{8027}(219,\cdot)\) \(\chi_{8027}(225,\cdot)\) \(\chi_{8027}(256,\cdot)\) \(\chi_{8027}(266,\cdot)\) \(\chi_{8027}(271,\cdot)\) \(\chi_{8027}(279,\cdot)\) \(\chi_{8027}(292,\cdot)\) \(\chi_{8027}(307,\cdot)\) \(\chi_{8027}(358,\cdot)\) \(\chi_{8027}(361,\cdot)\) \(\chi_{8027}(363,\cdot)\) \(\chi_{8027}(372,\cdot)\) \(\chi_{8027}(374,\cdot)\) \(\chi_{8027}(400,\cdot)\) ...

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 957 polynomial (not computed)

Values on generators

\((350,5935)\) → \((e\left(\frac{6}{11}\right),e\left(\frac{43}{87}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\( \chi_{ 8027 }(87, a) \) \(1\)\(1\)\(e\left(\frac{560}{957}\right)\)\(e\left(\frac{553}{957}\right)\)\(e\left(\frac{163}{957}\right)\)\(e\left(\frac{709}{957}\right)\)\(e\left(\frac{52}{319}\right)\)\(e\left(\frac{458}{957}\right)\)\(e\left(\frac{241}{319}\right)\)\(e\left(\frac{149}{957}\right)\)\(e\left(\frac{104}{319}\right)\)\(e\left(\frac{92}{319}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 8027 }(87,a) \;\) at \(\;a = \) e.g. 2