Properties

Label 8024.5
Modulus $8024$
Conductor $8024$
Order $464$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8024, base_ring=CyclotomicField(464))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,232,145,48]))
 
pari: [g,chi] = znchar(Mod(5,8024))
 

Basic properties

Modulus: \(8024\)
Conductor: \(8024\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(464\)
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 8024.db

\(\chi_{8024}(5,\cdot)\) \(\chi_{8024}(29,\cdot)\) \(\chi_{8024}(45,\cdot)\) \(\chi_{8024}(125,\cdot)\) \(\chi_{8024}(133,\cdot)\) \(\chi_{8024}(181,\cdot)\) \(\chi_{8024}(197,\cdot)\) \(\chi_{8024}(245,\cdot)\) \(\chi_{8024}(261,\cdot)\) \(\chi_{8024}(277,\cdot)\) \(\chi_{8024}(317,\cdot)\) \(\chi_{8024}(381,\cdot)\) \(\chi_{8024}(405,\cdot)\) \(\chi_{8024}(517,\cdot)\) \(\chi_{8024}(605,\cdot)\) \(\chi_{8024}(653,\cdot)\) \(\chi_{8024}(669,\cdot)\) \(\chi_{8024}(677,\cdot)\) \(\chi_{8024}(685,\cdot)\) \(\chi_{8024}(717,\cdot)\) \(\chi_{8024}(725,\cdot)\) \(\chi_{8024}(789,\cdot)\) \(\chi_{8024}(813,\cdot)\) \(\chi_{8024}(845,\cdot)\) \(\chi_{8024}(853,\cdot)\) \(\chi_{8024}(861,\cdot)\) \(\chi_{8024}(877,\cdot)\) \(\chi_{8024}(949,\cdot)\) \(\chi_{8024}(989,\cdot)\) \(\chi_{8024}(997,\cdot)\) ...

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: $\Q(\zeta_{464})$
Fixed field: Number field defined by a degree 464 polynomial (not computed)

Values on generators

\((2007,4013,3777,3129)\) → \((1,-1,e\left(\frac{5}{16}\right),e\left(\frac{3}{29}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(13\)\(15\)\(19\)\(21\)\(23\)
\( \chi_{ 8024 }(5, a) \) \(-1\)\(1\)\(e\left(\frac{457}{464}\right)\)\(e\left(\frac{317}{464}\right)\)\(e\left(\frac{139}{464}\right)\)\(e\left(\frac{225}{232}\right)\)\(e\left(\frac{127}{464}\right)\)\(e\left(\frac{47}{116}\right)\)\(e\left(\frac{155}{232}\right)\)\(e\left(\frac{187}{232}\right)\)\(e\left(\frac{33}{116}\right)\)\(e\left(\frac{111}{464}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 8024 }(5,a) \;\) at \(\;a = \) e.g. 2