Properties

Label 8007.145
Modulus $8007$
Conductor $2669$
Order $24$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8007, base_ring=CyclotomicField(24))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,3,20]))
 
pari: [g,chi] = znchar(Mod(145,8007))
 

Basic properties

Modulus: \(8007\)
Conductor: \(2669\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(24\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{2669}(145,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8007.ch

\(\chi_{8007}(145,\cdot)\) \(\chi_{8007}(484,\cdot)\) \(\chi_{8007}(1426,\cdot)\) \(\chi_{8007}(3442,\cdot)\) \(\chi_{8007}(4252,\cdot)\) \(\chi_{8007}(4384,\cdot)\) \(\chi_{8007}(5194,\cdot)\) \(\chi_{8007}(7210,\cdot)\)

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: \(\Q(\zeta_{24})\)
Fixed field: Number field defined by a degree 24 polynomial

Values on generators

\((5339,1414,7855)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{5}{6}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(5\)\(7\)\(8\)\(10\)\(11\)\(13\)\(14\)\(16\)
\( \chi_{ 8007 }(145, a) \) \(1\)\(1\)\(i\)\(-1\)\(e\left(\frac{11}{24}\right)\)\(e\left(\frac{7}{8}\right)\)\(-i\)\(e\left(\frac{17}{24}\right)\)\(e\left(\frac{5}{24}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{1}{8}\right)\)\(1\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 8007 }(145,a) \;\) at \(\;a = \) e.g. 2