Properties

Label 4023.23
Modulus $4023$
Conductor $4023$
Order $1332$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4023, base_ring=CyclotomicField(1332))
 
M = H._module
 
chi = DirichletCharacter(H, M([814,855]))
 
pari: [g,chi] = znchar(Mod(23,4023))
 

Basic properties

Modulus: \(4023\)
Conductor: \(4023\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(1332\)
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 4023.bi

\(\chi_{4023}(2,\cdot)\) \(\chi_{4023}(11,\cdot)\) \(\chi_{4023}(14,\cdot)\) \(\chi_{4023}(23,\cdot)\) \(\chi_{4023}(32,\cdot)\) \(\chi_{4023}(38,\cdot)\) \(\chi_{4023}(41,\cdot)\) \(\chi_{4023}(50,\cdot)\) \(\chi_{4023}(56,\cdot)\) \(\chi_{4023}(59,\cdot)\) \(\chi_{4023}(65,\cdot)\) \(\chi_{4023}(74,\cdot)\) \(\chi_{4023}(77,\cdot)\) \(\chi_{4023}(83,\cdot)\) \(\chi_{4023}(92,\cdot)\) \(\chi_{4023}(101,\cdot)\) \(\chi_{4023}(122,\cdot)\) \(\chi_{4023}(128,\cdot)\) \(\chi_{4023}(131,\cdot)\) \(\chi_{4023}(137,\cdot)\) \(\chi_{4023}(146,\cdot)\) \(\chi_{4023}(164,\cdot)\) \(\chi_{4023}(167,\cdot)\) \(\chi_{4023}(176,\cdot)\) \(\chi_{4023}(200,\cdot)\) \(\chi_{4023}(209,\cdot)\) \(\chi_{4023}(221,\cdot)\) \(\chi_{4023}(227,\cdot)\) \(\chi_{4023}(236,\cdot)\) \(\chi_{4023}(239,\cdot)\) ...

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: $\Q(\zeta_{1332})$
Fixed field: Number field defined by a degree 1332 polynomial (not computed)

Values on generators

\((299,3727)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{95}{148}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(5\)\(7\)\(8\)\(10\)\(11\)\(13\)\(14\)\(16\)
\( \chi_{ 4023 }(23, a) \) \(1\)\(1\)\(e\left(\frac{337}{1332}\right)\)\(e\left(\frac{337}{666}\right)\)\(e\left(\frac{541}{666}\right)\)\(e\left(\frac{617}{666}\right)\)\(e\left(\frac{337}{444}\right)\)\(e\left(\frac{29}{444}\right)\)\(e\left(\frac{1213}{1332}\right)\)\(e\left(\frac{1211}{1332}\right)\)\(e\left(\frac{239}{1332}\right)\)\(e\left(\frac{4}{333}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4023 }(23,a) \;\) at \(\;a = \) e.g. 2