Properties

Label 4024.17
Modulus $4024$
Conductor $503$
Order $502$
Real no
Primitive no
Minimal yes
Parity odd

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4024, base_ring=CyclotomicField(502))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,229]))
 
pari: [g,chi] = znchar(Mod(17,4024))
 

Basic properties

Modulus: \(4024\)
Conductor: \(503\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(502\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{503}(17,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 4024.k

\(\chi_{4024}(17,\cdot)\) \(\chi_{4024}(41,\cdot)\) \(\chi_{4024}(57,\cdot)\) \(\chi_{4024}(65,\cdot)\) \(\chi_{4024}(89,\cdot)\) \(\chi_{4024}(105,\cdot)\) \(\chi_{4024}(137,\cdot)\) \(\chi_{4024}(153,\cdot)\) \(\chi_{4024}(193,\cdot)\) \(\chi_{4024}(209,\cdot)\) \(\chi_{4024}(217,\cdot)\) \(\chi_{4024}(241,\cdot)\) \(\chi_{4024}(305,\cdot)\) \(\chi_{4024}(313,\cdot)\) \(\chi_{4024}(321,\cdot)\) \(\chi_{4024}(337,\cdot)\) \(\chi_{4024}(345,\cdot)\) \(\chi_{4024}(353,\cdot)\) \(\chi_{4024}(369,\cdot)\) \(\chi_{4024}(377,\cdot)\) \(\chi_{4024}(385,\cdot)\) \(\chi_{4024}(409,\cdot)\) \(\chi_{4024}(417,\cdot)\) \(\chi_{4024}(425,\cdot)\) \(\chi_{4024}(449,\cdot)\) \(\chi_{4024}(457,\cdot)\) \(\chi_{4024}(481,\cdot)\) \(\chi_{4024}(489,\cdot)\) \(\chi_{4024}(497,\cdot)\) \(\chi_{4024}(513,\cdot)\) ...

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: $\Q(\zeta_{251})$
Fixed field: Number field defined by a degree 502 polynomial (not computed)

Values on generators

\((1007,2013,2017)\) → \((1,1,e\left(\frac{229}{502}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(21\)
\( \chi_{ 4024 }(17, a) \) \(-1\)\(1\)\(e\left(\frac{41}{251}\right)\)\(e\left(\frac{229}{502}\right)\)\(e\left(\frac{58}{251}\right)\)\(e\left(\frac{82}{251}\right)\)\(e\left(\frac{40}{251}\right)\)\(e\left(\frac{142}{251}\right)\)\(e\left(\frac{311}{502}\right)\)\(e\left(\frac{233}{502}\right)\)\(e\left(\frac{57}{502}\right)\)\(e\left(\frac{99}{251}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4024 }(17,a) \;\) at \(\;a = \) e.g. 2