Properties

Label 4024.301
Modulus $4024$
Conductor $4024$
Order $502$
Real no
Primitive yes
Minimal yes
Parity even

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([0,251,152]))
 
pari: [g,chi] = znchar(Mod(301,4024))
 

Basic properties

Modulus: \(4024\)
Conductor: \(4024\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(502\)
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 4024.o

\(\chi_{4024}(13,\cdot)\) \(\chi_{4024}(21,\cdot)\) \(\chi_{4024}(61,\cdot)\) \(\chi_{4024}(69,\cdot)\) \(\chi_{4024}(77,\cdot)\) \(\chi_{4024}(85,\cdot)\) \(\chi_{4024}(117,\cdot)\) \(\chi_{4024}(141,\cdot)\) \(\chi_{4024}(173,\cdot)\) \(\chi_{4024}(189,\cdot)\) \(\chi_{4024}(197,\cdot)\) \(\chi_{4024}(205,\cdot)\) \(\chi_{4024}(229,\cdot)\) \(\chi_{4024}(237,\cdot)\) \(\chi_{4024}(253,\cdot)\) \(\chi_{4024}(285,\cdot)\) \(\chi_{4024}(293,\cdot)\) \(\chi_{4024}(301,\cdot)\) \(\chi_{4024}(317,\cdot)\) \(\chi_{4024}(325,\cdot)\) \(\chi_{4024}(373,\cdot)\) \(\chi_{4024}(389,\cdot)\) \(\chi_{4024}(397,\cdot)\) \(\chi_{4024}(413,\cdot)\) \(\chi_{4024}(421,\cdot)\) \(\chi_{4024}(429,\cdot)\) \(\chi_{4024}(445,\cdot)\) \(\chi_{4024}(469,\cdot)\) \(\chi_{4024}(493,\cdot)\) \(\chi_{4024}(509,\cdot)\) ...

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

\((1007,2013,2017)\) → \((1,-1,e\left(\frac{76}{251}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(21\)
\( \chi_{ 4024 }(301, a) \) \(1\)\(1\)\(e\left(\frac{369}{502}\right)\)\(e\left(\frac{403}{502}\right)\)\(e\left(\frac{10}{251}\right)\)\(e\left(\frac{118}{251}\right)\)\(e\left(\frac{109}{502}\right)\)\(e\left(\frac{23}{502}\right)\)\(e\left(\frac{135}{251}\right)\)\(e\left(\frac{85}{251}\right)\)\(e\left(\frac{131}{502}\right)\)\(e\left(\frac{389}{502}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 4024 }(301,a) \;\) at \(\;a = \) e.g. 2